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cond-mat0102521

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in this paper we have discussed the possibility of phase ordering of a sort which is dominated by strong fluctuations . in steady state , these fluctuations lead to variations of the order parameter of order unity , but the system stays ordered in the sense that with probability one , a finite fraction of the system is occupied by a single phase . the value of this fraction fluctuates in time , leading to a broad probability distribution of the order parameter . we demonstrated these features in two types of models having to do with surface fluctuations the first , a coarse - grained depth ( cd ) model where we could establish these properties analytically , and the second a model of sliding particles ( sp ) on the surface in question . for these models we found that besides ( a ) the broad probability distribution of the order parameter ( which we may take to be the defining characteristic of fdpo ) , the steady state was also characterised by ( b ) power laws of cluster size distributions and ( c ) cusps in the scaled two - point correlation function , associated with the breakdown of the porod law . the connection between ( b ) and ( c ) was elucidated using the independent interval approximation . further , an extremal statistics argument showed that the largest cluster drawn from the power law distribution is of the order of the system size ; this implies a macroscopic ordered region , so that within our models , properties ( a ) and ( b ) are connected . there are several open questions . does fluctuation - dominated phase ordering occur in other , completely different types of systems as well ? are properties ( b ) and ( c ) necessarily concomitant with the defining property ( a ) of fdpo ? can one characterize quantitatively the dynamical behaviour in the fdpo steady state ? our model of particles sliding on a fluctuating surface relates to several physical systems of interest . first , it describes a new mechanism of large scale clustering in vibrated granular media , provided the vibrations are random both in space and time . second , it describes a special case ( the passive scalar limit ) of a crystal driven through a dissipative medium , for instance a sedimenting colloidal crystal @xcite . finally , related models describe the formation of domains in growing binary films @xcite . it would be interesting to see if ideas related to fdpo play a role in any of these systems . it would also be interesting to examine fluctuating phase - ordered states in other nonequilibrium systems from the point of view of fdpo . for instance , in a study of jamming in the bus - route model studied in @xcite , the largest empty stretch in front of a bus was found to be of order @xmath18 , and it is argued that such a stretch survives for a time which is proportional to @xmath371 for a nonvanishing rate of arrival of the passengers . these features are reminescent of the behaviour of the cd and sp models derived from the edwards - wilkinson model discussed above . however , more work is required to make a clear statement about fdpo in the bus - route model . in general , fluctuation - dominated phase ordering is evidently a possibililty that should be kept in mind when discussing new situations involving phase ordering in nonequilibrium systems , both in theory and in experiment .

in which the order parameter has a broad distribution even in the thermodynamic limit , the distribution of particle cluster sizes decays as a power - law ( with an exponent ) , and the 2-point spatial correlation function has a cusp ( with an exponent ) at small values of the argument .

we study a new kind of phase ordering phenomenon in coarse - grained depth models of the hill - valley profile of fluctuating surfaces with zero overall tilt , and for hard - core particles sliding on such surfaces under gravity . we find that several such systems approach an ordered state with large scale fluctuations which make them qualitatively different from conventional phase ordered states . we consider surfaces in the edwards - wilkinson ( ew ) , kardar - parisi - zhang ( kpz ) and golubovic - bruinsma - das sarma - tamborenea ( gbdt ) universality classes . for ew and kpz surfaces , coarse - grained depth models of the surface profile exhibit coarsening to an ordered steady state in which the order parameter has a broad distribution even in the thermodynamic limit , the distribution of particle cluster sizes decays as a power - law ( with an exponent ) , and the 2-point spatial correlation function has a cusp ( with an exponent ) at small values of the argument . the latter feature indicates a deviation from the porod law which holds customarily , in coarsening with scalar order parameters . we present several numerical and exact analytical results for the coarsening process and the steady state . for linear surface models with dynamical exponent , we show that for , for , and there are logarithmic corrections for , implying for the ew surface and for the gbdt surface . within the independent interval approximation we show that . we also study the dynamics of hard - core particles sliding locally downwards on these fluctuating one - dimensional surfaces and find that the surface fluctuations lead to large - scale clustering of the particles . we find a surface - fluctuation driven coarsening of initially randomly arranged particles ; the coarsening length scale grows as . the scaled density - density correlation function of the sliding particles shows a cusp with exponent , and for the ew and kpz surfaces . the particles on the gbdt surface show conventional coarsening ( porod ) behavior with . 0.5 cm pacs numbers : 05.70.ln , 05.40.-a , 02.50.-r , 64.75.+g # 1#2#3 = 0.75 2

