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the results , in fact , are in good agreement with a vast amount of experimental analyses @xcite . the amplitudes develop poles corresponding to the @xmath6 , @xmath7 , @xmath8 , @xmath9 , the octet contribution to the @xmath10 , @xmath11 and @xmath12 @xcite . the total and partial decay widths of the resonances

c

hep-ph9908494

a non - perturbative method @xcite which combines constraints from chiral symmetry breaking and coupled channel unitarity is used to describe meson - meson interactions up to @xmath0 gev , extending in this way the range of applicability of the information contained in chiral perturbation theory ( @xmath1 ) @xcite , since this perturbative series is typically restricted to @xmath2 mev . the approach uses the @xmath3 and @xmath4 @xmath1 lagrangians . the seven free parameters resulting from the @xmath4 lagrangian are fitted to the experimental data . the approach makes use of the expansion of @xmath5 instead of the amplitude itself as done in @xmath1 . the former expansion is suggested by analogy with the effective range approximation in quantum mechanics and it appears to be very useful . the results , in fact , are in good agreement with a vast amount of experimental analyses @xcite . the amplitudes develop poles corresponding to the @xmath6 , @xmath7 , @xmath8 , @xmath9 , the octet contribution to the @xmath10 , @xmath11 and @xmath12 @xcite . the total and partial decay widths of the resonances are also well reproduced .

we have presented a method of resummation of the @xmath1 series based in the expansion of @xmath5 . in this way unitarity is fulfilled to all orders and resonances are well reproduced . the method is rather general and could be applied to any system whose dynamics is described by chiral lagrangians . we have applied it successfully to describe the s and p - wave meson - meson amplitudes giving rise to the resonances : @xmath6 , @xmath7 , @xmath8 , @xmath9 , the octet contribution to the @xmath10 , @xmath11 and @xmath12 . 200 j. a. oller , e. oset and j. r. pelez , phys . ( 1998 ) 3452 . j. gasser and h. leutwyler , nucl . b 250 ( 1985 ) 465 , 517 , 539 . f. guerrero and j. a. oller , nucl . b 537 ( 1999 ) 459 . j. a. oller , e. oset and j. r. pelez , phys . d 59 ( 1999 ) 074001 . j. v. steele , h. yamagishi and i. zahed , nucl . phys . a 615 ( 1997 ) 305 ; m. r. pennington and j. portoles , phys . b 344 ( 1995 ) 399 . v. bernard , n. kaiser and u. g. meissner , nucl . b 357 ( 1991 ) 129 . g. ecker , j. gasser , a. pich and e. de rafael , nucl . b 321 ( 1989 ) 311 .

the index @xmath6 controls the range of the interactions , in such a way that one recovers both the fully - coupled ( i.e. , mean - field limit ) and nearest - neighbour - interaction models in the particular limits @xmath7 and @xmath8 , respectively . the presence of quasi - stationary states ( qsss ) , whose durations @xmath11 increase for increasing values of @xmath0 , is verified for values of @xmath6 in the range @xmath12 , like the ones found for the similar model of xy rotators . the growth of @xmath11 with @xmath0 could be interpreted as a breakdown of ergodicity , which is shown herein to occur for any value of @xmath6 in this interval .

i

1409.5825

a numerical analysis of a one - dimensional hamiltonian system , composed by @xmath0 classical localized heisenberg rotators on a ring , is presented . a distance @xmath1 between rotators at sites @xmath2 and @xmath3 is introduced , such that the corresponding two - body interaction decays with @xmath1 as a power - law , @xmath4 ( @xmath5 ) . the index @xmath6 controls the range of the interactions , in such a way that one recovers both the fully - coupled ( i.e. , mean - field limit ) and nearest - neighbour - interaction models in the particular limits @xmath7 and @xmath8 , respectively . the dynamics of the model is investigated for energies @xmath9 below its critical value ( @xmath10 ) , with initial conditions corresponding to zero magnetization . the presence of quasi - stationary states ( qsss ) , whose durations @xmath11 increase for increasing values of @xmath0 , is verified for values of @xmath6 in the range @xmath12 , like the ones found for the similar model of xy rotators . moreover , for a given energy @xmath9 , our numerical analysis indicates that @xmath13 , where the exponent @xmath14 decreases for increasing @xmath6 in the range @xmath12 , and particularly , our results suggest that @xmath15 as @xmath16 . the growth of @xmath11 with @xmath0 could be interpreted as a breakdown of ergodicity , which is shown herein to occur for any value of @xmath6 in this interval .

classical spin models have called the attention of statistical - mechanics and magnetism researchers throughout many years @xcite . many techniques have been used in their study , both analytical and numerical , in such a way that a reasonable knowledge of their equilibrium thermodynamics has been achieved , and specially , of their critical properties . among those models , one could mention the classical spin models , which present the xy ( @xmath17 ) and heisenberg ( @xmath18 ) as particular cases . an interesting formulation of a @xmath19-vector classical model comes when one adds a kinetic term to its hamiltonian , i.e. , the spin variables may be interpreted as classical rotators ( see , e.g. , refs . @xcite ) , so that the terminology `` inertial model '' is currently used . this additional term does not pose difficulties in the calculation of equilibrium properties within a canonical - ensemble approach , but it turns possible to derive equations of motion for each rotator , which can be integrated by means of a molecular - dynamics procedure . in this way , the dynamical behaviour of these models can be investigated numerically without the need of introducing any particular type of probabilistic transition rules for changing the microscopic states . the inertial ferromagnetic xy model was introduced in ref . @xcite , within a fully - coupled framework ( i.e. , infinite - range interactions ) , a limit where the mean - field approach becomes exact . mostly referred to as `` hamiltonian mean field '' ( hmf ) model , it became paradigmatic in the study of the dynamical behaviour of classical many - body hamiltonian systems , and it has given rise to a large amount of works @xcite . one of the most interesting features in the hmf model concerns the appearance of metastable states , for some particular initial conditions , whose lifetime grows by increasing the total number of rotators , that could be interpreted as a breakdown of ergodicity in the thermodynamic limit . a generalization of the hmf model was proposed in ref . @xcite , by introducing a distance @xmath1 between rotators at sites @xmath2 and @xmath3 of a given lattice . moreover , the two - body interaction was assumed to decay with @xmath1 , like a power - law , @xmath4 ( @xmath5 ) . the index @xmath6 controls the range of the interactions , in such a way that one recovers both the hmf and nearest - neighbour - interaction models in the particular limits @xmath7 and @xmath8 , respectively . in between these two limits , one finds an important change of behaviour in the thermodynamic quantities , yielding two physically distinct regimes , namely , the long- ( @xmath20 ) and short - range ( @xmath21 ) interaction regimes @xcite . in the latter , one has the usual extensive and intensive quantities , whereas in the former , one may find also nonextensive thermodynamic quantities @xcite . this generalization is usually referred to as @xmath6-xy or @xmath6-hmf model , and it also has been studied by several groups @xcite . the dynamics of the fully - coupled inertial version of the ferromagnetic heisenberg model has been much less investigated in the literature @xcite . metastable , or quasi - stationary states ( qsss ) , also occur for this system , similar to those that appear in the hmf model ; their lifetime diverge by increasing the total number of rotators @xmath0 , which implies that the order in which the thermodynamic limit ( @xmath22 ) and the infinite - time limit ( @xmath23 ) are considered , becomes important . more specifically , if we let @xmath22 first , the system remains trapped in these qsss , never reaching the final boltzmann - gibbs ( bg ) equilibrium state , most probably being the qss itself the final state in such a case . in these metastable states , thermodynamical quantities , like temperature and magnetization , do not coincide with the canonical - ensemble predictions . herein , we will modify the fully - coupled inertial ferromagnetic heisenberg model , by introducing a distance @xmath1 between rotators at sites @xmath2 and @xmath3 of a given lattice . analogously to the @xmath6-hmf model @xcite , the rotator - rotator interaction will be taken to decay with the distance like a power - law , @xmath4 ( @xmath5 ) . the interaction part of this hamiltonian has already been studied analytically in ref . @xcite , within a canonical - ensemble approach to the equilibrium state of the corresponding model , where it was shown that if the two - body interaction is appropriately scaled , a universal thermodynamical behaviour is achieved for @xmath24 , e.g. , relations involving temperature @xmath25 , magnetization @xmath26 , and internal energy @xmath9 become @xmath6-independent in this interval . apart from this study of the equilibrium state , an investigation of the dynamical behaviour of the above - mentioned heisenberg model , and particularly , how the qsss may be affected by the exponent @xmath6 , has never been addressed in the literature , to our knowledge . in the present work we study this model on a ring , i.e , @xmath27 with periodic boundary conditions , using molecular - dynamics simulations . we perform a detailed analysis of the qsss behaviour by varying the energy , number of particles , and range of the interaction , i.e. , the exponent @xmath6 . in the next section we define the model , the appropriate scaling for the interactions , the canonical - ensemble solution , equations of motion , and initial conditions to be used in the molecular - dynamics procedure . in section [ sec : results ] we present the results of our simulations , showing an agreement with some analytical results known in the literature for the equilibrium state , in some particular limits ; most importantly , we show the existence of qsss for energies @xmath9 below criticality ( @xmath10 ) . such qsss , which were verified herein for initial conditions corresponding to zero magnetization , appear for values of @xmath6 in the range @xmath12 , being characterized by durations @xmath11 that increase for increasing values of @xmath0 , like those found numerically and analytically in previous works of the similar model of xy rotators @xcite . finally , in section [ sec : conclusions ] we present our main conclusions .

a problem of inducing a required sign of chirality in a racemic mixture of enantiomers of a chiral molecule is analyzed . it is shown that biharmonic raman excitation of the splitted due to the left - right conversion internal rotation levels can be effectively used for inducing optical activity in the initially racemic vapor of h@xmath0o@xmath0 molecules . an experiment to study this photoinduced optical rotation is discussed .

c

physics9906034

a problem of inducing a required sign of chirality in a racemic mixture of enantiomers of a chiral molecule is analyzed . as an example , a racemic mixture ( vapor ) of left- and right - handed enantiomers of hydrogen peroxide ( h@xmath0o@xmath0 ) molecule is considered . it is shown that biharmonic raman excitation of the splitted due to the left - right conversion internal rotation levels can be effectively used for inducing optical activity in the initially racemic vapor of h@xmath0o@xmath0 molecules . an experiment to study this photoinduced optical rotation is discussed .

in conclusion , an attempt was made to answer a question : how methods of nonlinear optics can be used to induce a required sign of chirality in a racemic mixture of enantiomers of a chiral molecule ? we consider a racemic mixture of left- and right - handed enantiomers of hydrogen peroxide molecule . torsional potential of this molecule has a characteristic double - well shape minima of which correspond to the left- and right - handed enantiomers and are mirror - symmetrically spaced . as a result , a splitting of eigenstates of the torsional hamiltonian arises from tunneling through the potential energy barrier separating the two wells . for h@xmath0o@xmath0 molecule this tunneling splitting is 11.4 cm-1 and 116.34 cm-1 for the internal rotation ground and first excited states , respectively , so that the the molecule shows rapid oscillations between left- and right - handed enantiomers . in a vapor or in a solution situation is complicated due to the averaging over ensemble . analysis of molecule - electromagnetic field interaction shows that dipole interaction does not contribute to the left - right conversion process ( this interaction we can use for orientation of dipole moments of molecules in the mixture ) , but the quadrupole interaction , which leads to the excitation of coherent precession between left- and right - handed enantiomers states . this gives us a tool for controlling the chiral symmetry of the molecule . we show that biharmonic raman excitation of the splitted internal rotation levels can be effectively used for inducing optical activity in an initially racemic mixture of left- and right - handed enantiomers of h@xmath0o@xmath0 molecules . an experiment to study this photoinduced optical rotation in h@xmath0o@xmath0 vapor is proposed . this work was initiated by prof . nikolai koroteev who devoted last years of his life to study chiral specificity of the bioorganic world and we dedicate it to his memory . authors acknowledge partial support by the russian foundation for basic research ( grant no . 96 - 15 - 96460 ) . we thank also v. i. tulin for providing information on the isomerization potential for hydrogen peroxide molecule and a. yu . chikishev for valuable discussion of an experimental observation of the photoinduced chirality .

a quantum memory at microwave frequencies , able to store the state of multiple superconducting qubits for long times , is a key element for quantum information processing . electronic and nuclear spins are natural candidates for the storage medium as their coherence time can be well above one second . benefiting from these long coherence times requires to apply the refocusing techniques used in magnetic resonance , a major challenge in the context of hybrid quantum circuits . here we report the first implementation of such a scheme , using ensembles of nitrogen - vacancy ( nv ) centres in diamond coupled to a superconducting resonator , in a setup compatible with superconducting qubit technology . this enables the storage of multiple microwave pulses at the picowatt level and their retrieval after up to @xmath0s , a three orders of magnitude improvement compared to previous experiments .

i

1401.7939

a quantum memory at microwave frequencies , able to store the state of multiple superconducting qubits for long times , is a key element for quantum information processing . electronic and nuclear spins are natural candidates for the storage medium as their coherence time can be well above one second . benefiting from these long coherence times requires to apply the refocusing techniques used in magnetic resonance , a major challenge in the context of hybrid quantum circuits . here we report the first implementation of such a scheme , using ensembles of nitrogen - vacancy ( nv ) centres in diamond coupled to a superconducting resonator , in a setup compatible with superconducting qubit technology . we implement the active reset of the nv spins into their ground state by optical pumping and their refocusing by hahn echo sequences . this enables the storage of multiple microwave pulses at the picowatt level and their retrieval after up to @xmath0s , a three orders of magnitude improvement compared to previous experiments .

the ability to store a quantum state over long times is a desirable feature in many quantum information protocols . in the optical domain , quantum memories ( qm ) are necessary to implement the quantum repeaters needed for future long - distance quantum networks , and are the object of active research @xcite . quantum memories at microwave frequencies have also become of great interest in recent years because of the development of superconducting qubits which have their resonance frequency in the ghz range , in the perspective of implementing holographic quantum computing @xcite . for such schemes , the memory should act as an ideal multi - qubit register , able to store over long times the state of large numbers of qubits and to retrieve them on - demand . spin ensembles have emerged as promising candidates for a multi - mode microwave quantum memory because of their long coherence time @xcite and of the multiple collective modes that a spin ensemble withstands . existing proposals @xcite ( inspired by optical quantum memory protocols @xcite ) proceed in two distinct steps . first , the microwave field prepared in a well - defined quantum state @xmath1 ( for instance by a superconducting qubit ) is absorbed by the spin ensemble . this generates a transverse magnetisation which decays rapidly in a time @xmath2 due to the spread of resonance frequencies in the ensemble . given the weakness of the coupling constant of a single spin to the microwave field , efficient absorption requires embedding the ensemble in a high - quality factor microwave resonator in order to reach the so - called high - cooperativity regime @xcite . the second step of the memory operation consists in retrieving the initial state , by a series of operations after which the spins emit a microwave pulse in a quantum state as close as possible to @xmath1 . in @xcite , this is achieved by a hahn - echo - like sequence consisting of two consecutive @xmath3 pulses on the spins , combined with dynamical tuning of the resonator frequency and quality factor . the maximum storage time of the memory is approximately the hahn - echo decay time @xmath4 , so that the maximal number of stored quantum states is of order @xmath5 , a figure which can be very large in many spin systems . the first step of this protocol ( quantum state transfer ) has been demonstrated at the single - photon level in recent experiments @xcite ; the remaining obstacle to a microwave quantum memory is therefore the implementation of hahn - echo refocusing sequences at the quantum level in a hybrid quantum circuit . the object of this work is precisely to identify the challenges posed by this task and to demonstrate experimentally that they can be solved . for simplicity , we consider from now on a protocol simpler than the full qm @xcite but which constitutes an essential building block : the two - pulse echo ( 2pe ) . as depicted in fig . [ fig1]a , the 2pe consists in storing weak pulses @xmath6 into the spin ensemble at times @xmath7 , and applying a single refocusing pulse at time @xmath8 which triggers the emission of echo pulses @xmath9 at times @xmath10 ( therefore in reverse order ) in the detection waveguide @xcite . performing the 2pe at the quantum level imposes a number of requirements which represent experimental challenges . for quantum states to be well defined , thermal excitations should be absent from the system . this implies both that the spin ensemble has a high degree of polarisation and that the microwave field is in its ground state with high probability , which can only be achieved if the experiments are performed at millikelvin temperatures . at these temperatures however , spins tend to relax very slowly towards their ground state , and an active spin reset is therefore needed in order to repeat the experimental sequence at a reasonable rate ( @xmath11hz ) as requested by experiments at the single photon level . then , applying refocusing pulses to the spins requires large microwave powers potentially incompatible with the detection of quantum fields . finally , the echo emitted by the spins should faithfully restore the initial field , which implies that the echo recovery efficiency @xmath12 , that we define as the ratio of the energy radiated during the echo to the energy of the incoming pulse , should be close to @xmath13 . to summarise , reaching the quantum regime requires a mean excitation per mode ( both microwave and spin ) @xmath14 , input microwave fields with intra - cavity photon number @xmath15 , and an echo efficiency @xmath12 close to @xmath13 . are stored in the spin ensemble . a refocusing pulse @xmath16 acts as time - reversal for the spins and triggers the retrieval of the stored pulses as echoes @xmath9 in reverse order . top and bottom time lines show the applied , and the reflected and echo signals , respectively . ( b ) setup placed in a dilution refrigerator : the cavity is a lumped - element parallel lc resonator in niobium coupled to a coplanar waveguide by a capacitor @xmath17 . it consists of an interdigitated capacitor @xmath18 and a meander wire inductor @xmath19 creating the ac magnetic field shown in inset , for a @xmath20 incident microwave power at resonance . the spin ensemble consists of nv centres in a diamond monocrystal pressed on top of the inductor . laser pulses can be shone on it through an optical fibre glued to its top face . a tunable dc magnetic field @xmath21 is applied parallel to the @xmath22 $ ] direction of the crystal . ( c ) negatively - charged nv centres in diamond consist of a nitrogen atom next to a vacancy of the diamond lattice , having trapped an electron . their electronic spin @xmath23 is coupled by hyperfine interaction to the nitrogen nuclear spin @xmath24 ( for the @xmath25 isotope ) . half of the electronic spins ( sub - ensemble denoted n - orth in blue ) make an angle @xmath26 with @xmath21 , whereas the other half ( sub - ensemble orth in red ) is orthogonal to the field . ( d ) nv simplified energy diagram ( top ) showing the ground @xmath27 and the excited @xmath28 electronic states as well as the zeeman and hyperfine structure of @xmath27 , with @xmath29ghz the zero - field splitting . ( bottom ) magnetic field dependence of the allowed transitions for both n - orth ( blue ) and orth ( red ) sub - ensembles , showing respectively a linear and quadratic zeeman effect . nvs can be optically repumped in their @xmath30 ground state by application of green ( @xmath31 nm ) laser pulses exciting the @xmath27 - @xmath28 transition.,width=377 ] these stringent requirements have never been met in an experiment , by far . the multi - mode character of the 2pe has been recently benchmarked in the classical regime @xcite with an ensemble of phosphorus donors in silicon at @xmath32k in the three - dimensional microwave cavity of an electron paramagnetic resonance spectrometer . that experiment reached @xmath33 , @xmath34 , and an echo recovery efficiency @xmath35 . here we use negatively - charged nitrogen - vacancy ( nv ) centres in diamond , which are colour centres consisting of a substitutional nitrogen atom sitting next to a vacancy of the lattice ( see fig . [ fig1]c ) with properties suitable for a quantum memory : their spin triplet ( @xmath23 ) electronic ground state has a long coherence time @xcite and can be optically repumped in the spin ground state @xmath36 ( see figs . [ fig1]c and d ) . we re - visit the 2pe protocol with an ensemble of nv centres at @xmath37mk coupled to a planar superconducting resonator , in a setup compatible with hybrid quantum circuits , with active reset of the spin at the beginning of each experimental sequence , and we demonstrate the storage of multiple pulses at the picowatt level for @xmath38 , three orders of magnitude longer than in earlier experiments @xcite . our experiment reaches @xmath39 , @xmath40 , @xmath41 , and @xmath42 , and comes therefore closer to the quantum regime than previous work by several orders of magnitude . we quantitatively identify the present limitations and show that they can be solved in future experiments , opening the way to the implementation of quantum memory protocols .

this estimate gives the critical value of the transverse trap frequency for which the quantum phase transition occurs , and which has a finite , measurable deviation from the critical point evaluated within the classical theory . a measurement is suggested for atomic systems which can probe the critical trap frequency at sufficiently low temperatures @xmath1 . we focus in particular on a trapped ion system , and estimate the implied limitations on @xmath1 and on the interparticle distance . we conclude that the experimental observation of the quantum critical behavior is in principle accessible .

i

1012.4332

a quasi one dimensional system of trapped , repulsively interacting atoms ( e.g. , an ion chain ) exhibits a structural phase transition from a linear chain to a zigzag structure , tuned by reducing the transverse trap potential or increasing the particle density . since it is a one dimensional transition , it takes place at zero temperature and therefore quantum fluctuations dominate . in [ fishman , _ et al . _ , phys . rev . b * 77 * , 064111 ( 2008 ) ] it was shown that the system close to the linear - zigzag instability is described by a @xmath0 model . we propose a mapping of the @xmath0 field theory to the well known ising chain in a transverse field , which exhibits a quantum critical point . based on this mapping , we estimate the quantum critical point in terms of the system parameters . this estimate gives the critical value of the transverse trap frequency for which the quantum phase transition occurs , and which has a finite , measurable deviation from the critical point evaluated within the classical theory . a measurement is suggested for atomic systems which can probe the critical trap frequency at sufficiently low temperatures @xmath1 . we focus in particular on a trapped ion system , and estimate the implied limitations on @xmath1 and on the interparticle distance . we conclude that the experimental observation of the quantum critical behavior is in principle accessible .

the structural transition from a linear chain of repulsively interacting particles to a planar configuration , in the form of a zigzag structure , has been often discussed in theoretical studies on atomic and condensed matter systems . examples include electrons in nanowires @xcite , ultracold dipolar gases @xcite , vortex lines in bose - einstein condensates @xcite , and ion coulomb crystals in traps @xcite . specifically in ion coulomb crystals this transition has been experimentally observed and characterized @xcite , thereby determining a phase diagram of the ionic structures as a function of the trap aspect ratio and of the mean interparticle distance @xcite . theoretical studies demonstrated that the transition from the string to the zigzag chain is associated with a symmetry breaking . more specifically , if the hamiltonian is invariant under rotation about the string axis , it is the rotational symmetry around the chain which is broken in the zigzag phase . if instead the motion of the interacting particles is confined to the plane , the zigzag phase breaks the symmetry by reflection about the chain axis . the phase transition predicted by the classical theory is hence second - order @xcite . it can be described by a landau model , of which critical values and exponents are well known @xcite , and where the soft mode is the zigzag mode of the linear chain namely , the transverse mode with the shorthest wavelength which drives the instability and determines the new structure . the corresponding ginzburg - landau equation in the continuum limit and in presence of damping was reported in ref . , where special focus was given on creation of defects when quenching the value of the transverse trap frequency across the mechanical instability . further works discussed the structural transitions when the external potential is not harmonic @xcite , showing that the statistical mechanics of the system at the instability may be profoundly modified . the results of these studies are strictly valid in the classical regime , when the thermal fluctuations can be neglected . is the temperature of the sample and the dimensionless parameter @xmath2 is tuned by the confining potential or the interparticle distance . the value @xmath3 corresponds to the value of the transverse frequency , where the linear chain is classically unstable @xcite . the quantum critical point , at @xmath4 , separates the linear chain from the zigzag phase at @xmath5 . for @xmath6 quantum fluctuations dominate , and the crystal is in the linear ( disordered ) phase . the dashed lines indicate the boundaries of the quantum critical region , where thermal fluctuations dominate . ] in ref . we addressed the question , whether quantum fluctuations significantly modify the location of the critical point and the behavior in its vicinity , focussing on ion coulomb crystals . this question draws on numerical studies in low dimensional dipolar systems , which showed a significant contribution of quantum fluctuations at the transition from a string to a zigzag order @xcite . in this article we provide the detailed calculations at the basis of the results presented in ref . , and extend the treatment to interacting atomic chains , with repulsive interaction potential scaling with @xmath7 with @xmath8 . we focus on the case where the motion of the particles is confined to a plane . as argued below , the string - to - zigzag transition is indeed a quantum phase transition analogous to the ferromagnetic transition of an ising chain in a transverse field @xcite . a phase diagram summarizing the behavior in its vicinity is depicted in fig . [ fig:1 ] . note that a similar mapping to the ising model was argued in the context of electronic systems in quantum wires @xcite . however , the validity of the assumed equivalence between a continuous field theoretical model and a discrete ( @xmath9 ) field - theory can not be justified on the basis of classification into universality classes below three space dimensions @xcite . in the present study we develop a quantum field theoretical approach , which allows a direct mapping to the quantum one dimensional ising model under plausible assumptions . on this basis we determine the quantum critical point at which the transition occurs and identify the experimental parameters , for which it can be distinguished from the value predicted by the classical theory @xcite . in particular , we relate the critical value of the transverse trap frequency @xmath10 to the ratio of the typical kinetic energy scale @xmath11 and interaction energy @xmath12 . defining a parameter @xmath13 , which describes the deviation of the transverse confinement from its stability point , we find that the critical point is given by @xmath14 . a measurement is suggested , which can demonstrate transverse quantum fluctuations in a long chain of trapped ions ( composed of hundreds of ions ) and probe the different regimes in the phase diagram . this paper is organized as follows . in sec . [ sec : model ] we derive a quantum field theory for the zigzag phonon mode . the mapping to the quantum ising model is described in sec . [ sec : mapping ] . in sec . [ sec : qcp ] we derive expressions for the ising model parameters , and in particular their critical values , in terms of microscopic parameters of the interacting atoms system . in sec . [ sec : experiment ] we discuss an experimental realization in trapped ions systems , and specify the conditions under which the quantum phase transition is likely to be observable . finally , our conclusions and outlook are summarized in sec . [ sec : conclude ] .

b * 77 * , 064111 ( 2008 ) ] it was shown that the system close to the linear - zigzag instability is described by a @xmath0 model . we propose a mapping of the @xmath0 field theory to the well known ising chain in a transverse field , which exhibits a quantum critical point .

c

1012.4332

a quasi one dimensional system of trapped , repulsively interacting atoms ( e.g. , an ion chain ) exhibits a structural phase transition from a linear chain to a zigzag structure , tuned by reducing the transverse trap potential or increasing the particle density . since it is a one dimensional transition , it takes place at zero temperature and therefore quantum fluctuations dominate . in [ fishman , _ et al . _ , phys . rev . b * 77 * , 064111 ( 2008 ) ] it was shown that the system close to the linear - zigzag instability is described by a @xmath0 model . we propose a mapping of the @xmath0 field theory to the well known ising chain in a transverse field , which exhibits a quantum critical point . based on this mapping , we estimate the quantum critical point in terms of the system parameters . this estimate gives the critical value of the transverse trap frequency for which the quantum phase transition occurs , and which has a finite , measurable deviation from the critical point evaluated within the classical theory . a measurement is suggested for atomic systems which can probe the critical trap frequency at sufficiently low temperatures @xmath1 . we focus in particular on a trapped ion system , and estimate the implied limitations on @xmath1 and on the interparticle distance . we conclude that the experimental observation of the quantum critical behavior is in principle accessible .

in this paper , it has been argued that the structural phase transition between a chain and a zigzag for ions or atoms interacting via a power - law interaction falling off as @xmath316 ( where @xmath317 is the distance and @xmath318 ) can be mapped on an ising model in a transverse field . in this way the classical theory for the phase transition can be extended to account for quantum fluctuations . such correspondence was proposed in the past for electronic systems @xcite . here the mapping is explicitly justified deep in the ordered zigzag phase [ see eq . ( [ condition ] ) ] . based on symmetry arguments ( [ tloc_gen ] ) ] we postulate that this mapping can be extended to the critical regime . the number of universality classes in two dimensions is restricted by conformal field theory @xcite . therefore , we argue that identifying the symmetry ( @xmath9 in our case ) determines the universality class , and implies that it is the same as of the one dimensional ising model in a transverse field . in other words , we assume that all operators obtained in our theory that differ from the ones of the conformal field theory of the one dimensional ising model in a transverse field are irrelevant in the sense of the renormalization group . to the best of our knowledge , there are no existing theoretical tools to verify such statements . however , this hypothesis is further supported by numerical studies @xcite . under these assumptions , we have estimated the quantum critical point as well as the regime of parameters where classically zigzag order would be found , but quantum tunneling and fluctuations suppress it and the linear chain is recovered . in this calculation it was assumed that the effective potential @xmath50 [ eq . ( [ v_loc ] ) ] , obtained in the vicinity of the critical point according to the classical theory , still holds . our analysis allows us to consider possible realizations of a suitable system in which the predicted quantum phase transition would be observable . in particular for trapped ion systems , we identify the physical parameters determining the critical point , as well as the experimental parameters which are required in order to access this regime . schemes for measuring the transition are proposed , which are based on photon scattering . we remark that this work addresses the two - dimensional case , in which the transition to a zigzag may only happen in a predetermined plane , and give also the full phase diagram including the thermal fluctuations . in three dimensions , where a goldstone mode is predicted corresponding to rotations of the plane , in which the zigzag is formed around the axis of the chain , one could consider an extension of this mapping . on this basis we conjecture that the system at the quantum phase transition can be mapped to the xy model , and the phase transition is of kosterlitz - thouless type . we finally note that our theory provides a general framework which allows one to study further effects , such as dynamics at the quantum critical point . it is worth mentioning that here one expects the creation of topological defects , i.e. domain walls . it would be interesting to apply this theory to defect formation , extending the work done on the classical system in ref . , and to explore whether these systems allow for the creation of special kind of entangled states of the ions . to conclude , using a quantum - field theoretical description we argue that the linear - zigzag instability in two - dimensional systems of trapped ions or polar molecules can be mapped to the one dimensional ising model in a transverse field . this result demonstrates once more the potentialities offered by these systems as quantum simulators @xcite , and more generally for quantum technological applications . we gratefully acknowledge useful discussions with e. altman , e. demler , j. eschner , r. fazio , j. feinberg , m. e. fisher , y. gefen , j. meyer , m. raizen and s. sachdev . this work has been partially supported by the israel science foundation ( isf ) , by the us - israel binational science foundation ( bsf ) , by the minerva center of nonlinear physics of complex systems , by the shlomo kaplansky academic chair , by the european commission ( ip aqute , strep picc ) , by the esf ( euroquam , cmmc ) , and by the spanish ministerio de ciencia y innovacin ( qoit , consolider - ingenio 2010 ; qnlp , fis2007 - 66944 ; ramon - y - cajal ) . e. s. acknowledges support from the ministry of science and technology ( grant 3 - 5792 ) . g. m. acknowledges the german research council ( dfg ) for support .

it is shown that the tdhf dynamics is more complex than a single monopolar collective motion at moderate energy . in particular the systematic of the minimum density reached during the expansion ( the so - called turning points ) appears to be different . *

c

nucl-th9810035

a recent interpretation of the caloric curve based on the expansion of the abraded spectator nucleus is re - analysed in the framework of the time - dependent hartree - fock ( tdhf ) evolution . it is shown that the tdhf dynamics is more complex than a single monopolar collective motion at moderate energy . the inclusion of other important collective degrees of freedom may lead to the dynamical creation of hollow structure . then , low density regions could be locally reached after a long time by the creation of these exotic density profiles . in particular the systematic of the minimum density reached during the expansion ( the so - called turning points ) appears to be different . * pacs : * 25.70.-z , 24.10.cn , 24.10.-i , 25.70.gh , 24.30.cz + * keywords : * mean - field , tdhf , compound nuclei , collective motions .

in this section , we study the evolution of the various considered nuclei . in fig.([fig3_eas ] ) , we have plotted the evolution of masses and entropies of the systems reported in table [ table2 ] . all these quantities are computed within a sphere of 15 fm . from this picture we can see that the smaller are the initial masses , the larger are the energies and entropies and so are the number of evaporated particles . indeed , one can observe that the evaporation is stronger for light highly excited systems with a rapid decrease of the mass and the entropy . moreover , in tdhf approach the evaporation is treated in quantum mechanics , particle may be reflected several time by the potential well before being ejected from the nucleus . therefore , the particle evaporation appears rather slow . this monopole motion can be clearly seen in figure [ fig4_rho ] which displays the time evolution of the central densities for different initial conditions . from this figure , as expected , collective motion is slower and presents a larger amplitude motion in the case of a soft eos . in these figures , we do not observe the fast expansion towards low density regions . indeed , at moderate energies ( @xmath84 mev ) , we observe that the first minimum ( i.e. the first turning point ) appears to be close from the initial dilution ( see for example @xmath85 ) . at low excitation energies , the small dilution of the abrasion - ablation stage is followed by a recompression phase . then , when the system expands again , the average density may reach values lower than the initial one . conversely , in a simple description assuming a collective dynamics at almost constant entropy and mass , this behavior should be normally understood considering the energetics of isentropes as shown in figure [ fig1_eos ] . indeed , schematically , if the system is initially with an excitation energy , @xmath86 , and an entropy , @xmath87 , it will expand or contract till it has reached the other point of the isentrope @xmath88 which cut a horizontal line corresponding to the energy @xmath89 . this schematic procedure is illustrated in figure [ fig7_sch ] . values of turning points obtained with this simple construction as well as the one of ref@xcite are compared to those extracted from the simulation in table [ table4 ] . for @xmath90 and @xmath91 , one can see only little differences between results of the schematic construction and those of the exact dynamics . however , they are different for @xmath85 and @xmath92 . considering table [ table4 ] and figure [ fig4_rho ] , several comments should be made : * \i ) for high excitation energies ( small masses ) , the schematic construction based on energy and entropy conservation predicts a total vaporization of the nucleus whereas in the dynamical simulations a small residue survives . this discrepancy can be accounted for by considering the energy and entropy variation due to the evaporation of particles ( see fig.[fig3_eas ] ) . * \ii ) for low excitation energy ( for example @xmath85 ) , evaporation is negligeable ( s = cte , t = cte ( fig . [ fig3_eas ] ) ) and the result could be directly compared to the schematic construction . however , we observe that tdhf predictions differ from schematic predictions . in the schematic model , from figure [ fig7_sch ] , starting with a nucleus of mass @xmath85 at @xmath77 , it appears impossible to reach a dilution lower than the initial one since the diluted nucleus is predicted to undergo a compression right after the beginning of the calculation . in tdhf simulations , the system is able to reach lower densities than the initial one by creating a hole at the center of the nucleus . moreover , instead of undergoing damped monopolar oscillations , the nucleus reaches a much lower value of central density at the second dilatation . as far as the comparison of tdhf simulation and the results of @xcite is concerned , the values of the turning points reported in table [ table4 ] appears to be different . at high initial temperature ( @xmath93 mev ) and for masses lower than @xmath94 , the amplitude of the expansion is larger in the collective model than in tdhf . at low temperature , the tdhf expansion is more complex than a breathing mode picture . in this picture , the central density is taken to be the only relevant variable since a self similar expansion is explicitly assumed . in fig . [ fig6_den ] . we show a typical example of density profile for different times of the evolution for @xmath85 . from this picture , it is clear that hollow structures are created during the evolution and that one density profile at a given time could not be obtained from another one by a simple scaling . the existence of exotic shapes which are created during the expansion , was already suggested in several works @xcite . the main novelty found here as we will see , is that these structures are consequences of the beating of intrinsic collective modes@xcite . in order to get a deeper insight , we will focus on the collective dynamics in the following ) . ] . in this section , we have generalized the analysis performed in ref.@xcite to many different initial conditions . in tdhf calculation , no assumption is made on which collective degrees of freedom could develop during the evolution . in order to better understand the complex dynamics of the density @xmath95 , we have plotted in the fig.[fig9_cont ] its fourier transform @xmath96 performed over 1500 fm / c . this corresponds to the expected breathing vibration and indeed the radial dependence of the density variation @xmath97 is well fitted by the usual tassie transition density@xcite . in fig.[fig9_cont ] , we observe several other collective higher at higher energies . for @xmath77 , we have many additional waves at frequencies @xmath98 , @xmath99 , @xmath100 and around @xmath101 . the collective motion located at @xmath102 corresponds to the two - phonon excitation of the breathing mode vibration . the other peaks at @xmath98 , @xmath99 and around @xmath101 could be associated to other collective degrees of freedom . in order to study either a possible anharmonicity or a coupling between modes , we have investigated the role of the vibration amplitude changing the initial conditions . in a pure harmonic picture , frequencies should remain constant and amplitudes of responses should vary linearly with the initial perturbation . focussing on the middle and bottom part of fig . [ fig9_cont ] , we see first that the frequencies are almost constant but the amplitude of the response do not depend linearly on the initial perturbation . therefore , the nuclei presents non - linearities and mode couplings but they are not strong enough to destroy the collective motions . this means that we are still far from a chaotic regime . in this chapter , we have pointed out that not only the breathing mode is excited in our tdhf calculation but also other modes . these modes are highly non - local in @xmath103 . this induces a complex dynamics and in particular may lead to the creation of hollow structure . up to now , many different macroscopic models@xcite have been used in order to extract information about the break - up of highly excited nuclear systems . in these approaches , the breathing vibration is taken to be dominant and the expansion is assumed to be a time - dependent self - similar expansion of the nucleus . however , this picture fails to reproduce our calculation which indicate that we must extend our collective phase space to include more degrees of freedom . in the next chapter , we will address this question and illustrate a possible generalization the eos of a finite nucleus in order to include hollow structures .

a recent interpretation of the caloric curve based on the expansion of the abraded spectator nucleus is re - analysed in the framework of the time - dependent hartree - fock ( tdhf ) evolution . then , low density regions could be locally reached after a long time by the creation of these exotic density profiles .

c

nucl-th9810035

a recent interpretation of the caloric curve based on the expansion of the abraded spectator nucleus is re - analysed in the framework of the time - dependent hartree - fock ( tdhf ) evolution . it is shown that the tdhf dynamics is more complex than a single monopolar collective motion at moderate energy . the inclusion of other important collective degrees of freedom may lead to the dynamical creation of hollow structure . then , low density regions could be locally reached after a long time by the creation of these exotic density profiles . in particular the systematic of the minimum density reached during the expansion ( the so - called turning points ) appears to be different . * pacs : * 25.70.-z , 24.10.cn , 24.10.-i , 25.70.gh , 24.30.cz + * keywords : * mean - field , tdhf , compound nuclei , collective motions .

we have used a quantum microscopic simulation in order to discuss the interpretation of the caloric curve recently proposed by papp and nrenberg@xcite . in their work the experimentally observed caloric curve may be interpreted as a line of turning - point reached in the low density region during the monopole expansion of excited nuclei where the nucleus could break . using analogous initial conditions , we have pointed out that many differences between a microscopic approach and the collective model . indeed at low and moderate energies , the tdhf dynamics indicates that different collective vibrations could develop on top of the self - similar vibration . this collective behavior may lead to the formation of hollow structures . since the density come from a superposition of many modes , we see that the lowest density region could be reached after a longer time ( see fig . [ fig4_rho ] ) than the first breathing of the nucleus . it should be noticed that experimental data of photon detection seems to indicate such a behavior@xcite . the presence of many collective modes in the dynamic has led us to generalize the simple breathing mode picture . by a suitable parameterization of the density , we have defined a generalized equation of state . this new approach , include the possible existence of exotic shape in the dynamic . as we have seen , the nucleus has a complex path in this new phase - space . on the other hand , at high initial excitation energy , when the breathing collective mode dominates , the amplitude of the monopole oscillation is also different from the one reported in@xcite . since our simulations demonstrate that the collective dynamics of an abraded nucleus could be complex and depends on the model used . the possible interpretation of the caloric curve as a line of turning - point has to be considered carefully .

a spherical two - distance set is a finite collection of unit vectors in @xmath0 such that the distances between any two distinct vectors assume only two values . we use the semidefinite programming method to compute improved estimates of the maximum size of spherical two - distance sets . exact answers are found for dimensions @xmath1 and @xmath2 where previous results gave divergent bounds . institute for systems research , university of maryland , college park , md 20742 . email : mathyu@math.umd.edu ]

i

1204.5268

a spherical two - distance set is a finite collection of unit vectors in @xmath0 such that the distances between any two distinct vectors assume only two values . we use the semidefinite programming method to compute improved estimates of the maximum size of spherical two - distance sets . exact answers are found for dimensions @xmath1 and @xmath2 where previous results gave divergent bounds . dept . of electrical and computer engineering and institute for systems research , university of maryland , college park , md 20742 , and institute for information transmission problems , russian academy of sciences , moscow , russia . email : abarg@umd.edu . ] dept . of mathematics and institute for systems research , university of maryland , college park , md 20742 . email : mathyu@math.umd.edu ]

this paper is devoted to the application of the semidefinite programming method to estimates of the size of the largest possible two - distance set on the sphere @xmath3 . a spherical two - distance set is a finite collection @xmath4 of unit vectors in @xmath0 such that the set of distances between any two distinct vectors in @xmath4 has cardinality two . estimating the maximum size @xmath5 of such a set is a classical problem in distance geometry that has been studied for several decades . we begin with an overview of known results . a lower bound on @xmath5 is obtained as follows . let @xmath6 be the standard basis in @xmath7 . the points @xmath8 form a spherical two - distance set in the plane @xmath9 ( after scaling ) , and therefore @xmath10 the first major result for upper bounds was obtained by delsarte , goethals , and seidel @xcite . they proved that , irrespective of the actual values of the distances , the following `` harmonic '' bound holds true : @xmath11 they also showed that this bound is tight for dimensions @xmath12 where it is attained by sets of equiangular lines . moreover , the results of @xcite , bannai et al . @xcite , and nebe and venkov @xcite imply that @xmath5 can attain the harmonic bound only if @xmath13 with the exception of an infinite sequence of values of @xmath14 that begins with @xmath15 . therefore , unless @xmath16 is of the above form , @xmath17 these results are proved using the link between 2-distance sets and tight spherical 4-designs established in @xcite . another advance in estimating the function @xmath5 was made by musin @xcite . let @xmath18 and suppose that @xmath19 where @xmath20 are the values of the squared distances between the points . musin proved that @xmath21 he then used delsarte s linear programming method to prove that @xmath22 if @xmath23 here we make another step for spherical two - distance sets , extending the range of dimensions in which the bound is tight . the state of the art for @xmath5 can be summarized as follows . we have @xmath24 @xmath25 and @xmath26 if @xmath27 then @xmath28 as detailed in the remarks after eq . above . the part of this theorem that is established in the present paper relates to dimensions @xmath1 and @xmath29 our results are computational in nature and are obtained using the semidefinite programming method . the other parts of this theorem follow from the results in @xcite . as far as actual constructions of spherical two - distance sets are concerned , rather little is known beyond the set of midpoints of the edges of a regular simplex mentioned above . another way of constructing such sets is to start with a set of equiangular lines in @xmath0 @xcite . if the angle between each pair of lines is @xmath30 then taking one point from each pair of points on @xmath31 defined by the line , we obtain a two - distance set with @xmath32 the largest possible number of equiangular lines in @xmath0 is @xmath33 ( this result is due to gerzon , see @xcite ) . this bound is attained for @xmath34 for instance , for @xmath35 the set of 6 lines is obtained from 6 diagonals of the icosahedron , which gives many ways of constructing inequivalent spherical two - distance sets of cardinality 6 . the only three instances in which the known spherical two - distance sets are of cardinality greater than @xmath33 occur in dimensions @xmath36 and @xmath37

a tree @xmath0 , in an edge - colored graph @xmath1 , is called _ a rainbow tree _ if no two edges of @xmath0 are assigned the same color . a _ @xmath2-rainbow coloring _ of @xmath1 is an edge coloring of @xmath1 having the property that for every set @xmath3 of @xmath2 vertices of @xmath1 , there exists a rainbow tree @xmath0 in @xmath1 such that @xmath4 . the minimum number of colors needed in a @xmath2-rainbow coloring of @xmath1 is the _ @xmath2-rainbow index of @xmath1 _ , denoted by @xmath5 . in this paper , we consider @xmath6-rainbow index @xmath7 of @xmath1 . we first show that for connected graph @xmath1 with minimum degree @xmath8 , the tight upper bound of @xmath7 is @xmath9)+4 $ ] , where @xmath10 is the connected @xmath11-dominating set of @xmath1 . and then we determine a tight upper bound for @xmath12 and a better bound for @xmath13-free graphs . * keywords * : @xmath6-rainbow index ; rainbow tree ; connected @xmath11-dominating set .

i

1310.2355

a tree @xmath0 , in an edge - colored graph @xmath1 , is called _ a rainbow tree _ if no two edges of @xmath0 are assigned the same color . a _ @xmath2-rainbow coloring _ of @xmath1 is an edge coloring of @xmath1 having the property that for every set @xmath3 of @xmath2 vertices of @xmath1 , there exists a rainbow tree @xmath0 in @xmath1 such that @xmath4 . the minimum number of colors needed in a @xmath2-rainbow coloring of @xmath1 is the _ @xmath2-rainbow index of @xmath1 _ , denoted by @xmath5 . in this paper , we consider @xmath6-rainbow index @xmath7 of @xmath1 . we first show that for connected graph @xmath1 with minimum degree @xmath8 , the tight upper bound of @xmath7 is @xmath9)+4 $ ] , where @xmath10 is the connected @xmath11-dominating set of @xmath1 . and then we determine a tight upper bound for @xmath12 and a better bound for @xmath13-free graphs . finally , we obtain a sharp bound for @xmath6-rainbow index of general graphs . * keywords * : @xmath6-rainbow index ; rainbow tree ; connected @xmath11-dominating set .

all graphs considered in this paper are simple , connected and undirected . we follow the terminology and notation of bondy and murty @xcite . an edge - colored graph @xmath1 is _ rainbow connected _ if any two vertices are connected by a path whose edges have distinct colors . the _ rainbow connection number _ @xmath14 of @xmath1 , introduced by chartrand et al . @xcite , is the minimum number of colors that results in a rainbow connected graph @xmath1 . later , another generalization of rainbow connection number was introduced by chartrand et al.@xcite in 2009 . a tree @xmath0 is a _ rainbow tree _ if no two edges of @xmath0 are colored the same . let @xmath2 be a fixed integer with @xmath15 . an edge coloring of @xmath1 is called a _ @xmath2-rainbow coloring _ if for every set @xmath3 of @xmath2 vertices of @xmath1 , there exists a rainbow tree in @xmath1 containing the vertices of @xmath3 . @xmath2-rainbow index _ @xmath5 of @xmath1 is the minimum number of colors needed in a @xmath2-rainbow coloring of @xmath1 . it is obvious that @xmath16 . let @xmath2 be a positive integer . a subset @xmath17 is a @xmath2-dominating set of the graph @xmath1 if @xmath18 for every @xmath19 . the @xmath2-domination number @xmath20 is the minimum cardinality among the @xmath2-dominating sets of @xmath1 . note that the @xmath21-domination number @xmath22 is the usual domination number @xmath23 . a subset @xmath3 is a connected @xmath2-dominating set if it is a @xmath2-dominating set and the graph induced by @xmath3 is connected . the connected @xmath2-domination number @xmath24 represents the cardinalities of a minimum connected @xmath2-dominating set . for @xmath25 , we write @xmath26 instead of @xmath27 . chakraborty et al . @xcite showed that computing the rainbow connection number of a graph is np - hard . so it is also np - hard to compute @xmath2-rainbow index of an arbitrary graph . chandran et al . @xcite use a strengthened connected dominating set ( connected @xmath11-way dominating set ) to prove @xmath28)+3 $ ] . this led us to the investigation of what is strengthening of a connected dominating set which can apply to consider @xmath6-rainbow index of a graph . recently , for @xmath6-rainbow index , li et al . did some basic results and they obtained the following theorem . @xcite[thm0 ] let @xmath1 be a @xmath11-connected graph of order @xmath29 @xmath30 . then @xmath31 , with equality if and only if @xmath32 or @xmath1 is a spanning subgraph of @xmath6-sun or @xmath1 is a spanning subgraph of @xmath33 or @xmath1 is a spanning subgraph of @xmath34 . here , a @xmath6-sun is a graph @xmath1 which is defined from @xmath35 = @xmath36 by adding three edges @xmath37 , @xmath38 and @xmath39 . chartrand et al . @xcite obtained that for integers s and t with @xmath40 , @xmath41{t},4\}$ ] . thus , @xmath42 . @xcite consider the regular complete bipartite graphs @xmath43 . they show @xmath44 for integer @xmath45 with @xmath46 . in this paper , we focus on @xmath6-rainbow index . in section @xmath11 , we adopt connected @xmath11-dominating set to study @xmath6-rainbow index . a coloring strategy is obtained which uses only a constant number of extra colors outside the dominating set . we prove that @xmath47)+4 $ ] , where @xmath10 is the connected @xmath11-dominating set of @xmath1 . in section @xmath6 , we determine a sharp bound of @xmath6-rainbow index for @xmath48 ( @xmath49 ) and an upper bound for @xmath13-free . in section @xmath50 , we investigate a sharp upper for @xmath7 of general graphs by block decomposition and an upper bound for graphs with @xmath8 by connected @xmath11-dominating set .

a wireless relay network ( wrn ) has recently emerged as an effective way to increase communication capacity and extend a coverage area with a low cost . in the wrn , multiple service providers ( sps ) can cooperate to share their resources ( e.g. , relay nodes and spectrum ) , to achieve higher utility in terms of revenue . such cooperation can improve the capacity of the wrn , and thus throughput for terminal devices ( tds ) .

i

1401.3506

a wireless relay network ( wrn ) has recently emerged as an effective way to increase communication capacity and extend a coverage area with a low cost . in the wrn , multiple service providers ( sps ) can cooperate to share their resources ( e.g. , relay nodes and spectrum ) , to achieve higher utility in terms of revenue . such cooperation can improve the capacity of the wrn , and thus throughput for terminal devices ( tds ) . however , this cooperation can be realized only if fair allocation of aggregated utility , which is the sum of the utility of all the cooperative sps , can be achieved . in this paper , we investigate the wrn consisting of sps at the upper layer and tds at the lower layer and present a game theoretic framework to address the cooperation decision making problem in the wrn . specifically , the cooperation of sps is modeled as an overlapping coalition formation game , in which sps should form a stable coalitional structure and obtain a fair share of the aggregated utility . we also study the problem of allocating aggregated utility based on the concept of shapley value , which stabilizes the cooperation of sps in the wrn . the cooperation of tds is modeled as a network formation game , in which tds establish links among each other to form a stable network structure . numerical results demonstrate that the proposed distributed algorithm obtains the aggregated utility approximating the optimal solutions and achieves good convergence speed . _ keywords- _ layered coalitional game , overlapping coalition formation , network structure formation , utility allocation solution , shapley value .

the multi - hop relay transmission has potential to offer low - cost , high - speed and long - range wireless communications . the multi - hop relay transmission will be adopted in the new standards ( e.g. , wimax or ieee 802.16 m ) . in such standards , the multi - hop relay capability is enabled for legacy network terminal devices ( tds ) ( e.g. , access points and routers ) . in this context , the wireless relay network ( wrn ) has recently emerged as one of the focuses on next generation wireless networks . in the wrn , relay transmission based on cooperation among tds can mitigate channel fading and exploit spatial reuse to accommodate concurrent transmissions , thus potentially increasing network capacity and coverage . existing works @xcite have demonstrated that a significant performance improvement can be achieved in the wrns in terms of higher throughput , lower bit error rate , better capacity , compared to traditional single - hop transmission used in the current cellular network @xcite . this paper considers the multi - hop network structure formed by tds from multiple service providers ( sps ) with the purpose of capacity improvement . multiple sps may form coalitions to let their tds serve the transmission demand of each other , with the goal to increase the sps aggregated revenue @xcite . the utilization of available resources , i.e. , vacant tds ( which can relay the data for other tds ) and network capacity , can be substantially improved through forming sp coalitions . this is beneficial to sps because , in some wrns , tds are deployed dispersedly . for each sp , if there is no cooperation , the limited number of available vacant tds and their dispersive locations largely confine the link capacity for data transmission . the cooperation among sps could increase the number of available vacant tds for each sp which in turn can improve network capacity . accordingly , a larger amount of traffic demand can be served by more efficiently resource utilization in the wrn , which leads to higher aggregated revenue for sps . the cooperation in the wrn also benefits tds because a cooperative relay may substantially lead to improved network capacity and thus increased throughput for the tds . we call the formation of this interrelated sp cooperation and td cooperation as the layered cooperation problem , which is the main focus of this paper . previous work has also considered game - theoretic framework with layers / hierarchies , e.g. , @xcite in the cognitive radio networks , @xcite in two - tier femtocell networks and @xcite in wrns . however , most of the works considered the competition relationship between different layers , which belongs to the stackelberg game concept @xcite . in our work , different layers interact to improve the benefit of each other cooperatively . although cooperation in the wrn brings significant benefits , three major challenges arise . first , what is the coalitional structure desirable for all sps ? second , how shall the aggregated utility ( i.e. , revenue ) be allocated to each sp in the coalition in a fair manner so that none of sps is willing to leave the coalition ? third , what is the stable network structure for tds of cooperative sps to perform uplink transmission ? this paper addresses these three challenges .

according to the gottesmann - knill theorem the non - gaussian states are necessary component for a nontrivial quantum computation . we show two efficient and deterministic methods of @xmath0 non - gaussian state generation for a cavity mode using a single trapped ion . both require ion motional state transfer to the cavity field . the first is based on the well - known protocol for an ion finite motional superposition state generation . we give criteria based on the wigner function which quantify the error resulting from the approximation . the second and novel method enables an exact non - gaussian state generation using one laser pulse only .

i

0810.2618

according to the gottesmann - knill theorem the non - gaussian states are necessary component for a nontrivial quantum computation . we show two efficient and deterministic methods of @xmath0 non - gaussian state generation for a cavity mode using a single trapped ion . both require ion motional state transfer to the cavity field . the methods are experimentally feasible . the first is based on the well - known protocol for an ion finite motional superposition state generation . it allows for an arbitrary good approximation of @xmath0 non - gaussian states . we give criteria based on the wigner function which quantify the error resulting from the approximation . the second and novel method enables an exact non - gaussian state generation using one laser pulse only .

the gottesmann - knill theorem for continuous variables ( cv ) states that quantum computing based only on components described by one- or two - mode quadratic hamiltonians , gaussian states input , and measurements on canonical variables can be efficiently simulated by a classical computation . that means , although some of the algorithms are of fundamentally quantum nature , they do not provide any speedup over classical processes @xcite . it has also been proved that construction of a cv universal quantum computer for transformations that are polynomial in those variables requires cubic or higher non - linear operations @xcite . therefore , investigation of the non - gaussian transformations and states generation is crucial for a nontrivial quantum computation . more recently it has been noted that kerr - like nonlinearities , in a variety of systems , enable high precision quantum metrology that would otherwise require entanglement to achieve it @xcite . over the last decade ion trap experiments have led the emerging technologies of coherent quantum control , especially in quantum information theory @xcite and quantum computation @xcite . those applications require efficient creation and precise manipulation of both electronic and motional trapped ion state . various theoretical proposals on how to produce nonclassical arbitrary states of ion motion have been discussed . in experiment , fock number states @xcite , coherent states @xcite , vacuum squeezed states @xcite , and schrdinger cat states @xcite have been realized . in this latter case , the state is an entangled state of the vibrational and electronic degrees of freedom . on the contrary , in this paper we give a deterministic way to prepare the vibrational degree of freedom in a non - gaussian state that is not entangled with the electronic states . according to our knowledge , neither non - gaussian state ( other than an entangled cat state ) nor a superposition of more than two coherent states has been observed so far . in the case of photons there is no practical method of non - gaussian state generation so far . efforts have been made to explore a class of the @xmath0 non - gaussian states produced using a photon coherent state @xmath1 interacting with @xmath0 kerr nonlinearity in an optical fiber @xmath2 this class of non - gaussian states , parametrized by the unitless evolution parameter @xmath3 @xcite , is the most popular one . the state ( [ eq : kerr ] ) is known also as the kerr state . in general , this is a highly nonclassical state and after a certain time of evolution @xmath3 in the fiber its wigner function would take negative values in the phase space @xcite . however , the nonlinearity in a fiber , or any other experimentally achievable kerr medium , is too small , @xmath4 , to reach a highly nonlinear regime and thus produce the negativity in an experimentally reasonable time , before it is destroyed by dissipation @xcite . although microstructured fibers seem to be more promising with @xmath5 , their length does not exceed @xmath6 with current technology . the most known examples of the kerr state are the cat states @xmath7 corresponding to @xmath8 , which have been found useful for studies of quantum decoherence and quantum - classical boundary @xcite . the larger cat states for which the two components @xmath9 and @xmath10 are almost orthogonal ( @xmath11 ) find their application in quantum information processing @xcite and quantum computation @xcite . recently , there has been introduced a probabilistic method of non - gaussian state generation relying on a conditional photon subtraction from a squeezed vacuum state @xcite . such a state is a good approximation for the cat state if the amplitude is small @xmath12 . however , it is neither practical to subtract more than two photons in the experiment nor to produce a state with @xmath13 @xcite . moreover , the state is not pure . another approach is suggested by recent achievements in the the polzik group @xcite based on their demonstration of teleportation of a quantum state from optical to matter degrees of freedom . if this process was reversed , so that a non - gaussian state is either teleported or mapped from matter to light , optical kerr states might be robustly generated and thus overcome obstacles which are met with in trying to generate optical non - gaussian states directly . of course this requires us to demonstrate a way to make non - gaussian states in matter degrees of freedom . the proposals for transferring an arbitrary motional quantum state of an atom to a cavity field already exist @xcite . the effort to integrate ion traps and optical fields @xcite might offer a path based on the extraordinary level of coherent quantum control one has over the vibrational degrees of freedom for trapped ions . in this paper we discuss two efficient and deterministic methods of @xmath0 non - gaussian state generation for light using a single trapped ion . both methods require ion motional state transfer to the cavity mode . the first method is based on the well - known protocol @xcite for an ion finite motional superposition state generation . it allows to produce the @xmath0 non - gaussian states with arbitrary good approximation . we give criteria , based on wigner function comparison and its measurement precision , which quantify the error resulting from the approximation . the second method is novel and it enables an exact non - gaussian state generation using one laser pulse only . we point out that a wigner function measurement of ion motional state can be performed using currently available technology and already existing experimental schemas . we also suggest a quantum metrology application , based on the work of caves and co workers @xcite . this paper is organized as follows . in section [ sec1 ] we show that , applying a well - known protocol , one can produce an approximated @xmath0 non - gaussian state of motion for a trapped ion . the method relies on using a series of laser pulses to couple electronic and vibrational degrees of freedom to effect the desired state preparation for the motional degree of freedom . we give the criteria for quantifying the extent to which the prepared state approximates the desired non - gaussian state , and discuss the technical limitations of the method . in section [ sec2 ] we present an alternative , and novel , method for generation of an exact @xmath0 non - gaussian state . we also discuss the range of application of this method . we finish the paper with conclusions and a brief discussion of possible applications to quantum metrology .

visible ( vlt / sphere , kervella et al . 2015 ) domains revealed that the nearby agb star l@xmath0 pup ( @xmath1pc ) is surrounded by a dust disk seen almost edge - on . l@xmath0 pup is currently a relatively `` young '' agb star , so we may witness the formation of a planetary nebula . the mechanism that breaks the spherical symmetry of mass loss is currently uncertain , but we propose that the dust disk and companion are key elements in the shaping of the bipolar structure . l@xmath0 pup emerges as an important system to test this hypothesis .

c

1512.03459

adaptive optics observations in the infrared ( vlt / naco , kervella et al . 2014 ) and visible ( vlt / sphere , kervella et al . 2015 ) domains revealed that the nearby agb star l@xmath0 pup ( @xmath1pc ) is surrounded by a dust disk seen almost edge - on . thermal emission from a large dust `` loop '' is detected at 4@xmath2 m up to more than 10au from the star . we also detect a secondary source at a separation of 32mas , whose nature is uncertain . l@xmath0 pup is currently a relatively `` young '' agb star , so we may witness the formation of a planetary nebula . the mechanism that breaks the spherical symmetry of mass loss is currently uncertain , but we propose that the dust disk and companion are key elements in the shaping of the bipolar structure . l@xmath0 pup emerges as an important system to test this hypothesis .

the environment of l@xmath0 pup hosts the two major ingredients suspected to play a role in the shaping of pne : a close - in companion ( whose physical nature is still largely enigmatic ) and a circumstellar dust disk . thanks to its proximity and the availability of the sphere adaptive optics providing 20mas angular resolution in the visible , it is now possible to monitor in real time the dynamical evolution of the different components of the immediate environment of l@xmath0 pup ( companion , spirals , plumes , ... ) . considering their linear scales , we expect a significant evolution over timescales of only a few years . l@xmath0 pup thus exhibits a strong potential to improve our understanding of the mass loss of low and intermediate mass stars and the formation of bipolar pne .

after the final analyses of the h1 and zeus collaborations for the diffractive photoproduction of dijets have appeared , we have recalculated these cross sections in next - to - leading order ( nlo ) of perturbative qcd to see whether they can be interpreted consistently . the results of these calculations are compared to the data of both collaborations . we find that at nlo the cross sections disagree with the data , showing that factorization breaking occurs at this order . desy 08 - 074 + lpsc

i

0806.2269

after the final analyses of the h1 and zeus collaborations for the diffractive photoproduction of dijets have appeared , we have recalculated these cross sections in next - to - leading order ( nlo ) of perturbative qcd to see whether they can be interpreted consistently . the results of these calculations are compared to the data of both collaborations . we find that at nlo the cross sections disagree with the data , showing that factorization breaking occurs at this order . if direct and resolved contributions are both suppressed by the same amount , the global suppression factor depends on the transverse - energy cut and is @xmath0 for the h1 and @xmath1 for the zeus analysis . however , by suppressing only the resolved contribution by a factor of approximately three , also reasonably good agreement with all the data is found . the size of the factorization breaking effects for resolved photons agrees with absorptive - model predictions . desy 08 - 074 + lpsc 08 - 070

it is well known that at high - energy colliders such as the @xmath2 collider hera at desy and the @xmath3 collider tevatron at fermilab , a large fraction of the observed events are diffractive . these events are defined experimentally by the presence of a forward - going hadronic system @xmath4 with four - momentum @xmath5 , low mass @xmath6 ( typically a proton that remained intact or a proton plus low - lying nucleon resonances ) , small four - momentum transfer @xmath7 , and small longitudinal - momentum transfer @xmath8 from the incoming proton with four momentum @xmath9 to the central hadronic system @xmath10 ( see fig.[fig:0 ] for the case of @xmath11 ) . experimentally , a large diffractive scattering process @xmath12 , where the hadronic systems @xmath10 and @xmath4 are separated by the largest rapidity gap in the final state . ] rapidity gap separates the hadronic system @xmath10 with invariant mass @xmath13 from the final - state system @xmath4 with invariant mass @xmath6 . theoretically , diffractive interactions are described in the framework of regge theory @xcite as the exchange of a trajectory with vacuum quantum numbers , the pomeron ( @xmath14 ) trajectory . then the object exchanged between the systems @xmath10 and @xmath4 , as indicated in fig . [ fig:0 ] , is the pomeron ( or additional lower - lying regge poles ) , and the upper vertex of the process @xmath15 can be interpreted as deep - inelastic scattering ( dis ) on the pomeron target for the case that the virtuality of the exchanged photon @xmath16 is sufficiently large . in analogy to dis on a proton target , @xmath17 , the cross section for the process @xmath18 in the dis region can be expressed as the convolution of partonic cross sections and universal parton distribution functions ( pdfs ) of the pomeron . the partonic cross sections are the same as for dis @xmath2 scattering . usually these pomeron pdfs are multiplied with vertex functions for the lower vertex in fig . [ fig:0 ] , yielding the diffractive parton distribution functions ( dpdfs ) . the @xmath19-evolution of the dpdfs is calculated with the usual dglap @xcite evolution equations known from @xmath17 dis . except for their evolution with @xmath19 , the dpdfs can not be calculated in the framework of perturbative qcd and must be determined from experiment . such dpdfs @xcite have been obtained from the hera inclusive measurements of the diffractive structure function @xmath20 @xcite , defined analogously to the proton structure function @xmath21 . similarly to diffractive dis , @xmath11 , where the presence of the large scale @xmath22 allows for the application of perturbative qcd and @xmath10 comprises the sum over all possible final states , many other processes with a hard scale provided by specific final states in the central system @xmath10 can be predicted using qcd perturbation theory . such processes , usually called hard diffractive processes , are e.g. dijet production in diffractive photoproduction ( @xmath23 ) and dis ( @xmath24 ) , where the large scale is given by the jet transverse energy @xmath25 and possibly @xmath22 , and diffractive open heavy - flavor production , where the large scale is given by the heavy - flavor mass and possibly @xmath26 and/or @xmath22 , in photoproduction or dis and many more diffractive processes induced by @xmath27 or @xmath28 collisions . the central problem in hard diffraction is the problem of qcd factorization , i.e. the question whether diffractive cross sections are factorisable into universal dpdfs and partonic cross sections , which are calculable in perturbative qcd . this question is the subject of the current debate in diffractive physics and is of particular interest for the prospects of discovery of new particles such as the higgs boson in diffractive reactions at the lhc @xcite . for the inclusive dis process , factorization has indeed been proven to hold @xcite , and on this basis dpdfs have been extracted at @xmath24 @xcite from high - precision inclusive measurements of the process @xmath11 using the usual dglap evolution equations . the proof of the factorization formula , usually referred to as the validity of qcd factorization in hard diffraction , also appears to be valid for the production of specific final states in dis , as e.g. the production of jets or heavy - flavor particles , and for the direct part of photoproduction ( @xmath29 ) or low-@xmath19 electroproduction of jets @xcite . however , factorization does not hold for hard processes in diffractive hadron - hadron scattering . the problem is that soft interactions between the ingoing hadrons and/or their remnants occur in both the initial and the final state . this agrees with experimental measurements at the tevatron @xcite . predictions of diffractive dijet cross sections for collisions as measured by cdf using dpdfs determined earlier by the h1 collaboration @xcite at hera overestimate the measured cross section by up to an order of magnitude @xcite . this large suppression of the cdf cross section can be explained by the rescattering of the two incoming hadron beams , which , by creating additional hadrons , destroy the rapidity gap @xcite . jet production with real photons involves direct interactions of the photon with quarks or gluons originating from the proton or pomeron , respectively , as well as resolved photon contributions leading to parton - parton interactions with an additional remnant jet coming from the photon as reviewed in @xcite ( see fig . [ fig:1 ] ) . for the direct interactions , we expect factorization diffractive production of dijets with invariant mass @xmath30 in direct ( left ) and resolved ( right ) photon - pomeron collisions , leading to the production of one or two additional remnant jets.,title="fig : " ] diffractive production of dijets with invariant mass @xmath30 in direct ( left ) and resolved ( right ) photon - pomeron collisions , leading to the production of one or two additional remnant jets.,title="fig : " ] to be valid as in the case of inclusive dis , as already mentioned , whereas we expect it to fail for the resolved process as in hadron - hadron scattering . for this part of photoproduction we would therefore expect a similar suppression factor ( sometimes also called rapidity - gap survival probability ) due to rescattering effects of the ingoing partons or hadrons . introducing vector - meson dominance photon fluctuations , such a suppression by about a factor of three was predicted for resolved photoproduction at hera @xcite . the first measurements of dijet cross sections in diffractive photoproduction have been presented by the h1 collaboration as contributions to two conferences @xcite . the kinematic range for these data were @xmath31 gev@xmath32 , @xmath33 , @xmath34 gev , @xmath35 gev and @xmath36 gev , where jets were identified using the inclusive @xmath37-cluster algorithm ( the definitions of these and the following variables will be given in the next section ) . the measured cross sections as a function of @xmath38 and @xmath39 were compared to leading - order ( lo ) qcd predictions , using the rapgap monte carlo model @xcite . for the dpdfs the lo ` h1 2002 fit ' was used @xcite . the two cross sections were found to be well described by the predictions in normalization and shape over the whole range of @xmath38 and @xmath39 , showing no breakdown of factorization neither in resolved nor in direct photoproduction . in addition , normalized cross sections as a function of various other variables were compared to the predictions with the result that all measured distributions were in good agreement . subsequently we calculated the next - to - leading order ( nlo ) corrections for the cross section of diffractive dijet production using the same kinematic cuts and with the same dpdfs as in the first h1 analysis @xcite on the basis of our previous work on nlo corrections for inclusive direct @xcite and resolved @xcite dijet photoproduction . while at lo good agreement with the h1 data @xcite was found , consistent with the finding in the h1 analysis @xcite , it was found that the nlo corrections increase the cross section significantly @xcite and require a suppression factor of the order of @xmath40 . since on theoretical grounds only a suppression of the resolved cross section would be acceptable , we demonstrated in @xcite that by multiplying the resolved cross section with the suppression factor @xmath41 , reasonably good agreement with the preliminary h1 data @xcite could be achieved . this value for the suppression factor turned out to be in good agreement with the prediction of @xcite . the first experimental data from the zeus collaboration were presented at the dis workshop in 2004 @xcite . the dijet cross sections were obtained in the kinematic range @xmath42 gev@xmath32 , @xmath43 and @xmath44 @xmath45 gev . for these kinematic constraints nlo calculations were not available in 2004 . so , the measurements were compared to lo calculations , unfortunately with previous h1 dpdfs @xcite with the result , that good agreement in the shape was achieved . but the normalization was off by a factor of @xmath46 , which was attributed to the older dpdf input @xcite , so that the h1 and zeus results were consistent with each other . the situation concerning the agreement of h1 and zeus data and the influence of nlo corrections improved already considerably in the fall of 2004 . these preliminary data from both hera collaborations together with comparisons to nlo calculations based on the dpdf fits from @xcite were presented at workshops and conferences in the following years . in 2006 the h1 collaboration published their final dpdf fits from their high - precision measurements using the dglap evolution equations @xcite . this analysis was based on the larger data sample of the years 1997 - 2000 as compared to the earlier preliminary dpdf sets @xcite . in @xcite two dpdf sets , the h1 2006 fit a and the h1 2006 fit b were presented , which both give a good description of the inclusive diffractive data . these two sets differ mainly in the gluon density at large fractional parton momenta , which is poorly constrained by the inclusive diffractive scattering data , since there is no direct coupling of the photon to gluons , so that the gluon density is constrained only through the evolution . the gluon density of fit a is peaked at the starting scale at large fractional momenta , whereas fit b is flat in this region . in 2007 the final publications for diffractive dijet production appeared @xcite . the comparison between these experimental results and the nlo theory was based on the new and final dpdfs from h1 @xcite . the differential cross sections as measured by h1 @xcite were compared to nlo predictions obtained with the frixione program @xcite interfaced to the ` h1 2006 fit b ' dpdfs . the conclusions deduced earlier from the comparison with the preliminary data and the preliminary ` h1 2002 fit ' @xcite are fully confirmed in @xcite with the new dpdfs fits @xcite . in particular , a global suppression is obtained , independent of the dpdfs fits used , i.e. fit a or fit b , by considering the ratio of measured dijet cross sections to nlo predictions in photoproduction in relation to the same ratio in dis . in this comparison the value of the suppression is @xmath47 . in addition , by using this overall suppression factor , h1 obtained a good description of all the measured distributions in the variables @xmath39 , @xmath38 , @xmath48 , @xmath49 , @xmath50 , @xmath51 , @xmath52 and @xmath30 interfaced with the ` h1 2006 fit b ' dpdfs and taking into account hadronization corrections @xcite . finally , the h1 collaboration investigated how well the data are describable under the assumption that in the nlo calculation the cross section for @xmath53 is not suppressed . the best agreement in a fit was obtained for a suppression factor 0.44 for the nlo calculation with @xmath54 , based on fitting the distributions for @xmath38 , @xmath49 , @xmath51 and @xmath50 . in this comparison they found disagreement for the largest @xmath38-bin and the lowest @xmath51 ( which are related ) , but better agreement in the @xmath50-distribution . in @xcite this leads to the statement , that the assumption that the direct cross section obeys factorization is strongly disfavored by their analysis . in total , it is obvious that in the final h1 analysis @xcite a global suppression in diffractive dijet photoproduction is clearly established and the model with resolved suppression only is not as well supported by the data . just recently also the zeus collaboration presented their final result on diffractive dijet photoproduction @xcite . as in their preliminary analysis , the two jets with the highest transverse energies @xmath25 were required to satisfy @xmath55 @xmath45 gev , which is higher than in the h1 analysis with @xmath56 @xmath57 gev @xcite . zeus compared their measurements with the nlo predictions for diffractive photoproduction of dijets based on our program @xcite . three sets of dpdfs were used , the zeus lps fit , determined from a nlo analysis of inclusive diffraction and diffractive charm - production data @xcite , and the two h1 fits , h1 2006 fit a and fit b @xcite . the nlo results obtained with the two h1 fits were scaled down by a factor of 0.87 @xcite , since the h1 measurements used to derive the dpdfs include low - mass proton dissociative processes with @xmath58 gev , which increases the photon - diffractive cross section by @xmath59 as compared to the pure proton final state as corrected to in the zeus analysis . the comparison of the measured cross sections and the theoretical predictions was based on the distributions in the variables @xmath60 , @xmath13 , @xmath48 , @xmath39 , @xmath50 , @xmath61 and @xmath38 . the data were reasonably well described in their shape as a function of these variables and lay systematically below the predictions . the predictions for the three dpdfs differed appreciably . the cross sections for the h1 2006 fit a ( fit b ) were the highest ( lowest ) and the one for the zeus lps fit lay between the two , but nearer to the fit a than the fit b predictions . for @xmath62 zeus also showed the ratio of the data and the nlo predictions using the zeus lps fit . it was consistent with a suppression factor of 0.7 independent of @xmath38 . this suppression factor depended on the dpdfs and ranged between 0.6 ( h1 2006 fit a ) and 0.9 ( fit b ) . taking into account the scale dependence of the theoretical predictions the ratio was outside the theoretical uncertainty for the zeus lps fit and the h1 2006 fit a , but not for fit b. in their conclusions the authors of the zeus analysis @xcite made the statement that the nlo calculations tend to overestimate the measured cross section , which would mean that a suppression is present . unfortunately , however , they continued , that , within the large uncertainties of the nlo calculations , the data were compatible with the qcd calculations , i.e. with no suppression . such a statement clearly contradicts the result of the h1 collaboration @xcite and casts doubts on the correctness of the h1 analysis . the authors of @xcite attribute this discrepancy to the fact that the h1 measurements @xcite were carried out in a lower @xmath25 and a higher @xmath48 range than those in the zeus study @xcite . besides the different @xmath25 and @xmath48 regions in @xcite and @xcite , the two measurements suffer also from different experimental cuts of some other variables , which makes it difficult to compare the two data sets directly ( note also the lower center - of - mass energy for the h1 data ) . in addition the comparison with nlo theory in @xcite and @xcite was done with two different programs @xcite versus @xcite , which , however agreed quite well with each other @xcite . the rather different conclusions concerning factorization breaking in diffractive dijet photoproduction calls for a new comparative study of the two data sets in @xcite and @xcite . we have therefore performed a new calculation of the nlo cross sections on the basis of our earlier work @xcite with the new h1 2006 dpdfs and revised hadronic corrections as compared to @xcite , in order to see whether we can confirm the very different conclusions achieved in the h1 @xcite and zeus @xcite analyses . in the comparison with the new data sets we shall follow more or less the same strategy as in our earlier work @xcite . we first calculate the unsuppressed nlo cross sections including an error band based on the scale variation and see how much and in which distribution the data points lie inside or outside this error band . then we determine a global suppression factor by fitting the differential cross section @xmath63 at the bin with the lowest @xmath50 . with this suppression factor we shall compare to the differential cross sections of all the other measured variables and look for consistency . in this new comparison between the experimental and the theoretical results we shall concentrate on using the h1 2006 fit b @xcite input , since it leads to smaller cross sections than the dpdfs from h1 2006 fit a @xcite or the zeus lps dpdf fit @xcite . actually the h1 collaboration constructed a third set of dpdfs , which is called the h1 2007 fit jets. this fit is obtained through a simultaneous fit to the diffractive inclusive and dis dijet cross sections @xcite . it is performed under the assumption that there is no factorization breaking in the diffractive dijet cross sections . under this assumption , including the diffractive dijet cross sections in the analysis leads to additional constraints , mostly on the diffractive gluon distribution . on average the h1 2007 fit jets is similar to the h1 2006 fit b except for the gluon distribution at high momentum fraction and smaller factorization scales . in our analysis we shall disregard this new set of dpdfs , since it would be compatible with the factorization test of the photoproduction data only if we restricted these tests to the case that only the resolved part has this breaking and not the direct part , which has the same structure as the dis dijet cross section . in sec . 2 we shall present the complete list of cuts on the experimental variables , give all the input used in the cross section calculations , and present the basic formul , from which the dijet cross sections have been calculated . the comparison with the h1 @xcite and the zeus @xcite experimental data is presented and discussed in sec . 3 . in this comparison we shall concentrate on the main question , whether there is a suppression in the photoproduction data at all . in addition we shall investigate also whether a reasonable description of the data is possible with suppression of the resolved cross section only , as we studied it already in our previous work in 2004 @xcite . in sec . 4 we shall finish with a summary and our conclusions .

if direct and resolved contributions are both suppressed by the same amount , the global suppression factor depends on the transverse - energy cut and is @xmath0 for the h1 and @xmath1 for the zeus analysis . however , by suppressing only the resolved contribution by a factor of approximately three , also reasonably good agreement with all the data is found .

r

0806.2269

after the final analyses of the h1 and zeus collaborations for the diffractive photoproduction of dijets have appeared , we have recalculated these cross sections in next - to - leading order ( nlo ) of perturbative qcd to see whether they can be interpreted consistently . the results of these calculations are compared to the data of both collaborations . we find that at nlo the cross sections disagree with the data , showing that factorization breaking occurs at this order . if direct and resolved contributions are both suppressed by the same amount , the global suppression factor depends on the transverse - energy cut and is @xmath0 for the h1 and @xmath1 for the zeus analysis . however , by suppressing only the resolved contribution by a factor of approximately three , also reasonably good agreement with all the data is found . the size of the factorization breaking effects for resolved photons agrees with absorptive - model predictions . desy 08 - 074 + lpsc 08 - 070

in this section , we present the comparison of the various theoretical predictions in nlo with the experimental data from the h1 collaboration @xcite . the corresponding kinematic cuts are given in tab . 1 . before we confront the calculated cross sections with the experimental data , we correct them for hadronization effects . the hadronization corrections are calculated by means of the lo rapgap monte carlo generator @xcite . the factors for the transformation from jets made up of stable hadrons to parton jets were supplied by the h1 collaboration @xcite . most of our calculations are done with the ` h1 2006 fit b ' @xcite dpdfs since they give they smaller diffractive dijet cross sections as compared to the ` h1 2006 fit a ' . these dpdf fits are based on @xmath169 massless flavors . the production of charm and bottom quarks was treated there in the fixed - flavor number scheme ( ffns ) in nlo with non - zero charm and bottom quark mass . instead of this extra treatment of the charm and bottom contribution in the pomeron we added a charm pdf in the pomeron as obtained in the ` h1 2002 fit ' @xcite , where the charm quark was also considered to be massless . the bottom contribution was neglected . this assumption simplifies the calculations considerably . since the charm contribution from the pomeron is small , this should be a good approximation . we then take @xmath170 with @xmath171 gev , which corresponds to the value used in the dpdfs ` h1 2006 fit a ' and ` h1 2006 fit b ' @xcite . as it is clear from the discussion of the various preliminary analyses of the h1 and zeus collaborations , there are two questions which we would like to answer from the comparison with the recent h1 and the zeus data . the first question is whether a suppression , which differs substantially from one , is needed to describe the data . the second question is whether the data are also consistent with a suppression factor applied to the resolved cross section only . to give an answer to these two questions we calculated first the cross sections with no suppression factor ( @xmath172 in the following figures ) with a theoretical error obtained from varying the common scale of renormalization and factorization by factors of 0.5 and 2 around the central scale ( highest @xmath25 ) . in a second step we show the results for the same differential cross sections with a global suppression factor , adjusted to @xmath63 in the smallest @xmath50-bin . as in the experimental analysis @xcite , we consider the differential cross sections in the variables @xmath38 , @xmath39 , @xmath173 , @xmath50 , @xmath30 , @xmath51 , @xmath52 and @xmath49 . the unsuppressed ( @xmath174 ) cross sections @xmath62 , @xmath175 , @xmath176 , @xmath63 , @xmath177 , @xmath178 , @xmath179 and @xmath180 ( @xmath181 in @xcite ) with their scale variation are shown in fig . 3a - h . in these figures we also plotted the experimental data with their errors . except for two points ( largest @xmath39 and largest @xmath50-bin ) all other experimental points lie , including their errors , outside the theoretical error band . this comparison clearly tell us , that an unsuppressed cross section is in disagreement with the data . it is clear , that with the dpdfs h1 2006 fit a cross section this conclusion would be even stronger , since with these dpdfs the unsuppressed cross sections are even larger . that @xmath175 overlaps in the largest bin with the lower limit of the prediction for @xmath174 ( see fig . 3b ) can be explained with the fact that the gluon dpdf in the h1 2006 fit b is not very well constrained for large @xmath101 and might be larger there . if we now determine the suppression factor from fitting the lowest @xmath50-bin experimental cross section we obtain @xmath182 . the indicated error corresponds to the experimental uncertainty , while we show in the figures explicitly the theoretical uncertainty . with this suppression factor we have calculated the eight distributions including their theoretical errors and compare with the experimental data including their errors . the results of this comparison is shown also in figs . 3a - h . differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd without ( @xmath174 ) and with ( @xmath183 ) global suppression ( color online).,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd without ( @xmath174 ) and with ( @xmath183 ) global suppression ( color online).,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd without ( @xmath174 ) and with ( @xmath183 ) global suppression ( color online).,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd without ( @xmath174 ) and with ( @xmath183 ) global suppression ( color online).,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd without ( @xmath174 ) and with ( @xmath183 ) global suppression ( color online).,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd without ( @xmath174 ) and with ( @xmath183 ) global suppression ( color online).,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd without ( @xmath174 ) and with ( @xmath183 ) global suppression ( color online).,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd without ( @xmath174 ) and with ( @xmath183 ) global suppression ( color online).,title="fig : " ] with the exception of figs . 3d and 3h , where the comparisons of @xmath63 and @xmath177 are shown , all other plots are such that the data points lie inside the error band based on the scale variation . most of the data points even agree with the @xmath184 predictions inside the much smaller experimental errors . in @xmath63 ( see fig . 3d ) the predictions for the second and third bin lie outside the data points with their errors . for @xmath172 and @xmath183 these cross sections falls off stronger with increasing @xmath50 than the data , the normalization being of course about two times larger for @xmath174 . in particular , the third data point agrees with the @xmath172 prediction . this means that the suppression decreases with increasing @xmath50 . such a behavior points in the direction that a suppression of the resolved cross section only would give better agreement with the data , as we shall see below . the same observations can be made by looking at @xmath177 in fig . the survival probability @xmath185 agrees with the result in @xcite , which quotes @xmath186 , determined by a fit to the double ratio of measured to predicted cross section in photoproduction by the corresponding ratio in dis given as a function of @xmath49 . in this double ratio many experimental errors and theoretical scale errors cancel to a large extent . this double ratio is also insensitive to the detailed shape of the diffractive gluon density . from our comparison we conclude that the h1 data show a global suppression of the order of two in complete agreement with the results @xcite and @xcite based on earlier preliminary @xcite and final h1 data @xcite . next we want to answer the second question , whether the data could be consistent with a suppression of the resolved component only . for this purpose we have calculated the cross sections in two versions : ( i ) suppression of the resolved cross section and ( ii ) suppression of the resolved cross section plus that part of the nlo direct part which depends on the factorization scale at the photon vertex and thereby eliminates the @xmath187-dependence in the combined direct and resolved cross section @xcite . of course , the needed suppression factors for the two versions will be different . we determine the suppression factors by fitting again the measured @xmath63 for the lowest @xmath50-bin ( see fig.4d ) . then , the suppression factor for version ( i ) is @xmath188 ( denoted res in the figures ) , and for version ( ii ) it is @xmath189 ( denoted res+dir - is ) . the comparison with the h1 data of @xmath62 , @xmath175 , @xmath176 , @xmath63 , @xmath177 , @xmath178 , @xmath190 and @xmath180 is shown in figs . 4a - h , where differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd with global , resolved , and resolved / direct - is suppression.,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd with global , resolved , and resolved / direct - is suppression.,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd with global , resolved , and resolved / direct - is suppression.,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd with global , resolved , and resolved / direct - is suppression.,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd with global , resolved , and resolved / direct - is suppression.,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd with global , resolved , and resolved / direct - is suppression.,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd with global , resolved , and resolved / direct - is suppression.,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd with global , resolved , and resolved / direct - is suppression.,title="fig : " ] we also have plotted the prediction for the global suppression ( direct and resolved ) with @xmath184 , already shown in figs . looking at figs . 4a - h we can distinguish three groups of results from the comparison with the data . in the first group , the cross sections as functions of @xmath39 , @xmath173 , @xmath30 , @xmath52 and @xmath49 , the agreement with the global suppression ( @xmath184 ) and the resolved suppression ( @xmath188 and @xmath189 ) is comparable . in the second group , which consists just of @xmath63 , the agreement is better for the resolved suppression only . in the third group , @xmath62 and @xmath178 , the agreement with the resolved suppression is worse than with the global suppression . in particular , for @xmath62 , which is usually considered as the characteristic distribution for distinguishing global versus resolved suppression , the agreement with resolved suppression does not improve . unfortunately , this cross section has the largest hadronic corrections of the order of @xmath191 @xcite . here , the bins with largest @xmath38 are particularly sensitive to the hadronic corrections and possible migrations of the data between the two bins . if we average the cross sections for these two bins , the agreement with the data point becomes much better . we also notice , that the predictions for the two suppression modes ( i ) and ( ii ) are almost the same . the only exception are the cross sections for the largest @xmath38-bin ( see fig.4a ) . in figs . 4a - h the theoretical errors coming from the scale uncertainty are not shown . if they are taken into account , the difference between experimental data and theory in figs . 4a and 4f is much less dramatic . on the other hand , for the cross section @xmath63 the agreement improves considerably with the suppression of the resolved part only ( note the logarithmic scale in fig . 4d ) . here , of course , we must admit that the suppression factor could be @xmath26-dependent , although we do not know of any mechanism , which could cause such a @xmath25-dependence of the suppression . we remark that this @xmath25-dependence of the global suppression is also visible in the h1 analysis of @xcite . we also checked for two distributions whether the predictions for resolved suppression depend on the chosen diffractive pdfs . for this purpose we have calculated for the two cases @xmath175 and @xmath63 the cross sections with the ` h1 2006 fit a ' parton distributions @xcite . the results are compared in figs . 5a and b to the results with differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd with resolved suppression and two different dpdfs.,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by h1 and compared to nlo qcd with resolved suppression and two different dpdfs.,title="fig : " ] the ` h1 2006 fit b ' and the experimental data . of course , since the ` h1 2006 fit a ' pdfs have a larger gluon component at large @xmath101 , the cross sections are larger and therefore need a larger suppression factor @xmath192 . from figs.5a and b we conclude that there is no appreciable dependence on the chosen dpdfs . note that in fig . 5b the cross section for the smallest @xmath50-bin has been fitted to determine the suppression factor . in total , we are tempted to conclude from the comparisons in figs . 4a - h that the predictions with a resolved - only ( or resolved+direct - is ) suppression are consistent with the h1 data @xcite . the only exceptions are two bins in the @xmath38 and one bin in the @xmath51-distribution . in this subsection we shall compare our predictions with the final analysis of the zeus data , which was published just recently @xcite . the kinematic cuts are given in tab . 2 . there are the following differences to the h1 cuts in tab . 1 : first the upper cut on @xmath19 is larger . second there is a larger range in the variable @xmath60 and the upper cut on @xmath48 is slightly smaller . the most important change is the larger @xmath193 cut , namely @xmath194 7.5 ( 6.5 ) gev , which leads to smaller cross sections . also the cut on @xmath129 is different . the different cuts on @xmath19 and @xmath129 have little influence . for example , the larger @xmath129-cut in tab . 2 as compared to tab . 1 increases the cross section only by @xmath195 . the constraint on @xmath6 is not explicitly given in the zeus publication @xcite . they give the cross section for the case that the diffractive final @xmath4 state consists only of the proton . for this they correct their measured cross section by subtracting in all bins the estimated contribution of a proton - dissociative background of @xmath196 . when comparing to the theoretical predictions with the dpdfs from the h1 2006 fits , they multiply the theoretical cross section with a ( slightly different ) factor of @xmath197 in order to correct for the proton - dissociative contributions , which are contained in these dpdfs by requiring @xmath58 gev . we do not follow this procedure . instead we leave the theoretical cross sections unchanged , i.e. they contain a proton - dissociative contribution with @xmath58 gev and multiply the zeus cross sections by @xmath198 to include the proton - dissociative contribution . in this comparison we shall follow the same strategy as before . before we do this , we correct our theoretical prediction by the hadronization corrections reported in @xcite . we first compare to the predictions with no suppression ( @xmath172 ) and then determine a suppression factor by fitting @xmath63 at the smallest @xmath50-bin . then we compare to the cross sections as a function of the seven observables @xmath38 , @xmath39 , @xmath48 , @xmath50 , @xmath60 , @xmath13 and @xmath199 instead of the eight variables in the h1 analysis . the distribution in @xmath60 is equivalent to the @xmath49-distribution in @xcite . the zeus collaboration have also published experimental measurements in the two regions @xmath200 , which do however not consider here due to space limitations . the theoretical predictions for these differential cross sections with no suppression factor ( @xmath172 ) are shown in figs . 6a - g , together with their scale errors and compared to differential cross sections for diffractive dijet photoproduction as measured by zeus and compared to nlo qcd without ( @xmath174 ) and with ( @xmath201 ) global suppression ( color online).,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by zeus and compared to nlo qcd without ( @xmath174 ) and with ( @xmath201 ) global suppression ( color online).,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by zeus and compared to nlo qcd without ( @xmath174 ) and with ( @xmath201 ) global suppression ( color online).,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by zeus and compared to nlo qcd without ( @xmath174 ) and with ( @xmath201 ) global suppression ( color online).,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by zeus and compared to nlo qcd without ( @xmath174 ) and with ( @xmath201 ) global suppression ( color online).,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by zeus and compared to nlo qcd without ( @xmath174 ) and with ( @xmath201 ) global suppression ( color online).,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by zeus and compared to nlo qcd without ( @xmath174 ) and with ( @xmath201 ) global suppression ( color online).,title="fig : " ] the zeus data points . except for the @xmath38 and @xmath50 distributions , most of the data points lie outside the theoretical error bands for @xmath172 . in particular , in figs . 6b , c , e , f and g , 2 , 3 , 4 , 4 and 5 points lie outside . this means that most of the data points disagree with the unsuppressed prediction . next , we determine the suppression factor from the measured @xmath63 at the lowest @xmath50-bin , 7.5 gev @xmath202 gev , and obtain @xmath203 . the indicated error corresponds again to the experimental uncertainty , while we show in the figures explicitly the theoretical uncertainty . this means that the suppression factor from the zeus data is larger than the one obtained from the analysis of the h1 data , which is actually consistent with the @xmath63 for the second bin in fig . the cross section is approximately larger by a factor of @xmath204 than the prediction with @xmath205 . if we now check how the predictions for @xmath206 compare to the data points inside the theoretical errors , we observe from figs . 6a - g that with the exception of @xmath175 ( largest bin ) , the data points agree with the predictions inside the theoretical error band . this is quite consistent with the h1 analysis , discussed in the previous subsection , and leads to the conclusion that also the zeus data agree much better with the suppressed predictions than with the unsuppressed one . in particular , the global suppression factor approximately agrees with the global suppression factor , which one would expect from the analysis of the h1 data at the second smallest @xmath50-bin . similarly as in the previous section we compared the zeus data also with the assumption that the suppression results only from the resolved cross section . here we consider again the two versions : ( i ) only resolved suppression ( res ) and ( ii ) resolved plus direct suppression of the initial - state singular part ( res+dir - is ) . for these two models we obtain the suppression factors @xmath207 and @xmath208 , respectively , where these suppression factors are again obtained by fitting the data point at the first bin of @xmath63 . the comparison to the global suppression with @xmath201 and to the data is shown in figs . 7a - g . differential cross sections for diffractive dijet photoproduction as measured by zeus and compared to nlo qcd with global , resolved , and resolved / direct - is suppression.,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by zeus and compared to nlo qcd with global , resolved , and resolved / direct - is suppression.,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by zeus and compared to nlo qcd with global , resolved , and resolved / direct - is suppression.,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by zeus and compared to nlo qcd with global , resolved , and resolved / direct - is suppression.,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by zeus and compared to nlo qcd with global , resolved , and resolved / direct - is suppression.,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by zeus and compared to nlo qcd with global , resolved , and resolved / direct - is suppression.,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by zeus and compared to nlo qcd with global , resolved , and resolved / direct - is suppression.,title="fig : " ] in general , we observe that the difference between global suppression and resolved suppression is not large , i.e. the data points agree with the resolved suppression almost as well as with the global suppression . in figs . 8a and b the difference between ` h1 2006 fit b ' and ` h1 2006 fit a ' differential cross sections for diffractive dijet photoproduction as measured by zeus and compared to nlo qcd with resolved suppression and two different dpdfs.,title="fig : " ] differential cross sections for diffractive dijet photoproduction as measured by zeus and compared to nlo qcd with resolved suppression and two different dpdfs.,title="fig : " ] is shown again for the case of the resolved suppression . in both figures we observe that the fit a suppression with the suppression factor @xmath209 agrees better with the data than with the factor @xmath207 for the fit b suppression . in particular , for @xmath63 the agreement with the three data points is perfect ( note the logarithmic scale ) .

an analytical description of arbitrary strongly aberrated axially symmetric focusing is developed . the corresponding canonical integral is the bessoid integral , which is a three - dimensional generalization of the pearcey integral that approximates the field near an arbitrary two - dimensional cusp . we first develop the description for scalar fields and then generalize it to the vector case . as a practical example the formalism is applied to the focusing of light by transparent dielectric spheres with a few wavelengths in diameter . the results are relevant for aerosol and colloid science where natural light focusing occurs and can be used in laser micro- and nano - processing of materials .

i

physics0606025

an analytical description of arbitrary strongly aberrated axially symmetric focusing is developed . this is done by matching the solution of geometrical optics with a wave pattern which is universal for the underlying ray structure . the corresponding canonical integral is the bessoid integral , which is a three - dimensional generalization of the pearcey integral that approximates the field near an arbitrary two - dimensional cusp . we first develop the description for scalar fields and then generalize it to the vector case . as a practical example the formalism is applied to the focusing of light by transparent dielectric spheres with a few wavelengths in diameter . the results demonstrate good agreement with the mie theory down to mie parameters of about 30 . compact analytical expressions are derived for the intensity on the axis and the position of the diffraction focus both for the general case and for the focusing by microspheres . the high intensity region is narrower than for an ideal lens of the same aperture at the expense of longitudinal localization and has a polarization dependent fine structure , which can be explained quantitatively . the results are relevant for aerosol and colloid science where natural light focusing occurs and can be used in laser micro- and nano - processing of materials .

axially symmetric focusing of wave fields occurs in various areas of science , since physical systems often possess an intrinsic rotational symmetry . in particular , the electromagnetic field enhancement by small spherical particles is important in many situations . spheres have minimal surface energy for a given volume and thus are naturally formed as a result of phase separation , for example as aerosols or colloids . applications of colloidal microspheres in photonic crystals and photonic crystal slabs led to an explosion of the experimental and theoretical studies of their optical properties.@xcite the majority of these investigations concentrate on their collective properties in a periodic arrangement . single microspheres are used as high quality optical resonators and as agents that allow controlled and highly localized wavelength - dependent field enhancement for non - linear optical studies and in resonance spectroscopy.@xcite here , the emphasis is placed on the eigenmode analysis and the distribution of the field within the sphere or in the immediate vicinity of its surface . lately , it was demonstrated that self - assembling arrays of transparent colloidal microspheres can be employed for high - throughput laser - assisted micro- and nano - structuring of materials.@xcite similar effects were observed in experiments on dry laser cleaning , where such particles are used as controlled contaminants.@xcite this necessitates better understanding of the focusing of light by microspheres with diameters of several wavelengths . only few rigorous results are available for the intermediate range of sphere sizes and distances from the particle . the majority of analytical approaches either deal with the properties of the eigenmodes , or refer to the integral characteristics and/or to the far field behavior.@xcite mie resonances were analyzed on the basis of advanced geometrical optics@xcite and detailed numerical calculations for transparent spheres of several wavelengths in size were performed in connection with the use of laser tweezers in biology@xcite and for needs of aerosol science.@xcite in this work we develop a theoretical description for an arbitrary non - paraxial strongly aberrated axially symmetric focusing and apply it to the case of dielectric microspheres . our emphasis is on the fine structure of the field distribution in the exterior of the sphere up to the focal region , which can be used to control and improve the concentration of energy . strong spherical aberration makes the focusing non - trivial . usually , the exact solution is obtained using the mie theory,@xcite which does not give much of a physical insight as it requires the summation of a large number of terms in a multipole expansion even for moderate sphere sizes . at the same time , the main focusing properties of transparent dielectric microspheres originate rather from the picture of geometrical optics . one might think that in the lowest approximation a small sphere acts as an ideal lens . however , in the range of sizes we are interested in , this picture does not even provide a description which is qualitatively correct . also classical formulas for weak spherical aberration @xcite do not yield useful results for the field behind a sphere : they predict that the maximum intensity is kept unchanged and its position does not depend on the wavelength . our approach , following the method of uniform caustic asymptotics,@xcite is based on the canonical integral for the cuspoid ray topology of strong spherical aberration . though this bessoid integral a member of the hierarchy of diffraction catastrophes@xcite appears naturally in the paraxial approximation , it can be used to describe arbitrary axially symmetric strong spherical aberration by appropriate coordinate and amplitude transformations . for angularly dependent vectorial amplitudes the formalism uses higher - order bessoid integrals . the bessoid integral is the axially symmetric generalization of the pearcey integral,@xcite which plays an important role in many short wavelength phenomena.@xcite therefore , the present approach can be applied in various areas of physics where axially symmetric focusing is of importance , e.g. , acoustics , semiclassical quantum mechanics , radio wave propagation and scattering theory .

an extremely deep x - ray survey ( @xmath0 ms ) of the hubble deep field north and its environs ( @xmath1 arcmin@xmath2 ) has been performed with the advanced ccd imaging spectrometer on board the _ chandra x - ray observatory_. this is one of the two deepest x - ray surveys ever performed ; for point sources near the aim point it reaches 0.52.0 kev and 28 kev flux limits of @xmath3 erg @xmath4 s@xmath5 and @xmath6 erg @xmath4 s@xmath5 , respectively . here we provide source catalogs along with details of the observations , data reduction , and technical analysis . observing conditions , such as background , we also detect two highly significant extended x - ray sources and several other likely extended x - ray sources . we present basic number count results for sources located near the center of the field .

i

astro-ph0108404

an extremely deep x - ray survey ( @xmath0 ms ) of the hubble deep field north and its environs ( @xmath1 arcmin@xmath2 ) has been performed with the advanced ccd imaging spectrometer on board the _ chandra x - ray observatory_. this is one of the two deepest x - ray surveys ever performed ; for point sources near the aim point it reaches 0.52.0 kev and 28 kev flux limits of @xmath3 erg @xmath4 s@xmath5 and @xmath6 erg @xmath4 s@xmath5 , respectively . here we provide source catalogs along with details of the observations , data reduction , and technical analysis . observing conditions , such as background , were excellent for almost all of the exposure . we have detected 370 distinct point sources : 360 in the 0.58.0 kev band , 325 in the 0.52.0 kev band , 265 in the 28 kev band , and 145 in the 48 kev band . two new sources in the hdf - n itself are reported and discussed . source positions are accurate to within 0.61.7@xmath7 ( at @xmath8% confidence ) depending mainly on the off - axis angle . we also detect two highly significant extended x - ray sources and several other likely extended x - ray sources . we present basic number count results for sources located near the center of the field . source densities of @xmath9 deg@xmath10 ( at ) and @xmath11 deg@xmath10 ( at ) are observed in the soft and hard bands , respectively .

we have performed a deep x - ray survey ( @xmath0 ms ) of the hubble deep field north (; williams et al . 1996 , hereafter w96 ; ferguson , dickinson , & williams 2000 ) and its environs with the _ chandra x - ray observatory _ ( hereafter ): the deep field north ( hereafter cdf - n ) survey . this is one of the two deepest x - ray surveys ever conducted , the other being the deep field south survey ( e.g. , tozzi et al . 2001 ; p. rosati et al . , in preparation ) . near the aim point , the cdf - n observation reaches 0.52.0 kev and 28 kev limiting fluxes of @xmath3 erg @xmath4 s@xmath5 and @xmath6 erg @xmath4 s@xmath5 , respectively ; these flux limits are @xmath12 and @xmath13 times fainter than achieved by pre- missions . in figure 1 we compare the 0.52.0 kev flux limit and solid angle of this survey to those of several other extragalactic x - ray surveys . this survey has both the sensitivity and positional accuracy needed to complement the deepest surveys at other wavelengths , and much of the @xmath1 arcmin@xmath2 area surveyed has extensive radio , submillimeter , infrared , and optical coverage ( see livio , fall , & madau 1998 and ferguson et al . 2000 for reviews ) . the main goals of the cdf - n survey are ( 1 ) to understand the broad - band emission and nature of the sources producing the x - ray background in the 0.58.0 kev band , and ( 2 ) to investigate the x - ray emission properties of physically interesting sources identified at other wavelengths . thus far , we have presented results for the hdf - n ( hornschemeier et al . 2000 , hereafter paper i ; brandt et al . 2001a , paper iv ) as well as for larger fields centered on the hdf - n ( hornschemeier et al . 2001 , paper ii ; garmire et al . 2001 , paper iii ; barger et al . 2001 ) . due to the fact that the observations were performed in an incremental manner from 1999 november to 2001 march , the studies above were all performed with less than the full @xmath0 ms exposure . in this paper , we provide source catalogs derived from the @xmath0 ms data set along with details of the observations , data reduction , and technical analysis . our intention is to provide this information to the community in as timely a manner as possible . we have deliberately avoided follow - up investigations and detailed scientific interpretation in this paper ; these will be presented in subsequent papers ( and many such results have been presented in the papers cited above ) . for example , companion papers by alexander et al . ( 2001 , paper vi ) , brandt et al . ( 2001b , paper vii ) , a.j . barger et al . , in preparation , and f.e . bauer et al . , in preparation present results on optically faint x - ray sources , x - ray emission from lyman break galaxies , optical follow - up imaging and spectroscopy , and extended x - ray sources . in 2 we describe the observations and data reduction . in 3 we describe the data analysis and results , with emphasis on the detection of point sources ( 3.2 ) and extended sources ( 3.3 ) . we also present basic number count results for point sources in 3.2 . our conclusions and summary are presented in 4 . the galactic column density along this line of sight is @xmath14 @xmath4 ( stark et al . @xmath15 km s@xmath5 mpc@xmath5 , @xmath16 , and @xmath17 are adopted throughout this paper . coordinates throughout this paper are j2000 . the hdf - n itself is centered at @xmath18 12@xmath19 36@xmath20 494 , @xmath21 @xmath2212@xmath2358@xmath7 , corresponding to @xmath24 , @xmath25 ( w96 ) .

were excellent for almost all of the exposure . we have detected 370 distinct point sources : 360 in the 0.58.0 kev band , 325 in the 0.52.0 kev band , 265 in the 28 kev band , and 145 in the 48 kev band . two new sources in the hdf - n itself are reported and discussed . source positions are accurate to within 0.61.7@xmath7 ( at @xmath8% confidence ) depending mainly on the off - axis angle .

r

astro-ph0108404

an extremely deep x - ray survey ( @xmath0 ms ) of the hubble deep field north and its environs ( @xmath1 arcmin@xmath2 ) has been performed with the advanced ccd imaging spectrometer on board the _ chandra x - ray observatory_. this is one of the two deepest x - ray surveys ever performed ; for point sources near the aim point it reaches 0.52.0 kev and 28 kev flux limits of @xmath3 erg @xmath4 s@xmath5 and @xmath6 erg @xmath4 s@xmath5 , respectively . here we provide source catalogs along with details of the observations , data reduction , and technical analysis . observing conditions , such as background , were excellent for almost all of the exposure . we have detected 370 distinct point sources : 360 in the 0.58.0 kev band , 325 in the 0.52.0 kev band , 265 in the 28 kev band , and 145 in the 48 kev band . two new sources in the hdf - n itself are reported and discussed . source positions are accurate to within 0.61.7@xmath7 ( at @xmath8% confidence ) depending mainly on the off - axis angle . we also detect two highly significant extended x - ray sources and several other likely extended x - ray sources . we present basic number count results for sources located near the center of the field . source densities of @xmath9 deg@xmath10 ( at ) and @xmath11 deg@xmath10 ( at ) are observed in the soft and hard bands , respectively .

in this paper we report on the emission detected in four standard x - ray bands : 0.58.0 kev ( full band ) , 0.52.0 kev ( soft band ) , 28 kev ( hard band ) and 48 kev ( ultrahard band ) . we have adopted 8 kev ( rather than the often - used 10 kev ) as the full - band , hard - band , and ultrahard - band maximum energy because from 810 kev the effective area of the hrma is steeply decreasing with energy while the background is increasing . inspection and searching of the data revealed no significant sources in the 810 kev band . we have employed the two grade sets defined in table 2 . as described in paper iv , the use of the `` restricted acis grade set '' in addition to the `` standard grade set '' improves our ability to detect faint sources in some cases . all photometry below , however , is reported using the standard grade set . we have registered the data sets following 3.1 of paper ii . briefly , we registered all the data sets to the coordinate frame of observation 966 using 1117 bright x - ray sources detected in the individual observations within @xmath44 of the aim point ; registration is accurate to within @xmath45 . absolute x - ray source positions were obtained by matching 72 sources from the registered total data set to 1.4 ghz radio sources detected by richards ( 2000 ) ; these 1.4 ghz sources have accurate ( @xmath46 ) positions , and the 1.4 ghz coverage encompasses the entire field . comparison with these sources allowed us to remove shift , rotation , and plate - scale effects . positions used in the data set registration and absolute astrometry determination were found using the wavelet - based source detection algorithm wavdetect ( dobrzycki et al . 1999 ; freeman et al . 2001 ) following 3.2.1 . figure 2 shows the accuracy of our astrometric solution by matching the full - band sources presented in 3.2.1 with 1.4 ghz sources from richards ( 2000 ) . there are 241 1.4 ghz sources within the field . in the matching , we consider only the 74 sources that match with 1.4 ghz sources to within @xmath47 ( the 72 sources used to determine the absolute astrometry in the previous paragraph excluded the two outliers in figure 2 with offsets @xmath48 ) . the vast majority of these 74 matches are expected to be correct , but @xmath42 are expected to be false matches . we also note that in some cases the x - ray source may be offset from the radio source even though both are associated with the same galaxy ( e.g. , a galaxy with a radio - emitting nuclear starburst that also has an off - nuclear `` super - eddington '' x - ray binary ) . figure 2 shows that the x - ray positions are usually good to within @xmath49 for off - axis angles @xmath50 . at larger off - axis angles , where the hrma point spread function ( psf ) rapidly broadens and becomes complex , the positional accuracy , as expected , degrades . most sources have positions good to within @xmath51 , but positional offsets up to @xmath52 1520 are possible . we do not find any systematic errors in our astrometric solution larger than @xmath53 in size . in figures 3 and 4 we show raw and adaptively smoothed images of our field in each of the four standard x - ray bands . these images have been made using the standard grade set . the adaptively smoothed images have been corrected for spatial variations of the effective exposure time using the exposure maps described below . the exposure maps were adaptively smoothed using the same `` scale maps '' as for the images themselves , and we excluded regions where the adaptively smoothed effective exposure time was less than 50 ks . the adaptively smoothed images were not used for source detection , but they do show many of the detected x - ray sources more clearly than the raw images . note that some of the sources discussed below are not visible in the adaptively smoothed images ; these sources fall below the significance level of the adaptive smoothing used to make the images . in figure 5 we show a color composite of the adaptively smoothed soft - band , hard - band and ultrahard - band images . soft sources appear red , moderately hard sources appear green , and the hardest sources appear blue . in figure 6 we show an adaptively smoothed full - band image of the hdf - n itself and its immediate environs ; this image will be discussed further in 3.2.3 . we have made maps of effective exposure time , defined as the equivalent amount of exposure time for a source located at the aim point , following the basic procedure described in 3.2 of paper ii ( see figure 7 ) . these `` exposure maps '' take into account the effects of vignetting , gaps between the ccds , bad column filtering , and bad pixel filtering . one exposure map has been created for each of the standard bands , and the maps were sampled every fourth pixel in both right ascension and declination . in creating these , we have assumed a typical power - law spectrum with a photon index of @xmath54 ( this is the slope of the x - ray background in the band ) . in figure 8 we show a cumulative plot of the survey solid angle as a function of effective exposure in the full band . point - source detection in each standard band was performed with wavdetect . wavdetect was run using a `` @xmath55 sequence '' of wavelet scales ; scales of 1 , @xmath55 , 2 , @xmath56 , 4 , @xmath57 , and 8 pixels were used . we found this choice of wavelet scales to give the best overall performance across the field , but we will also discuss the results for larger wavelet scales in 3.2.2 . in the wavdetect source detection the average aim point defined in 2.2 was used when calculating off - axis angles . our key criterion for source detection is that a source must be found with a false - positive probability threshold of @xmath58 in at least one of the four standard bands using either the standard or restricted acis grade sets . we have _ not _ run wavdetect with a low false - positive probability threshold and then performed _ ex post facto _ processing of the detected sources to attempt to separate true from spurious detections ; such a process would be subjective and counter to the philosophy of wavdetect ( freeman et al . 2001 ; p.e . freeman 2001 , private communication ) . our detection criterion is fairly conservative ; fainter but real sources are undoubtedly present in the field . however , our work on the cdf - n data thus far shows that we have struck an appropriate balance between sensitivity and source reliability . conservatively treating the eight images searched as entirely independent , @xmath59 false sources are expected statistically for the case of a uniform background . in reality , the background is far from uniform due to the large variation of effective exposure time across the field ( see figure 7 ) . in addition , the background increases near bright point sources due to the psf `` wings . '' it is difficult to quantify precisely the effects of a non - uniform background upon the performance of wavdetect . however , based upon the amount of area where background gradients are present and inspection of the sources detected in this area , we would not expect the number of false sources to be increased by more than a factor of @xmath60 23 . less than @xmath61% of the sources discussed below should be false . extensive analysis of the wavdetect source positions revealed that a significant fraction of the sources at off - axis angles @xmath62 suffered from centroiding errors of @xmath63@xmath64 . these apparently arise as a result of both limitations in the wavdetect centroiding method as well as the fact that there is not a single psf applicable for any given source ( due to the different observation pointings and roll angles described in 2.2 , the spatial profile of any given point source is the superposition of several psfs ) . testing and consultation with the cxc showed that the wavdetect centroiding could be significantly improved by running wavdetect without information about the psf ( p.e . freeman and d.e . harris 2001 , private communication ) . therefore , in as many cases as possible , we have replaced the original wavdetect source positions with those from wavdetect runs made excluding psf information ; note that these `` no - psf '' runs were only used for positional replacement and not for source detection . positional replacement was performed for 86% of the detected sources ; for the remaining sources it was not possible due to either a non - detection or a multiple detection in the the no - psf run . the average positional improvement was @xmath65 but in some cases was as large as @xmath66 ( as determined by matching with richards 2000 sources at 1.4 ghz ) . wavdetect was also used to search the standard - band images for lower - significance , cross - band counterparts to the highly significant sources already detected at the @xmath58 level in at least one of the four bands ; in these runs we used a false - positive probability threshold of @xmath67 . we found 110 cross - band counterparts in this manner . since the spatial - matching requirement greatly reduces the number of pixels being searched , the statistically expected number of false cross - band matches is small ( @xmath68 ) . all of the standard - band source lists created in the source detection described above were merged to create the point - source catalog given as table 3 . for cross - band matching , a matching radius of @xmath69 was used for sources within @xmath70 of the average aim point . for larger off - axis angles , a matching radius of @xmath71 was used . these matching radii were chosen based on inspection of histograms showing the number of matches obtained as a function of angular separation ( see 2 of boller et al . 1998 ) ; with these radii the mismatch probability is @xmath0% over the entire field . manual correction of the wavdetect results was required in several cases . for example , wavdetect detections of the brightest components of highly extended sources were removed since these sources will be discussed separately in 3.3 . in four cases , we have removed sources whose centroids appear to lie outside the field of view ; wavdetect had only detected the psf wings of these sources , and their positions and count rates are not well defined . manual separation of a few close doubles was required , and we have manually determined the position of each separated source . these sources suffer larger photometric errors due to the difficulty of the separation process . it was also necessary to perform manual photometry for two sources near the edge of the field of view and a few faint sources located close to much brighter sources . we have flagged all sources requiring manual correction in column 16 of table 3 ( see below ) . below we explain the columns in table 3 . * column 1 gives the source number . sources are listed in order of right ascension . * columns 2 and 3 give the right ascension and declination , respectively . these positions have been determined by wavdetect when possible . whenever possible , we quote the position determined in the full band ; when a source is not detected in the full band we use , in order of priority , the soft - band position , hard - band position , or ultrahard - band position . in addition , we adopt a soft - band position from a no - psf run over a full - band position when full - band positional replacement from a no - psf run was not possible ( see above ) . the priority ordering of position choices above was designed to generally maximize the signal - to - noise of the data being used for positional determination . to avoid truncation error , we quote the positions to higher precision than in the international astronomical union approved names beginning with the acronym `` cxo hdfn . '' * column 4 gives the positional error . sources within @xmath72 of the average aim point have positional errors of @xmath73 . sources farther than @xmath72 from the average aim point have positional errors given by the empirically determined equation : + @xmath74 + where @xmath75 is the positional error in arcsec and @xmath76 is the off - axis angle in arcmin ( compare with figure 2 ) . the positional error does not appear to be a strong function of the number of source counts ( although a mild dependence is probably present ) ; this is largely due to the relatively sharp core of the psf . the stated positional errors are for @xmath8% confidence , and the accuracy of our astrometric solution is discussed in 3.1 . * columns 58 give the counts in the four standard bands ; here and hereafter `` fb '' indicates full band , `` sb '' indicates soft band , `` hb '' indicates hard band , and `` uhb '' indicates ultrahard band . all values are for the standard grade set , and they have not been corrected for vignetting . source counts and @xmath77 statistical errors ( from gehrels 1986 ) have been calculated using circular aperture photometry ; extensive testing showed this method to be more reliable than the wavdetect photometry . the circular aperture was centered at the position given in columns 2 and 3 for all bands . a source - free local background has been subtracted , and unexposed regions were masked . + for sources with fewer than 1000 full - band counts , we have chosen the aperture radii based on the encircled - energy function of the psf as determined using the cxc s mkpsf software ( feigelson et al . 2000 ; jerius et al . 2000 ; m. karovska and p. zhao 2001 , private communication ) . in the soft band where the image quality is the best , the aperture radius was set to the 95% encircled - energy radius of the psf , and in the other bands the 90% encircled - energy radius of the psf was used . appropriate aperture corrections were applied to the source counts . + for sources with more than 1000 full - band counts , systematic errors in the aperture corrections often exceed the expected errors from photon statistics when the apertures described in the previous paragraph are used . therefore , for such sources we used larger apertures to minimize the importance of the aperture corrections ; this is appropriate since these bright sources dominate over the background . we set the aperture radii to be twice those used in the previous paragraph and manually inspected these sources to verify that the measurements were not contaminated by neighboring objects . + we have performed several consistency checks to verify the quality of the photometry . for example , we have checked that the sum of the counts measured in the soft and hard bands does not differ from the counts measured in the full band by an amount larger than that expected from measurement error . systematic errors in our photometry are estimated to be @xmath78% . photometry more accurate than this will require improved modeling of the psf at large off - axis angles by the cxc ( m. karovska and p. zhao 2001 , private communication ) as well as detailed treatment of the fact that there is not a single psf applicable for any given source ( due to the different observation pointings and roll angles described in 2.2 ) . in addition , it will probably be necessary to make the aperture corrections for each source dependent upon its spectral shape . + we have verified that the cosmic ray afterglow removal procedure ( see 2.3 ) has not led to significant systematic photometric errors . due to the low count rates of our sources , incident x - ray photons are almost never incorrectly flagged as afterglow events . + when a source is not detected in a given band , an upper limit is calculated . all upper limits are determined using circular apertures as above . when the number of counts in the aperture is @xmath79 , the upper limit is calculated using the bayesian method of kraft , burrows , & nousek ( 1991 ) for 95% confidence . the uniform prior used by these authors results in fairly conservative upper limits ( see bickel 1992 ) , and other reasonable choices of priors do not materially change our scientific results . for larger numbers of counts in the aperture , upper limits are calculated at the @xmath80 level for gaussian statistics . * column 9 gives the band ratio , defined as the ratio of counts between the hard and soft bands . errors for this quantity are calculated following the `` numerical method '' described in 1.7.3 of lyons ( 1991 ) ; this avoids the failure of the standard approximate variance formula when the number of counts is small ( see 2.4.5 of eadie et al . note that the error distribution is not gaussian when the number of counts is small . quoted band ratios have been corrected for differential vignetting between the hard band and soft band using the appropriate exposure maps . * column 10 gives the effective photon index ( @xmath81 ) for a power - law model with the galactic column density . this has been calculated based on the band ratio in column 9 whenever the number of counts is not `` low . '' a source with a low number of counts is defined as being ( 1 ) detected in the soft band with @xmath82 counts and not detected in the hard band , ( 2 ) detected in the hard band with @xmath83 counts and not detected in the soft band , ( 3 ) detected in both the soft and hard bands , but with @xmath83 counts in each , or ( 4 ) detected only in the full band . when the number of counts is low , the photon index is poorly constrained and set to @xmath54 , a representative value for faint sources that should give reasonable fluxes . * column 11 gives the effective exposure time derived from the full - band exposure map ( see 3.1 for details of the exposure maps ) . * columns 1215 give observed - frame fluxes in the four standard bands ; fluxes are in units of @xmath84 erg @xmath4 s@xmath5 . they have been corrected for vignetting but are not corrected for absorption by the galaxy or intrinsic to the source . for a power - law model with @xmath54 , the soft - band and hard - band galactic absorption corrections are @xmath85% and @xmath86% , respectively . fluxes have been computed using the counts in columns 58 , the appropriate exposure maps , and the spectral slopes given in column 10 . * column 16 gives notes on the sources . `` h '' and `` c '' denote objects lying in the and the caltech area , respectively ( see figure 3 ) . `` o '' refers to objects that have large cross - band positional offsets ( @xmath87 ) . `` np '' refers to objects where the source position could not be updated to that from a no - psf run . `` m '' refers to sources where the photometry was performed manually . `` s '' refers to close double sources where manual separation was required . for further explanation of many of these notes , see the above text in this section on manual correction of the wavdetect results . some of the sources in table 3 have been presented in papers i iv . the source properties in table 3 supersede those presented in earlier papers . figures 912 display the basic properties of the sources in table 3 . in figure 9 we plot the positions of the sources detected in the soft band and hard band ; this format removes the illusory effect produced by the changing psf size across the field of view . figure 10 shows the distribution of full - band effective exposure time ; this plot includes the ten sources that were not detected in the full band ( all of the sources that were not detected in the full band were detected in the soft band , and the full - band and soft - band effective exposure times are similar ) . figure 11 shows `` postage - stamp '' images in the full band for all detected sources . figure 12 displays the band ratio as a function of soft - band count rate for the detected sources . this plot shows the same qualitative behavior as those from shallower surveys ( e.g. , paper iv ; tozzi et al . 2001 ) and populates the faint flux region more densely . the sources generally become harder at low soft - band count rates , although there is substantial dispersion . at the lowest soft - band count rates , the source population is heterogeneous ; highly absorbed agn , high - redshift agn , low - luminosity agn , starburst galaxies , and normal galaxies all appear to make significant contributions ( e.g. , paper ii ; paper iv ; paper vi ; tozzi et al . understanding in detail the nature and relative contributions of the source populations represented in figure 12 will require extensive optical spectroscopic and multiwavelength follow - up studies . we have inspected the sources in table 3 for spatial extent , and they are generally consistent with being pointlike ( see figure 11 ) . the constraints on spatial extent are 2040% worse than for a single acis - i observation because , due to the different observation pointings and roll angles described in 2.2 , there is not a single psf applicable for any given source . the constraints at off - axis angles of @xmath88 are also substantially tighter than those at larger off - axis angles . spatially extended sources are discussed in 3.3 . in table 4 we summarize the source detections in the four standard bands , and in table 5 we summarize the number of sources detected in one band but not another . our faintest soft - band sources have @xmath89 counts ( about one every 1.8 days ) , and our faintest hard - band sources have @xmath90 counts ; these sources are detected near the aim point . for a @xmath54 power - law model with the galactic column density , the corresponding 0.52.0 kev and 28 kev flux limits are @xmath91 erg @xmath4 s@xmath5 and @xmath92 erg @xmath4 s@xmath5 , respectively . of course , these flux limits vary across the field of view . using the restricted acis grade set , the background level in our region of highest exposure ( see figures 7 and 8) is @xmath93 count pixel@xmath5 in the soft band and @xmath94 count pixel@xmath5 in the hard band . in both of these bands we are far from being background limited for point source detection near the aim point . unfortunately , there is no single choice of wavelet scales in wavdetect that provides perfect performance across an entire field ( freeman et al . 2001 ; p.e . freeman 2001 , private communication ) . compromises are required due to , for example , the dependence of the psf size and shape on off - axis angle . in addition , due to the different observation pointings and roll angles described in 2.2 , there is not a single psf applicable for any given source in this particular field . the wavelet scales used in 3.2.1 have been empirically found to provide very good performance across most of the field , but adding further large wavelet scales ( e.g. , @xmath95 and 16 pixels ) can improve the detection effectiveness at large off - axis angles where the psf is broad . however , the addition of these scales can cause real sources at smaller off - axis angles to be missed due to the incorrect merging of two sources . in addition , the `` rejection rule '' of wavdetect , designed to suppress poisson fluctuations on scales smaller than the psf , has limitations that can cause incorrect source rejections when large wavelet scales are employed ( see 3.2.3 of freeman et al . 2001 ; p.e . freeman 2001 , private communication ) . for example , incorrect source rejections may occur when only the relatively sharp core of the psf is apparent above the background level . to address this issue and provide the best possible performance at large off - axis angles , we have created a supplementary catalog of 11 additional sources found by wavdetect at large off - axis angles when wavelet scales of @xmath95 and 16 pixels are added to those used in 3.2.1 ( see table 6 ) . we have followed the same basic methodology as was used when making the main catalog ( see 3.2.1 ) ; we have again adopted a false - positive probability threshold of @xmath58 as the key criterion for source detection . the catalog columns are the same as for the main catalog . because the resulting sources tend to be the weakest ones detectable at the largest off - axis angles , their properties are in general less well defined than those of the sources in the main catalog . we have manually inspected these sources to confirm their reality . a comparison of the sources detected in the hdf - n here and in paper iv gives good agreement . all but one of the 12 sources detected in paper iv are detected here as well . the one source not detected here is cxohdfn j123643.9 + 621249 ; this faint source is known to be variable ( see paper iv ) and has dropped in flux , leading to a reduced signal - to - noise ratio in the longer observation . there is still a notable positive fluctuation at the location of cxohdfn j123643.9 + 621249 ( see figure 6 ) , and it is detected in the soft band if wavdetect is run with a false - positive probability threshold of @xmath96 . one other small difference from paper iv is that the position of cxohdfn j123649.4 + 621347 has moved closer to the nucleus of its @xmath97 elliptical host galaxy ( see 3.1 of paper iv ) ; it is no longer clear that this faint x - ray source lies outside the nucleus . with the additional data presented here , two new hdf - n x - ray sources have been discovered : cxohdfn j123656.6 + 621245 and cxohdfn j123657.4 + 621210 . both sources appear to be associated with optically bright hdf - n galaxies , extending the trend noted in paper iv . the first is w96 source 3 - 610.1 at @xmath98 ( cohen et al . 2000 ) , one of the optically brightest ( @xmath99 ) spirals in the hdf - n . the second is w96 source 3 - 965.0 at @xmath100 ( cohen et al . 2000 ) , a bright ( @xmath101 ) elliptical near the edge of the hdf - n . the full - band x - ray luminosities of these galaxies of @xmath102 erg s@xmath5 and @xmath103 erg s@xmath5 , respectively , can be explained via either low - luminosity agn or stellar remnants ( e.g. , x - ray binaries ) . both of these galaxies were included in the stacking analysis of paper iv , and their individual detections with additional data support the validity of the stacking analysis . we note that there are several other positive fluctuations in the hdf - n visible in figure 6 . while some of these align with bright hdf - n galaxies ( e.g. , the positive fluctuation near @xmath18 12@xmath19 36@xmath20 528 , @xmath21 @xmath2213@xmath2354@xmath7 aligns with w96 source 2 - 736.0 , a @xmath104 irregular ) and may well be real , they are not formally detected according to the criteria in 3.2.1 and will not be discussed further here . we have calculated cumulative number counts , @xmath105 , for the soft and hard bands using the data in table 3 and the basic method described in gioia et al . the results are shown in figure 13 , along with some results from and . the cdf - n number counts do not extend to higher fluxes due to the limited number of bright sources available in our data . we have been conservative in our source selection , taking several steps to prevent incompleteness ( due to the varying sensitivity as a function of spatial position ) from affecting the @xmath105 curves . to avoid incompleteness in the soft band , we have only used data which satisfy the soft - band requirements in table 7 on ( 1 ) distance from the average aim point and ( 2 ) soft - band effective exposure time . the second requirement has the effect of removing areas affected by the gaps between the ccds , where incompleteness is difficult to assess ( see figure 7 ) . in table 7 we also list the solid angle satisfying the above requirements . we have only extended the soft - band @xmath105 down to @xmath106 erg @xmath4 s@xmath5 since , even near the average aim point , incompleteness may affect the @xmath105 at fainter fluxes ; sources below this flux typically have @xmath107 soft - band counts . at this flux limit , the source density is @xmath9 deg@xmath10 . the and constraints on the soft - band @xmath105 are consistent in the limited region of overlap . we have fit the cdf - n @xmath105 curve in the flux range @xmath108 erg @xmath4 s@xmath5 to @xmath109 erg @xmath4 s@xmath5 using a maximum likelihood technique ( murdoch , crawford , & jauncey 1973 ) . the best fit is @xmath110 to avoid incompleteness in the hard band , we have only used data which satisfy the hard - band requirements in table 7 . we have only extended the hard - band @xmath105 down to @xmath111 erg @xmath4 s@xmath5 since , even near the average aim point , incompleteness may affect the @xmath105 at fainter fluxes ; sources below this flux typically have @xmath112 hard - band counts . at this flux limit , the source density is @xmath11 deg@xmath10 . there is very little overlap between the constraints on the hard - band @xmath105 and those from earlier missions . the best fit to the cdf - n @xmath105 curve in the flux range above @xmath113 erg @xmath4 s@xmath5 is @xmath114 at fainter fluxes the number counts clearly flatten ( see figure 13b ) , and parameterization of them requires a detailed analysis of the differential counts ( see jauncey 1975 and references therein ) . this analysis , along with a more detailed study of the number counts in the cdf - n , will be presented in g.p . garmire et al . , in preparation . we have also experimented with somewhat less conservative source - selection methods than those used above , and these give @xmath105 curves that are consistent with those presented above to within the expected statistical uncertainties . in the hard band , in fact , varying the source selection method gives almost identical results . in figure 14 we compare our @xmath105 curves with those from mushotzky et al . ( 2000 ) and tozzi et al . ( 2001 ) . in the soft band , our @xmath105 curve is above those of both mushotzky et al . ( 2000 ) and tozzi et al . ( 2001 ) , even at quite bright x - ray fluxes . however , the results are not discrepant given the error bars , and any small differences could be due to field - to - field `` cosmic variance . '' in the hard band , our @xmath105 curve is consistent with those of mushotzky et al . ( 2000 ) and tozzi et al . ( 2001 ) at fluxes above @xmath115 erg @xmath4 s@xmath5 , and at fainter fluxes it is intermediate between the two curves . we have searched the standard - band images for extended x - ray sources using the cxc s voronoi tessellation and percolation algorithm vtpdetect ( ebeling & wiedenmann 1993 ; dobrzycki et al . we have used a false - positive probability threshold of @xmath58 , and we require at least 50 counts per source . extended source detections were checked by inspection of adaptively smoothed images . in figure 15 we show the two most significant extended sources revealed by our source detection : cxohdfn j123620.0 + 621554 and cxohdfn j123756.0 + 621506 . both of these sources are detected most clearly in the soft - band image . we have checked for possible problems with these source detections and find none . the exposure map is relatively smooth near both of these sources , so background gradients should not have confused the extended source detection . in addition , both of these sources are visible in adaptively smoothed soft - band images made using only data with roll angles of 36.444.5@xmath116 or 134.3143.8@xmath116 ( see table 1 ) ; this argues against an instrumental origin of these sources . cxohdfn j123620.0 + 621554 has @xmath117 soft - band counts and no obvious optical counterpart in the @xmath118-band image of barger et al . ( 1999 ) , suggesting a fairly high redshift group or cluster . the counts for extended sources here and hereafter were determined with manual aperture photometry excluding point sources and regions of strongly varying background ; for cxohdfn j123620.0 + 621554 we used an elliptical aperture with semimajor axis @xmath119 , semiminor axis @xmath120 , and position angle @xmath121 . cxohdfn j123756.0 + 621506 has @xmath122 soft - band counts ( in an elliptical aperture with semimajor axis @xmath120 , semiminor axis @xmath123 , and position angle @xmath124 ) . in the @xmath125-band image of liu ( 1999 ) , it coincides with a pair of optically bright galaxies that appear to be interacting ; the x - ray source is likely to be a low - to - moderate redshift group . one additional extended source detected by vtpdetect with lower significance than the two above is cxohdfn j123645.0 + 621142 ( see figure 16 ) ; we consider this source to be marginally detected . this source is notable because it is in the hdf - n itself near the @xmath126 fanaroff - riley i ( fr i ) radio galaxy vla j123644.3 + 621133 and a number of other @xmath127 objects ( e.g. , richards et al . 1998 ) . in paper iv we detected the fr i ( as cxohdfn j123644.3 + 621132 ) and searched for cluster x - ray emission in its vicinity because fr i sources are often located in clusters of galaxies . no cluster emission was found , but with the additional data here it appears likely that such emission was present just below the detection threshold attainable in paper iv . the fr i lies within the emission but appears offset from its ( poorly defined ) center . cxohdfn j123645.0 + 621142 has @xmath128 soft - band counts ( in a circular aperture with radius @xmath129 ) . because there are substantially more counts in the putative cluster emission than from the fr i , we are confident that this emission is not merely due to counts from the fr i in the wings of the psf . inspection of the raw and adaptively smoothed soft - band images revealed the likely presence of diffuse emission near the positions 123557.0 + 621551 , 123704.6 + 621652 , and 123721.2 + 621526 . possible groups or clusters are apparent in the @xmath125-band image of liu et al . ( 1999 ) or the @xmath118-band image of barger et al . ( 1999 ) near these positions . optical spectroscopy is required for confirmation . dawson et al . ( 2001 ) have discovered a @xmath130 cluster centered near , . unfortunately , this position is near one of the strongest ccd gap features in the exposure map ( see figure 7 ) . inspection of the adaptively smoothed soft - band image for diffuse emission shows a possible @xmath131 event enhancement near cluster member f 36397 + 1547 ( see table 4 of dawson et al . 2001 ) , but this is not formally detected by vtpdetect and could be due to a faint point source . we do clearly detect x - ray emission from cluster member f 36421 + 1545 ; this source appears to be pointlike . we have also inspected the images near the wide angle tail ( wat ) radio galaxy vla j123725.7 + 621128 ( muxlow et al . 1999 ) since wats are often found in clusters of galaxies . we find no hint of any extended x - ray emission centered near this source . extended sources will be discussed in further detail in f.e . bauer et al . , in preparation .

at existing and planned neutrino factories ( high energy and high intensity neutrino beam facilities ) precision studies of qcd in neutrino - nucleon interactions are a realistic opportunity . neutrino experiments at a future muon collider will acquire sufficient event rate to accurately measure color octet matrix element contributions . the currently running high energy neutrino experiments nomad and nutev could also observe several such events .

r

hep-ph9906254

at existing and planned neutrino factories ( high energy and high intensity neutrino beam facilities ) precision studies of qcd in neutrino - nucleon interactions are a realistic opportunity . we investigate charmonium production in fixed target neutrino experiments . we find that @xmath0 production in neutrino - nucleon collision is dominated by the color octet @xmath1 nrqcd matrix element in a neutral current process , which is not accessible in photo or leptoproduction . neutrino experiments at a future muon collider will acquire sufficient event rate to accurately measure color octet matrix element contributions . the currently running high energy neutrino experiments nomad and nutev could also observe several such events .

due to its clean experimental signature , one of the most important charmonium production processes is @xmath0 production . we have calculated the total cross section and the differential @xmath34 distribution of @xmath0 s at various experiments , both currently running and proposed . for lack of knowledge of the size of the nrqcd matrix elements we set them equal to a reasonable baseline size " value , defined as @xmath86 these values satisfy the restrictions imposed by heavy quark symmetry and are compatible with the existing extractions @xcite . the results below were found using mrst parton distribution functions ( pdf ) @xcite , substituting @xmath87 for the charm quark mass and imposing a cut @xmath88 in the calculation of the total cross section . the energy dependence of the total cross section , taken at various representative incident neutrino energies , is shown in table [ tab : crs-1 ] . we find that the total cross section is very sensitive to the neutrino beam energy @xmath89 . the origin of this strong dependence can be traced to the fact that the main contribution to the integral in eq . ( [ eq : struct1 ] ) comes from the smallest available @xmath90 , so that larger @xmath73 probes a smaller region of @xmath74 where the gluon pdf s are enhanced . it becomes obvious that in order to have a reasonably large event number , the neutrino beams with the highest possible energy should be employed . .[tab : crs-1]total cross sections for the @xmath0 production in @xmath91 for various representative incident neutrino energies . the values are taken to correspond to the minimal , average and maximum neutrino beam energy at nomad and maximum available neutrino beam energy at nutev respectively . [ cols="^,^,^,^,^",options="header " , ] we have calculated the total cross section for the two presently running high energy neutrino experiments , nomad at cern and nutev at fermilab , as well as for the much - discussed high energy muon collider . table [ tab : crs ] shows the results for each term in the spectral decomposition . the values support our previous expectations that the @xmath36 contribution dominates the total cross section . note that these numbers refer to direct @xmath0 production ; a cascade mechanism involving @xmath20 decay into @xmath0 can be easily calculated from our @xmath19 contribution and its ratio to direct @xmath19 production is universal and can be taken from other experiments . we should emphasize that due to the expected small number of events the question of background suppression becomes very important . in particular , in the case of the currently running experiments , nomad and nutev , the leptonic decay channel of @xmath0 becomes virtually the only possibility of detecting the produced @xmath0 s . this makes electromagnetic lepton pair production a very important source of background @xcite . c||c|c|c|c|c|c|c|c spectral & & & & + decomp . ' '' '' & @xmath92 $ ] & @xmath93&@xmath92 $ ] & @xmath93&@xmath92 $ ] & @xmath93&@xmath92 $ ] & @xmath93 + @xmath94&@xmath95&@xmath96&@xmath97&@xmath98&@xmath99&@xmath100&@xmath101&@xmath102 + @xmath103&@xmath104&@xmath105&@xmath106&@xmath107&@xmath108&@xmath109&@xmath110&@xmath111 + @xmath112&@xmath113&@xmath114&@xmath115&@xmath116&@xmath117&@xmath118&@xmath119&@xmath120 + @xmath121&@xmath122&@xmath123&@xmath124&@xmath125&@xmath126&@xmath127&@xmath128&@xmath129 + @xmath130&@xmath131&@xmath132&@xmath133&@xmath134&@xmath135&@xmath136&@xmath137&@xmath138 + & @xmath139&@xmath140&@xmath141&@xmath142&@xmath143&@xmath144&@xmath145&@xmath146 + & & & & another important issue is diffractive @xmath0 production . it is difficult to separate , both theoretically and experimentally , diffractive and color octet contributions . this is due to the fact that both of these processes contribute at @xmath147 . in principle , the absence of a rapidity gap in the color - octet nrqcd process may help @xcite . in addition , a perturbative qcd calculation of the diffractive leptoproduction @xcite suggests that this process falls off at high @xmath34 as @xmath148 . we expect this behavior to hold for the case of diffractive `` neutrinoproduction '' as well . as indicated in our calculation , the color octet contribution falls off only as @xmath149 which makes the diffractive process negligible at sufficiently high @xmath34 . show the @xmath34 distribution of the events . as expected , these decrease quickly with increasing @xmath34 . the decrease , however , is not so drastic as not to let us use higher @xmath34 cut up to @xmath150 which may also allow to reduce the nonperturbative background . now we turn to the discussion of some of the presently running and planned neutrino experiments . a proposal to build a high energy @xmath151 storage ring has recently drawn much attention . although seemingly a sideline , luminous neutrino beams are unavoidably generated by the decaying muons , and provide an ideal environment for charmonium generation . such machines comprise both necessary ingredients , high luminosity and high neutrino beam energy , that are needed for detailed studies of charmonium production . the proposed first muon collider @xcite would use @xmath152 muons , boosted in linear accelerators . these muons and antimuons decay into the @xmath153 s ( or @xmath154 s ) in both final booster ( called rla3 ) and in the accelerator ring . a straight section of the ring was proposed in order to achieve a highly collimated neutrino beam . the resulting neutrino spectra that have been calculated by harris and mcfarland @xcite peak in the @xmath155 region . with a representative set of parameters @xmath156 dis events/(g/@xmath157 year ) are expected . this high number of events allows a measurement of the partial distributions without the need for extremely costly dedicated detectors . with the cross sections given in table [ tab : crs ] , this translates to @xmath158 events/(g/@xmath157 year ) . we will now sample the various suggestions for the neutrino detectors to get a rough idea of the yield and capabilities . in all cases we look at a detector diameter of @xmath159 , in which almost all of the neutrino beam fits . as an obvious minimal suggestion , we might look at a @xmath160 thick , table - top sized detector @xcite , containing approximately @xmath161 of water - density target . we estimate a yield of @xmath162 , providing just enough statistics for a crude estimate of the octet matrix elements . by contrast , a light target considered e.g. in @xcite ( a @xmath163 thick liquid hydrogen detector ) would only produce approximately @xmath164 , not much better than presently running experiments . the best answer may be the general purpose detector " suggested by b. king @xcite . this detector consists of a one meter long stack of silicon ccd tracking planes , providing @xmath165 g/@xmath166 density . in such a detector an estimated @xmath167 would occur and the high efficiency and precise reconstruction capabilities should allow for disentangling the contribution from the color octet @xmath19 and @xmath33 matrix elements , through the measurement of the differential @xmath34 distributions . note that an increase in the length of the straight section of the storage ring provides a relatively cheap way of increasing the luminosity of the neutrino beam , resulting in better statistics . ref . @xcite actually considers a @xmath168 long straight section , gaining a factor of @xmath169 over our estimates . another option is a conventional fixed target type heavy detector @xcite . a representative example of a 2 ton iron calorimeter @xmath170 long , would see very high event rates ( approximately @xmath171 before cuts and detection efficiencies are included ) . if background difficulties can be overcome , this option provides an excellent opportunity to study all differential rate distributions with precise statistics . as fig . [ fmc.q3.il.eps ] shows , the differential cross section quickly decreases with @xmath34 . however , the decrease is not as fast as in the leptoproduction case . comparing the @xmath34 behavior of formula for the @xmath19 contribution to eq . ( 3 ) in ref . @xcite , we find @xmath172 where @xmath173 is slightly @xmath34-dependent . we have checked that our curves actually reproduce this relationship with @xmath174 . the upshot is that the absence of a photon propagator results in a much wider tail of the @xmath34 distribution than in leptoproduction , allowing for better discrimination between @xmath175- and @xmath85-wave contributions . [ fmc-ring.ratio.1.eps ] shows the ratio of the contributions from these matrix elements as a function of @xmath34 . at low @xmath34 , where the contribution into the cross section is large , the @xmath19 dominates but a determination of the differential cross section in the range @xmath176 , where the event number is still sizable , would allow a reliable extraction of both @xmath19 and @xmath33 matrix elements . higher @xmath34 s will only measure a linear combination of these , as the ratio in fig . [ fmc-ring.ratio.1.eps ] becomes @xmath34-independent . given the above calculation , it is easy to estimate the production rate of other charmonium states , for instance @xmath68 . using heavy quark symmetry , it is possible to relate , at leading order in @xmath177 , the leading @xmath63 matrix elements of @xmath68 , @xmath178 to the corresponding @xmath0 matrix elements . a simple calculation shows , using the data in table [ tab : crs ] with baseline - sized matrix elements , that the @xmath68 yield will be one third of the @xmath0 s . this fact and the absence of a clear signature will make @xmath68 quite elusive in this experiment . a similar remark holds for the @xmath41 , whose only contributing matrix element , the @xmath67 level @xmath32 , is related to the @xmath19 matrix elements of the @xmath20 s . the nomad detector at cern uses the cern sps neutrino beam , mainly designed for detecting neutrino oscillations . the average neutrino energy is small , @xmath179 , and , even with the huge mass of the detector , the event number is small . one would expect approximately @xmath180 events per year in the main detector with its fiducial mass of @xmath181 tons . the situation is somewhat better in the front calorimeter , where such a search is underway , simply because of the larger mass of the detector . with a mass of @xmath182 tons , and the detector characteristics given in ref . @xcite , the yield becomes @xmath183 , which must be multiplied by the decay ratios and detector efficiencies to find the number of observable events . given the inaccuracies of our calculation and the crude estimate of the size of the matrix element , it does not seem impossible that several such events would be seen . another high energy neutrino oscillation experiment has a chance of probing , as a byproduct , our process . the larger average neutrino energy at the fermilab experiment , compared to cern , results in approximately twenty times larger cross section , compensating for the smaller size of the detector . the fermilab experiment nutev detected , during its lifetime of one year , about @xmath184 million dis events . using the numbers in table [ tab : crs ] , this would imply @xmath185 events . this is again on the verge of observability .

at low redshifts , measurements of the total baryon content in stars , atomic and molecular hydrogen , and cluster gas fall a factor of two to four below the baryon density derived from observed light - element ratios and nucleosynthesis arguments . a possible hiding place for a significant fraction of the missing baryons is in the warm / hot gas at temperatures t@xmath0 . we present predictions of the contribution to the soft x - ray background from warm / hot gas emission calculated using new hydrodynamical simulations and discuss the possibility of detecting the spectral signature of this gas using the chandra x - ray observatory .

i

astro-ph0012451

at low redshifts , measurements of the total baryon content in stars , atomic and molecular hydrogen , and cluster gas fall a factor of two to four below the baryon density derived from observed light - element ratios and nucleosynthesis arguments . a possible hiding place for a significant fraction of the missing baryons is in the warm / hot gas at temperatures t@xmath0 . we present predictions of the contribution to the soft x - ray background from warm / hot gas emission calculated using new hydrodynamical simulations and discuss the possibility of detecting the spectral signature of this gas using the chandra x - ray observatory .

lyman @xmath1 measurements of the total baryon density ( rauch et al . 1998 ) at high redshift ( @xmath2 ) are in remarkable agreement with those derived from observed light - element ratios and nucleosynthesis arguments ( burles & tytler 1998 ) , which yield a value of @xmath3 , assuming @xmath4 however , in the local universe , the combined observed contributions of stars , atomic and molecular hydrogen , and cluster gas fall a factor of two to four below this number ( fukugita , hogan , & peebles 1998 ) . recent simulations suggest that at low redshift a large fraction of the baryons in the universe could be in the form of warm / hot gas in filaments ( cen et al . 1995 ; cen & ostriker 1999 ; dav et al . 2000 , and references therein ) . this diffuse gas is also known as the warm / hot intergalactic medium ( whim ) . it is located outside of clusters of galaxies and is heated to temperatures , @xmath5k , intermediate between those of the hot cluster gas and the warm gas in voids . the comparatively low density and temperature of the whim make it a challenge to detect and as yet , attempts to observe it emission have yielded marginal or negative results ( briel & henry 1995 ; wang , connolly & brunner 1997 ; boughn 1998 ; kull & bhringer 1999 ; scharf et al . 2000 ) . as part of on - going work to characterize the x - ray background from the whim , we have calculated the integrated @xmath6 kev spectrum from this gas ( phillips , ostriker , & cen 2000 ) . we compare predicted flux levels with existing limits from observations . we have also generated model spectra to estimate the possibility of detecting the signature of this gas using the high spatial resolution , energy resolution , and soft x - ray detection capabilities of the acis - s chips on the chandra x - ray observatory ( phillips 2000 ) .

atomically resolved imaging and spectroscopic characteristics of graphene grown by chemical vapor deposition ( cvd ) on copper are investigated by means of scanning tunneling microscopy and spectroscopy ( stm / sts ) . for cvd - grown graphene remaining on the copper substrate , the monolayer carbon structures exhibit ripples and appear strongly strained , with different regions exhibiting different lattice structures and electronic density of states ( dos ) . in particular , ridges appear along the boundaries of different lattice structures , which exhibit excess charging effects . additionally , the large and non - uniform strain induces pseudo - magnetic field up to @xmath0 tesla , as manifested by the dos peaks at quantized energies that correspond to pseudo - magnetic field - induced integer and fractional landau levels . in contrast , for graphene transferred from copper to sio@xmath1 substrates after the cvd growth , the average strain on the whole diminishes , so do the corresponding charging effects and pseudo - magnetic fields except for sample areas near topological defects . these findings suggest feasible nano - scale `` strain engineering '' of the electronic states of graphene by proper design of the substrates and growth conditions .

c

1009.0081

atomically resolved imaging and spectroscopic characteristics of graphene grown by chemical vapor deposition ( cvd ) on copper are investigated by means of scanning tunneling microscopy and spectroscopy ( stm / sts ) . for cvd - grown graphene remaining on the copper substrate , the monolayer carbon structures exhibit ripples and appear strongly strained , with different regions exhibiting different lattice structures and electronic density of states ( dos ) . in particular , ridges appear along the boundaries of different lattice structures , which exhibit excess charging effects . additionally , the large and non - uniform strain induces pseudo - magnetic field up to @xmath0 tesla , as manifested by the dos peaks at quantized energies that correspond to pseudo - magnetic field - induced integer and fractional landau levels . in contrast , for graphene transferred from copper to sio@xmath1 substrates after the cvd growth , the average strain on the whole diminishes , so do the corresponding charging effects and pseudo - magnetic fields except for sample areas near topological defects . these findings suggest feasible nano - scale `` strain engineering '' of the electronic states of graphene by proper design of the substrates and growth conditions . scanning tunneling microscopy , scanning tunneling spectroscopies , chemical vapor deposition , quantum effects , surface structure , morphology , roughness , and topography , carbon

we have conducted spatially resolved topographic and spectroscopic studies of cvd - grown graphene - on - copper and transferred graphene - on - sio@xmath1 samples . our investigation reveals the important influence of the substrate and strain on the carbon atomic arrangements and the electronic dos of graphene . for cvd - grown graphene remaining on the copper substrate , the monolayer carbon structures exhibit ripples and are strongly strained , with different regions exhibiting varying lattice structures and electronic density of states . in particular , topographical ridges appear along the boundaries between different lattice structures , which also exhibit excess charging effects . additionally , the large and non - uniform strain induces pseudo - magnetic fields up to @xmath0 tesla , as manifested by the tunneling conductance peaks at quantized energies that are associated with both integer and fractional pseudo - magnetic field - induced landau levels . in contrast , for graphene transferred from copper to sio@xmath1 after cvd growth , the typical graphene structure is largely restored and the average strain on the whole is much reduced , so are the corresponding charging effects and pseudo - magnetic fields , with the exception of limited areas that are associated with topological defects and therefore the resulting strain can not be relaxed after the transfer of sample from copper to sio@xmath1 substrates . our findings suggest feasible nano - scale strain engineering of the electronic states of cvd - grown graphene by proper design of the substrates and growth conditions . k. v. emtsev , a. bostwick , k. horn , j. jobst , g. l. kellogg , l. ley , j. l. mcchesney , t. ohta , s. a. reshanov , j. rohrl , e. rotenberg , a. k. schmid , d. waldmann , h. b. weber , t. seyller nat . ( 2009 ) 203 .

background : : mixed - symmetry @xmath0 states in vibrational nuclei are characterized by a sign change between dominant proton and neutron valence - shell components with respect to the fully symmetric @xmath0 state . the sign can be measured by a decomposition of proton and neutron transition radii with a combination of inelastic electron and hadron scattering [ c. walz _ et al . _ , phys . rev . purpose : : determination of the ground - state ( g.s . ) transition strength of the mixed - symmetry @xmath2 state and verification of the expected vanishing of the proton transition radii difference between the one - phonon @xmath0 states in @xmath1zr . conclusions : : electron scattering at low momentum transfers can provide information on transition radii differences of one - phonon @xmath0 states even in heavy nuclei .

i

1211.6363

background : : mixed - symmetry @xmath0 states in vibrational nuclei are characterized by a sign change between dominant proton and neutron valence - shell components with respect to the fully symmetric @xmath0 state . the sign can be measured by a decomposition of proton and neutron transition radii with a combination of inelastic electron and hadron scattering [ c. walz _ et al . _ , phys . rev . lett . * 106 * , 062501 ( 2011 ) ] . for the case of @xmath1zr , a difference could be experimentally established for the neutron components , while about equal proton transition radii were indicated by the data . purpose : : determination of the ground - state ( g.s . ) transition strength of the mixed - symmetry @xmath2 state and verification of the expected vanishing of the proton transition radii difference between the one - phonon @xmath0 states in @xmath1zr . method : : differential cross sections for the excitation of one - phonon @xmath0 and @xmath3 states in @xmath1zr have been measured with the ( @xmath4 ) reaction at the s - dalinac in a momentum transfer range @xmath5 @xmath6 . results : : transition strengths @xmath7 , @xmath8 and @xmath9 weisskopf units are determined from a comparison of the experimental cross sections to quasiparticle - phonon model ( qpm ) calculations . it is shown that a model - independent plane wave born approximation ( pwba ) analysis can fix the ratio of @xmath10 transition strengths to the @xmath11 states with a precision of about 1% . the method furthermore allows to extract their proton transition radii difference . with the present data @xmath12 fm is obtained . conclusions : : electron scattering at low momentum transfers can provide information on transition radii differences of one - phonon @xmath0 states even in heavy nuclei . proton transition radii for the @xmath11 states in @xmath1zr are found to be identical within uncertainties . the g.s . transition probability for the mixed - symmetry state can be determined with high precision limited only by the available experimental information on the @xmath13 ) value .

collectivity , isospin symmetry and shell structure are generic features of the nuclear many - body quantum system . collective nuclear valence - shell excitations are a key to understand how these features coexist , interplay and compete . in vibrational nuclei , the development of predominantly proton - neutron symmetric collective nuclear structures at low excitation energies is governed by the strong residual proton - neutron interaction . their existence implies - due to quantum - mechanical orthogonality - the formation of collective states with , at least partial antisymmetry with respect to the contribution of proton and neutron valence - space components to their wave functions . such excited states are said to have mixed symmetry @xcite . the investigation of mixed - symmetry states ( mss ) is an important source of information on the effective proton - neutron interaction in the valence shell of heavy atomic nuclei @xcite . mss have been defined in the framework of the proton - neutron interacting boson model ( ibm-2 ) @xcite . in analogy to the isospin symmetry of nucleons , the symmetry of a multi - boson wave function formed by @xmath14 proton bosons and @xmath15 neutron bosons is quantified by the so - called @xmath16-spin . states with @xmath17 have wave functions that contain at least one pair of proton and neutron bosons antisymmetric under the exchange of proton and neutron labels . the signatures of @xmath0 mss are ( @xmath18 ) strong @xmath19 transitions to fully symmetric states ( fss ) with matrix elements of about 1@xmath20 and ( @xmath21 ) weakly collective @xmath22 transitions to fss . the prediction of the ibm-2 with respect to a multi - phonon structure of mss in vibrational nuclei was confirmed about ten years ago by the observation of large @xmath19 transition strengths between low - energy states of @xmath23mo @xcite . the @xmath24 states were also investigated with electron scattering experiments at the superconducting electron accelerator s - dalinac and with proton scattering at ithemba labs @xcite . the combined analysis supported a one - phonon structure of the @xmath25 states of @xmath23mo . in the neighboring even - even isotone @xmath1zr with two neutrons outside the @xmath26 closed shell and with the @xmath27 sub - shell closure , a stronger configurational isospin polarization of the one - phonon states than in @xmath23mo is expected @xcite . recent work showed that the collectivity of the low - lying symmetric and mixed - symmetric quadrupole excitation in vibrational nuclei originates from the coupling of the giant quadrupole resonance to the dominant valence - space configurations @xcite . experimental evidence in @xmath1zr and @xmath23mo stems from the observation of a difference of the respective matter - transition radii ( deduced from proton scattering ) while charge - transition radii ( deduced from electron scattering ) were found to be about equal . the difference results from a sign change of the dominant valence neutron amplitude in mss with respect to the fss . the present work provides an in - depth study of the electron scattering results on @xmath1zr . in particular , we discuss a new method for a model - independent determination of the ratio of the @xmath22 transition strengths of fully symmetric and mixed - symmetric one - phonon excitations in heavy vibrational nuclei , which at the same time provides an estimate of the sensitivity to the transition - radius difference between these two states . the results are furthermore interpreted in the framework of the qpm ( for an introduction to the model see @xcite ) .

lett . * 106 * , 062501 ( 2011 ) ] . for the case of @xmath1zr , method : : differential cross sections for the excitation of one - phonon @xmath0 and @xmath3 states in @xmath1zr have been measured with the ( @xmath4 ) reaction at the s - dalinac in a momentum transfer range @xmath5 @xmath6 . transition probability for the mixed - symmetry state can be determined with high precision limited only by the available experimental information on the @xmath13 ) value .

i

1211.6363

background : : mixed - symmetry @xmath0 states in vibrational nuclei are characterized by a sign change between dominant proton and neutron valence - shell components with respect to the fully symmetric @xmath0 state . the sign can be measured by a decomposition of proton and neutron transition radii with a combination of inelastic electron and hadron scattering [ c. walz _ et al . _ , phys . rev . lett . * 106 * , 062501 ( 2011 ) ] . for the case of @xmath1zr , a difference could be experimentally established for the neutron components , while about equal proton transition radii were indicated by the data . purpose : : determination of the ground - state ( g.s . ) transition strength of the mixed - symmetry @xmath2 state and verification of the expected vanishing of the proton transition radii difference between the one - phonon @xmath0 states in @xmath1zr . method : : differential cross sections for the excitation of one - phonon @xmath0 and @xmath3 states in @xmath1zr have been measured with the ( @xmath4 ) reaction at the s - dalinac in a momentum transfer range @xmath5 @xmath6 . results : : transition strengths @xmath7 , @xmath8 and @xmath9 weisskopf units are determined from a comparison of the experimental cross sections to quasiparticle - phonon model ( qpm ) calculations . it is shown that a model - independent plane wave born approximation ( pwba ) analysis can fix the ratio of @xmath10 transition strengths to the @xmath11 states with a precision of about 1% . the method furthermore allows to extract their proton transition radii difference . with the present data @xmath12 fm is obtained . conclusions : : electron scattering at low momentum transfers can provide information on transition radii differences of one - phonon @xmath0 states even in heavy nuclei . proton transition radii for the @xmath11 states in @xmath1zr are found to be identical within uncertainties . the g.s . transition probability for the mixed - symmetry state can be determined with high precision limited only by the available experimental information on the @xmath13 ) value .

to summarize , an investigation of the nature of one - phonon symmetric and mixed - symmetric @xmath24 states in @xmath1zr has been performed using inelastic electron scattering at low momentum transfers . a comparison of the measured form factors with qpm calculations confirms the dominant one - phonon structure of the transitions to the @xmath36 and @xmath40 states . it is shown that a pwba analysis of the form factors , which usually fails for heavy nuclei , can nevertheless be applied to extract the ratio of the g.s . @xmath90 ) transition strengths in a relative analysis . this is a new promising approach to determine the g.s . transition strength of the @xmath0 mss in vibrational nuclei with a precision limited only by the experimental information about the @xmath91 strength . the pwba approach furthermore provides information about differences of the proton transition radii of the respective states , containing independent information about the mixed - symmetry character of @xmath0 states and the sign change of leading valence shell components between fss and mss @xcite . for @xmath1zr , the proton transition radii agree within about 0.5 fm , consistent with predictions that the sign change arises in this case from the neutron component . further analysis of the data indicates that an improved precision for the proton transition radii difference can be achieved by additional data , in particular in momentum transfer ranges presently not covered well ( e.g. , @xmath92 @xmath93 ) . elementary to the present approach is an approximate cancellation of coulomb corrections of the fss and mss . this may be questioned when moving away from shell closures , where the collectivity of the mss ground - state decay decreases . systematic investigations are necessary to establish the range of applicability of this new promising method . work along these lines ( e.g. studies of @xmath94zr and mo isotopes ) is underway .

numerically , we find that this unitarization technique yields the correct complex analytic structure in terms of cuts and poles . indeed , using the chiral parameter estimates obtained from low energy experiments we obtain the poles associated with the @xmath2 and @xmath3 resonances . we have obtained the chiral parameters and scattering lengths , which can be relevant for future experiments .

i

hep-ph9604416

based on a dispersive approach , we apply the inverse amplitude method to unitarize one - loop @xmath0 and @xmath1 chiral perturbation theory . numerically , we find that this unitarization technique yields the correct complex analytic structure in terms of cuts and poles . indeed , using the chiral parameter estimates obtained from low energy experiments we obtain the poles associated with the @xmath2 and @xmath3 resonances . just by fixing their actual masses we obtain a parametrization of the @xmath4 and @xmath5 phase shifts in eight different channels . with this fit we have then calculated several low - energy phenomenological parameters estimating their errors . among others , we have obtained the chiral parameters and scattering lengths , which can be relevant for future experiments . pacs : 14.40.aq , 14.40.cs,11.80.et,13.75.lb 6.5 in 8.5 in epsf lbl-38645 ucm - ft 3/96 april 1996 revised nov96 to appear in : prd 1-sept-97 * the inverse amplitude method in chiral + perturbation theory * .5 cm a. dobado@xmath6 + departamento de fsica terica . + universidad complutense . 28040 madrid , spain + and .3 cm j.r . pelez@xmath7 + theoretical physics group . lawrence berkeley laboratory + university of california . berkeley , california 94720 . usa . .5 cm

even though qcd yields a remarkably good description of the strong interaction , the low energy hadron physics has to be modelled phenomenologically . this is due to the fact that the usual perturbative approach in the coupling constant can not be applied to qcd below energies of the order of 1 gev . most of the phenomenological results were based on pcac and current algebra . however , in 1979 , weinberg @xcite showed how to reobtain many of these predictions by means of an effective lagrangian . the fields in that lagrangian are the light mesons , ( pions , kaons and etas ) which are understood as the goldstone bosons ( gb ) arising from the spontaneous breaking of chiral symmetry . the lagrangian is built as an expansion in derivatives , that respects the symmetry breaking pattern of qcd . indeed , the first term in the expansion is fixed by the symmetry requirements and accounts for the current algebra results . the next terms in the expansion produce further corrections , which depend on several phenomenological parameters but are always consistent with the qcd symmetry constraints . these techniques were later developed to one loop in a set of papers by gasser and leutwyler @xcite . they showed how to obtain amplitudes involving light mesons , as functions of their momenta , their masses and those few phenomenological parameters . by fitting these parameters from a few low energy experiments it is then possible to obtain successful predictions for other processes the whole approach is known as chiral perturbation theory ( chpt ) . very recently some partial higher order calculations @xcite have appeared in the literature as well as a complete two loop calculation of @xmath4 scattering @xcite , which will be needed in order to analyze new data to come from da@xmath8ne and brookhaven . for a general review of the available experimental data on pion physics and future prospects , we refer the reader to @xcite . nevertheless , there are some intrinsic limitations when applying chpt , namely , the fact that the amplitudes calculated within the chiral approach are only unitary in the perturbative sense , that is , up to the next order in the external momenta . such a breakdown of unitarity is most severe at high energies , where the external momenta is no longer a good expansion parameter , although it can also occur at moderate energies @xcite . as a result , it is not possible to reproduce resonant states , which are one of the most characteristic features of the strongly interacting regime . many different methods have been proposed in order to improve this behavior and thus to extend the applicability of chpt to higher energies ; among them : the use of pad approximants @xcite , the explicit introduction of resonances @xcite , the k - matrix @xcite , the large @xmath9 limit @xcite ( n being the number of gb ) or the inverse amplitude method ( iam ) @xcite . this work is devoted precisely to the last method , which can be justified within a dispersive approach and can easily reproduce the two lightest resonances : the @xmath2 in @xmath4 scattering @xcite and the @xmath10 in @xmath11 scattering @xcite . but not only that , the iam also improves considerably the fit to data even in non - resonant channels , almost up to the first two particle inelastic threshold ( the many particle inelastic thresholds can be neglected since they are suppressed by phase space factors ) . this fit provides a remarkably good parametrization that can be used for other processes . indeed , in a previous work @xcite , the authors showed how it can be used together with a simple unitarization prescription to obtain successful results on @xmath12 up to 700 mev . of course , it is also possible to obtain very good parametrizations @xcite of @xmath4 or @xmath11 elastic scattering by including all resonant states explicitly . however , our aim choosing the iam is to reproduce these phenomena just with the few phenomenological parameters present in the chpt lagrangian . in this way , even though their masses and widths will not be obtained with great accuracy , resonances can be regarded as real predictions . that is one of the relevant features of the iam since other very popular unitarization methods are not able to reproduce resonances unless they are explicitly introduced in the calculation . that is , for instance , the case with the k - matrix . the purpose of this work is , first , to study how high in energies the iam yields good results and what are its limitations . we would also like to know whether it is possible to reproduce further resonance states . it is clear that the best candidates are the lightest resonances whose dominant decay modes are @xmath4 or @xmath11 . we have listed them in table 1 . in case these resonances were not accommodated after our unitarization , it would be interesting to understand why . second , once we have a good fit to these resonances , we want to make a complete numerical analysis of several low - energy quantities of interest , like the chiral parameters or the scattering lengths , including estimations for their errors . as we will see below , we expect that the iam somehow will include effects that can not be obtained from the pure @xmath13 expansion . [ cols="^,^,^,^,^",options="header " , ] lightest resonances with @xmath4 or @xmath11 dominant decay modes . data taken from @xcite . 0.cm finally , we would like to comment on another motivation of the present work , which at first may not seem very related to the main topic . the philosophy of the chiral approach has also reached the description of the strongly interacting symmetry breaking sector ( sisbs ) of the standard model @xcite . the scalar sector of such a model displays the same symmetry breaking pattern as two flavor massless qcd . hence it is possible to build an effective lagrangian , much as it is done for chpt @xcite . although the electroweak gb are not physical , using this lagrangian it is possible to obtain predictions for the scattering of longitudinal gauge bosons @xcite at future colliders , like the lhc . indeed , there are already experimental proposals to measure the electroweak chiral parameters at cms @xcite . most of the works on the sisbs make use of the equivalence theorem @xcite , which allows us to read the observable amplitudes , in terms of longitudinal gauge bosons , directly from those with gb . this theorem has been recently proved in the chiral lagrangian formalism @xcite and seems to be severely constrained by the lack of unitarity . at this point is when the unitarization procedures come into play and it is crucial to know whether they are reliable , since what we are now looking for are real predictions and not elaborated fits to still unavailable data . in section 2 we review some basic aspects of exact and perturbative unitarity and we define the partial waves in elastic scattering . section 3 introduces the iam , first with a derivation from dispersion theory and then by studying the constraints to its applicability . section 4 and section 5 are organized in the same way , although they refer to @xmath0 and @xmath1 chpt , respectively : first we apply the iam to chpt with the chiral parameters obtained from low energy experiments in order to study the iam predictive power . next , we present an iam fit to the data . for the best @xmath1 fit we present the unitarized results for the scattering lengths and some other phenomenological parameters . then , in section 6 , we study the analytic structure on the complex plane of the iam amplitudes . in section 7 we present the conclusions . there is also an appendix where we give the elastic scattering formulae used in this work , as well as a discussion on perturbative unitarity .

based on a dispersive approach , we apply the inverse amplitude method to unitarize one - loop @xmath0 and @xmath1 chiral perturbation theory . pacs : 14.40.aq , 14.40.cs,11.80.et,13.75.lb 6.5 in 8.5 in epsf lbl-38645 ucm - ft 3/96 april 1996 revised nov96 to appear in : prd 1-sept-97 * the inverse amplitude method in chiral + perturbation theory * .5 cm a. dobado@xmath6 + departamento de fsica terica .