cond-mat0508551

i

an equation - free framework has recently been developed as a means of computationally analyzing the dynamical behavior of a large class of complex , multiscale dynamical systems . the systems may be either stochastic or deterministic with many of degrees of freedom and subject to random initial data . the key observation behind the equation - free framework is that in many cases the quantities of interest are averages or low - order moments of evolving distributions which are smooth in space and time and which evolve effectively as closed , low - dimensional systems . in effect the low - order moments evolve as though they are governed by reduced closed equations , even though the reduced equations are not analytically available . algorithms for performing scientific computing tasks such as numerical integration , or bifurcation and stability analysis of these unavailable reduced equations have been developed ( e.g. coarse projective integration , coarse newton - gmres , see @xcite and references therein ) . these algorithms are based on traditional , continuum numerical analysis , wrapped " around direct fine - scale simulation . the purpose of this paper is to establish a mathematical framework for understanding the behavior of coarse dynamics and coarse bifurcation methods on problems which exhibit metastable behavior . the systems we consider are exemplified by the following model . a particle , called the distinguished particle , with position @xmath0 and momentum @xmath1 sits in a potential well @xmath2 . it is coupled via linear springs to a large number @xmath3 of particles comprising a heat bath ; see figure [ fig : sketch ] . the potential well considered here is a slightly asymmetric double well . the full system is an @xmath4 degree of freedom hamiltonian system . a detailed description of the model , including the choice of spring constants , masses , and initial data for the bath particles is given below and in @xcite . the important point is that the dynamics of this simple model ( and the others that we consider in this paper ) is typical of many more complex molecular and stochastic systems in which the state is primarily confined to a few conformations ( here defined by the minima of @xmath5 ) with rare switching events between them . this is illustrated in figure [ fig : intro_qp ] with a typical trajectory and time series for the distinguished particle . other ( bath ) particles ( three are shown as illustration ) . the full system has @xmath4 degrees of freedom . , width=240 ] most of the time the distinguished particle is located in one of the two potential wells , but occasionally it makes a jump between wells.,width=192 ] consider now the dynamics of an ensemble of trajectories for the model system . figure [ fig : intro_ensemble ] illustrates the evolution of an ensemble of trajectories all with the same initial conditions @xmath6 for the distinguished particle , but with different initial data for the bath particles . ( the total initial energy of the bath is approximately the same for all realizations . [ sec : models ] . ) over a time of order @xmath7 the initial density evolves to a nearly gaussian density centered near the bottom of the right well , where it remains roughly constant for some time . while not immediately evident , during the initial @xmath7 time units , the density is never very far from gaussian . however , it is evident from the left - hand plot that a small percentage of the realizations are located in the left well at time @xmath7 . over a much longer time scale , @xmath8 , the density evolves to the bimodal equilibrium distribution and is hence far from gaussian . thus the system exhibits _ metastability _ with near equilibration within one well dominating over medium time scales , before the system ultimately converges to an equilibrium distribution which sees both wells . the time it takes the system to reach equilibrium clearly depends on the potential barrier height ; the time scale of the intermediate time evolution to the well bottom depends only on properties of the particular well . realizations for the model system . on the left density plots of position and momentum of the distinguished particle are shown at four times as labeled . for clarity only the first @xmath9 realizations are plotted . the initial conditions are @xmath10 . the right shows the trajectory and time series for the ensemble expectations . red points indicate the four times shown on the left . there are @xmath11 particles in the heat bath . , width=384 ] our aim is to study the behavior of coarse dynamics and coarse bifurcation methods on problems which exhibit metastable behavior of this type . in 2 we introduce a hierarchy of model problems , all of which exhibit rare transitions between a small number of states , and which we then use throughout as illustrations . in 3 we define the discrete - time _ moment map _ @xmath12 for the first @xmath13 moments of the ensemble of solutions to a time evolving system . specifically , @xmath12 will be a low - dimensional map for only the low - order moments , defined in a general setting which applies to both systems of ordinary differential equations ( odes ) , with randomness from initial data , and stochastic differential equations ( sdes ) with randomness from initial data and brownian driving noise . figure [ fig : intro_moments ] illustrates the _ first - order moment map _ for the heat bath example . the short - term dynamics of the map resemble those of the ensemble , but significantly , the moment map has _ stable fixed points _ corresponding to means of metastable densities centered in each well . the second - order moment map additionally captures the widths of the metastable measures . the algorithms we study are based on these maps . the heart of the paper is 4 . it is devoted to the study of the moment map , when applied to a variety of model systems . we use a combination of exact solutions for gaussian problems , approximate solutions for metastable systems and numerical experiments . of central interest is the observation that the moment maps stabilize the metastable states in the model problems of interest . the moment map is a nonlinear map , defined from the linear flow of probability densities for odes and sdes , with the nonlinearity entering through the process of repeatedly projecting onto the space of moments . this process of _ nonlinearization _ creates interesting fixed points which are associated with metastable behavior , and are amenable to low dimensional bifurcation analyses ; related issues are addressed in @xcite . 5 contains our concluding remarks . and momentum @xmath1 of the distinguished particle . the map has three fixed points ; two stable foci and one unstable saddle shown as blue cross . two trajectories are shown ; one evolving to each of the stable fixed points . the right trajectory has initial condition @xmath14 , corresponding to that in figure [ fig : intro_ensemble ] . there are @xmath11 particles in the heat bath . , width=192 ]