m

hep-ph9604416

based on a dispersive approach , we apply the inverse amplitude method to unitarize one - loop @xmath0 and @xmath1 chiral perturbation theory . numerically , we find that this unitarization technique yields the correct complex analytic structure in terms of cuts and poles . indeed , using the chiral parameter estimates obtained from low energy experiments we obtain the poles associated with the @xmath2 and @xmath3 resonances . just by fixing their actual masses we obtain a parametrization of the @xmath4 and @xmath5 phase shifts in eight different channels . with this fit we have then calculated several low - energy phenomenological parameters estimating their errors . among others , we have obtained the chiral parameters and scattering lengths , which can be relevant for future experiments . pacs : 14.40.aq , 14.40.cs,11.80.et,13.75.lb 6.5 in 8.5 in epsf lbl-38645 ucm - ft 3/96 april 1996 revised nov96 to appear in : prd 1-sept-97 * the inverse amplitude method in chiral + perturbation theory * .5 cm a. dobado@xmath6 + departamento de fsica terica . + universidad complutense . 28040 madrid , spain + and .3 cm j.r . pelez@xmath7 + theoretical physics group . lawrence berkeley laboratory + university of california . berkeley , california 94720 . usa . .5 cm

let us briefly review the standard derivation @xcite of the inverse amplitude method , since we will use it later in order to understand the applicability of the method . any partial wave obtained from a relativistic quantum field theory should present a characteristic analytic structure in the complex @xmath42 plane . indeed , the reaction threshold becomes a cut in the from @xmath43 to @xmath44 . due to crossing symmetry , there should be another left cut along the negative axis . if we now apply cauchy s theorem to our complex amplitudes we obtain integral equations known as dispersion relations . for instance , a three times subtracted dispersion relation is @xmath45 where we have not written explicitly the left cut ( lc ) contribution . the number of subtractions needed depends on how the amplitude behaves at infinity in order to ensure the vanishing of the contributions coming from closing the integral contour . we have chosen three subtractions since we are going to use @xmath39 chpt amplitudes which at high @xmath42 behave as @xmath46 . but our arguments remain valid for @xmath41 amplitudes when using four times subtracted dispersion relations , etc ... the chpt partial waves present both cuts and we can calculate both the subtraction constants @xmath47 and the integrand inside eq.[disp ] _ perturbatively _ @xmath48 where we have expanded the subtraction constants in terms of @xmath49 . the iam is based on the fact that the function @xmath50 displays the very same analytic structure of @xmath51 , apart from some possible pole contributions . for later convenience , we will make use of @xmath52 . notice that we have multiplied @xmath53 by a real function without singularities ; thus we keep the same analytic structure and we can write a very similar dispersion relation : @xmath54 where @xmath55 stands for possible pole contributions . the advantage of using @xmath56 is that , using eqs.[uni ] and [ punit ] , we can calculate exactly the integral over the right cut ( but not on the left , since those equations only hold on the elastic cut ) , as follows : @xmath57 note that we are denote by @xmath51 the exact amplitude , which is unknown , although we know its analytic properties . in contrast , the expressions for @xmath36 and @xmath38 , etc ... have been calculated explicitly . as we did before , we can also expand the @xmath58 subtraction coefficients in powers of @xmath59 , and then rewrite the dispersion relation for @xmath56 , which now reads @xmath60 where we have approximated @xmath61 on the left cut and we have neglected the pole contribution . in other words , @xmath62 this is the iam result that we are going to use in the present work . incidentally , eq.[iam ] can be understood as the formal @xmath63 $ ] pad approximant of the chpt amplitude . it is important to remark that if we expand again eq.[iam ] at low energies , we find @xmath64 that is , we recover the chpt expansion . hence , up to @xmath65 our method and chpt yield the same low energy results if the same chiral lagrangian parameters are used . let us review all the approximations made in the previous section , in order to comment how they will constraint the iam applicability : in eq.[preiam ] we have replaced the @xmath56 left cut integral by that of @xmath66 . as we have remarked in the preceeding discussion , eqs.[uni ] and [ punit ] are only exact on the right cut . on the left cut we can not write the chain of equalities that lead to eq.[img ] . nevertheless , if we use the chpt result as an approximation : @xmath67 we get @xmath68 notice that , in order to obtain the @xmath34 phase shifts , we are going to calculate @xmath69 for real @xmath70 . that means that the denominator @xmath71 inside the integrals is never going to be very small , which somehow will wash out the error on the left cut . but note also that treating differently the right and left cuts violates crossing symmetry . indeed , in @xcite it has already been pointed out that the pad approximants do not reproduce correctly the subleading logarithms that would appear at _ next order _ in the chiral expansion ( @xmath65 in this case ) . of course they would be obtained if we applied the iam to the chiral amplitudes at @xmath65 , but still the method would not yield the correct logarithms at @xmath72 and so on . at high energies chiral logarithms are not so relevant , but at low energies they are a very important feature of chpt and indeed they can give the dominant contribution in some channels . nevertheless , from eq.[recover ] we see that at low energies the iam yields the very same @xmath73 chpt expansion , _ including _ the _ dominant _ chiral logarithms . the contribution from the left cut and subleading logarithms is @xmath65 . as a consequence , if we try to make a low energy fit to the data , the parameters that we would obtain with the iam would not lie very far from those of chpt , but they will not be the same . that is the reason why , in the following sections , we will denote with a hat the parameters obtained from any iam fit . in eq.[preiam ] , we have neglected the contributions coming from zeros in the amplitude , that will appear as poles of the inverse function . there is no way to know _ a priori _ whether or not a partial wave will vanish for a given value of @xmath42 , although it is known that chiral amplitudes have zeros below threshold , which are known as adler zeros . their position is not known except for the @xmath74 channel , where the pole is located at threshold . in our derivation it is compensated by the same zero in the @xmath75 channel . that is not the case of the @xmath76 amplitudes and therefore we are neglecting the contribution of their residue . consequently , our amplitudes are not valid to obtain adler zeros and that will affect our results at low energy ( but no more than @xmath65 ) . that is another reason to differentiate the parameters obtained from our fit from those of the pure chiral expansion . this is apparently a harmless assumption in the above reasoning , although it dramatically affects the results of the iam . in fact , it can happen that @xmath77 . in the @xmath78 channels of @xmath4 scattering or in the @xmath79 in @xmath11 , this only occurs for isolated values of @xmath42 , at or below threshold . in particular , that means that the iam amplitudes will have the same zeros as the lowest order chiral amplitudes . however , every other partial wave vanishes at @xmath37 , for any @xmath42 . as a consequence , the formula in eq.[iam ] is no longer valid . nevertheless , we can generalize our previous derivation , in order to include those channels whose leading order is @xmath39 . we only have to go through the very same steps , although now we would write a dispersion relation for @xmath80 . but let us remember that the main improvement of the approach is that we are calculating exactly the integral of @xmath81 over the right cut . however , for that purpose we need an imaginary part , and by looking at eq.[punit ] we can see that @xmath77 implies that @xmath82 . therefore , unless we have a calculation up to @xmath83 , the corresponding imaginary part will vanish . hence when following the derivation of the iam if @xmath77 the best we can get is plain chpt again . at present , only @xmath84 calculations are available and we can only expect to obtain a real improvement with our approach in the six channels listed above . thus , we will not be able to reproduce the @xmath85 resonance . in order to obtain @xmath86 on the right cut , eq.[img ] , we have just made use of the elastic unitarity condition of eq.[uni ] . however , the right cut is composed of many superimposed cuts , each one corresponding to a different inelastic intermediate channel . actually , eq.[uni ] is only true below the first inelastic threshold , and the real unitarity condition reads @xmath87 the sum is over all the physically accessible intermediate states @xmath88 , whose phase space is @xmath89 . as far as we are neglecting electromagnetic interactions , the first inelastic channel in @xmath4 is the four pion intermediate state , at 550 mev . similarly , for @xmath11 is @xmath90 , whose threshold is @xmath91 910 mev . strictly speaking , only for lower energies the elastic approximation is exact . nevertheless , the contribution of these intermediate states is strongly suppressed by the four particle phase space and we expect the iam to provide a good approximation . unfortunately within the range of energies we are interested in , there are intermediate channels which are not suppressed by phase space . indeed , at approximately @xmath92 mev the inelastic @xmath93 threshold opens up . its phase space factor is the @xmath89 in eq.[sigma ] , with @xmath94 . therefore , above the two kaon threshold we have to reconsider the derivation of the iam . let us illustrate with @xmath4 scattering how inelastic effects modify our result . as the starting point , for @xmath95 , we have a new unitarity relation : @xmath96 where we have denoted by @xmath97 the generic @xmath51 pion elastic scattering amplitude and by @xmath98 the @xmath34 partial wave of the process @xmath99 . thus we now have , for @xmath100 , that @xmath101 which differs from eq.[img ] in the term coming from two kaon intermediate production . if we follow the very same steps of our previous derivation , we arrive at @xmath102 notice that , using chpt , @xmath103 . but at these high energies that is not negligible . besides , we are interested in the above integral for physical values of @xmath42 and therefore the denominator will be almost divergent for some @xmath104 . for these reasons we can not neglect this integral and then we should not trust the iam since it could miss some relevant physical features . that is indeed the case in pion scattering since , as it can be seen in table 1 , there is one resonance , the @xmath105 , whose nature is closely related to the @xmath93 threshold . nowadays , the interpretation of that resonance is still controversial : different authors propose different poles ( not always just one ) in the vicinity of the @xmath93 inelastic cut @xcite . as we will see later , our approach is not able to reproduce any of these poles , consistent with the fact that the iam makes use just of elastic unitarity . at this point we want to remark the importance of understanding why and when the method does no longer yield the right results . let us remember that we are also thinking in possible applications of this unitarization procedures to the electroweak chiral effective lagrangian , whose reference model is the standard model with a heavy higgs . in such case , one would expect to see a broad resonance in the scalar channel and we want to have a unitarization procedure whose predictions we can trust . throughout the derivation of the iam we have been using the chiral amplitudes up to @xmath39 . nevertheless , it is possible to extend the argument to include higher order terms , as for instance the @xmath41 contributions . in that case we would have started from a four times subtracted dispersion relation for the two - loop calculation . once more , the integral over the right cut would be related to the one for @xmath52 . working out the expansion of the subtraction constants , we would then arrive to @xmath106 again that is the formal [ 1,2 ] pad approximant , and it satisfies the elastic unitarity condition . as we have already mentioned two recent papers have appeared with @xmath41 calculations of @xmath4 scattering within @xmath0 chpt @xcite . we have not used these results , since , as we have just seen , they will not help us to overcome any of the preceeding objections to the iam . however it is quite likely that , have we used them , the parameters of the fits that we will present in the next sections would had been slightly modified .

biopolymer looping is a dynamic process that occurs ubiquitously in cells for gene regulation , protein folding , etc . in cellular environments , biopolymers are often subject to tensions which are either static , or temporally fluctuating far away from equilibrium . we study the dynamics of semiflexible polymer looping in the presence of such tensions by using brownian dynamics simulation combined with an analytical theory . , we find the phenomenon of resonant activation , where the looping time can be the minimum at an optimal flipping time . we discuss our results in connection with recent experiments .

i

1112.0450

biopolymer looping is a dynamic process that occurs ubiquitously in cells for gene regulation , protein folding , etc . in cellular environments , biopolymers are often subject to tensions which are either static , or temporally fluctuating far away from equilibrium . we study the dynamics of semiflexible polymer looping in the presence of such tensions by using brownian dynamics simulation combined with an analytical theory . we show a minute tension dramatically changes the looping time , especially for long chains . considering a dichotomically flipping noise as a simple example of the nonequilibrium tension , we find the phenomenon of resonant activation , where the looping time can be the minimum at an optimal flipping time . we discuss our results in connection with recent experiments .

the kinetics of polymer loop formation has been studied for several decades and recently has attracted renewed attention due to the particular importance in biology . the dna loop formation is a basic process that underlies genetic expression , replication , and recombination @xcite . for example , in _ e. coli _ the _ lac _ repressor ( laci)-mediated loop is crucial for the repressive regulation of _ lac _ genes . the hairpin loop formation is the elementary step in protein folding @xcite and structure formation in rna folding @xcite . a cell is crowded with a multitude of subcellular structures including globular proteins and rnas @xcite , with which dna is constantly interacting . a dna fragment about to loop is often subject to temporally fluctuating forces due to its dynamic environment including the other part of the chain . recently , the power spectrum of the fluctuating force exerted on cytoskeleton was measured to be an order of magnitude larger than that expected from thermal equilibrium condition @xcite . this indicates that the cell interior is an active and nonequilibrium medium . the advance of single molecule experiment techniques provides detailed information on the dna loop formation . finzi and gelles @xcite observed laci - mediated dna loop formation and dissociation by monitoring nano - scale brownian motion of the micron - sized particle attached to one end of the dna . et al . _ @xcite showed that in _ gal _ repressor and dna - bending protein hu mediated looping , mechanical constraints such as tension and torsion play a pivotal role . gemmen _ et al . _ @xcite studied effects of tension in the presence of two - site restriction enzymes which can cut the dna upon binding on two sites simultaneously . they found that the cleavage activity decreases approximately 10-fold as the tension increases from 30 fn to 700 fn . they also found that the optimum loop size decreases with the tension , which is qualitatively in agreement with theoretical predictions @xcite . more recently , chen _ et al . _ @xcite studied effects of tension in femtonewton range on the kinetics of laci - mediated dna looping . they found that small tension of 100 fn scale on the substrate dna can not only increases the looping time @xcite but also found that the looping time is greatly reduced in the presence of a fluctuating tension @xcite . these results suggest the ubiquitous roles of the static and temporally fluctuating tensions in regulation of the dna loop formation . yet , there appears to be no unifying conceptual or theoretical framework that explains a variety of experiments including these . theoretically , on the other hand , yan _ et al . _ @xcite developed a transfer matrix method to calculate semiflexible polymer end - to - end distance distribution function and loop formation probability ( or @xmath0-factor ) . they studied various effects of nonlinear elasticity arising from dna bending protein - induced kinks @xcite or thermal - fluctuation - induced bubbles on the @xmath0-factor . their study provides a valuable insight to understand dna bending on short length scale @xcite , which has attracted much attention recently @xcite . they also studied effects of tension on the @xmath0-factor @xcite , which is related to the free energy barrier for loop formation @xcite , thus to the loop formation rate . similar results are obtained by using an elastic theory of a semiflexible polymer @xcite . however , since the loop formation rate is not proportional to the @xmath0-factor alone but depends on the free energy given an arbitrary chain end - to - end distance , it is hard to quantitatively compare these theories to the experiment @xcite . independently , blumberg _ et al . _ @xcite studied effects of static tension on protein - mediated dna loop formation by modeling the dna conformation to be either one of two states , looped and unlooped states . in their appealing calculations of free energy change associated with the transition under the tension , they considered not only the stretching free energy of dna but also dna alignment constraint imposed by protein binding . they found that for the loop size larger than 100 base pair distance ( @xmath1 nm ) , a tension of 0.5 pn can increase the looping time by more than two order of magnitude . there is room for improvement in their approach , however , on the evaluation of the free energy that can be valid for short end - to - end distance of the chain as well as a description of detailed kinetic process using the mean first - passage time approach . in this paper , in an effort to understand the basic physical mechanism of the biopolymer looping in a coherent manner , we perform brownian dynamics simulation of semiflexible polymers treated as extensible wormlike chain , combined with one - dimensional theory of barrier crossing over the free energy of loop formation . for analytical understanding , we use , as an example , the mean - field wormlike chain model @xcite , which is shown to be a good approximation for the free energy for the chain lengths we consider here . with static tensions , we find that the looping time , defined as the mean first - passage time to cross the free energy barrier , steeply increases with the applied tension @xmath2 , in an agreement with our simulation results but distinct from the previous theoretical result @xcite . for the case of time - dependent tension , we consider dichotomically fluctuating tension , where the looping times are found to be reduced , consistent with the experiment @xcite . most importantly , we find so - called the resonant activation , where the looping time is the minimum at an optimal flipping time of the dichotomic force . in this exploratory study , we neglect the alignment constraint on the loop formation , which is minor effect for the chain lengths we consider here @xcite . in the following section , we describe our polymer model and simulation method , whose results are discussed in sec . [ sec : results ] . we summarize our results in sec . [ sec : conclusion ] .

by removing one empty site between two occupied sites , we map the ground states of chains of hardcore bosons and spinless fermions with infinite nearest - neighbor repulsion to ground states of chains of hardcore bosons and spinless fermions without nearest - neighbor repulsion respectively , and ultimately in terms of the one - dimensional fermi sea .

m

0907.4228

by removing one empty site between two occupied sites , we map the ground states of chains of hardcore bosons and spinless fermions with infinite nearest - neighbor repulsion to ground states of chains of hardcore bosons and spinless fermions without nearest - neighbor repulsion respectively , and ultimately in terms of the one - dimensional fermi sea . we then introduce the intervening - particle expansion , where we write correlation functions in such ground states as a systematic sum over conditional expectations , each of which can be ultimately mapped to a one - dimensional fermi - sea expectation . various ground - state correlation functions are calculated for the bosonic and fermionic chains with infinite nearest - neighbor repulsion , as well as for a ladder model of spinless fermions with infinite nearest - neighbor repulsion and correlated hopping in three limiting cases . we find that the decay of these correlation functions are governed by surprising power - law exponents .

in sec . [ sect : nnetonni ] , we establish a one - to - one correspondence between states of the nearest - neighbor excluded and nearest - neighbor included chains . we explain how the hamiltonian matrices of the two chains , and hence their energy spectra , are identical to one another . in the infinite - chain limit , we then show how we can write the ground state of the excluded chain in terms of the ground state of the ordinary chain , and ultimately be written in terms of the one - dimensional fermi sea . in sec . [ sect : nnegsexp ] , we show how the ground - state expectation between two local operators can be calculated for the excluded chain , by writing it as a systematic sum over conditional expectations , each of which associated with a fixed configuration of intervening particles . for the sake of definiteness , let us consider open chains of a finite length @xmath18 and total particle number @xmath19 . sites on these chains are indexed by @xmath20 . since the models in eq . and eq . conserve @xmath19 , the infinite - chain limit is obtained by letting @xmath21 , keeping the density of particles @xmath22 fixed . ultimately , the results we present in this section will not depend on what boundary conditions we impose on the chain ( which is what we would expect in the infinite chain limit ) . for convenience , we establish some notations to cover boson and fermion cases together in the same formula . let us call @xmath23 an excluded configuration , where @xmath24 for hardcore bosons , @xmath25 for spinless fermions , and the sites @xmath26 are such that @xmath27 . we will also employ the labels @xmath28 and @xmath29 for distinct @xmath19-particle configurations @xmath30 and @xmath31 , i.e. the @xmath19-particle configurations @xmath32 and @xmath33 differ in at least one site . similarly , let us call @xmath34 an ordinary configuration , where @xmath35 for hardcore bosons , @xmath36 for spinless fermions , and the the sites @xmath26 are such that @xmath37 . the labels @xmath28 and @xmath29 will again denote distinct @xmath19-particle configurations @xmath38 and @xmath39 . we will also consistently denote the hamiltonian of an excluded chain by @xmath40 , where @xmath41 for hardcore bosons , @xmath42 for spinless fermions , and the hamiltonian of an ordinary chain by @xmath43 , where @xmath44 for hardcore bosons , @xmath45 for spinless fermions . in this subsection , our goal is to establish the one - to - one correspondence between states of the excluded and ordinary chains , and to show that as matrices , the hamiltonians and are identical . to do this , let us note that an excluded chain with @xmath18 sites has fewer @xmath19-particle states than an ordinary chain of @xmath18 sites , because of the infinite nearest - neighbor repulsion . therefore , we can form a one - to - one correspondence between excluded and ordinary states only if the length @xmath46 of the ordinary chain is shorter than @xmath18 . there are several ways to systematically map excluded configurations to ordinary configurations : we can ( i ) delete the site to the right of every particle , if it is not the rightmost particle ; or ( ii ) delete the site to the left of every particle , if it is not the leftmost particle . we can easily check that these maps produce the same ordinary configurations for finite open chains . we expect this to hold true even as we go to the infinite chain limit . for the rest of this paper , we will adopt _ right - exclusion map _ @xmath47 that maps a @xmath19-particle configuration on an open excluded chain of length @xmath18 to a @xmath19-particle configuration on an open ordinary chain of length @xmath46 . the empty site to the right of each occupied site in the open excluded chain is deleted , to give a corresponding configuration for an open ordinary chain .. ] as illustrated in fig . [ fig : rightexclusionmap ] , we do not delete any empty site to the right of the @xmath19th particle , and thus the effective length of the open ordinary chain is @xmath48 . this nearest - neighbor exclusion map was first used by fendley to map a supersymmetric chain of spinless fermions to the @xmath49 chain @xcite . it tells us that an excluded chain with density @xmath50 gets mapped to an ordinary chain with density @xmath51 thus , in the limit of @xmath52 , @xmath53 -particle configurations on an open excluded chain of length @xmath18 to @xmath19-particle configurations on an open ordinary chain of length @xmath48 , by deleting one empty site to the right of a particle that is not the rightmost particle . ] for @xmath19-particle excluded configurations @xmath30 and @xmath31 , the matrix element @xmath54 is nonzero only when @xmath30 and @xmath31 can be obtained from one another by a single particle hopping to the left or the right . when this is so , the ordinary @xmath19-particle configurations @xmath38 and @xmath39 they map to under the right - exclusion map are also related to each other by a single particle hop . thus , we have @xmath55 since there is a one - to - one correspondence between @xmath19-particle configurations on an open excluded chain and @xmath19-particle configurations on an open ordinary chain , eq . tells us that @xmath40 and @xmath43 are identical as matrices in their respective configurational bases . we therefore conclude that the @xmath19-particle energy spectra of the two chains coincide , and that there is a one - to - one correspondence between the energy eigenstates , @xmath56 for the excluded chain , and @xmath57 for the ordinary chain . that is , if @xmath58 , and @xmath59 , then @xmath60 and @xmath61 have the same amplitudes in @xmath62 and @xmath63 respectively . this result has profound implications on the thermodynamics of the two chains , as well as that of the ladder model in the three limiting cases described in sec . [ sect : briefthreelimits ] , because their partition functions are the same . however , for the rest of this paper , we limit ourselves to the ground states of the infinite excluded and ordinary chains , as well as those of the infinite ladder . in this subsection , we explain how the expectation @xmath64 of an observable @xmath65 in the ground state of the excluded chain can be computed , by relating it to the expectation @xmath66 in the ground state of the ordinary chain , for an appropriately chosen observable @xmath67 satisfying some basic correspondence requirements that we shall outline . specifically , we are interested in the correlations @xmath68 between two local observables @xmath69 and @xmath70 separated by a distance @xmath71 within the excluded - chain ground state . however , the right - exclusion map maps excluded matrix elements @xmath72 to ordinary matrix elements @xmath73 in which @xmath74 and @xmath75 are separated by varying separations . to deal with this problem , we develop a method of intervening - particle expansion involving a sum over conditional expectations . to begin , let us look at the ground states @xmath76 of the excluded and ordinary chains respectively . to take advantage of the equality of amplitudes , @xmath77 if @xmath58 under the right - exclusion map , we want @xmath78 to have a simple relation with @xmath79 . while it is possible to pick @xmath67 such that @xmath80 for all @xmath28 and @xmath29 , we find that it is more convenient to pick @xmath67 such that @xmath81 for example , if @xmath82 , we can pick the corresponding observable to be @xmath83 , in which case we find that @xmath84 which satisfies eq . we call @xmath65 and @xmath67 a _ corresponding pair of observables _ , if eq . is satisfied for all @xmath28 and @xmath29 , allowing us to write the very simple relation @xmath85 between their ground - state expectations . since we are mostly interested in correlation functions within the excluded chain ground state , let us look at expectations of the product form @xmath86 , where @xmath87 acts locally about site @xmath88 , and @xmath89 acts locally about site @xmath90 . becasue the number of particles @xmath91 between sites @xmath88 and @xmath92 varies from excluded configuration to excluded configuration , these sites get mapped by the right - exclusion map to sites on the ordinary chain with varying separations @xmath93 . therefore , to calculate the excluded chain ground - state expectation @xmath86 in terms of ordinary chain ground - state expectations , we first write down an _ intervening - particle expansion _ @xmath94 where @xmath95 are conditional expectations . here @xmath96 is a vector of occupation numbers within the intervening sites , and @xmath97 is a string of factors , each of which is either @xmath98 or @xmath99 , @xmath100 . the sum is over all possible ways to have intervening particles between @xmath87 and @xmath89 . for each excluded term @xmath95 in eq . , we then write down the corresponding ordinary expectation @xmath101 , and thereafter sum over all corresponding ordinary expectations , @xmath102 making use of eq . . the vector @xmath103 of occupation numbers is obtained from @xmath96 using the right - exclusion map , and contains the same number @xmath91 of occupied intervening sites . to illustrate how the corresponding expectations @xmath104 can be constructed , let us write eq . out explicitly as @xmath105 each of which contains intervening particles at fixed sites . we call terms in the expansion with @xmath91 intervening @xmath106 s the _ @xmath91-intervening - particle expectations_. because of nearest - neighbor exclusion , most of the terms in eq . vanish . next , we map each conditional excluded expectation in eq . to a corresponding conditional ordinary expectation following the simple rules given below : 1 . * nearest - neighbor exclusion . * to ensure that we do not violate nearest - neighbor exclusion , we make the assignment @xmath107 note that this is intended not as a statement on the operator algebra , but as a mere bookkeeping device for evaluating expectations . the assignment @xmath108 follows from eq . . * right - exclusion map . * the right - exclusion map described in section [ sect : nnetonni ] is then implemented by making the substitution @xmath109 the assignment @xmath110 follows from eq . . re - indexing . * because the right - exclusion map in eq . merges the occupied site @xmath111 and the empty site @xmath112 to its right , operators to the right of site @xmath112 must be re - indexed . the index @xmath111 on the excluded chain becomes @xmath113 on the ordinary chain . thus , two ending operators @xmath71 sites apart in the @xmath91-intervening - particle excluded expectation becomes @xmath93 sites apart in the corresponding @xmath91-intervening - particle ordinary expectation .

we then introduce the intervening - particle expansion , where we write correlation functions in such ground states as a systematic sum over conditional expectations , each of which can be ultimately mapped to a one - dimensional fermi - sea expectation . we find that the decay of these correlation functions are governed by surprising power - law exponents .

i

0907.4228

by removing one empty site between two occupied sites , we map the ground states of chains of hardcore bosons and spinless fermions with infinite nearest - neighbor repulsion to ground states of chains of hardcore bosons and spinless fermions without nearest - neighbor repulsion respectively , and ultimately in terms of the one - dimensional fermi sea . we then introduce the intervening - particle expansion , where we write correlation functions in such ground states as a systematic sum over conditional expectations , each of which can be ultimately mapped to a one - dimensional fermi - sea expectation . various ground - state correlation functions are calculated for the bosonic and fermionic chains with infinite nearest - neighbor repulsion , as well as for a ladder model of spinless fermions with infinite nearest - neighbor repulsion and correlated hopping in three limiting cases . we find that the decay of these correlation functions are governed by surprising power - law exponents .

in this paper , we established a one - to - one correspondence between @xmath19-particle configurations on the excluded chain and @xmath19-particle configurations on the ordinary chain using the right - exclusion map . we then showed that the hamiltonian matrices of the models given in eq . and eq . are identical , therefore solving for the ground states of the former in terms of those of the latter . these results were obtained for finite chains subject to open boundary conditions , but continues to hold for infinite chains . based on this one - to - one correspondence between ground states , we showed that the ground - state expectation @xmath64 of an excluded chain observable @xmath65 can be evaluated using eq . in terms of the ground - state expectation @xmath66 of a carefully chosen corresponding observable @xmath67 on the ordinary chain . we then developed the method of intervening - particle expansion , to write the ground - state expectation @xmath86 of a product of local excluded chain operators @xmath87 and @xmath89 , first as a sum over excluded chain expectations @xmath409 conditioned on the occupations of the sites between @xmath88 and @xmath92 , and then as a sum over the corresponding ordinary chain expectations @xmath410 . using these analytical results from sec . [ sect : maptech ] , we calculated the fl , cdw , and sc correlations of the excluded chains of hardcore bosons and spinless fermions in sec . [ sect : correlationsnnebosons ] . based on nonlinear curve fits of the numerically evaluated correlations , to reasonable asymptotic forms , we find all three types of correlations decaying with separation @xmath71 as power laws , for hardcore bosons as well as for spinless fermions . more interestingly , we find for both hardcore bosons and spinless fermions a universal exponent @xmath411 for the oscillatory power - law decay of the sc correlation , but a non - universal , density - dependent , exponent @xmath412 for the oscillatory power - law decay of the cdw correlation . also , the leading asymptotic behaviour for the hardcore boson fl correlation was found to a non - oscillating power - law decay with universal exponent @xmath128 , while that for the spinless fermion fl correlation was found to be oscillations in a power - law envelope , with a non - universal exponent that approaches @xmath157 as @xmath149 , and @xmath187 as @xmath151 . we then analyzed our spinless - fermion ladder model , eq . , in sec . [ sect : laddermodels ] . this ladder model can be solved exactly in three limiting cases : ( i ) the paired limit @xmath413 ; ( ii ) the two - leg limit @xmath414 ; and ( iii ) the rung - fermion limit @xmath415 . in the paired limit , which we solved in sec . [ sect : infinitelystrongcorrelatedhops ] , spinless fermions form correlated - hopping bound pairs , and so the ladder model can be mapped to the excluded chain of hardcore bosons . the ground state of this latter model was solved exactly in sec . [ sect : maptech ] and its ground - state correlations calculated in sec . [ sect : correlationsnnebosons ] . by reinterpreting the excluded chain correlations in ladder terms , we realized that ladder sc correlations dominates at large distances over ladder cdw correlations , both of which decay as power laws with separation , with leading exponents @xmath416 and @xmath417 respectively , @xmath227 being the ladder density . we also showed , using a restricted probabilities argument , that ladder fl correlations decay exponentially with separation , with a density - dependent correlation length . next , in the two - leg limit , which we solved in sec . [ sect : independentlegs ] , we argued based on a `` particle - in - a - box '' picture that successive spinless fermions in the two - fold degenerate _ staggered ground states _ occupy different legs of the ladder . we write these ground states exactly in terms of the one - dimensional fermi sea in sec . [ sect : nointerleggs ] , before calculating correlations in sec . [ sect : weakxy ] . we found , using a different restricted probabilities argument , that fl correlations decay exponentially with separation , with a density - dependent correlation length . cdw and sc correlations symmetric ( antisymmetric ) with respect to a reflection about the ladder axis decay as power laws , with universal leading exponents @xmath418 and @xmath419 respectively . finally , in the rung - fermion limit , we mapped the ladder model to an excluded chain of spinless fermions in sec . [ sect : independentrungs ] . since we have already solved this latter model in sec . [ sect : maptech ] and calculated its ground - state correlations in sec . [ sect : correlationsnnebosons ] below half - filling ( which corresponds to quarter - filling on the ladder ) , we discussed the phase separations that occurs on ladders with greater than quarter filling in sec . [ sect : stronginterleggs ] . correlation exponents obtained for the three limiting cases of our ladder model eq . , as well as those for the excluded chains of hardcore bosons and spinless fermions , are summarized in table [ table : summaryofexponents ] . .a summary of the leading correlation exponents and wave vectors of various correlation functions that decay as power laws in the ( i ) paired limit @xmath231 ; ( ii ) two - leg limit @xmath233 , @xmath317 ; and ( iii ) rung - fermion limit @xmath237 , @xmath317 . the wave vector @xmath135 of the leading terms in the correlation functions are reported in terms of @xmath420 , where @xmath421 is the excluded chain density . the suffixes @xmath266 and @xmath422 indicate further symmetries possible in the ladder model . [ cols="^,^,^,^ " , ] in this study , we find the emergence of surprising universal correlation exponents . in the luttinger liquid paradigm , all correlation exponents can be written in terms of the exponents @xcite @xmath423 appearing in the quantum - mechanical propagator , also called the ( equal - time ) two - point function @xmath424 } \cos k_f r \\ & = a_1\ , r^{-\frac{1}{4}\left[(k_{\rho } + k_{\rho}^{-1 } ) + ( k_{\sigma } + k_{\sigma}^{-1})\right ] } \cos k_f r. \end{aligned}\ ] ] the parameters @xmath425 and @xmath426 depend generically on the filling fraction and the interaction strength , and thus all correlation exponents are non - universal . in particular , various theoretical approaches ( see review by slyom @xcite ) tell us that the charge density waves ( cdw ) , spin density wave ( sdw ) , singlet superconductivity ( ssc ) and triplet superconductivity ( tsc ) correlations decay as power laws [ eqn : expkrhoksigma ] @xmath427 in a tomonaga - luttinger liquid . when the chain of interacting spinfull fermions is spin - rotation invariant ( for example , in the absence of an external magnetic field ) , the spin stiffness constant must be @xmath428 , and the ground - state properties become completely determined by the single nontrivial luttinger parameter @xmath425 . the spinfull power laws thus become @xmath429 for spinless fermions , there is only one independent stiffness constant @xmath430 @xcite , so that the spinfull power laws which have proper spinless analogs are @xmath431 in the luttinger liquid paradigm , universal correlation exponents only arise in the special case of the fermi liquid , where we have @xmath432 . consequently , the two - point function decays as @xmath433 , while the cdw and sc correlations both decay as @xmath434 . however , the universal correlations exponents that we find in our exact solutions are different from these . furthermore , the correlation exponents @xmath28 , @xmath29 , and @xmath435 of the fl , cdw , and sc correlations ought to obey definite relations in a luttinger liquid , because they can all be written in terms of a single luttinger parameter @xmath436 . again , the universal and non - universal correlation exponents we find in our exact solutions do not obey these relations . these observations bring us to the paper by efetov and larkin , who first calculated the universal fl correlation exponent for an ordinary chain of hardcore bosons to be @xmath437 @xcite . if we accept for the moment that the luttinger paradigm is correct , and that universal correlation exponents can only be found at the fermi liquid fixed point , then we are led to the conclusion that @xmath211 must be a correlation exponent of the fermi liquid . clearly , this exponent does not belong to the fermi liquid fl correlation ( which should be @xmath240 , so what correlation does it belong to ? in the seminal paper by jordan and wigner , the ordinary chain of hardcore bosons is mapped to the ordinary chain of spinless fermions using the jordan - wigner transformation ( see appendix [ sect : jwtrans ] ) . in this transformation , the hardcore boson point operators @xmath11 and @xmath438 are each mapped to spinless fermion _ string operators _ @xmath439 and @xmath440 respectively . the fl correlation @xmath186 between two hardcore boson point operators thus become the expectation @xmath441 of the string operator @xmath442 . which efetov and larkin found to decay with separation @xmath71 as @xmath443 . string correlations such as this have never been systematically studied . one reason for this lack of interest is that typical string correlations , which receive contributions only from restricted classes of configurations , decay exponentially with @xmath71 , as we have seen for the fl correlation in the paired limit ( sec . [ sect : tonkscorr ] ) and the two - leg limit ( sec . [ sect : weakxy ] ) . however , there appear to many string correlations that decay with separation @xmath71 as power laws . these power law decays are associated with ( quasi-)long - range order that we have not been creative enough to imagine . in sec . [ sect : nointerleggs ] , we found in the two - leg limit that the staggered ground state has long - range order , in that if we know the @xmath91th particle is on leg @xmath444 , then we know for certain that the @xmath445th particle is on leg @xmath444 , and the @xmath446th particle is on leg @xmath447 , even as @xmath448 , and even though we have no idea where these particles are on the ladder . this long - range order is not the usual kind of long - range order , which can be written in terms of the correlation between local order parameters , but is a long - range _ string _ order . the map from the ordinary chain ground state to the staggered ladder ground state , which is the inverse of the one constructed in sec . [ sect : nointerleggs ] , implicitly involves string operators , in that if we take the @xmath91th particle in the ordinary ground state configuration , we will know whether to map it to a particle on leg @xmath444 or leg @xmath447 , _ after _ we know which legs the preceding particles are on . also , while it is deceptively simple to describe what the string operator in this inverse map does , which is to project out any combination of more than or equal to two consecutive particles on the same leg of the ladder , we know of no compact way to write down the string operator , even in this simple limit , unlike for the case of the jordan - wigner string . what we do know , drawing parallels from the jordan - wigner map from hardcore bosons on ordinary chains to noninteracting spinless fermions , is that a string map from one model to another will map some products of local operators to string operators , for example , the hardcore boson @xmath449 to the spinless fermion @xmath450 , and other products of local operators to products of local operators , for example , the hardcore boson @xmath451 to the spinless fermion @xmath452 . having understood this , we realized that the cdw@xmath358 and sc@xmath358 correlations in the staggered ground state get mapped to the the correlation of local operators , because the string operators involved in the map multiply and cancel each other . on the other hand , when we map the cdw@xmath360 and sc@xmath360 staggered ground - state correlations to correlations of a chain of noninteracting spinless fermions , the string operators involved in the map do not cancel each other , and thus the resulting ordinary chain spinless - fermion correlations are string correlations . we also realized that these string correlations are operationally defined by the intervening - particle expansions we used to compute them . since all the exact solutions we have obtained in this paper can ultimately be mapped to the one - dimensional fermi sea , we conjecture that all correlation exponents are universal . we claim that : ( i ) all exponents that are explicitly universal are simple rational polynomials of the single universal spinless fermi liquid parameter @xmath453 ; and ( ii ) non - universal exponents are the result of ( under)fitting linear combinations of universal power laws to a single power law . for example , in the two - leg limit , the leading universal exponent @xmath367 of the cdw@xmath360 correlation in the staggered ground state can be shown using a bosonization calculation of the string correlation it is mapped to , to follow automatically from the universal fermi liquid parameter @xmath454 @xcite . in this same limiting case , the leading universal correlation exponent @xmath455 of the sc@xmath360 correlation , which gets mapped to a significantly more complicated string correlation , can conceivably be written as the combination @xmath456 of the universal fermi liquid parameter @xmath454 , even though the bosonized form of this string correlation is not known . for the excluded chain of hardcore bosons or spinless fermions , nonlinear curve fitting of the sc correlation to the sum of one leading power - law decay and one subleading power - law decay leads to weakly non - universal correlation exponents for both power laws , whereas a complicated sum of power - law decays , eq . , produces a better fit visually . we believe good fits can also be obtained , using similar complicated sum of power - law decays , for those numerical correlations which we found to have strongly non - universal correlation exponents . finally , we asked ourselves whether all these string correlations that we have predicted will decay with separation @xmath71 slower than the two - point function @xmath457 can be measured in a chain of noninteracting spinless fermions . since these string operators are nonlocal observables , they do not in general couple to local measurements , so direct experimental measurement would be challenging , if not downright impossible however , we would like to suggest the following possibility : for a given string correlation of the one - dimensional fermi sea , cook up in the laboratory an experimental system in which the corresponding correlation is a point correlation . if the ground - state of the experimental system can be mapped to the one - dimensional fermi sea , we expect a measurement of the point correlation exponent in the experimental system to be an indirect measurement of the string correlation exponent in the fermi sea .

comparing numerically evaluated excitation gaps of dimerized spin-@xmath0 xxz chains with the gap formula for the low - energy effective sine - gordon theory , we determine coefficients @xmath1 and @xmath2 of bosonized dimerization operators in spin-@xmath0 xxz chains , which are defined as @xmath3 and @xmath4 . we also calculate the coefficients of both spin and dimer operators for the spin-@xmath0 heisenberg antiferromagnetic chain with a nearest - neighbor coupling @xmath5 and a next - nearest - neighbor coupling @xmath6 . as applications of these coefficients ,

i

1005.1704

comparing numerically evaluated excitation gaps of dimerized spin-@xmath0 xxz chains with the gap formula for the low - energy effective sine - gordon theory , we determine coefficients @xmath1 and @xmath2 of bosonized dimerization operators in spin-@xmath0 xxz chains , which are defined as @xmath3 and @xmath4 . we also calculate the coefficients of both spin and dimer operators for the spin-@xmath0 heisenberg antiferromagnetic chain with a nearest - neighbor coupling @xmath5 and a next - nearest - neighbor coupling @xmath6 . as applications of these coefficients , we present ground - state phase diagrams of dimerized spin chains in a magnetic field and antiferromagnetic spin ladders with a four - spin interaction . the optical conductivity and electric polarization of one - dimensional mott insulators with peierls instability are also evaluated quantitatively .

quantum magnets in one dimension are a basic class of many - body systems in condensed matter and statistical physics ( see e.g. , refs . ) . they have offered various kinds of topics in both experimental and theoretical studies for a long time . in particular , the spin-@xmath0 xxz chain is a simple though realistic system in this field . the hamiltonian is defined by @xmath7 where @xmath8 is @xmath9-component of a spin-@xmath0 operator on @xmath10-th site , @xmath11 is the exchange coupling constant , and @xmath12 is the anisotropy parameter . this model is exactly solved by integrability methods , @xcite and the ground - state phase diagram has been completed . three phases appear depending on @xmath12 ; the antiferromagnetic ( af ) phase with a nel order @xmath13 ( @xmath14 ) , the critical tomonaga - luttinger liquid ( tll ) phase ( @xmath15 ) , and the fully polarized phase with @xmath16 ( @xmath17 ) . in and around the tll phase , the low - energy and long - distance properties can be understood via effective field theory techniques such as bosonization and conformal field theory ( cft ) . @xcite these theoretical results nicely explain experiments of several quasi one - dimensional ( 1d ) magnets . the deep knowledge of this model is also useful for analyzing plentiful related magnetic systems , such as spin-@xmath0 chains with some perturbations ( e.g. external fields , @xcite additional magnetic anisotropies , @xcite dimerization @xcite ) , coupled spin chains , @xcite spatially anisotropic 2d or 3d spin systems , @xcite etc . a recent direction of studying spin chains is to establish solid correspondences between the model ( [ eq : xxz ] ) and its effective theory . for example , lukyanov and his collaborators @xcite have analytically predicted coefficients of bosonized spin operators in the tll phase . hikihara and furusaki @xcite have also determined them numerically in the same chains with and without a uniform zeeman term . using these results , one can now calculate amplitudes of spin correlation functions as well as their critical exponents . furthermore , effects of perturbations on an xxz chain can also be calculated with high accuracy . it therefore becomes possible to quantitatively compare theoretical and experimental results in quasi 1d magnets . the purpose of the present study is to attach a new relationship between the spin-@xmath0 xxz chain and its bosonized effective theory . namely , we numerically evaluate coefficients of bosonized dimer operators in the tll phase of the xxz chain . dimer operators @xmath18 , as well as spin operators , are fundamental degrees of freedom in spin-@xmath0 af chains . in fact , the leading terms of both bosonized spin and dimer operators have the same scaling dimension @xmath19 at the @xmath20-symmetric af point @xmath21 ( see sec . [ sec : dimer ] ) . in refs . , hikihara and furusaki have used density - matrix renormalization - group ( dmrg ) method in an efficient manner in order to accurately evaluate coefficients of spin operators of an xxz chain in a magnetic field . instead of such a direct powerful method , we utilize the relationship between a dimerized xxz chain and its effective sine - gordon theory @xcite to determine the coefficients of dimer operators ( defined in sec . [ sec : dimer ] ) , i.e. , excitation gaps in dimerized spin chains are evaluated by numerical diagonalization method and are compared with the gap formula of the effective sine - gordon theory . in other words , we derive the information on uniform spin-@xmath0 xxz chains from dimerized ( deformed ) chains . moreover , we also determine the coefficients of both spin and dimer operators for the spin-@xmath0 heisenberg ( i.e. , xxx ) af chain with an additional next - nearest - neighbor ( nnn ) coupling @xmath6 in the similar strategy . as seen in sec . [ subsec : su2_dimer ] , evaluated coefficients are more reliable for the @xmath5-@xmath22 model , since the marginal terms vanish in its effective theory . the plan of this paper is as follows . in sec . [ sec : dimer ] , we shortly summarize the bosonization of xxz spin chains . both the xxz chain with dimerization and the chain in a staggered magnetic field are mapped to a sine - gordon model . we also consider the af heisenberg chain with nnn coupling @xmath6 . in sec . [ sec : delta ] , we explain how to obtain the coefficients of dimer and spin operators by using numerical diagonalization method . the evaluated coefficients are listed in tables [ tb : dimer_coeff ] and [ tb : a1 ] and fig . [ fig : dimer_coeff ] . these are the main results of this paper . for comparison , the same dimer coefficients are also calculated by using the formula of the ground - state energy of the sine - gordon model . we find that the coefficients fixed by the gap formula are more reliable . we apply these coefficients to several systems and physical quantities related to an xxz chain ( dimerized spin chains under a magnetic field , spin ladders with a four - spin exchange and optical response of dimerized 1d mott insulators ) in sec . [ sec : apply ] . finally our results are summarized in sec . [ sec : con ] .

curiously overlooked in physics is its dependence on the transmission of numbers . the transmission of numbers and other logical distinctions is often achieved over a computer - mediated communications network in the face of an unpredictable environment . by unpredictable we mean something stronger than the spread of probabilities over given possible outcomes , namely an opening to unforeseeable possibilities . based on recent proofs within quantum theory that provide a theoretical foundation to unpredictability , here we show how regularities in physics rest on a background of channels over which numbers are transmitted .

c

1508.01119

curiously overlooked in physics is its dependence on the transmission of numbers . for example the transmission of numerical clock readings is implicit in the concept of a coordinate system . the transmission of numbers and other logical distinctions is often achieved over a computer - mediated communications network in the face of an unpredictable environment . by unpredictable we mean something stronger than the spread of probabilities over given possible outcomes , namely an opening to unforeseeable possibilities . unpredictability , until now overlooked in theoretical physics , makes the transmission of numbers interesting . based on recent proofs within quantum theory that provide a theoretical foundation to unpredictability , here we show how regularities in physics rest on a background of channels over which numbers are transmitted . as is known to engineers of digital communications , numerical transmissions depend on coordination reminiscent of the cycle of throwing and catching by players tossing a ball back and forth . in digital communications , the players are computers , and the required coordination involves unpredictably adjusting `` live clocks '' that step these computers through phases of a cycle . we show how this phasing , which we call _ logical synchronization _ , constrains number - carrying networks , and , if a spacetime manifold in invoked , put `` stripes '' on spacetime . via its logically synchronized channels , a network of live clocks serves as a reference against which to locate events . such a network in any case underpins a coordinate frame , and in some cases the direct use of a network can be tailored to investigate an unpredictable environment . examples include explorations of gravitational variations near earth .

as a gentle illustration of logical synchronization , in the previous section we invoked the familiar assumption of a coordinate system on a spacetime manifold relative to which to describe an example of polygonal ring of rotating live clocks with nearest neighbors linked by logically synchronized channels . however , as already emphasized , the concept of logical synchronized channels does not in itself make any assumption of a spacetime manifold , let alone a coordinate system on that manifold . indeed the bringing about of a pattern of logically synchronized channels provides a background against which to locate events , tailored to one or another particular situation , and this background provides some or all of the services asked of a coordinate frame . that is , in a network of logically synchronized channels linking live clocks , events are located by their proximity to live - clock readings that , via these channels are related to readings of the other live clocks of the network . as discussed in @xcite , gravitation affects the reference patterns of channels toward which a network of live clocks can successfully steer , so that at high precision the reference patterns are themselves hypotheses arrived at in part by unpredictable guesswork , subject to revision in response to failures to come within tolerable deviations from them . the events that are critical to location are acts of transmitting and receiving numbers , or , to put it a little more generally acts of transmitting and receiving logical distinctions , such as the distinction between 0 and 1 or the distinction between ` yes ' and ` no ' . it is the communication of logical distinctions in the face of an unpredictable environment that gives digital computers their power , and indeed gives life the capacity to propagate through the mechanisms of dna replication . the communication of logical distinctions depends on regenerative amplification that reshapes signals to maintain logical distinctions while allowing for tolerances in system components @xcite . besides regenerative amplification , the communication of logical distinctions requires phase management in the face of unpredictable environmental behavior . the live clocks of a network function primarily not to tell `` time '' in the sense of a spacetime coordinate , but to regulate the phasing needed for logical synchronization . we have stressed unpredictability of guesses that enter reference patterns , but as discussed in @xcite , unpredictable events are also physical , as in the detections by a photodetector . while in some experiments , one accumulates such detections passively to get an average rate of detections that can be related to a probability , in other experiments , notably the operation of an atomic clock , detections that can not be individually predicted have to be responded to promptly , and so enter the operation of clocks that realize the si units of the hertz and the second . 1 . can one retrieve some notion of a time coordinate that is available without the assumption of a spacetime manifold , based on tracing the implications of the relations between the transmissions of numbers and their receptions , as expressed by the channels of a network ? regenerative amplification is found in biology , for example in the propagation of electrical spikes in nerve fibers @xcite . is phase management present in biology ? there are questions to ask and to answer concerning possibilities for patterns of channels among live clocks , whether in engineered systems or as found in living organisms . to get a glimpse of the issue , for any live clock @xmath0 , in principle there is a ( likely variable ) tick rate that will make it logically synchronized to signals from an arbitrary second live clock @xmath1 , but the issue is not so simple if live clock @xmath0 wants to steer toward logical synchronization with a third live clock @xmath60 in addition to @xmath1 . and there are bigger questions . quantum mechanics depends on coordinate systems which , as we have seen , depend on clocks ; however , the concept of a coordinate system abstracts the clocks out of sight . when we look into the clocks and their communication by the transmission of number - carrying signals , we find a situation readily described , as above , in terms of computer engineering or its abstract turing machines , without the use of quantum language . realized clock networks depend on regenerative amplification thermodynamically non - reversible ( even if logically reversible @xcite ) and outside of any graceful description in the language of quantum theory . question : can some novel quantum - theoretic description ( involving decoherence ? ) represent networks of live clocks , or is quantum mechanics irreducibly dependent on systems for locating events that are outside its descriptive reach ? finally there is the question of accepting or rejecting unpredictability as a fundamental feature of life . one often thinks of a coordinate system working like rigid fences that organize a landscape , but if unpredictability is pervasive , if the earth on which we stand shifts , which at present levels of clock stability it always does , how is one to locate objects of interest ? there can be no rigid body on which to stand . the application of physical laws that underpin predictions requires number - carrying channels . channels operate in the face of unpredictability that no law can shut out . when channels of a network fail , as on occasion they do , the applications that depend on them fragment . sometimes that fragmentation of a network calls us to search for a different background pattern toward which to steer . if needs to adjust our reference patterns are in the cards , it is perhaps better to be nimble . recognizing unpredictability can be a first step toward that nimbleness . 99 j. m. myers and f. h. madjid , `` ambiguity in quantum - theoretical descriptions of experiments , '' in k. mahdavi and d. koslover , eds . , _ advances in quantum computation _ , contemporary mathematics series , vol . 482 ( american mathematical society , providence , i , 2009 ) , pp . 107123 ; arxiv:1409.5678 . j. m. myers and f. h. madjid , `` distinguishing between evidence and its explanations in the steering of atomic clocks , '' annals of physics 350 , 2949 ( 2014 ) ; arxiv:1407.8020 . m. soffel et al . , `` the iau resolutions for astrometry , celestial mechanics , and metrology in the relativistic framework : explanatory supplement , '' the astronomical journal , * 126 * , 26872706 ( 2003 ) . a. einstein , `` zur elektrodynamik bewegter krper , '' annalen der physik , * 17 * , 891921 ( 1905 ) . a. m. turing , `` on computable numbers with an application to the entscheidungsproblem , '' proc . london math . soc . , series 2 , * 42 * , 230265 ( 1936 ) . f. h. madjid and j. m. myers , `` clocking in the face of unpredictability beyond quantum uncertainty , '' arxiv:1504.04345 ( 2015 ) . c. e. shannon , `` a mathematical theory of communication , '' the bell system technical journal , vol . 27 , 379423 , 623656 , july , october , 1948 f. h. madjid and j. m. myers , `` matched detectors as definers of force , '' j. m. myers and f. h. madjid , `` rhythms of memory and bits on edge : symbol recognition as a physical phenomenon , '' arxiv/1106.1639 , 2011 . physics * 319 * ( 2005 ) , 251273 ; arxiv : quant - ph/0404113 .. j. m. myers , `` modeling the effect of an external electric field on the velocity of spike propagation in a nerve fiber , '' phys . e , * 60 * , 59185925 ( 1999 ) . c. h. bennett , `` logical reversibility of computation , '' ibm journal of research and development , * 17 * , no . 6 , 525532 ( 1973 ) .

heavy elements ( ` metals ' ) are produced by stars , and the star formation history deduced by these surveys implies that a significant fraction of all metals in the universe today should already exist at @xmath1 . however , only 10% of the total metals expected to exist at this redshift have so far been accounted for ( in damped lyman alpha absorbers and the lyman forest ) . in this paper , we use the results of submillimetre surveys of the local and high redshift universe to show that there was much more dust in galaxies in the past . ( ism):dust , extinction

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astro-ph0210260

deep surveys in many wavebands have shown that the rate at which stars were forming was at least a factor of 10 higher at redshifts @xmath0 than today . heavy elements ( ` metals ' ) are produced by stars , and the star formation history deduced by these surveys implies that a significant fraction of all metals in the universe today should already exist at @xmath1 . however , only 10% of the total metals expected to exist at this redshift have so far been accounted for ( in damped lyman alpha absorbers and the lyman forest ) . in this paper , we use the results of submillimetre surveys of the local and high redshift universe to show that there was much more dust in galaxies in the past . we find that a large proportion of the missing metals are traced by this dust , bringing the metals implied from the star formation history and observations into agreement . we also show that the observed distribution of dust masses at high redshift can be reproduced remarkably well by a simple model for the evolution of dust in spheroids , suggesting that the descendants of the dusty galaxies found in deep submm surveys are the relatively dust - free spiral bulges and ellipticals in the universe today . galaxies : evolution galaxies : ism galaxies : luminosity function , mass function submillimetre ( ism):dust , extinction

the star formation history ( sfh ) of the universe deduced from optical / uv surveys ( lilly et al . 1996 ; madau et al . 1996 , 1998 ) has recently been revised to account for dust extinction ( steidel et al . 1999 ) , largely motivated by the detection of a population of dusty star - forming objects in deep submm surveys with scuba ( hughes et al . 1998 ; eales et al . 1999 ; smail , ivison & blain 1997 ; scott et al . 2002 ) . the current best estimate of the sfh is that the global star - formation rate in the universe was fairly constant over the redshift interval @xmath2 , falling by a factor @xmath3 to the present epoch , see fig . [ sfrdf ] . ( steidel et al . 1999 ; ivison et al . 2002 ) . a simple integration of this history implies that @xmath4% of all stars and metals today should have formed by a redshift of @xmath5 . however , the metal content of objects believed to contain most of the baryonic matter at high - z principally the lyman alpha forest and damped lyman alpha absorption systems ( dlas) is only 2.5% of the total amount of metals in the universe today ( pettini 1999 ; pagel 2002 ) . thus 90% of metals expected to exist at @xmath6 have not yet been seen or recognised the ` missing metals ' . the submm surveys revealed a population of extremely dusty and obscured objects with very high bolometric luminosities , probably residing at high redshifts , @xmath7 ( dunlop 2001a ; ivison et al . if the dust is heated by stars , the star formation rates implied by the submm fluxes are @xmath8 , high enough to produce an entire galaxy worth of stars in @xmath9 gyr . since the properties of low - redshift ellipticals suggest that most of their stars formed quickly at high redshift ( bower et al . 1992 ; renzini 1997 ; jimenez et al . 1999 ) , several authors have argued that the scuba sources may be elliptical galaxies in the process of formation ( lilly et al . 1999 ; eales et al . 2000 ; dunlop 2001b ; granato et al . it has been claimed ( cen & ostriker 1999 ) that the regions of greatest over - density in the universe at any epoch are the most metal enriched , and that these regions will have reached a given metallicity much earlier than lower density environments . this argument suggests that scuba galaxies should be a large reservoir for metals at high redshift , since if they are proto - ellipticals they should have formed from the highest density peaks at high redshift when there has been less time for pollution of the low density inter - galactic medium ( igm ) . in this paper , we wish to investigate the connection between the ` missing metals ' , the formation of the spheroids and the dusty sources seen by scuba . however , instead of using the bolometric luminosities of the submm sources to infer their physical properties , we interpret the results of the deep submm surveys and our submm survey of the nearby universe in a completely different way , by carrying out the first investigation into the cosmic evolution of the dust mass in galaxies . this provides a new way of looking at the chemical evolution of the universe , as there is evidence that the fraction of ism metals which are bound up in dust grains is @xmath10 percent , a value which seems remarkably constant from galaxy to galaxy and which also appears to apply at higher redshifts ( issa , maclaren & wolfendale 1990 ; edmunds 2001 ; pei , fall & hauser 1999 ; james et al . we will determine the dust content of the low and high - z universe by constructing dust mass functions , i.e. the space densities of galaxies as a function of dust mass . at low - z , we will use the results of the scuba local universe galaxy survey ( dunne et al . 2000 ) , the first attempt at an unbiased submm survey of the local universe . for the high redshift dust mass function , we will use submm data from the deep scuba submm surveys . in section 4 we will use these dust mass functions , together with a simple chemical evolution model , to estimate the co - moving density of metals and baryons associated with the ism of galaxies at low and high redshift . finally , we will produce a simple prediction for the dust mass function of the spheroids during the epoch in which they had their maximum dust masses , and compare with our observational estimate of the dust mass function of the scuba sources .

diverse models of engines energised by quantum - coherent , hence non - thermal , baths allow the engine efficiency to transgress the standard thermodynamic carnot bound . the carnot bound is inapplicable to such a hybrid machine . we conclude that even though a machine powered by a quantum bath may exhibit an unconventional performance , it still abides by the traditional principles of thermodynamics .

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1508.06519

diverse models of engines energised by quantum - coherent , hence non - thermal , baths allow the engine efficiency to transgress the standard thermodynamic carnot bound . these transgressions call for an elucidation of the underlying mechanisms . here we show that non - thermal baths may impart not only heat , but also mechanical work to a machine . the carnot bound is inapplicable to such a hybrid machine . intriguingly , it may exhibit dual action , concurrently as engine and refrigerator , with up to 100% efficiency . we conclude that even though a machine powered by a quantum bath may exhibit an unconventional performance , it still abides by the traditional principles of thermodynamics .

scully and co - workers @xcite have introduced a model of a carnot heat engine based on a bath comprised of partly - coherent three - level atoms ( nicknamed `` phaseonium '' ) that interact with a cavity - mode `` working fluid '' ( wf ) while they cross the cavity . their astounding conclusion was that the efficiency of such an engine may exceed the universal carnot bound @xcite because the phaseonium bath endows the cavity mode with a temperature @xmath0 that , depending on the phase @xmath1 of the atomic coherence , may surpass the corresponding temperature of thermal atoms without coherence . this research has initiated diverse suggestions of quantum resources for boosting heat - machine efficiency above the carnot bound , with a focus on non - thermal baths possessing quantum coherence @xcite . in traditional heat engines , energy exchange between the wf and the ( hot and cold ) thermal baths are entropy - changing heat transfers , whereas parametric changes of the wf hamiltonian are isentropic processes that produce or invest work @xcite . the main questions we raise here are : does the same division between heat and work necessarily hold in engines fuelled by non - thermal ( quantum - coherent ) baths and how does this division affect the engine efficiency ? to what extent is the quantum character of non - thermal baths and ( or ) the wf relevant to the engine performance ? here we address the above questions by means of the fundamental notion of _ non - passivity _ @xcite that defines the ability of a quantum state to deliver work . the maximal work extractable from a non - passive state is known as ergotropy @xcite ( [ app_ergotropy ] ) . the significance of non - passivity as a work resource has been previously demonstrated for a heat machine with a quantised piston @xcite . by resorting to this notion , we point out that there are two kinds of machines fuelled by non - thermal baths . in machines of the first kind ( exemplified by the intriguing @xcite ) the energy imparted by a non - thermal bath to the wf consists of an isentropic part that transfers ergotropy ( work ) to the wf , which has hitherto been unaccounted for , and an entropy - changing part that corresponds to heat transfer , but the total energy received by the wf can not be associated with heat . by contrast , in machines of the second kind ( exemplified by the pioneering @xcite ) the entire energy transfer from the non - thermal bath to the wf can indeed be considered as heat . a correct division of the energy transfer from the bath to the wf into heat and work is crucial for the realisation that the efficiency of machines of the first kind does not have a thermodynamic bound that may be deduced from the second law . this becomes evident when the energy of the non - thermal bath has a vanishingly small thermal component : the engine can then produce work without heat input . our analysis of these two kinds of machines is focused on an otto cycle for an harmonic - oscillator wf under the assumption that the non - thermal bath that powers the machine is unitarily generated from a thermal one . a central result of this analysis is that such non - thermal baths may produce a non - passive steady state of the wf and thereby change its ergotropy . we use this result to identify the two distinct kinds of machines powered by quantum non - thermal baths : ( i ) machines of the first kind are exemplified by setups fuelled by a squeezed thermal bath or a coherently - displaced thermal bath @xcite ) which render the wf state _ non - passive _ ( and therefore non - thermal ) . our central finding is that this kind of machine does not act as a heat engine , but rather as a _ hybrid thermo - mechanical machine energised by work as well as heat _ imparted by this bath . the thermodynamic carnot bound does not apply to the efficiency of such a machine , which is shown to operate not only as an engine , but concurrently as a heat pump / refrigerator that moves heat from the `` cold '' bath to the `` hot '' non - thermal bath , at the expense of mechanical work invested by the latter . ( ii ) machines of the second kind are obtained for wf bath interactions whereby , in contrast to machines of the first kind , the wf is rendered _ thermal _ ( i.e. , passive ) by the non - thermal bath . an engine fuelled by a phaseonium bath @xcite exemplifies this kind of machines . it is shown to act as a genuine heat engine , whose efficiency is limited by the carnot bound corresponding to the _ real _ temperature of the wf . in the case of a phaseonium bath @xcite , this temperature is @xmath0 . we analyse an otto cycle @xcite for both kinds of machines ( sections [ sec_otto ] and [ sec_thermal_otto ] ) . for machines of the first kind we then propose a modification of the otto cycle ( section [ sec_modified_otto ] ) , aimed at attaining an efficiency as high as unity , well above the otto - cycle bound , again at the expense of mechanical work provided by the non - thermal bath . the general criteria allowing us to distinguish between the two kinds of machines are analysed ( section [ sec_conditions ] ) and the role of their quantum features is discussed ( section [ sec_quantum ] ) . our conclusions ( section [ sec_conclusions ] ) are that despite their superior performance bounds compared to standard heat engines , machines powered by non - thermal baths still adhere to the traditional rules of thermodynamics , whether or not they are powered by quantum baths or exhibit quantum features .

during the initial data reduction of the wisconsin h - alpha mapper ( wham ) h@xmath0 sky survey , we have discovered several very long ( @xmath180 ) filaments superimposed on the diffuse h@xmath0 background . these features have no clear correspondence to the other phases of the interstellar medium revealed by 21 cm , x - ray , ir , or radio continuum surveys , and they have no readily identifiable origin or source of ionization . in this letter ,

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astro-ph9805151

during the initial data reduction of the wisconsin h - alpha mapper ( wham ) h@xmath0 sky survey , we have discovered several very long ( @xmath180 ) filaments superimposed on the diffuse h@xmath0 background . these features have no clear correspondence to the other phases of the interstellar medium revealed by 21 cm , x - ray , ir , or radio continuum surveys , and they have no readily identifiable origin or source of ionization . in this letter , the data for two of these faint ( @xmath2 0.51.5 r ) structures are presented . the first is an 80-long , 2-wide arch that extends nearly perpendicular to the galactic plane at @xmath3 and attains a maximum latitude of @xmath4 near @xmath5 before reaching the southern boundary of our survey map at @xmath6 , @xmath7 . the vertical portion of this feature between @xmath8 and @xmath9 is associated with a single radial velocity component centered at @xmath10 km s@xmath11 with a full width at half maximum of 27 km s@xmath11 . a decrease in the velocity is observed from @xmath12 through @xmath13 as the feature arches toward higher galactic longitudes . at this end , the emission component is centered near @xmath14 km s@xmath11 . where this feature appears to meet the galactic plane near @xmath15 , it is directly above the region surrounding cma r1/ob1 . a second filament consists of a @xmath1630-long arc spanning @xmath17240 at @xmath18 to 40 . the radial velocity of this feature increases systematically from 0 km s@xmath11 at @xmath19 , @xmath20 to + 18 km s@xmath11 at @xmath21 , @xmath22 . both features have rather constant intensities along their entire lengths , ranging from 0.51.5 r ( em = 13 @xmath23 pc ) with no obvious trends .

the wisconsin h - alpha mapper ( wham ) survey is providing the first velocity - resolved map of the h@xmath0 emission from our galaxy s diffuse interstellar medium . the combination of wham s sensitivity ( @xmath24 r ) and velocity resolution ( 12 km s@xmath11 ) reveals new details about the large - scale structure and kinematics of the warm ionized medium ( wim ) . studies of faint emission structures in the wim may help us understand the distribution and morphology of the ionized gas and may even provide direct evidence of ionization sources . in this letter , we present the discovery of two large , faint filaments in our galaxy .

the first is an 80-long , 2-wide arch that extends nearly perpendicular to the galactic plane at @xmath3 and attains a maximum latitude of @xmath4 near @xmath5 before reaching the southern boundary of our survey map at @xmath6 , @xmath7 . the vertical portion of this feature between @xmath8 and @xmath9 is associated with a single radial velocity component centered at @xmath10 km

r

astro-ph9805151

during the initial data reduction of the wisconsin h - alpha mapper ( wham ) h@xmath0 sky survey , we have discovered several very long ( @xmath180 ) filaments superimposed on the diffuse h@xmath0 background . these features have no clear correspondence to the other phases of the interstellar medium revealed by 21 cm , x - ray , ir , or radio continuum surveys , and they have no readily identifiable origin or source of ionization . in this letter , the data for two of these faint ( @xmath2 0.51.5 r ) structures are presented . the first is an 80-long , 2-wide arch that extends nearly perpendicular to the galactic plane at @xmath3 and attains a maximum latitude of @xmath4 near @xmath5 before reaching the southern boundary of our survey map at @xmath6 , @xmath7 . the vertical portion of this feature between @xmath8 and @xmath9 is associated with a single radial velocity component centered at @xmath10 km s@xmath11 with a full width at half maximum of 27 km s@xmath11 . a decrease in the velocity is observed from @xmath12 through @xmath13 as the feature arches toward higher galactic longitudes . at this end , the emission component is centered near @xmath14 km s@xmath11 . where this feature appears to meet the galactic plane near @xmath15 , it is directly above the region surrounding cma r1/ob1 . a second filament consists of a @xmath1630-long arc spanning @xmath17240 at @xmath18 to 40 . the radial velocity of this feature increases systematically from 0 km s@xmath11 at @xmath19 , @xmath20 to + 18 km s@xmath11 at @xmath21 , @xmath22 . both features have rather constant intensities along their entire lengths , ranging from 0.51.5 r ( em = 13 @xmath23 pc ) with no obvious trends .

figure [ fig : images ] displays four velocity integrated images of h@xmath0 emission from our selected region of the sky . the two filaments of interest are most easily seen in the narrow ( 12 km s@xmath11 ) velocity interval images , although their overall structure can also be seen on the `` broad - band '' map ( figure [ fig : images]a ) . the vertical portion of the longest filament ( hereafter filament 1 ) is most prominent in the map centered on @xmath51 km s@xmath11 ( figure [ fig : images]d ) , stretching nearly perpendicular to the galactic plane along @xmath3 . it then extends toward higher galactic longitudes , turning over near @xmath52 while shifting to more negative velocities in figures [ fig : images]c and [ fig : images]b . a second long filament ( filament 2 ) can been seen as an arc extending across the images near @xmath18 to @xmath53 . its peak emission moves from @xmath54 in the @xmath14 km s@xmath11 map ( figure [ fig : images]b ) to @xmath55 in the @xmath51 km s@xmath11 map ( figure [ fig : images]d ) . other filaments are also apparent , including the feature running from @xmath56 , @xmath57 to @xmath54 , @xmath58 . in this letter we focus primarily on the 80-long filament 1 . an @xmath27-@xmath59 map is presented in figure [ fig : lv / bcut ] along @xmath60 . from this representation , filament 1 appears to be a narrow ( @xmath61 ) feature at @xmath3 that is offset in velocity from the smooth emission present near the lsr at other galactic longitudes . an analysis of the spectra reveal that this velocity offset is about @xmath62 km s@xmath11 . the spectrum of filament 1 averaged over six of the wham pointings taken around @xmath63 , @xmath64 is displayed in figure [ fig : spectra ] as a dashed line . because the velocity separation of the two components ( @xmath65 km s@xmath11 ) is less than the typical doppler width of wim h@xmath0 lines ( fwhm @xmath66 30 km s@xmath11 ) , a straightforward two - component fit of this spectrum is not well constrained . instead , we attempt to isolate the filament from gas near the lsr by subtracting an estimate of the general wim contribution in this direction . the spectra of two `` background '' regions taken at the same galactic latitude are also displayed in figure [ fig : spectra ] as dotted lines . these directions are averages of nine pointings around @xmath67 , @xmath64 and 12 pointings around @xmath68 , @xmath64 . an average of these spectra is subtracted from the average filament spectrum to produce the final filament - only spectrum in figure [ fig : spectra ] ( solid line ) . the resulting component is fit well by a single gaussian with a mean of @xmath69 km s@xmath11 , a fwhm of @xmath70 km s@xmath11 , and an intensity of @xmath71 r. using this method , we have determined fit parameters for several directions along filament 1 and 2 and present the results in table [ tab : params ] . regions where the filaments cross are deliberately excluded . the accuracy of the filament component parameters depends primarily on how well the background regions represent the true emission near @xmath72 km s@xmath11 in the filament direction . the errors of the parameters listed in table [ tab : params ] are conservatively estimated by examining subtractions of different background directions from the filament spectra . the fitting errors are an order of magnitude smaller and do not contribute significantly . note the velocity gradients in both filaments with increasing galactic longitude , decreasing from @xmath73 @xmath62 km s@xmath11 to @xmath74 km s@xmath11 in filament 1 and increasing from @xmath73 @xmath75 km s@xmath11 to @xmath62 km s@xmath11 in filament 2 . also note the nearly constant h@xmath0 intensities and line widths .

where this feature appears to meet the galactic plane near @xmath15 , it is directly above the region surrounding cma r1/ob1 . a second filament consists of a @xmath1630-long arc spanning @xmath17240 at @xmath18 to 40 . both features have rather constant intensities along their entire lengths , ranging from 0.51.5 r ( em = 13 @xmath23 pc ) with no obvious trends .

c

astro-ph9805151

during the initial data reduction of the wisconsin h - alpha mapper ( wham ) h@xmath0 sky survey , we have discovered several very long ( @xmath180 ) filaments superimposed on the diffuse h@xmath0 background . these features have no clear correspondence to the other phases of the interstellar medium revealed by 21 cm , x - ray , ir , or radio continuum surveys , and they have no readily identifiable origin or source of ionization . in this letter , the data for two of these faint ( @xmath2 0.51.5 r ) structures are presented . the first is an 80-long , 2-wide arch that extends nearly perpendicular to the galactic plane at @xmath3 and attains a maximum latitude of @xmath4 near @xmath5 before reaching the southern boundary of our survey map at @xmath6 , @xmath7 . the vertical portion of this feature between @xmath8 and @xmath9 is associated with a single radial velocity component centered at @xmath10 km s@xmath11 with a full width at half maximum of 27 km s@xmath11 . a decrease in the velocity is observed from @xmath12 through @xmath13 as the feature arches toward higher galactic longitudes . at this end , the emission component is centered near @xmath14 km s@xmath11 . where this feature appears to meet the galactic plane near @xmath15 , it is directly above the region surrounding cma r1/ob1 . a second filament consists of a @xmath1630-long arc spanning @xmath17240 at @xmath18 to 40 . the radial velocity of this feature increases systematically from 0 km s@xmath11 at @xmath19 , @xmath20 to + 18 km s@xmath11 at @xmath21 , @xmath22 . both features have rather constant intensities along their entire lengths , ranging from 0.51.5 r ( em = 13 @xmath23 pc ) with no obvious trends .

the intensities in table [ tab : params ] are converted to emission measures using the formula : @xmath76 where @xmath77 represents the temperature of the emitting gas in units of @xmath78 k. with typical values for the temperature of the wim gas , @xmath79 ( @xcite ) , an h@xmath0 intensity of 1 r corresponds to an em of 2.25 @xmath23 pc . since we are examining mostly high - latitude features , we expect corrections for interstellar extinction to be small . no such correction has been applied to the data presented here . to derive further physical parameters for the filaments , we must make an assumption about the distances to them . some evidence suggests that the lower part of filament 1 is at a distance of about 1 kpc , based on its radial velocity and possible association with cma r1/ob1 . the lower portion has a radial velocity of @xmath80 km s@xmath11 , which is consistent with a kinematic distance of approximately 1 kpc at this galactic longitude for a value of oort s constant @xmath81 km s@xmath11 kpc@xmath11 ( @xcite ) . unfortunately , this argument is weakened by the radial velocities of the filament s high - latitude portion , which are `` forbidden '' in the galactic rotation model . however , in figure [ fig : images]d ( @xmath51 km s@xmath11 ) , the vertical portion of filament 1 appears to end in the prominent region surrounding the star - forming association cma r1/ob1 . in fact , the center of the brighter , arc - shaped , h@xmath0 emission features in this region , as seen on the palomar sky survey red plates , is at @xmath3 , @xmath82 ( @xcite ) . also , the velocity centroid of the region ( table [ tab : params ] ) is similar to that of the first 1520 of the filament away from the plane . unless the agreement between the spatial and velocity information of these two regions is a coincidence , we can use the distance of the region as an estimate of the distance to the filament . the distance to the cma ob1 association has been determined photometrically by clari ( 1974 ) to be @xmath83 pc , consistent with a kinematic distance of 800 - 1100 pc for the h@xmath0 emitting gas in the region ( @xcite ) . in this letter , we adopt a distance of 1 kpc for filament 1 but include @xmath84 kpc in the derived parameters . at a distance of 1 kpc , the vertical extent of filament 1 ( @xmath85 ) translates to a vertical height above the galactic mid - plane , @xmath86 , of @xmath87 pc and a width ( @xmath88 ) of @xmath89 pc . if we assume the filament is a cylinder of uniform density gas of width @xmath90 , then the emission measure , @xmath91 of the feature can be used to estimate the density . for filament 1 , where @xmath92 pc and @xmath93 @xmath23 pc , @xmath94 @xmath95 . the typical column density through the filament is @xmath96 @xmath30 . the mass of the material in the filament s vertical section can be estimated by @xmath97 m@xmath98 , where the factor 1.4 is a correction for helium . if the filament is photoionized , our observed em implies an incident ionizing flux of at least @xmath99 ph @xmath30 s@xmath11 . the hydrogen recombination rate within the filament is given by @xmath100 @xmath95 s@xmath11 , implying that the power required to sustain this rate throughout the volume of the filament is @xmath101 erg s@xmath11 . the value of @xmath102 used in these calculations , @xmath103 @xmath104 sec@xmath11 , is interpolated from osterbrock ( 1989 ) assuming a gas temperature of 8000 k. the narrow shape and location of filament 1 , particularly the coincidence in location and radial velocity of one end of the filament with an energetic source in the plane ( cma r1/ob1 ) , suggest one possibility for its origin a jet - like ejection from the association . however , given the length of the filament at the distance of cma r1/ob1 , the apparently low velocities associated with it ( table [ tab : params ] ) , and the near constant h@xmath0 intensity profile along its entire length , it is difficult to reconcile a scenario in which ionized hydrogen is being ejected from cma r1/ob1 with the gas s short recombination times . a parcel of ionized gas at these temperatures and densities will recombine in @xmath105 yr . to reach the observed height and remain ionized , the gas would need to be ejected at speeds in excess of @xmath106 km s@xmath11 . we see no evidence for such speeds in our data . furthermore , we would expect a significant gradient in the filament s intensity as a function of height above the galactic plane , since gas at larger distances from the plane has had more time to recombine . if another source is responsible for maintaining the ionization of filament 1 , an ejection scenario could still be plausible . if the filament s arc shape is caused by free - fall of ejected gas back to the galactic plane , an initial velocity of about 70 km s@xmath11 is required to reach the observed height above the plane at the distance of cma r1/ob1 . such speeds agree better with the measured filament component velocities in table [ tab : params ] , particularly when projection effects are considered . however , the filament s length would then require that the ejecting source be more than @xmath107 yr old . this number can be compared to estimates of @xmath108 yr for the age of cma ob1 by clari ( 1974 ) and @xmath109 yr for the age of a supernova put forth by herbst & assousa ( 1977 ) as being responsible for generating the ring - shaped h@xmath0 nebulosity in the vicinity of cma ob1/r1 and for being the progenitor of star formation in the r1 association . in this scenario , a diffuse ionization source is probably required to maintain a constant intensity along the filament , since the growing distance from cma r1/ob1 would produce an intensity gradient if it were the sole source . the efficiency of leaking lyman continuum radiation from the disk is a longstanding problem for ionizing a thicker layer of the galaxy . however , bland - hawthorn & maloney ( 1998 ) , dove & shull ( 1994 ) , and miller & cox ( 1993 ) have argued that a substantial ionizing flux can diffuse into the galaxy s halo from the disk . the required ionizing flux of at least @xmath110 ph @xmath30 s@xmath11 is consistent with these models . several other phenomena may produce large , faint filaments . large - scale , kinematic galactic structures such as superbubbles , chimneys , or worms have been popular explanations for filamentary structures seen in as well as h@xmath0 ( _ e.g. _ @xcite ; @xcite ) . the velocity gradient of filament 1 is outside the range expected from a simple model of galactic rotation and therefore may be evidence for a dynamical influence on the filament . however , the observed velocity gradient is inconsistent with this feature being the edge of an expanding shell , since a shell s projected edges should be at a constant radial velocity . furthermore , for the two cases presented here , we find no obvious correlation between these h@xmath0 filaments and emission at other wavelengths , including 21 cm , rosat all - sky survey x - ray , and iras bands , making it difficult to relate them to previously identified `` worms '' and superbubbles . since the leiden / dwingeloo survey is sensitive to below @xmath111 @xmath30 ( @xcite ) , the ionized column density of the filament , @xmath112 @xmath30 , suggests that the gas is fully ionized . other possibilities include a suggestion by dupree & raymond ( 1983 ) that faint , ionized trails of ionized hydrogen could be produced by high - velocity white dwarfs . however , the recombination time discussed above suggests unreasonable velocities for the star . in summary , we present the discovery of two long , faint h@xmath0 filaments at high latitudes from the wham h@xmath0 survey . their origin is not yet identified , but the existence of such features may help to explain processes responsible for the maintenance of the general wim layer . as additional portions of the h@xmath0 survey are reduced , new clues about the nature of these structures may be revealed . we plan to follow these observations with [ ] and [ ] observations of this region . additional observations will provide information about the gas s temperature and ionization state , which are useful in narrowing the kinds of processes that can be producing these filaments . we thank kurt jaehnig and jeff percival of the university of wisconsin s _ space astronomy lab _ for their dedicated engineering support of wham ; nikki hausen , mark quigley , and brian babler for data reduction support ; and trudy tilleman for essential night - sky condition reports from kitt peak , which have made remote observing possible . we acknowledge the use of nasa s _ skyview _ facility ( http://skyview.gsfc.nasa.gov ) , located at nasa goddard space flight center and the simbad database , operated at cds , strasbourg , france . this work is supported by the national science foundation through grants ast9619424 and ast9122701 .

electron spin diffusion is investigated in monolayer mos@xmath0 in the absence of external electric and magnetic fields . the electron - impurity scattering , which is shown to play a negligible role in spin relaxation in time domain in this material , has a marked effect on the in - plane spin diffusion due to the anisotropic spin precession frequency in the spatial domain . with the electron - impurity and inter - valley electron - phonon scatterings separately included in the scattering term , we study the intra- and inter - valley diffusion processes of the in - plane spins by analytically solving the kinetic spin bloch equations . the intra - valley process is found to be dominant in the in - plane spin diffusion , in contrast to the case of spin relaxation in time domain , where the inter - valley process can be comparable to or even more important than the intra - valley one . for the intra - valley process , we find that the in - plane spin diffusion is suppressed with the increase of impurity density but effectively enhanced by increasing electron density in both the degenerate and nondegenerate limits . interestingly , we find that in the nondegenerate limit , the intra - valley spin diffusion length presents an opposite trend in the electron density dependence compared to the one with only electron - impurity scattering .

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1403.5629

electron spin diffusion is investigated in monolayer mos@xmath0 in the absence of external electric and magnetic fields . the electron - impurity scattering , which is shown to play a negligible role in spin relaxation in time domain in this material , has a marked effect on the in - plane spin diffusion due to the anisotropic spin precession frequency in the spatial domain . with the electron - impurity and inter - valley electron - phonon scatterings separately included in the scattering term , we study the intra- and inter - valley diffusion processes of the in - plane spins by analytically solving the kinetic spin bloch equations . the intra - valley process is found to be dominant in the in - plane spin diffusion , in contrast to the case of spin relaxation in time domain , where the inter - valley process can be comparable to or even more important than the intra - valley one . for the intra - valley process , we find that the in - plane spin diffusion is suppressed with the increase of impurity density but effectively enhanced by increasing electron density in both the degenerate and nondegenerate limits . we also take into account the electron - electron coulomb scattering in the intra - valley process . interestingly , we find that in the nondegenerate limit , the intra - valley spin diffusion length presents an opposite trend in the electron density dependence compared to the one with only electron - impurity scattering .

monolayer mos@xmath0 has attracted much attention due to its promising applications in electronics,@xcite optoelectronics,@xcite valleytronics@xcite and also spintronics.@xcite for the application of spintronic devices , the suitable spin lifetime and spin diffusion length are required.@xcite this indicates the importance of the investigations on the spin relaxation and spin diffusion in this material . very recently , spin relaxation has been studied in monolayer mos@xmath0.@xcite wang and wu@xcite calculated the in - plane spin relaxation time of electrons due to the dyakonov - perel@xcite ( dp ) and elliot - yafet@xcite ( ey ) mechanisms with the intra- and inter - valley processes included . they pointed out that the dp mechanism , which results from the inhomogeneous broadening@xcite together with any scattering process , dominates the spin relaxation . the inhomogeneous broadening is from the spin - orbit coupling ( soc ) of the conduction band@xcite @xmath1\hat{\bf z } , \label{soctime}\ ] ] where the @xmath2-axis is perpendicular to the monolayer mos@xmath0 plane ; @xmath3 , @xmath4 and @xmath5 are the strengths of the soc ; @xmath6 represents the k(k@xmath7 ) valley . the first term of the soc , which is momentum independent , only induces the inter - valley dp spin relaxation whereas the last two terms are momentum dependent , which lead to the intra- and inter - valley spin relaxation processes . in addition , as only the last term ( i.e. , negligible anisotropic cubic one ) causes the dp spin relaxation with the electron - impurity scattering , the electron - impurity scattering is shown to play a marginal role in the spin relaxation.@xcite in contrast to the spin relaxation in time domain , the inhomogeneous broadening in spin diffusion for in - plane spins is determined by the spin precession frequency@xcite @xmath8\hat{\bf z } \label{socspatial}\ ] ] when the spin diffusion is along the @xmath9-axis . here , @xmath10 stands for the effective mass . due to the existence of @xmath11 , all three terms become momentum dependent , which can induce the intra- and inter - valley relaxations for in - plane spins along the diffusion . this is different from the case of the spin relaxation in time domain as previously mentioned . in addition , @xmath11 also makes the first two terms ( i.e. , the leading ones ) anisotropic . this suggests that the electron - impurity scattering may play an important role in the in - plane spin diffusion , which is of great difference from the case of the spin relaxation in time domain in monolayer mos@xmath0,@xcite but similar to the case of the spin diffusion in semiconductors@xcite and single - layer graphene.@xcite as for the out - of - plane spins , the spin diffusion length is infinite since the spin precession frequency @xmath12 [ see eq . ( [ socspatial ] ) ] is along the out - of - plane direction . however , this is not the case in the presence of an out - of - plane electric field . very recently , bishnoi and ghosh@xcite investigated the out - of - plane spin diffusion with this electric field applied . they showed that the out - of - plane spins relax during the spin diffusion since the out - of - plane electric field induces a rashba soc , which provides an inhomogeneous broadening in the spatial domain for out - of - plane spins.@xcite however , the rashba soc they used is incomplete according to the recent work by kormnyos _ et al._.@xcite in addition , the electron - electron coulomb and electron - impurity scatterings , which have been shown to play an important role in spin diffusion in semiconductors@xcite and single - layer graphene,@xcite are absent in their work.@xcite moreover , they also overlooked the inter - valley electron - phonon scattering , which is of crucial importance in spin relaxation in time domain.@xcite it is noted that in addition to the out - of - plane electric field , an in - plane magnetic field can also lead to the out - of - plane spin relaxation along the spin diffusion.@xcite this is because the in - plane magnetic field ( * b * ) gives rise to a spin precession frequency in the spatial domain as @xmath13 , which provides an inhomogeneous broadening for out - of - plane spins during the spin diffusion . in this work , we investigate the electron spin diffusion in monolayer mos@xmath0 in the absence of the external electric and magnetic fields . as the contribution of the spin - flip scattering due to the ey mechanism is negligible,@xcite we only take into account the spin conserving scattering . with the electron - impurity ( inter - valley electron - phonon ) scattering included , the intra - valley ( inter - valley ) diffusion process for in - plane spins is studied by analytically solving the kinetic spin bloch equations ( ksbes).@xcite we find that the intra - valley process dominates the in - plane spin diffusion , which is very different from the case of the spin relaxation in time domain in monolayer mos@xmath0 where the inter - valley process can be comparable to or even more important than the intra - valley one.@xcite moreover , it is shown that the in - plane spin diffusion length decreases with the increase of the impurity density but increases with increasing electron density in both the degenerate and nondegenerate limits . very interestingly , with the electron - electron coulomb scattering further taken into account , the in - plane spin diffusion length shows an opposite electron density dependence in the nondegenerate limit compared to the one with only the electron - impurity scattering . this paper is organized as follows . in sec . ii , we introduce our model and the ksbes . in sec . iii , we investigate the in - plane spin diffusion by analytically solving the ksbes . we summarize in sec . iv .

email is a ubiquitous communications tool in the workplace and plays an important role in social interactions . previous studies of email were largely based on surveys and limited to relatively small populations of email users within organizations . in this paper , we report results of a large - scale study of more than 2 million users exchanging 16 billion emails over several months . we quantitatively characterize the replying behavior in conversations within pairs of users . in particular , we study the time it takes the user to reply to a received message and the length of the reply sent . we consider a variety of factors that affect the reply time and length , such as the stage of the conversation , user demographics , and use of portable devices . in addition , we study how increasing load affects emailing behavior . however , their responsiveness remains intact , and they may even reply to emails faster . finally , we predict the time to reply , length of reply , and whether the reply ends a conversation . our findings have important implications for understanding human behavior and designing better email management applications for tasks like ranking unread emails .

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1504.00704

email is a ubiquitous communications tool in the workplace and plays an important role in social interactions . previous studies of email were largely based on surveys and limited to relatively small populations of email users within organizations . in this paper , we report results of a large - scale study of more than 2 million users exchanging 16 billion emails over several months . we quantitatively characterize the replying behavior in conversations within pairs of users . in particular , we study the time it takes the user to reply to a received message and the length of the reply sent . we consider a variety of factors that affect the reply time and length , such as the stage of the conversation , user demographics , and use of portable devices . in addition , we study how increasing load affects emailing behavior . we find that as users receive more email messages in a day , they reply to a smaller fraction of them , using shorter replies . however , their responsiveness remains intact , and they may even reply to emails faster . finally , we predict the time to reply , length of reply , and whether the reply ends a conversation . we demonstrate considerable improvement over the baseline in all three prediction tasks , showing the significant role that the factors that we uncover play , in determining replying behavior . we rank these factors based on their predictive power . our findings have important implications for understanding human behavior and designing better email management applications for tasks like ranking unread emails . [ communications applications ]

electronic mail email remains an essential tool for social interactions and a popular platform for computer - mediated communication . it is used within organizations to exchange information and coordinate action , but also by ordinary people to converse with friends . patterns of email interactions reveal circadian rhythms @xcite and bursty dynamics of human activity @xcite , and the structure of evolving conversations @xcite . understanding how these patterns shape email use is necessary for designing the next generation of interaction tools that will improve the efficiency of communication and coordination in social groups . early studies of email examined how people process @xcite , organize @xcite , and respond @xcite to email messages . by surveying users within organizations , researchers uncovered common email triage strategies , with some users processing emails serially , while others read and reply to important messages first @xcite . those studies had relatively small sample sizes and were limited by their methodology to answering qualitative questions about email behavior . as a result , we do not have answers to a number of questions about how people use email . how many email conversations do people have ? how long are these conversations and how do they end ? when do people respond to a message in a conversation ? do they adapt their replies to the behavior of their conversation partner ? furthermore , as the volume of email has increased steadily over the years , the concept of `` email overload '' has grown in prominence . dabbish & kraut @xcite defined `` email overload '' as _ `` email users perceptions that their own use of email has gotten out of control because they receive and send more email than they can handle , find , or process effectively.''_. this motivates a whole set of questions that have been recently addressed in the setting of online social networks @xcite , but never fully in the context of email . how does the volume of incoming email , information or email load , affect user behavior ? how do people compensate for the increased load : do they take longer to reply , or do they send shorter replies that take less time to compose ? we address these questions with a largest study to date of email conversations ( 16b emails ) . we focus our analyses on the replying behavior within _ dyadic interactions _ , i.e. , conversations between pairs of users . specifically , we measure the time a user takes to reply to a message , the length of the reply , as well as the fraction of messages a user replies to . first , we empirically characterize replying behavior in email conversations in a large population of users , and also how these behaviors vary by gender and age . although we find no significant variation due to gender , we find that younger email users reply faster and write shorter replies than older users . next , we study how email load , measured by the number of received email messages , affects replying behavior . we find that while users attempt to adapt to the rising information load by replying to more emails , they do not adequately compensate . as email load increases , they reply faster but to a decreasing fraction of incoming emails . these findings suggest that email overload is a problem , with users generally unable to keep up with rising load . we also study how replying behavior evolves over the course of a conversation . we find that users initially synchronize their behaviors , with reply times and length of replies becoming more similar in the first half of the conversation . however , they become desynchronized in the second half of the conversation . in contrast , users continue to coordinate their linguistic styles , as messages exchanged over the course of the entire conversation become more similar in content and style . finally , we develop a model to predict users replying behavior in a conversation , namely , how long it will take the user to reply to a message , the length of the reply , and if the reply will end the thread . the features that we use for prediction include history of communication between the users , user demographics , email load , as well as the day of the week and time the message was received . our predictive model considerably outperforms the baseline in all three cases . we obtain accuracy of 58.8% for reply time , which is a 67.1% relative improvement over the baseline , and 71.8% accuracy for length of replies ( 113.7% relative improvement over the baseline ) . we also predict the last email of the thread with accuracy of 65.9% , a 30.2% relative improvement over the baseline . ability to accurately predict what messages a user will reply to can be used by email clients to rank emails in the users inbox by their replying priority , thus helping ease the burden of information overload . the key contributions of our work are : 1 . we empirically characterize email _ replying behavior _ of users , focusing on reply time , length of the reply , and the correlation between them . we quantify how different factors , including the day and time the message was received , the device used , the number of attachments in the email , and user demographics affect replying . we show that _ email overload _ is evident in email usage and has adverse effects , resulting in users replying to a smaller fraction of received emails . users tend to send shorter replies , but with shorter delays when receiving many emails . we find that different age groups cope with overload differently : younger users shorten their replies , while older users reply to smaller fraction of received messages . we find evidence of _ synchronization _ in dyadic interactions within a thread : users become more similar in terms of reply time and length of replies until the middle of a thread , and start acting more independently after that . 4 . we can predict reply time and length , and the last email in a thread with a much higher accuracy than the baseline . this has important implications for designing future email clients .

entropy , under a variety of names , has long been used as a measure of diversity in ecology , as well as in genetics , economics and other fields . leinster and cobbold @xcite proposed a one - parameter family of diversity measures taking into account both this variation and the varying similarities between species . because of this latter feature , diversity is not maximized by the uniform distribution on species . thus , there is a single distribution that maximizes diversity from all viewpoints simultaneously , and any list of species has an unambiguous maximum diversity value . + although we phrase our results in ecological terms , they apply very widely , with applications in graph theory and metric geometry .

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1512.06314

entropy , under a variety of names , has long been used as a measure of diversity in ecology , as well as in genetics , economics and other fields . there is a spectrum of viewpoints on diversity , indexed by a real parameter @xmath0 giving greater or lesser importance to rare species . leinster and cobbold @xcite proposed a one - parameter family of diversity measures taking into account both this variation and the varying similarities between species . because of this latter feature , diversity is not maximized by the uniform distribution on species . so it is natural to ask : which distributions maximize diversity , and what is its maximum value ? + in principle , both answers depend on @xmath0 , but our main theorem is that neither does . thus , there is a single distribution that maximizes diversity from all viewpoints simultaneously , and any list of species has an unambiguous maximum diversity value . furthermore , the maximizing distribution(s ) can be computed in finite time , and any distribution maximizing diversity from some particular viewpoint @xmath1 actually maximizes diversity for all @xmath0 . + although we phrase our results in ecological terms , they apply very widely , with applications in graph theory and metric geometry .

for decades , ecologists have used entropy - like quantities as measures of biological diversity . the basic premise is that given a biological community or ecosystem containing @xmath2 species in proportions @xmath3 , the entropy of the probability distribution @xmath4 indicates the extent to which the community is balanced or ` diverse ' . shannon entropy itself is often used ; so too are many variants , as we shall see . but almost all of them share the property that for a fixed number @xmath2 of species , the entropy is maximized by the uniform distribution @xmath5 . however , there is a growing appreciation that this crude model of a biological community is too far from reality , in that it takes no notice of the varying similarities between species . for instance , we would intuitively judge a meadow to be more diverse if it consisted of ten dramatically different plant species than if it consisted of ten species of grass . this has led to the introduction of measures that do take into account inter - species similarities @xcite . in mathematical terms , making this refinement essentially means extending the classical notion of entropy from probability distributions on a finite set to probability distributions on a finite metric space . the maximum entropy problem now becomes more interesting . consider , for instance , a pond community consisting of two very similar species of frog and one species of newt . we would not expect the maximum entropy ( or diversity ) to be achieved by the uniform distribution @xmath6 , since the community would then be @xmath7 frog and only @xmath8 newt . we might expect the maximizing distribution to be closer to @xmath9 ; the exact answer should depend on the degrees of similarity of the species involved . we return to this scenario in example [ eg : three ] . for the sake of concreteness , this paper is written in terms of an ecological scenario : a community of organisms classified into species . however , nothing that we do is intrinsically ecological , or indeed connected to any specific branch of science . our results apply equally to any collection of objects classified into types . it is well understood that shannon entropy is just one point ( albeit a special one ) on a continuous spectrum of entropies , indexed by a parameter @xmath10 $ ] . this spectrum has been presented in at least two ways : as the rnyi entropies @xmath11 @xcite and as the so - called tsallis entropies @xmath12 ( actually introduced as biodiversity measures by patil and taillie prior to tsallis s work in physics , and earlier still in information theory @xcite ) : @xmath13 both @xmath11 and @xmath12 converge to shannon entropy as @xmath14 . moreover , @xmath11 and @xmath12 can be obtained from one another by an increasing invertible transformation , and in this sense are interchangeable . when @xmath11 or @xmath12 is used as a diversity measure , @xmath0 controls the weight attached to rare species , with @xmath15 giving as much importance to rare species as common ones , and the limiting case @xmath16 reflecting only the prevalence of the most common species . different values of @xmath0 produce genuinely different judgements on which of two distributions is the more diverse . for instance , if over time a community loses some species but becomes more balanced , then the rnyi and tsallis entropies decrease for @xmath15 but increase for @xmath16 . varying @xmath0 therefore allows us to incorporate a spectrum of viewpoints on the meaning of the word ` diversity ' . here we use the diversity measures introduced by leinster and cobbold @xcite , which both ( i ) reflect this spectrum of viewpoints by including the variable parameter @xmath0 , and ( ii ) take into account the varying similarities between species . we review these measures in sections [ sec : spectrum][sec : measures ] . in the extreme case where different species are assumed to have nothing whatsoever in common , they reduce to the exponentials of the rnyi entropies , and in other special cases they reduce to other diversity measures used by ecologists . in practical terms , the measures of @xcite have been used to assess a variety of ecological systems , from communities of microbes @xcite and crustacean zooplankton @xcite to alpine plants @xcite and arctic predators @xcite , as well as being applied in non - biological contexts such as computer network security @xcite . mathematically , the set - up is as follows . a biological community is modelled as a probability distribution @xmath17 ( representing the proportions of species ) together with an @xmath18 matrix @xmath19 ( whose @xmath20-entry represents the similarity between species @xmath21 and @xmath22 ) . from this data , a formula gives a real number @xmath23 for each @xmath10 $ ] , called the ` diversity of order @xmath0 ' of the community . as for the rnyi entropies , different values of @xmath0 make different judgements : for instance , it may be that for two distributions @xmath24 and @xmath25 , @xmath26 now consider the maximum diversity problem . fix a list of species whose similarities to one another are known ; that is , fix a matrix @xmath19 ( subject to hypotheses to be discussed ) . the two basic questions are : * which distribution(s ) @xmath24 maximize the diversity @xmath23 of order @xmath0 ? * what is the value of the maximum diversity @xmath27 ? this can be interpreted ecologically as follows : if we have a fixed list of species and complete control over their abundances within our community , how should we choose those abundances in order to maximize the diversity , and how large can we make that diversity ? in principle , both answers depend on @xmath0 . after all , we have seen that if distributions are ranked by diversity then the ranking varies according to the value of @xmath0 chosen . but our main theorem is that , in fact , both answers are _ independent _ of @xmath0 : * * theorem [ thm : main ] ( main theorem)**__there exists a probability distribution on @xmath28 that maximizes @xmath29 for all @xmath10 $ ] . moreover , the maximum diversity @xmath27 is independent of @xmath10 $ ] . _ _ so , there is a ` best of all possible worlds ' : a distribution that maximizes diversity no matter what viewpoint one takes on the relative importance of rare and common species . this theorem merely asserts the _ existence _ of a maximizing distribution . however , a second theorem describes how to _ compute _ all maximizing distributions , and the maximum diversity , in a finite number of steps ( theorem [ thm : comp ] ) . better still , if by some means we have found a distribution @xmath24 that maximizes the diversity of _ some _ order @xmath1 , then a further result asserts that @xmath24 maximizes diversity of _ all _ orders ( corollary [ cor : irrelevance ] ) . for instance , it is often easiest to find a maximizing distribution for diversity of order @xmath30 ( as in example [ eg : naive ] and proposition [ propn : graph - main ] ) , and it is then automatic that this distribution maximizes diversity of all orders . let us put these results into context . first , they belong to the huge body of work on maximum entropy problems . for example , the normal distribution has the maximum entropy among all probability distributions on @xmath31 with a given mean and variance , a property which is intimately connected with its appearance in the central limit theorem . this alone would be enough motivation to seek maximum entropy distributions in other settings ( such as the one at hand ) , quite apart from the importance of maximum entropy in thermodynamics , machine learning , macroecology , and so on . second , we will see that maximum diversity is very closely related to the emerging invariant known as magnitude . this is defined in the extremely wide generality of enriched category theory ( * ? ? ? * section 1 ) , and specializes in interesting ways in a variety of mathematical fields . for instance , it automatically produces a notion of the euler characteristic of an ( ordinary ) category , closely related to topological euler characteristic @xcite ; in the context of metric spaces , magnitude encodes geometric information such as volume and dimension @xcite ; in graph theory , magnitude is a new invariant that turns out to be related to a graded homology theory for graphs @xcite ; and in algebra , magnitude produces an invariant of associative algebras that can be understood as a homological euler characteristic @xcite . this work is self - contained . to that end , we begin by explaining and defining the diversity measures in @xcite ( sections [ sec : spectrum][sec : measures ] ) . then come the results : preparatory lemmas in section [ sec : invt ] , and the main results in sections [ sec : main ] and [ sec : comp ] . examples are given in sections [ sec : examples - simple][sec : examples - pos - def ] , including results on special cases such as when the similarity matrix @xmath19 is either the adjacency matrix of a graph or positive definite . perhaps counterintuitively , a distribution that maximizes diversity can eliminate some species entirely . this is addressed in section [ sec : elim ] , where we derive necessary and sufficient conditions on @xmath19 for maximization to preserve all species . finally , we state some open questions ( section [ sec : questions ] ) . the main results of this paper previously appeared in a preprint of leinster @xcite , but the proofs we present here are substantially simpler . of the new results , lemma [ lemma : elim - main ] ( the key to our results on preservation of species by maximizing distributions ) borrows heavily from an argument of fremlin and talagrand @xcite . [ [ p : conventions ] ] conventions + + + + + + + + + + + a vector @xmath32 is * nonnegative * if @xmath33 for all @xmath21 , and * positive * if @xmath34 for all @xmath21 . the * support * of @xmath35 is @xmath36 and @xmath37 has * full support * if @xmath38 . a real symmetric @xmath18 matrix @xmath19 is * positive semidefinite * if @xmath39 for all @xmath40 , and * positive definite * if this inequality is strict .

existing data on @xmath0cu - nuclear spin relaxation reveal two independent relaxation processes : the one that is temperature independent we link to incommensurate peaks seen by neutrons , while the universal temperature dependent contribution coincides with @xmath1 for two - chain ybco 124 . we argue that this new result substitutes for a pseudogap regime in a broad class of high-@xmath2 cuprates and stems from the 1st order phase transition that starts well above the superconductivity @xmath2 but becomes frustrated because of broken electroneutrality in the cuo@xmath3 plane .

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cond-mat0402589

existing data on @xmath0cu - nuclear spin relaxation reveal two independent relaxation processes : the one that is temperature independent we link to incommensurate peaks seen by neutrons , while the universal temperature dependent contribution coincides with @xmath1 for two - chain ybco 124 . we argue that this new result substitutes for a pseudogap regime in a broad class of high-@xmath2 cuprates and stems from the 1st order phase transition that starts well above the superconductivity @xmath2 but becomes frustrated because of broken electroneutrality in the cuo@xmath3 plane . superconductivity , pseudogap , magnetic properties , nmr

we attempt below to put the results in the context of a phase separation @xcite . the decomposition of @xmath11 into two terms , as it will be discussed below in more details , manifests itself in a broad temperature interval above @xmath2 . it is limited from above by a @xmath12 that depends on the concentration , @xmath6 . we consider @xmath12 defined in this way as a temperature of a 1st order phase transition , which , however , can not complete itself in spatial coexistence of two phases because of the electroneutrality condition @xcite . it was already argued in @xcite that such a frustrated 1st order phase transition may actually bear a dynamical character . the fact that a single resonant frequency for the @xmath0cu nuclear spin is observed in the nmr experiments , confirms this suggestion . although in what follows , we use the notions of the lattice model @xcite , even purely electronic models @xcite for cuprates may reveal a tendency to phase separation . the basic assumption in @xcite are the following . at large enough doping holes move between coppers and oxygens . spins in the system are @xmath13-holes trapped to the cu - sites at the expense of local lattice distorsions . elastic attractive interactions between these distorsions give rise to a lattice driven frustrated transition below some @xmath12 . exchange interactions , as in the parent la@xmath14cuo@xmath10 , tend to organize the cu - spins in the antiferromagnetic ( af ) sub - phases . excess charge of the dopants ions in af regions must be compensated by accumulation of holes in metallic regions . we now turn to experimental data . in what follows we address only @xmath15 behaviour because for cuprates af fluctuations prevail over the korringa mechanisms . in fig . 1a we collected data on @xmath16 in lsco from @xcite . note the following : 1 ) according to @xcite @xmath1 at higher temperatures tends to 2.7 msec@xmath17 _ for all _ sr concentrations , in spite of considerable spread seen in fig . 1a . beginning of deviation from that value could serve us as a definition of @xmath18 ; 2 ) note that dissipation @xmath16 monotonically decreases from small @xmath6 to 0.24 ; 3 ) after an appropriate _ vertical _ offset all curves in fig . 1a collapse onto the @xmath19 dependence of @xmath16 for the `` optimal '' @xmath20 above 50 k ( fig . we have checked that last tendency works well for ybco ( 6.5 ) doped with ca i.e. , the data for different @xmath21 in y@xmath22ca@xmath23ba@xmath3 cu@xmath24 o@xmath25 @xcite may be put on the top of each other after proper offsets . this prompts us to verify whether same off - settings of the @xmath16 data apply to a broader group of materials . the stoichiometric yba@xmath3cu@xmath26o@xmath27 possesses no structural or defect disorder and we adjust all data to the @xmath16 behaviour for this material @xcite . 2 shows that after a vertical shift in @xmath16 all the materials indeed follow the same universal temperature dependence above their @xmath2 and below 300 k. in other words , in this temperature range the nuclear spin relaxation in these cuprates is a sum of contributions from two parallel processes : @xmath28 in eq . ( 1 ) @xmath29 depends on a material and a degree of disorder @xmath30 , but does not depend on temperature , while @xmath31 , depends only on temperature , is the same for all these compounds and coincides with the @xmath16 for the two chains ybco 124 above its @xmath2=62 k. thus , to some surprise the only pseudogap feature in the nmr data that may be discerned in fig.2 is the one for ybco 124 : a change in the temperature regime between 130 and 180 k. it would be tempting to take again this feature as a mark of the ps regime taking place now in the stoichiometric material where doping most definitely comes about as a spill - over of carriers from the cuo - chains into cuo@xmath3 planes . it is also natural to think that the number of the transferred carriers is not small : actually the low temperature hall effect measurements @xcite show a rapid increase in the number of carriers ( i.e. fermi surface size ) up to one hole per unit cell even in the single layer material like lsco , at the optimal doping @xmath32 0.15 . recall , however , that little is known for the homogeneous phase ( i.e. above @xmath18 ) . properties of both ybco 124 and the optimally doped lsco ( see @xcite for review ) are unusual and best described in a very broad temperature interval in terms of the marginal fermi liquid @xcite . we have not found a reliable experiment to define @xmath12 for these compounds and therefore leave the origin of the @xmath33-term for further discussions . the decomposition ( 1 ) into two parallel dissipation processes show that usual definitions of @xmath12 @xcite have no grounds . in fig.1a the lsco data with @xmath34 are spread even above 250 k. as a rough estimate for @xmath12 , it is much higher than the sc onset temperature . 3 presents the dependence on @xmath6 for @xmath35 in la@xmath36sr@xmath9cuo@xmath37 the inset provides the offsets ( i.e. @xmath38 terms ) for other materials . we return to discussion of fig.3 later . the observation that is central for the following is that in all the materials with non - zero @xmath35 ( see the inset in fig.3 ) incommensurate ( ic ) peaks have been observed in neutron scattering @xcite . peaks are close to the @xmath39 $ ] point : at @xmath40 $ ] and @xmath41 $ ] @xcite . we will now look for the connection between these two phenomena . we first make an attempt to agree on a semi - quantitative level the observed ic magnetic peaks in la@xmath8sr@xmath9cuo@xmath10 with the values of the first term in eq . we concentrate on la@xmath42sr@xmath43cuo@xmath10 for which the most detailed data are available @xcite . with the notation from @xcite @xmath44where @xmath45 stands for one peak , hyperfine tensor @xmath46\}^{2}$ ] and for @xmath47 we take near single peak , say @xmath48 $ ] @xmath49 ^{2}}\]]where @xmath50 and @xmath51 and @xmath52 are the correlation lengths in the two proper directions . after integration the contribution from stripes with @xmath53 along the @xmath6-direction is @xmath54\}^{2}\chi _ { peak}^{\prime \prime } \]]experimentally @xcite @xmath55 and for @xmath56 @xmath571/4 . assuming the @xmath58 dependence @xcite only for the one of @xmath59 s , @xmath51 and usingfor @xmath60 and @xmath61 the known values @xcite one obtains : @xmath62 msec@xmath17 . with the af correlation length @xmath63 4 this is the correct order of magnitude . the descending dependence of the offset ( fig.3 ) agrees qualitatively with the behavior of @xmath64 @xcite in eq.(4 ) . for a quantitative description one need to know the @xmath6-dependence for @xmath65 . such data in the absolute units are absent yet except aeppli . another fact that may underlie this behaviour is that with the _ x_-increase buckling in the cuo@xmath3-planes is known to decrease diminishing pinning effects and making the local symmetry of the cuo@xmath3-unit same as in other materials from the class with small offset in fig.3 . also , the system grows more metallic with a high holes content 31,33,34 . next comes the question concerning the origin and the role played by ic peaks and the physics of fluctuations related to them . discovery of ic spin fluctuations presented a challenge for explaining the nmr results for the oxygen spin relaxation times : hyperfine field leaks originated by the af incommensurate fluctuations , would considerably increase the oxygen s relaxation rates , but this was not seen experimentally . slichter ( see in ref.@xcite ) interpreted these contradictions in terms of discommensurations : a periodic array of soliton - like walls separating regions with a short - range af order . unlike neutrons , the nmr as a local probe , does not feel the overall periodicity . existence of stripes looks just natural in terms of a static phase separation . at doping the system ( lsco ) must screen the excess charge ( sr@xmath66-ions ) in af regions . therefore stripes of the af ordered phase must alternate with domain walls . the stripe arrangement by itself is nothing but an optimization of the competing coulomb and lattice forces @xcite . ( the phenomena is well known in physics of surface . ) stripes in a dynamical regime need better understanding . for instance , often the ic peaks are seen by neutrons only at low enough temperatures or for large energy transfer at an inelastic scattering @xcite . at low temperatures stripes may form a long - range order even in lsco ( at smaller @xmath6 , @xcite ) , breaking the symmetry of the ground state . a better example of the pinned stripe order is given by nd ( or eu)-doped lsco @xcite . ( la@xmath67nd@xmath68sr@xmath69cuo@xmath10 reproduces all features of la@xmath70sr@xmath9cuo@xmath10 , including sc and same positions for ic peaks at given @xmath6 . ) the transition into the ordered stripe phase is driven by appearance first of the lattice / charge peaks @xcite . at finite temperatures stripes could be viewed as a new type of excitations above the ordered state . on the other hand in lsco itself stripes are seen through the inelastic scattering processes for arbitrary low energy transfer even at high temperatures 100 - 300 k @xcite . while the ordered ic ground state sets in only well below , at about @xmath71 30k @xcite . this example provides the argument against treating stripes as excitations : at so high a temperature the underlying long - range ic ground state would be already melted . therefore the two - phase description seems to be closer to reality meaning that in the dynamical regime the af regions get coupled via coulomb forces with the metallic layer . note that with the further x - increase @xmath64 increases as well and saturates making it meaningless to speak in terms of a strictly monolayer wall already above @xmath72 0.14 , where @xmath73 @xcite . ( note the difference in notations for ic peaks : ( @xmath74 from @xcite equals @xmath75 from @xcite equals @xmath76 from @xcite ) . fig.3 demonstrates same tendency to increase the share of the metallic fraction with increase of sr - concentration : @xmath29 continues to drop with @xmath6 above 1/8 . coexistence of a sc and the ic af phases at low temperatures was confirmed recently by the neutron diffraction experiments @xcite for la@xmath8sr@xmath69cuo@xmath10 @xmath77 in the vortex state . ( the coexistence of sc and af formations was found also from the @xmath78sr spectra @xcite ) . the way of the coexistence of sc and the stripe order in the same sample remains unresolved : one view treats the new stripe symmetry as a superstructure superimposed on the fermi surface that changes the energy spectrum like any sdw / cdw can do it ( e.g. @xcite ) . another plausible alternative would be a spatially inhomogeneous coexistence of the nonsuperconducting ic af phase and a metallic phase with strong fluctuations .

, we found that the filament before the eruption was stable for vertical displacements , but was liable to violation of the horizontal equilibrium . [ firstpage ] sun : activity sun : filaments , prominences sun : magnetic fields infrared : stars .

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1405.5784

filament eruption on 30 april - 1 may 2010 , which shows the reconnection of one filament leg with a region far away from its initial position , is analyzed . observations from three viewpoints are used for as precise as possible measurements of endpoint coordinates . the northern leg of the erupting prominence loop jumps laterally to the latitude lower than the latitude of the originally southern endpoint . thus , the endpoints reshuffled their positions in the limb view . although this behaviour could be interpreted as the asymmetric zipping - like eruption , it does not look very likely . it seems more likely to be reconnection of the flux - rope field lines in its northern leg with ambient coronal magnetic field lines rooted in a quiet region far from the filament . from calculations of coronal potential magnetic field , we found that the filament before the eruption was stable for vertical displacements , but was liable to violation of the horizontal equilibrium . this is unusual initiation of an eruption with combination of initial horizontal and vertical flux - rope displacements showing a new unexpected possibility for the start of an eruptive event . [ firstpage ] sun : activity sun : filaments , prominences sun : magnetic fields infrared : stars .

many solar filaments ( or prominences when they are observed above the solar limb ) end their life with a sudden rapid rise called an eruption . sometimes a filament rises like an enlarging loop lying in a plane containing filament endpoints anchored in the chromosphere and the centre of the sun @xcite . a famous example suggestive of such behaviour is the eruption of the giant prominence on 28 june 1945 ( granddaddy ) observed at the high altitude observatory . some eruptive prominences deviate significantly from this plane and move in a non - radial direction @xcite . moreover , the loop may be not flat but the apex exhibits writhing motion as it rotates about the direction of ascent @xcite . there are also partial filament eruptions when only a section of a long filament starts to ascend while other parts of the filament are observed unchanged @xcite . usually a prominence stretched along the limb consists of a number of arches with feet ( called also barbs ) connected to the chromosphere like a long road bridge with several spans . after the start of ascending , the feet successively break one after another except the filament endpoints for a full eruption or feet of undisturbed filament sections for a partial eruption . of course , in real solar environment , events are often asymmetric . one leg of an eruptive prominence may be fixed to the chromosphere at the prominence endpoint while the other point connecting the prominence with the chromosphere changes its position following after successive breaking of intermediate feet . @xcite identified two types of asymmetric filament eruptions : whipping - like , where the active leg whips upward , occasionally extending high into the corona ; and zipping - like , where the visible end of the active leg moves along the polarity inversion line ( pil ) like the unfastening of a zipper . it should be noted that the visibility of a filament depends on the loading of its magnetic skeleton with dense plasma . during the asymmetric filament eruption , the active leg can either whip upward , if it is anchored at the location where the eruption initiates ; or zip away from the visible end of the active leg , where the eruption initiates , toward the invisible end of the active leg . the invisible end later becomes visible during the zipping process with mass draining down along axial filament field lines . image at 16:15 ut ( courtesy of the meudon observatory ) . the red line shows the position of the east limb for _ stereo a _ , the green line indicates the position of the west limb for _ stereo b_. the green circle shows the final position of the new filament end region before the filament faded . bottom : h@xmath0 image at 16:34 ut ( courtesy of the kanzelhoehe solar observatory ) overlaid with line - of - sight field strength from _ soho_/mdi ( only field strengths @xmath1 gauss are shown ; red negative ; blue positive ( courtesy of the _ soho_/mdi consortium ) ) . , width=317 ] while , falling back to the chromosphere , eruptive prominence material can move along pre - existing magnetic flux tubes , possibly highly stretched and deformed , which belong to the prominence magnetic skeleton , there are also indications that sometimes prominence plasma returns to the chromosphere along trajectories that were formed by reconnection of the prominence magnetic field with the ambient coronal magnetic field . @xcite reported an explosive filament eruption on 13 july 2004 in which one part of the ejecta escaped as a cme , and another one fell back onto the sun . the latter part consisted of fragments of the filament dispersed into a cloud covering almost the whole nw quadrant of the solar disk . obviously , some areas where filament fragments landed had not been connected by field lines with the filament . on 7 june 2011 , an active region filament near the west solar limb rose and erupted , hurling an enormous amount of material into the solar atmosphere @xcite . the diagonal scale of the ejecta appears at least an order of magnitude larger than the initial foot - point separation , and suggests the filament carried a very large amount of mass . a significant fraction of the prominence mass was observed falling back to the solar surface along newly reconfigured magnetic field lines . @xcite consider this event as clear evidence that large - scale re - configuration of the coronal magnetic field takes place during solar eruptions via the process of magnetic reconnection . @xcite reported a disk event on 25 october 1994 , which provided evidence for a large - scale magnetic reconnection occurring between the expanding twisted loops and overlying transequatorial loops that interconnect quiet solar regions . in this work , we analyze observations of the eruptive filament on 30 april - 1 may 2010 , which shows reconnection of one filament leg with a region far away from its initial position . in contrast to above - mentioned examples of the coronal reconnection , the erupting filament loop does not disintegrate but keeps its shape of a rather thin loop even after a fast jump of the endpoint over a distance of 0.7 solar radius @xmath2 . we calculated parameters of coronal potential magnetic field and found that the eruption began with instability not in the vertical direction , as typical for eruptive filaments , but after violation of the horizontal equilibrium .

filament eruption on 30 april - 1 may 2010 , which shows the reconnection of one filament leg with a region far away from its initial position , is analyzed . observations from three viewpoints are used for as precise as possible measurements of endpoint coordinates . the northern leg of the erupting prominence loop jumps laterally to the latitude lower than the latitude of the originally southern endpoint . thus , the endpoints reshuffled their positions in the limb view . although this behaviour could be interpreted as the asymmetric zipping - like eruption , it does not look very likely . it seems more likely to be reconnection of the flux - rope field lines in its northern leg with ambient coronal magnetic field lines rooted in a quiet region far from the filament . from calculations of coronal potential magnetic field this is unusual initiation of an eruption with combination of initial horizontal and vertical flux - rope displacements showing a new unexpected possibility for the start of an eruptive event .

i

1405.5784

filament eruption on 30 april - 1 may 2010 , which shows the reconnection of one filament leg with a region far away from its initial position , is analyzed . observations from three viewpoints are used for as precise as possible measurements of endpoint coordinates . the northern leg of the erupting prominence loop jumps laterally to the latitude lower than the latitude of the originally southern endpoint . thus , the endpoints reshuffled their positions in the limb view . although this behaviour could be interpreted as the asymmetric zipping - like eruption , it does not look very likely . it seems more likely to be reconnection of the flux - rope field lines in its northern leg with ambient coronal magnetic field lines rooted in a quiet region far from the filament . from calculations of coronal potential magnetic field , we found that the filament before the eruption was stable for vertical displacements , but was liable to violation of the horizontal equilibrium . this is unusual initiation of an eruption with combination of initial horizontal and vertical flux - rope displacements showing a new unexpected possibility for the start of an eruptive event . [ firstpage ] sun : activity sun : filaments , prominences sun : magnetic fields infrared : stars .

we studied the filament eruption on 30 april - 1 may 2010 , which shows the reconnection of one filament leg with the region far away from its initial position . observations from three viewpoints were used , namely on - disk h@xmath0 observations by the mauna loa solar observatory , culgoora solar observatory together with euv observations by _ proba2 _ and on - limb observations by _ stereo a _ and _ stereo b_. at the beginning of the event , the eruptive prominence looked like a typical one , that is as an expanding loop with anchored endpoints . then the top of the loop folded over showing writhing of the filament axis and deflected to the south during the ascending . a little later , the endpoints reshuffled their positions in the limb view . the northern leg of the erupting prominence loop jumps laterally to the latitude lower than the latitude of the former southern endpoint . this behaviour could be interpreted as the asymmetric zipping - like eruption , although it does not look very likely . although there is a pil stretched at a height above 40 mm from the former filament position to the new eastern end point ( fig . 10(f ) ) , no manifestations of the presence of the flux rope were observed there and any flare - ribbon - like brightening along the path of this pil was absent . hence , observations do not support the interpretation of the event as a whipping - like or a zipping - like asymmetric filament eruption . more probable seems reconnection of the flux - rope field lines in its northern leg with ambient coronal magnetic field lines rooted in a quiet region far from the filament . the eruption of the prominence was followed by a cme . due to the geometrical factor , it was brightest in the field - of - view of the _ stereo a _ cor2 coronagraph . at the late stage , the legs of the cme connecting its core with the sun show noticeable twisted structure . we calculated parameters of coronal potential magnetic field and found that the eruption is likely to begin with an instability not in the vertical direction , as typical for eruptive filaments , but after the violation of the horizontal equilibrium . observations show that the trajectory of the eruptive filament deviates from the vertical line by an angle of about 45@xmath6 . this is unusual initiation of an eruption with combination of horizontal and vertical initial flux - rope displacements showing new unexpected possibility for the start of eruptive events .

we conclude that observations of the galactic centre are well consistent with continuous star formation following the canonical imf and do not suggest a systematic variation as a result of the region s properties such as high density , metallicity , strong tidal field etc . if the young stellar discs prove to follow a top - heavy imf , the circumstances that led to their formation must be very rare , since these have not affected most of the central cluster .

c

0910.4960

for half a century , evidence has been growing that the formation of stars follows a universal distribution of stellar masses . in fact , no stellar population has been found showing a systematic deviation from the canonical initial mass function ( imf ) found for example for the stars in the solar neighbourhood . the only exception may be the young stellar discs in the galactic centre , which have been argued to exhibit a top - heavy imf . here we discuss the question whether the extreme circumstances in the centre of the milky way may be the reason for a significant variation of the imf . by means of stellar evolution models using different codes , we show that the observed luminosity in the central parsec is too high to be explained by a long - standing top - heavy imf as suggested by other authors , considering the limited amount of mass inferred from stellar kinematics in this region . in contrast , continuous star formation over the galaxy s lifetime following a canonical imf results in a mass - to - light ratio and a total mass of stellar black holes ( sbhs ) consistent with the observations . furthermore , these sbhs migrate towards the centre due to dynamical friction , turning the cusp of visible stars into a core as observed in the galactic centre . for the first time here we explain the luminosity and dynamical mass of the central cluster and both the presence and extent of the observed core , since the number of sbhs expected from a canonical imf is just enough to make up for the missing luminous mass . we conclude that observations of the galactic centre are well consistent with continuous star formation following the canonical imf and do not suggest a systematic variation as a result of the region s properties such as high density , metallicity , strong tidal field etc . if the young stellar discs prove to follow a top - heavy imf , the circumstances that led to their formation must be very rare , since these have not affected most of the central cluster . [ firstpage ] black hole physics stars : formation stars : luminosity function , mass function galaxy : centre . [ cols="^,<,^,^,>,>,>,>,>,>",options="header " , ]

various attempts have been made to study star formation in the galactic centre , but so far neither theory or simulations nor observations led to an agreement on the ( initial ) distribution of stellar masses . here we have shown that theory and observations are consistent with star formation generally following a canonical imf @xcite in the galactic centre , just as anywhere else in the universe . our main results can be summarised as follows : 1 . the mass - to - light ratio of the central parsec of the milky way is consistent with a constant or exponentially decreasing star formation rate following a canonical imf . models of constant star formation following an imf with @xmath111 are consistent with the observed luminosities but create @xmath112 sbhs in the central parsec , ten times more than expected by other authors . mass functions flatter than @xmath113 can be safely ruled out , since they can not explain the observed number of bright stars and the diffuse light . the core observed in the luminosity distribution with a radius of @xmath114pc does not imply a core in the mass profile , but can be well explained by mass segregation as suggested by @xcite , where dark remnants mass - dominate this region . again , the observations are best explained by a canonical imf , and are not compatible with star formation following a top - heavy imf with @xmath115 , as this would create a core radius one order of magnitude larger . recent observations revealing a deficit of b - type stars in the young stellar discs suggest a top - heavy imf for this population , which may be explained by tidal stripping of an infalling mass - segregated cluster , or unusual modes of star formation in a fragmenting accretion disc . however , these results do not allow conclusions on star formation in the galactic centre in general , for which we have no reason to assume it to be non - canonical . while other authors generally predicted a flat imf ( e.g. * ? ? ? * ) or a higher low - mass cut - off ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) from state - of - the - art theoretical star formation models of the galactic centre , we find that observations suggest star formation follows a canonical imf even under the extreme circumstances present in the central cluster . this universality of the imf poses a major challenge to our understanding of star formation processes ( see also @xcite ) . our results rely on the assumption that the stars observed within 1pc from the galactic centre also formed there , suggesting star formation with a canonical imf even under such exotic conditions . it is possible that some of the stars were brought in by massive star clusters which spiralled towards the smbh through dynamical friction @xcite . however , this scenario is unlikely because a star cluster is stripped on its way towards the centre and loses mostly low - mass stars , since it would be in a mass segregated state soon after its formation . therefore , the most likely scenario is a central cluster that formed over a hubble time with a canonical imf , where the very young stellar population of the stellar discs observed to have a very top - heavy imf @xcite constitutes a rare star formation event not typical for the bulk stellar population in the central cluster .

frustrated quantum magnets can harbor unconventional spin - liquid ground states in which the elementary magnetic moments fractionalize into new emergent degrees of freedom . while the fractionalization of quantum numbers is one of the recurring themes in modern condensed matter physics here we discuss the physics of fractionalization in _ three - dimensional _ kitaev models and demonstrate that the itinerant majorana fermions generically form a ( semi)metal which , depending on the underlying lattice structure , exhibits majorana fermi surfaces , nodal lines , or topologically protected weyl nodes .

i

1511.05569

frustrated quantum magnets can harbor unconventional spin - liquid ground states in which the elementary magnetic moments fractionalize into new emergent degrees of freedom . while the fractionalization of quantum numbers is one of the recurring themes in modern condensed matter physics , it often remains a challenge to devise a controlled analytical framework tracking this phenomenon . a notable exception is the exactly solvable kitaev model , in which spin degrees of freedom fractionalize into majorana fermions and a z@xmath0 gauge field . here we discuss the physics of fractionalization in _ three - dimensional _ kitaev models and demonstrate that the itinerant majorana fermions generically form a ( semi)metal which , depending on the underlying lattice structure , exhibits majorana fermi surfaces , nodal lines , or topologically protected weyl nodes . we show that the nature of these majorana metals can be deduced from an elementary symmetry analysis of the projective time - reversal and inversion symmetries for a given lattice . this allows us to comprehensively classify the gapless spin liquids of kitaev models for the most elementary tricoordinated lattices in three dimensions . we further expand this classification by addressing the effects of time - reversal symmetry breaking and additional interactions .

the low - temperature collective physics of interacting quantum many - body systems often calls for a novel description in terms of emergent degrees of freedom that are not only distinct from those of the original constituents of the system , but describe certain `` fractions '' thereof . familiar examples include the spin - charge separation in one - dimensional metals @xcite , the electron fractionalization in fractional quantum hall states of two - dimensional electron gases @xcite , as well as the emergence of monopoles in spin ice @xcite or chiral magnets @xcite . quantum spin liquids in frustrated quantum magnets @xcite provide another important venue for such quantum number fractionalization . for these spin liquids the theoretical formulation of this phenomenon is often closely linked to a lattice gauge theory description of the quantum magnet ; the spin degrees of freedom typically decompose into spinons coupled to an emergent @xmath1 or z@xmath0 gauge field whose elementary excitations remain deconfined @xcite . one of the paradigmatic examples of a model harboring a z@xmath0 spin liquid ground state is kitaev s exactly solvable honeycomb model @xcite . it describes a spin-@xmath2 quantum magnet subject to strong exchange frustration arising from bond - directional interactions of the form @xmath3 where @xmath4 labels the three different bond directions of the honeycomb lattice . the low - energy physics of this spin model can be captured in terms of majorana degrees of freedom and a z@xmath0 gauge field . crucially , the gauge field remains static for the pure kitaev model , and identifying the ground state configuration of the gauge field reduces to an essentially classical problem . typically this yields a unique ground state with a finite gap for the elementary vison excitations of the z@xmath0 gauge field . fixing the gauge structure then allows to recast the original spin model as a free majorana fermion model and thus paves the way to a full analytical solution . the phase diagram of the kitaev model generically exhibits two types of spin - liquid phases . around the limits where one of the three couplings dominates over the other two one finds a gapped spin liquid which , for the two - dimensional honeycomb model , is known to exhibit abelian topological order @xcite . the second phase , which is found for roughly isotropic couplings ( i.e. , @xmath5 ) is gapless and can generically be understood as a metallic state of the itinerant majorana fermions . for the two - dimensional honeycomb model the itinerant majorana fermions form a graphene - like band structure with two dirac cones @xcite . l13 mm | c70 mm c15 mm c20 mm c20 mm c c lattice & alternative & sites in & sublattice & inversion & + & names & unit cell & symmetry & symmetry & symbol & no . + ( 10,3)a & hyperoctagon @xcite , laves graph @xcite , k@xmath6 crystal @xcite & 4 & @xmath7 & chiral & i@xmath8 & 214 + ( 10,3)b & hyperhoneycomb @xcite & 4 & & & fddd & 70 + ( 10,3)c & & 6 & & chiral & p@xmath9 & 151 + ( 9,3)a & & 12 & & & r@xmath10 m & 166 + ( 9,3)b & & 24 & & & p4@xmath11/nmc & 137 + ( 8,3)a & & 6 & @xmath7 & chiral & p@xmath12 & 180 + ( 8,3)b & & 6 & @xmath7 & & r@xmath10 m & 166 + ( 8,3)c & & 8 & & & p@xmath13 / mmc & 194 + ( 8,3)n & & 16 & & @xmath14 & i4 / mmm & 139 + ( 6,3 ) & honeycomb & 2 & & & & in this paper , we comprehensively classify the nature of the gapless spin liquids and their underlying majorana metals for _ three - dimensional _ kitaev models . our motivation has been rooted in the mounting experimental evidence that spin - orbit entangled mott insulators can provide solid - state realizations of the kitaev model following the theoretical guidance by khaliullin and coworkers @xcite . this materials - oriented search @xcite has produced various candidate 4d and 5d compounds , most notably na@xmath15iro@xmath16 , @xmath17-li@xmath15iro@xmath16 and rucl@xmath16 , which realize hexagonal arrangements of local , spin - orbit entangled @xmath18 moments that are indeed subject to strong bond - directional exchanges as indicated by recent experiments @xcite . a byproduct of this experimental search has been the discovery @xcite of the polymorphs @xmath19-li@xmath15iro@xmath16 and @xmath20-li@xmath15iro@xmath16 , which realize three - dimensional arrangements of the spin - orbit entangled moments which retain the _ tricoordination _ familiar from the hexagonal lattice . this has sparked a surge of interest in three - dimensional variants of the kitaev model which , hitherto , had evaded the attention of the broader community @xcite . it was quickly recognized that the analytical tractability of the two - dimensional kitaev model largely carries over to the three - dimensional variants , and it has recently been demonstrated that such three - dimensional kitaev models harbor a rich variety of gapless z@xmath0 spin liquids in which the emergent majorana metals form nodal structures which include majorana fermi surfaces @xcite , nodal lines @xcite as well as topologically protected weyl nodes @xcite . the purpose of this paper is to go beyond these initial examples and to impart a more systematic classification of gapless kitaev spin liquids in three spatial dimensions . in particular , we comprehensively discuss how the nature of the emergent majorana metal depends on the underlying lattice geometry . we do so by considering kitaev models for the most elementary three - dimensional , tricoordinated lattices , i.e. , lattices that have elementary loops of only one fixed length @xcite . for instance , the well - known honeycomb lattice is the only tricoordinated lattice with elementary loops of length 6 . however , there are multiple lattice structures with elementary loops of lengths 7 , 8 , 9 or 10 ( and possibly higher ) , which are all three - dimensional . in fact , such three - dimensional , tricoordinated structures have been comprehensively classified in the work of wells in the 1970 s @xcite . here , we focus on those lattice structures that exhibit equidistant bonds and approximately 120@xmath21 bond angles at every vertex @xcite . an overview of the so - identified family of three dimensional , tricoordinated lattice structures and their basic properties is provided in table [ tab : lattice_overview ] . a convenient way to systematically label the individual lattices is to use the so - called schlfli symbol @xmath22 followed by a letter , where @xmath23 is the fixed polygonality ( or elementary loop length ) of the lattice , @xmath24 refers to the tricoordination of the vertices , and the additional letter simply enumerates the lattices for a given schlfli symbol . it should be noted that some of these lattices are well known in the literature under alternative names . these include the ( 10,3)a lattice , which has long been known as the laves graph @xcite in the crystallographic literature or as @xmath25 crystal @xcite in the mathematical literature . it has also been renamed hyperoctagon lattice @xcite by some of the authors of this manuscript in an earlier study . similarly , the ( 10,3)b lattice has recently gained some attention under the name hyperhoneycomb lattice @xcite after it had been discovered as the iridium - sublattice in the iridate @xmath19-li@xmath15iro@xmath16 . it is precisely this family of tricoordinated lattice structures that serves as principal input in our quest to comprehensively discuss three - dimensional kitaev models in the following . we show that these kitaev models harbor a plethora of gapless spin liquids that can be cast as different incarnations of majorana metals whose precise nature can be systematically understood from a basic symmetry analysis . l13 mm | c3 cm | c3 cm lattice & majorana metal & trs breaking + ( 10,3)a & fermi surface & fermi surface + ( 10,3)b & nodal line & weyl nodes + ( 10,3)c & nodal line & fermi surface + ( 9,3)a@xmath26 & weyl nodes & weyl nodes + ( 8,3)a & fermi surface & fermi surface + ( 8,3)b & weyl nodes & weyl nodes + ( 8,3)c@xmath26 & nodal line & weyl nodes + ( 8,3)n & gapped & weyl nodes + ( 6,3 ) & dirac cones & gapped before going into a detailed discussion of the kitaev models for these individual lattices , we provide a brief overview of our main results . for all but one lattice , i.e. , ( 8,3)n , we find that there is an extended gapless spin - liquid phase around the point of isotropic coupling , i.e. , @xmath5 . this gapless phase is best described as a majorana metal ( or semimetal ) , since it is the band structure of the itinerant majorana fermions that exhibits gapless excitations , while the vison excitations of the static z@xmath0 gauge field remain gapped for all lattices @xcite . a summary of our results characterizing the various majorana metals for different lattice geometries is provided in table [ tab : majorana_metals ] . we do so by listing the nodal manifold of gapless excitations in the band structure of the itinerant majorana fermions . as can be seen from the table , the various three - dimensional lattice geometries realize multiple examples for the emergence of fermi surfaces , nodal lines , or weyl nodes . as we will lay out in detail in the remainder of the paper , an understanding of the systematics in this table is closely linked to a symmetry analysis of the kitaev models for the respective lattice geometries ( see in particular sec . [ sec : symmetries ] ) . for instance , the occurrence of majorana fermi surfaces for the two lattices ( 10,3)a and ( 8,3)a is closely linked to a non trivial sublattice symmetry for these lattices . similarly , the emergence of weyl nodes can be understood from a close inspection of time - reversal and inversion symmetry . for instance , for a lattice with an _ odd _ number of bonds in the elementary loop , such as the ( 9,3)a lattice , time - reversal symmetry has to be broken spontaneously for the emergent majorana degrees of freedom , which in turn allows for the occurrence of weyl nodes . for the lattice ( 8,3)b it is a more intricate interplay of time - reversal symmetry , inversion symmetry , and non - trivial sublattice symmetry that allows for the emergence of weyl nodes in the majorana band structure without breaking time - reversal symmetry _ nor _ inversion symmetry , a situation that can not occur for electronic band structures . we will discuss these different incarnations of weyl physics in a broader context in sec . [ sec : weyl ] . for the two - dimensional kitaev honeycomb model , it is well known that the dirac spin - liquid of the pure kitaev model gaps out into a massive phase with non - abelian topological order when perturbing the spin system with a magnetic field pointing along the 111-direction , i.e. , by considering a hamiltonian @xmath27 it may , thus , be a natural question to ask whether the breaking of time - reversal symmetry can give rise to gapped phases with non - trivial topological order also for three - dimensional kitaev models . bearing in mind that the kitaev model can be recast as a free majorana fermion system , one can immediately answer this question in the negative by considering the classification of topological insulators @xcite rooted in the symmetry classification of free - fermion systems @xcite . in this free - fermion classification scheme , the pure kitaev model falls into symmetry class bdi , while the one with broken time - reversal symmetry of eq . belongs to symmetry class d. as can readily be seen from the classification tables of refs . , there are no topologically non - trivial band insulators in either symmetry class bdi or d for three spatial dimensions in contrast to two spatial dimensions where symmetry class d allows for this possibility [ and as realized for hamiltonian on the honeycomb lattice ] . it is , of course , nevertheless an interesting question to ask what effect the breaking of time - reversal symmetry has on the majorana metals for the three - dimensional kitaev models of table [ tab : majorana_metals ] . the answer is provided in the third column of that table and is discussed in much detail in the remainder of the paper . generically , we find that the metallic nature per se remains untouched by the breaking of time - reversal symmetry , i.e. , for no system do we observe a transition into a ( topologically trivial ) massive phase . instead , we find that the nodal structure remains robust under this perturbation for systems that exhibit majorana fermi surfaces or weyl nodes . the only effect of a ( small ) magnetic field is to either deform the majorana fermi surface or move the positions of the weyl nodes . a different picture emerges for those lattices where the pure kitaev model exhibits nodal lines . here , the magnetic field does alter the nodal structure . for the lattices ( 10,3)b and ( 8,3)c the magnetic field gaps out the nodal line with the exception of two or six nodes , respectively . these nodes turn out to be one or three pairs of weyl nodes . a symmetry analysis again indicates that another symmetry plays a crucial role in stabilizing this unusual band structure . it is the presence of inversion symmetry that fixes these weyl nodes to the fermi energy ( at zero energy ) for these lattices . inversion symmetry is absent for the chiral lattice ( 10,3)c , which also exhibits nodal lines for the unperturbed kitaev model . upon applying a magnetic field the nodal lines vanish and the system creates six pairs of weyl nodes , which in the absence of inversion symmetry are no longer fixed to the fermi energy and move away from it . the result is the emergence of 12 pockets of majorana fermi surfaces , each of which encapsulates a weyl node . as a result , these fermi surfaces also acquire some non - trivial topological properties from the weyl nodes , as we discuss in further detail in sec . [ ssec : topfermisurface ] . as such , the kitaev model for lattice ( 10,3)c stands out as the only system where the effect of breaking time - reversal symmetry is to _ increase _ the nodal structure and the associated density of states of the majorana metal . finally , we briefly comment on the z@xmath0 gauge structure of these models . as we will discuss in more detail in sec . [ sec : kitaev ] , the assignment of local z@xmath0 gauges ( on the bonds of the lattice ) corresponds to an assignment of z@xmath0 fluxes through the elementary loops in the lattice . for the two - dimensional kitaev honeycomb model , this correspondence can be used to readily fix the gauge structure of the ground state via a theorem by lieb @xcite , which states that the ground state of the honeycomb model has no fluxes through any of the hexagonal plaquettes ( corresponding to the elementary loops ) . lieb s theorem can also be applied to three - dimensional kitaev models if the lattice structure exhibits certain mirror symmetries . as it turns out , only one of the lattices in our family , namely the lattice ( 8,3)b , fulfills this criterion . it is thus the only lattice for which we can rigorously assign the flux configuration of the ground state . for all other lattices , we have to resort to alternative ways to identify precisely this ground state configuration of the ( static ) z@xmath0 gauge field . in this study , we have resorted to numerical simulations of this essentially classical problem for finite systems . in general , we find that the result of this numerical procedure is a flux configuration that precisely corresponds to the one indicated by lieb s theorem if it were to apply to the lattice structure at hand . specifically , all elementary loops of length 2 ( mod 4 ) carry zero flux , while elementary loops of length 0 ( mod 4 ) carry @xmath28 flux . non - bipartite lattices with elementary loops of odd length are not covered by lieb s theorem at all . for these lattices we assign the flux configuration using symmetry arguments . notably , however , for the lattice ( 9,3)a our numerical checks indicate the possibility of low - energy flux assignments that break at least one of the point - group symmetries of the lattice . such an exotic scenario might also be relevant to lattice ( 8,3)c where the @xmath28-fluxes are subject to geometric frustration . we have not explored this possibility in full detail in the paper at hand , but instead have provided results for the lowest - energy z@xmath0 flux structure that does not break any point - group symmetries . we revisit this point in an outlook at the end of the paper . the paper is structured as follows . in sec . [ sec : kitaev ] , we briefly review the general framework to analytically solve the kitaev model in arbitrary spatial dimensions . a detailed analysis of the relevant symmetries of three - dimensional kitaev models is presented in sec . [ sec : symmetries ] . we then go through all lattices of table [ tab : lattice_overview ] one by one in sec . [ sec:3d ] and provide further details on the underlying lattices , the definition of the kitaev model , and its solution for each of these lattices . this includes the overall phase diagram of the model along with a detailed discussion of the gapless phase around the point of isotropic couplings . in the subsequent sec . [ sec : weyl ] , we take a step back and discuss the different scenarios for the emergence of weyl physics in these three - dimensional kitaev models . this also includes a discussion of the topological properties of some of the observed majorana fermi surfaces . section [ sec : spin - peierls ] focuses on a discussion of majorana fermi surfaces in general and their bcs - type spin - peierls instabilities . we round off the paper with an outlook in sec . [ sec : outlook ] that touches on the possibility of realizing some of the kitaev models of interest here in spin - orbit entangled mott insulators . we further lay out some future directions to be pursued for this family of three - dimensional kitaev models . the main paper is complemented by an extensive appendix that provides many of the technical details on the lattice structures .

some of the ysos are massive ( b stars ) and therefore very young , suggesting that a new generation of star formation is occurring , possibly triggered by stellar winds and shocks generated by the older ( 2 - 3 myr ) central massive cluster . the _ spitzer _

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glimpse imaging using the infrared array camera ( irac ) on the _ spitzer space telescope _ indicates that star formation is ongoing in the rcw 49 giant region . a photometric comparison of the sources in rcw 49 to a similar area to its north finds that at least 300 stars brighter than 13th magnitude in band [ 3.6 ] have infrared excesses inconsistent with reddening due to foreground extinction . these are likely young stellar objects ( ysos ) more massive than 2.5 @xmath0 suggesting that thousands more low - mass stars are forming in this cloud . some of the ysos are massive ( b stars ) and therefore very young , suggesting that a new generation of star formation is occurring , possibly triggered by stellar winds and shocks generated by the older ( 2 - 3 myr ) central massive cluster . the _ spitzer _ irac camera has proven to be ideally suited for distinguishing young stars from field stars , and the glimpse survey of the galactic plane will likely find thousands of new star formation regions .

rcw 49 is one of the most luminous and massive regions in the galaxy . at its center lies the westerlund 2 ( hereafter w2 ; westerlund 1960 ) compact cluster which contains over a dozen ob stars and a wolf - rayet star ; another wolf - rayet star lies several arc minutes away in the extended nebula ( moffat & vogt 1975 ; moffat , shara , & potter 1991 ; carraro & munari 2004 ; van der hucht 2001 ) . the age of the w2 cluster is estimated to be 2 - 3 myr ( piatti et al . 1998 ) . as discussed in churchwell et al . ( 2004 ; hereafter , c04 ) , distance estimates range from @xmath1 kpc and we follow their adoption of 4.2 kpc . at this distance , we estimate the cluster luminosity is 1.4@xmath2 @xmath3 based on the iras flux and a relationship derived between far - infrared and bolometric luminosity @xcite . the stellar mass is estimated to be @xmath4m@xmath5 from the radio - derived ionizing flux @xcite the rcw 49 region was observed with the _ spitzer _ ( werner et al . 2004 ) infrared array camera ( irac ; fazio et al . 2004 ) as part of the @xmath6alactic @xmath7egacy @xmath8nfrared @xmath9id-@xmath10lane @xmath11urvey @xmath12xtraordinaire ( glimpse * ? ? ? * ) observing strategy validation . c04 presents irac images of this region that show highly - structured , extended polycyclic aromatic hydrocarbon ( pah ) and gas emission , extending out to @xmath13 from the w2 cluster center . the pah emission is likely excited by the strong ultraviolet / optical radiation from the central w2 cluster ( leger & puget 1984 ; allamandola et al . 1989 ) , suggesting that large regions of the cloud are optically thin to the central cluster radiation . furthermore , radio and infrared imaging show that at least the southwest part of the cloud is blown out @xcite ( all directions in this paper are referred to in galactic coordinates ) . without detailed studies of the molecular gas in the rcw 49 region , it is unknown if dense cores of gas and dust remain or if the dust is optically thin . has star formation ceased and is the cloud in the process of disruption ? or is star formation ongoing , perhaps triggered by winds and shocks from the central cluster ? this paper presents irac photometry of the rcw 49 region which reveals several hundred sources with large infrared excesses , likely indicating youth . after discussing the observations in 2 , we present images of selected regions in 3 and color - color and color - magnitude diagrams in 4 . in 5 we show spectral energy distributions ( seds ) of two massive ( b2 ) ysos . 6 concludes with a discussion of the current generation of star formation and how it may relate to the w2 cluster .

glimpse imaging using the infrared array camera ( irac ) on the _ spitzer space telescope _ indicates that star formation is ongoing in the rcw 49 giant region . a photometric comparison of the sources in rcw 49 to a similar area to its north finds that at least 300 stars brighter than 13th magnitude in band [ 3.6 ] have infrared excesses inconsistent with reddening due to foreground extinction .

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glimpse imaging using the infrared array camera ( irac ) on the _ spitzer space telescope _ indicates that star formation is ongoing in the rcw 49 giant region . a photometric comparison of the sources in rcw 49 to a similar area to its north finds that at least 300 stars brighter than 13th magnitude in band [ 3.6 ] have infrared excesses inconsistent with reddening due to foreground extinction . these are likely young stellar objects ( ysos ) more massive than 2.5 @xmath0 suggesting that thousands more low - mass stars are forming in this cloud . some of the ysos are massive ( b stars ) and therefore very young , suggesting that a new generation of star formation is occurring , possibly triggered by stellar winds and shocks generated by the older ( 2 - 3 myr ) central massive cluster . the _ spitzer _ irac camera has proven to be ideally suited for distinguishing young stars from field stars , and the glimpse survey of the galactic plane will likely find thousands of new star formation regions .

the large number of infrared excess sources in rcw 49 indicates that star formation is ongoing in this giant region . we find that at least 300 stars brighter than 13@xmath38 magnitude in the [ 3.6 ] band are pre - main sequence or young stars of mass @xmath39 m@xmath5 . based on integration of a standard imf , we conclude that the ysos in the rcw 49 complex comprise a stellar mass of @xmath274500 m@xmath5 . if the ysos represent a second generation of star formation , this suggests that the mass of the second generation is about 15% of the first . the presence of ysos of b spectral type does indeed suggest that some star formation is very recent . whether it is continuous or triggered by the w2 cluster is uncertain . the apparent excess of star formation near the radio / ir ring ( figure [ 3col ] ) and several of the sites of star formation near the ring and blowout region perimeters ( regions 2,3 , and 6 in figure [ regions ] ) suggest that energy input from w2 may have triggered recent star formation . on the other hand , regions 4 and 5 appear to be forming stars in a relatively quiescent region of the cloud . the detailed nature of the star formation in rcw 49whether triggered or continuous , clustered or distributed , and the spatial distribution of mass requires further study by the wider astronomical community . the images of this field have been released with the opening of the public archive ; the glimpse catalog and mosaic images will be available to the community from the _ spitzer _ science center in the fall of 2004 . we are grateful to stephan jansen for his invaluable work maintaining the glimpse computing network . support for this work , part of the spitzer space telescope legacy science program , was provided by nasa through contract numbers ( institutions ) 1224653 ( uw ) , 1225025 ( bu ) , 1224681 ( umd ) , 1224988 ( ssi ) , 1242593 ( ucb ) , 1253153 ( umn ) , 11253604 ( uwy ) , 1256801 ( uww ) by the jet propulsion laboratory , california institute of technology under nasa contract 1407 .

explanations of this behavior include models invoking a dense medium environment which makes the shock wave evolve quickly into the sub - relativistic phase , a jet - like outflow , and a wind - shaped circumburst medium environment . recently , frail et al . ( 1999a ) found that the latter two cases are consistent with the radio afterglow of this burst . here , optical extinction due to the dense medium is not important if the prompt optical - uv flash accompanying the @xmath0-ray emission can destroy dust by sublimation out to an appreciable distance . -0.5 cm gamma - rays : bursts hydrodynamics : shock waves

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grb980519 is characterized by its rapidly declining optical and x - ray afterglows . explanations of this behavior include models invoking a dense medium environment which makes the shock wave evolve quickly into the sub - relativistic phase , a jet - like outflow , and a wind - shaped circumburst medium environment . recently , frail et al . ( 1999a ) found that the latter two cases are consistent with the radio afterglow of this burst . here , by considering the trans - relativistic shock hydrodynamics , we show that the dense medium model can also account for the radio light curve quite well . the potential virtue of the dense medium model for grb980519 is that it implies a smaller angular size of the afterglow , which is essential for interpreting the strong modulation of the radio light curve . optical extinction due to the dense medium is not important if the prompt optical - uv flash accompanying the @xmath0-ray emission can destroy dust by sublimation out to an appreciable distance . comparisons with some other radio afterglows are also discussed . -0.5 cm gamma - rays : bursts hydrodynamics : shock waves

in the standard model of gamma - ray bursts ( grbs ) ( see piran 1999 for a review ) , an afterglow is generally believed to be produced by the synchrotron radiation or inverse compton scattering of the shock - accelerated electrons in an ultra - relativistic shock wave expanding in a homogeneous medium . as more and more ambient matter is swept up , the shock gradually decelerates while the emission from such a shock fades down , dominating at the beginning in x - rays and progressively at the optical to radio energy bands ( mszros & rees 1997 ; waxman 1997a ; wijers & galama 1999 ) . in general , the light curves of x - ray and optical afterglows are expected to exhibit power - law decays ( i.e. @xmath1 ) with the temporal index @xmath2 in the range @xmath3 , given the energy spectral index of electrons @xmath4 . the observations of the earliest afterglows are in good agreement with this simple model ( e.g. wijers , rees & mszros 1997 ; waxman 1997b ) . however , over the past year , we have come to recognize a class of grbs whose afterglows showed light curve breaks ( e.g. grb , grb ; kulkarni _ et al . _ 1999a ; harrison _ et al . _ 1999 ) or steeper temporal decays ( i.e. @xmath5 ; e.g. grb , grb ; bloom _ et al . explanations for these behaviors include three scenarios : 1 ) a jet - like relativistic shock has undergone the transition from the spherical - like phase to a sideways - expansion phase ( rhoads 1999 ) , as suggested by some authors ( e.g. sari , piran & halpern 1999 ; kulkarni _ et al . _ 1999a ; harrison _ et al . 2 ) the shock wave propagates in a wind - shaped circumburst environment with the number density @xmath6 ( dai & lu 1998 ; mszros , rees & wijers 1998 ; chevalier & li 1999 ; chevalier & li 2000 ; li & chevalier 1999 ) ; 3 ) a dense medium environment ( @xmath7 ) makes the shock wave evolve into the sub - relativistic phase after a short relativistic one ( dai & lu 1999a , b ) . in the last model , since an afterglow from the shock at the sub - relativistic stage decays more rapidly than at the relativistic one , we will expect a light curve break or a long - term steeper decay , depending on the time when it begins to enter into the sub - relativistic stage . this scenario has reasonably interpreted the break in the r - band afterglow of grb ( dai & lu 1999a ) and the steep decays of the x - ray and optical afterglows of grb ( dai & lu 1999b ) . recently , frail _ et al . _ ( 1999a ) tried to test the first two models ( the jet and wind cases ) by means of the radio afterglow behavior of grb and found that the wind model described it rather well . due to the strong modulation of the light curve , however , they could not draw a decisive conclusion for the jet case . in this paper , we will examine the possibility of describing the evolution of the radio afterglow in terms of the dense medium model . since this scenario involves the transition phase of the shock wave from the relativistic stage to the sub - relativistic , we have considered the trans - relativistic shock hydrodynamics in the numerical study . we first present the asymptotic result of the fitting of the radio data in section 2 , and then the numerical result in section 3 . in section 4 , we show that the optical extinction due to the dense circumburst medium is not important , since the prompt optical - uv radiation , caused by the reverse shock , can destroy the dust by sublimation out to a substantial distance , as proposed by waxman & draine ( 1999 ) . finally , we give our discussions and conclusions .

grb980519 is characterized by its rapidly declining optical and x - ray afterglows . by considering the trans - relativistic shock hydrodynamics , we show that the dense medium model can also account for the radio light curve quite well . the potential virtue of the dense medium model for grb980519 is that it implies a smaller angular size of the afterglow , which is essential for interpreting the strong modulation of the radio light curve . comparisons with some other radio afterglows are also discussed .

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grb980519 is characterized by its rapidly declining optical and x - ray afterglows . explanations of this behavior include models invoking a dense medium environment which makes the shock wave evolve quickly into the sub - relativistic phase , a jet - like outflow , and a wind - shaped circumburst medium environment . recently , frail et al . ( 1999a ) found that the latter two cases are consistent with the radio afterglow of this burst . here , by considering the trans - relativistic shock hydrodynamics , we show that the dense medium model can also account for the radio light curve quite well . the potential virtue of the dense medium model for grb980519 is that it implies a smaller angular size of the afterglow , which is essential for interpreting the strong modulation of the radio light curve . optical extinction due to the dense medium is not important if the prompt optical - uv flash accompanying the @xmath0-ray emission can destroy dust by sublimation out to an appreciable distance . comparisons with some other radio afterglows are also discussed . -0.5 cm gamma - rays : bursts hydrodynamics : shock waves

the detection of strong diffractive scintillation requires that the angular size of the source vla should be less than @xmath117 even 15 days after the burst ( frail _ et al . _ 1999a ) , otherwise the fluctuations would be suppressed . this small inferred size is not consistent with the spherical , homogeneous model with a normal density ( @xmath118 ) , but can marginally be consistent with the jet model and the wind - shaped circumburst medium model . we note that the dense medium model may have a potential advantage for this requirement , simply because that the shock will be quickly decelerated to a sub - relativistic velocity and therefore have a shorter shock radius . this can be clearly seen from the following comparison : @xmath119 for the relativistic case while @xmath120 for the sub - relativistic one . here , for the afterglow of grb , we assume that before @xmath121 , the shock is adiabatic and relativistic ; thus the shock radius is @xmath122^{-1/4 } \rm cm$ ] ( sari , piran & narayan 1998 ) . then , the shock radius should follow the sedov - von neumann - taylor self - similar solution as @xmath123 . thus , we obtained the angular size of the afterglow @xmath124 . the agreement would be even improved if we note that at the beginning of the assumed sub - relativistic stage , the radius should increase more slowly than the self - similar solution in the trans - relativistic regime . the strong modulations caused by scintillation also make the estimate of the spectral slope in the radio band less accurate . the _ averaging _ value of the spectral slope from day 12 on is @xmath125 ( where @xmath126 ) , implying that the time averaged self - absorption frequency @xmath33 is between 1.43 ghz and 4.86 ghz ( frai _ et al . _ 1999b ) . in our model , the time ( @xmath127 ) when the fitting curve begins to decline corresponds to @xmath128 . since the self - absorption frequency decays as @xmath129 for @xmath130 , we expect that @xmath33 shifted quickly below 4.86 ghz at day 21 , but was above 1.43 ghz over all the detecting time , which is in reasonable agreement with the observations . the radio afterglow of grb , the longest light curve ( @xmath131-day ) obtained by far , exhibited different behavior from grb ( frail et al . 1997 ; waxman , kulkarni & frail 1998 ; frail , waxman & kulkarni 1999 ) . from the spectral and temporal radio behavoir , frail , waxman & kulkarni ( 1999 ) inferred that the fireball has undergone a transition to sub - relativistic expansion at @xmath132 , consistent with the inferred low ambient density @xmath133 ( but also see chevalier & li 1999a ) . on the other hand , some radio afterglows ( e.g. grb , grb ; frail _ et al . _ 1999b ) show similar behaviors to grb , that is , they exhibit a slow rise to the maximum for a relatively short time and then a fast decline until below detectability . it is likely that the shocks of these bursts entered into the sub - relativistic stage after a short relativistic one and our above model can also describe their radio afterglows . ( 1999 ) had interpreted the broad - band lightcurve break in the afterglows of grb as due to a jet - like outflow . we speculate that another possible explanation is that the shock had entered into the sub - relativistic stage after @xmath134 as the result of the combination of the dense medium and jet effects ( wang _ et al . _ 1999b ) , the latter of which may be real in consideration of the large inferred isotropic energy . the radio afterglow of grb is unique for its flare " behavior ( kulkarni _ et al . _ 1999b ) , whose most natural explanation is that it arises from the reverse shock , as evidenced by the prompt optical flash ( sari & piran 1999 ) . our preliminary computation ( using the trans - relativistic model ) shows that the radio emission from the forward shock in the dense medium model is significantly lower than that from the reverse shock and declines quickly after the peak time , if a jet - like outflow with an opening angle @xmath135 , as required by the energy crisis " of this burst , is invoked ( wang _ et al . _ moreover , the fast decline of the radio emission from the forward shock , which is caused by the deceleration of the shock in the sub - relativistic stage , can be consistent with the non - detection even 3 days after the burst . in summary , we argue that the dense medium model , which has interpreted the optical to x - ray afterglows of grb quite well , can also account for the radio afterglow excellently . the circumburst environment can affect the evolution of grbs afterglows significantly ( mszros , rees & wijers 1998 ; panaitescu , meszaros & rees 1998 ; wang _ et al . _ for a low ( @xmath133 ) , homogeneous density environment , the shock waves stay at the relativistic shock stage for quite a long time , while for the dense medium case , the shock wave quickly enters into the sub - relativistic stage . recently , a generic dynamic model for the evolution of shocks from ultra - relativistic phase to the sub - relativistic one has been also developed by huang _ ( 1999a ) . the afterglows of the optically thin radiation ( e.g. optical and x - rays ) from the shock at the sub - relativistic stage decays more rapidly than at the relativistic one . as for the radio afterglow ( usually @xmath136 at the sub - relativistic stage for this model ) , the dense medium model predicts a slow rise ( @xmath137 ) , followed by a round peak and a late steep decline ( @xmath138 ) , trending towards the behavior of the optical and x - ray afterglows . clearly , this behavior is different from the jet model in the early epoch . but it is somewhat similar to the wind model , making it difficult to distinguish between them through the radio observations .

this suggests they are a relatively generic feature of the galaxy evolution process and a source of fuel for galaxy disks . in this review , two main sources of disk star formation fuel , satellite material and clouds condensing from the hot halo medium , are discussed and their contribution to fueling the galaxy quantified . the origin of the halo gas of m31 and m33 is also discussed .

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0803.3069

halo clouds have been found about the three largest galaxies of the local group and in the halos of nearby spirals . this suggests they are a relatively generic feature of the galaxy evolution process and a source of fuel for galaxy disks . in this review , two main sources of disk star formation fuel , satellite material and clouds condensing from the hot halo medium , are discussed and their contribution to fueling the galaxy quantified . the origin of the halo gas of m31 and m33 is also discussed .

beautiful stellar disks only come to be with the accretion of gaseous clouds of star formation fuel . there are several reasons why this fuel is thought to be gradually accreted from a galaxy s halo . the first is that halo gas exists around our galaxy and other spiral galaxies ( e.g. , oort 1970 ; thilker et al . 2004 ; oosterloo , fraternali & sancisi 2007 ) . halo gas therefore appears to be a relatively common phenomenon and the gas velocities indicate it will not escape from the galaxy , but rather eventually fall towards the disk . the second reason is the metallicity distribution of the long - lived stars in the galactic disk , which indicates low metallicity fuel must be continually accreted , i.e. , the g - dwarf problem . the metallicity distribution of the g and k dwarfs in the solar neighborhood can not be reproduced with simple closed box models , and the need for gaseous inflow for the majority of the life of the disk has persisted with further observations and increasingly complex chemical evolution models ( e.g. , larson 1972 ; fenner & gibson 2003 ; kotoneva et al . 2002 ; chiappini , matteucci & romano 2001 ; magrini , corbelli & galli 2007 ; worthey et al . a third reason to bring in star formation fuel from the halo is the lack of radial gaseous inflow observed in the disk of spiral galaxies ( wong et al . 2004 ) . bringing the outer , relatively unenriched gas to the inner regions of the disk would potentially provide a fresh source of star formation fuel . there are two main potential sources of gaseous fuel in a galaxy halo : gas - rich satellites and condensed material from the hot diffuse halo . the latter may be a combination of material left from the initial collapse of baryons into the dark matter halo , stripped material from the satellites that was integrated into this hot halo , and some level of galactic fountain material at low latitudes . in this review , we discuss these two reservoirs of disk star formation fuel with a focus on the milky way , given this is where we have the most information on the satellite distribution and the low column density halo gas . we will also discuss the halo gas of m31 and m33 in the context of its origin and fate .

hard x - ray selection is the most efficient way to discriminate between accretion - powered sources , such as agn , from sources dominated by starlight . hard x - rays are also less affected than other bands by obscuration . we have then carried out the bepposax high energy large area survey ( hellas ) in the largely unexplored 5 - 10 kev band , finding 180 sources in @xmath0 deg@xmath1 of sky with flux @xmath2 . after correction for the non uniform sky coverage this corresponds to resolving about 30 % of the hard cosmic x - ray background ( xrb ) . seven agn show evidence for obscuration in x - ray and optical bands , a fraction higher than in previous rosat or asca - rosat surveys ( at a 95 - 99 % and 90 % confidence level respectively ) , thus supporting the scenario in which a significant fraction of the xrb is made by obscured agn . = -0.5 in x ray : selection background galaxies

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astro-ph9903447

hard x - ray selection is the most efficient way to discriminate between accretion - powered sources , such as agn , from sources dominated by starlight . hard x - rays are also less affected than other bands by obscuration . we have then carried out the bepposax high energy large area survey ( hellas ) in the largely unexplored 5 - 10 kev band , finding 180 sources in @xmath0 deg@xmath1 of sky with flux @xmath2 . after correction for the non uniform sky coverage this corresponds to resolving about 30 % of the hard cosmic x - ray background ( xrb ) . here we report on a first optical spectroscopic identification campaign , finding 12 agn out of 14 x - ray error - boxes studied . seven agn show evidence for obscuration in x - ray and optical bands , a fraction higher than in previous rosat or asca - rosat surveys ( at a 95 - 99 % and 90 % confidence level respectively ) , thus supporting the scenario in which a significant fraction of the xrb is made by obscured agn . = -0.5 in x ray : selection background galaxies

while it is now clear that the cosmic x - ray background ( xrb ) is made by the superposition of many discrete sources , and that the soft ( 0.52 kev ) xrb is mostly produced by agn ( hasinger et al . 1998 , schmidt et al . 1998 ) , the nature of the sources making the energetically dominant hard ( 250 kev ) xrb is still largely unknown . this is due to the lack , until recent years , of sensitive imaging instruments above 23 kev . thanks to asca and bepposax , the 2 - 10 kev band is now accessible to surveys ( boyle et al . 1998 , ueda et al . 1998 , giommi et al . 1998 , giommi , fiore & perri 1998 , fiore et al . 1998a , b ) . the hard x - ray sky poses major problems : no known large class of sources has an emission spectrum matching the kt@xmath3 kev thermal like spectrum of the xrb ; fluctuation analyses of ginga data ( warwick & stewart 1989 ) , and asca ( georgantopoulos et al . 1997 , cagnoni et al . 1998 ) and bepposax ( giommi et al . 1998 , giommi , fiore & perri 1998 ) 210 kev source counts , require 23 times as many sources as expected from rosat counts , if they have the steep power law spectrum typical of rosat sources ( @xmath4 , @xmath5 ) . the leading suggestion to reconcile the source counts , based both on theoretical grounds ( setti & woltjer 1989 , madau et al . 1994 , matt & fabian 1994 , comastri et al . 1995 ) and high energy observations of bright nearby agn ( zdziarski et al 1995 , smith & done 1996 ) , is that heavily obscured agn , emerging strongly at high energies , are the main contributors to the hard xrb . ( these agn are probably not completely invisible at low x - ray energies , i.e. @xmath6 kev , because even if the nuclear emission is completely blocked , different components , like starburts , optically thin gas or scattering of the nuclear radiation , may still be detectable at the 1%10% level , giommi , fiore & perri 1998 , schachter et al . it is crucial to test these suggestions observationally in a band where the nucleus is directly visible and down to fluxes where the bulk of the hard xrb is produced . hard x - ray selection would also help in distinguishing between different scenarios . for instance , if the bulk of the xrb is made by obscured luminous ` quasar 2 ' , following the evolution of type 1 agn , the peak of their activity should be at z=23 and then decrease quickly toward lower redshifts . on the other hand , the xrb could be mostly made by a large population of less luminous / active obscured agn , spread in a broader interval of redshifts . the solution of these problems may have impact also on agn unification schemes . the bepposax mecs ( boella et al . 1997a , b ) provides a good opportunity to investigate the hard x - ray sky , thanks to its good sensitivity above 5 kev ( 5 - 10 kev flux limit of @xmath7 mcrab in 100 ks ) , and improved point spread function ( psf ) . we have thus carried out the high energy llarge area survey ( hellas ) . the survey has been performed in the hard 5 - 10 kev band because this is the band closest to the maximum of the xrb energy density that is reachable with the current imaging x - ray telescopes . including the softer 1.5 - 5 kev range would only increase the background for faint , heavily absorbed sources , thus reducing the chances of their detection . secondly , the bepposax mecs psf improves with energy , and in the 5 - 10 kev band provides error circles of 1 arcmin , 95% confidence radius , small enough to allow the optical identification of the x - ray sources . the hellas survey has so far cataloged 180 sources ( fiore et al . 1999 , in preparation ) . the sky coverage is @xmath8 square degrees at @xmath9 respectively . at the fainter limit we find between 16 and 20 sources deg@xmath10 ( fiore et al . 1998a , b , giommi , fiore & perri 1998 , comastri 1998 ) , implying that about 30 % of the xrb is resolved . cross - correlations of the hellas sample with catalogs of cosmic sources provides 18 coincidences ( 7 radio - loud agn , 6 radio - quiet agn , 3 clusters of galaxies , 1 cv and 1 normal star ) , suggesting that most of the hellas sources are agn . however , the 13 agn were discovered in radio , soft x - ray , and optical surveys , and so this sample is biased against highly obscured sources . to remove this bias we have started a program to spectroscopically identify the rest of the hellas sample . in this letter we report on the first results of this program . the sources studied have not been selected according to their x - ray or optical properties but solely because of visibility during our observing runs . as a result , they can be considered representative of the whole hellas sample .

hasse constants and their basic properties are introduced to facilitate the connection between the lattice of subalgebras of an algebra @xmath0 and the natural action of the automorphism group @xmath1 on @xmath0 . these constants are then used to describe the lattice of subloops of the smallest nonassociative simple moufang loop .

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math0701704

hasse constants and their basic properties are introduced to facilitate the connection between the lattice of subalgebras of an algebra @xmath0 and the natural action of the automorphism group @xmath1 on @xmath0 . these constants are then used to describe the lattice of subloops of the smallest nonassociative simple moufang loop .

to completely describe the lattice of subalgebras @xmath2 of a finite algebra @xmath0 is a difficult task . moreover , it is not obvious how to store the information about @xmath2 efficiently , as the cardinality and complexity of @xmath2 is typically much larger than that of @xmath0 . fortunately , sometimes there is a procedure that allows us to calculate the join @xmath3 and meet @xmath4 for every @xmath5 , @xmath6 . for instance , it is easy to find the join and meet in any boolean algebra @xmath0 , although @xmath7 grows exponentially in @xmath8 . it is this ability to calculate @xmath9 and @xmath10 that is often understood as a complete description of @xmath2 . most of the time we are not so lucky , though , and there is no apparent way to find joins and meets . the main reason is that @xmath3 and @xmath4 can be far from both @xmath5 and @xmath11 in the lattice @xmath2 . it is therefore more convenient to have access to a procedure that gives a complete _ local _ description of @xmath2 . assuming that it is possible to find all maximal subalgebras of @xmath12 and all subalgebras @xmath13 in which @xmath5 is maximal , the lattice @xmath2 can be built up inductively . we will refer to all subalgebras immediately above and immediately below @xmath5 in @xmath2 as _ neighbors _ of @xmath5 , and we denote the set they form by @xmath14 . in this context , it is worth paying attention to the automorphism group @xmath1 and its natural action on @xmath0 , since the neighborhoods of @xmath5 and @xmath11 will be `` the same '' for @xmath5 , @xmath6 belonging to the same orbit of transitivity of @xmath1 . thus , the lattice @xmath2 can be fully described as long as we find 1 . one representative @xmath5 from each orbit of @xmath1 , 2 . the neighborhood @xmath14 for every representative @xmath5 , and 3 . an automorphism of @xmath0 mapping @xmath11 onto @xmath5 , for every representative @xmath5 and every @xmath11 from the orbit of @xmath5 . to save space , we can store subalgebras by their generating sets , and substitute @xmath14 and the automorphisms required by @xmath15 with an efficient algorithm producing those . the purpose of this paper is twofold . first , to introduce a general tool hasse constants that is of some help in all three tasks @xmath16 , @xmath17 , @xmath15 . secondly , to use hasse constants to describe the subloop lattice of the smallest nonassociative simple moufang loop @xmath18 . the investigation of @xmath19 occupies most of this paper , and is inevitably of rather detailed nature . we maintain that the power of hasse constants is sufficiently demonstrated by the fact that @xmath19 was not known before ( see acknowledgement ) , especially given the importance of @xmath18 for the real octonions . although considerable invention will be required in each particular case , we believe that hasse constants will help to keep track in investigation of any subalgebra lattice . a word about the notation : we write @xmath20 for the cyclic group of order @xmath21 , @xmath22 for the dihedral group of order @xmath23 , and @xmath24 for the elementary abelian @xmath25-group of order @xmath26 . a subalgebra generated by the set @xmath27 well be denoted by @xmath28 .

helices are a key folding motif in protein structure . the question which factors determine helix stability for a given polypeptide or protein is an ongoing challenge . here we use van der waals corrected density - functional theory to address a part of this question in a bottom - up approach . we show how intrinsic helical structure is stabilized with length and temperature for a series of experimentally well studied unsolvated alanine based polypeptides , ac - ala@xmath0-lysh@xmath1 . by exploring extensively the conformational space of these molecules , we find that helices emerge as the preferred structure in the length range @xmath2=4 - 8 not just due to enthalpic factors ( hydrogen bonds and their cooperativity , van der waals dispersion interactions , electrostatics ) , but importantly also by a vibrational entropic stabilization over competing conformers at room temperature . the stabilization is shown to be due to softer low - frequency vibrational modes in helical conformers than in more compact ones . this observation is corroborated by including anharmonic effects explicitly through _ ab initio _ molecular dynamics , and generalized by testing different terminations and considering larger helical peptide models .