we explore situations in which certain stochastic and high - dimensional deterministic systems behave effectively as low - dimensional dynamical systems . we define and study moment maps , maps on spaces of low - order moments of evolving distributions , as a means of understanding equations - free multiscale algorithms for these systems . examples are shown for a hierarchy of models , ranging from simple stochastic differential equations to molecular dynamics simulations of a particle in contact with a heat bath . equation - free , multiscale , moment map , metastable states .

we explore situations in which certain stochastic and high - dimensional deterministic systems behave effectively as low - dimensional dynamical systems . we define and study moment maps , maps on spaces of low - order moments of evolving distributions , as a means of understanding equations - free multiscale algorithms for these systems . we demonstrate how nonlinearity arises in these maps and how this results in the stabilization of metastable states . examples are shown for a hierarchy of models , ranging from simple stochastic differential equations to molecular dynamics simulations of a particle in contact with a heat bath . equation - free , multiscale , moment map , metastable states .

1312.6226

i

the wide use of gaussian and non - gaussian electromagnetic field states for various quantum tasks and protocols renders the generation and investigation of these quantum states an essential aspect of modern research . entangled states generated using both linear and nonlinear quantum optical operations have been extensively used in quantum information @xcite and communications @xcite applications . the accessibility of continuous variable ( cv ) processing in quantum information theory has led to successful implementation of novel quantum tasks such as quantum teleportation @xcite , quantum cryptography @xcite and quantum memory @xcite ( for reviews , see @xcite ) . a recent method of generating nonclassicality in electromagnetic field states is by the operation of photon addition ( @xmath2 ) @xcite and subtraction ( @xmath1 ) @xcite . a remarkable aspect of the non - gaussian photon addition and subtraction operations is the relative efficiency with which these operations can be experimentally realised using linear optical devices and parametric down - converters @xcite . these non - gaussian operations are known to enhance entanglement @xcite and quantum information protocols , such as quantum teleportation @xcite . an extension of these non - gaussian operations , such as photon addition followed by photon subtraction or vice - versa , has also been implemented to show improvements in quantum correlations and other quantum tasks @xcite . the study of nonclassical optical states generated by such non - gaussian operations has received considerable theoretical attention in quantum optics @xcite . further , the experimental implementation of these operations has been used to prove the canonical commutation relation @xcite . a useful operation based on the non - gaussian photon - addition and subtraction protocols is the number - conserving generalised superposition of products ( gsp ) of field annihilation ( @xmath1 ) and creation ( @xmath2 ) operators of the form @xmath0 , with @xmath3 . such an operation is a generalization of the experimental scheme proposed to study the bosonic canonical commutation in optical fields @xcite . using an analysis of quasi - probability functions , quadrature squeezing and sub - poissonian statistics , we have recently shown that such gsp operations introduces nonclassicality in single - mode coherent and thermal states @xcite . the experimental scheme to implement the gsp operation using linear optical devices and parametric down - converters has been illustrated and mathematically explained in ref . however , the feasibility of such a scheme is reliant on the efficiency with which photon addition and subtraction can be experimentally achieved . in particular , it is limited by the low efficiency with which a single photon can be detected in the relevant