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1208.6133

helices are a key folding motif in protein structure . the question which factors determine helix stability for a given polypeptide or protein is an ongoing challenge . here we use van der waals corrected density - functional theory to address a part of this question in a bottom - up approach . we show how intrinsic helical structure is stabilized with length and temperature for a series of experimentally well studied unsolvated alanine based polypeptides , ac - ala@xmath0-lysh@xmath1 . by exploring extensively the conformational space of these molecules , we find that helices emerge as the preferred structure in the length range @xmath2=4 - 8 not just due to enthalpic factors ( hydrogen bonds and their cooperativity , van der waals dispersion interactions , electrostatics ) , but importantly also by a vibrational entropic stabilization over competing conformers at room temperature . the stabilization is shown to be due to softer low - frequency vibrational modes in helical conformers than in more compact ones . this observation is corroborated by including anharmonic effects explicitly through _ ab initio _ molecular dynamics , and generalized by testing different terminations and considering larger helical peptide models .

polypeptide helices are a key secondary structure motif in a wide range of proteins @xcite . it is well known that some amino acids ( e.g. , alanine ) exhibit a stronger helix propensity than others @xcite , but the fact that the helical structure is so abundant in proteins is still intriguing . from a thermodynamic point of view , there are at least two possible limits in which helices compete with other structure prototypes . towards high temperature , one expects the transition to a random coil @xcite , which should become entropically favored as the temperature increases . towards low temperature , however , helices may themselves compete with other enthalpically stable conformations . however , in the most interesting regime , namely intermediate , physiological temperatures , stability may be determined by a delicate balance between enthalpy and entropy @xcite . we here unravel this balance quantitatively for the emergence of helical structure in a particularly well studied series of unsolvated polyalanine based peptides ac - ala@xmath0-lysh@xmath1 , @xmath2=4 - 8 @xcite . we consider explicitly not just the helical part of conformational space , but actually the much larger , general low - energy conformational space of the peptides , of which helices are a part . in this paper we show : ( i ) a comprehensive search of the conformational space for ac - ala@xmath0-lysh@xmath1 , @xmath2=4 - 8 ; ( ii ) harmonic free energy calculations for several structural candidates ; ( iii ) outlook on the role of anharmonicities in the potential energy surface ; and ( iv ) a theoretical comparison for longer model peptides , considering only helical motifs , with a different termination , in order to clarify the impact of lys on the soft vibrational modes . our key finding is that there is a significant vibrational entropic stabilization of helices compared to other , more compact conformers , a contribution that should indeed make a difference in actual proteins as well . this contribution is intrinsic to the helix and should therefore act largely independently , not entangled with environment - dependent terms such as a solvent entropy . interestingly , an essential role of low - frequency modes is also actively debated in other areas of protein science , related to their function . beginning with the terms that shape the potential - energy surface ( pes ) , known reasons for helix stability include @xcite ( i ) their efficient hydrogen - bond ( h - bond ) network and increasing h - bond cooperativity with helix length @xcite , ( ii ) suitably bonded and/or electrostatically favorable termination , for instance the lysh@xmath1 termination considered here @xcite , and ( iii ) remarkably , a rather specific favorable contribution of van der waals ( vdw ) interactions for @xmath3-helices @xcite . clearly , the peptide chain length plays a role : too short chains have too few and too weak hydrogen bonds for helices to compensate the cost of strain in the backbone . in practice , environment effects will necessarily influence helix stability @xcite . in an aqueous medium , the hydrophobic effect will be prominent @xcite . in water - poor conditions , like membranes , helices are frequently observed @xcite . finally , in vacuum conditions , the longer members ( @xmath48 ) of the polyalanine based peptide series studied here assume helical structure in experiment @xcite . these helices are stable _ in vacuo _ even up to extreme temperatures ( not expected in solution ) @xcite , or after soft landing on a surface @xcite . the potential energy surface also shapes entropy , and thus the effect of temperature @xmath5 . with increasing @xmath5 , the conformational entropy of the backbone will favor an unfolded state @xcite ( so - called `` random coil '' ) , while at low @xmath5 helices may also compete with other , enthalpically more stable conformers . for instance , gas - phase ion mobility spectrometry ( ims ) by jarrold and coworkers @xcite showed that the ac - ala@xmath6-gly@xmath7-ala@xmath6h@xmath1 polypeptide is helical at @xmath5=400 k but globular at room temperature . a similar structural change was observed in experiments involving multiply protonated polyalanine in the gas - phase in ref . @xcite . empirical force - field based simulations by ma and coworkers @xcite of more than 60 small peptides indicate that the _ vibrational _ entropy ( harmonic approximation ) could stabilize @xmath3-helices or @xmath8-hairpins over competing low - temperature conformers . very recently , plowright and coworkers @xcite used density - functional theory ( dft ) including dispersion contributions ( the b97-d @xcite exchange - correlation functional ) to suggest that , for a small neutral four - residue peptide , @xmath8-sheets and conformers containing 3@xmath9 helical loops are stabilized by the harmonic vibrational entropy at finite temperatures . in the present work , we provide independent , unambiguous , and quantitative computational evidence that the vibrational entropy acts to stabilize helical conformers with increasing temperature over more compact , enthalpically competitive structures . the reason , in short , is traced to the softer low - frequency modes of helices , which are also reflected in the dynamics ( anharmonic case ) . we focus on polyalanine - based peptides , since alanine is known to have a high helix propensity both in solution @xcite and _ in vacuo _ @xcite . for ac - ala@xmath0-lysh@xmath1 ( @xmath2=4 - 20 ) in the gas phase , ims @xcite and first - principles calculations compared to experimental vibrational spectroscopy at room temperature @xcite suggest a cross - over from non - helical to helical preferred conformers as a function of polyalanine chain length . for @xmath2=5 there is a competition between different conformers , while the @xmath2=10 and @xmath2=15 conformers are found to be firmly in the helical range @xcite . in a previous publication @xcite we have quantified , from first principles , the contributions from electrostatics , h - bond cooperativity , and van der waals interactions on the stability of unsolvated polylalanine - based helices against unfolding . this class of systems is thus an ideal testing ground to clarify the structural competition of non - helical ( compact ) and helical conformers as a function of chain length also toward the opposite temperature limit ( low temperature , folded state ) . in the following , we address conformational preference of ac - ala@xmath0-lysh@xmath1 _ in vacuo _ for @xmath2=4 - 8 , i.e. , the length range in which the helical preference at room temperature develops . our work is based on an exhaustive prediction of low - energy conformers using dft and the pbe @xcite exchange - correlation functional , corrected to account for long - range vdw interactions @xcite ( here called pbe+vdw ) . this level of theory treats accurately , and without system - specific empirical parameters , critical length - dependent contributions such as h - bond cooperativity @xcite and vdw interactions @xcite , including their effect on vibrational frequencies and in _ ab initio _ molecular dynamics .

heterogeneous wireless networks ( hetnets ) provide a powerful approach to meet the dramatic mobile traffic growth , but also impose a significant challenge on backhaul . caching and multicasting at macro and pico base stations ( bss ) are two promising methods to support massive content delivery and reduce backhaul load in hetnets . in this paper , we jointly consider caching and multicasting in a large - scale cache - enabled hetnet with backhaul constraints . we propose a hybrid caching design consisting of identical caching in the macro - tier and random caching in the pico - tier , and a corresponding multicasting design . by carefully handling different types of interferers and adopting appropriate approximations , we derive tractable expressions for the successful transmission probability in the general region as well as the high signal - to - noise ratio ( snr ) and user density region , utilizing tools from stochastic geometry . then , we consider the successful transmission probability maximization by optimizing the design parameters , which is a very challenging mixed discrete - continuous optimization problem . by using optimization techniques and exploring the structural properties , we obtain a near optimal solution with superior performance and manageable complexity . this solution achieves better performance in the general region than any asymptotically optimal solution , under a mild condition .

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1604.00645

heterogeneous wireless networks ( hetnets ) provide a powerful approach to meet the dramatic mobile traffic growth , but also impose a significant challenge on backhaul . caching and multicasting at macro and pico base stations ( bss ) are two promising methods to support massive content delivery and reduce backhaul load in hetnets . in this paper , we jointly consider caching and multicasting in a large - scale cache - enabled hetnet with backhaul constraints . we propose a hybrid caching design consisting of identical caching in the macro - tier and random caching in the pico - tier , and a corresponding multicasting design . by carefully handling different types of interferers and adopting appropriate approximations , we derive tractable expressions for the successful transmission probability in the general region as well as the high signal - to - noise ratio ( snr ) and user density region , utilizing tools from stochastic geometry . then , we consider the successful transmission probability maximization by optimizing the design parameters , which is a very challenging mixed discrete - continuous optimization problem . by using optimization techniques and exploring the structural properties , we obtain a near optimal solution with superior performance and manageable complexity . this solution achieves better performance in the general region than any asymptotically optimal solution , under a mild condition . the analysis and optimization results provide valuable design insights for practical cache - enabled hetnets . cache , multicast , backhaul , stochastic geometry , optimization , heterogenous wireless network

the rapid proliferation of smart mobile devices has triggered an unprecedented growth of the global mobile data traffic . hetnets have been proposed as an effective way to meet the dramatic traffic growth by deploying short range small - bss together with traditional macro - bss , to provide better time or frequency reuse@xcite . however , this approach imposes a significant challenge of providing expensive high - speed backhaul links for connecting all the small - bss to the core network@xcite . caching at small - bss is a promising approach to alleviate the backhaul capacity requirement in hetnets@xcite . many existing works have focused on optimal cache placement at small - bss , which is of critical importance in cache - enabled hetnets . for example , in @xcite and @xcite , the authors consider the optimal content placement at small - bss to minimize the expected downloading time for files in a single macro - cell with multiple small - cells . file requests which can not be satisfied locally at a small - bs are served by the macro - bs . the optimization problems in @xcite and @xcite are np - hard , and low - complexity solutions are proposed . in @xcite , the authors propose a caching design based on file splitting and mds encoding in a single macro - cell with multiple small - cells . file requests which can not be satisfied locally at a small - bs are served by the macro - bs , and backhaul rate analysis and optimization are considered . note that the focuses of @xcite are on performance optimization of caching design . in @xcite , the authors consider caching the most popular files at each small - bs in large - scale cache - enabled small - cell networks or hetnets , with backhaul constraints . the service rates of uncached files are limited by the backhaul capacity . in @xcite , the authors propose a partion - based combined caching design in a large - scale cluster - centric small - cell network , without considering backhaul constraints . in @xcite , the authors consider two caching designs , i.e. , caching the most popular files and random caching of a uniform distribution , at small - bss in a large - scale cache - enabled hetnet , without backhaul constraints . file requests which can not be satisfied at a small - bs are served by macro - bss . in @xcite , the authors consider random caching of a uniform distribution in a large - scale cache - enabled small - cell network , without backhaul constraints , assuming that content requests follow a uniform distribution . note that the focuses of @xcite are on performance analysis of caching designs . on the other hand , enabling multicast service at bss in hetnets is an efficient way to deliver popular contents to multiple requesters simultaneously , by effectively utilizing the broadcast nature of the wireless medium@xcite . in @xcite and @xcite , the authors consider a single macro - cell with multiple small - cells with backhaul costs . specifically , in @xcite , the optimization of caching and multicasting , which is np - hard , is considered , and a simplified solution with approximation guarantee is proposed . in @xcite , the optimization of dynamic multicast scheduling for a given content placement , which is a dynamic programming problem , is considered , and a low - complexity optimal numerical solution is obtained . the network models considered in @xcite do not capture the stochastic natures of channel fading and geographic locations of bss and users . the network models considered in @xcite are more realistic and can reflect the stochastic natures of signal and interference . however , the simple identical caching design considered in @xcite does not provide spatial file diversity ; the combined caching design in @xcite does not reflect the popularity differences of files in each of the three categories ; and the random caching design of a uniform distribution in @xcite can not make use of popularity information . hence , the caching designs in @xcite may not lead to good network performance . on the other hand , @xcite consider analysis and optimization of caching in large - scale cache - enabled single - tier networks . specifically , @xcite considers random caching at bss , and analyze and optimize the hit probability . reference @xcite considers random caching with contents being stored at each bs in an i.i.d . manner , and analyzes the minimum offloading loss . in @xcite , the authors study the expected costs of obtaining a complete content under random uncoded caching and coded caching strategies , which are designed only for different pieces of a single content . in @xcite , the authors consider analysis and optimization of joint caching and multicasting . however , the proposed caching and multicasting designs in @xcite may not be applicable to hetnets with backhaul constraints . in summary , to facilitate designs of practical cache - enabled hetnets for massive content dissemination , further studies are required to understand the following key questions . @xmath0 how do physical layer and content - related parameters fundamentally affect performance of cache - enabled hetnets ? @xmath0 how can caching and multicasting jointly and optimally assist massive content dissemination in cache - enabled hetnets ? in this paper , we consider the analysis and optimization of joint caching and multicasting to improve the efficiency of massive content dissemination in a large - scale cache - enabled hetnet with backhaul constraints . our main contributions are summarized below . @xmath0 first , we propose a hybrid caching design with certain design parameters , consisting of identical caching in the macro - tier and random caching in the pico - tier , which can provide spatial file diversity . we propose a corresponding multicasting design for efficient content dissemination by exploiting broadcast nature of the wireless medium . @xmath0 then , by carefully handling different types of interferers and adopting appropriate approximations , we derive tractable expressions for the successful transmission probability in the general region and the asymptotic region , utilizing tools from stochastic geometry . these expressions reveal the impacts of physical layer and content - related parameters on the successful transmission probability . @xmath0 next , we consider the successful transmission probability maximization by optimizing the design parameters , which is a very challenging mixed discrete - continuous optimization problem . we propose a two - step optimization framework to obtain a near optimal solution with superior performance and manageable complexity . specifically , we first characterize the structural properties of the asymptotically optimal solutions . then , based on these properties , we obtain the near optimal solution , which achieves better performance in the general region than any asymptotically optimal solution , under a mild condition . @xmath0 finally , by numerical simulations , we show that the near optimal solution achieves a significant gain in successful transmission probability over some baseline schemes .

high-@xmath0 metal oxides are a class of materials playing an increasingly important role in modern device physics and technology . here we report theoretical investigations of the properties of structural and lattice dielectric constants of bulk amorphous metal oxides by a combined approach of classical molecular dynamics ( md ) - for structure evolution , and quantum mechanical first principles density function theory ( dft ) - for electronic structure analysis . using classical md based on the born - mayer - buckingham potential function within a melt and quench scheme , amorphous structures of high-@xmath0 metal oxides hf@xmath1zr@xmath2o@xmath3 with different values of the concentration @xmath4 , are generated .

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1302.4534

high-@xmath0 metal oxides are a class of materials playing an increasingly important role in modern device physics and technology . here we report theoretical investigations of the properties of structural and lattice dielectric constants of bulk amorphous metal oxides by a combined approach of classical molecular dynamics ( md ) - for structure evolution , and quantum mechanical first principles density function theory ( dft ) - for electronic structure analysis . using classical md based on the born - mayer - buckingham potential function within a melt and quench scheme , amorphous structures of high-@xmath0 metal oxides hf@xmath1zr@xmath2o@xmath3 with different values of the concentration @xmath4 , are generated . the coordination numbers and the radial distribution functions of the structures are in good agreement with the corresponding experimental data . we then calculate the lattice dielectric constants of the materials from quantum mechanical first principles , and the values averaged over an ensemble of samples agree well with the available experimental data , and are very close to the dielectric constants of their cubic form .

in the complementary metal oxide semiconductor ( cmos ) devices , sio@xmath3 has been the first and only choice of gate oxide material for a long time . however , with the continued decrease in the feature size of the cmos devices , sio@xmath3 is no longer reliable as a gate oxide due to the high tunneling leakage current through it at small thickness . major research efforts are continuously being carried out in search for a suitable replacement of the sio@xmath3 as a gate material.@xcite several promising candidates are metal oxides such as hfo@xmath3,@xcite zro@xmath3@xcite and al@xmath3o@xmath5,@xcite all of which have high value of dielectric constant @xmath0 . high-@xmath0 metal oxides in their amorphous ( a- ) form are more preferable as a gate oxide over their crystalline form due to several important advantages they provide : ( i ) isotropic physical properties ; ( ii ) no crystalline domain boundary which leads to less defects at the interface with the si substrate ; and ( iii ) good compatibility with the conventional cmos fabrication process . some alloy structures of these high-@xmath0 metal oxides are also being studied extensively@xcite and , in fact , a hf based alloy material has already been in its third generation of production as a gate oxide in the semiconductor industry and further improvements of thermal stability , dielectric constant and material preparations are underway.@xcite in clear contrary to the abundance of experimental results in the literature , theoretical studies of the structure and dielectric properties of amorphous metal oxides and their alloys are quite limited . one of the reasons is the difficulties in generating reasonable and reliable amorphous structures with the available theoretical methods . experimentally , the high-@xmath0 materials are deposited on silicon substrate by vapor deposition followed by annealing processes at around @xmath6 k.@xcite simulating the deposition process and the resulting amorphous high-@xmath0 material structures by molecular dynamics ( md ) is extremely time consuming because . the as - deposited a - hfo@xmath3 and a - al@xmath3o@xmath5 films have been generated by kinetic monte carlo ( kmc ) methods@xcite with certain assumptions such as the atoms are kept fixed on pre - determined crystal sites and less important dynamics processes of atomic motion are omitted . both md and kmc are useful for the simulation of the initial atomic layer deposition processes of the amorphous film growth . to generate bulk amorphous structures , _ ab inito _ md simulations can be used in a melt and quench scheme , a - hfo@xmath3,@xcite a - zro@xmath3@xcite and their silicates@xcite have been successfully simulated this way . the activation - relation technique is another method to generate structures of continuous disordered systems@xcite and has been applied to generate a - zro@xmath3 structures.@xcite in this method , one optimizes the structures many times to determine a local energy minima ( in configurational space ) using a force field which can be calculated from quantum mechanical first principles or described by an empirical potential function . for the former the calculation cost is high while for the latter a reliable potential function is required . recently , several extended - tersoff potentials@xcite were proposed for certain metal oxides and applied to generate their amorphous structures from classical md.@xcite amorphous structures are long range disordered systems which typically requires much larger than @xmath7 atoms to simulate . another issue , perhaps more difficult to deal with , is the simulation time scale that is needed for the atoms to evolve into the amorphous structure . while _ ab initio _ methods have simulated up to picoseconds time scale , one certainly wishes to investigate the structures and electronic properties of metal oxides at much larger time scales and much larger sizes in order to reveal the long time limit of the structural evolution and the physical properties of the resulting amorphous material . it is the purpose of this work to report such an investigation . generated by classical md starting from the cubic crystal form of hfo@xmath3 with different lattice constants , corresponding to different densities . if the density is high , the system recrystallizes to its cubic form ( a ) or any other crystal form ( b ) ; if the density is low , the system tends to form disordered structure with big holes ( d ) , whereas with moderate density of @xmath8 g/@xmath9 which corresponds to lattice constant of @xmath10 for crystalline hfo@xmath3 , a reasonable amorphous structure is generated ( c ) . blue spheres represent hf atoms , red spheres are for o atoms.,title="fig : " ] + in particular , we calculate the lattice dielectric constants of bulk amorphous metal oxides by a combined approach of classical md - for structure evolution , and quantum mechanical first principles dft - for electronic structure analysis . we overcome the size and time scale difficulty by classical md simulations in a melt and quench scheme and generate amorphous structures of hfo@xmath3 , zro@xmath3 and their alloys in the form of hf@xmath1zr@xmath2o@xmath3 with different values of the concentration x ( @xmath11 ) . the classical md is based on the interatomic born - mayer - buckingham potential function.@xcite this potential has been developed over many years and extensively applied to investigate the growth processes of y@xmath3o@xmath5 , zro@xmath3 and mg - al - o thin films.@xcite detailed analysis of the amorphous structures are carried out including the coordination number , the radial distribution function and the potential energy per atom of the structures . using the atomic structures generated this way , we carry out first principles density functional theory ( dft ) calculations of the lattice dielectric constant and the results are averaged over ten independent samples for each material . the sample averaged dielectric constants show very good agreement with the corresponding experimental data . the combined approach of classical md and dft is an excellent way to deal with the problem of large sizes and large time scales required by the materials physics of metal oxides . several advantages can be summarized : ( i ) classical md is inexpensive for simulating systems containing large number of atoms which is important for a proper characterization of the amorphous structures having long range disorders , here we have gone up to 768 atoms although several thousand atoms can be easily handled ; ( ii ) in the melt and quench scheme a much longer relaxation time scale , here to several nano seconds , can be evolved after the material is heated above the melting point . such a long time scale is important for erasing the memory of the initial structure thereby the final outcome becomes independent of the initial conditions . here we show that the same kind of amorphous structure is obtained by evolving from different initial structures including from a completely random structure . ( iii ) since the calculated physical properties of amorphous material should be averaged over an ensemble of samples due to the randomness of the structure , the combined classical - quantum approach allows such configurational average to be done . here we show that the calculated dielectric constants of the metal oxides become spatially isotropic after configurational average , but it is typically anisotropic if only one sample is calculated . the paper is organized as follows . in sec . ii we present the classical md method as employed in this work . in sec . iii we discuss the structural properties of our simulated amorphous structures , and also present our results for the lattice dielectric constants of these structures . section iv concludes the paper . structure obtained by the classical md simulations . green , red and blue lines in ( b ) represent hf - o , o - o and hf - hf rdf , respectively . the results are obtained from structures having 768 atoms.,title="fig : " ] +

we identify systematically the universal quantities in the beta function equations , and we give explicit formulae for the universal coefficients at next - to - leading order in terms of integrated correlation functions . as an example , we analyse the radius - dependence of the conformal dimension of some boundary operators for the case of a single neumann brane on a circle , and for an intersecting brane configuration on a torus , reproducing in both cases the expected geometrical answer .

c

0811.3149

higher order conformal perturbation theory is studied for theories with and without boundaries . we identify systematically the universal quantities in the beta function equations , and we give explicit formulae for the universal coefficients at next - to - leading order in terms of integrated correlation functions . as an example , we analyse the radius - dependence of the conformal dimension of some boundary operators for the case of a single neumann brane on a circle , and for an intersecting brane configuration on a torus , reproducing in both cases the expected geometrical answer .

in this paper we have studied conformal perturbation theory beyond the leading order . we have shown that , at least up to quadratic order , the combined bulk boundary perturbation problem is renormalisable , using the minimal subtraction scheme . we also discussed the more commonly used ` wilsonian ' ope scheme , and found it to have some shortcomings at higher order in perturbation theory . we identified systematically the universal ( scheme - independent ) quantities , and gave explicit formulae for them at third order in terms of integrals of conformal 4-point functions . finally , we explained how essentially the same analysis works for the pure bulk and pure boundary case . it seems plausible that similar techniques should allow one to prove renormalisability at arbitrary order in perturbation theory , but we have not attempted to do so . our work was originally motivated by the question of how the dependence of the conformal dimension of a boundary changing field upon a bulk modulus can be understood from the world - sheet perspective . our considerations demonstrate that this effect is captured by a certain universal quadratic rg coefficient , for which we gave an explicit formula . this result should also have interesting applications in other contexts ; in particular , it provides a world - sheet method to study the stability of brane setups under arbitrary bulk deformations .

highly sensitive imaging observations of the galactic center ( gc ) at high energies with an angular resolution of order 10 arcminutes , is a very recent development in the field of high - energy astrophysics . the ibis / isgriimager on the _ two years and an effective exposure of 4.7@xmath2@xmath3 @xmath4 have allowed us to obtain more stringent positional constraints on this high - energy source and to construct its spectrum in the range 20400 @xmath1 . our complete and updated analysis of the emission properties of the _ this result , together with the spectral characteristics of the soft and hard x - rayemission from this region , suggests that the source is most likely not point - like but , rather , that it is a compact , yet diffuse , non - thermal emission region . the centroid of igrj174562901is estimated to be r.a.=@xmath6 , decl.=@xmath7 ( j2000 ) , offset by 1@xmath8from the radio position of sgra@xmath0and with a positional uncertainty of 1@xmath8 . its 20400 @xmath1 luminosity at 8 @xmath9 is @xmath10=(5.37@xmath110.21)@xmath2@xmath12ergs@xmath13 . a 3@xmath5 upper limit on the flux at the electron - positron annihilation energy of 511 @xmath1 from the direction of sgra@xmath0is set at 1.9@xmath2@xmath14ph@xmath15s@xmath13 .

r

astro-ph0508128

highly sensitive imaging observations of the galactic center ( gc ) at high energies with an angular resolution of order 10 arcminutes , is a very recent development in the field of high - energy astrophysics . the ibis / isgriimager on the _ integral_observatory detected for the first time a hard x - raysource , igrj174562901 , located within 1 arcminute of sagittariusa@xmath0 ( sgra@xmath0 ) over the energy range 20100 @xmath1 . here we present the results of a detailed analysis of approximately 7@xmath2@xmath3 @xmath4 of observations of the gcobtained since the launch of _ october 2002 . two years and an effective exposure of 4.7@xmath2@xmath3 @xmath4 have allowed us to obtain more stringent positional constraints on this high - energy source and to construct its spectrum in the range 20400 @xmath1 . furthermore , by combining the isgrispectrum together with the total x - rayspectrum corresponding to the same physical region around sgra@xmath0from _ xmm - newton_data , and collected during part of the gamma - ray observations , we constructed and present the first accurate wide band high - energy spectrum for the central arcminutes of the galaxy . our complete and updated analysis of the emission properties of the _ integral_source shows that it is faint but persistent with no variability above 3@xmath5 , contrary to what was alluded to in our first paper . this result , together with the spectral characteristics of the soft and hard x - rayemission from this region , suggests that the source is most likely not point - like but , rather , that it is a compact , yet diffuse , non - thermal emission region . the centroid of igrj174562901is estimated to be r.a.=@xmath6 , decl.=@xmath7 ( j2000 ) , offset by 1@xmath8from the radio position of sgra@xmath0and with a positional uncertainty of 1@xmath8 . its 20400 @xmath1 luminosity at 8 @xmath9 is @xmath10=(5.37@xmath110.21)@xmath2@xmath12ergs@xmath13 . a 3@xmath5 upper limit on the flux at the electron - positron annihilation energy of 511 @xmath1 from the direction of sgra@xmath0is set at 1.9@xmath2@xmath14ph@xmath15s@xmath13 . very recently , the _ hess_collaboration presented the detection of a source of @xmath16tev @xmath17-raysalso located within an arcminute of sgra@xmath0 . we present arguments in favor of an interpretation according to which the photons detected by _ integral_and _ hess_arise from the same compact region of diffuse emission near the central black hole and that the supernova remnant sgraeastcould play an important role as a contributor of very high - energy @xmath17-raysto the overall spectrum from this region . there is also evidence for hard emission from a region located between the central black hole and the radio arc near l@xmath160.1@xmath18along the galactic plane and known to contain giant molecular clouds .

we now come to the results we have obtained on the morphology of the galactic nuclear region and on igrj174562901 , which we tentatively associated with the supermassive black hole sgra@xmath0 in blanger et al . ( 2004 ) , and whose features we investigate more thoroughly in the present paper . we use three means of investigation to study the various characteristics of the source . the mosaic provides the fine positioning and general shape of the emission from the source and its close neighbours . the individual sky maps provide the elements needed for a variability study from kilosecond to month time scales and the average spectrum of the source can be used to constrain the nature of the emission . section[s : mosaic ] begins with a presentation of the results obtained from the mosaic in the range 2040 @xmath1 on the morphology of the emission from the central degrees . this is followed by a discussion of the changes in the emission s morphology as a function of energy by looking at the mosaics in the different energy bands up to 85 @xmath1 , and ends with our results on the electron - positron annihilation line at 511 @xmath1 . in [ s : lightcurves ] we discuss the light curves and variability of the central source on different timescales , and in [ s : spectrum ] present the broad - band high - energy spectrum of the central arcmins of the galaxy . preliminary results on the gcwith the x - raymonitor jem - xare briefly discussed . the mosaic shown in figure[f : mosaic ] was constructed by summing 2174 sky images from individual pointings and amounts to an effective exposure time of 4.7@xmath2@xmath3 @xmath4 at the position of sgra@xmath0 . this figure presents the highest signal - to - noise ibis / isgri2040 @xmath1 image of the gcyet published , showing an excess of more than 45 in siginificance from the direction of sgra@xmath0 . to model the observed morphology we have assumed that the emission is due to the sum of the known high - energy point - sources of the region that have been detected by _ integral_at least once . the main sources are 1e1740.72942 , ks1741293 , 1a1742294 , slx1744299/300 , 1e1743.12853 , igrj174562901and saxj1747.02853 . the respective positions of these sources were derived from a simultaneous fit of all 8 sources in the 2040 @xmath1 mosaic . all positions were left as free parameters except for that of saxj1747.02853 that was fixed . this source was quite active for the period refered to as spring 2004 and thus contibutes to the emission near the gcbut since its global contribution is weak and it can not be clearly resolved from 1e1743.12853 we must fix its position . the result of the fitting procedure is well illustrated in figure[f : fit ] where we see the mosaic ( left ) , the model ( middle ) , and the residual map after subtraction of the model from the sky map ( right ) . we can see that the spatial distribution of the modeled image resembles very closely that of the mosaic , even if the residues hint at the presence of a non - uniform underlying emission that is not properly taken into account in the tested model . the fitted source positions are listed in table[t : sourcepositions ] where we also report the signal - to - noise , the estimated error radius corresonding to the 90% confidence level and the offset with respect to the proposed counterpart . we find that the position of igrj174562901 , detected at a signal - to - noise level of 45 in this energy band , is r.a.=@xmath49 , decl.=@xmath7 ( j2000 ) with an uncertainty of 0@xmath8.75 . the reliability of the derived position for this excess is supported by the fact that all the other sources in the field are very well positioned . the brightest source , 1e1740.72942 , is well within its associated error radius . for 1a1742294 , the reported offset is very close to the value of psla , while in the case of ks1741293 the best known coordinate position itself has an uncertainty of about 1@xmath8@xcite . the source we labeled slx1744299 , is in fact a system composed of two known x - ray bursters located within @xmath163@xmath8of each other @xcite and for this reason we do not expect the fit to yield a position within the pslafor either one of the two sources , independently of the detection significance . 1e1743.12853 , a well known , bright x - ray source @xcite is almost certainly contributing to the high - energy emission in the region . however , performing the simultaneous fit using a single source to model the emission from the region around this source gives a centroid offset by about 2@xmath8from the _ xmm - newton_position known to arcsecond accuracy ; a result that is not compatible with the expected error . since , as mentioned above , we know of one source detected by isgrithat was active over the course of the first part of 2004 , namely saxj1747.02853 , we included it and fixed its position . this yields a fitted position for 1e1743.12853 that is well within the uncertainty derived from the source s detection significance . the position of igrj174752822 was compared to the center of the sgrb2 complex and discussed below . igrj174562901is located at 1@xmath8.1 from the radio position of sgra@xmath0and 0@xmath8.9 from the center of sgraeast . it is therefore compatible with either of these sources . indeed , even if its associated positional uncertainty of 0@xmath8.75 is somewhat smaller than the offset , we expect this pslato be slightly overestimated when fitting multiple close sources ( i.e. within the full width of the psf ) . for example , in the case of the known source 1a1742294 , the measured offset can be 2030% times larger than the psla . morever we have found that the positions of 1e1743.12853 and igrj174562901can change by 0@xmath8.30@xmath8.4 depending on the model adopted , and in some cases igrj174562901is positioned only 0@xmath8.6 from sgra@xmath0 . for this reason we adopt a final error radius for the central source ( and for 1e1743.12853 that has a comparable signal - to - noise ratio ) of 1@xmath8 , about 30% larger than the pslavalue of 0@xmath8.75 derived from the relation given by gros et al . ( 2003 ) . on the other hand , we can safely exclude a number of other candidates such as the transient _ asca_source axj1746.52901 @xcite mentioned by revnivtsev et al . ( 2004 ) as a possible counterpart for the central excess based on the fact that it is located at a distance of more than 2@xmath8from it . a similar analysis was performed on the mosaics from the same data set in different energy bands . as is clearly seen from the iso - significance contours in figure[f : mosaic_4bands ] , the morphology of the central degrees does not radically change with increasing energy . however , we notice that the emission that seems to bridge the sources labelled sgra@xmath0and 1e1743.12843 at low - energy persists at higher energies such that in the 56 to 85 @xmath1 range , the emission from the region seems to be centered between the two sources . this is a surprising result that we can not readily interpret . an investigation of this based on a comparison of the emission detected by ibis / isgriwith the 20 @xmath25 radio map , the 6.4 @xmath1 fe line - emission contours and the cs map of the region raises several other interesting questions . figure[f : radio20 cm ] is a radio continuum map at 20 @xmath25 @xcite on which we have overlayed the 2030 @xmath1 iso - significance isgricontours as they are shown in figure[f : mosaic_4bands ] ( top left ) . firstly , the centroid of the very bright sgra complex which includes the luminous sgraeast appears to be in best agreement with the 2030 @xmath1 isgricontours ( fig.[f : mosaic_4bands ] top left ) . for completeness , we performed the simultaneous fit using the position of sgraeastinstead of the one for sgra@xmath0and obtained very similar results . the offset of the fitted source is nonetheless slightly smaller for sgraeastthat for sgra@xmath0 but both are within the pslaand thus statistically equivalent . we also see that the radio arc is quite distant from the peak near sgra@xmath0and can therefore be confidently excluded as a possible contributor to the flux at that position . however , the rough alignment of the radio arc with the elongation on the 2030 @xmath1 contours in the direction of negative latitudes is intriguing . in the 5685 @xmath1 contours ( fig.[f : mosaic_4bands ] bottom right ) we see that the centroid of the emission is almost exactly between the sgra complex and the radio arc . this region is known to harbour large molecular clouds and there appears to be a very good agreement between this high - energy emission feature and both the 6.4 @xmath1 fe line - emission , tracing irradiated molecular regions , and the cs map , tracing regions with high gas density . furthermore , the centroid of this high - energy source is strikingly close to that of the unidentified _ egret_source 3egj17462851 and could in fact be its soft @xmath17-raycounterpart . we extracted a spectrum for this source by fitting three sources , two of which had their positions fixed to those of sgra@xmath0and 1e1743.12853 , and obtained a power - law photon index of @xmath31@xmath162.3 , and a luminosity of @xmath27@xmath162.6@xmath2@xmath12ergs@xmath13 for a distance of 8 @xmath9 . a more detailed analysis of this source will be presented in future work . moving in the direction of positive longitudes , we clearly see an emission region depicted in the 2030 @xmath1 contours and whose centroid is labeled as igrj174752822 ; a source associated with sgrb2 by revnivtsev et al . ( 2004 ) . indeed this source coincides with the radio - bright sgrb2 complex composed of molecular clouds and several compact hii regions . the fitted centroid for this source , taken to be point - like in the 2040 @xmath1 image , is positioned 1@xmath8.6 from the estimated center of the cloud . as was pointed out by revnivtsev et al . ( 2004 ) , there is good agreement between the 6.4 @xmath1 fe line contours and the emission detected by isgrias igrj174752822 . moreover , the extension toward the north could tentatively be associated with the composite snrg0.9 + 0.1 @xcite . the x - rayemission of its pulsar wind nebula ( pwn ) has been mapped with _ xmm - newton _ @xcite and the extrapolation of the flux towards 20 @xmath1 of about 9@xmath2@xmath50ph@xmath15s@xmath13 , is consistent with the residual flux of roughly 0.06 @xmath51 ( 2040 @xmath1 ) or 8@xmath2@xmath50ph@xmath15s@xmath13 . it is therefore tempting to interpret it as a detection of the highest energy synchrotron radiation from this source that was detected for the first time this year by the _ hess_instrument @xcite . it is worth noting that a long _ xmm - newton_exposure of this object has revealed the presence of variable source probably of an accreting binary type , located at a distance of 1@xmath8@xcite . having a luminosity close to that of g0.9 + 0.1 , its contribution to the residual isgriemission could be significant . lrcccc 1e1740.72942 & 241.8 & @xmath52 & 0.28 & 0.14 + 1a1742294 & 98.6 & @xmath53 & 0.40 & 0.55 + slx1744299 & 61.8 & @xmath54 & 0.60 & 1.14 + ks1741293 & 63.9 & @xmath55 & 0.59 & 1.23 + 1e1743.12843 & 46.3 & @xmath56 & 0.74 & 0.54 + sgra@xmath0 & 45.4 & @xmath57 & 0.75 & 1.13 + igrj174752822 & 18.9 & @xmath58 & 1.24 & 1.51 + saxj1747.02853 & 16.5 & @xmath59 & 1.45 & 0.0 + [ t : sourcepositions ] we performed the analysis of the entire data subset used to construct the mosaics in the narrow band between 500 and 522 @xmath1 . this corresponds to the fwhmof the emission line in the isgriinstrument @xcite . a background map that corresponds to this energy range was used and thus the resulting mosaic is free of systematic effects . no sources are detected in the field spanning 10 degrees on either side of the gcboth in longitude and latitude . we obtain a 3@xmath5 upper limit of 1.9@xmath2@xmath14ph@xmath15s@xmath13to the flux from a point - source at the position of sgra@xmath0where the exposure and thus the sensitivity is maximal . this limit is calculated taking into account corrections derived from the probability of photoelectric interaction at 511 @xmath1 in the isgridetector ( 34% ) and the fact that we have selected events using a band corresponding to 78% of line flux . spidetected a 511 @xmath1 line flux of about @xmath60ph@xmath15s@xmath13with intrinsic line width of 2.7 @xmath1 ( fwhm ) from a region well described by a gaussian with a fwhmof about 8@xmath18and that coincides approximately with the galactic bulge @xcite . if we assume that our sensitivity is more or less uniform over the central 10 degrees around sgra@xmath0 , our upper limit implies that if this emission is due to a collection of @xmath61 point - sources clustered together such that they can not be resolved by spi , then under the simplifying assumption that they all contribute equally to the total flux , each must have a flux of about @xmath62@xmath2@xmath60ph@xmath15s@xmath13 . therefore , at least 5 individual sources would be necessary to account for this extended 511 @xmath1 emission in general agreement with the spiresult @xcite . finally , jem - xmosaics in four energy bands , with a total exposure is 3.2 @xmath40 and effective exposure at the location of sgra@xmath0of about 500 @xmath41 , were constructed from 1204 science windows taken between 2003 february to 2004 october . we used the following energy ranges : 34 , 48 , 814 , 1435 @xmath1 and find no evidence in this data sample for the presence of a jem - xsource in the sagittariusa complex except for a very marginal excess in the 814 @xmath1 mosaic . although this analysis is preliminary and at this point somewhat qualitative , it is an interesting result in the light of the strong isgridetection and obvious intense x - rayemission from this region seen by _ xmm - newton_and _ chandra_. it may be an additional indication that the emission is not due to a point - source but rather to a compact diffuse emission region were thermal and non - thermal processes take place . the complete light curve of igrj174562901 in the 2040 @xmath1 energy range , with a resolution of about 1800 @xmath4 corresponding to the duration of a single pointing , is shown in figure[f : unbinnedlc ] . since low amplitude variability on kilosecond time scales can not be meaningfully studied for such a weak source due to statistical limitations , we have also done a search on longer time scales by rebinning the total light curve on the basis of 1 day , 2 weeks and 1 month . these rebinned data sets are presented in figure[f : binnedlc ] . no individual point deviates from the mean by more than 3@xmath5 . the level of variability in the flux from the central source was evaluated by means of a simple chi - squared test . for the unbinned data set shown in figure[f : unbinnedlc ] , the reduced chi - squared value is @xmath63=1.3 ( 2758/2093 ) . for the light curve with 1-day time resolution ( fig.[f : binnedlc ] top ) we found @xmath63=1.7 ( 180/109 ) . in the case of the 2-week time resolution light curve ( fig.[f : binnedlc ] middle ) , the reduced @xmath64 value was found to be 3.6 ( 61/17 ) . however , if we exclude the first point in this data set which corresponds to the data collected during revolution 46 , the first observation of the gcjust after the initial calibration phase , we find a value of @xmath63=2.1 ( 34/16 ) , in closer agreement with the previous two . finally , in the case of the 1-month time resolution light curve ( fig.[f : binnedlc ] bottom ) we find values of 5.2 ( 52/10 ) and 3.1 ( 28/9 ) if we exclude the first data point , heavily affected by the revolution 46 data given that there is a three - week gap between this revolution and the second observation of the gcduring revolution 53 . these reduced chi - squared values tend to increase as the binning gets coarser and thus we might be seeing a small level of variability on monthly timescales . disregarding the data point associated with rev . 46 , the only deviation that almost reaches 3@xmath5 from the mean is at the very end of the light curve where . this lack of evidence for significant variations in flux other than the low level of variability seen on monthly timescales is in contradiction with the previous detection of a flare from igrj174562901@xcite that we therefore do not confirm . we point out that those results were obtained with the preliminary analysis procedures and without background corrections . the data subset covering the observation period of the reported flare ( 2003 april ) processed with the most recent analysis software and background correction maps do not indicate significant variability with respect to the mean count rate . similarly , the sources 1e1743.12843 and igrj174752822 seem rather constant unlike the four well known x - raybinaries that show very large intensity variations over the two - year observation period . figure[f : isgri_ufs ] shows the isgrispectrum of the gcsource that we modelled with a simple power - law of index @xmath31=3.04@xmath110.08 ( @xmath65=7.92 for 5 dof and 3% systematics ) . the pegged power - law model _ pegpwrlw _ in xspecuses the total flux as normalization and in this way the photon index and normalization are independent paraters . the total flux in the range from 20 to 400 @xmath1 is @xmath66=(7.02@xmath110.27)@xmath2@xmath67erg@xmath15s@xmath13 , which corresponds to a luminosity of @xmath27=(5.37@xmath110.21)@xmath2@xmath12ergs@xmath13at a distance of 8 @xmath9 to the gc . in the 20100 @xmath1 range , the luminosity is @xmath27=(4.56@xmath110.10)@xmath2@xmath12ergs@xmath13 , somewhat higher than our first estimate of @xmath163@xmath2@xmath12ergs@xmath13 @xcite . this is not surprising given that the first estimate was based on a rough comparison with the crab s count rate in only two energy bands , 2040 and 40100 @xmath1 , and that we now have 5 points to constrain the slope . furthermore , the detection significance of the central source was much lower than in the present case . now turning to the broad - band high - energy spectrum of igrj174562901 , we can see in figure[f : gcspec - ufs ] , the spectrum of the central source from 1 to 400 @xmath1 where the x - rayportion ( 110 @xmath1 ) is from _ xmm - newton_data collected during the multiwavalength campaign , and therefore contemporaneous with part of the isgridata from 2004 used to construct the soft @xmath17-rayportion ( 20400 @xmath1 ) of the spectrum that was discussed earlier and is shown by itself in figure[f : isgri_ufs ] . the x - rayspectrum was made by extracting the photon flux from a region centered at the position of igrj174562901and with an radius of 8@xmath8 . this integration radius was chosen to be compatible with the ibis / isgripsf because there is no obvious x - raypoint - source counterpart to igrj174562901within 1@xmath8of sgra@xmath0 . such a point - source would have to be hard , persistant and extremely bright in x - rayin order to be compatible with the high - energy flux of the _ integral_gcsource . the model fitting for large extended regions near the gcis challenging for two main reasons . first , the x - rayspectra of such extended regions give a corse , averaged spectral behaviour of a complex field heavily dominated by diffuse emisson that we know to have several different spectral components @xcite but that also includes all the point sources some of which surely contribute to the hard x - rayflux . of course , this difficulty dissipates as integration radius decreases since fewer components are summed together . second , we have no _ a priori _ knowledge of the nature of the emission detected as igrj174562901and therefore do not know whether the comparison with the total x - rayspectrum from a region that roughly corresponds to isgri s angular resolution is an appropriate one . keeping these caveats in mind , we justify this type of comparison by pointing to the fact that the source coincident with the gc , detected by _ integral_as what appears to be a point - source , must undoubtedly contribute to the x - rayspectrum from the region that corresponds to its spatial extent . the spectral transition from 10 to 20 @xmath1 must be more or less continuous and therefore we expect the high - energy component present in the x - rayspectrum and from which igrj174562901arises , to stand out beyond the thermally dominated spectrum at around 20 @xmath1 . therefore , a large @xmath65 value should not be surprising for it points to the fact that the emission in the range from 1 to 3 @xmath1 is not modelled properly for the reason mentioned above . our aims in this section is to constrain the high - energy characteristics of this source in the range 1400 @xmath1 using the isgrispectrum above 20 @xmath1 . the broad - band spectrum can be modelled using a simple broken power - law over the entire range to get an idea of the change of spectral index with increasing energy . however , in order to be as constraining as possible without overlooking possibly important components to this emssion like the hot temperature plasma present in the gcregion , we performed the fit with the same model as the one used by muno et al . ( 2004a ) to fit the diffuse emission from the various regions in the @xmath68@xmath2@xmath68 field around sgra@xmath0referred to as southeast , southwest , northwest , east , close , and northeast by the authors . this model comprises a two - temperature plasma with different absorption columns , a power - law and a gaussian line to fit the 6.4 @xmath1 neutral fe emission line absorbed with the same column density . although providing a reasonable fit to the data from 28 @xmath1 , the model does not work well in the isgrirange of the spectrum . the power - law fit with index @xmath31@xmath282 underestimates the flux in the 2040 @xmath1 range and overestimates it above 85 @xmath1 . a somewhat better fit is provided by replacing the simple power - law with either a cutoff or broken power - law . in the case of the cutoff power - law , we found a photon index @xmath31@xmath281 and cutoff energy of about 25 @xmath1 , and in the case of the broken power - law , the photon indeces were found to be @xmath69@xmath281.5 and @xmath70@xmath283.2 with a break energy of about 27 @xmath1 . the best fit parameters values are given in table[t : fitparams ] where only the free parameters are listed ; all abundances are fixed to solar abundance . looking closely at the unfolded spectra shown in figure[f : gcspec - ufs ] , we can distinguish the low and high temperature plasma components drawn in red and green respectively , the gaussian line in light blue and the broken power - law in dark blue . the hot thermal component clearly dominates the spectrum at low - energies but its contribution is already well below that of the power - law component in the 2030 @xmath1 band and is totally negligible beyond that . if we fix the temperature of the hot component at 8 @xmath1 , the effect on the other parameters is small . the photon index in the cutoff power - law decreases from 1.09 to 1.05 and the high - energy cutoff from 24.4 to 27.7 @xmath1 . the @xmath64 value increases to 4849.0 for one more dof and therefore the reduced chi - squared is slightly larger i.e. @xmath71=1.82 , and the contribution of this component to the overall flux in the 2030 and 3040 @xmath1 bands increases by a factor of 2 but still lies 3 times below the power - law in the first band and a factor of 7 below in the second . lcc @xmath72 ( @xmath73@xmath74 ) & @xmath75 & @xmath76 + @xmath77 ( @xmath1 ) & @xmath78 & @xmath79 + @xmath80 & @xmath81 & @xmath82 + @xmath83 ( @xmath73@xmath74 ) & @xmath84 & @xmath85 + @xmath86 ( @xmath1 ) & @xmath87 & @xmath88 + @xmath80 ( @xmath89 ) & @xmath90 & @xmath91 + @xmath69 & @xmath92 & @xmath93 + @xmath94 ( @xmath1 ) & @xmath95 & @xmath96 + @xmath70 & & @xmath97 + @xmath98 ( @xmath60ph@xmath15s@xmath13kev@xmath13 ) & @xmath99 & @xmath100 + @xmath64(dof ) & 4490.7(2658 ) & 4458.0(2657 ) + a multi - wavelength campaign to study sgra@xmath0with a total exposure time of about 500 @xmath41 was performed in two segments , the first of which was from 2004 march 28 to april 1 and that we refer to as epoch1 , and the second from 2004 august 31 to september 3 refered to as epoch2 . the primary aim of this campaign was to study correlated variability , particularly in the ir , x - rayand soft @xmath17-rayenergy bands . figures[f : xmm - integ1 ] and [ f : xmm - integ2 ] show the 210 @xmath1 _ xmm - newton_light curve of a 10@xmath26region around sgra@xmath0 in the bottom panels , and the 2030 @xmath1 isgrilight curve of igrj174562901 in the upper panels for epochs1 and 2 respectively . as is clearly visible , the periods during which the factor-40 flares from the direction of sgra@xmath0occured do not have simultaneous coverage in the _ integral_data . unfortunately , both data gaps in the isgrilight curve correspond to the period between orbits . for this reason we are still unable to conclude whether or not we can expect to detect a correlated variability in the x - rayand soft @xmath17-raybands . there are two features worth mentioning that can be noticed in figure[f : xmm - integ2 ] although they have marginal statistical significance . first , two points in the isgrilight curve , approximately in the middle of the upper panel , stand out at about 2.5@xmath5 above the mean . these are temporally coincident with the two hiccups at the end of the first data subset in the x - raylight curve shown in the bottom panel . second , the weighted mean x - raycount rate is somewhat higher in the first data subset ( @xmath101 ) than in the second ( @xmath102 ) , a behaviour apparently seen also in the two corresponding segments of the isgrilight curve where the weighted mean count rate is @xmath103 in the first and @xmath104 in the second . this indicates that there may be a relationship between the flaring activity of sgra@xmath0and emission at higher energies . future simultaneous observations will undoubtedly help elucidate this point which remains uncertain .

october 2002 . furthermore , by combining the isgrispectrum together with the total x - rayspectrum corresponding to the same physical region around sgra@xmath0from _ xmm - newton_data , and collected during part of the gamma - ray observations , we constructed and present the first accurate wide band high - energy spectrum for the central arcminutes of the galaxy . integral_source shows that it is faint but persistent with no variability above 3@xmath5 , contrary to what was alluded to in our first paper . very recently , the _ hess_collaboration presented the detection of a source of @xmath16tev @xmath17-raysalso located within an arcminute of sgra@xmath0 . we present arguments in favor of an interpretation according to which the photons detected by _ integral_and _ hess_arise from the same compact region of diffuse emission near the central black hole and that the supernova remnant sgraeastcould play an important role as a contributor of very high - energy @xmath17-raysto the overall spectrum from this region . there is also evidence for hard emission from a region located between the central black hole and the radio arc near l@xmath160.1@xmath18along the galactic plane and known to contain giant molecular clouds .

i

astro-ph0508128

highly sensitive imaging observations of the galactic center ( gc ) at high energies with an angular resolution of order 10 arcminutes , is a very recent development in the field of high - energy astrophysics . the ibis / isgriimager on the _ integral_observatory detected for the first time a hard x - raysource , igrj174562901 , located within 1 arcminute of sagittariusa@xmath0 ( sgra@xmath0 ) over the energy range 20100 @xmath1 . here we present the results of a detailed analysis of approximately 7@xmath2@xmath3 @xmath4 of observations of the gcobtained since the launch of _ october 2002 . two years and an effective exposure of 4.7@xmath2@xmath3 @xmath4 have allowed us to obtain more stringent positional constraints on this high - energy source and to construct its spectrum in the range 20400 @xmath1 . furthermore , by combining the isgrispectrum together with the total x - rayspectrum corresponding to the same physical region around sgra@xmath0from _ xmm - newton_data , and collected during part of the gamma - ray observations , we constructed and present the first accurate wide band high - energy spectrum for the central arcminutes of the galaxy . our complete and updated analysis of the emission properties of the _ integral_source shows that it is faint but persistent with no variability above 3@xmath5 , contrary to what was alluded to in our first paper . this result , together with the spectral characteristics of the soft and hard x - rayemission from this region , suggests that the source is most likely not point - like but , rather , that it is a compact , yet diffuse , non - thermal emission region . the centroid of igrj174562901is estimated to be r.a.=@xmath6 , decl.=@xmath7 ( j2000 ) , offset by 1@xmath8from the radio position of sgra@xmath0and with a positional uncertainty of 1@xmath8 . its 20400 @xmath1 luminosity at 8 @xmath9 is @xmath10=(5.37@xmath110.21)@xmath2@xmath12ergs@xmath13 . a 3@xmath5 upper limit on the flux at the electron - positron annihilation energy of 511 @xmath1 from the direction of sgra@xmath0is set at 1.9@xmath2@xmath14ph@xmath15s@xmath13 . very recently , the _ hess_collaboration presented the detection of a source of @xmath16tev @xmath17-raysalso located within an arcminute of sgra@xmath0 . we present arguments in favor of an interpretation according to which the photons detected by _ integral_and _ hess_arise from the same compact region of diffuse emission near the central black hole and that the supernova remnant sgraeastcould play an important role as a contributor of very high - energy @xmath17-raysto the overall spectrum from this region . there is also evidence for hard emission from a region located between the central black hole and the radio arc near l@xmath160.1@xmath18along the galactic plane and known to contain giant molecular clouds .

we have studied the morphology of the high - energy emission from the central few degrees of the galaxy in the energy range from 20 to 400 @xmath1 based on a sample of _ integral_data collected from 2003 february to 2004 october with a total livetime of 7@xmath2@xmath3 @xmath4 . we paid particular attention to the characteristics of the emission from the galactic nuclear region where we detect a source with high significance in the 2040 @xmath1 energy range located at r.a.=@xmath49 , decl.=@xmath7 ( j2000 ) with an uncertainty of 1@xmath8and therefore compatible with the position of the central black hole sgra@xmath0 . this detection confirms the results obtained by blanger et al . ( 2004 ) on the gcsource igrj174562901 . the source igrj174562901is persistent and shows no variability at the 3@xmath5 level in contradiction with what was suggested to in blanger et al . this result holds at kilosecond , daily , bi - weekly and monthly timescales . the spectrum of the central source in the 20400 @xmath1 range is well fit by a power - law of index @xmath31@xmath283 . we have combined this dataset with the x - rayspectrum of a circular region with radius 8@xmath8centered the _ integral_gc source derived from partially contemporaneous _ xmm - newton_data collected during observations of the gcperformed in 2004 in the range 110 @xmath1 . from this we find that the broad - band high - energy spectrum can be fit equally well with a model that comprises a two - temperature plasma ( @xmath105@xmath281.0 , @xmath106@xmath286.5 ) , a gaussian line to account for the neutral fe emission at 6.4 @xmath1 , and either a cutoff power - law with photon index @xmath31@xmath281 and cutoff energy of about 25 @xmath1 or a broken power - law with photon indeces @xmath69@xmath281.5 and @xmath70@xmath283.2 , and break energy @xmath2827 @xmath1 . we also detect hard ( @xmath31@xmath162.2 ) emission from a region located between sgra@xmath0and the radio arc that seems to coincides with the 6.4 @xmath1 emission from neutral to weakly ionised fe and with the cs map of the region . as is the case with igr174752822 , we believe that this new detection of hard x - rayemission orginates in one or several large molecular clouds known to exist in that region . the nature of the emission from the direction of the sgra complex detected as igrj174562901is unknown . in what follows we discuss a number of scenarios in an attempt to identify the source of the emission detected by _ integral_and apparently centered on sgra@xmath0 . the hot component at 68 @xmath1 of the two - temperature plasma at the gc is well known and its presence is viewed by many as problematic in terms of it being confined given the escape velocity of a hydrogen plasma at that temperature or of the heating mechanisms that would be required to supply energy to the plasma were it not confined . it is interesting to ask what is this hot plasma s extrapolated flux at energies between 2030 @xmath1 in order to assess its possible contribution to the flux detected from the central arcminutes . in [ s : spectrum ] we showed that although the hot plasma component totally dominates the spectrum in the range from 2 to 5 @xmath1 , its contribution to the overall flux is several times less than that of the power - law in the 2030 @xmath1 range and drops to a negligible level with respect to the power - law component in the range 3040 @xmath1 . these estimates are based on the best fit value for the temperature of 6.5 @xmath1 and clearly the contribution increases somewhat if we fix the temperature at 8 @xmath1 . nonetheless this hot plasma can only provide a very small fraction of the emission detected from the direction of the gcby _ integral _ , and this solely in the first band , from 20 to 30 @xmath1 . a large number of x - raytransients have been detected in the neighbourhood of sgra@xmath0 in the last few years @xcite . in fact , there even appears to be an over - abundance of such sources near the gcwhere four x - raybinaries lie within 1 @xmath107 ( 25@xmath26 ) of sgra@xmath0@xcite . these sources , observed at luminosities between @xmath29 and @xmath32 ergs@xmath13 in the 210 @xmath1 range , are not particularly bright since these luminosities are intermediate between quiescence and outburst . in the paragraphs that follow we attempt to estimate the effect of such sources on the flux of igrj174562901 in the 20120 @xmath1 range . we restrict ourselves to this energy range because it is here that we have the best estimate of flux from the isgridata . the gcsource igrj174562901shows very little variability and hence its persistant quality demonstrates that it is probably not heavily influenced by the sometimes radical brightening of an individual x - raytransient as it moves from quiesence to outburst . furthermore , the high detection significance in the 2040 @xmath1 band permits an accurate determination of the emission centroid and yields an uncertainty of about 1@xmath8 . for this reason , we do not consider transients that lie outside the error radius of igrj174562901but turn our investigation to the 4 transients detected by _ chandra_within 30@xmath26of the central bh@xcite and pay particular attention to the remarkable lmxblocated just 3@xmath26south of sgra@xmath0@xcite . this transient , cxogcj174540.0290031 , was very bright during both epochs of the multiwavelength campaign , the only period for which we have contemporaneous x - rayand _ integral_data , and will therefore be the main focus of the discussion . the four transients detected within 30@xmath26of sgra@xmath0are also the hardest of the seven transients discussed by muno et al . ( 2005a ) . these are : cxogcj174535.5290124 , cxogcj174538.0290022 , cxogcj174540.0290005 and cxogcj174540.0 - 290031 . using the available _ chandra_data for these ( and _ xmm - newton_for cxogcj174540.0290031 ) , we constructed their respective light curves in the range 28 @xmath1 and rebinned to make the long term trends more apparent ( the _ chandra_results were published in muno et al . ( 2005a ) ) . we plotted the light curve for igrj174562901rebinned in 2 week segments on the same time line . the 2040 @xmath1 range is used because it has the highest signal - to - noise ratio . figure[f : transients ] shows these light curves where that of igrj174562901appears as the top most . the flux is in units of ph@xmath15s@xmath13and the time is in modified julian days . the observation cycles are clearly depicted by the isgrilight curve where each data subset corresponds to a season , the first one being spring 2003 and the last , fall 2004 . as was found in [ s : lightcurves ] , there is no clear sign of variability in the _ integral_light curve other than the close to 3@xmath5 deviation in the very last part of the light curve . furthermore , it is difficult to draw conclusions from the general comparison with the flux levels of the four hardest _ chandra_transients shown in figure[f : transients ] . we will now take a closer look at the unusual transient cxogcj174540.0290031 . this source was discovered during the 2004 july _ chandra_observations of the gc @xcite and was also seen to be active throughout both epochs of the multiwavelenth campaign of 2004 , reaching its peak x - raybrightness in april . a very clear periodic signal was detected from this source during epoch2 and the orbital period was determined to be about 8 @xmath108 @xcite . this source , located remarkably close to the supermassive bhat only @xmath163@xmath26 from the radio position of sgra@xmath0 , was observed in radio during the campaign @xcite , and seen to produce a jet with luminosity @xmath109@xmath16@xmath110ergs@xmath13 . in order to estimate the possible contribution of this source to the _ integral_flux , we used the spectral parameters derived from the contemporaneous _ xmm - newton_observations and presented in porquet et al . 2005 . taking a photon index of @xmath31=1.6 and 210 @xmath1 flux normalization of 1.3@xmath2@xmath111erg@xmath15s@xmath13we find that the extrapolated 20120 @xmath1 luminosity is about 5@xmath2@xmath112ergs@xmath13 . for an index @xmath31=1.98 and flux @xmath66=1.8@xmath2@xmath111erg@xmath15s@xmath13 , we get an extrapolated luminosity of 2.5@xmath2@xmath112ergs@xmath13 . the largest of these values amounts to about one tenth of the derived luminosity of igrj174562901 and is probably still over - estimated given that the spectrum of a lmxbin outburst is rarely a pure power - law above energies @xmath16100 @xmath1 . a more realistic description would be a comptonization model where the seed photons are boosted to higher energies as they encounter fast thermal electrons in the hot ( 3050 @xmath1 ) corona . in this case , the contribution in the isgriband would very likely be even less than the above extrapolations . according to this simple estimate , ten sources similar to cxogcj174540.0290031 in luminosity and spectral index within a few arcminutes of sgra@xmath0would have to be active more or less continuously to account for the 20120 luminosity of igrj174562901 . of course , the flux could be due to a substantially larger number of dim and hard sources that have until now evaded detection by _ chandra_and _ xmm - newton_and that are clustered around sgra@xmath0 . this however , is an unlikely scenario . we have considered and tried to quantify the effect of the known x - raytransients located within 30@xmath26of sgra@xmath0on the isgricount rate . we find that the flux of igrj174562901can not be explained by the contribution of transients located very close to the central bh , and that their contribution appears to be negligeable over the range from 20 to 120 @xmath1 . our campaign to search for correlated variability in the x - rayand soft @xmath17-rayflux from the central bhwas inconclusive due to _ integral_data gaps during the sgra@xmath0flares . of the two factor-40 flares that occured on 2004 march 31 and august 31 , the first was somewhat harder with a photon index of @xmath31=1.52 compared to @xmath31=1.87 for the second flare @xcite . by extrapolating the flux of the hardest flare to the 2030 @xmath1 energy band we find that its contribution to the isgricount rate using an average effective area in this band of 650 @xmath113 should be about 0.05 @xmath51 . taking a peak flare flux equivalent to twice the average gives 0.1 @xmath51 and so since igrj174562901 s observed isgricount rate in this range is around 0.4 @xmath51 we would expect a rise of @xmath1625% due to the flare . based on these simple assumptions , this type of event would therefore not be detectable by isgri , and for the same reason , can not explain the emission seen as igrj174562901 . furthermore , the derived luminosity of the gcsource of around 5@xmath2@xmath12ergs@xmath13 , can not result directly from the integration of successive flares from the central black hole . the flares occur on average once per day and have typical luminosities of @xmath12ergs@xmath13for durations of a few thousand seconds . if the flares last 3 to 20 @xmath41 , even if they all reached peak luminosities of around @xmath32ergs@xmath13 , this would still not be enough to make up the persistant luminosity of igrj174562901 . this is not to say , that the acceleration of particles to very high lorentz factors during such a flare could not lead to a secondary high - energy emission that would not be detected by x - rayinstruments but that would contribute to the flux in the range 20400 @xmath1 . the detection of a persistant source up to about 120 @xmath1 compatible with the position of the central bhraises the very interesting possibility that it may be related to the tev source detected from the same region by _ these observations lend crucial support to the idea that acceleration of particles to very high energies is taking place at the gc@xcite . furthermore , all of them agree on the apparent absence of variability from the central source . the _ hess_collaboration has been particularly successful at determining the high - energy properties of this source detected over two epochs , 2003 june - july and 2003 july - august , and together with the earlier 30 @xmath36 to 10 @xmath20 _ egret_detection of the continuum source 3egj17462851 within 1@xmath18of the nucleus @xcite , this tev detection provides some evidence of hadronic acceleration at the gc , either by sgra@xmath0itself , within the shocked shell of an snr , such as sgraeastor by some other mechanism inlcuding the interaction of non - thermal filaments with dense molecular environments . protons could be accelerated , either via @xmath114 order fermi acceleration at a shock , or via stochastic acceleration ( a @xmath115 order fermi process ) in a turbulent magnetic field , and then scatter with ambient protons to produce pions . the @xmath116 s subsequently decay into 2@xmath17-rays , whereas the @xmath117 s and @xmath118 s initiate a muon , electron , positron , and neutrino cascade ( see e.g. , markoff , melia & sarcevic 1997,1999 ) . some evidence for a pion origin of the @xmath17-raysis provided directly by the _ egret_spectrum , which exhibits a clear break at @xmath161 @xmath20 , and therefore can not be fit by a single power law . instead , this break is usually attributed to the rest - frame energy of pion - decay photons . the secondary electrons and positrons produced by the charged pions in concert with the @xmath116-decay photons , are capable of producing their own @xmath17-rayemission via bremsstrahlung and compton scattering . for example , if these leptons build up to a steady - state distribution balanced by bremsstrahlung and coulomb losses , they naturally account for the lowest energy _ this is rather important because the pion decays link the lepton and photon generation rates , so the bremsstrahlung and pion - decay photon emissivities are tightly correlated . the possibility that the relativistic protons may be accelerated close to sgra@xmath0was first explored by markoff , melia & sarcevic ( 1997 , 1999 ) , who concluded that the maximum attainable energy is of the order of 4@xmath2@xmath119 @xmath21 . however , there appear to be two principal reasons why the @xmath120 scatterings that lead to pionic @xmath17-rayemission probably do not occur in the acceleration zone itself . first , the ensuing particle cascade would produce a copious supply of energetic leptons that , in the presence of the inferred @xmath16110 @xmath121 magnetic field for this source , would greatly exceed sgra@xmath0 s observed radio flux . second , the lack of variability in the data from kev to tev energies , argues against a compact point - source like sgra@xmath0 . the more recent analysis of proton acceleration within sgra@xmath0(liu , petrosian & melia 2004 ; liu , melia & petrosian 2005 ) has shown that these relativistic particles actually diffuse to distances @xmath1623 @xmath107 away from the acceleration site before scattering with the ambient protons , and therefore the ensuing leptonic cascade does not overproduce emission at longer wavelengths having left the region where the magnetic fields are very strong . in support of this picture , wherein the relativistic particles responsible for the _ hess_and _ integral_source are accelerated near sgra@xmath0 , it is worth noting that the mechanism responsible for accelerating the electrons required to account for sgra@xmath0 s 7 @xmath122 emissivity , also accelerates protons in the system . these protons do not radiate as efficiently as electrons and therefore diffuse away from the acceleration site . the electron acceleration rate implied by the radio measurements also corresponds to the right @xmath16tev luminosity from the protons flooding the region surrounding the black hole to match the _ hess_measurements . in addition , the time required for these particles to diffuse outwards is @xmath16@xmath123@xmath124 years , which would argue against any rapid variability in the tev @xmath17-rayemission , as observed . thus , although both the _ hess_and _ integral_gcsources appear to be slightly extended , the origin of the particles responsible for the broad band spectrum of the nuclear region may ultimately still be sgra@xmath0 . the supernova renmant sgraeastwhose centroid is located 50@xmath26from sgra@xmath0 , is another likely source of @xmath17-raysnear the gc(see melia & falcke 2001 ) . it is a member of a class of remnants detected at 1720 @xmath125 ( the transition of oh maser emission ) , a signature of shocks produced at the interface between supersonic outflow and the dense molecular cloud environments with which they interact . it has already been shown @xcite that sgraeastis capable of producing the observed @xmath17-rayluminosity detected by _ egret_once the unusually - high ambient particle density ( @xmath126@xmath127 @xmath128 ) and strong magnetic field ( @xmath1260.10.2 @xmath39 ) are taken into account . in a thorough examination of the particle acceleration and energetics in this source , crocker et al . ( 2005 ) demonstrated that sgraeastcould very well also be the source of the tev spectrum measured by _ hess_. one should note , however , that the _ egret_and _ hess_sources are probably not coincident . the centroid of the _ egret_emission @xcite appears to be significantly displaced away from sgra@xmath0 , whereas the tev source lies within @xmath161@xmath8 . in addition , although the _ egret_and _ hess_spectral indices are similar ( @xmath162.2 ) , the corresponding fluxes at gev and tev energies differ by over an order of magnitude . it appears that the _ egret_source must cutoff well below the tev range suggesting , together with the relative spatial displacement of the two sources , that we must be dealing with at least two separate regions of @xmath17-rayemissivity . sgraeastmay in fact be a very good candidate as the source of the emission detected by _ hess_at the galactic center . this composite snrin its radiative phase has several observational characteristics akin to supernovae in molecular clouds or dense environments : a bright radio shell with a strong non - thermal synchrotron component , x - rayemission from the compact central core dominated by the hot thermal plasma component and a strong he - like 6.7 @xmath1 fe emission line . it shares some of these features with g0.9 + 0.1 that was recently confirmed as a source of tev radiation by the _ hess_collaboration @xcite and its local environment make it a good candidate for powerful particle acceleration . there is one important distinction between g0.9 + 0.1 and sgraeasthowever ; the compact core of g0.9 + 0.1 is known to be a pwnfor which is central pulsar has been detected @xcite and that has a hard , non - thermal x - rayemission . the x - raycore of sgraeastis so highly dominated by thermal emission that non - thermal x - rayemission does not even seem to be present . we know however , that such behaviour is not unexpected for snrin molecular clouds or dense environments @xcite . moreover , there is preliminary evidence that several of the new _ hess _ sources detected during the galactic plane scan might be snrwith weak x - rayemission @xcite . the isgriinstrument on the _ integral_satellite has detected with a high significance hard x - rayand soft @xmath17-rayemission centered within 1@xmath8of the galactic nucleus . we have analyzed two years of _ integral_observations and thoroughly examined this data over the energy range from 20 to 400 @xmath1 . combining these results with _ xmm - newton_data in the energy range from 1 to 10 @xmath1 , we have found that this emission can not be attributed to the hot thermal plasma in the sagittarius complex , it can not be explained by the integrated flux from known x - raytransients near the central black hole , and it can not be the simple extrapolation of the x - rayflux of flares from sgra@xmath0 . the fact that igrj174562901is comparable in brightness to the well known binary system 1e1743.12853 in the 2040 @xmath1 range but that unlike this source it does not produce the large x - rayflux that makes 1e1743.12853 so incredibly conspicuous in the soft x - rayband suggests that igrj174562901is not point - like . in addition , the fact that jem - x , with its @xmath163@xmath8angular resolution , easily detects the known binaries in the region including 1e1743.12853 but does not see any emission from the gcalso suggests that the nature of igrj174562901is not point - like . these considerations lead us to conclude that igrj174562901is a compact diffuse emission region a few arcminutes in size and where astrophysical processes give rise to thermal and non - thermal emission . the power of investigation and discovery at our disposal through combining the use of very high resolution x - rayinstruments like _ xmm - newton_and _ chandra _ , radio observatories like the vla , and the new generation of @xmath17-raytelescopes like _ integral_and _ hess_at the highest energies is astounding . to be faced with data from observations that can not be readily explained nor understood is stimulating and inspiring . this is the kind of puzzle that we face in trying to understand the nature of the emission detected from the direction of the galactic nucleus with _ hess_. finally , in section[s : mosaic ] we discussed the 2040 @xmath1 morphology of the emission near the gcand due to the very long effective exposure of 4.7 @xmath40 , the maps in the different energy bands revealed that 1 ) as the brighter and softer sources igrj174562901and 1e1743.12853 become fainter with increasing energy , a hard but dim emission about 6@xmath8from sgra@xmath0 in the direction of positive longitudes appears , and 2 ) that the spectral index of this emission is quite hard and apparently qualitatively similar to that of igrj174752822 ( sgrb2 ) . this new source of soft @xmath17-rayscould well be closely related to the unidentified _ egret_source 3egj17462851 and to the giant molecular cloud g0.13 - 0.13 . dummy aharonian , f. et al . 2004 , , 425 , l13 aharonian , f. et al . 2005a , , 432 , l25 aharonian , f. , et al . 2005b , science , 307 , 1938 aharonian , f. & neronov , a. 2005 , , 619 , 306 atoyan , a. , & dermer , c. d. 2004 , , 617 , l123 balick , b. & brown , r. l. 1974 , , 194 , 265 baganoff , f. k. et al . 2001 , , 413 , 45 baganoff , f. k. et al . 2003 , , 591 , 891 b ' elanger , g. et al . 2004 , , 601 , l163 blanger , g. et al . 2005 , , submitted bower , g. , yusef - zadeh , f. & roberts , d. 2005 , , submitted bykov , a. m. 2002 , , 390 , 327 courvoisier , t. j .- l . , et al . 2003 , , 411 , l53 crocker , r. m. , et al . 2005 , , in press . cuadra , j. , et al . 2005 , , l44 eckart , a. , et al . 2004 , , 427 , 1 eisenhauer , f. et al . 2005 , , submitted ( astro - ph/0502129 ) fatuzzo , m. and melia , f. 2003 , , 596 , 1035 gaensler , b. m. , pivovaroff , m. j. , & garmire , g. p. 2001 , , 556 , l107 genzel , r. , & townes , c. h. 1987 , , 25 , 377 genzel , r. et al . 2003 , , 425 , 934 ghez , a. m. , et al . 2004 , , 601 , l159 ghez , a. m. et al . 2005 , , 620 , 744 goldoni et al . 1999 , aplc , 38 , 305 goldwurm , a. , et al . 1994 , , 371 , 589 goldwurm , a. et al . 2003a , , 584 , 751 goldwurm , a. et al . 2003b , , 411 , l223 goldwurm , a. et al . 2004 , proc . of 5th integral workshop , esa - 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how and when the mass distribution of stars in the galaxy is set is one of the main issues of modern astronomy . here we present a statistical study of mass and density distributions of infrared dark clouds ( irdcs ) and fragments within them . these regions are pristine molecular gas structures and progenitors of stars and so provide insights into the initial conditions of star formation . the irdc properties reported here provide a representative view of the density and mass structure of dense molecular clouds before and during the earliest stages of star formation .

i

1009.0716

how and when the mass distribution of stars in the galaxy is set is one of the main issues of modern astronomy . here we present a statistical study of mass and density distributions of infrared dark clouds ( irdcs ) and fragments within them . these regions are pristine molecular gas structures and progenitors of stars and so provide insights into the initial conditions of star formation . this study makes use of a irdc catalogue ( peretto & fuller 2009 ) , the largest sample of irdc column density maps to date , containing a total of @xmath011,000 irdcs with column densities exceeding @xmath1 @xmath2 and over 50,000 single peaked irdc fragments . the large number of objects constitutes an important strength of this study , allowing detailed analysis of the completeness of the sample and so statistically robust conclusions . using a statistical approach to assigning distances to clouds , the mass and density distributions of the clouds and the fragments within them are constructed . the mass distributions show a steepening of the slope when switching from irdcs to fragments , in agreement with previous results of similar structures . irdcs and fragments are divided into unbound / bound objects by assuming larson s relation and calculating their virial parameter . irdcs are mostly gravitationally bound , while a significant fraction of the fragments are not . the density distribution of gravitationally unbound fragments shows a steep characteristic slope such as @xmath3 , rather independent of the range of fragment mass . however , the incompleteness limit at a number density of @xmath4 @xmath5 does not allow us to exclude a potential lognormal density distribution . in contrast , gravitationally bound fragments show a characteristic density peak at @xmath6 @xmath5 but the shape of the density distributions changes with the range of fragment masses . an explanation for this could be differential dynamical evolution of the fragment density with respect to their mass as more massive fragments contract more rapidly . the irdc properties reported here provide a representative view of the density and mass structure of dense molecular clouds before and during the earliest stages of star formation . these should serve as constraints on any theoretical or numerical model to identify the physical processes involved in the formation and evolution of structure in molecular clouds .

while low mass stars dominate the mass of galaxies , massive stars regulate their energy budget . understanding how and when the mass distribution of stars is determined is therefore essential in establishing a comprehensive picture of galactic evolution , and star formation , throughout the universe . since stars form in molecular clouds the comparison of the internal structure of the clouds and the initial mass function ( imf ) of stars can provide insights on the processes responsible for the formation of stars . the mass distribution of molecular clouds , and cores within them have been extensively studied in the past twenty years . until recently , it was believed that the mass distribution of co clumps was described by @xmath7 with @xmath8 for the milky way ( kramer et al . 1998 , rosolowski 2004 ) . the mass distribution of prestellar cores , the direct progenitors of stars and stellar systems , as observed in dust continuum is much steeper , resembling the salpeter imf with a power law index of @xmath9 ( motte et al . 1998 ; enoch et al . however , recent papers questioned the impact of the source extraction scheme used to segment the data on the final mass distribution shape ( pineda et al . buckle et al . ( 2010 ) found a steeper mass distribution for small scale co clumps . also , in most cases , different tracers are required to trace different structures such as dense cores and molecular clumps , raising the question of detection biases . statistics is often a problem too , binning small number of objects introduce artifacts ( reid & wilson 2006 ) . therefore some confusion exists on what is the real mass structure of molecular clouds . another important physical aspect of molecular cloud structure is the probability density function ( pdf ) of the gas volume density . this quantity has received only little attention ( e.g. dring et al . 1996 for hi ; smith & scalo 2009 for co ) but potentially contains crucial information on the processes at the origin of the density fluctuations . for instance , turbulence - driven fragmentation models develop initial lognormal density fluctuations ( e.g. padoan et al . 1997 ) , which could be the main driver of the lognormal part of the imf ( chabrier 2003 ) . studying the density distribution of fragments within molecular clouds could set important constraints on such models . to perform such studies , we decided to focus on a specific type of molecular clouds , i.e. infrared dark clouds ( irdcs ) . irdcs are dense molecular clouds seen in silhouette against the bright emission of the galactic plane ( e.g. perault et al . 1996 ; teyssier et al . 2002 ; rathborne et al . 2006 ; simon et al . they are cold and only slightly processed by star formation activity , still containing the initial conditions of star formation . peretto & fuller ( 2009 ; hereafter pf09 ) recently constructed the column density maps of more than 11,000 of such irdcs , the largest database of such structures to date . this catalogue provides the opportunity to probe molecular clouds in the galaxy over a wide range of size scales and column density at high angular resolution using the 8@xmath10 m dust absorption and a new source extraction scheme . in section 2 of the present paper we discuss the dataset we used . in section 3 we describe and re - analyze previous results on the distance distribution of irdcs , while in section 4 we estimate completeness limits . section 5 displays our main results on the size , density and mass distributions of irdcs and fragments . discussion is in section 6 . and finally we summarize the main findings of this paper in section 7 .

this study makes use of a irdc catalogue ( peretto & fuller 2009 ) , the largest sample of irdc column density maps to date , containing a total of @xmath011,000 irdcs with column densities exceeding @xmath1 @xmath2 and over 50,000 single peaked irdc fragments . the large number of objects constitutes an important strength of this study , allowing detailed analysis of the completeness of the sample and so statistically robust conclusions . using a statistical approach to assigning distances to clouds , the mass and density distributions of the clouds and the fragments within them the mass distributions show a steepening of the slope when switching from irdcs to fragments , in agreement with previous results of similar structures . however , the incompleteness limit at a number density of @xmath4 @xmath5 does not allow us to exclude a potential lognormal density distribution . an explanation for this could be differential dynamical evolution of the fragment density with respect to their mass as more massive fragments contract more rapidly . these should serve as constraints on any theoretical or numerical model to identify the physical processes involved in the formation and evolution of structure in molecular clouds .

i

1009.0716

how and when the mass distribution of stars in the galaxy is set is one of the main issues of modern astronomy . here we present a statistical study of mass and density distributions of infrared dark clouds ( irdcs ) and fragments within them . these regions are pristine molecular gas structures and progenitors of stars and so provide insights into the initial conditions of star formation . this study makes use of a irdc catalogue ( peretto & fuller 2009 ) , the largest sample of irdc column density maps to date , containing a total of @xmath011,000 irdcs with column densities exceeding @xmath1 @xmath2 and over 50,000 single peaked irdc fragments . the large number of objects constitutes an important strength of this study , allowing detailed analysis of the completeness of the sample and so statistically robust conclusions . using a statistical approach to assigning distances to clouds , the mass and density distributions of the clouds and the fragments within them are constructed . the mass distributions show a steepening of the slope when switching from irdcs to fragments , in agreement with previous results of similar structures . irdcs and fragments are divided into unbound / bound objects by assuming larson s relation and calculating their virial parameter . irdcs are mostly gravitationally bound , while a significant fraction of the fragments are not . the density distribution of gravitationally unbound fragments shows a steep characteristic slope such as @xmath3 , rather independent of the range of fragment mass . however , the incompleteness limit at a number density of @xmath4 @xmath5 does not allow us to exclude a potential lognormal density distribution . in contrast , gravitationally bound fragments show a characteristic density peak at @xmath6 @xmath5 but the shape of the density distributions changes with the range of fragment masses . an explanation for this could be differential dynamical evolution of the fragment density with respect to their mass as more massive fragments contract more rapidly . the irdc properties reported here provide a representative view of the density and mass structure of dense molecular clouds before and during the earliest stages of star formation . these should serve as constraints on any theoretical or numerical model to identify the physical processes involved in the formation and evolution of structure in molecular clouds .

we used the largest sample of irdc column density maps to date in order to better characterize the size , mass , and density structure of dense molecular clouds . the large number of objects , 11,000 irdcs and 50,000 fragments , allows a detailed analysis of the completeness of the sample . using a statistically attribute distances to each irdc , we have demonstrated that above the completeness limit the mass distribution of the irdcs are consistent with a power - law @xmath91 , where @xmath92 is the number of clouds . for the fragments the high mass end of the mass distribution shows a steeper slope , consistent with the slope of the salpeter imf , with the overall distribution well fitted by a lognormal function . using larson s law to estimate the linewidth of each irdc and fragment , we have shown that above our completeness limit all the irdcs and the majority of fragments are likely to be bound . this implies that the transition in the shape of the mass distribution does not reflect a transition from unbound to graviationally bound structures . looking at the distribution of fragment density shows that bound fragments dominate the high density ( @xmath93 @xmath5 ) end of the distribution for all mass ranges , and dominate the whole distribution for the highest range of fragment masses . there is also a distinct broadening of the distribution with increasing fragment mass . this could be a result of the higher mass fragments evolving to being bound more rapidly that lower mass fragments . the number of unbound fragments as a function of number density has the form @xmath94 ( where @xmath95 is the number of fragments ) down to a density of @xmath4 @xmath5 where the completeness limit is reached . the absence of bright infrared sources embedded in irdcs indicates that the mass distributions and density distributions as a function of mass and degree of gravitational binding derived here are representative of the initial conditions of star formation within dense molecular clouds . these results should serve as constraints on theoretical and numerical models in order to identify and characterize the physical processes responsible for the formation and early fragmentation of molecular clouds . _ acknowledgements . we thank the anonymous referee and john scalo for their thorough reports which helped significantly improve the initial version of the paper . we would also like to thank patrick hennebelle for some useful discussions . _

hyperlinks and other relations in wikipedia are a extraordinary resource which is still not fully understood . in this paper we study the different types of links in wikipedia , and contrast the use of the full graph with respect to just direct links . we apply a well - known random walk algorithm on two tasks , word relatedness and named - entity disambiguation . we show that using the full graph is more effective than just direct links by a large margin , that non - reciprocal links harm performance , and that there is no benefit from categories and infoboxes , with coherent results on both tasks . we set new state - of - the - art figures for systems based on wikipedia links , comparable to systems exploiting several information sources and/or supervised machine learning .