modes @xcite ( cf . @xcite ) . it is known that gsp operations can be suitably manipulated to generate nonclassical output states when applied on single- and two - mode coherent , thermal and squeezed vacuum states @xcite . hence , the primary motivation of the present article is to analyze the nonclassicality introduced by the gsp operations from a quantum information perspective and investigate if the generated nonclassicality can enhance the performance of specific quantum information tasks . these nonclassical optical states , in mode _ a _ , can then be converted into two - mode entangled states by interacting with a secondary mode _ b _ , via a linear optical device such as a 50:50 beam - splitter . for a single - mode input state , the secondary mode is the vacuum , while for a two - mode input state , one mode serves as _ a _ and the other mode as _ b _ ( see figure [ fig1 ] ) . we note that the generated entanglement is characteristic of the nonclassicality of the gsp operated state , as beam - splitters do not generate entanglement for classical inputs @xcite . thus the generated entanglement is an indicator of the resource obtained due to the gsp operations . the suitability of the two - mode entangled state is investigated for potential use as a quantum channel in a cv quantum teleportation , under the braunstein and kimble ( bk ) protocol @xcite . the success of the protocol is evaluated in terms of the average fidelity obtained in teleporting a single - mode optical state . the efficiency of the quantum channel for cv teleportation can be justified in terms of the phase - quadrature or the einstein - podolsky - rosen ( epr ) correlations present in the quantum channels . the main results obtained in our investigation can be summarized in the following points : 1 ) at low field intensities , the gsp operation can be suitably tuned to generate highly entangled two - mode discrete level optical states for both single- and two - mode coherent , thermal and squeezed input states . this is a signature of the nonclassicality generated by the gsp operation on these input states . 2 ) these two - mode entangled states can be used as quantum channels in cv quantum teleportation of single - mode coherent and squeezed states , under the bk protocol . 3 ) we observe that while the average fidelity of cv teleportation is enhanced for the squeezed input states under gsp operations , the fidelity does not rise above the classical threshold for coherent and thermal inputs . this shows that the generated nonclassicality in coherent and thermal states , under gsp operations , is not resourceful for cv teleportation . 4 ) investigating further , we observe that the gsp operations do not enhance the nonclassicality of coherent and thermal input states in terms its phase - quadrature or the epr correlations , which is crucial for gaining an advantage in cv teleportation . interestingly , the above results show that though gsp operations introduce nonclassicality and discrete level entanglement for all input states , the injected nonclassicality is not resourceful for cv teleportation when the input state is coherent or thermal , as it fails to enhance the epr correlations . the real advantage is observed only when the input state is already nonclassical , such as the squeezed state . this result is important from the consideration of noisy quantum channels , where classical noise can be modelled using coherent or thermal states . the paper is organised as follows . the introduction in section [ ss1 ] is followed by a discussion on the characterization of nonclassicality and two - mode entanglement in section [ ent ] . we then discuss the state generation protocol for single - mode ( section [ ss2 ] ) and two - mode ( section [ ss3 ] ) coherent , thermal and squeezed state inputs . we investigate the entanglement properties in section [ ss5 ] followed by the investigation of average teleportation fidelities in section [ ss6 ] . in section [ sec - epr ] , we look at the epr correlations of the quantum channels , and end with a discussion of the results in section [ discuss ] .