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1503.01655

hyperlinks and other relations in wikipedia are a extraordinary resource which is still not fully understood . in this paper we study the different types of links in wikipedia , and contrast the use of the full graph with respect to just direct links . we apply a well - known random walk algorithm on two tasks , word relatedness and named - entity disambiguation . we show that using the full graph is more effective than just direct links by a large margin , that non - reciprocal links harm performance , and that there is no benefit from categories and infoboxes , with coherent results on both tasks . we set new state - of - the - art figures for systems based on wikipedia links , comparable to systems exploiting several information sources and/or supervised machine learning . our approach is open source , with instruction to reproduce results , and amenable to be integrated with complementary text - based methods .

hyperlinks and other relations between concepts and instances in wikipedia have been successfully used in semantic tasks @xcite . still , many questions about the best way to leverage those links remain unanswered . for instance , methods using direct hyperlinks alone would wrongly disambiguate _ lions _ in figure [ fig : example - show - disamb ] to ` b&i_lions ` , a rugby team from britain and ireland , as it shares two direct links to potential referents in the context ( _ darrel fletcher _ , a british football player , and _ cape town _ , the city where the team suffered some memorable defeats ) , while ` highveld_lions ` , a cricket team from south africa , has only one . when considering the whole graph of hyperlinks we find that the cricket team is related to two cricketers named _ alan kourie _ and _ duncan fletcher _ and could thus pick the right entity for _ lions _ in this context . in this paper we will study this and other questions about the use of hyperlinks in word relatedness @xcite and named - entity disambiguation , ned @xcite . previous work on this area has typically focused on novel algorithms which work on a specific mix of resource , information source , task and test dataset ( cf . [ sec : comp - relat - work ] ) . in the case of ned , the evaluation of the disambiguation component is confounded by interactions with mention spotting and candidate generation . with very few exceptions , there is little analysis of components and alternatives , and it is very difficult to learn any insight beyond the fact that the mix under study attained certain performance on the target dataset . the number of algorithms and datasets is growing by the day , with no well - established single benchmark , and the fact that some systems are developed on test data , coupled with reproducibility problems ( * ? ? ? * on word relatedness ) , makes it very difficult to know where the area stands . there is a need for clear points of reference which allow to understand where each information source and algorithm stands with respect to other alternatives . we thus depart from previous work , seeking to set such a point of reference , and focus on a single knowledge source ( hyperlinks in wikipedia ) with a clear research objective : given a well - established random walk algorithm ( personalized pagerank @xcite ) we explore sources of links and filtering methods , and contrast the use of the full graph with respect to using just direct links . we follow a clear development / test / analysis methodology , evaluating on a extensive range of both relatedness and ned datasets . the results are confirmed in both tasks , yielding more support to the findings in this research . all software and data are publicly available , with instructions to obtain out - of - the - box replicability . the contributions of our research are the following : ( 1 ) we show for the first time that performing random walks over the full graph is preferable than considering only direct links . ( 2 ) we study several sources of links , showing that non - reciprocal links hurt and that the contribution of the category structure and links in infoboxes is residual . ( 3 ) we set the new state - of - the - art for systems based on wikipedia links for _ both _ word relatedness and named - entity disambiguation . the results are close to the best systems to date , which use several information sources and/or supervised machine learning techniques , and specialize on either relatedness or disambiguation . our work shows that a careful analysis of varieties of graphs using a well - known random walk algorithm pays off more than most ad - hoc algorithms . the article is structured as follows . we first present previous work , followed by the different options to build hyperlink graphs . [ sec : pager - pers - pager ] reviews random walks for relatedness and ned . [ sec : note - exper - meth ] sets the experimental methodology , followed by the analysis and results on development data ( sect . [ sec : studying - graph ] ) and the comparison to the state of the art ( sect . [ sec : comp - relat - work ] ) . finally , sect . [ sec : concl - future - work ] draws the conclusions .

can be computationally demanding , an obvious solution is to take advantage of the multiprocessing capabilities of modern multicore processors . unfortunately , many solutions employed for the data distribution management service of the high level architecture are either inefficient , or can only partially be parallelized . in this paper itm is based on a simple interval tree data structure , and exhibits an embarrassingly parallel structure . we implement the itm algorithm , and compare its sequential performance with two widely used solutions ( brute force and sort - based matching ) . we also analyze the scalability of itm on shared - memory multicore processors . the results show that the sequential implementation of itm is competitive with sort - based matching ; moreover , the parallel implementation provides good speedup on multicore processors .

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1309.3458

identifying intersections among a set of @xmath0-dimensional rectangular regions ( @xmath0-rectangles ) is a common problem in many simulation and modeling applications . since algorithms for computing intersections over a large number of regions can be computationally demanding , an obvious solution is to take advantage of the multiprocessing capabilities of modern multicore processors . unfortunately , many solutions employed for the data distribution management service of the high level architecture are either inefficient , or can only partially be parallelized . in this paper we propose the interval tree matching ( itm ) algorithm for computing intersections among @xmath0-rectangles . itm is based on a simple interval tree data structure , and exhibits an embarrassingly parallel structure . we implement the itm algorithm , and compare its sequential performance with two widely used solutions ( brute force and sort - based matching ) . we also analyze the scalability of itm on shared - memory multicore processors . the results show that the sequential implementation of itm is competitive with sort - based matching ; moreover , the parallel implementation provides good speedup on multicore processors . data distribution management ; high level architecture ; parallel algorithms ; interval tree

the specification @xcite defines several services to forward events generated on _ update _ regions to a set of _ subscription _ regions . for example , consider a simulation of vehicles moving on a two - dimensional terrain . each vehicle may be interested in events happening inside its area of interest ( e.g. , its field of view ) that might be approximated with a rectangular region centered at the vehicle position . this kind of problem also arises in the context of massively multiplayer online games , where the game engine must send updates only to players that might be affected by game events , in order to reduce computation cost and network traffic . in this paper we assume that a region corresponds to a single _ extent _ in terminology ) , that is , a @xmath0-dimensional rectangle ( @xmath0-rectangle ) in a @xmath0-dimensional routing space . spatial data structures that can solve the region intersection problem have been developed over the years ; examples include the @xmath1-@xmath0 tree @xcite and r - tree @xcite . however , it turns out that simpler , less efficient solutions are actually preferred in practice and widely deployed in implementations . the reason is that efficient spatial data structures tend to be complex to implement , and therefore their theoretical performance is affected by high constant factors . the increasingly large size of computer simulations employing techniques is posing a challenge to the existing solutions . as the number of regions increases , so does the execution time of the service . given the current trend in microprocessor design where a single cpu contains multiple independent execution units , significant improvements could be achieved if the existing matching algorithms were capable of taking advantage of the computational power provided by multi - core processors . there are two opportunities for parallelizing algorithms . the first is based on the observation that the problem of identifying whether two @xmath0-rectangles intersect can be reduced to @xmath0 independent intersection problems among one - dimensional segments ( details will be given in section [ sec : ddm - algorithms ] ) . therefore , given an algorithm that can identify intersections among two sets of segments , we can execute @xmath0 instances in parallel , each computing the intersections among the projections of the extents along each dimension . the extent intersections can be easily computed from the segments overlap information . the idea above can be regarded as the `` low hanging fruit '' which is easy to get , but does not solve the problem in the long run . in fact , the number of cores in modern processors is often larger than the number of dimensions of most routing spaces ; this gap is likely to increase ( e.g. , the tilera tile - gx8072 processor @xcite offers 72 general - purpose cores on the same chip , connected through an on - chip mesh network ) . here comes the second parallelization opportunity : distribute the regions to the available cores so that each core can work on a smaller problem . this is quite difficult to achieve on the existing algorithms , since they are either inefficient ( and therefore there is little incentive in splitting the workload ) , or inherently sequential ( and therefore there is no easy way to achieve parallelism over the set of extents ) . in this paper we describe the algorithm for solving the one - dimensional segment intersection problem . the algorithm uses a simple implementation of the interval tree data structure based on an augmented balanced search tree . experimental performance measures indicate that the sequential version of is competitive in the sequential case with the best algorithm used for , namely sort - based matching . we also observed good scalability of the parallel implementation of on shared - memory architectures . an important feature of is that it can be used to efficiently update overlap information in a dynamic setting , that is , in case extents can be moved or resized dynamically . this paper is organized as follows . in section [ sec : related - work ] we briefly review the state of the art and compare with existing solutions to the matching problem . in section [ sec : ddm - algorithms ] we describe three commonly used algorithms for : brute force , grid - based and sort - based matching . in section [ sec : parallel - ddm ] we describe and analyze its computational cost . in section [ sec : experimental - evaluation ] we experimentally evaluate the performance of the sequential version of compared with brute force and sort - based matching ; additionally , we study the scalability of a parallel implementation of on a multicore processor . finally , conclusions and future works will be discussed in section [ sec : conclusions ] .

if @xmath0 is frobenius split , then so is its normalization and we explore conditions which imply the converse . to do this , we recall that given an @xmath1-linear map @xmath2 , it always extends to a map @xmath3 on the normalization of @xmath0 . in this paper our result has geometric consequences including a connection between @xmath5-pure singularities and semi - log canonical singularities , and a more familiar version of the ( @xmath5-)inversion of adjunction formula . frobenius map , frobenius splitting , f - purity , semi - log canonical , log canonical , inversion of adjunction , normalization , seminormal

i

1101.1033

if @xmath0 is frobenius split , then so is its normalization and we explore conditions which imply the converse . to do this , we recall that given an @xmath1-linear map @xmath2 , it always extends to a map @xmath3 on the normalization of @xmath0 . in this paper , we study when the surjectivity of @xmath3 implies the surjectivity of @xmath4 . while this does nt occur generally , we show it always happens if certain tameness conditions are satisfied for the normalization map . our result has geometric consequences including a connection between @xmath5-pure singularities and semi - log canonical singularities , and a more familiar version of the ( @xmath5-)inversion of adjunction formula . frobenius map , frobenius splitting , f - purity , semi - log canonical , log canonical , inversion of adjunction , normalization , seminormal

frobenius splittings of algebraic varieties appear prominently in tight closure theory , have emerged as a fundamental tool in the study of the representation theory of algebraic groups , and have tantalizing links to concepts in the minimal model program . suppose that @xmath6 is a reduced ring of characteristic @xmath7 with normalization in its total ring of fractions @xmath8 . it follows from ( * ? ? ? * exercise 1.2.4(e ) ) that if @xmath9 is frobenius split then so is @xmath10 . the goal of this paper is to study to what extent the converse holds . of course , there are many non - frobenius split affine varieties whose normalizations are regular and thus frobenius split ( for example , the cusp @xmath11 in any characteristic ) and so we focus our attention not just on the ring , but on the ring and a choice of a potential frobenius splitting . by definition , frobenius splitting _ on a variety @xmath12 is an @xmath13-linear map @xmath14 which sends the section @xmath15 to @xmath15 . when @xmath0 is affine , the existence of a frobenius splitting is equivalent to existence of a map @xmath14 such that @xmath16 for some section @xmath17 ( in other words , to require that @xmath4 is surjective ) . on a normal @xmath12 , surjective maps @xmath18 are very closely related to boundary divisors @xmath19 such that @xmath20 is log canonical , see @xcite and @xcite . based upon our intuition with non - normal log canonical singularities ( which are usually called _ semi - log canonical _ ) one should be able to detect surjective @xmath18 by studying the normalization of @xmath0 . in fact , this correspondence between log canonical pairs @xmath20 and surjective @xmath4 suggests that the following question should have an affirmative answer . [ quest.motivation ] suppose that @xmath0 is an affine variety in characteristic @xmath7 with normalization @xmath21 , and set @xmath22 to be the @xmath23-iterated frobenius . given a map @xmath24 , it always extends to a unique map @xmath25 . if @xmath26 is surjective , does it follow that @xmath4 is also surjective ? perhaps unfortunately , this question has a negative answer . a counterexample is given by the scheme @xmath27/(x^2y - z^2)$ ] , ( * ? ? ? * example 8.4 ) . however , that counterexample possesses substantial inseparability : if @xmath28 is the non - normal locus of @xmath0 and @xmath29 is its pre - image inside @xmath30 , then the induced map @xmath31 is generically inseparable . we show that if we can avoid this inseparability and also a certain variant of wild ramification , then the question has a positive answer . in particular , we say that a ring possesses _ _ if it avoids these positive characteristic pathologies ( see definition [ def.hst ] for a precise definition ) . our main theorem follows : [ thm : maintheorem ] [ theorem [ thm : main ] ] suppose that @xmath0 is a reduced @xmath5-finite affine scheme having . further suppose that @xmath24 is an @xmath13-linear map . if the unique extension @xmath25 is surjective , then @xmath4 is also surjective . the main theorem should also be viewed as complementary to ( * ? ? ? * theorem 6.26 ) . in the context of a finite surjective map @xmath32 between _ normal _ varieties , that result answers the same question for @xmath14 and its extension @xmath33 ( if it exists ) . also see @xcite where 1-dimensional non - normal @xmath5-pure rings are studied . we now discuss in more detail the motivation for this theorem . in this context , maps @xmath34 correspond to @xmath35-divisors @xmath19 on @xmath30 such that @xmath36 is @xmath35-cartier , see @xcite and section [ sec : prelim ] . the condition @xmath4 being surjective ( _ i.e. _ the pair @xmath37 being @xmath5-pure ) corresponds to the pair @xmath37 having log canonical singularities @xcite , @xcite . on a characteristic zero variety @xmath0 that is s2 ( _ i.e. _ serre s second condition ) and g1 ( _ i.e. _ gorenstein in codimension @xmath15 ) with normalization @xmath38 and conductor divisor @xmath39 , if there exists a @xmath40-divisor @xmath41 on @xmath0 such that @xmath42 is @xmath35-cartier and furthermore that @xmath43 is log canonical , then @xmath44 is called _ semi - log canonical_. via the map-(@xmath4 ) divisor-(@xmath19 ) correspondence , our main theorem should be interpreted as saying : ll as an explicit example of this statement , and of the translation between maps @xmath45 and divisors , we have the following corollary of our main theorem , a criterion for certain non - normal algebraic varieties to be @xmath5-split . * corollary [ cor.hstnormalizationqgorenstein ] . * _ suppose that @xmath12 is an affine @xmath5-finite scheme satisfying and which is also s2 , g1 and @xmath40-gorenstein with index not divisible by the characteristic @xmath46 . set @xmath30 to be the normalization of @xmath0 and set @xmath29 to be the divisor on @xmath30 corresponding to the conductor ideal , _ i.e. _ @xmath47 . then @xmath0 is @xmath5-pure ( equivalently @xmath5-split ) if and only if @xmath48 is @xmath5-pure . _ in the above corollary , if one replaces the two occurrences of the word @xmath5-pure by semi - log canonical and log canonical ( respectively ) , one obtains a well known criterion for a scheme having semi - log canonical singularities , see @xcite . more generally , the correspondence between log canonical and @xmath5-pure singularities is still conjectural , although an area of active research . [ conj.fpurevslogcanonical ] suppose that @xmath49 is a normal variety of characteristic zero and that @xmath19 is a divisor on @xmath49 such that @xmath50 is @xmath35-cartier . the pair @xmath51 is log canonical if and only if @xmath51 has dense @xmath5-pure type pair @xmath52 has dense @xmath5-pure type if the map corresponding to @xmath19 is surjective after reduction to characteristic @xmath7 for infinitely many @xmath7 . see @xcite for more details . ] . see @xcite and @xcite for connections between this conjecture and open conjectures in arithmetic geometry ( these connections will not be utilized in this paper ) . the setting for our applications will necessarily deal with geometry on non - normal schemes , and as such we will be dealing with an extended notion of divisors , see @xcite . for us , the important divisors are the @xmath35-almost cartier divisor ( or simply _ @xmath35-ac divisors _ ) , and we will review the definitions in detail in section [ sec : divisors ] . our main result implies the following : * corollary [ cor.fpurevsslc ] . * _ assume now that @xmath0 is an s2 , g1 and seminormal variety in characteristic zero . further suppose that @xmath19 is an @xmath35-ac divisor ( _ i.e. _ @xmath35-weil sheaf ) on @xmath53 assuming that conjecture [ conj.fpurevslogcanonical ] holds , @xmath20 has semi - log canonical singularities if and only if it has dense @xmath5-pure type . _ another application of theorem [ thm : maintheorem ] is to give a statement of inversion of adjunction for divisors on characteristic @xmath7 schemes with that closely aligns with the characteristic @xmath54 picture , compare with @xcite . inversion of adjunction for characteristic @xmath7 schemes was studied first in @xcite , see also takagi @xcite and @xcite . however the direct analog of kawakita s result is not possible in characteristic @xmath7 ( * ? ? ? * example 8.4 ) . the culprit is the same conditions of inseparability and wild ramification which obstruct a positive answer to the motivating question . however : * corollary [ cor.invofadj ] . * _ suppose that @xmath0 is a normal scheme of characteristic @xmath7 , @xmath19 is a @xmath35-divisor on @xmath0 and @xmath55 is a reduced integral weil divisor on @xmath0 , with no common components with @xmath19 , such that @xmath56 is @xmath35-cartier with index not divisible by @xmath46 . denote by @xmath57 the normalization of @xmath55 and @xmath58 the natural map . there exists a canonically determined @xmath35-divisor @xmath59 on @xmath57 such that @xmath60 . furthermore , if @xmath61 has , then @xmath62 is @xmath5-pure near @xmath55 if and only if @xmath63 is @xmath5-pure . _ -12pt_acknowledgements : _ the authors would like to thank bryden cais , neil epstein and kevin tucker for inspiring conversations related to this project . the authors would also like to thank the referee , shunsuke takagi and kevin tucker for numerous useful comments on an earlier draft of this manuscript . this work was initiated when the second author was visiting the university of utah during fall 2010 .

we examine such supersymmetric qcd effects in bottom pair production associated with a light higgs boson at the lhc and tevatron . we find that if the relevant sparticles ( gluinos and squarks ) are well above the tev scale , too heavy to be directly produced , they can still have sizable virtual effects in this process . for large @xmath0 , such residual effects can alter the production rate by as much as 40 percent , which should be observable in future measurements of this process .

c

hep-ph0412356

if all the supersymmetry particles ( sparticles ) except a light higgs boson are too heavy to be directly produced at the large hadron collider ( lhc ) and tevatron , a possible way to reveal evidence for supersymmetry is through their virtual effects in other processes . we examine such supersymmetric qcd effects in bottom pair production associated with a light higgs boson at the lhc and tevatron . we find that if the relevant sparticles ( gluinos and squarks ) are well above the tev scale , too heavy to be directly produced , they can still have sizable virtual effects in this process . for large @xmath0 , such residual effects can alter the production rate by as much as 40 percent , which should be observable in future measurements of this process . = # 1,nucl . phys . * b#1 * , # 1,phys . lett . b * # 1 * , # 1,phys . rev . d * # 1 * , # 1,phys . rev . lett . * # 1 * , # 1,z . phys . c * # 1 * , # 1#20.5ex

we examined the supersymmetric qcd effects in bottom pair production associated with a light higgs boson at the lhc and tevatron . we found that when the relevant sparticles are heavy , well above the tev scale , they nevertheless contribute sizable virtual effects in this process . for large @xmath0 , these residual effects can alter the production cross section by as much as 40 percent and thus should be measurable in observations of this process at the lhc or tevatron . if only one light higgs boson , or perhaps several higgs bosons , are discovered at the lhc or tevatron , it could indicate that the susy scale is quite high ; above the tev scale . of course , the fine - tuning problem then remains and supersymmetry loses one of its merits . but this might possibly happen since supersymmetry does not have to solve the fine - tuning problem , as argued recently by arkani - hamed and dimopoulos @xcite . in that case , a possible way to reveal a hint of supersymmetry is through its residue effects . higgs production associated with a pair of bottom quarks is then well suited for such a seeking a clue for supersymmetry .

here we extend this result to a larger set of contact seifert fibered @xmath0-manifolds with many singular fibers and observe that these @xmath0-manifolds are singularity links . in addition , we prove that the contact structures induced by the stein fillings are the canonical contact structures on these singularity links . as a consequence , we verify a prediction of andrs nmethi @xcite by providing examples of isolated complex surface singularities whose links with their canonical contact structures admitting infinitely many exotic simply - connected stein fillings .

i

1206.2468

in @xcite , it was shown that there exist infinitely many contact seifert fibered @xmath0-manifolds each of which admits infinitely many exotic ( homeomorphic but pairwise non - diffeomorphic ) simply - connected stein fillings . here we extend this result to a larger set of contact seifert fibered @xmath0-manifolds with many singular fibers and observe that these @xmath0-manifolds are singularity links . in addition , we prove that the contact structures induced by the stein fillings are the canonical contact structures on these singularity links . as a consequence , we verify a prediction of andrs nmethi @xcite by providing examples of isolated complex surface singularities whose links with their canonical contact structures admitting infinitely many exotic simply - connected stein fillings . moreover , for infinitely many of these contact singularity links and for each positive integer @xmath1 , we also construct an infinite family of exotic stein fillings with fixed fundamental group @xmath2 .

the link of a normal complex surface singularity carries a milnor fillable ( also known as canonical ) contact structure @xmath3 which is uniquely determined up to isomorphism @xcite . a milnor fillable contact structure is stein fillable since a regular neighborhood of the exceptional divisor in a resolution of the surface singularity provides a holomorphic filling which can be deformed to be a blow - up of a stein surface without changing the contact structure @xmath3 on the boundary @xcite . moreover , if a singularity admits a smoothing then the corresponding milnor fiber is also a stein filling of @xmath3 . in this paper , we generalize the main result in @xcite to a larger family of contact seifert fibered @xmath0-manifolds admitting many singular fibers . we also observe an additional feature of these contact @xmath0-manifolds : they appear as the links of some isolated complex surface singularities , and the contact structures are the canonical ones on these singularity links . the following theorems verify a prediction of nmethi @xcite filling a gap in the literature . + * theorem 4.4 . * _ there exist infinitely many seifert fibered singularity links each of which admits infinitely many exotic simply - connected stein fillings of its canonical contact structure . _ + * theorem 5.3 . * _ there exists an infinite family of seifert fibered singularity links such that for each positive integer @xmath1 , each member of this family equipped with its canonical contact structure admits infinitely many exotic stein fillings whose fundamental group is @xmath4 . _ + one should contrast our result with what is known for links of some other isolated complex surface singularities . for example , ohta and ono showed that the diffeomorphism type of any minimal strong symplectic filling of the link of a simple singularity is unique which implies that the minimal resolution of the singularity is diffeomorphic to the milnor fiber @xcite . they also showed that any minimal strong symplectic filling of the link of a simple elliptic singularity is diffeomorphic either to the minimal resolution or to the milnor fiber of the smoothing of the singularity @xcite . moreover , lisca showed that the canonical contact structure on a lens space ( the oriented link of some cyclic quotient singularity ) has only _ finitely _ many distinct stein fillings , up to diffeomorphism @xcite ( see also earlier work of mcduff @xcite ) . recently , it was shown that these stein fillings correspond bijectively to the milnor fibres coming from all possible distinct smoothings of the singularity @xcite . in summary , in all the previously studied examples in the literature , it was shown that an isolated complex surface singularity with its canonical contact structure admits finitely many diffeomorphism types of stein fillings such that each stein filling is diffeomorphic either to the minimal resolution or to the milnor fiber of one of the smoothings of the singularity . we should mention that in ( * ? ? ? * theorem 1.2 ) ohta and ono showed the existence of singularity links which admit infinitely many distinct minimal symplectic fillings distinguished by their @xmath5 . these fillings , however , are _ not necessarily stein or simply - connected_. on the other hand , using log transforms , akbulut and yasui ( * ? ? ? * theorem 1.1 ) constructed contact @xmath0-manifolds admitting infinitely many exotic simply - connected stein fillings with @xmath6 , inspired by an earlier paper by akbulut @xcite . in these articles , however , the contact @xmath0-manifolds in question are _ not singularity links_. finally , we would like to point out that in @xcite , _ using very different methods _ , we were able to prove the statement of theorem 5.3 by replacing @xmath7 by any finitely presented group @xmath8 .

in a previous article ( _ int . math . res . not . _ 2014 , 27302745 ) t. orponen and the authors proved that the fourier dimension of the graph of any real - valued function on @xmath0 is bounded above by @xmath1 . this partially answered a question of kahane ( 93 ) by showing that the graph of the wiener process @xmath2 ( brownian motion ) is almost surely not a salem set . in this article we complement this result by showing that the fourier dimension of the graph of @xmath2 is almost surely @xmath1 . in the proof we also give some applications to the equidistribution of orbits under toral endomorphisms .

i

1506.03773

in a previous article ( _ int . math . res . not . _ 2014 , 27302745 ) t. orponen and the authors proved that the fourier dimension of the graph of any real - valued function on @xmath0 is bounded above by @xmath1 . this partially answered a question of kahane ( 93 ) by showing that the graph of the wiener process @xmath2 ( brownian motion ) is almost surely not a salem set . in this article we complement this result by showing that the fourier dimension of the graph of @xmath2 is almost surely @xmath1 . in the proof we introduce a new method based on it calculus to estimate fourier transforms by reformulating the question in the language of it drift - diffusion processes and combine it with the classical work of kahane on brownian images . we also give some applications to the equidistribution of orbits under toral endomorphisms .

gaussian processes are standard models in modern probability theory and perhaps the most well studied example is the _ wiener process _ ( or standard _ brownian motion _ ) @xmath3 defined such that @xmath4 , the map @xmath5 is almost surely continuous and @xmath2 has independent increments such that @xmath6 for @xmath7 is normally distributed : @xmath8 the wiener process has far reaching importance throughout mathematics and it is a topic of particular interest to understand the geometric structure of the process . this can be achieved by studying several random fractals associated to the process such as _ images _ @xmath9 of compact sets @xmath10 , _ level sets _ @xmath11 for @xmath12 , _ graphs _ @xmath13 and other more delicate constructions such as @xmath14-curves . due to the properties of the brownian motion , these random fractals enjoy a certain statistical self - similarity which facilitates computation of their hausdorff dimensions @xmath15 . classical results include mckean s proof @xcite that @xmath16 almost surely for each compact @xmath10 . moreover , for the level sets @xmath17 almost surely for @xmath18 by taylor @xcite and for all @xmath12 by perkins @xcite whenever @xmath19 is non - degenerate . for the brownian graph @xmath20 , taylor @xcite proved that @xmath21 almost surely and beffara computed hausdorff dimensions of @xmath14-curves @xcite . moreover , hausdorff dimensions for similar sets given by many other gaussian processes , such as fractional brownian motion , have been also considered , see for example adler s classical results @xcite for fractional brownian graphs and the recent work for variable drift by peres and sousi @xcite . the hausdorff dimension is the most commonly used tool for measuring the size of a set @xmath22 but there is also another fundamental notion based on fourier analysis which reveals more arithmetic and geometric features of @xmath22 , including curvature , which are not seen by the hausdorff dimension . this is based on studying the _ fourier coefficients _ of a probability measure @xmath23 on @xmath24 , which are defined by @xmath25 now the size of @xmath22 can be linked to the existence of probability measures @xmath23 on @xmath22 with decay of fourier coefficients @xmath26 when @xmath27 . the following connection between hausdorff dimension and decay of fourier coefficients is well - known and goes back to salem and kaufman , but we refer the reader to @xcite for the details . if @xmath28 , then @xmath22 supports a probability measure @xmath23 with @xmath29 `` on average '' , that is , @xmath30 and vice versa the hausdorff dimension can be bounded from below if such a measure @xmath23 can be found . it is possible , however , that @xmath31 but no measure @xmath23 on @xmath22 has fourier decay at infinity , this happens for example when @xmath22 is the middle - third cantor set on @xmath0 . therefore , one defines the notion of _ fourier dimension _ @xmath32 of a set @xmath33 as the supremum of @xmath34 $ ] for which there exists a probability measure @xmath23 supported on @xmath22 such that @xmath35 and if the two dimensions coincide then @xmath22 is called a _ salem set _ or a _ round set _ after kahane @xcite . in general fourier dimension and hausdorff dimension have no relationship other than this ; in fact , krner @xcite established that for any @xmath36 it is possible to construct examples @xmath37 with @xmath38 and @xmath39 . further theory for fourier dimension was recently developed by ekstrm , persson and schmeling @xcite . for a more in depth account of fourier dimension , the reader is referred to @xcite . finding measures @xmath23 on @xmath22 with polynomially decaying fourier transform ( i.e. for some @xmath40 ) has deep links to absolute continuity , arithmetic and geometric structure and curvature . if @xmath22 supports a measure @xmath23 such that holds with @xmath41 , then parseval s identity yields that @xmath23 is absolutely continuous to lebesgue measure and @xmath22 must contain an interval . an application of weyl s criterion known as the davenport - erds - leveque criterion ( see @xcite ) yields that in @xmath0 polynomial decay of @xmath42 guarantees that @xmath23 almost every number is normal in every base and a interesting result of aba and pramanik @xcite shows that if the @xmath43 in is sufficiently close to @xmath1 for a measure @xmath23 on @xmath37 , then @xmath22 contains non - trivial @xmath44-term arithmetic progressions . moreover , an analogous result also holds for higher dimensions with arithmetic patches @xcite . on the curvature side , if @xmath22 is a line - segment in @xmath45 , then @xmath22 can not contain any measure with fourier decay at infinity so @xmath22 can not be a salem set . however , if @xmath22 is an arc of a circle or more generally a @xmath1-dimensional smooth manifold with non - vanishing curvature when the @xmath1-dimensional hausdorff measure @xmath23 on @xmath22 satisfies with @xmath46 , see @xcite . in particular , @xmath22 is a salem set . in these examples of @xmath22 one can observe that the important arithmetic or curvature features present are not seen from the hausdorff dimension . constructing explicit salem sets ( which are not manifolds ) , or just sets @xmath22 supporting a measure @xmath23 satisfying for some @xmath40 , can be achieved through , for example , diophantine approximation by kaufman s works @xcite , bluhm @xcite or via thermodynamical tools by jordan and sahlsten @xcite . however , for random sets it has been observed in many instances that @xmath22 is either almost surely salem or at least supports a measure @xmath23 with for some @xmath40 . this was first done for random cantor sets by salem @xcite , where salem sets were also introduced . later kahane published his classical papers @xcite , where he found out that the wiener process and other gaussian processes provide natural examples . the study of fourier analytic properties of natural sets for gaussian processes and more general random fields has since been an active topic . for the brownian images kahane @xcite proved that for any compact @xmath47 the image @xmath48 is almost surely a salem set of hausdorff dimension @xmath49 . kahane also established a similar result for fractional brownian motion . aba and pramanik @xcite then applied these to the additive structure of brownian images . later shieh and xiao @xcite extended kahane s work to very general classes of gaussian random fields . however , understanding the fourier analytic properties of the level sets and graphs remained an important problem for some time . in 1993 , kahane @xcite outlined the problem explicitly . [ prob : kahane ] are the graph and level sets of a stochastic process such as fractional brownian motion salem sets ? in this form kahane s problem was formulated by shieh and xiao ( * ? ? ? * question 2.15 ) . for the wiener process kahane @xcite had already established that the level sets @xmath19 are salem almost surely for any fixed @xmath12 provided that @xmath19 is non - degenerate . the fractional brownian motion case has recently been considered in the case @xmath18 by fouch and mukeru @xcite . [ fig : browngraph ] for the brownian motion @xmath2.,title="fig : " ] kahane s problem for graphs , even in the case of the standard brownian motion @xmath2 , however , remained open for quite a while until , together with t. orponen , we established that the brownian graph @xmath20 is almost surely _ not _ a salem set @xcite . it turned out that the reason for this is purely geometric : the proof was based on the following application of a fourier - analytic version of marstrand s slicing lemma . [ thm : prequel ] for any function @xmath50 \to { \mathbb{r}}$ ] the fourier dimension of the graph @xmath51 can not exceed @xmath1 . indeed , since the hausdorff dimension @xmath52 almost surely ( see @xcite ) , this result shows that the graph @xmath20 can not be a salem set almost surely , which answers problem [ prob : kahane ] in the negative for the wiener process . note that this also gives a negative answer for fractional brownian motion since the hausdorff dimension in that case is also strictly larger than 1 almost surely . the methods in @xcite are purely geometric and involve no stochastics , so they do not shed any light on the precise value for the fourier dimension of @xmath20 . note that even though @xmath53 for any continuous @xmath50\to{\mathbb{r}}$ ] by theorem [ thm : prequel ] , it is completely possible that the fourier dimension @xmath54 . for example this happens by just taking @xmath55 to be affine or even any _ baire generic _ @xmath56 $ ] satisfies @xmath54 , see ( * ? ? ? * theorem 1.3 ) . the main result of this paper is to complete the work initiated by kahane s problem [ prob : kahane ] in the case of brownian motion by establishing the precise almost sure value of the fourier dimension of @xmath20 . [ thm : main ] the graph @xmath20 has fourier dimension @xmath1 almost surely . moreover , the random measure @xmath23 we use to realise the fourier dimension is lebesgue measure @xmath57 on @xmath58 $ ] lifted onto the graph @xmath20 via the mapping @xmath59 . the precise estimate we obtain is that almost surely @xmath60 which combined with theorem [ thm : prequel ] yields theorem [ thm : main ] . a natural direction in which to continue this line of research would be to study other gaussian processes with different covariance structure , see the discussion in section [ sec : gaussian ] . the key method we introduce to estimate the fourier transform of the graph measure @xmath23 is based on _ it calculus _ , which has previously been a natural framework in the theory of stochastic differential equations . as far as we know , it calculus has not been previously considered in this fourier analytic context . in section [ sec : further ] we will discuss the prospects of this approach . next we will discuss this method and give a brief summary of the main steps in the proof . when written in polar coordinates , asks about the rate of decay for the integral @xmath61 for @xmath62 , @xmath63 , @xmath64 , as @xmath65 . there are two distinct cases we will consider depending on the direction of @xmath66 , which we give a heuristic description of here . if we ignore the random component @xmath67 , that is , set @xmath68 or @xmath69 , then standard integration using the chain rule shows that @xmath26 equals the fourier transform of lebesgue measure @xmath57 at @xmath70 , which decays to @xmath71 with the polynomial rate @xmath72 , so we are done for these directions . however , if @xmath73 is not equal to @xmath71 or @xmath69 , we still have a small random ( non - smooth ) term @xmath74 , so a classical change of variable formula or other tools from classical analysis can not be used . the new approach we introduce is to utilise tools from stochastic analysis . the key observation is that we can write @xmath75 , where the stochastic process @xmath76 is a so called _ it drift - diffusion process _ , where @xmath77 is the _ drift coefficient _ of @xmath78 and @xmath79 is the _ diffusion coefficient _ of @xmath78 . it processes have many useful analytic tools from it calculus ( see section [ sec : ito ] ) associated to them , in particular _ it s lemma _ , which works as an analogue for the chain rule . the price we pay is that it s lemma introduces some multiplicative error terms involving stochastic integrals , but they can be estimated with other tools from it calculus using moment analysis . the estimates we obtain from it calculus allow us to obtain the correct fourier decay for @xmath23 when @xmath73 is close to @xmath71 or @xmath69 with respect to @xmath80 ( more precisely , @xmath81 ) . in other words , when @xmath66 is close to pointing in the horizontal directions . thus another estimate is needed for @xmath73 bounded away from @xmath71 and @xmath69 . this is where kahane s classical work @xcite on brownian images comes into play . if we completely ignore the deterministic component @xmath82 , by setting @xmath83 or @xmath84 , then @xmath85 is the fourier transform the brownian image measure @xmath86 , that is the @xmath5 push - forward of the lebesgue measure @xmath57 on @xmath58 $ ] at @xmath70 . kahane @xcite in fact already established that almost surely the decay of @xmath87 is almost surely of the order @xmath88 so holds for these directions . now a simple modification to kahane s argument reveals that whenever @xmath89 or @xmath69 , then almost surely @xmath90 . now one notices that when @xmath73 approaches @xmath71 or @xmath69 , this estimate blows up , and so one can not obtain a uniform estimate over all directions from this . however , this gives if @xmath91 , so combining with the estimates we obtained through it calculus , we are done . see section [ sec : proof ] for more details on the main steps of the proof . as mentioned in the introduction , fourier coefficients of @xmath23 on a set @xmath22 are deeply linked to arithmetic properties of the set @xmath22 . in this section we will point out one application one can achieve from theorem [ thm : main ] ( in particular the decay ) . let @xmath92 be the unit circle or @xmath1-torus , which is naturally identified with @xmath58 $ ] . a sequence @xmath93 is _ equidistributed _ if @xmath94\}}{n } \to b - a\ ] ] as @xmath95 for any interval @xmath96 \subset [ 0,1]$ ] . if the sequence @xmath97 equidistributes for a fixed @xmath98 , then we say @xmath99 is _ normal _ in base @xmath100 . checking normality of a specific @xmath99 is often difficult so instead one often tries to check if a _ random _ number ( with respect to a measure @xmath23 ) is normal . this is where the decay of the fourier coefficients of @xmath23 are crucial : [ thm : del ] let @xmath23 be a measure on @xmath0 for which there is some @xmath101 such that @xmath102 then for any strictly increasing sequence of reals @xmath103 the sequence @xmath104 is equidistributed for @xmath23 almost every @xmath99 . in particular , @xmath23 almost every @xmath99 is normal in every base . davenport - erds - leveque criterion was established in @xcite and in this form by quefflec - ramar @xcite and it is a consequence of the classical _ weyl s equidistribution criterion _ ( 1908 ) , which says that a sequence @xmath105 equidistributes if and only if the exponential sums @xmath106 for any @xmath107 . in higher dimensions one can also study analogues of equidistribution on the @xmath108-torus @xmath109 . here a sequence @xmath110 is _ equidistributed _ if in the weak topology @xmath111 weyl s criterion in the higher dimensions has the following form : [ thm : weyl ] a sequence @xmath110 is equidistributed if and only if for any @xmath112 we have @xmath113 the natural analogue of sequences @xmath114 on the torus is to consider orbits under suitable expanding maps . for example , being normal is base @xmath100 precisely means that for the @xmath115 map @xmath116 the orbit @xmath117 of @xmath99 is equidistributed . the map @xmath118 is an example of an _ expanding toral endomorphism _ , that is , @xmath119 grows in norm as @xmath120 and @xmath118 preserves the algebraic structure of the unit circle @xmath121 . a similar notion can be defined for _ toral endomorphisms _ on @xmath122 , that is , maps of the form @xmath123 for some matrix @xmath124 . we say that the map @xmath125 is _ expanding _ if the singular values of @xmath22 are all strictly greater than @xmath1 . we prove the following higher dimensional analogue of the davenport - erds - leveque criterion : [ thm : delhigh ] let @xmath23 be a measure on @xmath126 for which there is some @xmath101 such that @xmath102 then the @xmath125-orbit @xmath127 of @xmath99 equidistributes at @xmath23 almost every @xmath99 for any expanding toral endomorphism @xmath128 . the proof of theorem [ thm : delhigh ] follows the same lines as the @xmath0-version by davenport - erds - leveque and we postpone the proof until section [ sec : delhigh ] . thus as an immediate corollary of theorem [ thm : main ] , we obtain the following equidistribution theorem for brownian motion : [ cor : equi ] almost surely for lebesgue almost every @xmath129 $ ] the orbit @xmath130 equidistributes for any expanding toral endomorphism @xmath131 . [ fig : browntorus ] embedded onto the @xmath132-torus @xmath133 with the beginning of a @xmath125-orbit of @xmath134.,title="fig : " ] in section [ sec : ito ] we give the necessary background from it calculus . in section [ sec : proof ] we will give the proof of our main result theorem [ thm : main ] . the key estimates are obtained in section [ sec : horizontal ] and section [ sec : vertical ] corresponding to the two cases discussed above . in section [ sec : delhigh ] we prove the equidistribution theorem [ thm : delhigh ] and finally in section [ sec : further ] we discuss further prospects for this work .

thus , there are two conflicting theories as of now , the one based on the 5th force which _ predicts _ this phenomena and the established cabibbo - kobayashi - maskawa ( ckm ) theory which was invented to _ explain _ this phenomena . in this article a test of these two theories against the recent experimental data is presented . it is found in this test that the ckm theory fares poorly , whereas the one based on the 5th force withstands the test well , in both accuracy and precision . for example , for the ckm matrix entry @xmath0 , we have @xmath1

i

1205.2494

in a recent article , this author proposed a program for physics beyond the standard model , solely based on modifying the twin pillars of fundamental physics by replacing lorentz structure with euclidean jordan algebra while keeping quantum theory . this program predicts not only quarks and leptons but also a short - range 5th fundamental force accompanying gravity . this 5th force predicts quark mixing and the related cp violation , which in fact was a phenomena observed in labs about fifty years ago . thus , there are two conflicting theories as of now , the one based on the 5th force which _ predicts _ this phenomena and the established cabibbo - kobayashi - maskawa ( ckm ) theory which was invented to _ explain _ this phenomena . in this article a test of these two theories against the recent experimental data is presented . it is found in this test that the ckm theory fares poorly , whereas the one based on the 5th force withstands the test well , in both accuracy and precision . for example , for the ckm matrix entry @xmath0 , we have @xmath1

it was experimentally observed in the 1960s that a quark of high generation can decay into a quark of low generation : a diagram of the mixed quark decay . ( http://en.wikipedia.org/wiki/user:army1987/quark ) this phenomenon , referred to as _ the mixed quark decay _ in this article , has been thought to be explained by the ckm theory @xcite in which it is assumed that the weak interaction pairs are @xmath2 , @xmath3 and @xmath4 rather than the more natural pairs @xmath5 , @xmath6 and @xmath7 , where @xmath8=v\left[\begin{matrix } d\cr s \cr b \end{matrix}\right]\ ] ] with @xmath9 being the ckm matrix @xmath10.\ ] ] for example , via weak interaction , instead of decaying into @xmath11 , @xmath12 decays into @xmath13 , and hence decays into @xmath14 , @xmath15 or @xmath11 with the relative probability @xmath16 , @xmath17 and @xmath18 respectively . in this theory , the ckm matrix @xmath9 is simply an input parameter whose actual value must be determined by experiments , but one thing is clear : @xmath9 has to be unitary _ exactly_. a great success of this theory is the prediction of the third generation of quarks , for which kobayashi and maskawa shared one half of the 2008 nobel physics prize in physic @xcite . from the particle data group @xcite , the best experimental determination for the magnitudes of the ckm matrix elements is @xmath19 @xmath20 . } \end{aligned}\ ] ] it is worth to mention that , the values of @xmath21 and @xmath22 quoted here ( the highlighted matrix entries ) are obtained under the theoretical assumption that @xmath23 , see equation ( 11.13 ) of page 159 in ref . @xcite and the line above this equation . if we took the experimentally determined value of @xmath24 , i.e. , @xmath25 , we would have @xmath26 the phases of the ckm matrix elements determine the amount of cp violation . with the observed amount of cp violation taken into account , the currently best known standard " fit for the ckm matrix elements in the sense of chau and keung @xcite is @xmath27 @xmath28 . \nonumber\end{aligned}\ ] ] note that only the two highlighted entries are not nearly being real numbers . because of this observation , _ @xmath29 , @xmath30 , @xmath31 , @xmath32 , @xmath33 shall be assumed to be real numbers hereafter_. the assumption that @xmath12 interacts with @xmath34 ( rather than @xmath11 ) via weak interaction is made purely for explaining the mixed quark decay . there is no theoretical reason why this must be so . in any case , this assumption is mysterious and now the experimental data strongly suggests that it is incorrect . for example , the norm square of the 3rd column should be exactly @xmath35 ; however , based on the experimental data for the 3rd column , a simulation of any size @xmath36 shows that this norm square has an average @xmath37 , a standard deviation @xmath38 , and is less than @xmath39 more than @xmath40 of time . it is perhaps not a secret among some experts that the ckm theory is less than accurate . however , to reject the ckm theory , one must provide an alternative theory which is both theoretically sound as well as quantitatively more accurate . a major message in this article is that such a theory indeed exists .

we present a theory of superconducting states where the cooper pairs have a nonzero center of mass momentum , inhomogeneous superconducting states known as a pair - density - waves ( pdw ) states . we show that several superfluid phases that may arise in this phase can be treated within a controlled bcs mean field theory , with the strength of the spin - triplet nematic order parameter playing the role of the small parameter of this theory . we find that in a spin - triplet nematic phase , in addition of a triplet @xmath0-wave and spin - singlet @xmath1-wave ( or @xmath2 depending on the nematic phase ) uniform superconducting states , it is also possible to have a @xmath1-wave ( or @xmath2 ) pdw superconductor . the pdw phases found here can be either unidirectional , bidirectional or tridirectional depending on the spin - triplet nematic phase and which superconducting channel is dominant . in addition , a triple - helix state is found in a particular channel .

i

1403.7530

in conventional superconductors the cooper pairs have a zero center of mass momentum . in this paper we present a theory of superconducting states where the cooper pairs have a nonzero center of mass momentum , inhomogeneous superconducting states known as a pair - density - waves ( pdw ) states . we show that in a system of spin-1/2 fermions in 2 dimensions in an electronic nematic spin triplet phase where rotational symmetry is broken both in real and in spin space pdw phases arise naturally in a theory that can be analyzed using controlled approximations . we show that several superfluid phases that may arise in this phase can be treated within a controlled bcs mean field theory , with the strength of the spin - triplet nematic order parameter playing the role of the small parameter of this theory . we find that in a spin - triplet nematic phase , in addition of a triplet @xmath0-wave and spin - singlet @xmath1-wave ( or @xmath2 depending on the nematic phase ) uniform superconducting states , it is also possible to have a @xmath1-wave ( or @xmath2 ) pdw superconductor . the pdw phases found here can be either unidirectional , bidirectional or tridirectional depending on the spin - triplet nematic phase and which superconducting channel is dominant . in addition , a triple - helix state is found in a particular channel . we show that these pdw phases are present in the weak coupling limit , in contrast to the usual fulde - ferrell - larkin - ovchinnikov phases which require strong coupling physics in addition to a large magnetic field ( and often both ) .

the problem of the interplay between superconductivity and other broken symmetry states is one of the central problems in the physics of strongly correlated systems . this issue is particularly pressing in the context of the cuprate and their complex phase diagram . in addition to nel antiferromagnetic order and high @xmath3 uniform @xmath4 superconductivity , a host of other ordered phases , including incommensurate spin stripes ( which exhibit spin - density - wave ( sdw ) order ) , incommensurate charge stripes ( with charge - density - wave ( cdw ) order ) , electronic nematic order , and time - reversal ( and/or mirror - plane ) symmetry - breaking have been reported essentially in all the cuprate .@xcite static spin stripe order is seen in the lanthanum family of the cuprate superconductors.@xcite static charge stripe order is seen in ( lbco),@xcite in ( ybco),@xcite in high magnetic fields ( where otherwise is seen as short range order@xcite ) , and in ( bscco).@xcite nematic charge order is seen in ybco@xcite and in bscco@xcite over a wide range of doping and temperatures . time - reversal and/or mirror plane ( or inversion ) symmetry breaking has also been reported in ybco , in lbco and in bscco@xcite although recent nmr measurements do not detect magnetism in the same samples.@xcite stripe and/or nematic orders of these types are also seen in the iron superconductors@xcite and in heavy fermion materials.@xcite a key feature of the orders that are seen in these strongly correlated materials is that the orders are intertwined with each other rather instead of competing with each other.@xcite by intertwined orders what we mean@xcite is that the orders appear either together and/or with similar strengths , e.g. at critical temperatures of similar magnitude , over a significant range of parameters ( doping , coupling constants , etc . ) instead , if the orders were competing with each other , one of the orders will be stronger and the others will be strongly suppressed . the exception to this rule are systems which are close to a multicritical point at which not only the critical temperatures but also all the couplings between the different orders are finely - tuned to very specific relations ( and values ) . while this can happen in a particular material at a particular doping it is unnatural to assume that multicriticality should generically occur in all materials and for a wide range of parameters . a case that is particularly relevant from the perspective of intertwined orders is lbco , particularly near the so - called 1/8 anomaly . in this material the @xmath3 of the uniform @xmath1-wave superconductivity is suppressed ( down to low - temperatures ) . yet , a variety of experimental probes show that over essentially the same temperature range where at other dopings lbco is a @xmath1-wave superconductors , near 1/8 doping a host of other orders are observed , including charge - stripe order , spin stripe order and a most peculiar phase in which the cuo planes appear to be superconducting but yet the material remains insulating along the c - axis.@xcite the layer - decoupling effect is also seen in lbco away from @xmath5 at finite fields@xcite and also in underdoped lsco materials at finite magnetic fields@xcite where a field - induced stripe - ordered state had been observed previously.@xcite it was suggested by berg and coworkers that this peculiar layer - decoupling effect can be naturally explained if the cuo planes are in an inhomogeneous , striped , superconducting state with the symmetry of a pair - density wave ( pdw ) state in which charge , spin and superconducting orders are intertwined with each other.@xcite the local superconducting order parameter @xmath6 in a pdw state is spatially modulated and a spin singlet . for a state with unidirectional modulation , @xmath6 has the form @xmath7 where @xmath8 are two slowly - varying complex fields and @xmath9 is the ordering wave vector . hence , the unidirectional pdw superconducting state is characterized by two complex order parameters , @xmath8 . a state with the pdw pattern of superconducting order was proposed already in 1964 by larkin and ovchinnikov @xcite ( lo ) and by fulde and ferrell@xcite ( ff ) to arise in the presence of a zeeman field . as is the case of all ordered phases with a finite wave vector , the lo state , and its time - reversal breaking ( spiral ) cousin ff , requires that a nesting condition be satisfied for this state to occur in the weak coupling bcs regime ( for a review on fflo states see ref . [ ] ) . in most cases this nesting conditions is hardly ever satisfied . thus , states of this type can only exist in a strongly coupled regime which is clearly outside the applicability of a weak coupling theory such as bcs . motivated by the lbco results , and using the bcs framework , loder and coworkers @xcite found a pdw state in a tight - binding model with @xmath1-wave pairing in the absence of an external magnetic field . however , these authors found that the critical value of the coupling constant for which the pdw is the ground state is quite large and hence well outside the regime in which bcs theory is reliable . more recently , a pdw state has been found in variational monte carlo simulations of the @xmath10 and @xmath11 model at zero magnetic field , @xcite although in these simulations appear to favor the uniform sc state over the pdw state only by a small amount of energy . however , recent , sophisticated ipeps ( infinite projected entangled pair - states@xcite ) simulations have found strong evidence for intertwined orders ( in which several orders , including the pdw state , appear to be essentially degenerate in energy ) in the @xmath10 model over a significant range of coupling constants and doping.@xcite a recent paper by p. a. lee ( which appeared as this work was being finished ) suggests that pdw states may arise in a slave - particle rvb approach@xcite by postulating an `` amperian '' interaction among the spinons.@xcite on the other hand , a pdw state is known to exist in the spin - gap state of the kondo - heisenberg chain@xcite and also in a two - leg ladder,@xcite even in the weak coupling limit . fflo states have been proposed to explain some of the properties of heavy fermion superconductors @xcite and have been conjectured to arise in cold atomic systems . @xcite fflo states were studied in two dimensions by shimahara @xcite where the fflo states seem to be more robust . here we will investigate the relation between pdw states and nematic order . although charge nematic order ( a spatially - uniform spin - singlet state that breaks rotational invariance ) does neither favor nor disfavor superconductivity , except in regimes in which @xmath2-wave and @xmath1-wave superconductivity are in close competition@xcite ( see , however , ref . [ ] ) , here we will show that a nematic state in the spin triplet channel@xcite can favor unconventional superconducting phases , including a pdw state . in this work we present the study of the presence of an inhomogeneous superconducting instability in an system that is already in an @xmath12 or @xmath13 nematic phase . we will use a mean field analysis in the weak coupling limit to show that in a region of the phase diagram , an inhomogeneous superconducting state is the ground state of the system . oganesyan and coworkers@xcite ( as well as refs . [ ] ) studied a spinless nematic fermi fluid ( fl ) , where the breaking of rotational symmetry manifest in a spontaneous quadrupolar ( elliptical ) distortion of the fermi surface , while the translation invariance is preserved ( for a review see ref . [ ] ) . in the charge nematic state the fs has a spontaneous quadrupolar ( elliptical ) distortion . nematic phases of fermi fluids can arise either via a pomeranchuk instability of a fermi liquid@xcite or by quantum melting of charge stripe phases.@xcite the resulting anisotropic fluids are non - fermi liquids if the lattice effects are weak enough . @xcite generalized the aforementioned work of oganesyan and coworkers to a system of spin-1/2 fermions and found a generalization of the nematic state to the spin triplet channel which they called an @xmath12-phase . in this phase rotational symmetry is broken both in real and in the internal spin space , while while remaining invariant under a combination of a discrete set of rotations in both sectors . in addition , they also found another , spatially isotropic phase , which they called the @xmath13-phase ( in analogy to the @xmath14 phase in liquid @xmath15he ) . this state is uniform and spatially isotropic , but the spin quantization axis of a fermionic quasiparticle on the fermi surface lies in - plane and winds around the fs with an integer - valued winding number . in both phases the fs for spin up and down is distorted in different ways ( see figs . [ fig : ellipses ] , [ fig : betaw2 ] , and [ fig : betaw1 ] ) providing a natural system to studied the presence of an instability to an inhomogeneous superconducting state . in a fermi liquid setting , the phase transition to the spin triplet nematic phases occurs as a pomeranchuk instability and hence the tuning parameter is a landau parameter in the spin triplet channel . in a strong coupling setting it can occur by quantum melting of a spin - stripe state . in what follows we will refer to both the @xmath12 and the @xmath13 phases as spin - triplet nematic phases ( although in a strict sense they are not ) . in the conventional bcs approach@xcite the fflo states arise only in a regime in which there is a sufficiently weak zeeman coupling to an uniform magnetic field so that the sc instability can only occur for cooper pairs with finite momentum by suppressing the nesting between electronic states at the fermi surfaces for both spin projections . however , this assumption is a severe limitation and , to this date , zeeman - field - tuned fflo states have not been clearly seen in experiment . in contrast here we we will see that in the spin triplet nematic phases ( which although magnetic have a zero uniform zeeman field ) the tuning parameter for the sc instability is the distance to the nematic spin triplet quantum critical point . in particular we will find that depending on whether the nematic is an @xmath12 or a @xmath13 phase a host of different sc states , both uniform and inhomogeneous , can occur . unfortunately to this date there is no clear evidence for a spin triplet nematic state . on the theoretical side a recent paper by maharaj and coworkers@xcite found a spin - triplet @xmath13-phase in a fermionic system on a honeycomb lattice via a pomeranchuk instability . fischer and kim found a nematic - spin - nematic state ( the @xmath12 spin - triplet nematic state ) in a mean - field analysis of the three - band emery model of the cuprates in a regime in which the hubbard @xmath16 on the cu sites and on the o sites ( @xmath17 ) are both large ( and comparable).@xcite on the experimental side , there is evidence of time reversal - symmetry - breaking in close to the pseudogap temperature in spin - polarized neutron scattering@xcite and , with some caveats , in kerr rotation experiments.@xcite however , the kerr rotation experiments can also be interpreted as evidence of inversion symmetry breaking via a gyrotropic effect in a system with charge order.@xcite hence the kerr effect measurements do not on their own prove the existence of as state with broken time reversal invariance since the cuprate superconductors are now known to exhibit charge order . on the other hand , the spin - polarized neutron experiments can be interpreted either as evidence for loop current order@xcite or as evidence of a nematic spin triplet state which on a cuo lattice means that the oxygens are spin - polarized but their polarization is opposite along the @xmath18 and @xmath19 axis ( as shown in fig . [ ybco ] ) . however such a state is incompatible with nmr measurements which do not find evidence of any sublattice magnetization in ybco and hbco which have instead a substantial spin gap . aside from these important caveats and reservations , we find that it is nevertheless useful to consider the possible role of spin triplet nematic phases in a weak - coupling mechanism for pair - density - wave phases . in this work we will consider a system in a spin triplet nematic state but close to the pomeranchuk quantum critical point . by restricting ourselves to this regime enable us to use controlled approximations . we will assume that the system of interest is inside a spin - triplet nematic state , sufficiently close to the quantum phase transition so that the magnitude of the order parameter . however we will also assume that we are deep enough in the spin - triplet nematic phase so that the quantum critical fluctuations can be safely ignored . furthermore we will also ignore the possible non - fermi liquid physics which may arise in the spin - triplet nematic state . thus , the main assumption that we will use throughout is the existence to the pomeranchuk quantum critical point and that the resulting @xmath12 and @xmath13 phases are stable . for this reason we will not consider the @xmath20 case since these phases are unstable in the absence of sufficiently strong spin - orbit interactions.@xcite we will show that , depending on the particular spin triplet nematic phase that is considered , different uniform superconducting phases arise ( @xmath2 , @xmath0 or @xmath1 wave ) and that these phases are in close competition with inhomogeneous phases with the symmetry of a pair - density - wave of the lo type . ff states are generally found to be metastable at least close to the thermal phase boundary . the main results of this work are summarized in three phase diagrams , one for the spin triplet nematic @xmath12 phase with pairing in the @xmath1-wave superconducting channel ( shown in fig.[phasediagram ] ) and two for the spin triplet nematic @xmath13 phase with pairing in the @xmath2 and @xmath1 wave superconducting channels ( shown in fig.[fig : beta - diagram - swave ] and fig.[fig : beta - diagram - dwave ] respectively . ) we also determine the structure of the landau - ginzburg free energies close to the thermal transition and calculate the coefficients and stiffnesses . the resulting phase diagrams turn out to be quite complex . in the case of the @xmath12 phase the superconducting states which arise are , in addition to a spin - triplet @xmath0 wave state , a uniform spin singlet @xmath1-wave sc , a bidirectional pdw state , and a unidirectional pdw state . on the other hand , in the case of the @xmath13 phase the uniform state may be an @xmath2-wave or a @xmath1 wave sc . if the pairing channel is @xmath2 wave , in the @xmath13 phase we find unidirectional , bidirectional and tridirectional pdw states and , in addition , a triple - helix ff - type state . if the pairing channel is @xmath1-wave , in addition to an uniform @xmath1-wave sc , we also find both a unidirectional and two bidirectional pdw phases . we also investigate the nature of the phase transitions between these states close to the thermal phase boundary . a rich set of different behaviors are found , including continuous and first order phase transitions as well as lifshitz points and other multicritical points . it is important to emphasize that these results , obtained using a weak coupling bcs theory , are controlled by the distance to the spin triplet nematic quantum critical point . thus the spin triplet nematic quantum critical point plays the role of a complex multicritical point . this paper is organized as follows . in section [ sec : spin - triplet - nematic ] we summarize the theory and description of the spin - triplet nematic phases and follow closely the results and notation of ref . [ ] . this caveats are discussed in this section in some detail . in section [ sec : scinst ] we discuss the sc instabilities of the @xmath12 ( subsection [ sec : alpha - phase ] ) and @xmath13 ( subsection [ sec : beta - phase ] ) phases by calculating explicitly the respective sc susceptibilities . in section [ sec : mft ] we present a bcs - type mean - field theory of the different sc states and show that it is well controlled in the regime where the spin - triplet nematic order parameter is small enough . in this section we derive the landau - ginzburg free energy for each phase and derive the phase diagrams and in section [ sec : conclusions ] we present our conclusions . the details of the calculations are presented in the appendix .

in mixing highly viscous materials , like polymers , foods , and rubbers , the geometric structure of the mixing device is a determining factor for the quality of the mixing process . in pitched - tip kneading disks ( ptkd ) , a novel type of mixing element , based on conventional kneading disks ( kd ) , the tip angle is modified to change the channel geometry as well as the drag ability of kd .

r

1612.08121

in mixing highly viscous materials , like polymers , foods , and rubbers , the geometric structure of the mixing device is a determining factor for the quality of the mixing process . in pitched - tip kneading disks ( ptkd ) , a novel type of mixing element , based on conventional kneading disks ( kd ) , the tip angle is modified to change the channel geometry as well as the drag ability of kd . we discuss the effects of the tip angle in ptkd on mixing characteristics based on numerical simulation of the flow in the melt - mixing zone under different feed rates and a screw rotation speed . it turns out that the passage of fluid through the high - stress regions increases in ptkd compared to conventional kd regardless of the directions and sizes of the tip angle , while the fluctuation in residence time stays at the same level as the conventional kd . furthermore , pitched tips of backward direction increase the mean applied stress on the fluid elements during its residence in the melt - mixing zone , suggesting the enhancement of dispersive mixing quality in ptkd . these understandings of the role of the tip angle on kd can give a basic guide in selecting and designing suitable angle parameters of ptkd for different mixing purposes . polymer processing , mixing , twin - screw extrusion , numerical simulation

in order to see the effect of the tip angle on the inhomogeneity of cross - sectional mixing , we computed the fluctuation of the residence time . figure [ fig2 ] shows the probability density of the residence time normalized by the mean residence time for five different ptkds under @xmath34cm@xmath21 . from this figure , we observe that the residence time distribution is almost unaffected by the forward tip angle while the fraction of the longer residence increases with a backward tip angle . in fig . [ fig3 ] , there is drawn the relative standard deviation of the residence time to its mean value as a function of @xmath26 . it turns out that the fluctuation of the residence time in ptkds hardly depends on @xmath26 , and takes the value of 0.50.6 . at higher values of @xmath26 , the residence time fluctuation is approximately the same level as that of the conventional kd . this fact suggests that ptkds have as good mixing ability as the conventional kd with the same disk - stagger angle at sufficiently high @xmath26 . the effect of the tip angle on the residence time distribution depends on the tip direction . while for ft type the residence time fluctuation does not show any angle - dependence , for bt type the residence time fluctuation decreases slightly with the backward tip angle . although this slight change of residence time fluctuation reflects the effect of the tip angle , this change does not seem to be substantial in terms of mixing ability . in short , the residence time distribution is not substantially modified by the addition of a tip angle to a conventional kd . next , we discuss the effects of a pitched tip on dispersive mixing . the mean applied stress during residence , @xmath35 , is calculated by inserting the stress magnitude @xmath36 into eq . ( [ eq : lagrangian_average_of_f ] ) . figure [ fig4 ] shows the probability density function of @xmath35 for ft15 , ft30 , and nt under @xmath34cm@xmath21 . as the forward tip angle increases , the fluctuation of @xmath35 increases , whereas the average of @xmath35 stays at a similar level as that of nt . the average value and the relative standard deviation of @xmath35 as a function of @xmath26 are drawn in figs . [ fig5](a ) and ( b ) , respectively . the average value of @xmath35 is insensitive to @xmath26 , and takes a similar value as that of nt . in contrast , the fluctuation of @xmath35 increases with @xmath26 , and is larger for a larger forward tip angle . these results clearly indicate that the forward tip increases the inhomogeneity of dispersive mixing quality especially at high throughput operation . figure [ fig6 ] shows the probability density function of @xmath35 for bt15 , bt30 , and nt under @xmath34cm@xmath21 . in fig . [ fig6 ] , we observe an increase both in the average level and the fluctuation of @xmath35 with an increase in the backward tip angle . the average value and the relative standard deviation of @xmath35 as a function of @xmath26 are drawn in figs . [ fig7](a ) and ( b ) , respectively . in fig . [ fig7 ] , the average value of @xmath35 becomes larger for a larger backward tip angle , suggesting that the bt type enhances the dispersive mixing ability compared to the nt type . in contrast , the fluctuation of @xmath35 is rather insensitive to the backward tip angle . that is , irrespective of bt angle , the inhomogeneity of the dispersive mixing is at the same level as that of the nt type with an increase of @xmath26 , the fluctuation of @xmath35 for bt slightly increases , suggesting that inhomogeneity in the dispersive mixing is smaller for lower @xmath26 . in short , for bt type , both high level and small inhomogeneity of @xmath35 is achieved at low @xmath26 conditions , indicating that that dispersive mixing in bt type is most effective when @xmath26 is low and the bt angle is large . in order to further study the effects of the tip - angle on dispersive mixing , the passage of fluid at high - stress regions has been investigated . irrespective of the tip angle , the highest shear stress is achieved in the small gap regions like the tip barrel clearance and the inter - meshing region . the substantial dispersion process mainly takes place when fluid elements pass through such high - stress regions . however , since the high - stress region occupies only a small fraction of the whole channel , the fraction of the fluid passing through these regions and the number of passages are essentially determined by the flow pattern at the low - stress ( low - shear - rate ) regions . thus , the geometric structures of the mixing elements are directly responsible for the passage of fluid through the high - stress regions , eventually leading to a better dispersive mixing performance . by setting a threshold value for the magnitude of the shear stress tensor , the regions of tip barrel clearance and the screw inter - meshing region are defined as the high - stress regions . for instance , the region where the shear stress magnitude is larger than 0.35mpa for nt type under @xmath37cm@xmath21 is shown in fig . [ figa ] , which clearly shows that the high - stress region is localized at around tip - clearance and inter - meshing regions . we calculated the fraction of the tracers passing through the high - stress regions as well as the residence time in those regions . for each tracer , the residence time in the high - stress regions , @xmath38 , as well as the residence time in the whole mixing zone , @xmath30 , has been studied . figures [ fig8](a ) and ( b ) show the probability density function of the ratio @xmath39 under @xmath34cm@xmath21 . at a first look at figs . [ fig8](a ) and ( b ) , the residence time in the high - stress regions is at most 0.1 during the residence in whole zone , irrespective of the tip angle . both for ft and bt types , the residence in the high - stress regions becomes longer compared to the nt type , indicating that the pitched - tip geometry can enhance the efficiency of conveying the fluid to the high - stress regions . the increase of the relative residence in the high - stress regions is more pronounced with the bt type . this observation partly explains the enhancement of the dispersive mixing by the pitched tip . from figs . [ fig8](a ) and ( b ) , we also observe that the probability of vanishing @xmath38 takes a finite value , indicating that not all the fluid elements pass through the high - stress regions . in order to study this aspect , we discuss the fraction of the tracers passing the high - stress regions , denoted by @xmath40 . in figs . [ fig9](a ) and ( b ) , @xmath40 is plotted to the mean residence time of high - stress regions , @xmath41 , for different @xmath26 values , in which the larger symbol is for the larger value of @xmath26 . in the plot of @xmath42 and @xmath43 , the upper locations means that a large fraction of tracers pass through the high - stress regions , while the right locations means that the tracers stay long time in the high - stress regions . hence , the upper and right locations indicate a high potential for dispersive mixing . for conventional nt type , a fraction , 0.40.5 , of the fluid passes through the high - stress region for the @xmath26 value studied . furthermore , @xmath42 and @xmath43 are rather insensitive to the value of @xmath26 . in contrast , for ft and bt types , @xmath42 and @xmath43 show a relatively large dependence on @xmath26 . we observe a general trend such that , as @xmath26 decreases , both @xmath42 and @xmath43 increase . in addition , the characteristics of the passage through the high - stress region have different tip - angle dependencies with different directions of the tip angle . while for ft type , @xmath42 and @xmath43 does not depend on the tip angle , for bt type , @xmath42 and @xmath43 take larger values for larger backward tip angles . this fact is consistent with the tip - angle dependence of the mean applied stress during residence in fig . [ fig5](a ) and [ fig7](a ) . the characteristics of the passage through the high - stress region reveal that the backward tip is effective at enhancing the dispersive mixing ability . from the data above , it turns out that the pitched tip modifies the dispersive mixing ability of kneading disks , and the backward tip enhanced the potential of dispersive mixing while keeping the distributive mixing ability . we discuss the relation between the flow pattern induced by the geometry of the pitched - tip kd and the dispersive mixing ability . pitched tips add an additional drag ability along the screw rotation to conventional kd . for backward tips increase the drag in the backward extrusion direction , for @xmath44 condition , the pressure drop in bt type becomes larger than that in nt , leading to the pressure flow in the extrusion direction being more pronounced in bt . the enhanced pressure flow in bt promotes the passage of fluid across the small gap at the backward tips , resulting in an increase of the passage through the high - stress regions and the mean applied stress . in other words , the geometry of backward tips cause a counteracting effect by blocking against the forward flow and the additional forward pressure flow while keeping the leakage flow in the inter - disk spaces . since this effect is driven by the screw rotation , it is maximized with the small @xmath26 condition , which is clearly demonstrated by the characteristics of the passage through the high - stress region in fig . [ fig9 ] . in the case of ft type , since the forward pitched tips increase the drag in the forward direction , for @xmath44 conditions the pressure drop become smaller than for nt , or even becomes negative , depending on @xmath26 . thus , the counteracting effect of the pressure flow and the blockage by the tips is weaker in the ft type than in the bt type . in short , the geometric modification of conventional kd by pitched tips induces both a change in the channel geometry and a modification of the pressure flow , causing a change in dispersive mixing ability .

we discuss the effects of the tip angle in ptkd on mixing characteristics based on numerical simulation of the flow in the melt - mixing zone under different feed rates and a screw rotation speed . it turns out that the passage of fluid through the high - stress regions increases in ptkd compared to conventional kd regardless of the directions and sizes of the tip angle , while the fluctuation in residence time stays at the same level as the conventional kd . furthermore , pitched tips of backward direction increase the mean applied stress on the fluid elements during its residence in the melt - mixing zone , suggesting the enhancement of dispersive mixing quality in ptkd . these understandings of the role of the tip angle on kd can give a basic guide in selecting and designing suitable angle parameters of ptkd for different mixing purposes . polymer processing , mixing , twin - screw extrusion , numerical simulation

c

1612.08121

in mixing highly viscous materials , like polymers , foods , and rubbers , the geometric structure of the mixing device is a determining factor for the quality of the mixing process . in pitched - tip kneading disks ( ptkd ) , a novel type of mixing element , based on conventional kneading disks ( kd ) , the tip angle is modified to change the channel geometry as well as the drag ability of kd . we discuss the effects of the tip angle in ptkd on mixing characteristics based on numerical simulation of the flow in the melt - mixing zone under different feed rates and a screw rotation speed . it turns out that the passage of fluid through the high - stress regions increases in ptkd compared to conventional kd regardless of the directions and sizes of the tip angle , while the fluctuation in residence time stays at the same level as the conventional kd . furthermore , pitched tips of backward direction increase the mean applied stress on the fluid elements during its residence in the melt - mixing zone , suggesting the enhancement of dispersive mixing quality in ptkd . these understandings of the role of the tip angle on kd can give a basic guide in selecting and designing suitable angle parameters of ptkd for different mixing purposes . polymer processing , mixing , twin - screw extrusion , numerical simulation

in pitched - tip kneading disks ( ptkd ) , a novel melt - mixing element used in twin - screw extrusion , the effects of the direction and size of the tip angle on the mixing characteristics were investigated based on the numerical simulation of a three - dimensional flow . under a material feed rate and a screw rotation speed , the tip angle on a conventional kneading - disk ( kd ) element modifies the following two properties of the flow : ( i ) additional drag ability caused by screw rotation modifies the pressure flow , ( ii ) the pitched - tip acts as a blockage to the pressure flow induced by the pitched - tip . these counteracting effects result in an increase of the fraction of the fluid elements passing through the high - stress regions , leading to a modification of the dispersive mixing ability . forward tips on neutrally staggered kd increase the inhomogeneity of the applied stress during residence compared to the conventional kd , while keeping the residence time fluctuation . in contrast , backward tips on neutrally staggered kd increase the mean applied stress during residence , suggesting an enhancement of the dispersive mixing ability . these effects are more pronounced for larger tip angles , and are dependent on the ratio of the material feed rate to the screw rotation speed . these findings about the role of the tip angle can be useful for a better understanding of the mixing characteristics of a general class of ptkd elements and for choosing the optimal combination of the disk - stagger angle and tip angle .

in rotationally constrained percolation models , a site of a percolation cluster could be occupied more than once from different directions due to the nature of the rotational constraint . a state variable @xmath0 is assigned to each lattice site whose value corresponds to the number times it has been visited during the growth of a cluster . it is proposed here that the percolation transition and the multifractal aspects of infinite percolation clusters under rotational constraint can be studied defining suitable measures in terms of the state variable @xmath0 . this method does not require to introduce any external agency like an electric current or a random walker in order to explore multifractality as in the case of ordinary percolation .

i

0807.2297

in rotationally constrained percolation models , a site of a percolation cluster could be occupied more than once from different directions due to the nature of the rotational constraint . a state variable @xmath0 is assigned to each lattice site whose value corresponds to the number times it has been visited during the growth of a cluster . it is proposed here that the percolation transition and the multifractal aspects of infinite percolation clusters under rotational constraint can be studied defining suitable measures in terms of the state variable @xmath0 . this method does not require to introduce any external agency like an electric current or a random walker in order to explore multifractality as in the case of ordinary percolation . the state variable representation also describes the universality class of the percolation models appropriately .

multifractals appear in a wide range of situations like energy dissipation in turbulent flows@xcite , electronic eigenstates at metal insulator transition@xcite , diffusion in porous structures@xcite , diffusion limited aggregation@xcite , fluctuations in finance@xcite , dynamics of human heartbeat@xcite and many others . the multifractal properties associated with the infinite percolation clusters at the percolation threshold @xmath1 is considered in this paper . in ordinary percolation ( op)@xcite , a cluster is generated by occupying a lattice site randomly with a probability @xmath2 or remains empty with a probability @xmath3 . each site of a percolation cluster then has two states , occupied or empty . the average @xmath4 moments of the cluster size distribution of percolation clusters are linearly dependent on the moment @xmath4 and described by a single fractal dimension @xmath5@xcite . in order to study the multifractal aspects of percolation clusters , usually , a current distribution@xcite or a random walker@xcite is introduced . however , in the presence of rotational constraint on the percolation model , an occupied site has always a direction associated with it and a site can be re - occupied from different directions . a site can be occupied at most @xmath6 times from @xmath6 different directions on a given lattice with coordination number @xmath6 . there are two such well studied rotational percolation models exists , spiral percolation sp@xcite and directed spiral percolation@xcite . in these models , a state variable @xmath0 then can be assigned to each lattice site and whose value will correspond to the number of times a site is visited during the growth of the cluster . the value of @xmath0 then can change from @xmath7 to @xmath8 on a square lattice and @xmath7 to @xmath9 on a triangular lattice for sp and dsp models whereas it has only two states @xmath10 and @xmath7 in case of op . in this paper , a new methodology is proposed to study the percolation transition in terms of the state variable @xmath0 . studying the physical properties associated with the state variable @xmath0 , the percolation transition is possible to establish at the same percolation threshold @xmath1 defined geometrically . the spanning clusters at @xmath11 are fractal . distribution of @xmath0 on the fractal substrate is very similar to mass distribution on a geometrical support usually taken for multifractal study@xcite . in order to explore the multifractal aspects of the spanning percolation clusters in these rotationally constrained percolation models at @xmath11 , it is now possible to define a suitable multifractal measure in terms of @xmath0 . in this way , one does not need to introduce any other external agency like electric current or random walker in the model as it is usually done in the case of op clusters . the variable @xmath0 is inbuilt in the rotational models and represents an inherent property of sp and dsp . it is found that the exponents associated with the @xmath4 moments of the measure defined in terms of @xmath0 are not limited by any linear dependence on the moment @xmath4 for the rotational percolation models . it then indicates that the measure has multifractal character . below , description of the rotational percolation models will be given and the multifractal aspects of the spanning clusters will be investigated .

the model includes two ( anti)sextet higgs scalars , @xmath9 with @xmath10=0 and @xmath11 with @xmath10=2 , which , respectively , couple to @xmath12 for the electron mass and masses of atmospheric neutrinos and to @xmath13 for the @xmath14- and @xmath15-masses and one - loop radiative neutrino masses relevant to solar neutrinos .

i

hep-ph0103265

in the minimal @xmath0 gauge model with a global @xmath1 ( @xmath2 ) symmetry and a discrete @xmath3 symmetry , it is found that the interplay between neutrinos and charged leptons contained in triplets of @xmath4=(@xmath5 , @xmath6 , @xmath7 ) ( @xmath8=1,2,3 ) naturally leads to the large mixing angle ( lma ) msw solution . the model includes two ( anti)sextet higgs scalars , @xmath9 with @xmath10=0 and @xmath11 with @xmath10=2 , which , respectively , couple to @xmath12 for the electron mass and masses of atmospheric neutrinos and to @xmath13 for the @xmath14- and @xmath15-masses and one - loop radiative neutrino masses relevant to solar neutrinos . this mechanism is realized by utilizing an additional residual discrete symmetry supplied by explicitly broken @xmath10 , which guarantees the absence of tree - level neutrino mass terms of the @xmath13-type . pure rotation effects due to the diagonalization of neutrino and charged - lepton mass matrices are estimated to yield @xmath16 but the radiative effects supersede the rotation effects to yield @xmath17 as the lma solution . epsf # 1#2#3#4#1 * # 2 * ( # 4 ) # 3 # = `` 0023 $ = ' ' 0024 % = `` 0025 = ' ' 705c = `` 336e = ' ' 336f = `` 331a = ' ' 331b = `` 3328 = ' ' 3329 = " 0350

in the recent report on the detailed analysis of solar neutrino oscillations @xcite done by the super - kamiokande collaboration @xcite , it has been suggested that solutions with large mixing angles are favored while solutions with small mixing angles are disfavored at the 95@xmath18 confidence level . neutrino oscillations controlled by such large mixing angle have also been observed and confirmed for atmospheric neutrinos @xcite . both observed oscillations are characterized by the same property of neutrino mixings , namely , large neutrino mixings , which are theoretically consistent with bimaximal mixing scheme @xcite . the difference arises in their oscillation scales denoted by @xmath19 for atmospheric neutrinos and @xmath20 for solar neutrinos , which are specified by @xmath21 ev@xmath22 and @xmath23 ev@xmath22 , thereby , indicating a hierarchy of @xmath24 . neutrino oscillations arise for massive neutrinos @xcite . since neutrino masses of @xmath25 ev are implied by @xmath19 , models for neutrino oscillations must be equipped with mechanisms generating such tiny masses of neutrinos @xcite , which include breaking of the lepton number conservation for majorana neutrino masses . it has been long known @xcite that such lepton number breaking interactions are inevitably contained in the minimal @xmath26 model for electroweak interactions ( called the 331 model ) @xcite because a charged lepton ( @xmath27 ) and its antiparticle ( @xmath28 ) together with a neutrino ( @xmath29 ) are placed in a triplet of @xmath30 as @xmath31=(@xmath32 , @xmath33 , @xmath34)@xmath35 . as a result , the model provides a charged - lepton mass term included in @xmath36 , which simultaneously contains @xmath37 as a neutrino mass term . namely , the need for majorana mass term is linked to the existence of the massive charged leptons . therefore , the 331 model is suitable for incorporating majorana neutrino masses @xcite . with this nice feature of the 331 model in mind , we introduce the bimaximal mixing scheme into the model to accommodate observed neutrino oscillations . one of the possible scenario for bimaximal mixing scheme is to employ a new @xmath38 symmetry based on @xmath1 ( @xmath39 @xmath10 ) @xcite . neutrino mixings are predicted to be maximal for solar neutrinos with @xmath20=0 but arbitrary for atmospheric neutrinos with @xmath40 . the hierarchy of @xmath24 is trivially satisfied since @xmath20=0 . one has to next explain how a nonvanishing @xmath20 is induced while preserving @xmath24 . an elaborated mechanism is to generate @xmath20 as radiative effects @xcite , whose generic smallness explains the relative smallness of @xmath20 over @xmath19 @xcite . in this article , we construct our interactions that induce phenomenologically consistent neutrino and charged - lepton mass matrix , @xmath41 and @xmath42 , with appropriate radiative effects for @xmath20 . since the model describes both matrices in a unified form , masses for charged leptons and neutrinos are correlated to each other . the mass term of @xmath36 transforms as @xmath43 and @xmath44 , which requires @xmath45 and/or @xmath46 as higgs scalars . the coupling of the triplet higgs scalar to @xmath36 is antisymmetrized with respect to the @xmath30-index . the spin and statistics , then , requires antisymmetrized flavor indices carried by @xmath31 , in turn , generating antisymmetrized @xmath42 with eigenvalues corresponding to @xmath47 , which contradicts with the observed hierarchy of @xmath48 . the triplet higgs scalar alone is not consistent with the observed lepton mass spectrum . therefore , the sextet scalar , which provides symmetrized mass terms , is the key ingredient of the 331 model @xcite .- singlet vector - like heavy @xmath49electron " without introducing a sextet scalar @xcite has been advocated to describe consistent mass spectra of neutrinos and charged leptons @xcite . ] because the sextet higgs scalar contains both an @xmath50-doublet scalar for charged leptons and an @xmath50-triplet scalar for neutrinos , we naturally expect @xmath49degeneracy `` in the structure of their mass matrices . the charged leptons should contain a diagonal mass term such as the @xmath15-mass , which forces @xmath41 to have a diagonal term . however , @xmath41 should not contain diagonal terms to be consistent with bimaximal mixing scheme based on @xmath10 . to avoid this @xmath49degeneracy '' , we use the conservation of the @xmath10 quantum number supplemented by an appropriate @xmath3 parity as well as a specific breaking pattern of @xmath10 yielding a residual discrete symmetry . the collaboration of these symmetries allows neutrinos to develop no diagonal mass terms . as a result , atmospheric neutrino oscillations are controlled by those tree - level off - diagonal masses while solar neutrino oscillations are to be induced by one - loop effects . and a discrete symmetry have been done in ref.@xcite . ] in the following section , we first introduce particles and their interactions and discuss how the required vacuum alignment is realized . section iii deals with the diagonalization of @xmath41 , which reflects rotation effects due to the diagonalization of @xmath42 . the bimaximal condition on the neutrino masses determines a pattern of the matrix elements for the electron mass . one - loop radiative mass of @xmath51 is also calculated . the discussions in sec.iv include to examine @xmath20 by utilizing the correlation between @xmath41 and @xmath42 and to confirm that the partial @xmath49degeneracy " between @xmath41 and @xmath42 suppresses the rotation effects to yield the lma solution based on the radiative effects . the final section is devoted to summary and discussions .

this mechanism is realized by utilizing an additional residual discrete symmetry supplied by explicitly broken @xmath10 , which guarantees the absence of tree - level neutrino mass terms of the @xmath13-type . pure rotation effects due to the diagonalization of neutrino and charged - lepton mass matrices are estimated to yield @xmath16 but the radiative effects supersede the rotation effects to yield @xmath17 as the lma solution .

i

hep-ph0103265

in the minimal @xmath0 gauge model with a global @xmath1 ( @xmath2 ) symmetry and a discrete @xmath3 symmetry , it is found that the interplay between neutrinos and charged leptons contained in triplets of @xmath4=(@xmath5 , @xmath6 , @xmath7 ) ( @xmath8=1,2,3 ) naturally leads to the large mixing angle ( lma ) msw solution . the model includes two ( anti)sextet higgs scalars , @xmath9 with @xmath10=0 and @xmath11 with @xmath10=2 , which , respectively , couple to @xmath12 for the electron mass and masses of atmospheric neutrinos and to @xmath13 for the @xmath14- and @xmath15-masses and one - loop radiative neutrino masses relevant to solar neutrinos . this mechanism is realized by utilizing an additional residual discrete symmetry supplied by explicitly broken @xmath10 , which guarantees the absence of tree - level neutrino mass terms of the @xmath13-type . pure rotation effects due to the diagonalization of neutrino and charged - lepton mass matrices are estimated to yield @xmath16 but the radiative effects supersede the rotation effects to yield @xmath17 as the lma solution . epsf # 1#2#3#4#1 * # 2 * ( # 4 ) # 3 # = `` 0023 $ = ' ' 0024 % = `` 0025 = ' ' 705c = `` 336e = ' ' 336f = `` 331a = ' ' 331b = `` 3328 = ' ' 3329 = " 0350

we have successfully demonstrated that the minimal 331 model with the global @xmath1 and @xmath3 symmetry , which involves two ( anti-)sextet higgs scalars , @xmath113 , indeed explains solar neutrino oscillations based on the lma solution . the lma solution is explicitly obtained by the use of the plausible parameter values for masses and couplings . the model has the following properties , which do not depend on the parameterization , that 1 . the global @xmath1 symmetry is explicitly broken by @xmath150 down to a discrete @xmath155 symmetry defined by @xmath154 that forbids the @xmath116-breaking interactions for @xmath11 , the absence of which is the essence of our discussions to be consistent with the bimaximal neutrino mixing scheme based on @xmath1 ; 2 . the @xmath116 conservation is explicitly broken by @xmath367 , which generates the vev of @xmath129 for neutrinos calculated to be @xmath368 , where @xmath133 is the trigger for @xmath369 ; 3 . the mechanism generating the diagonal electron mass via @xmath187 ( @xmath8=2,3 ) is linked to the requirement realizing the bimaximal neutrino mixing via @xmath175 owing to the proportionality of @xmath370 ; 1 . the smallness of @xmath371 ev for @xmath19 is realized by @xmath372 estimated to be @xmath373 ; 2 . solar neutrino oscillations are induced by * the one - loop radiative effects , which yield @xmath374 corresponding to the lma solution provided @xmath0 @xmath185 @xmath117 occurs at @xmath332 tev , * the effects of the simultaneous diagonalization of the neutrino and charged - lepton mass matrices , which are expected to yield @xmath375 and which certainly yield the @xmath359 matrix element estimated to be @xmath376 , + where , in the present model , the dominance of one - loop radiative effects yields the lma solution . it should be stressed that the choice of @xmath92=@xmath333(1 tev ) automatically leads to the lma solution . the present radiative mechanism generates the majorana mass of @xmath51 , @xmath238 , given by the effective coupling of @xmath377 . this coupling is induced by @xmath128 and @xmath138 as in fig.[fig : loopdiagrams_ee ] and is of the @xmath10-conserving type . the less - dominant radiative masses are induced by @xmath378 for @xmath379 with @xmath69=1 contributing to @xmath238 and for @xmath380 with @xmath69=2,3 contributing to @xmath172 . the @xmath380-terms involve the @xmath10-breaking coupling of @xmath150 as in fig.[fig : loopdiagrams_mutau ] . the splitting of @xmath381 and @xmath382 is provided by @xmath238 , which is about @xmath383 ev , leading to the lma solution . the mass of @xmath345 is provided by @xmath348 at most of order @xmath384 ev but the diagonalization due to @xmath287 may give @xmath255 @xmath385 @xmath347 ev . 1 . for the hierarchical texture with @xmath386 , @xmath387 2 . for the democratic texture with @xmath388 , @xmath389 with @xmath390 and @xmath391 constrained by @xmath280 , 3 . for the democratic texture with @xmath392 , @xmath393 with @xmath394 , where @xmath395=@xmath188 , @xmath396 and the asterisks stand for the suppressed entries to generate @xmath20 . the partial @xmath49degeneracy " between @xmath41 to @xmath42 suppresses the rotation effects on @xmath281 due to the diagonalization of @xmath41 and @xmath42 . as a result , the solar neutrino oscillations are , respectively , characterized by @xmath337 ev@xmath22 for @xmath353 tev . of course , if our mechanism explaining neutrino oscillations works further , one should next consider some reasons for the emergence of the approximate equality of @xmath397 in the hierarchical case and of the hierarchy of either @xmath301 or @xmath302 in the democratic case . the masses of higgs scalars are simply assumed to be about @xmath296 for those related to the weak boson masses for the order - of - magnitude estimate for radiative neutrino masses , namely , @xmath398 @xmath399 @xmath400 @xmath399 @xmath401 @xmath399 @xmath402 @xmath399 @xmath296 . on the other hand , the @xmath97 scalar that generates masses for the exotic quarks and gauge bosons is assumed to have @xmath403 @xmath399 @xmath92(@xmath404 @xmath296 ) because @xmath405 is related to the spontaneous breakdown of @xmath0 to @xmath117 . we have estimated @xmath92 to lie in @xmath332 tev in order to reproduce the observed neutrino mass pattern . it is further known that the 331 model contains peculiar particles , _ i.e. _ doubly - charged bilepton gauge bosons @xcite with masses of the order @xmath406 , that couple to @xmath407 . since @xmath92 can be @xmath332 tev , the bilepton gauge bosons can be as light as and even lighter than 1 tev . it is , therefore , quite conceivable that we will observe the bilepton gauge bosons with masses around 1 tev , which provide striking phenomena with clean @xmath408-@xmath408 jets @xcite . now equipped with the plausible mechanism that generates phenomenologically consistent masses for neutrinos and charged leptons , the 331 model may be a physically interested model of leptons . it not only explains three families of quarks and leptons because of the specific anomaly - cancellation mechanism used together with the asymptotic free condition on @xmath409 but also involves majorana mass terms demanded by charged - lepton mass terms . there remain dynamical questions about the smallness of the @xmath116-violating coupling of @xmath182 and the fine tuning of the lepton mass parameters to reproduce @xmath410 , which require some new physics beyond @xmath411 . it is also required to have extensive analyses on physics of the quark and gauge boson sectors as well to fully clarify potential power of the 331 model . d. v. ahluwalia , ; v. barger , p. pakvasa , t.j . weiler and k. whisnant , ; a. baltz , a.s . goldhaber and m. goldhaber , ; m. jezabek and y. sumino , ; r.n . mohapatra and s. nussinov , ; y. nomura and t. yanagida , ; i. starcu and d.v.ahluwalia , ; c. jarlskog , m. matsuda , s. skadhauge and m. tanimoto , ; q. shafi and z. tavartkiladze , ; ; p.h . frampton and s.l . glashow , ; c.h . albright and s.m . barr , ; h. georgi and s.l . glashow , ; r.n . mohapatra , a. prez - lorenzana and c. a. de s. pires , . t. yanagida , in _ proceedings of the workshop on unified theories and baryon number in the universe _ edited by a. sawada and a. sugamoto ( kek report no.79 - 18 , tsukuba , 1979 ) , p.95 ; ; m. gell - mann , p. ramond and r. slansky , in _ supergravity _ edited by p. van nieuwenhuizen and d.z . freedmann ( north - holland , amsterdam 1979 ) , p.315 ; r.n . mohapatra and g. senjanovi , . valle and m. singer , ; r. barbieri and r.n . mohapatra , ; j. liu , ; r. foot , o. f. hernndez , f. pisano and v. pleitez , ; v. pleitez and m.d . tonasse , ; ; ; j. liu and d. ng , ; p.h . frampton , p.i . krastev and j.t . liu , ; f. pisano , v. pleitez and m.d . tonasse , hep - ph/9310230 v2 ( feb , 1994 ) ; m. @xmath412zer , ; f. pisano , j.a . silva - sobrinho and m.d . tonasse , f. -z . chen , ; m.b . tully and g.c . joshi , hep - ph/9810282.v2 ( jan,1999 ) ; y. okamoto and m. yasu@xmath413 , ; n.a . long and d.v . soa , . t. kitabayashi and m. yasu , ; ; hep - ph/0102228 v3 ( feb . , 2001 ) to be published in phys . lett . b ( 2001 ) ; t. kitabayashi , hep - ph/0010341 ( oct . , 2000 ) ; hep - ph/0103195 ( mar . , 2001 ) to appear in phys . d ( 2001 ) . tully and g.c . joshi , hep - ph/0011172 to appear in phys . rev d ( 2001 ) ; j.c . montero , c.a . de s. pires and v. pleitez , . see for example , g.c . w. grimus and l. lavoura , ; w. grimus and h. neufeld , ; l. bento and j.w.f . valle , ; s.y . tsai , ; k.s . babu , r.n . mohapatra and l. rothstein , ; j.t . peltoniemi , a.yu . smirnov and j.w.f . valle , in ref . @xcite ; j.t . peltoniemi , d. tommasini and j.w.f . valle , ; j.t . peltoniemi and j.w.f . e. ma , ; ; ; ; ; for recent discussions , see for example , a.s . joshipura and s.d . rindani , ; r.n . mohapatra , a. prez - lorenzana and c.a . de s. pires , in ref.@xcite . d. chang and a. zee , ; r. adhikari , e. ma and g. rajasekaran , . w. grimus and h. neufeld , ; w. grimus and l. lavoura , ; t. kitabayashi and m. yasu , in ref.@xcite ; t. kitabayashi , in ref.@xcite . for supersymmetric models , see for example , e. ma , m. raidal and u. sarkar , ; j.c . romo , m.a . daz , m. hirsch , w. porod and j.w.f . valle , ; f. takayama and m. yamaguchi , ; o.c.w . kong , ; ; e.j . chun , ; s. davidson and m. losada , ; m. hirsch , m.a . daz , w. porod , j.c . romo and j.w.f . valle , . g. t hooft , in _ recent development in gauge theories _ , proceedings of the cargese summer institute , cargese , france , 1979 , edited by g. t hooft _ et al . _ , nato advanced study institute series b : physics vol . 59 ( plenum press , new york , 1980 ) . for recent studies , see for example , p.h . frampton and x .- hu guan , ; f. pisano , j.a . silva - sobrinho and m.d . tonasse , ; b. dion , t. gregoire , d. london , l. marleau and h. nadeau , ; m.b . tully and g.c . joshi , ; p.h . frampton , ; p.h . frampton and a. ra , . .[tab : lnumber0 ] @xmath10 , @xmath119 , @xmath3 and @xmath155 for leptons and higgs scalars , where the lepton number @xmath116 is related to @xmath119 as @xmath116 = @xmath415 + @xmath119 . [ cols="<,^,^,^,^,^,^,^",options="header " , ]

in this article , i examine several observational trends regarding protoplanetary disks , debris disks and exoplanets in binary systems in an attempt to constrain the physical mechanisms of planet formation in such a context . furthermore , they form planetesimals and mature planetary systems at a similar rate as wider binaries and single stars , albeit with the peculiarity that they predominantly produce high - mass planets .

r

0912.3025

in this article , i examine several observational trends regarding protoplanetary disks , debris disks and exoplanets in binary systems in an attempt to constrain the physical mechanisms of planet formation in such a context . binaries wider than about 100au are indistinguishable from single stars in all aspects . binaries in the 5100au range , on the other hand , are associated with shorter - lived but ( at least in some cases ) equally massive disks . furthermore , they form planetesimals and mature planetary systems at a similar rate as wider binaries and single stars , albeit with the peculiarity that they predominantly produce high - mass planets . i posit that the location of a stellar companion influences the relative importance of the core accretion and disk fragmentation planet formation processes , with the latter mechanism being predominant in binaries tighter than 100au .

les us turn our attention to mature planetary systems . as of this writing , there are 38 exoplanets that are in a system with at least 2 stellar components ( using 1400au as the upper limit for binary separation ) , including 5 systems with a stellar companions within 25au ( * ? ? ? * and references therein ) . most of these planet - bearing stars are of solar type . the overall detection rates of gas giant planets in binary systems and in single stars are undistinguishable @xcite . there is marginal evidence that planets in binaries tighter than @xmath0au may be somewhat less frequent than one would assume based on the frequency of planets in wider binaries ( by 6.0@xmath182.7% , * ? ? ? however , the small sample size , adverse selection biases and incompleteness of current multiplicity surveys are such that it is premature to reach definitive conclusions . in any case , we can use this sample to test whether the separation of the stellar binary has any influence on planet properties . despite an earlier claim for a distinct period - mass distribution @xcite , @xcite have shown that there is essentially no difference in the properties of planetary systems around single stars and in binary systems . however , a previously unrecognized trend is evident in figure[fig : planets ] . while planets covering two orders of magnitude in mass can be found in wide binaries ( as around single stars ) , systems tighter than @xmath0au appear to host only high - mass , @xmath19 , planets . to quantify this effect , i used the two - sided fischer exact test to determine whether close and wide binaries ( with the usual sliding threshold ) have different proportion of high- and low - mass planets . i used 1.6@xmath20 , the median for all planets known to date , to separate low- from high - mass planets . figure[fig : proba ] confirms that _ binary systems tighter than about 100au produce a distribution of planets that is strongly biased towards the highest masses . _ this conclusion is significant at the 3@xmath1 level . it is important to test whether this trend is not a mere consequence of a selection bias , as a close stellar companion can alter the detectability of a planet - induced radial velocity signal . to evaluate this possibility , i build on the `` uniform detectability '' sample defined by @xcite which contains all stars for which close - in planets as low mass as 0.3@xmath20 ( well below the apparent cut - off in mass for planets in tight binaries ) , as well as 1@xmath20 planets on a 4yr orbit , could be detected . in the current sample of binary planet hosts , the proportions of stars that belong to the uniform detectability sample among binaries tighter and wider than 100au are indistinguishable ( 5/9 and 24/40 , respectively ) . i therefore conclude that the trend discussed above is unlikely to be the consequence of a selection bias or of observational limitations . an indirect signpost of planet formation is the debris disk phenomenon . in these systems , small dust grains are produced via the collisions of large solid bodies @xcite . @xcite observed 69 a- and f - type known binaries with _ spitzer _ and found debris disks in systems spanning 6 decades in separation . they further suggested that intermediate separation ( 330au ) binaries are substantially less likely to host a debris disks than either tighter or wider systems , although the formal significance of this difference is marginal at best . no such trend was found by @xcite , who included 24 a- through m - type binaries in their own _ spitzer _ survey . this latter survey focused on targets that are more similar in mass to exoplanet hosts and the pms population discussed in the previous section . i used the two - sided fischer test to determine whether the occurrence of debris disks is indeed different in tight and wide binaries , using the same sliding threshold as above ( see figure[fig : proba ] ) . there is no significant difference for any value of the threshold in the sample from @xcite , nor in a combined sample that also includes systems from @xcite . the combined sample contains 52 binaries in the 51400au range , with a median separation of 50au , an increase of 15 sources from the sole sample of @xcite . in addition , the occurrence rates of debris disks in binary systems and single stars are very similar @xcite . in other words , _ any 0.52@xmath3 star , irrespective of the presence of a companion ( within the 51400au range studied here ) , may experience the early phases of planet formation up to the planetesimal stage_.

in this article , we study the null controllability of linearized compressible navier - stokes system in one and two dimension . we first study the one - dimensional compressible navier - stokes system for non - barotropic fluid linearized around a constant steady state . we prove that the linearized system around @xmath0 , with @xmath1 @xmath2 is not null controllable by localized interior control or by boundary control . but the system is null controllable by interior controls acting everywhere in the velocity and temperature equation for regular initial condition . we also prove that the the one - dimensional compressible navier - stokes system for non - barotropic fluid linearized around a constant steady state @xmath3 , with @xmath1 @xmath4 @xmath5 is not null controllable by localized interior control or by boundary control for small time @xmath6 next we consider two - dimensional compressible navier - stokes system for barotropic fluid linearized around a constant steady state @xmath7 we prove that this system is also not null controllable by localized interior control . * key words . * linearized compressible navier - stokes system , null controllability , localized interior control , boundary control , gaussian beam .

i

1410.4351

in this article , we study the null controllability of linearized compressible navier - stokes system in one and two dimension . we first study the one - dimensional compressible navier - stokes system for non - barotropic fluid linearized around a constant steady state . we prove that the linearized system around @xmath0 , with @xmath1 @xmath2 is not null controllable by localized interior control or by boundary control . but the system is null controllable by interior controls acting everywhere in the velocity and temperature equation for regular initial condition . we also prove that the the one - dimensional compressible navier - stokes system for non - barotropic fluid linearized around a constant steady state @xmath3 , with @xmath1 @xmath4 @xmath5 is not null controllable by localized interior control or by boundary control for small time @xmath6 next we consider two - dimensional compressible navier - stokes system for barotropic fluid linearized around a constant steady state @xmath7 we prove that this system is also not null controllable by localized interior control . * key words . * linearized compressible navier - stokes system , null controllability , localized interior control , boundary control , gaussian beam . * ams subject classifications . * 35q30 , 93c20 , 93b05

control of fluid flow has been an important area of research and has many practical applications . the question about controllability of fluid flows has attracted the attention of many researchers , more for incompressible flow but much less for compressible flow . in this paper we are interested in controllability properties of linearized compressible navier - stokes system . for a compressible , isothermal barotropic fluid ( density is a function of only pressure ) , the navier - stokes system in @xmath8 consists of equation of continuity @xmath9 = 0 , \end{array}\ ] ] and the momentum equation @xmath10 \\ [ 3.mm ] \displaystyle = -\nabla p(x , t ) + \mu \bigtriangleup { \bf u}(x , t ) + ( \lambda + \mu ) \nabla [ \mbox{div } { \bf u}(x , t ) ] , \end{array}\ ] ] where @xmath11 is the density of the fluid , @xmath12 denotes the velocity vector in @xmath13 and @xmath14 is an external force field in @xmath15 the pressure satisfies the following constitutive law @xmath16 for some constants @xmath17 , @xmath18 the viscosity coefficients @xmath19 and @xmath20 are assumed to be constant satisfying the following thermodynamic restrictions , @xmath21 , @xmath22 for non - barotropic fluid ( when density is a function of pressure and temperature of the fluid ) , the navier - stokes system consists of the equation of continuity , the momentum equation and an additional thermal energy equation @xmath23(x , t ) + \theta(x , t ) \frac{\partial p}{\partial \theta}(x , t ) \mbox{div } { \bf u}(x , t ) \\ [ 3.mm ] \displaystyle = \kappa \bigtriangleup \theta ( x , t ) + \lambda ( \mbox{div } { \bf u}(x , t))^2 + 2 \mu \sum_{i , j=1}^n \frac{1}{4 } \left(\frac{\partial { \bf u}_i}{\partial x_j } + \frac{\partial { \bf u}_j}{\partial x_i}\right)^2 , \end{array}\ ] ] where @xmath24 denotes the temperature of the fluid , @xmath25 is the specific heat constant and @xmath26 is the heat conductivity constant . for ideal gas , the pressure is given by boyle s law : @xmath27 where @xmath28 is the universal gas constant ( see @xcite ) . in this article , we first consider the compressible navier - stokes system for non - barotropic fluid in a bounded interval @xmath29 linearized around a constant steady state @xmath30 with @xmath31 and @xmath32 more precisely we consider the system @xmath33 where @xmath34 is the characteristic function of an open subset @xmath35 we choose the following initial and boundary conditions for the system : @xmath36 u(0,t ) = 0 , \quad u(l , t ) = 0 \quad \forall \ \ t > 0 , \\ [ 2.mm ] \theta(0,t ) = 0 , \quad \theta(l , t ) = 0 \quad \forall \ \ t > 0 . \end{array}\ ] ] in - , @xmath37 , @xmath38 and @xmath39 are distributed controls . we are interested in the following question : given @xmath40 and @xmath41 can we find interior control functions such that the solution @xmath42 of - satisfies @xmath43 our first main result regarding interior null controllability is the following , [ thm1 ] let @xmath44 i.e. , @xmath45 is a proper subset of @xmath46 let us assume @xmath47 . the system - is not null controllable in any @xmath48 by the interior controls @xmath49 , @xmath50 and @xmath51 acting on density , velocity and temperature equation respectively . the above negative result can be extended to the case of less regular interior controls or boundary control . see remark [ rem : lessregcontrol ] and remark [ rem : bdycontrol ] for more details . our next positive result shows that , if initial density @xmath52 lies in a more regular space then the linearized system is null controllable by velocity and temperature controls acting everywhere in the domain . [ thm2 ] let @xmath53 in . let us denote @xmath54 let us assume @xmath55 . then for any @xmath56 there exist controls @xmath57 and @xmath58 acting everywhere in the velocity and temperature equation respectively , such that the solution of - satisfies @xmath59 the next result shows that the above result is sharp as null controllability can not be achieved by localized interior velocity and temperature controls . [ thm3 ] let @xmath53 in . let @xmath60 i.e. , @xmath61 is a proper subset of @xmath46 let us assume @xmath55 . the system - is not null controllable in any @xmath48 by the interior controls @xmath62 and @xmath63 acting on velocity and temperature equation respectively . the proof of these results relies on the observability inequality . we know that the null controllability of a linear system is equivalent to a certain observability inequality for the solutions of adjoint system ( see @xcite , chapter 2 ) . to prove the negative results , we will construct particular solutions for the adjoint system such that the observability inequality can not hold . in order to do that first we will consider the adjoint system in @xmath64 as a terminal value problem . we will construct highly localized solutions known as `` gaussian beam '' . similar kind of construction has been used for hyperbolic equations by ralston ( @xcite ) and for wave equations by maci and zuazua ( @xcite ) . we will prove that solutions are localized in a small neighbourhood of any @xmath65 thus given an observation set , we can always find an interval away from the observation set such that the solutions are localized in that interval . using this we are able to prove the negative results . to the author s best knowledge these are new results regarding controllability issues of navier - stokes system for non - barotropic fluid . in theorem [ thm3 ] , we proved a positive result when controls acting everywhere in the equation . the question then arises : whether positive results could be obtained by using control supported in a small , but moving region , as in @xcite . rosier and rouchon in @xcite proved that the structurally damped wave equation in one dimension is not null controllable by a boundary control . later on martin , rosier and rouchon in @xcite proved that the same equation in one dimension with periodic boundary conditions , is null controllable with a moving distributed control for sufficiently large time . chaves - silva , rosier and zuazua in @xcite extend the above result to higher dimension . the structure of the system considered by the authors in @xcite , in some sense , is similar to the linearized compressible , barotropic navier - stokes system in one dimension as well as in higher dimension . these issues will be discussed in a future work which is in progress . we have studied in this paper the null controllability of the linearized compressible navier - stokes system only . the `` gaussian beam '' construction is used to show negative results . however one may use other techniques based on the use of nonlinearity ( see @xcite for example ) to achieve controllability results for the full nonlinear system . there have been some results regarding the control of compressible barotropic fluid models in recent years . amosova in @xcite considers compressible navier - stokes system for viscous barotropic fluid in one dimension in lagrangian coordinates in a bounded domain @xmath66 with dirichlet boundary condition . she proves local exact controllability to trajectories for the velocity in any time @xmath56 using a localized interior control on the velocity equation , provided that the initial density is already on the targeted trajectory and initial condition lies in @xmath67 ervedoza , glass , guerrero and puel in @xcite consider the compressible navier - stokes system in one space dimension in a bounded domain @xmath68 . they prove local exact controllability to constant states @xmath69 with @xmath70 using two boundary controls , both for density and velocity , in time @xmath71 when initial condition lies in @xmath72 chowdhury , ramaswamy and raymond in @xcite consider the compressible barotropic navier - stokes system linearized around a constant steady state @xmath73 with @xmath74 in a bounded domain @xmath75 . they proved that the linearized system is not null controllable by a localized control or by boundary control . they also proved that the linearized system is null controllable by an interior control acting everywhere in the velocity equation when initial condition lies in @xmath76 chowdhury in @xcite considers the compressible barotropic navier - stokes system linearized about a constant steady state @xmath77 with @xmath78 in @xmath79 with dirichlet boundary condition and an interior control on the velocity equation acting on open subset @xmath80 he proves that the system is approximately controllable in @xmath81 when @xmath82 he also proves a similar result in two dimension . chowdhury , mitra , ramaswamy and renardy in @xcite consider the compressible barotropic navier - stokes system linearized about a constant steady state @xmath77 with @xmath78 in @xmath83 with periodic boundary condition . they proved that the linearized system is null controllable by a localized velocity control when @xmath84 and initial condition lies in @xmath85 our linearized system - is similar to the linearized system considered by the authors in @xcite . so we expect similar controllability results . their method is based on explicit expression for eigenfunctions and the behaviour of the spectrum of the linearized operator . they proved that there is an accumulation point in the spectrum of the linearized operator . this system behaves very badly with respect to controllability properties and a similar type of controllability behaviour is also observed in @xcite for different types of systems where an accumulation point is present in the spectrum of linearized operator . but the method used in @xcite does not seem to fit very well in our case . in fact one can prove that there is an accumulation point in the spectrum of the linearized operator considered here , for certain boundary condition . but the expressions of eigenvalues and eigenfunctions are complicated . so here we use gaussian beam approach to achieve the negative results . this technique does not require the knowledge of the spectrum and it seems to extend to higher dimension also . the controllability properties are completely different , if we consider compressible navier - stokes system linearized around non null velocity . for barotropic fluid , the system linearized around @xmath86 is not controllable in any time @xmath87 by localized interior control but the system linearized around @xmath88 is null controllable by localized interior control for large time @xmath6 it is interesting to note that there is no accumulation point in the spectrum of the linearized operator in the latter case and better controllability behaviour at least for @xmath87 large enough(see @xcite ) . but the question remains what happens when time @xmath87 is small enough . our results answer this question in the negative . we consider the compressible non - barotropic navier - stokes equation linearized around constant steady state @xmath89 @xmath90 @xmath91 \displaystyle u_t - \frac{\lambda + 2\mu}{{\bar \rho } } u_{xx } + \frac{r { \bar \theta}}{{\bar \rho}}\;\rho_x + \bar v u_x + r \theta_x \ ; = g \chi_{\mathcal{o}_2 } , \mbox { in } ( 0,l ) \times ( 0,t ) , \\[3.mm ] \displaystyle \theta_t ( x , t ) -\frac{\kappa}{{\bar \rho}c_v } \theta_{xx } + \frac{r { \bar \theta}}{c_v } u_x + \bar v \theta_x \ ; = h \chi_{\mathcal{o}_3 } , \mbox { in } ( 0,l ) \times ( 0,t ) , \\[3.mm ] \displaystyle \rho(0 ) = \rho_0,\quad \quad u(0)= u_0 , \mbox { and } \quad \theta(0 ) = \theta_0 , \quad \mbox { in } ( 0,l ) , \\ [ 2.mm ] \displaystyle \rho(0,t ) = 0 , \;\;\ ; u(0,t ) = 0 = u(l , t ) , \;\ ; \forall \ t \in ( 0,t ) , \\ [ 2.mm ] \displaystyle \theta(0,t ) = 0 = \theta(l , t ) , \;\ ; \forall \ t \in ( 0,t ) . \end{array}\ ] ] we prove the following theorem . [ thm1.4 ] let @xmath92 i.e. , @xmath45 is a proper subset of @xmath46 let us assume @xmath47 . if @xmath93 then the system is not null controllable by localized interior controls @xmath94 @xmath50 and @xmath51 acting on density , velocity and temperature equation respectively . as a corollary of the above theorem , one can rule out null controllability of compressible barotropic navier - stokes system linearized around constant steady state @xmath95 in small time @xmath96 using a boundary control or localized interior control . we consider compressible barotropic navier - stokes system linearized around a constant steady state @xmath95 , @xmath97 in @xmath98 or in @xmath99 as in @xcite . * for initial condition belonging to @xmath100 the system with dirichlet boundary condition is not null controllable at any time @xmath40 by a interior control acting only in the velocity equation . the control may act in a non empty open subset of @xmath79 or in the whole domain @xmath101 * the system with periodic boundary condition is not null controllable by interior control localized in @xmath102 acting only in the velocity equation when initial condition lies in @xmath103 and time @xmath104 * for initial condition belonging to @xmath100 the same system is not null controllable by boundary control if time @xmath105 from the above corollary we see that the condition @xmath106 in ervedoza , glass , guerrero and puel ( @xcite ) is natural . next we will show that , our method can be extended to higher dimension also . for simplicity we consider the compressible barotropic navier - stokes system in two - dimensional bounded domain @xmath107 , linearized around a constant steady state solution @xmath108 , @xmath1 @xmath109 \displaystyle { \bf u } - \frac{\mu}{{\bar \rho } } \delta { \bf u } - \frac{\lambda + \mu}{{\bar \rho}}\nabla[\mathrm{div } \ { \bf u } ] + \;a \gamma { \bar \rho}^{\gamma-2 } \nabla \rho \;=\;{\bf g } \chi_{{\mathcal o}_2 } , \mbox { in } \omega \times ( 0,t ) , \\[2.mm ] \displaystyle \rho(0 ) = \rho_0 \quad \mbox{and}\quad { \bf u}(0)= { \bf u}_0 , \quad \mbox { in } \omega , \\ [ 2.mm ] \displaystyle { \bf u } = { \bf 0 } \ \ \mbox { on } \partial \omega \times ( 0,t ) . \end{array}\ ] ] where @xmath110 and @xmath111 are open subsets of @xmath112 we obtain the following negative null controllability result for the system . [ thm1.5 ] let @xmath113 i.e. , @xmath45 is a proper open subset of @xmath112 let us assume that @xmath114 then the system is not null controllable in time any @xmath40 by interior controls @xmath115 and @xmath116 the plan of the paper is as follows . in section 2 , we study the control system linearized around a constant steady state @xmath0 in one dimension . we prove theorem [ thm1 ] , theorem [ thm2 ] and theorem [ thm3 ] here . in section 3 , we study the control system linearized around a constant steady state @xmath117 theorem [ thm1.4 ] is proved here . in section 4 we consider the linearized system in two dimension around constant steady state @xmath7 we prove theorem [ thm1.5 ] here . * acknowledgement * : the author would like to thank prof . sylvain ervedoza for providing important references on gaussian beams . the author also would like to thank him and prof . mythily ramaswamy for very useful discussions which improved the initial version . the author acknowledges the financial support under the project `` pde control '' from the indo french centre for applied mathematics ( ifcam ) .

in this article we investigate the structure of the non - local part of the symmetry term , that leads to a splitting of the effective masses of protons and neutrons in asymmetric matter . based on microscopic transport simulations we suggest some rather sensitive observables in collisions of neutron - rich ( unstable ) ions at intermediate ( @xmath0 ) energies . in particular we focus the attention on pre - equilibrium nucleon emissions . we discuss interesting correlations between the @xmath1 content of the fast emitted particles and their rapidity or transverse momentum , that show a nice dependence on the prescription used for the effective mass splitting .

i

nucl-th0508008

in this article we investigate the structure of the non - local part of the symmetry term , that leads to a splitting of the effective masses of protons and neutrons in asymmetric matter . based on microscopic transport simulations we suggest some rather sensitive observables in collisions of neutron - rich ( unstable ) ions at intermediate ( @xmath0 ) energies . in particular we focus the attention on pre - equilibrium nucleon emissions . we discuss interesting correlations between the @xmath1 content of the fast emitted particles and their rapidity or transverse momentum , that show a nice dependence on the prescription used for the effective mass splitting .

effective interactions have been extensively used in transport codes to gain knowledge about nuclear matter properties in conditions far from equilibrium . they predict very different behaviours for some physical properties , such as the momentum dependence of the mean field in the iso - scalar and iso - vector channel ( see @xcite for recent reviews ) . in general , the momentum dependence of the potential is strictly related to the concept of in - medium reduction of the nucleon mass . in particular , the non - local part of the symmetry potential has become an interesting subject of investigation , because it leads to a splitting of the masses of different nucleonic species in asymmetric matter , and the sign of this splitting already is an open and controversial problem ( @xcite ) . considering separately the local and non - local contributions to the potential part of the symmetry energy , a sharp change is observed , for instance , going from the earlier skyrme forces to the lyon parametrizations , with almost an inversion of the signs of the two contributions @xcite . the important repulsive non - local part of the lyon forces leads to a completely different behavior of the neutron matter @xmath2 , of great relevance for the neutron star properties . actually this substantially modified parametrization was mainly motivated by a very unpleasant feature in the spin channel of the earlier skyrme forces , the collapse of polarized neutron matter @xcite . in correspondence the predictions on isospin effects on the momentum dependence of the symmetry term are quite different . a very important consequence for the reaction dynamics is the expected inversion of the sign of the @xmath3 effective mass splitting , i.e. in the lyon forces neutron effective masses are below the proton ones for n - rich matter . we note that the same is predicted from microscopic relativistic dirac - brueckner - hartree - fock ( @xmath4 ) calculations @xcite and in general from the introduction of scalar isovector virtual mesons in relativistic mean field ( @xmath5 ) approaches @xcite . at variance , non - relativistic brueckner - hartree - fock ( @xmath6 ) calculations are leading to opposite conclusions @xcite . however , the comparison between relativistic effective ( @xmath7 ) masses and non - relativistic effective masses requires some attention , see the ch.6 of @xcite and refs . therein . in fact , though the neutron @xmath7-mass is below the proton one , in correspondence the non - relativistic @xmath8-mass splitting can have any sign . indeed this is just the case of the very recent @xmath4 analysis of the tbingen group @xcite . such puzzling effect is related to the intrinsic momentum dependence of the nucleon self - energies , it is then beyond the @xmath5 approach and it represents a very sensitive test of the treatment of dirac - brueckner correlations . all that clearly shows that sensitive experimental observables are largely needed . the sign of the splitting will directly affect the energy dependence of the so - called lane potential , i.e. the difference between @xmath9 optical potentials on charge asymmetric targets , normalized by the target asymmetry @xcite . a decreasing behaviour is observed in the case @xmath10 , while a positive slope is obtained in the opposite case . an important physical consequence of the negative slopes is that the isospin effects on the optical potentials tend to disappear at energies just above @xmath11 ( or even change the sign for `` old '' skyrme - like forces ) . also , we expect a crossing of the two prescriptions at low energies , i.e. low momentum nucleons will see exactly the same lane potentials , as shown in detail in ref . @xcite . unfortunately results derived from neutron / proton optical potentials at low energies are not conclusive @xcite , since the effects due to the mass splitting appear of the same order of the uncertainty on the determination of the local contribution to the symmetry energy . moreover at low energies , due to the crossing discussed before , it is difficult to appreciate differences between positive or negative slopes . a positive slope is obtained , for instance , within the phenomenological dirac optical potential ( @xmath12 ) , with different implicit momemtum dependences in the self - energies @xcite . this potential has been constructed fitting simultaneously proton and neutron ( mostly total cross sections ) data for collisions with a wide range of nuclei at energies up to @xmath11 . recently such dirac optical potential has been proven to reproduce very well the new neutron scattering data on @xmath13 at @xmath14 @xcite measured at the svendberg laboratory in uppsala . more data are needed at higher energies ( around / above @xmath11 ) , to improve the systematics , in order to clearly disentangle between the two trends of the lane potential and of the effective mass splitting . we note however that these properties of the interaction will also affect the dynamical evolution of heavy ion collisions . so we can get indipendent information about it just by looking at some suitable reaction observables . we can expect important effects on transport properties ( fast particle emission , collective flows ) of the dense and asymmetric @xmath15 that will be reached in radioactive beam collisions at intermediate energies . here we will focus on the study of pre - equilibrium emission in neutron - rich central collisions , at 50 and 100 mev / a . we will see that the energy dependence of the n / z content of fast emitted particles is particularly sensitive to the sign of the effective mass splitting . hence it would be possible to answer many fundamental questions in isospin physics by looking at appropriate observables in intermediate energy @xmath16 .

in this paper , we have studied @xmath0 gravity as an arbitrary function of curvature and torsion scalars in friedmann lematre robertson the novelty of this model is that the universe includes both cases curvature and torsion , and one dominated by a chaplygin gas . in order to calculate cosmological solutions subsequently , we reconstructed the model by an origin of a scalar field entitled quintessence model with a field potential . the cosmological parameters have been written in terms of redshift @xmath1 . next , we plotted cosmological parameters with respect to three variable of cosmic time , redshift @xmath1 and @xmath2-folding number @xmath3 , and the figures showed us an accelerated expansion of universe . also , we have described the scenario in three status early time , late time and future time by @xmath2-folding number . finally , the stability of scenario has been investigated by a useful function named sound speed , and the graph of sound speed versus @xmath2-folding number has been showed us that there is the stability in late time .

c

1412.0560

in this paper , we have studied @xmath0 gravity as an arbitrary function of curvature and torsion scalars in friedmann lematre robertson walker ( flrw ) background . then , we have considered interacting model between @xmath0 gravity and modified chaplygin gas . the novelty of this model is that the universe includes both cases curvature and torsion , and one dominated by a chaplygin gas . in order to calculate cosmological solutions , we obtained friedmann equations and also equation of state ( eos ) parameter of dark energy . by employing interacting model we considered the total energy density and the total pressure of universe as the combination of components of dark energy and chaplygin gas . subsequently , we reconstructed the model by an origin of a scalar field entitled quintessence model with a field potential . the field potential has been calculated in terms of free parameters of @xmath0 gravity and modified chaplygin gas . in what follows , we used a parametrization , and the cosmological parameters have been written in terms of redshift @xmath1 . next , we plotted cosmological parameters with respect to three variable of cosmic time , redshift @xmath1 and @xmath2-folding number @xmath3 , and the figures showed us an accelerated expansion of universe . also , we have described the scenario in three status early time , late time and future time by @xmath2-folding number . finally , the stability of scenario has been investigated by a useful function named sound speed , and the graph of sound speed versus @xmath2-folding number has been showed us that there is the stability in late time .

in this paper , we have studied @xmath0 gravity in terms of an arbitrary function of curvature and torsion scalars . for simplicity , the function @xmath0 has been gotten as a linear function of the curvature and torsion scalars , and have computed in flrw metric . the motivation of this research is based on existence of both cases curvature and torsion in the universe , while so far the research carried out on just implications existence of the curvature in the universe . afterwards , we have considered the @xmath0 gravity model by interacting with modified chaplygin gas . we wrote the corresponding action as the combination of @xmath0 gravity and a matter lagrangian . in order to obtain the friedmann equations , we used a different mathematical notations for curvature scalar and torsion scalar by levi - civita connection and wienzbck connection , respectively . in what follows , we considered total energy density and total pressure of universe as dominated with a perfect fluid , in which dark energy contribution is taken the combination of @xmath0 gravity and modified chaplygin gas as eq . . then , by dividing these two functions we obtained the eos of dark energy for the scenario . subsequently , we reconstructed the model by an origin of a scalar field entitled quintessence model with a field potential . with correspondence between our model and quintessence model , we plotted the eos of scalar field in terms of cosmic time by taking the scale factor as power law . the graph of corresponding eos described the accelerated expanding of universe . next , we used a parametrization , and the cosmological parameters have been written in terms of redshift @xmath1 . in that case , we drew them with respect to @xmath1 and @xmath2-folding number @xmath123 in figs . [ rhopde ] and [ omegade ] . these figures showed us the existence of an accelerating universe , especially graph of eos showed us that its value in late time is @xmath121 which one is consistent with ref . we noted that the free parameters play an important role in plotting figures , the motivation of these selections are based on positivity energy density and negativity pressure . finally , in order to investigate the stability , we tried to compute speed sound in this scenario in terms of @xmath2-folding number , so we plotted the @xmath141 with respect to @xmath2-folding number and have obtained its corresponding values in three status @xmath118 , late time ( @xmath119 ) and @xmath120 . therefore , the fig . [ c2s2n ] showed us that there is the stability in late time . abazajian , k. , adelman - mccarthy , j. k. , ageros , m. a. , allam , s. s. , anderson , k. s. , anderson , s. f. , ... and hogan , c. j. ( 2004 ) . the second data release of the sloan digital sky survey . the astronomical journal , 128(1 ) , 502 . pope , a. c. , matsubara , t. , szalay , a. s. , blanton , m. r. , eisenstein , d. j. , gray , j. , ... and sdss collaboration . cosmological parameters from eigenmode analysis of sloan digital sky survey galaxy redshifts . the astrophysical journal , 607(2 ) , 655 . spergel , d. n. , verde , l. , peiris , h. v. , komatsu , e. , nolta , m. r. , bennett , c. l. , ... and wright , e. l. ( 2003 ) . first - year wilkinson microwave anisotropy probe ( wmap ) observations : determination of cosmological parameters . the astrophysical journal supplement series , 148(1 ) , 175 . farooq , m. u. , jamil , m. , and rashid , m. a. ( 2010 ) . interacting entropy - corrected new agegraphic k - essence , tachyon and dilaton scalar field models in non - flat universe . international journal of theoretical physics , 49(9 ) , 2278 - 2287 . setare , m. r. , and saridakis , e. n. ( 2009 ) . braneworld models with a non - minimally coupled phantom bulk field : a simple way to obtain the1-crossing at late times . journal of cosmology and astroparticle physics , 2009(03 ) , 002 . einstein , a. ( 1928 ) . new possibility for a unified field theory of gravitation and electricity . sitzungsberichte der preussischen akademie der wissenschaften , physikalisch - mathematische klasse , 17 , 224227 . lu , j. , xu , l. , li , j. , chang , b. , gui , y. , and liu , h. ( 2008 ) . constraints on modified chaplygin gas from recent observations and a comparison of its status with other models . physics letters b , 662(2 ) , 87 - 91 . khurshudyan , m. , kahya , e. o. , pasqua , a. , and pourhassan , b. ( 2014 ) . higher derivative corrections of @xmath146 gravity with varying equation of state in the case of variable @xmath147 and @xmath148 . arxiv preprint arxiv:1401.6630 . amanullah , r. , lidman , c. , rubin , d. , aldering , g. , astier , p. , barbary , k. , ... and yasuda , n. ( 2010 ) . spectra and hubble space telescope light curves of six type ia supernovae at 0.511 < z < 1.12 and the union2 compilation . the astrophysical journal , 716(1 ) , 712 .

we consider both lattices in a perturbative framework , whereby the technique of hamiltonian perturbation theory can be used to obtain information about the existence of solutions , and the same approach , as well as eigenvalue count considerations , can be used to obtained detailed conditions about their linear stability . we find that the analytical results are in very good agreement with our numerical findings and can also be used to predict features of the dynamical evolution of such solutions .

i

0707.1162

in this paper , we study the competition of linear and nonlinear lattices and its effects on the stability and dynamics of bright solitary waves . we consider both lattices in a perturbative framework , whereby the technique of hamiltonian perturbation theory can be used to obtain information about the existence of solutions , and the same approach , as well as eigenvalue count considerations , can be used to obtained detailed conditions about their linear stability . we find that the analytical results are in very good agreement with our numerical findings and can also be used to predict features of the dynamical evolution of such solutions .

the field of bose - einstein condensates ( becs ) in atomic physics @xcite has provided a renewal of interest in solitary wave and nonlinear excitations . this is especially so because the leading order , mean - field description of interatomic interactions corresponds to a cubic nonlinearity . this , in turn , is responsible for the emergence and experimental observation of a variety of matter - wave solitons in becs , including bright @xcite , dark @xcite and gap @xcite solitons . furthermore , atom optical devices have been proposed , such as , for instance , the atom chip @xcite that would allow the possibility to controllably manipulate such nonlinear structures . it is well - known that bright ( respectively , dark ) matter - wave solitons arise in becs with attractive ( respectively , repulsive ) interatomic interactions , i.e. , for atomic species with negative ( respectively , positive ) scattering length @xmath0 . one of the particularly appealing features of the bec setting is the existence of a wide variety of experimental `` knobs '' that can be used to manipulate or control the relevant structures . in particular , interfering laser beams can be used to produce a standing wave pattern , known as the optical lattice , providing a periodic linear potential for the condensate . this type of structure offers a large variety of interesting phenomenology including bloch oscillations , landau - zener tunneling , dynamical instabilities , gap excitations among many others and a considerable amount of review works have already been dedicated to this topic @xcite . on the other hand , magnetically - induced feshbach resonances can be used to modify at will both the magnitude and the sign of the scattering length by tuning the external magnetic field ; see e.g. @xcite and also @xcite where the feshbach resonance in @xmath1li becs was used for the formation of bright matter - wave solitons . the ability to modulate the scattering length has led to a large variety of studies where this mechanism has been used . for instance , time - dependent modulations of the scattering length were proposed as a means of preventing collapse in higher - dimensional becs @xcite , or as a way of producing robust matter - wave breathers @xcite , among others . a more recent suggestion has been to add to a constant bias magnetic field a gradient in the vicinity of a feshbach resonance , allowing for a spatial variation of the scattering length , thereby providing what has come to be termed a `` collisionally inhomogeneous environment '' . notice that , given the availability of magnetic and optical ( laser- ) fields , the external trapping potential and the spatial variation of the scattering length can be adjusted independently ( see @xcite for more details on the relevant configuration ) . in this latter setting , a variety of propositions of interesting dynamical phenomena have been made concerning scenarios for the emission of solitons @xcite , delocalizing transition of matter waves @xcite , or the dynamics of the waves in random @xcite , linear @xcite , periodic @xcite or localized @xcite spatial modulations . a number of more mathematically minded results on the existence and stability of waves have also appeared in @xcite and a technique for analytically constructing exact solutions in @xcite . the framework of collisionally inhomogeneous environments in combination with external optical lattices provides an ideal environment for competition . this was illustrated in examples of modulational instability of bloch states @xcite and of the delocalizing transition in one - dimension @xcite . in the present work we develop these ideas exploring more general lattice profiles . in particular , external ( linear ) potentials and collisional ( nonlinear ) potentials in ( as well as out of ) phase will be considered . it will be demonstrated that when in phase , these potentials provide a competition leading to a number of interesting effects including stabilization / destabilization thresholds and even the mutual annihilation of the two potentials to provide an effectively quasi - translationally - invariant environment . the effective potential landscape where the solitary waves ( of the bright type ) live will be obtained following the lyapunov - schmidt considerations of @xcite . then , the relevant ( translational ) eigenvalue of the linearization will be computed based on the curvature of this effective potential landscape and the stability / instability of the waves will be assessed ( and the relevant transition points will be obtained ) . these results will be confirmed by a second independent method based on a direct count of unstable eigenvalues . finally , we will examine the variation of a number of relevant key parameters ( such as the amplitude , the wavenumbers or the relative phase ) of the potentials , in order to evaluate the validity of the approach . furthermore , when the structures are unstable , we will examine what this approach can suggest regarding the actual instability evolution dynamics . the understanding that we will develop will enable us to manipulate the ensuing solitary waves in such a complex territory and to understand their dynamical behavior in the presence of linear and nonlinear lattices . our presentation will be structured as follows . in section ii , we will present our analytical results ; in section iii , we will corroborate these results by means of numerical computations . finally , in section iv , we will summarize our findings and present some interesting directions for future study .

in this paper numerical methods of computing distances between two radon measures on @xmath0 are discussed . efficient algorithms for wasserstein - type metrics are provided . in particular , we propose a novel algorithm to compute the flat metric ( bounded lipschitz distance ) with a computational cost @xmath1 . the flat distance has recently proven to be adequate for the escalator boxcar train ( ebt ) method for solving transport equations with growth terms . therefore , finding efficient numerical algorithms to compute the flat distance between two measures is important for finding the residual error and validating empirical convergence of different methods .

i

1304.3501

in this paper numerical methods of computing distances between two radon measures on @xmath0 are discussed . efficient algorithms for wasserstein - type metrics are provided . in particular , we propose a novel algorithm to compute the flat metric ( bounded lipschitz distance ) with a computational cost @xmath1 . the flat distance has recently proven to be adequate for the escalator boxcar train ( ebt ) method for solving transport equations with growth terms . therefore , finding efficient numerical algorithms to compute the flat distance between two measures is important for finding the residual error and validating empirical convergence of different methods . * keywords : * metric spaces , flat metric , wasserstein distance , radon measures , optimal transport , linear programming , minimum - cost flow

recent years witnessed large developments in the kinetic theory methods applied to mathematical physics and more recently also to mathematical biology . among important branches of the kinetic theory are optimal transportation problems and related to them wasserstein metrics , and monge - kantorovich metrics @xcite . partial differential equations in metric spaces are being applied to transportation problems @xcite , gradient flows @xcite and structured population models @xcite . output of mathematical modeling can often be described as radon measures . comparing the results of the models requires then a definition of distance in the space of measures . the desired properties of such metrics depend on the structure of the considered problem . in most of the cases , the topology of total variation is too strong for applications , and weaker metrics had to be introduced , see @xcite for details . well known @xmath2-wasserstein metric , on the other hand , is only applicable to processes with mass conservation . to cope with growth in the process , various modifications have been proposed , including flat metric and centralized wasserstein metric . in the present paper , we additionally introduce a normalized wasserstein distance . for comparison of different metrics , their interpretation and examples see table [ table ] . even though , all those distances can be computed using linear programming ( lp ) , its computational complexity becomes often larger than the complexity of solving the original problem . for example , the equations for which the stability of numerical algorithm is proven in @xmath3 require an efficient algorithm for the flat metric to find the residual error . algorithms proposed in this paper are designed to compute efficiently wasserstein - type distance between two radon measures in the form of @xmath4 , where @xmath5 is the dirac delta . the algorithms can be also applied for the case of an arbitrary pair of measures , by approximating those measures by the sum of dirac deltas . in the process of finding numerical solutions to partial differential equations , the distance between a discrete and absolutely continuous measures is needed to evaluate the quality of the initial condition approximation , while the distance between two discrete measure is needed to find the residual error . the paper is organized as follows . in section [ metrics ] we introduce and compare four wasserstein - type metrics . additionally , we introduce a two - argument function , based on the wasserstein distance , which is not a metric , however , provides a good tool to estimate the flat metric from above . section [ algorithms ] is devoted to numerical algorithms proposed to calculate distances between two measures in respect to the considered metrics . we justify the algorithms and provide respective pseudocodes . the novelty of this paper is the algorithm for flat metric , which has been recently proven to be adequate for the escalator boxcar train ( ebt ) method for solving transport equations @xcite . we propose an efficient algorithm which computation cost is @xmath6 and optimize it further to @xmath1 . to judge the efficiency of the algorithms , we compare the times needed to compute the flat distance between two sums of a large number of dirac deltas randomly distributed over [ -1,1 ] .

in this paper we consider a model which describes a polymer chain interacting with an infinity of equi - spaced linear interfaces . the distance between two consecutive interfaces is denoted by @xmath0 and is allowed to grow with the size @xmath1 of the polymer . when the polymer receives a positive reward for touching the interfaces , its asymptotic behavior has been derived in @xcite , showing that a transition occurs when @xmath2 . in the present paper i.e. , the polymer is repelled rather than attracted by the interfaces . using techniques from renewal theory , we determine the scaling behavior of the model for large @xmath1 as a function of @xmath3 , showing that two transitions occur , when @xmath4 and when @xmath5 respectively .

i

0901.2902

in this paper we consider a model which describes a polymer chain interacting with an infinity of equi - spaced linear interfaces . the distance between two consecutive interfaces is denoted by @xmath0 and is allowed to grow with the size @xmath1 of the polymer . when the polymer receives a positive reward for touching the interfaces , its asymptotic behavior has been derived in @xcite , showing that a transition occurs when @xmath2 . in the present paper , we deal with the so called _ depinning case _ , i.e. , the polymer is repelled rather than attracted by the interfaces . using techniques from renewal theory , we determine the scaling behavior of the model for large @xmath1 as a function of @xmath3 , showing that two transitions occur , when @xmath4 and when @xmath5 respectively .

we consider a @xmath6-dimensional model of a polymer depinned at an infinity of equi - spaced horizontal interfaces . the possible configurations of the polymer are modeled by the trajectories of the simple random walk @xmath7 , where @xmath8 and @xmath9 is an i.i.d . sequence of symmetric bernouilli trials taking values @xmath10 and @xmath11 , that is @xmath12 . the polymer receives an energetic penalty @xmath13 each times it touches one of the horizontal interfaces located at heights @xmath14 , where @xmath15 ( we assume that @xmath16 is even for notational convenience ) . more precisely , the polymer interacts with the interfaces through the following hamiltonian : @xmath17 where @xmath18 is the number of monomers constituting the polymer . we then introduce the corresponding polymer measure @xmath19 ( see figure [ fig:1 ] for a graphical description ) by @xmath20 where the normalizing constant @xmath21 $ ] is called the _ partition function_. the polymer measure @xmath22 , for @xmath23 and @xmath24 . the circles indicate the points where the polymer touches the interfaces , that are penalized by @xmath25 each . ] we are interested in the case where the interface spacing @xmath26 is allowed to vary with the size @xmath1 of the polymer . more precisely , we aim at understanding whether and how the asymptotic behavior of the polymer is modified by the interplay between the energetic penalty @xmath27 and the growth rate of @xmath28 as @xmath29 . in the _ attractive case _ @xmath30 , when the polymer is rewarded rather than penalized to touch an interface , this question was answered in depth in a previous paper @xcite , to which we also refer for a detailed discussion on the motivation of the model and for an overview on the literature ( see also [ sec : slit ] below ) . in the present paper we extend the analysis to the _ repulsive case _ @xmath25 , showing that the behavior of the model is sensibly different from the attractive case . for the reader s convenience , and in order to get some intuition on our model , we recall briefly the result obtained in @xcite for @xmath31 . we first set some notation : given a positive sequence @xmath32 , we write @xmath33 to indicate that , on the one hand , @xmath34 is tight ( for every @xmath35 there exists @xmath36 such that @xmath37 for large @xmath1 ) and , on the other hand , that for some @xmath38 and @xmath39 we have @xmath40 for large @xmath1 . this notation catches the rate of asymptotic growth of @xmath41 somehow precisely : if @xmath33 and @xmath42 , for some @xmath35 we must have @xmath43 , for large @xmath1 . theorem 2 in @xcite can be read as follows : for every @xmath44 there exists @xmath45 such that @xmath46 let us give an heuristic explanation for these scalings . for fixed @xmath47 , the process @xmath48 under @xmath49 behaves approximately like a time - homogeneous markov process ( for a precise statement in this direction see [ sec : renewal ] ) . a quantity of basic interest is the first time @xmath50 at which the polymer visits a neighboring interface . it turns out that for @xmath31 the typical size of @xmath51 is of order @xmath52 , so that until epoch @xmath1 the polymer will make approximately @xmath53 changes of interface . assuming that these arguments can be applied also when @xmath0 varies with @xmath1 , it follows that the process @xmath48 jumps from an interface to a neighboring one a number of times which is approximately @xmath54 . by symmetry , the probability of jumping to the neighboring upper interface is the same as the probability of jumping to the lower one , hence the last visited interface will be approximately the square root of the number of jumps . therefore , when @xmath55 , one expects that @xmath41 will be typically of order @xmath56 , which matches perfectly with the first line of . on the other hand , when @xmath57 the polymer will never visit any interface different from the one located at zero and , because of the attractive reward @xmath31 , @xmath41 will be typically at finite distance from this interface , in agreement with the third line of . finally , when @xmath58 is bounded , the polymer visits a finite number of different interfaces and therefore @xmath41 will be of the same order as @xmath28 , as the second line of shows . also in the repulsive case @xmath25 one can perform an analogous heuristic analysis . the big difference with respect to the attractive case is the following : under @xmath59 , the time @xmath51 the polymer needs to jump from an interface to a neighboring one turns out to be typically of order @xmath60 ( see section [ sec : preliminary ] ) . assuming that these considerations can be applied also to the case when @xmath0 varies with @xmath1 , we conclude that , under @xmath61 , the total number of jumps from an interface to the neighboring one should be of order @xmath62 . one can therefore conjecture that if @xmath63 the typical size of @xmath41 should be of order @xmath64 , while if @xmath65 remains bounded one should have @xmath66 . in the case @xmath67 , the polymer will never exit the interval @xmath68 . however , guessing the right scaling in this case requires some care : in fact , due to the repulsive penalty @xmath25 , the polymer will _ not _ remain close to the interface located at zero , as it were for @xmath31 , but it will rather spread in the interval @xmath68 . we are therefore led to distinguish two cases : if @xmath69 then @xmath41 should be of order @xmath28 , while if @xmath70 we should have @xmath71 ( of course we write @xmath72 iff @xmath73 and @xmath74 iff @xmath75 ) . we can sum up these considerations in the following formula : @xmath76 it turns out that these conjectures are indeed correct : the following theorem makes this precise , together with some details on the scaling laws . [ th : main ] let @xmath13 and @xmath77 be such that @xmath78 as @xmath79 . [ part:1 ] + ' '' '' + if @xmath80 , then @xmath81 . more precisely , there exist two constants @xmath82 such that for all @xmath83 with @xmath84 we have for @xmath1 large enough @xmath85 \;\le\ ; \bp_{n,\delta}^{t_n } \left ( a < \frac{s_n}{c_\delta \ , \textstyle\sqrt{\frac{n}{t_n } } } \le b \right ) \;\le\ ; c_2 \ , p\big [ a < z \le b \big ] \,,\ ] ] where @xmath86 is an explicit positive constant and @xmath87 . [ part:2 ] + ' '' '' + if @xmath88 , then @xmath66 . more precisely , for every @xmath35 small enough there exist constants @xmath89 such that @xmath90 @xmath91 3 . [ part:3 ] + ' '' '' + if @xmath92 , then @xmath66 . more precisely , for every @xmath35 small enough there exist constants @xmath93 such that @xmath94 @xmath95 4 . [ part:4 ] + ' '' '' + if @xmath96 , then @xmath97 . more precisely , for every @xmath35 small enough there exist constants @xmath98 such that @xmath94 @xmath99 to have a more intuitive view on the scaling behaviors in , let us consider the concrete example @xmath100 : in this case we have @xmath101 as the speed of growth of @xmath28 increases , in a first time ( until @xmath102 ) the scaling of @xmath41 decreases , reaching a minimum @xmath103 , after which it increases to reattain the initial value @xmath104 , for @xmath105 . we have thus shown that the asymptotic behavior of our model displays two transitions , at @xmath5 and at @xmath106 . while the first one is somewhat natural , in view of the diffusive behavior of the simple random walk , the transition happening at @xmath106 is certainly more surprising and somehow unexpected . let us make some further comments on theorem [ th : main ] . * about regime ( [ part:1 ] ) , that is when @xmath107 , we actually conjecture that equation can be strengthened to a full convergence in distribution : @xmath108 . the reason for the slightly weaker result that we present is that we miss precise renewal theory estimates for a basic renewal process , that we define in [ sec : renewal ] . as a matter of fact , using the techniques in @xcite one can refine our proof and show that the full convergence in distribution holds true in the restricted regime @xmath109 , but we omit the details for conciseness ( see however the discussion following proposition [ th : bound_renewal ] ) . * equation implies that the sequence @xmath110 is _ tight _ , and that the limit law of any converging subsequence is absolutely continuous w.r.t . the lebesgue measure on @xmath111 . moreover , the density of this limit law is bounded above and below by a multiple of the standard normal density . * the case when @xmath112 as @xmath79 has not been included in theorem [ th : main ] for the sake of simplicity . however a straightforward adaptation of our proof shows that in this case equation still holds true , with @xmath113 replaced by a different ( @xmath16-dependent ) constant @xmath114 . * we stress that in regimes ( [ part:3 ] ) and ( [ part:4 ] ) the polymer really touches the interface at zero a finite number of times , after which it does not touch any other interface . it turns out that our model @xmath19 is closely related to a model which has received quite some attention in the recent physical literature , the so - called _ polymer confined between two attractive walls _ @xcite ( also known as polymer in a slit ) . this is a model for the steric stabilization and sensitized flocculation of colloidal dispersions induced by polymers , which can be simply described as follows : given @xmath115 , take the first @xmath1 steps of the simple random walk constrained not to exit the interval @xmath116 , and give each trajectory a reward / penalization @xmath117 each time it touches @xmath118 or @xmath16 ( one can also consider two different rewards / penalties @xmath119 and @xmath120 , but we will stick to the case @xmath121 ) . we are thus considering the probability measure @xmath122 defined by @xmath123 where @xmath124 is the law of the simple random walk _ constrained _ to stay between the two walls located at @xmath118 and @xmath16 . and @xmath16 , in a trajectory of polymer in a slit . the dotted lines correspond to the parts of trajectory that appear upside - down after the reflection . ] consider now the simple random walk _ reflected _ on both walls @xmath118 and @xmath16 , which may be defined as @xmath125 , where @xmath126 is the ordinary simple random walk and @xmath127_{2 t } , 2 t - [ x]_{2 t } \big\}\ , , \qquad \text{with } \qquad [ x]_{2 t } \;:=\ : 2t\ , \big(\frac{x}{2 t } - \big\lfloor \frac{x}{2 t } \big\rfloor\big)\,,\ ] ] that is , @xmath128_{2t}$ ] denotes the equivalence class of @xmath129 modulo @xmath130 ( see figure [ fig : multuni1 ] for a graphical description ) . we denote by @xmath131 the law of the first @xmath1 steps of @xmath132 . of course , @xmath131 is different from @xmath133 : the latter is the uniform measure on the simple random walk paths @xmath48 that stay in @xmath116 , while under the former each such path has a probability which is proportional to @xmath134 , where @xmath135 is the number of times the path has touched the walls . in other terms , we have @xmath136 if we consider the reflection under @xmath137 of our model , that is the process @xmath138 under @xmath19 , whose law will be simply denoted by @xmath139 , then it comes @xmath140 at this stage , a look at equations , and points out the link with our model : we have the basic identity @xmath141 , for all @xmath142 and @xmath143 . in words , the polymer confined between two attractive walls is just the reflection of our model through @xmath137 , up to a shift of the pinning intensity by @xmath144 . this allows a direct translation of all our results in this new framework . let us describe in detail a particular issue , namely , the study of the model @xmath145 when @xmath0 is allowed to vary with @xmath1 ( this is interesting , e.g. , in order to interpolate between the two extreme cases when one of the two quantities @xmath16 and @xmath1 tends to @xmath146 before the other ) . this problem is considered in @xcite , where the authors obtain some asymptotic expressions for the partition function @xmath147 of a polymer in a slit , in the case of two different rewards / penalties ( we are following their notation , in which @xmath148 , @xmath149 , @xmath150 and @xmath151 ) and with the boundary condition @xmath152 . focusing on the case @xmath153 , we mention in particular equations ( 6.4)(6.6 ) in @xcite , which for @xmath154 read as @xmath155 where we have neglected a combinatorial factor @xmath156 ( which just comes from a different choice of notation ) , and where the function @xmath157 is such that @xmath158 the regime @xmath154 corresponds to @xmath159 , hence , in view of the correspondence @xmath160 described above , we are exactly in the regime @xmath25 for our model @xmath161 . we recall and , with the help of equation , we can express the partition function with boundary condition @xmath162 as @xmath163 where , with some abuse of notation , we denote by @xmath164 a quantity which stays bounded away from @xmath118 and @xmath146 as @xmath165 . in this formula , @xmath166 is the _ free energy _ of our model and @xmath167 is a basic renewal process , introduced respectively in [ sec : free_energy ] and [ sec : renewal ] below . in the case when @xmath168 , we can use the asymptotic development for @xmath166 , which , combined with the bounds in , gives as @xmath169 @xmath170 since @xmath171 , we can rewrite this relation using the notation of @xcite : @xmath172 we have therefore obtained a refinement of equations , . this is linked to the fact that we have gone beyond the first order in the asymptotic development of the free energy @xmath166 , making an additional term of the order @xmath173 appear . we stress that this new term gives a non - negligible ( in fact , exponentially diverging ! ) contribution as soon as @xmath107 ( @xmath174 in the notation of @xcite ) . this corresponds to the fact that , by theorem [ th : main ] , the trajectories that touch the walls a number of times of the order @xmath173 are actually dominating the partition function when @xmath107 . of course , a higher order development of the free energy ( cf . appendix [ sec : fe_estimates ] ) may lead to further correction terms . proving theorem [ th : main ] requires to settle some technical tools , partially taken from @xcite , that we present in section [ sec : preliminary ] . more precisely , in [ sec : free_energy ] we introduce the free energy @xmath175 of the polymer and we describe its asymptotic behavior as @xmath176 ( for fixed @xmath13 ) . in [ sec : renewal ] we enlighten a basic correspondence between the polymer constrained to hit one of the interfaces at its right extremity and an explicit renewal process . in [ sec : asymp ] we investigate further this renewal process , providing estimates on the renewal function , which are of crucial importance for the proof of theorem [ th : main ] . sections [ sec : parti ] , [ sec : partii ] , [ sec : partiii ] and [ sec : partiv ] are dedicated respectively to the proof of parts ( [ part:1 ] ) , ( [ part:2 ] ) , ( [ part:3 ] ) and ( [ part:4 ] ) of theorem [ th : main ] . finally , some technical results are proven in the appendices . we stress that the value of @xmath25 is kept fixed throughout the paper , so that the generic constants appearing in the proofs may be @xmath177-dependent .

in this paper we derive analytical relations between probabilities of the excited state transfers and entanglements calculated by both the wootters and positive partial transpose ( ppt ) criteria for the arbitrary spin system with single excited spin in the external magnetic field and hamiltonian commuting with @xmath0 . we apply these relations to study the arbitrary state transfers and entanglements in the simple systems of nuclear spins having two- and three - dimensional geometrical configurations with @xmath1 hamiltonian . it is shown that high - probability state transfers ( hpsts ) are possible among all four nodes placed in the corners of the rectangle with the proper ratio of sides as well as among all eight nodes placed in the corners of the parallelepiped with the proper ratio of sides . entanglements responsible for these hpsts have been identified .

i

0901.3424

in this paper we derive analytical relations between probabilities of the excited state transfers and entanglements calculated by both the wootters and positive partial transpose ( ppt ) criteria for the arbitrary spin system with single excited spin in the external magnetic field and hamiltonian commuting with @xmath0 . we apply these relations to study the arbitrary state transfers and entanglements in the simple systems of nuclear spins having two- and three - dimensional geometrical configurations with @xmath1 hamiltonian . it is shown that high - probability state transfers ( hpsts ) are possible among all four nodes placed in the corners of the rectangle with the proper ratio of sides as well as among all eight nodes placed in the corners of the parallelepiped with the proper ratio of sides . entanglements responsible for these hpsts have been identified .

this paper is devoted to the problem of the high probability state transfer ( hpst ) @xcite among many nodes of the spin system and to the relationship between probabilities of hpsts and entanglements responsible for these transfers . we consider nuclear spin-1/2 systems with xxz - hamiltonian and different geometrical configurations . however , the above relationship remains valid for any hamiltonian @xmath2 commuting with the total projection operator @xmath0 . by `` state transfer '' we mean the following phenomenon @xcite . consider the chain of spin-1/2 with dipole - dipole interaction in the strong external magnetic field . let all spins be directed along the external magnetic field except the @xmath3th one whose initial state is arbitrary . in other words , let the spin system be prepared in the state @xmath4 is a ground state , i.e. all spins are directed along the magnetic field and @xmath5 means that only @xmath3th spin is directed opposite to the external magnetic field ( i.e. @xmath3th spin is excited ) . let the energy of the ground state be zero . if the state becomes @xmath6 with @xmath7 at the time moment @xmath8 then we say that the initial state has been transferred from the @xmath3th to the @xmath9th node with the phase shift @xmath10 . since @xmath11 , all other spins are directed along the field at @xmath8 . here @xmath12 and @xmath13 is the transition amplitude of an excited state from the @xmath3th to the @xmath9th node : @xmath14 . it is known @xcite that the effectiveness of the state transfer between the @xmath3th and @xmath9th nodes may be characterised by the fidelity @xmath15 @xmath16 we see that the fidelity is maximal for @xmath17 @xmath18 . if the external magnetic field is homogeneous and we are interested in the state propagation between two nodes , say between @xmath19th and @xmath20th nodes at the moment @xmath21 , then condition @xmath22 may be simply satisfied by the proper choice of the constant magnetic field value @xcite . in this case the fidelity @xmath23 takes maximal value together with absolute value of the transition amplitude @xmath24 . for this reason , namely @xmath25 ( rather then @xmath26 ) is considered as the characteristic of the state transfer in many refs , see , for instance , @xcite . it is clear that @xmath27 may be replaced by the probability of the excited state transfer @xmath28 and @xmath29 @xcite . more general case of the hpsts among many nodes of the @xmath30 node spin chain has been studied in @xcite . in this case any particular state transfer between the @xmath3th and @xmath9th nodes is associated with its own phase shift @xmath31 , @xmath32 ( note that @xmath3 may be equal to @xmath9 which means return of the state to the @xmath3th node ) . however , it is important that all these shifts may be eliminated using magnetic field properly depending on time @xcite . for this reason the effectiveness of the state transfer between the @xmath3th and the @xmath9th nodes may be equivalently described either by the fidelity @xmath33 or by the probability of the excited state transfer @xmath34 even in this generalized case . namely optimization of @xmath34 allows us to find all necessary parameters of the geometrical spin configuration providing hpsts among many nodes while phases @xmath31 may be removed by the appropriate time dependent external magnetic field as it was done in @xcite . for this reason , we will study the probability of the single excited state transfer instead of the fidelity ( [ fidelity ] ) of arbitrary state transfer in the subsequent sections of this paper . this means that the spin 1/2 system of @xmath30 nodes is prepared in the initial state @xmath35 where @xmath3 takes one of the values @xmath36 . the problem of the perfect state transfers ( psts ) , hpsts and entanglements in the spin systems is very attractive and different aspects of this problem have been studied in many details @xcite . nevertheless , most of the results are devoted to the linear and circular spin chains , which are considered as communication channels in the quantum information systems . different hamiltonians describing these chains have been studied , such as @xmath37 , @xmath38 , heisenderg hamiltonians . usually , the approximation of the nearest neighbour interactions is taken as a basic tool for such studies . note , that this is a good approximation in the case of , for instance , exchange interaction , when coupling constants decrease exponentially with increase in the distance . however , this approximation is not satisfactory for the spin systems with dipole - dipole interaction ( such as nuclear spin systems in solids ) and a wide spread of the coupling constants . most efforts have been turned to the study of two phenomena : the state transfer along chains @xcite and two - qubit entanglements in chains ( such as entanglement between end nodes or between nearest nodes @xcite ) . the wootters criterion is applicable in this case allowing one to describe the entanglement in terms of so - called concurrence @xcite . it is important that there is an analytical dependence of the concurrence between two nodes on the probability of the state transfer between these nodes which was derived in @xcite for the system with single excited spin . however , complicated system of @xmath30 spins exhibits entanglements not only between two nodes , but also between arbitrary two subsystems . these entanglements may be effectively described by the positive partial transpose ( ppt ) criterion @xcite introducing so - called double negativity as a measure of entanglement . explicit relations of the double negativity associated with two subsystems on the probabilities of the excited state transfers between different nodes will be derived in this paper for the spin system with single excitation . although the pst would be preferable in the quantum communication chains , it is hardly realizable in experiments with long chains because of the following two basic reasons : 1 . theoretical prediction of the pst in the long chains is associated with the approximation of the hamiltonian by the nearest neighbour interaction , while the complete hamiltonian must be used in practice . as we have already noted , this approximation is well applicable to the systems with exchange interaction and is not always valid for the systems with dipole - dipole interaction . coupling constants may not be always known as accurately as we want in the case of both exchange and dipole - dipole interaction . thus , hpst between different nodes of the spin system @xcite seems to be more realistic in comparison with pst . in this paper we will study the spin systems with dipole - dipole interaction in the external magnetic field with single excited node described by the @xmath1 hamiltonian . we will study the spin systems with different geometrical configurations of nodes and initial state ( [ initial ] ) which may provide the hpsts of the excited state among all of nodes . we will show which parts of the spin system must be entangled in order to provide each of these transfers . the study of two- and three - dimensional spin systems is important because they are more compact and consequently they are more promising as quantum registers and/or short communication channels . it will be shown in this paper , that namely such configurations ( more precisely , spin configurations with nodes placed in the corners of either rectangle or parallelepiped ) provide the hpsts among several different nodes of the spin system during relatively short time interval in comparison with the line systems @xcite which is important for the development of the quantum information systems and/or short communication channels . our study is also stimulated by the experiments on the quantum information processes in solids @xcite . this paper is organized as follows . in sec.[section : xyz ] ( and in appendices [ app : wootters ] and [ app : ppt ] ) we obtain analytical dependence of the either concurrences ( wootters criterion ) or double negativities ( ppt criterion ) between different two subsystems of the spin system on the probabilities of the state transfers , generalizing the results of refs.@xcite . in sec.[section : two_nodes ] we consider the simplest one - dimensional model of two nodes where the relationship between entanglement and probability of the state transfer is most transparent and an equivalent result may be obtained using either the wootters @xcite or ppt criterion . two - dimensional spin systems will be considered in sec.[section : four_nodes ] , see also appendix [ app:4nodes ] . we arrange hpst among all nodes of the four - node spin system ( rectangular geometry ) and show that the external magnetic field directed along one of the sides of the rectangle decreases significantly ( more then twice ) the time intervals needed for the hpsts among nodes in comparison with the case when the field is perpendicular to the plane of the rectangle . similar study of the three - dimensional eight - node system ( with spins placed in the corners of the parallelepiped ) is represented in sec.[section : eight_nodes ] , see also appendix [ app:8nodes ] . it is evident that hpsts may not be effectively arranged in the arbitrary system of nodes . detailed algorithm allowing one to obtain parameters of the rectangle spin system ( namely , the ratio of sides of the rectangle ) with the hpsts among all four nodes is given in appendix [ app:4nodes ] . particular example of the eight - node three - dimensional spin system with hpsts among all nodes ( parallelepiped configuration ) is represented in appendix [ app:8nodes ] .

in this paper we extend the classical theory of combinatorial manifolds to the non - homogeneous setting . @xmath0-manifolds are polyhedra which are locally like euclidean spaces of varying dimensions . we show that many of the properties of classical manifolds remain valid in this wider context . @xmath0-manifolds appear naturally when studying pachner moves on ( classical ) manifolds . we introduce the notion of @xmath0-factorization and prove that @xmath1-homeomorphic manifolds are related by a finite sequence of @xmath0-factorizations involving @xmath0-manifolds .

i

1108.4955

in this paper we extend the classical theory of combinatorial manifolds to the non - homogeneous setting . @xmath0-manifolds are polyhedra which are locally like euclidean spaces of varying dimensions . we show that many of the properties of classical manifolds remain valid in this wider context . @xmath0-manifolds appear naturally when studying pachner moves on ( classical ) manifolds . we introduce the notion of @xmath0-factorization and prove that @xmath1-homeomorphic manifolds are related by a finite sequence of @xmath0-factorizations involving @xmath0-manifolds .

the notion of manifold ( piecewise linear , topological , differentiable ) is central in mathematics . an @xmath2-manifold is an object which is locally like the euclidean space @xmath3 . concretely , in the piecewise linear setting a pl - manifold of dimension @xmath2 is a polyhedron in which every point has a ( closed ) neighborhood which is a pl - ball of dimension @xmath2 . the theory of combinatorial manifolds ( which are the triangulations of pl - manifolds ) has been widely developed during the last ninety years . alexander s theorem on regular expansions , newman s result on the complement of an @xmath2-ball in an @xmath2-sphere , whitehead s regular neighborhood theory and the s - cobordism theorem are some of its most important advances @xcite . more recently pachner @xcite studied a set of elementary combinatorial operations or _ moves _ , and showed that any combinatorial manifold can be transformed into any other pl - homeomorphic one by using these moves ( see also @xcite ) . it is well known that any combinatorial @xmath2-manifold is a homogeneous ( or pure ) simplicial complex , which means that all the maximal simplices have the same dimension . it is natural to ask whether it is possible to extend the theory of combinatorial manifolds to the non - homogeneous context . more concretely , the main goal of this article is to investigate the properties of those polyhedra which are locally like euclidean spaces of varying dimensions ( see figures [ fig : ejemplos_nh_variedades_locales ] and [ fig : ejemplos_nh_variedades ] below ) . in this paper we introduce the theory of _ non - homogeneous manifolds _ or @xmath0-manifolds , for short . we will show that many of the basic properties of ( classical ) manifolds are also satisfied in this much wider setting . we investigate shellability in the non - homogeneous context . it is well - known that any shellable complex is homotopy equivalent to a wedge of spheres and that the only shellable manifolds are balls and spheres ( see @xcite and @xcite ) . we prove that every shellable @xmath0-manifold is in particular an @xmath0-bouquet , which extends the classical result for manifolds . we also study the notion of regular expansion for @xmath0-manifolds and prove a generalization of alexander s theorem . non - homogeneous manifolds appear naturally when studying pachner moves between manifolds . we introduce the notion of @xmath0-factorization and prove that any two pl - homeomorphic manifolds ( with or without boundary ) are related by a finite sequence of factorizations involving @xmath0-manifolds . when the manifolds are closed , the converse also holds .

in this paper we find different types of black holes for the born - infeld extended new massive gravity . our solutions include ( un)charged warped @xmath0 black holes for four and six derivative expanded action . we also look at the black holes in unexpanded bi action . in each case

i

1010.2434

in this paper we find different types of black holes for the born - infeld extended new massive gravity . our solutions include ( un)charged warped @xmath0 black holes for four and six derivative expanded action . we also look at the black holes in unexpanded bi action . in each case we calculate the entropy , angular momentum and mass of the black holes . we also find the central charges for the cft duals . ahmad ghodsi and davood mahdavian yekta + +

in this paper we have found different black hole solutions for the born - infeld extension of new massive gravity . we have extended the nmg in two directions , gravity and electromagnetism . the electromagnetic part contains maxwell term and chern - simons term . we have found three types of warped @xmath0 solutions . these are uncharged , maxwell charged and maxwell - chern - simons charged black holes . for each of them we have found the domain of validity ( ctc - free and reality of the gauge field strength ) . we have found these black holes for expanded ( up to four and six derivative ) and unexpanded bi action . the physical properties of the solutions in each case are totally different and one can not find the four or six derivative properties form the bi properties . in this theory we have two types of parameters . the first type includes parameters in the lagrangian . the @xmath55 which is the mass parameter for our massive gravity theory and the cosmological constant @xmath68 . the second type includes the parameters which are coming from the solutions . from ( [ admmetr ] ) we see three parameters . the parameter @xmath120 or equivalently @xmath31 which is limited by ctc free condition , and two free parameters @xmath35 and @xmath36 . there is another parameter @xmath3 , in ( [ x ] ) , which corresponds to the electric or magnetic charge of the solutions . among these parameters in all the solutions , the values of @xmath55 , @xmath68 and @xmath3 are controlled by the value of the @xmath31 parameter . our computation shows that each of these parameters may have positive or negative values . so we may have de sitte or anti de sitte solutions in our theory which depends on the level of expansion and existence of the m - charges or mcs - charges in the theory . our results is summarized as follows : in four derivative case we have only one set of roots for @xmath55 which is either positive or negative depending on the solution . but in six derivative case for uncharged and m - charged cases we have two sets of roots one positive and one negative . for mcs - charged solutions we have three sets of roots , one positive and two negative . in bi case the situation is totally different . for uncharged case we find only a single point for @xmath55 . for the bi case there is not m - charged solution and for mcs - charged black holes there is only one set of roots for @xmath55 . in four derivative action for uncharged solutions @xmath86 and @xmath96 . for m - charged solutions @xmath84 but @xmath68 changes its sign in a specific point @xmath31 . for mcs - charged black holes @xmath84 and @xmath97 . in six derivative action for uncharged solutions @xmath55 and @xmath68 can have both signs , this is true for m - charged solutions . for mcs - charged black holes we have the same behavior but there are situations where @xmath68 changes its sign in a specific value of @xmath31 . in unexpanded bi action , for uncharged solutions @xmath55 has fixed value and the cosmological constant has both plus and minus signs . for m - charged solutions there is no solution . for mcs - charged black holes @xmath84 and the cosmological constant has a fixed value @xmath121 . for all the above solutions we have found the entropy , angular momentum and mass . our results satisfy the differential form of the first law of the thermodynamics for black holes . we have used the free parameters of the theory , @xmath35 and @xmath36 to show this . in all of the solutions , the entropy is proportional to the area of the horizon . using the cardy s formula we have found the central charges of the cft duals . for our solutions in despite of presence of maxwell - chern - simons term the left and right central charges are equal . in general as shown in @xcite if there is a gravitational chern - simons term ( tmg model ) then this equality will be broken and we obtain different left and right central charges .

the breaking is done at the seesaw scale , in such a way that what remains of the flavor symmetry is a @xmath1 symmetry , which stabilizes the dark matter . we have proposed two models based on this idea , for which we have calculated their neutrino mass matrices achieving two - zero texture in both cases . accordingly , we have updated this two - zero texture phenomenology finding an interesting correlation between the reactor mixing angle and the sum of the light neutrino masses . we also have a correlation between the lightest neutrino mass and the neutrinoless double beta decay effective mass , obtaining a lower bound for the effective mass within the region of the nearly future experimental sensitivities .

c

1603.02190

in this paper we present a scenario where the stability of dark matter and the phenomenology of neutrinos are related by the spontaneous breaking of a non - abelian flavor symmetry ( @xmath0 ) . in this scenario the breaking is done at the seesaw scale , in such a way that what remains of the flavor symmetry is a @xmath1 symmetry , which stabilizes the dark matter . we have proposed two models based on this idea , for which we have calculated their neutrino mass matrices achieving two - zero texture in both cases . accordingly , we have updated this two - zero texture phenomenology finding an interesting correlation between the reactor mixing angle and the sum of the light neutrino masses . we also have a correlation between the lightest neutrino mass and the neutrinoless double beta decay effective mass , obtaining a lower bound for the effective mass within the region of the nearly future experimental sensitivities .

we have constructed two models based on the discrete dark matter mechanism where the non - abelian @xmath0 flavor symmetry is spontaneously broken at the seesaw scale , into a remanent @xmath1 . in these models , we have a total of five rh neutrinos . in this case , two rh neutrinos are in the @xmath1 odd sector , and the other three rh are even under @xmath1 . these three rh neutrinos are responsible for giving the light neutrino masses via type i seesaw . additionally , we have added flavon scalar fields @xmath47 leading to the @xmath0 breaking in such a way that we obtained two - zero textures for the light majorana neutrinos . these textures give rise to rich neutrino phenomenology : the results are in agreement with the experimental data of the reactor mixing angle and accommodate the two possible neutrino mass hierarchies , nh and ih . another consequence of the way @xmath0 is broken , in addition to dictating the neutrino phenomenology , is that these models contain a dm candidate stabilized by the remnant @xmath1 symmetry . the dm phenomenology in this case will be different than the original ddm @xcite , where the limit for large dm masses ( @xmath48 gev ) was not allowed , and will be similar to the inert higgs doublet model @xcite with extra scalar fields . a detailed discussion of the dm phenomenology is beyond the scope of the present work and will be presented in a further work @xcite . additionally , we have updated the analysis for the two - zero textures mass matrix obtained for both models @xmath30 and @xmath28 . we presented the correlation between the atmospheric mixing angle and the sum of the light neutrino masses as well as the lower bounds for neutrinoless double beta decay effective mass parameter ; the latter being in the region of sensitivity of the near future experiments . finally , if the flavon fields acquire vevs at a scale slightly higher than the seesaw scale , the remaining symmetry at the seesaw scale is the @xmath1 , and this would imply a mixing of the three @xmath1 even rh neutrinos , which could be crucial if we want to have a scenario for leptogenesis , since in the @xmath0 symmetric case this was not possible .

in this paper we use the theory of viscosity solutions for hamilton - jacobi equations to study propagation phenomena in kinetic equations . we perform the hydrodynamic limit of some kinetic models thanks to an adapted wkb ansatz . our models describe particles moving according to a velocity - jump process , and proliferating thanks to a reaction term of monostable type . the scattering operator is supposed to satisfy a maximum principle . when the velocity space is bounded , we show , under suitable hypotheses , that the phase converges towards the viscosity solution of some constrained hamilton - jacobi equation which effective hamiltonian is obtained solving a suitable eigenvalue problem in the velocity space . in the case of unbounded velocities , in particular , a front acceleration phenomena can occur . nevertheless , we expect that when the spectral problem is solvable one can extend the convergence result . no : * 35q92 , 45k05 , 35c07

i

1406.1898

in this paper we use the theory of viscosity solutions for hamilton - jacobi equations to study propagation phenomena in kinetic equations . we perform the hydrodynamic limit of some kinetic models thanks to an adapted wkb ansatz . our models describe particles moving according to a velocity - jump process , and proliferating thanks to a reaction term of monostable type . the scattering operator is supposed to satisfy a maximum principle . when the velocity space is bounded , we show , under suitable hypotheses , that the phase converges towards the viscosity solution of some constrained hamilton - jacobi equation which effective hamiltonian is obtained solving a suitable eigenvalue problem in the velocity space . in the case of unbounded velocities , the non - solvability of the spectral problem can lead to different behavior . in particular , a front acceleration phenomena can occur . nevertheless , we expect that when the spectral problem is solvable one can extend the convergence result . * key - words : * kinetic equations , front propagation , hyperbolic limit , hopf - cole transformation , spectral problem , geometric optics approximation . + * ams class . no : * 35q92 , 45k05 , 35c07

in this paper , we aim to study propagation phenomena in some kinetic models . the main motivation for this work comes from the study of pulse waves in bacterial colonies of _ escherichia coli_. kinetic models have been proposed to describe the run - and - tumble motion of individual bacteria at the mesoscopic scale . it has been shown recently that these kinetic models are much more accurate than their diffusion approximations , see @xcite and the references therein for details . in this work , and contrary to works on chemotaxis models , we focus on propagation driven by growth effects ( _ la _ fisher - kpp ) . this is one major difference between the initial motivation and this paper . we consider a population of cells which is described by a probability density @xmath0 on @xmath1 , where @xmath2 denotes the velocity space , which is a symmetric subset of @xmath3 . we assume that the velocity of cells changes randomly following a velocity - jump process given by some operator @xmath4 analogous to the scattering operator in radiative transfer theory . we model the cell division with a kinetic nonlinearity of monostable type . our kinetic model reads @xmath5 where @xmath6 stands for a _ growth parameter _ and @xmath7 is the macroscopic density in position @xmath8 at time @xmath9 . the _ linear _ operator @xmath10 acting only on the velocity variable describes the tumbling in the velocity space and is _ mass preserving _ , that is @xmath11 we assume that @xmath12 , where the distribution @xmath13 is assumed to be nonnegative and satisfies @xmath14 we note that @xmath15 and @xmath16 are thus stationary solutions of . a first attempt to understand the long time behavior of kinetic equations such as is to perform scaling limits . due to the unbiased velocity jump process contained in our model , the diffusive limit seems particularly relevant at first glance . this issue has been particularly studied in the particular case of a bgk equation without any growth term ( see @xcite and the references therein ) . as a corollary , the fisher - kpp equation can be obtained as a parabolic limit of when @xmath17 . the long time behavior of this latter parabolic equation is now well understood since the pioneering works of kolmogorov - petrovskii - piskunov @xcite and aronson - weinberger @xcite . for nonincreasing inital data with sufficiently fast decay at infinity , the solution behaves asymptotically as a travelling front . it is thus natural to study propagation phenomena for kinetic equations such as . let us emphasize that travelling wave solutions for kinetic equations raised a lot of interest recently . caflisch and nicolaenko construct weak shock profiles solutions of the boltzmann equation using a micro - macro decomposition @xcite . liu and yu s main result in @xcite is the establishment of the positivity of shock profiles for the boltzmann equation . in @xcite , a compactness argument as in @xcite also proves existence and positivity of big waves for a nonlinear bgk equation . the caflisch and nicolaenko micro - macro decomposition has been used to construct waves in a parabolic regime for a particular version of for the fisher - kpp equation @xcite . in @xcite , travelling waves have been constructed in the full kinetic regime . golse @xcite uses compactness properties to prove existence of big waves for the kinetic perthame - tadmor model . an important technique to derive the propagating behavior in reaction - diffusion equations is to revisit the schrdinger wkb expansion to study hyperbolic limits @xcite . let us quickly present this approach on the standard fisher - kpp equation , as it contains all the heuristic ideas needed to understand the present work . this equation reads @xmath18 where here @xmath8 is the _ space _ variable , and @xmath19 are positive parameters . in the hyperbolic limit @xmath20 , we make the so - called _ wkb ansatz _ : @xmath21 so that the _ phase _ @xmath22 is nonnegative and satisfies the following viscous hamilton - jacobi equation @xmath23 the theory of viscosity solutions concerns the locally uniform convergence of @xmath22 towards @xmath24 , the viscosity solution of the following so - called _ variational hamilton - jacobi equation _ @xmath25 one can find rigorous justifications in @xcite and complements in @xcite . this limit phase contains all the information we need to understand the propagating behavior . more precisely , it is possible to prove @xcite that in the hyperbolic limit @xmath26 , the population is contained in the nullset of the phase @xmath24 . the main interests of this technique is that @xmath22 can be expected to be more uniformly regular than @xmath27 , and that the full theory of hamilton - jacobi equations and lagrangian dynamics can be used to understand the limit equation . as an example , studying the nullset of @xmath24 , we recover the propagation at the minimal speed @xmath28 for the previous fisher - kpp equation . this fruitful wkb technique has also much been used to describe the evolution of dominant phenotypical traits in a given population ( see @xcite and the references therein ) and also to describe propagation in reaction - diffusion models of kinetic types @xcite . in @xcite , the authors have proposed a preliminary work on a bgk equation which combines hamilton - jacobi equations and kinetic equations to perform the wkb approach . this latter work shows that it is necessary to stay at the kinetic level to understand the large deviation regime ; one misses something while performing the wkb approach on a macroscopic approximation of the bgk equation . in this work , we develop the results announced in @xcite for a wider class of linear kinetic equations . we derive rigorously the hydrodynamic limit of in some special situations given by the hypothesis below . unless otherwise stated in the sequel , we suppose that @xmath4 takes the form : @xmath29 where @xmath30 and @xmath31 is a linear operator that satisfies some structural assumptions that we specify below . the examples of such operators to keep in mind are the following our analysis is able to cover local and non - local situations : 1 . elliptic operators with neumann boundary conditions on @xmath32 , _ e.g. _ the laplacian : @xmath33 , @xmath34 . kernel operators : @xmath35 and @xmath36 , where @xmath37 is a nonnegative kernel @xmath38 . as for the fisher - kpp equation , we perform the hyperbolic scaling @xmath39 in . note that at this moment we do not rescale the velocity variable . by analogy with , our _ kinetic wkb ansatz _ writes @xmath40 we assume that initially @xmath41 as a consequence , thanks to the maximum principle of hypothesis ( h1 ) below , the phase @xmath22 is well defined and remains nonnegative for all times . plugging in , one obtains the following equation for @xmath22 : @xmath42 to perform the limiting equation , we would rather define the operator @xmath43 and the associated decomposition @xmath44 we can now transform on the following form @xmath45 this formulation is the kinetic equivalent of what was for the fisher - kpp case . we shall assume that for all @xmath46 , there exists a unique solution @xmath47 of the cauchy problem associated to given some initial condition @xmath48 . we stress out that if boundary conditions are needed in the velocity variable , they are implicitly contained in the definition of the operator @xmath49 . we now formulate our convergence results . for this purpose , let us specify the assumptions on the different operators involved and on the velocity set @xmath2 . * [ h0 ] the velocity set @xmath50 is * _ bounded_*. + this hypothesis is very helpful to prove theorem [ hjlimit ] and will be discussed and extended in section [ extensions ] . * [ h1 ] the operator @xmath31 satisfies a _ * maximum principle * _ , which will be used in the following way in the sequel : + suppose that @xmath51 is nonnegative and that @xmath52 attains a maximum in @xmath53 . then @xmath54 this first hypothesis is rather standard and strong but nevertheless crucial in viscosity solution procedures . it is structural and not technical . it is also helpful for space and time lipschitz estimates , see section [ estimates ] . to facilitate lipschitz estimates in velocity , we will assume a maximum principle for the differentiated operator in velocity . indeed , in light of the wkb ansatz , let us assume the following * there exists @xmath55 , an operator satisfying ( h1 ) with @xmath56 and @xmath57 a bounded function such that , @xmath58 this hypothesis holds for our typical examples , see the dedicated section [ estimates ] below . let us specify hypothesis ( h2 ) on our typical examples . for a kernel operator of the form @xmath59 then @xmath60 as a consequence , we have @xmath61 dv ' , \qquad \mathfrak{u}^{\varepsilon}= - \frac{1}{{\varepsilon } } \vert \nabla_v \varphi^{\varepsilon}\vert \int_v \psi(v , v ' ) \left [ e^ { \frac{\varphi^{\varepsilon}(v ) - \varphi^{\varepsilon}(v')}{{\varepsilon } } } \right ] dv'.\ ] ] hypothesis ( h2 ) is satisfied after proposition [ estimate ] ( i ) , ( ii ) , ( iii ) . now we come to elliptic operators . as an example , let us consider @xmath62 with neumann boundary conditions on @xmath32 . the diffusivity matrix @xmath63 is here assumed to be positive definite . then the hypothesis ( h1 ) and ( h2 ) are well satisfied , with @xmath64 we finally need to state a structural hypothesis on @xmath65 in order to characterize the behavior with respect to @xmath66 in the limit . roughly speaking , we need coercivity . * there exists a linear operator @xmath67 which satisfies the maximum principle of hypothesis ( h1 ) , a continuous and nonnegative hamiltonian @xmath68 such that every viscosity solution of @xmath69 is constant , and @xmath70 , such that the following inequality holds true @xmath71 for a kernel operator , one has @xmath72 for the laplacian equation , one has @xmath73 and @xmath74 . let us now state our kinetic convergence result in the theorem [ hjlimit ] below . the main difficulty in the kinetic framework is to understand what to do with the velocity variable in the limit @xmath26 . roughly speaking , we will show that up to extraction , @xmath22 converges towards a viscosity solution of an hamilton - jacobi equation , whose effective hamiltonian is obtained through an eigenvalue problem in the velocity variable that we write in ( h4 ) below . in fact , the limiting phase @xmath24 will be independent from the velocity variable , but the kinetic nature of the @xmath75-problem is contained in this following spectral problem . we notice finally that , the roles of the velocity variable @xmath66 and the spectral problem in ( h4 ) below are respectively similar to the ones of the fast variable and the cell problem in homogenization theory . + * * _ spectral problem._*[evpb ] for all @xmath76 , there exists a unique @xmath77 such that there exists a positive normalized eigenvector @xmath78 such that @xmath79 moreover , @xmath80 and @xmath81 are smooth functions of @xmath82 . section [ evpb ] is devoted to giving relevant conditions on the operator @xmath83 which ensure that has a solution . we also provide there some classical examples . we are now ready to state the main result : * * [ hjlimit ] let @xmath2 be a symmetric subset of @xmath84 satisfying ( h0 ) , @xmath85 be nonnegative and symmetric and @xmath6 . suppose that the initial data is well - prepared , @xmath86 and that the hypotheses ( h1 ) , ( h2 ) , ( h3 ) and ( h4 ) are satisfied . then , @xmath87 converges locally uniformly towards @xmath24 , where @xmath24 does not depend on @xmath66 . moreover @xmath24 is the unique viscosity solution of one of the following hamilton - jacobi equations : * if @xmath88 , then @xmath24 solves the standard hamilton - jacobi problem @xmath89 * if @xmath90 , then the limiting equation is the following constrained hamilton - jacobi equation @xmath91 where in both cases @xmath77 is an hamiltonian given by ( h4 ) . we point out that the assumption concerning the non - dependency on @xmath66 of the initial data @xmath92 in theorem [ hjlimit ] is to avoid a boundary layer in @xmath93 when @xmath26 . the result can be easily extended to the case of an initial condition with small velocity perturbations , that is @xmath94 uniformly in @xmath95 . our paper is organized as follows . the following section [ estimates ] proves @xmath96 type estimates on @xmath22 after assuming hypothesis ( h1 ) and ( h2 ) . in section [ hjproof ] , we provide the proof of theorem [ hjlimit ] . we dedicate section [ evpb ] to solving the eigenvalue problem of hypothesis ( h4 ) which gives the hamiltonian @xmath80 in some particular situations . we conclude this first part of results with a section [ asymptotics ] , giving refined asymptotics on @xmath97 , and recalling some elements to study the speed of propagation of the fronts when the constrained hamilton - jacobi equation is derived , following @xcite . the last section [ extensions ] is devoted to discussing the results when the velocity set is unbounded . we put forward the fact that when the spectral problem of hypothesis ( h4 ) is not solvable , a front acceleration can occur . finally , we show two cases for which hypothesis ( h4 ) holds and where we expect the convergence result to be also true in the whole space despite additional difficulties .

furthermore , we now have access to hst imagery to add to radio interferometry . from such observations we can derive fundamental parameters of the central systems , investigate the variation of physical parameters across the resolved nebulae and this review complements that by corradi ( this volume ) which mainly considers the larger scale emission from the ionized nebulae of these objects .

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astro-ph0401469

in this review , i concentrate on describing observations of spatially resolved emission in symbiotic stars at sub - arcsecond scales . in some of the closer objects , the highest resolutions discussed here correspond to linear dimensions similar to the supposed binary separation . a total of 17 stars well accepted as symbiotics are now observed to show sub - arcsecond structure , almost twice the number at the time of the last review in 1987 . furthermore , we now have access to hst imagery to add to radio interferometry . from such observations we can derive fundamental parameters of the central systems , investigate the variation of physical parameters across the resolved nebulae and probe the physical mechanisms of mass loss and interactions between ejecta and the circumstellar medium . suggestions for future work are made and the potential of new facilities in both the radio and optical domains is described . this review complements that by corradi ( this volume ) which mainly considers the larger scale emission from the ionized nebulae of these objects . # 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in

it is now fifteen years since taylor s review of high resolution radio imagery of symbiotic stars was presented at the torun conference ( taylor 1988 ) . in that time , we have not only seen the sensitivity and frequency range of radio interferometers such as the vla and merlin increase , but also , and perhaps more importantly , we have witnessed the advent of the hubble space telescope . the hst has allowed `` routine '' sub - arcsecond imaging in optical wavebands . taking the capabilities of each of these facilities in turn : _ the very large array . _ the vla can operate in 8 frequency bands for continuum work from 0.07 to @xmath0ghz . in its largest configuration ( a - array ) with a baseline of @xmath1 km , it can achieve @xmath2arcsecond resolution . at @xmath3ghz , its rms sensitivity is quoted as 50@xmath4jy / beam in 10 minutes . _ possibly less well known outside the international radio community are the capabilities of the merlin array , centered on jodrell bank . merlin comprises an array of radio telescopes distributed across the uk with a maximum baseline of @xmath5 km . it operates in three main bands at 1.7 , 5 and @xmath6ghz . at the highest of these frequencies , merlin has a resolution of 0.008 arcseconds . it can achieve an rms sensitivity of 50@xmath4jy / beam in a 12 hour track . _ _ the primary instruments that have provided the results discussed in this review are the wide field and planetary camera ( wfpc2 ) and the space telescope imaging spectrograph ( stis ) . both instruments can perform imaging through a range of filters . stis can of course also perform long slit spectroscopy at a range of spectral resolutions . the operating wavelength range of these instruments is approximately 1200 to @xmath7@xmath8 and the spatial resolution of order @xmath9arcseconds . from this , it can be seen that for a `` typical '' symbiotic at a distance of 1kpc , merlin for example can theoretically resolve features with spatial extent @xmath10au , which is only a few times larger than the binary separation in s - types ( and of course , d - types have much larger separations ) . with observations down to these scales , in combination with modeling , and particularly if temporal variations can be monitored , we could potentially answer the following fundamental questions : * what are the orbital parameters ( particularly of d - types ) ? * how is the nebular morphology linked to the parameters and activity of the central system , and can we test competing models of nebular formation ? * are we really seeing jets in some sources , and if so , what is their origin ? * how is circumstellar dust distributed and can we disentangle the true value of interstellar extinction ? * are there additional systematic differences between different sub - types ? it turns out that in some instances we can now make considerable headway on several of these points . however , as shown in the final section , the real breakthroughs will come with the next generation of ground - based facilities now in advanced planning or the early phases of construction .

in this review , i concentrate on describing observations of spatially resolved emission in symbiotic stars at sub - arcsecond scales . in some of the closer objects , a total of 17 stars well accepted as symbiotics are now observed to show sub - arcsecond structure , almost twice the number at the time of the last review in 1987 .

c

astro-ph0401469

in this review , i concentrate on describing observations of spatially resolved emission in symbiotic stars at sub - arcsecond scales . in some of the closer objects , the highest resolutions discussed here correspond to linear dimensions similar to the supposed binary separation . a total of 17 stars well accepted as symbiotics are now observed to show sub - arcsecond structure , almost twice the number at the time of the last review in 1987 . furthermore , we now have access to hst imagery to add to radio interferometry . from such observations we can derive fundamental parameters of the central systems , investigate the variation of physical parameters across the resolved nebulae and probe the physical mechanisms of mass loss and interactions between ejecta and the circumstellar medium . suggestions for future work are made and the potential of new facilities in both the radio and optical domains is described . this review complements that by corradi ( this volume ) which mainly considers the larger scale emission from the ionized nebulae of these objects . # 1_#1 _ # 1_#1 _ = # 1 1.25 in .125 in .25 in

as i hope the above summary of results for individual objects demonstrates , a good deal of progress has been made since the time of the last review to answer some of the major questions posed in the introduction . however , much more work remains . in summary : * observations and modeling of resolved emission at sub - arcsecond scales are consistent with much greater binary separations in d - types compared to s - types . it is suggested that changes in radio morphology may be directly linked to orbital periods , which may be particularly important for our understanding of d - type systems . * we have shown that the nebular morphology can be directly linked to parameters of the central system . however , there is no doubt that we are dealing with a complex and diverse set of phenomena in a relatively heterogeneous class of objects and that the models discussed here are essentially `` first order '' . the observational data set now warrants the application of more detailed and physically realistic models such as those discussed by nussbaumer and kilpio ( this volume ) . * in d - types , the presence of ejection via a jet is well established in r aqr , but more work is needed to establish this beyond doubt in rx pup . similarly , for the s - types , it now appears that the expanding features resolved in the radio in ch cyg are indeed jets whose axis of ejection may be undergoing precession . the non - thermal emission detected in this object ( and in the d - type hm sge ) confirms , amongst other things , the presence of enhanced magnetic fields in extended regions . a central accretion disk may act as the jet collimator whilst the presence of a magnetic white dwarf may explain apparent precession of the jet ejection axis and its occasional one - sidedness , plus being a plausible source of the magnetic field inferred to be swept out in the jets . in z and and ag dra , there may be some evidence for jet ejection from direct imaging , but the evidence is as yet nowhere near as compelling as for ch cyg . as always , we need to be wary of ascribing the word `` jet '' too early to miscellaneous `` blobs '' of emission . * the potential has been demonstrated for probing the distribution of circumstellar dust in a few objects using a combination of radio and narrow - band hst imagery . disentangling interstellar and circumstellar contributions to the visual extinction is obviously of great importance in determination of the most fundamental of parameters , the distance . * as to the final question posed in the introduction , we need a much larger sample of objects to be resolved at sub - arcsecond scales to draw any compelling conclusions about further systematic differences between the sub - types , and hence possibly to derive important additional information on their evolution . however , the advent of new facilities promises that such large samples are less than a decade away . in the near - term , we should continue our radio monitoring program of selected objects ( in particular hm sge , v1016 cyg and ch cyg ) . in the optical , spatially - resolved spectroscopy of circumstellar nebulae with stis on hst shows great potential , but has not been fully exploited . such observations would turn the semi - qualitative initial results from narrow band imaging into more secure , quantitative measures . as already noted , we should also begin to apply more sophisticated models to the full multi - frequency data set . over the next few years , and certainly before another fifteen have passed , a new generation of ground - based optical and radio facilities will be available . in the radio , projects to enhance the performance of both the vla ( evla ) and merlin ( e - merlin ) are now underway . these instruments have the potential to revolutionize the subject . for example , based on the survey of seaquist , krogulec & taylor ( 1993 ) , e - merlin , with up to @xmath83 times the sensitivity of the present array , will be able to detect extended emission in @xmath84 times as many symbiotics as at present , with resolutions as high as @xmath85 m.a.s . around half of these will be s - types ( see www.merlin.ac.uk/e-merlin/ for further details of the e - merlin project ) . in the optical , great strides are being made in the application of adaptive optics on large telescopes . in addition , we have already seen that interferometric arrays such as coast can produce significant results , but at present only on a very limited set of very bright objects such as ch cyg . arrays on better sites , with larger total collecting area and longer baselines have already been , or are in the process of being built ( baldwin & haniff 2001 ) . however , more ambitious than these is the large optical array ( loa ) which is the next generation coast . importantly , the loa would have a relatively large number of moderate aperture telescopes , enabling `` snapshot '' optical imaging of sources in an analogous fashion to the vla in the radio . in its original conception the loa comprises 15 @xmath86 m optical telescopes distributed over an area of @xmath87 m @xmath88 @xmath87 m and operating between 0.6 and 2.4@xmath4 m in wavelength . this gives a resolution equivalent to @xmath89au at @xmath90kpc and the ability to map sources to j , h , k @xmath91 . thus the loa could probe to within the central binaries of s - type symbiotics and follow morphological changes around their binary orbits . although the full loa is unlikely to be built with purely uk funding , it is almost certain that something approaching its capabilities will be built through international collaboration within the next decade . i would like to thank all my collaborators over the years ( particularly my students and postdoc s who end up doing most of the hard work ! ) ; dr john young of mrao , cambridge , for provision of coast results on ch cyg ; dr andy newsam and mr david hyder of the astrophysics research institute for assistance with the figures , and finally the conference organizers for facilitating my attendance at such a splendid meeting .

i focus on new physics effects associated to the scalar sector which are naturally enhanced for the heaviest fermions due to the large hierarchy of the fermion masses . i will discuss two topics within this context : lepton flavour violation in the @xmath0 ( @xmath1 ) sector and violations of lepton universality in tauonic @xmath2 decays . tau lepton , lepton flavour violation , lepton universality

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1410.8125

in this talk i discuss the role of heavy quarks in new physics searches with tau leptons . i focus on new physics effects associated to the scalar sector which are naturally enhanced for the heaviest fermions due to the large hierarchy of the fermion masses . i will discuss two topics within this context : lepton flavour violation in the @xmath0 ( @xmath1 ) sector and violations of lepton universality in tauonic @xmath2 decays . tau lepton , lepton flavour violation , lepton universality

heavy quarks @xmath3 play an important role in many searches for physics beyond the standard model ( sm ) with tau ( @xmath4 ) leptons . i will focus here on the possibility of new physics effects associated to the scalar sector for which a connection between heavy quarks and the tau lepton is established due to their large mass . the discovery of a sm - like higgs boson by the atlas and cms collaborations seems to confirm that a scalar sector is responsible for the breaking of the ew gauge symmetry @xcite . the strong hierarchy of the fermion mass spectrum implies that the sm higgs couplings to light quarks and leptons are very suppressed . the heaviest fermions offer then a unique place where exotic effects associated to the higgs sector can be sizable due to their larger masses . i will discuss two topics within this context : * lepton flavour violating ( lfv ) higgs decays and higgs mediated lfv @xmath4 decays . * violation of lepton universality in @xmath5 decays due to charged scalar contributions at tree level .

in this talk i review the recent progress on the numerical evaluation of the hadronic light - by - light contribution to the anomalous magnetic moment of the muon and i discuss the role of experimental data on the accuracy of its determination . anomalous magnetic moment of the muon , hadronic light - by - light contribution

i

1411.6397

in this talk i review the recent progress on the numerical evaluation of the hadronic light - by - light contribution to the anomalous magnetic moment of the muon and i discuss the role of experimental data on the accuracy of its determination . anomalous magnetic moment of the muon , hadronic light - by - light contribution

the anomalous magnetic moment of the muon @xmath0 is one of the most accurately measured quantities in particle physics , and as such is a very promising signal of new physics if a deviation from its prediction in the standard model is found . the present experimental value for @xmath1 , is given by @xmath2 , as an average of @xmath3 and @xmath4 @xcite . since statistical errors are the largest source of uncertainties , a proposal to measure it again to a precision of @xmath5 has recently been submitted to fnal @xcite and jparc @xcite , using different experimental techniques . at the level of the experimental accuracy , the qed contributions has been completed up to the fifth order @xmath6 , giving the qed contribution @xmath7 @xcite , using the rydberg constant and the ratio @xmath8 as inputs @xcite . also electroweak ( ew ) and hadronic contributions are necessary . the latter represents the main uncertainty in the standard model in terms of the hadronic vacuum polarization ( hvp ) and the hadronic light - by - light scattering ( hlbl ) . the present estimates for qed , hvp , hlbl , and ew corrections are collected in table [ smcont ] . .standard model contributions to @xmath0 . [ cols="^,^,^ " , ] [ t2 ]

in this work , we extend the analysis of brown and york to find the quasilocal energy in a spherical box in the schwarzschild spacetime . we show that although the brown - york expression for the quasilocal energy is correct , one needs to supplement their derivation with an extra set of boundary conditions on the interior end of the spatial hypersurfaces inside the hole in order to obtain it from an action principle . replacing this set of boundary conditions with another set yields the louko - whiting hamiltonian , which corresponds to time - evolution of spatial hypersurfaces in a different foliation of the schwarzschild spacetime .

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gr-qc9702038

in this work , we extend the analysis of brown and york to find the quasilocal energy in a spherical box in the schwarzschild spacetime . quasilocal energy is the value of the hamiltonian that generates unit magnitude proper - time translations on the box orthogonal to the spatial hypersurfaces foliating the schwarzschild spacetime . we call this hamiltonian the brown - york hamiltonian . we find different classes of foliations that correspond to time - evolution by the brown - york hamiltonian . we show that although the brown - york expression for the quasilocal energy is correct , one needs to supplement their derivation with an extra set of boundary conditions on the interior end of the spatial hypersurfaces inside the hole in order to obtain it from an action principle . replacing this set of boundary conditions with another set yields the louko - whiting hamiltonian , which corresponds to time - evolution of spatial hypersurfaces in a different foliation of the schwarzschild spacetime . we argue that in the thermodynamical picture , the brown - york hamiltonian corresponds to the _ internal energy _ whereas the louko - whiting hamiltonian corresponds to the _ helmholtz free energy _ of the system . unlike what has been the usual route to black hole thermodynamics in the past , this observation immediately allows us to obtain the partition function of such a system without resorting to any kind of euclideanization of either the hamiltonian or the action . in the process , we obtain some interesting insights into the geometrical nature of black hole thermodynamics . = 10000 epsf

after more than two decades of investigations , black hole thermodynamics is still one of the most puzzling subjects in theoretical physics . one approach to studying the thermodynamical aspects of a black hole involves considering the evolution of quantum matter fields propagating on a classical ( curved ) background spacetime . this gives rise to the phenomenon of black hole radiation that was discovered by hawking in 1974 @xcite . combining hawking s discovery of black hole radiance with the classical laws of black hole mechanics @xcite , leads to the laws of black hole thermodynamics . the entropy of a black hole obtained from this approach may be interpreted as resulting from averaging over the matter field degrees of freedom lying either inside the black hole @xcite or , equivalently , outside the black hole @xcite , as was first anticipated by bekenstein @xcite even before hawking s discovery . the above approach was further developed in the following years @xcite . a second route to black hole thermodynamics involves using the path - integral approach to quantum gravity to study _ vacuum _ spacetimes ( i.e. , spacetimes without matter fields ) . in this method , the thermodynamical partition function is computed from the propagator in the saddle point approximation @xcite and it leads to the same laws of black hole thermodynamics as obtained by the first method . the second approach was further developed in the following years @xcite . the fact that the laws of black hole thermodynamics can be derived without considering matter fields , suggests that there may be a purely geometrical ( spacetime ) origin of these laws . however , a complete geometrical understanding of black hole thermodynamics is not yet present . in general , a basic understanding of the thermodynamical properties of a system requires a specification of the system s ( dynamical ) degrees of freedom ( d.o.f . ) . obtaining such a specification is a nontrivial matter in quantum gravity . in the path - integral approach one avoids the discussion of the dynamical d.o.f .. there , the dominant contribution to the partition function comes from a saddle point , which is a classical euclidean solution @xcite . calculating the contribution of such a solution to the partition function does not require an identification of what the dynamical d.o.f.s of this solution are . though providing us with an elegant way of getting the laws of black hole thermodynamics , the path - integral approach does not give us the basic ( dynamical ) d.o.f . from which we can have a better geometrical understanding of the origin of black hole thermodynamics . it was only recently that the dynamical geometric d.o.f . for a spherically symmetric vacuum schwarzschild black hole were found @xcite under certain boundary conditions . in particular , by considering general foliations of the complete kruskal extension of the schrawzschild spacetime , kucha @xcite finds a reduced system of _ one _ pair of canonical variables that can be viewed as global geometric d.o.f .. one of these is the schwarzschild mass , while the other one , its conjugate momentum , is the difference between the parametrization times at right and left spatial infinities . using the approach of kucha , recently louko and whiting @xcite ( henceforth referred to as lw ) studied black hole thermodynamics in the hamiltonian formulation . as shown in fig . 2 , they considered a foliation in which the spatial hypersurfaces are restricted to lie in the right exterior region of the kruskal diagram and found the corresponding reduced phase space system . this enabled them to find the unconstrained hamiltonian ( which evolves these spatial hypersurfaces ) and canonically quantize this reduced theory . they then obtain the schrdinger time - evolution operator in terms of the reduced hamiltonian . the partition function @xmath0 is defined as the trace of the euclideanised time - evolution operator @xmath1 , namely , @xmath2 , where the hat denotes a quantum operator . this partition function has the same expression as the one obtained from the path - integral approach and expectedly yields the laws of black hole thermodynamics . in a standard thermodynamical system it is not essential to consider _ euclidean_-time action in order to study the thermodynamics . if @xmath3 is the lorentzian time - independent hamiltonian of the system , then the partition function is defined as @xmath4 where @xmath5 is the inverse temperature of the system in equilibrium . however , in many cases ( especially , in time- independent systems ) the euclidean time - evolution operator turns out to be the same as @xmath6 . nevertheless , there are cases where , as we will see in section [ subsec : lwham ] , the euclidean time - evolution operator is not the same as @xmath7 . this is the case for example in the lw approach , i.e. , @xmath8 , where @xmath9 is the reduced hamiltonian of the quantized lw system . there is a geometrical reason for this inequality and in this work we discuss it in detail . in this paper , we ask if there exists a hamiltonian @xmath3 ( which is associated with certain foliations of the schwarzschild spacetime ) appropriate for finding the partition function of a schwarzschild black hole enclosed inside a finite - sized box using ( [ partition - trace ] ) . such a procedure will not resort to euclideanization . in our quest to obtain the hamiltonian that is appropriate for defining the partition function for ( [ partition - trace ] ) , we also clarify the physical significance of the lw hamiltonian . by doing so we hope to achieve a better understanding of the geometrical origin of the thermodynamical aspects of a black hole spacetime . in a previous work @xcite , brown and york ( henceforth referred to as by ) found a general expression for the quasilocal energy on a timelike two - surface that bounds a spatial three - surface located in a spacetime region that can be decomposed as a product of a spatial three - surface and a real line interval representing time . from this expression they obtained the quasilocal energy inside a spherical box centered at the origin of a four - dimensional spherically symmetric spacetime . they argued that this expression also gives the correct quasilocal energy on a box in the schwarzschild spacetime . in this paper we show that , although their expression for the quasilocal energy on a box in the schwarzschild spacetime is correct , the analysis they use to obtain it requires to be extended when applied to the case of schwarzschild spacetime . in this case , one needs to impose extra boundary conditions at the timelike boundary inside the hole ( see fig . 3 ) . as mentioned above , in principle , one can use the hamiltonian @xmath10 so obtained to evaluate the partition function , @xmath11 . this partition function corresponds to the canonical ensemble and describes the thermodynamics of a system whose volume and temperature are fixed but whose energy content is permitted to vary . such a hamiltonian , @xmath10 would then lead to a description of black hole thermodynamics without any sort of euclideanisation . the only obstacle to this route to the partition function is that the trace can be evaluated only if one knows the density of the energy eigenstates . unfortunately , without knowing what the thermodynamical entropy of the system is , it is not clear how to find this density in terms of the reduced phase - space variables of kucha @xcite . so how can one derive the thermodynamical laws of the schwarzschild black hole using a lorentzian hamiltonian without knowing the density of states ? based on an observation that identifies the thermodynamical roles of the by and the lw hamiltonians we succeed in studying black hole thermodynamics within the hamiltonian formulation but without euclideanization . in section [ sec : thermoconsi ] we describe the thermodynamical roles of the by and the lw hamiltonians . identifying these roles allows us to immediately calculate the partition function and recover the thermodynamical properties of the schwarzschild black hole . in section [ sec : geoconsi ] we study the geometrical significance of these hamiltonians . in particular , we extend the work of brown and york @xcite to find the nature of the spatial slices that are evolved by the by hamiltonian in the full kruskal extension of the schwarzschild spacetime . in section [ geothermo ] we use the observations made in sections [ sec : thermoconsi ] and [ sec : geoconsi ] to ascribe geometrical basis to the thermodynamical parameters of the system , thus gaining insight into the geometrical nature of black hole thermodynamics . we conclude the paper in section [ sec : conclu ] by summarising our results and discussing the connection between the foliation geometry and equilibrium black hole thermodynamics . in appendix a we extend our results to the case of two - dimensional dilatonic black holes . in appendix b we discuss an alternative foliation ( see fig . 4 ) , in which the spatial slices are again evolved by the by hamiltonian @xmath12 . this illustrates the non - uniqueness of the foliation associated with the by hamiltonian . we shall work throughout in `` geometrized - units '' in which @xmath13 .

quasilocal energy is the value of the hamiltonian that generates unit magnitude proper - time translations on the box orthogonal to the spatial hypersurfaces foliating the schwarzschild spacetime . we argue that in the thermodynamical picture , the brown - york hamiltonian corresponds to the _ internal energy _ whereas the louko - whiting hamiltonian corresponds to the _ helmholtz free energy _ of the system .

c

gr-qc9702038

in this work , we extend the analysis of brown and york to find the quasilocal energy in a spherical box in the schwarzschild spacetime . quasilocal energy is the value of the hamiltonian that generates unit magnitude proper - time translations on the box orthogonal to the spatial hypersurfaces foliating the schwarzschild spacetime . we call this hamiltonian the brown - york hamiltonian . we find different classes of foliations that correspond to time - evolution by the brown - york hamiltonian . we show that although the brown - york expression for the quasilocal energy is correct , one needs to supplement their derivation with an extra set of boundary conditions on the interior end of the spatial hypersurfaces inside the hole in order to obtain it from an action principle . replacing this set of boundary conditions with another set yields the louko - whiting hamiltonian , which corresponds to time - evolution of spatial hypersurfaces in a different foliation of the schwarzschild spacetime . we argue that in the thermodynamical picture , the brown - york hamiltonian corresponds to the _ internal energy _ whereas the louko - whiting hamiltonian corresponds to the _ helmholtz free energy _ of the system . unlike what has been the usual route to black hole thermodynamics in the past , this observation immediately allows us to obtain the partition function of such a system without resorting to any kind of euclideanization of either the hamiltonian or the action . in the process , we obtain some interesting insights into the geometrical nature of black hole thermodynamics . = 10000 epsf

in this work our goal was to seek a geometrical basis for the thermodynamical aspects of a black hole . we find that the value of the brown - york hamiltonian can be interpreted as the internal energy of a black hole inside a box . whereas the value of the louko - whiting hamiltonian gives the helmholtz free energy of the system . after finding these thermodynamical roles played by the by and lw hamiltonians , we ask what the geometrical significance of these hamiltonians is . in this regard the geometrical role of the lw hamiltonian was already known . it was recently shown by lw that their hamiltonian evolves spatial hypersurfaces in a special foliation of the kruskal diagram . the characteristic feature of this foliation is that it is limited to only the right exterior region of this spacetime ( see fig . 2 ) and the spatial hypersurfaces are required to converge onto the bifurcation 2-sphere , which acts as their inner boundary ( the box itself being the outer boundary ) . on the other hand , the geometrical significance of the by hamiltonian as applied to the black hole case was not fully known , although it had been argued that its value is the energy of the schwarzschild spacetime region that is enclosed inside a spherical box . in this work we establish the geometric role of the by hamiltonian by showing that it is the generator of time - evolution of spatial hypersurfaces in certain foliations of the schwarzschild spacetime . establishing the thermodynamic connection of the by and lw hamiltonians allowed us to obtain a geometrical interpretation for the equilibrium temperature of a black hole enclosed inside a box , i.e. , as measured by a stationary observer on the box . geometrically , the temperature turns out to be the rate at which the lw spatial hypersurfaces are boosted at the bifurcation 2-sphere . one could however ask what happens if the lw hypersurfaces are evolved at a different rate , i.e. , if the label time @xmath24 is chosen to be boosted with respect to the proper time of a stationary observer on the box . in that case , it can be shown that the by hamiltonian and the rate at which the lw hypersurfaces are evolved at the bifurcation 2-sphere get `` blue - shifted '' by the appropriate boost - factor . on the other hand , the entropy of the system can still be interpreted as the change in free energy per unit change in the temperature of the system .

in this work we include electron - electron interaction beyond hartree - fock level in our non - equilibrium green s function approach by a crude form of gw through the single plasmon pole approximation . this is achieved by treating all conduction band electrons as a single effective band screening the coulomb potential .

i

1602.03997

in this work we include electron - electron interaction beyond hartree - fock level in our non - equilibrium green s function approach by a crude form of gw through the single plasmon pole approximation . this is achieved by treating all conduction band electrons as a single effective band screening the coulomb potential . we describe the corresponding self - energies in this scheme for a multi - subband system . in order to apply the formalism to heterostructures we discuss the screening and plasmon dispersion in both 2d and 3d systems . results are shown for a four well quantum cascade laser with different doping concentration where comparisons to experimental findings can be made . + _ accepted for publication in * journal of physics : conference series * by iop publishing ltd . , as a proceeding of the pngf6 workshop in lund , sweden , 2015 .

since the quantum cascade laser ( qcl ) was introduced more than 20 years ago @xcite it has continuously been improved and redesigned to operate from the mid - infrared all the way down to the terahertz ( thz ) range . compact laser sources at these wavelengths are valuable for spectroscopic applications @xcite but a major problem is that thz qcls do not operate at room temperature . this can be overcome via difference frequency generation which recently has been demonstrated at powers in the milli - watt range @xcite . direct thz - qcls still generate a lot of interest in the research community due to the promise of higher wall - plug efficiency and the prospects of miniaturization of cryo - coolers . the main temperature degrading mechanism of the thz qcls is currently not fully understood and is still debated by the community @xcite . this is a challenge to theory and there is a great need of realistic modeling tools that are able to treat all important quantum effects on the same footing . a summary of different methods for simulating these structures is found in @xcite . monte carlo simulations have shown that electron - electron interaction , beyond the meanfield or hartree approximation can influence the dynamics of thz qcls @xcite . in this work we include and study the effects of a simple electron - electron scattering via the single plasmon pole approximation ( sppa ) @xcite . in this approximation we capture both the static limit as well as dynamic effects . this gives an energy dependent ( non - local in time ) interaction beyond the hartree - fock approximation . this has been studied in a similar model with promising results @xcite , and with this work we want to adapt the idea into our model described in ref . @xcite . in other methods based on non - equilibrium green s functions ( negf ) and applied to qcls , electron - electron scattering has previously been implemented in a low order @xmath0 approximation employing a purely static screening model @xcite . to simulate the periodic structure of the qcl , we use a product space of plane waves and confined states . the green s function evaluation provides us with the energy resolution of the states , labeled by state and @xmath1 index , at the cost of inverting the self - energy matrices at each @xmath1 and energy grid point . a number of elastic scattering processes as well as longitudinal optical phonon scattering is treated in this formalism at a high computational cost . adding a many - body term fully dependent on the polarization would increase the complexity by one order , a formidable task in this model , leading us to consider simpler schemes as done in this work . this paper is organized as follows : first the theory of the sppa is discussed and we show how it is implemented in the context of our formalism . then the dispersion of the plasmons is discussed as well as the exchange shift . in the last part a test structure is used to evaluate the effect of the inclusion of the new scattering mechanism . finally , we present the conclusions of our study .

the difference in the peak amplitudes disappears with time . at a certain time the two peaks diffuse almost along the entire cyclotron orbit . then tail and head of the diffused wave packet interfere and as a result a completely randomized pattern of the wave packet

r

1310.7749

in this work we study wave packet dynamics and @xmath0 , an oscillatory quantum motion , of heavy holes in iii - v semiconductor quantum wells in presence of a quantizing magnetic field . it is revealed that a gaussian wave - packet describing a heavy hole diffuses asymmetrically along the circular orbit while performing cyclotron motion . the wave packet splits into two peaks with unequal amplitudes after a certain time depending on spin - orbit coupling constant . this unequal splitting of the wave packet is attributed to the cubic rashba interaction for heavy holes . the difference in the peak amplitudes disappears with time . at a certain time the two peaks diffuse almost along the entire cyclotron orbit . then tail and head of the diffused wave packet interfere and as a result a completely randomized pattern of the wave packet is observed . the diffusion rate of the wave packet increases with increase of the spin - orbit interaction strength . also strong spin - orbit coupling expedite the splitting and the randomization of the wave packet . we also study the @xmath0 in various physical observables such as position , charge current and spin angular momentum of the heavy hole . the @xmath0 oscillations are very much sensitive to the initial wave vector of the gaussian wave packet and the strength of the rashba spin - orbit coupling .

in this section we shall visualize and discuss how the spatial distribution of probability density for the heavy holes changes with time . we shall also discuss the time dependencies of the expectation values of the position , current and spin operators and their various consequences . for numerical calculations , we adopt the material parameters appropriate for gaas quantum wells . we took @xmath107 with @xmath108 as the free electron mass , @xmath109 m@xmath110 and @xmath111 t. it was reported that the value of the effective lande g - factor for heavy hole is highly anisotropic@xcite , we take its value @xmath112 for gaas system . the magnitude of rashba strength ( @xmath25 ) depends explicitly on the external parameters@xcite like electric field , detail of confinement and hence can be tuned experimentally . so in this study , we take various values of @xmath25 in such a way that the corresponding length scale @xmath113 is of the order of few angstroms . in fig . ( 1 ) we show the time - evolution of the probability density @xmath114 + @xmath115 of the heavy hole . to do this we numerically evaluate the components of the wave packet @xmath116 and @xmath117 at a later time @xmath66 as described by eqs . ( [ wavefn1 ] ) and ( [ wavefn2 ] ) . the infinite series in eqs . ( [ wavefn1 ] ) and ( [ wavefn2 ] ) converge approximately when @xmath118 for @xmath119 . however the convergence of these infinite series also depends on the value of @xmath120 . for larger @xmath120 larger @xmath121 is required . we have checked that @xmath122 is appropriate for the convergence when @xmath123 . 1(a)-1(i ) are plotted for @xmath124 and @xmath125 , respectively . initially the wave packet is situated at the origin . we know that in a perpendicular magnetic field a charge particle ( without soi ) moves in a cyclotron orbit with time period @xmath126 . the radius of this circular orbit is @xmath127 . the presence of soi modifies @xmath128 and @xmath129 marginally . in presence of the rsoi the hole wave packet starts to diffuse asymmetrically around the cyclotron orbit while making circular motion as time goes on . the diffused wave packet is making circular motion with time period @xmath130 and radius @xmath131 . at @xmath132 [ fig 1(c ) ] the hole wave packet splits into two unequal peaks which are rotating with different velocities along the cyclotron orbit . the difference in the peak amplitudes nearly vanishes around @xmath133 [ fig . 1(f ) ] . at the same time , the wave packet diffuses almost along the entire cyclotron orbit . now the interference effect begins to occur between the tail and head of the diffused wave packet and as a result a completely randomized pattern of hole wave packet is observed after some more cycles as shown in fig . 1(i ) . recalling the case of two - dimensional electron system ( 2des ) with linear rsoi in a perpendicular magnetic field where this kind of splitting of wave packet occurs around @xmath134@xcite for @xmath135 t. but in the present case of 2dhs this splitting occurs at much lesser time than the 2des case . moreover , the wave - packet does not diffuse along the circular orbit in the case of 2des with linear rashba term . these features can be attributed to the cubic rashba term in the 2dhs . , ( b ) @xmath136 , ( c ) @xmath132 , ( d ) @xmath137 , ( e ) @xmath138 , ( f ) @xmath133 , ( g ) @xmath139 , ( h ) @xmath140 , and ( i ) @xmath141 . in this case @xmath25 is fixed in such a way that @xmath142 nm . in each plot the color bar represents the dimensionless parameter @xmath143.,width=415 ] for different values of @xmath144 namely ( a ) @xmath142 nm , ( b ) @xmath145 nm , ( c ) @xmath146 nm , and ( d ) @xmath147 nm . in this case magnetic field and the initial wave vector are fixed to @xmath111 t and @xmath119 . in each plot the color bar represents the dimensionless parameter @xmath143.,width=453 ] in fig . 2 spatial distribution of probability density at time @xmath132 is shown . different panels are plotted for different values of @xmath25 such that @xmath142 nm , @xmath148 nm , @xmath149 nm , and @xmath150 nm . it is clear that as @xmath25 increases the wave packet diffuses very fast and covers the entire cyclotron orbit . the diffusion rate of the wave packet increases with increase of the spin - orbit strength . also strong @xmath25 helps to expedite the splitting and the randomization of the hole wave packet . , ( b ) @xmath151 , ( c ) @xmath152 , and ( d ) @xmath153 . here in each panel solid and dashed lines correspond to @xmath154 and @xmath155 , respectively . here @xmath156 is defined as @xmath157.,width=434 ] , ( b ) @xmath151 , ( c ) @xmath152 , and ( d ) @xmath153 . here in each panel dotted , solid and dashed lines correspond to @xmath142 , @xmath158 , and @xmath159 nm , respectively . here we define @xmath157.,width=415 ] in fig . 3 we plot the average values of the position and current operators in @xmath72 and @xmath91 directions as a function of time @xmath66 for a fixed value of magnetic field @xmath111 t and fixed @xmath25 such that @xmath142 nm . here , we define the current operators as @xmath160 with @xmath161 , @xmath91 . in this case we consider two different values of initial wave vector @xmath154 ( solid line ) and @xmath119 ( dashed line ) . when @xmath154 , oscillations appearing in @xmath162 and @xmath163 are persistent in time . but in the case of higher @xmath120 , the amplitude of zb decreases at later time which shows some kind of localization of zb oscillations . this is because higher landau levels are involving for higher values of @xmath120 . comparing figs . 3(a ) and 3(b ) we mention that @xmath164 is oscillating about zero for both values of @xmath120 whereas @xmath151 is oscillatory but always positive because eq . ( [ posy ] ) contains a constant term . there is also a definite phase difference between @xmath165 and @xmath166 and @xmath167 and @xmath168 as clearly shown in fig . 3 . investigating all the graphs in fig . ( 3 ) one can conclude that although initially there is no phase difference but an increment in @xmath120 introduces a phase difference at later times . figure 4 describes the time dependence of position and current operators for a fixed magnetic field @xmath111 t and @xmath119 . different values of @xmath25 such that @xmath142 nm ( dotted ) , @xmath158 nm ( solid ) , and @xmath159 nm ( dashed ) have been considered . it can be seen from fig . 4 that the amplitude of zb oscillation decreases as @xmath25 increases . one interesting point is to be mentioned here that at stronger @xmath25 ( @xmath169 nm ) the zb oscillations start to reappear at large time . and @xmath91 components of the spin operator : ( a ) @xmath154 , ( b ) @xmath119 , and ( c ) @xmath123 . here in each panel solid and dashed lines represent @xmath170 and @xmath171 , respectively which are plotted in units of @xmath172.,width=415 ] component of spin operator : ( a ) @xmath173 , ( b ) @xmath154 , ( c ) @xmath119 , and ( d ) @xmath123 . here in each panel @xmath174 is plotted in units of @xmath172.,width=415 ] the time - dependent average values of the spin components are shown in fig . 5 and 6 . we consider various cases corresponding to the different values of the initial wave vector , namely @xmath173 , @xmath175 , @xmath155 and @xmath176 as mentioned in both figures . figure 5 describes the variations of @xmath170 and @xmath171 with time @xmath66 for different values of @xmath120 . it can be seen that @xmath170 and @xmath171 maintains same oscillatory pattern apart from a definite phase difference . an increase in @xmath120 results a change in the oscillatory pattern significantly . the amplitude of the zb oscillations , appearing in @xmath170 and @xmath171 increases as @xmath120 increases . we have shown the time dependence of @xmath174 in fig . it should be noted that @xmath174 does not vanish when there is no initial momentum i.e. @xmath173 . this fact can be confirmed from eq . ( [ spinz ] ) which contains a non - zero term @xmath177 . as @xmath120 increases the oscillatory pattern of @xmath174 changes abruptly . when @xmath154 a beating - like pattern appears in the oscillations of @xmath174 . from fig 6(b ) , ( c ) , ( d ) it can be seen that the number of oscillations before the first beating node decreases drastically as @xmath120 increases . this complicated oscillatory pattern can be attributed to the fact that the infinite series in eqs . ( [ spinx]-[spinz ] ) converges for higher values of @xmath121 as @xmath120 increases . as a result more and more frequencies appear in the oscillations because of the involvement of higher landau levels . comparing fig . 5 and 6 at @xmath178 @xmath179 where as @xmath180 and this is consistent with the fact that the initial wave packet is polarized along the @xmath69-direction . the jittery motion in @xmath181 induces jittery motion in @xmath182 and @xmath183 .

in this work we study wave packet dynamics and @xmath0 , an oscillatory quantum motion , of heavy holes in iii - v semiconductor quantum wells in presence of a quantizing magnetic field . the wave packet splits into two peaks with unequal amplitudes after a certain time depending on spin - orbit coupling constant . the diffusion rate of the wave packet increases with increase of the spin - orbit interaction strength . also strong spin - orbit coupling expedite the splitting and the randomization of the wave packet . we also study the @xmath0 in various physical observables such as position , charge current and spin angular momentum of the heavy hole . the @xmath0 oscillations are very much sensitive to the initial wave vector of the gaussian wave packet and the strength of the rashba spin - orbit coupling .

i

1310.7749

in this work we study wave packet dynamics and @xmath0 , an oscillatory quantum motion , of heavy holes in iii - v semiconductor quantum wells in presence of a quantizing magnetic field . it is revealed that a gaussian wave - packet describing a heavy hole diffuses asymmetrically along the circular orbit while performing cyclotron motion . the wave packet splits into two peaks with unequal amplitudes after a certain time depending on spin - orbit coupling constant . this unequal splitting of the wave packet is attributed to the cubic rashba interaction for heavy holes . the difference in the peak amplitudes disappears with time . at a certain time the two peaks diffuse almost along the entire cyclotron orbit . then tail and head of the diffused wave packet interfere and as a result a completely randomized pattern of the wave packet is observed . the diffusion rate of the wave packet increases with increase of the spin - orbit interaction strength . also strong spin - orbit coupling expedite the splitting and the randomization of the wave packet . we also study the @xmath0 in various physical observables such as position , charge current and spin angular momentum of the heavy hole . the @xmath0 oscillations are very much sensitive to the initial wave vector of the gaussian wave packet and the strength of the rashba spin - orbit coupling .

in summary , we have studied wave packet propagation and @xmath0 of a heavy hole in iii - v semiconductor quantum wells . we have visualized and discussed various consequences of the time - evolution of the hole wave packet along the cyclotron orbit . the hole wave packet diffuses asymmetrically along the circular orbit while making cyclotron motion . it is shown that the hole wave packet splits into two peaks with unequal amplitudes at certain time which depends on the spin - orbit interaction strength . the two peaks rotate with different frequencies . the amplitude of the two peaks become nearly equal as time goes on . after many cycles , tail and head of the diffused wave packet interfere with each other and produces a complete randomized pattern . the diffusion rate of the wave packet increases with increase of the spin - orbit interaction strength . also strong spin - orbit coupling expedite the splitting and the randomization of the wave packet . our results for the hole is compared with an electron in a linear rashba system in presence of the magnetic field . we have also studied zb phenomenon in position , current and spin angular momentum of the heavy hole . the @xmath0 oscillations are very much sensitive to the initial momentum of the wave packet and the rashba spin - orbit coupling constant .

institute of solid state chemistry , ural branch of the russian academy of sciences , 620219 , ekaterinburg , russia + electronic band structure of boron - rich low - temperature superconductors ub@xmath0-like dodecaboride yb@xmath0 and cab@xmath1-like hexaboride yb@xmath1 are investigated using the first - principle flmto calculations and compared with one for layered yb@xmath2 and the new `` medium - t@xmath3 '' superconductor mgb@xmath2 diborides .

i

cond-mat0202015

institute of solid state chemistry , ural branch of the russian academy of sciences , 620219 , ekaterinburg , russia + electronic band structure of boron - rich low - temperature superconductors ub@xmath0-like dodecaboride yb@xmath0 and cab@xmath1-like hexaboride yb@xmath1 are investigated using the first - principle flmto calculations and compared with one for layered yb@xmath2 and the new `` medium - t@xmath3 '' superconductor mgb@xmath2 diborides . + pacs : 71.15.la , 74.25.jb + keywords : electronic band structure , superconductors , hexaboride , dodecaboride .

the discovery of the superconductivity in mgb@xmath2 ( t@xmath4 @xmath5 40 k ) @xcite and creation of promising materials based thereon ( in the form of single crystals , ceramics , thin films , tapes and wires , see reviews @xcite have attracted a great deal of interest in superconducting properties of other boron - containing phases . + comparison between different classes of binary ( semi-(m@xmath2b ) , mono-(mb ) , di- ( mb@xmath2 ) , tetra-(mb@xmath6 ) ) and some highest borides ( hexa-(mb@xmath1 ) , dodeca-(mb@xmath0 ) and mb@xmath7-like borides ) , ternary and quaternary borides ( review @xcite ) shows that the majority of known superconductors ( sc ) are found among low - boron - containing compounds ( b / m @xmath8 2 - 2.5 ) , in which b atoms are in the form of isolated groups ( atoms ) or planar sublattices ( boron sheets ) . the superconducting state is far less typical of highest borides ( b / m @xmath9 6 ) having a structure made up of stable polyhedra of boron atoms ( octahedra b@xmath1 ( mb@xmath1 ) , icosahedra b@xmath0 ( mb@xmath0 ) or their combination ( mb@xmath7 ) ) . among a large number of these boron - rich phases , the low - temperature superconductivity was observed only for eight compounds : mb@xmath1 ( m = y , la , th , nd ) and mb@xmath0 ( m = sc , y , zr , lu ) @xcite . + it is significant that ( i ) lower borides of these metals , in particular sc and y diborides , are not sc , and ( ii ) the stable polymorphy of the elemental boron ( @xmath10 -b@xmath0 , @xmath11-b@xmath12 ) , which under equilibrium conditions contain the boron polyhedra ( icosahedra or `` gigantic '' icosahedra b@xmath13 ) as structural elements , are semiconductors [ 4 - 8 ] . only recently it was found that polycrystalline boron ( rombohedral -b@xmath12 ) transforms from a semiconductor to a superconductor ( t@xmath3 @xmath5 11.2 k ) at about 250 gpa @xcite . in this work we calculate the electronic band structures of low - temperature scs - boron - rich phases yb@xmath0 and yb@xmath1 - and compare them with two representatives of layered alb@xmath2-type diborides , namely the non - superconducting yb@xmath2 and new `` medium - t@xmath3 '' sc mgb@xmath2 . the results obtained are analyzed in terms of ( i ) electronic bands , ( ii ) density of states ( dos ) and ( iii ) site - projected l - decomposed dos near the fermi energy ( e@xmath14 ) of these borides . the fermi surfaces for yb@xmath2 and mgb@xmath2 are also presented .

it has been hypothesized recently that core collapse supernovae are triggered by mildly relativistic jets following observations of radio properties of these explosions . association of a jet , similar to a gamma - ray burst jet but only slower , allows shock acceleration of particles to high energy and non - thermal neutrino emission from a supernova . the detection prospect of these neutrinos in water or ice detector is also discussed in this brief review . jetted core collapse supernovae in nearby galaxies may provide the strongest high energy neutrino signal from point sources .

i

astro-ph0509729

it has been hypothesized recently that core collapse supernovae are triggered by mildly relativistic jets following observations of radio properties of these explosions . association of a jet , similar to a gamma - ray burst jet but only slower , allows shock acceleration of particles to high energy and non - thermal neutrino emission from a supernova . detection of these high energy neutrinos in upcoming kilometer scale cherenkov detectors may be the only direct way to probe inside these astrophysical phenomena as electromagnetic radiation is thermal and contains little information . calculation of high energy neutrino signal from a simple and slow jet model buried inside the pre - supernova star is reviewed here . the detection prospect of these neutrinos in water or ice detector is also discussed in this brief review . jetted core collapse supernovae in nearby galaxies may provide the strongest high energy neutrino signal from point sources .

core collapse of massive stars which lead to supernovae ( sne ) of type ib , c and ii are in some cases associated with long duration ( @xmath0-@xmath1 s ) gamma - ray bursts ( grbs ) , as evidenced by observed correlations of grb 980425/sn 1998bw , grb 021211/sn 2002lt , grb 030329/sn 2003dh and grb 0131203/sn 2003lw.@xcite a relativistic jet with bulk lorentz factor @xmath2 , powered by a black hole and an accretion disc which form after the core collapse in the most likely scenario , is believed to lead to the grb event.@xcite observational evidence of only a small fraction of detected sne associated with grbs hints that the frequency of highly relativistic jets in core collapse sne is at best 1 in 1000 , roughly the ratio of grb to sn rates.@xcite however , a significantly larger fraction ( @xmath3 of type ib / c rate@xcite ) of sne ( also called _ hypernovae _ ) may have mildly relativistic jets associated with them.@xcite one or more of the following observations support the jetted sn hypothesis : high expansion velocity ( 30 - 40 @xmath4 km / s ) first observed in sn 1998bw.@xcite radio afterglow not associated with @xmath5-ray emission.@xcite asymmetric explosion supported by polarimetry observations of sn type ib / c.@xcite numerical simulations of core collapse sne , carried out over the last three decades have failed to produce a successful explosion by a prompt shock wave created due to the collapse of its iron core.@xcite the deposition of bulk kinetic energy in a jet form into the stellar envelope may help disrupt and blow it up making the sn possible.@xcite the presence of a jet is also conducive to shock acceleration of particles . in case of a grb , internal shocks of plasma material along the jet accelerate protons and electrons which radiate observed @xmath5-rays.@xcite high energy protons may escape as cosmic rays and/or produce 100 tev neutrinos by interacting with @xmath5-rays _ in situ_.@xcite while the grb jet is making its way out of the collapsing stellar progenitor it is expected to produce 10 tev neutrio precursor burst.@xcite these neutrinos are emitted even in the cases when the jets do not manage to burrow through the stellar envelope and choke inside without producing observable @xmath5-rays . the jets in core collapse sne or hypernovae which is the topic of this review are slow with @xmath6 few and choke inside the stellar envelope.@xcite neutrinos produce from such jets are typically of a hundred gev to tev energy.@xcite as opposed to 10 mev thermal neutrinos produced by the core collapse sn shocks which have been detected from sn 1987a in our own galaxy,@xcite high energy neutrinos from the jets may be detected from a longer distance because of an increasing detection prospect with neutrino energy . kilometer scale ice and water cherenkov detectors such as icecube@xcite and antares@xcite which are currently being built in antarctica and in the mediterranean will have an excellent chance to detect these neutrinos from sne within the nearest 20 mpc . the organization of this brief review is as follows : in sec . [ sec : core - collapse ] a basic core collapse sn picture is outlined and a particular slow jet model in sec . [ sec : jet - model ] . shock acceleration and the maximum energy reachable by protons are discussed in sec . [ sec : proton - acc ] . neutrino flux on earth from a point source and diffuse sources is calculated in sec . [ sec : nu - flux ] and their detection prospects in sec . [ sec : events ] . conclusions are given in sec . [ sec : summary ] .

detection of these high energy neutrinos in upcoming kilometer scale cherenkov detectors may be the only direct way to probe inside these astrophysical phenomena as electromagnetic radiation is thermal and contains little information . calculation of high energy neutrino signal from a simple and slow jet model buried inside the pre - supernova star is reviewed here .

c

astro-ph0509729

it has been hypothesized recently that core collapse supernovae are triggered by mildly relativistic jets following observations of radio properties of these explosions . association of a jet , similar to a gamma - ray burst jet but only slower , allows shock acceleration of particles to high energy and non - thermal neutrino emission from a supernova . detection of these high energy neutrinos in upcoming kilometer scale cherenkov detectors may be the only direct way to probe inside these astrophysical phenomena as electromagnetic radiation is thermal and contains little information . calculation of high energy neutrino signal from a simple and slow jet model buried inside the pre - supernova star is reviewed here . the detection prospect of these neutrinos in water or ice detector is also discussed in this brief review . jetted core collapse supernovae in nearby galaxies may provide the strongest high energy neutrino signal from point sources .

while a core collapse sn in a typical galaxy is a rare event , their rate of occurence within 20 mpc could be more than 1/yr , and the physics and astrophysics one can learn from such an explosion is enormous . a buried slow jet from the collapsing core of the supernova progenitor star is an attractive possibility for solving the long standing problem of how to understand the ejection of the envelope in sn explosions , by re - energizing the shock wave through energy deposition by the jet . alternatively it could be that only a fraction of core collapses leads to such jets . these hypothetical mildly relativistic jets in sne may be related to the ultra relativistic jets thought to be responsible for long duration grbs , which are thought to originate from the core collapse of massive progenitor stars , some of which have been positively associated with observed envelope ejection supernova events . while all typical core collapses should produce 10 mev thermal neutrinos , the presence of a jet would allow proton acceleration by shocks , and produce 1 tev non - thermal neutrinos . detection of these high energy neutrinos by upcoming cherenkov detectors would be a smoking gun signal of a sn jet , and would allow one to study the conditions inside a collapsing star which may not be possible otherwise .

it is demonstrated that measurements of positions of atoms scattered from a quasi - condensate in a raman process provide information on the temperature of the parent cloud . in particular , the widths of the density and second order correlation functions are sensitive to the phase fluctuations induced by non - zero temperature of the quasi - condensate .

c

1203.0894

it is demonstrated that measurements of positions of atoms scattered from a quasi - condensate in a raman process provide information on the temperature of the parent cloud . in particular , the widths of the density and second order correlation functions are sensitive to the phase fluctuations induced by non - zero temperature of the quasi - condensate . it is also shown how these widths evolve during expansion of the cloud of scattered atoms . these results are useful for planning future raman scattering experiments and indicate the degree of spatial resolution of atom - position measurements necessary to detect the temperature dependence of the quasi - condensate .

we have analyzed in detail the properties of the field of atoms scattered out of a quasi - condensate in the raman process . we have demonstrated that the density of scattered atoms , when measured in the far - field regime , strongly depends on the temperature of the quasi - condensate . however , this dependence is much weaker , when the expansion time is finite . furthermore , we have calculated the second order correlation function in both expansion time regimes . in each case , @xmath142 broadens with growing @xmath108 , although in the latter the effect is less pronounced . the presence of the temperature - induced phase fluctuations can be also deduced from the peak height of @xmath142 . while for the pure condensate , @xmath143 , this value can substantially rise at higher @xmath108 . in summary , the measurements of the position of scattered atoms could provide some information on the temperature of the mother quasi - condensate . nevertheless , physical quantities such as the density or the correlation functions do not change drastically in a wide range of temperatures @xmath144\,\mu$]k . if the experiment is aimed at determining the temperature of the quasi - condensate , it requires very high spatial resolution low detection noise and long expansion time . note that in our calculations we have neglected the possible impact of the atomic transition rules on the field of scattered atoms . in the case of particular atomic transitions , due to polarization of the stokes field , some scattering directions are forbidden . we underline , that such effect could be easily taken into account by modifying the coupling function @xmath145 .

it is known that any subharmonic quadrature domain in two dimensions satisfies a natural inner ball condition , in other words there is a specific upper bound on the curvature of the boundary . this result directly applies to free boundaries appearing in obstacle type problems and in hele - shaw flow . in the present paper we make partial progress on the corresponding question in higher dimensions . specifically , we prove the equivalence between several different ways to formulate the inner ball condition , and we compute the brouwer degree for a geometrically important mapping related to the schwarz potential of the boundary . the latter gives in particular a new proof in the two dimensional case .

i

1112.4673

it is known that any subharmonic quadrature domain in two dimensions satisfies a natural inner ball condition , in other words there is a specific upper bound on the curvature of the boundary . this result directly applies to free boundaries appearing in obstacle type problems and in hele - shaw flow . in the present paper we make partial progress on the corresponding question in higher dimensions . specifically , we prove the equivalence between several different ways to formulate the inner ball condition , and we compute the brouwer degree for a geometrically important mapping related to the schwarz potential of the boundary . the latter gives in particular a new proof in the two dimensional case .

in the present paper we study the curvature of a free boundary which comes up in some obstacle type problems , more specifically laplacian growth ( hele - shaw flow moving boundary problem ) , quadrature domains and partial balayage . the final aim of the investigations is to show that the free boundary in question satisfies a certain inner ball condition ( a specific upper bound on the curvature ) . this goal has previously been achieved in the case of two dimensions ( see @xcite and @xcite ; compare also @xcite ) . here we shall give some partial results ( but no complete solution ) in higher dimensions , and in passing also obtain a new proof for the two dimensional case . the geometric property we aim at proving can most easily be stated in terms of quadrature domains for subharmonic functions @xcite . let @xmath0 a positive borel measure with compact support in @xmath1 . a bounded open set @xmath2 is called a _ quadrature open set _ for subharmonic functions with respect to @xmath0 if @xmath3 and @xmath4 for all integrable ( with respect to lebesgue measure @xmath5 ) subharmonic functions @xmath6 in @xmath7 . a quadrature open set which is connected is a _ quadrature domain_. there is a natural process of balayage of measures to a prescribed density ( partial balayage ) by which @xmath7 can be constructed from @xmath0 when it exists , see e.g. @xcite , @xcite , @xcite . this balayage process is also equivalent to solving a certain obstacle problem @xcite . in terms of the difference @xmath8 between the newtonian potentials of @xmath0 and @xmath7 , the latter considered as a body of density one , the quadrature property spells out to @xmath9 the function @xmath10 appearing here is sometimes called the modified schwarz potential of @xmath11 , see @xcite for example . what has been proved in two dimensions , and what we like to extend to higher dimension , is that @xmath7 in the above situation can be written as the union of open balls centered in the closed convex hull @xmath12 of @xmath13 : @xmath14 here @xmath15 denotes the radius of the ball at @xmath16 , allowing the possibility @xmath17 , i.e. , that the ball is empty . we refer to ( [ innerball ] ) as @xmath7 satisfying the inner ball property with respect to @xmath12 . for further discussion and motivations in the present context , see @xcite , @xcite . the inner ball property concerns the geometry of @xmath11 outside any closed half - space @xmath18 containing @xmath13 . by a certain `` localization '' procedure the part @xmath19 of @xmath7 which is outside @xmath18 can be shown to be identical with a quadrature open set for some positive measure with support on @xmath20 , see @xcite , @xcite . for this reason it is enough to prove ( [ innerball ] ) in the case that @xmath0 has support in a hyperplane , and by a further localization one may even assume @xmath0 to have a continuous density on it . for convenience we shall take the hyperplane in question to be @xmath21 . it is known ( see @xcite , @xcite ) that given any positive measure with compact support in this hyperplane , which we identify with @xmath22 , there is a uniquely determined quadrature open set , which moreover is symmetric about the hyperplane and is convex in the @xmath23-direction ( i.e. , the intersection with any straight line perpendicular to the hyperplane is connected ) . thus the quadrature open set can be described in terms of a graph of a function @xmath24 defined in an open subset @xmath25 of the hyperplane . it is known from the regularity theory of free boundaries ( see @xcite , @xcite , and in the present context @xcite ) that this function @xmath24 is real analytic . it will be enough to consider the case that @xmath25 is connected , because in the disconnected case the discussions will apply to each component separately . in the paper we shall therefore study the geometry of quadrature domains for a measure with support in the hyperplane @xmath22 , the corresponding modified schwarz potential @xmath10 , and various differential geometric objects derived from it . the paper consists of two main parts . the first part starts with some differential geometric preliminaries ( section [ sec : diffgeom ] ) and ends up with a proof of equivalence of several different formulations of the inner ball condition ( section [ sec : innerball ] ) . this part is analogous to a corresponding part in @xcite , but new difficulties appear in the higher dimensional case . in the second part of the paper , section [ sec : boundaries ] , we develop tools for studying the geometry by means of vector fields and differential forms defined in terms of @xmath10 . to briefly explain , in terms the two dimensional situation , what we do in the second part of the paper , let @xmath26 denote the part of the quadrature domain which lies in the upper half space ( half plane ) and let @xmath27 be the schwarz function ( see @xcite , @xcite ) of @xmath28 . this is in our case given by @xmath29 , it is analytic in @xmath26 , and equals @xmath30 on @xmath28 . what we study in the second part of the paper is the higher dimensional counterpart of the mapping @xmath31 defined by @xmath32 the last member referring to polar coordinates . we also study in higher dimensions that curve @xmath33 which in two dimensions is defined by @xmath34 . in the two dimensional case a proof of the inner ball property can be based on the topological property of @xmath33 that it separates the two domains @xmath35 and @xmath36 from each other , see @xcite . there seems to be no direct counterpart of this kind of proof in higher dimensions . a slightly different proof in two dimensions uses the argument principle for @xmath37 , see corollary [ cor : main ] in the present paper . we have not been able to generalize this proof either to higher dimensions , even though we think that such a proof may not be completely out of reach . at least we have computed the relevant mapping degree of @xmath37 in higher dimensions , and this result , theorem [ thm : main ] , may be considered to be the main result in the second part of the paper . another avenue which we have pursued to some extent is the investigation of the general behaviour of the curve @xmath33 . this curve starts out at the origin and reaches @xmath28 only at points where the largest inner ball centered at the origin touches @xmath28 , see proposition [ prop : gamma ] . if we could establish for example that @xmath33 were a smooth curve ( no branchings ) a proof of the inner ball property would not be far away . thus we hope that the partial results we obtain in this paper will turn out to be useful in forthcoming attempts to prove the inner ball property for quadrature domains , explicitly formulated in conjecture [ conj : main ] .

it has recently been recognized that this process exhibits another type of power law : the moment of the stochastic variable scales as a function of the additive noise strength . we clarify the mechanism for this power - law behavior of moments by treating a simple langevin - type model both approximately and exactly , and argue this mechanism is universal . we also discuss the relevance of our findings to noisy on - off intermittency and to singular spatio - temporal chaos recently observed in systems of non - locally coupled elements .

i

cond-mat9802030

it is well known that a random multiplicative process with weak additive noise generates a power - law probability distribution . it has recently been recognized that this process exhibits another type of power law : the moment of the stochastic variable scales as a function of the additive noise strength . we clarify the mechanism for this power - law behavior of moments by treating a simple langevin - type model both approximately and exactly , and argue this mechanism is universal . we also discuss the relevance of our findings to noisy on - off intermittency and to singular spatio - temporal chaos recently observed in systems of non - locally coupled elements .

power laws are observed in a wide variety of natural phenomena and mathematical models . some examples are the critical behavior near second order phase transitions , kolmogorov s law of fully developed turbulence , size distribution of avalanches in models of self - organized criticality , gutenberg - richter s law of earthquakes , distribution of price fluctuations in economic activities , and zipf s law in linguistics . clarifying the mechanisms for the emergence of these power laws has long been a subject of many challenges . the random multiplicative process ( rmp ) is a well - known mechanism leading to power - law behavior . it is a stochastic process where the stochastic variable is driven by a multiplicative noise . it has been extensively used as a model for a variety of systems such as on - off intermittency @xcite , lasers @xcite , economic activity @xcite , variation of biological populations in fluctuating environment @xcite , and passive scalar field advected by fluid @xcite . in real systems , the stochastic variable may often be driven not only by the multiplicative noise , but also by some weak additive noise . this weak additive noise becomes important when the amplitude of the stochastic variable @xmath0 takes small values , and introduces an effective lower bound of @xmath0 . actually , this lower bound may be crucial , because it guarantees the existence of a stationary probability distribution function ( pdf ) . furthermore , the pdf here has a power - law form over a wide range of @xmath0 @xcite . for example , venkataramani _ et al . _ @xcite introduced a langevin equation with multiplicative and additive noise terms as a model for noisy on - off intermittency . they obtained a stationary pdf with a power - law tail . the same form of langevin equation was treated by takayasu _ et al . _ @xcite as a model for economic activity , and they also showed that the pdf obeys a power law . a similar model was introduced by levy _ et al . _ @xcite : it describes a discrete stochastic process driven by a multiplicative noise . they introduced a lower bound to the stochastic variable explicitly , and showed again that the pdf obeys a power law . et al . _ and takayasu _ et al . _ treated the additive noise explicitly , while the lower bound introduced by levy _ et al . _ plays a role similar to the additive noise . in this paper , we are concerned with this type of stochastic processes . recently , another type of asymptotic power law was found in the above type of stochastic processes . in previous papers @xcite , we introduced a stochastic process in order to explain the power law displayed by the spatial correlation function @xmath1 , i.e. , @xmath2 for small enough @xmath3 , observed in the spatio - temporal chaotic regime of systems with non - locally coupled elements . our explanation was based on a rmp with weak additive noise such as described above . note , however , that the power - law correlation here is not a direct result of the power - law tail of the pdf itself , but it is a result of the asymptotic power law of moments @xmath4 of the stochastic variable @xmath0 as a function of the strength @xmath5 of the additive noise , i.e. , @xmath6 . this gives another mechanism leading to power - law behavior in such stochastic processes . the goal of this paper is to clarify this mechanism for the emergence of the power law of moments with respect to the strength of the additive noise . we achieve this by using a simple langevin - type model , and argue that the mechanism proposed is a universal one in generating various power laws . the outline of this paper is as follows : in sec . ii we introduce the model to be studied , and display its typical behavior . in sec . iii we treat the model approximately in order to outline the mechanism for the emergence of the power law of moments , and then exactly in sec . iv . in sec . v we discuss the robustness of the power law with regard to boundary conditions and nature of the noise . we also show some results obtained by numerical calculations with colored noises . in sec . vi we discuss an application of our theory to noisy on - off intermittency . as an example , we show a result obtained by a numerical calculation of coupled chaotic elements . furthermore , we discuss the relation of the power law of moments to the power - law spatial correlations observed in systems of non - locally coupled chaotic elements . we summarize our results in sec .

the first correction transforms the molecular shear viscosity into a ( rotation independent ) effective viscosity . the second perturbative correction leads to a new large scale non - dissipative force proportional to the fluid angular velocity in the slow rotation regime . both dynamically generated corrections can be identified with certain components of the most general axisymmetric `` viscosity tensor '' for a newtonian fluid .

i

physics0301071

large scale features of a randomly isotropically forced incompressible and unbounded rotating fluid are examined in perturbation theory . at first order in both the random force amplitude and the angular velocity we find two types of modifications to the fluid equation of motion . the first correction transforms the molecular shear viscosity into a ( rotation independent ) effective viscosity . the second perturbative correction leads to a new large scale non - dissipative force proportional to the fluid angular velocity in the slow rotation regime . this effective force does no net work and alters the dispersion relation of inertial waves propagating in the fluid . both dynamically generated corrections can be identified with certain components of the most general axisymmetric `` viscosity tensor '' for a newtonian fluid . # 1 pacs : 47.27-i , 47.32.-y

the special features of turbulence in the presence of rotation have attracted the interest of many authors @xcite . relying on some experiments , the methods of study used have ranged from analytic approaches to numerical simulations @xcite . the central theme in rotating fluids is the effect of the coriolis force , which induces anisotropy ( there is a preferred direction , that of the rotation axis ) . this anisotropy is extreme in the limit of fast rotation , which actually forces the flow to become two - dimensional ( proudman - taylor theorem ) @xcite . in this work we apply perturbation theory to the randomly forced navier - stokes equation with coriolis force as a model for the turbulent regime of a rotating fluid . the perturbative study of the ordinary randomly forced navier - stokes equation , in combination with the renormalization group ( as an improvement of perturbation theory ) , has a long tradition @xcite . the addition of the coriolis force , induced by the rotation of the fluid , introduces one additional parameter , the angular velocity @xmath0 or , in dimensionless form , either the rossby or ekman numbers ( in addition to the reynolds number ) @xcite . let us focus on the ekman number , @xmath1 , that depends on the viscosity @xmath2 and a scale @xmath3 , roughly associated with the size of the fluid system . the ekman number gives the relative importance of the viscosity and coriolis forces . we will _ assume _ henceforth that for small @xmath0 ( @xmath4 ) the turbulence is isotropic and the only relevant parameter is the viscosity . in this limit , the results of the study of the ordinary randomly forced navier - stokes equation hold ( the random force is always assumed isotropic ) . for larger @xmath0 we will encounter new features . in fact , the only restriction on perturbative correction terms is that they respect the basic _ symmetry _ of the equations , in our case , the axial symmetry about the rotation axis . we will see that perturbation theory generates new terms fulfilling these symmetry constraints . therefore , one must find the complete set of allowed terms that can arise in perturbation theory . we will determine all the terms that can be represented by the components of an axisymmetric `` viscosity tensor '' and , in particular , the ones that arise at first order in perturbation theory . the part of this `` viscosity tensor '' that is pair - antisymmetric in the indices plays a significant role ; however , it does not lead to dissipation , and therefore , is not truly viscous . as in homogeneous and isotropic turbulence , we assume that the physical region of study is sufficiently far from the surfaces , where the boundary conditions are imposed , for them not to have any _ direct _ effect , except the presence of the scale @xmath3 . in contrast to ordinary turbulence , this condition only implies that we can have homogeneous turbulence but , due to rotation , it can not be isotropic . it is pertinent to mention here that the possibility of anisotropic forced turbulence , and precisely with axial symmetry , has already been considered @xcite . in this reference , however , the authors assume that the breakdown of isotropy occurs through a random force whose two - point correlation function depends on the anisotropy vector @xmath5 . they derive a renormalized force proportional to second and fourth powers of @xmath5 . in our case , we will see that the first perturbative correction is linear in @xmath6 , like the coriolis force itself . this paper is organized as follows . in section [ sec : basic+perturbation ] we introduce the randomly forced hydrodynamical equations with rotation . we assume that the fluid is incompressible and show how to formulate them as a problem of homogeneous but anisotropic incompressible turbulence . fourier analysis of the turbulent velocity field is used to organize the perturbation expansion @xcite in subsection [ sec : fourier ] . we introduce in subsection [ sec : response ] the linear response function . unlike the isotropic case , the coriolis term leads to a _ non - symmetric _ linear response function matrix . in subsection [ sec : perturbative ] we define the non - linear response function and present its perturbative expansion ( slow rotation ) . we also compute the first order perturbative correction to the response function , which allows the identification of the ( rotation independent ) effective shear viscosity ( proportional to the cube of the reynolds number ) , and a new anisotropic force . in section [ sec : effective - tensor ] we write down the most general axially symmetric `` viscosity tensor '' , as the existence of a preferred direction , singled out by the fluid rotation , requires the introduction and use of axisymmetric tensors . this rank four `` viscosity tensor '' expresses the proportionality between the fluid stress tensor and the rate of strain tensor . in isotropic and homogeneous incompressible turbulence , the viscosity tensor depends only on one parameter , the fluid shear viscosity . in the case of rotating turbulence , and for slow rotation , we find that the axisymmetric `` viscosity tensor '' depends on two parameters : the molecular shear viscosity ( coming from the isotropic terms of the `` viscosity tensor '' ) and a new one , that arises from the anisotropic terms in the `` viscosity tensor '' . we also show that this new parameter can be identified as the coefficient of the anisotropic force calculated perturbatively ( in the previous section [ sec : perturbative ] ) . having thus established the equivalence between the perturbatively corrected randomly forced navier - stokes equation with coriolis force on the one hand , and a ( newtonian ) rotating incompressible fluid with an effective axisymmetric `` viscosity tensor '' on the other , we proceed , in section [ sec : effective ] , to discuss some physical consequences of the new terms in the perturbed fluid equations . in subsection [ sec : axial - force ] we consider the quasi - local force induced by the anisotropic components of the `` viscosity tensor '' and show that it is proportional to the cube of the reynolds number , and that it does not lead to dissipation . in subsection [ sec : waves ] we study the dynamical effects of this force on the propagation of inertial waves . we end by discussing our results and proposing further work on the problem of rotating turbulence . in appendix [ sec : app - diag ] we introduce the diagrammatic representation of the exact navier - stokes equation and the diagram encoding the first order correction to the response function and in appendix [ sec : app - perturbation ] we present the technical details needed to carry out the perturbative calculation in the slow rotation limit .

large scale features of a randomly isotropically forced incompressible and unbounded rotating fluid are examined in perturbation theory . at first order in both the random force amplitude and the angular velocity we find two types of modifications to the fluid equation of motion . this effective force does no net work and alters the dispersion relation of inertial waves propagating in the fluid .

c

physics0301071

large scale features of a randomly isotropically forced incompressible and unbounded rotating fluid are examined in perturbation theory . at first order in both the random force amplitude and the angular velocity we find two types of modifications to the fluid equation of motion . the first correction transforms the molecular shear viscosity into a ( rotation independent ) effective viscosity . the second perturbative correction leads to a new large scale non - dissipative force proportional to the fluid angular velocity in the slow rotation regime . this effective force does no net work and alters the dispersion relation of inertial waves propagating in the fluid . both dynamically generated corrections can be identified with certain components of the most general axisymmetric `` viscosity tensor '' for a newtonian fluid . # 1 pacs : 47.27-i , 47.32.-y

we have applied perturbation theory to a homogeneous incompressible viscous fluid subject to solid body rotation and isotropic random forcing . at small scales , we assume that only the molecular shear viscosity and the coriolis force are needed in writing down the _ transverse _ navier - stokes equation ( [ u - field2 ] ) . our ( first order ) perturbative results demonstrate that ( i ) anisotropic components of the effective `` viscosity tensor '' are dynamically generated at large scales by the combined interplay of the coriolis force , the random forcing term , and the inherent non - linearity of the navier - stokes equation , ( ii ) the molecular shear viscosity @xmath2 gets corrected in the same manner as for isotropic randomly stirred turbulence @xcite . these perturbative results are corroborated by a symmetry principle . by making use of the axial symmetry of a rotating fluid , we have constructed the most general `` viscosity tensor '' that is invariant under such symmetry . the preferred direction singled out by the angular velocity @xmath11 breaks the isotropy and leads to new terms in the `` viscosity tensor '' absent in the isotropic case @xcite . we have also determined and described the role of the first order perturbative new term in the effective fluid equation of motion . it acts as a quasi - local force and , like the coriolis force , is not dissipative and does no net work on the fluid . most importantly , we find that this quasi - local force affects the propagation of inertial waves in rotating fluids . for small wave amplitudes a fraction of the wave energy is transported in the same direction as the phase velocity . the perturbative calculation is developed as a double expansion : in both the amplitude of the random force and the angular velocity . the actual dimensionless expansion parameters turn out to be the cube of the reynolds number and this number times the inverse of the ekman number , respectively . for simplicity , we have restricted ourselves to the computation of the lowest order in both : that is , first order in the random force amplitude and linear order in @xmath11 . this is sufficient to generate two , out of the total of eight tensor terms ( seven , on account of incompressibility ) allowed by axial symmetry [ see eqs . ( [ nus ] ) and ( [ nua ] ) ] . we conjecture that , at first order in the random force amplitude , all the remaining tensor terms are generated for higher powers in @xmath0 : @xmath189 , @xmath190 , and @xmath129 at quadratic order , @xmath191 at cubic order , and finally @xmath192 at quartic order . of course , as increasing powers of @xmath0 are taken into account , the coefficient functions ( [ beta ] ) must be expanded out to the order of @xmath0 being investigated . the higher order terms will be needed to study the effects of fast rotation and to track the onset of the bi - dimensionalization of the fluid @xcite . an important step in this direction will be provided by a complete renormalization group ( rg ) analysis of the large scales properties of a rotating incompressible fluid . in order to carry out this rg analysis one may need to calculate the ( perturbative ) corrections to the non - linear coupling term @xmath28 , as well as the random force amplitude @xmath96 , and combine these two with the response function calculation presented in this paper . once in hand , the rg fixed points can be determined and the corresponding asymptotic behavior of the rotating fluid deduced , allowing us to compute quantities such as the scale - dependent reynolds and ekman numbers , among others . we hope to report on these developments elsewhere .