we investigate the states generated in continuous variable ( cv ) optical fields on operating them with a number - conserving operator of the type , formed by the generalised superposition of products of field annihilation ( ) and creation ( ) operators , with . such an operator is experimentally realizable and can be suitably manipulated to generate nonclassical optical states when applied on single- and two - mode coherent , thermal , and squeezed input states . at low intensities , these nonclassical states can interact with a secondary mode via a linear optical device to generate two - mode discrete entangled states , which can serve as a resource in quantum information protocols . the advantage of these operations are tested by applying the generated entangled states as quantum channels in cv quantum teleportation , under the braunstein and kimble protocol . we observe that , under these operations , while the average fidelity of cv teleportation is enhanced for the nonclassical channel formed using input squeezed states , it remains at the classical threshold for input coherent and thermal states . this is due to the fact that though these operations can introduce discrete entanglement in all input states , it enhances the einstein - podolosky - rosen ( epr ) correlations only in the nonclassical squeezed state inputs , leading to an advantage in cv teleportation . ( some figures may appear in colour only in the online journal ) _ keywords _ : continuous variable system , non - gaussian operation , entanglement , quantum teleportation , epr correlation

we investigate the states generated in continuous variable ( cv ) optical fields on operating them with a number - conserving operator of the type , formed by the generalised superposition of products of field annihilation ( ) and creation ( ) operators , with . such an operator is experimentally realizable and can be suitably manipulated to generate nonclassical optical states when applied on single- and two - mode coherent , thermal , and squeezed input states . at low intensities , these nonclassical states can interact with a secondary mode via a linear optical device to generate two - mode discrete entangled states , which can serve as a resource in quantum information protocols . the advantage of these operations are tested by applying the generated entangled states as quantum channels in cv quantum teleportation , under the braunstein and kimble protocol . we observe that , under these operations , while the average fidelity of cv teleportation is enhanced for the nonclassical channel formed using input squeezed states , it remains at the classical threshold for input coherent and thermal states . this is due to the fact that though these operations can introduce discrete entanglement in all input states , it enhances the einstein - podolosky - rosen ( epr ) correlations only in the nonclassical squeezed state inputs , leading to an advantage in cv teleportation . this shows that nonclassical optical states generated using the above operations on classical coherent and thermal state inputs are not resourceful for cv teleportation . this investigation could prove useful in efficient implementation of noisy non - gaussian channels , formed by linear operations , in future teleportation protocols . ( some figures may appear in colour only in the online journal ) _ keywords _ : continuous variable system , non - gaussian operation , entanglement , quantum teleportation , epr correlation

1312.6226

c

in this paper , we have used a generalised superposition of products of annihilation and creation operators to obtain nonclassical continuous variable field states . we have applied the gsp operator along with linear optical interaction on single- and two - mode cv states such as coherent , thermal and squeezed states to obtain highly entangled two - mode output states . the primary findings of the paper can be efficiently summarised in two logical parts . the first is the generation of highly entangled , two - mode discrete level output states using the gsp operation . upon application of the gsp protocol , the classical cv inputs , such as coherent and thermal states , can be converted to entangled two - mode states , in the low field - intensity limit . manipulating the gsp parameter @xmath10 along with the field parameters , one can obtain highly entangled discrete photonic systems . entangled photons are useful in a wide range of applications in quantum optics and are of fundamental importance in practical implementation of discrete level quantum information theory . the second aspect of the study is the application of the gsp operated states as quantum channels in cv quantum teleportation . we observe that the gsp operations enhance average teleportation fidelity of teleporting single - mode coherent and squeezed states using two - mode entangled channels obtained from single- and two - mode squeezed state inputs . the average fidelity obtained is higher than the fidelity of cloning even at low squeezing regime and betters the performance of the non - operated two - mode squeezed channel . the optimised gsp operation outperforms most non - gaussian operations with regard to fidelity enhancement in cv teleportation . interestingly , the gsp operation does not enhance the classical fidelity when the two - mode gsp operated thermal and coherent channels are used . the maximum fidelity possible using the coherent and thermal channels is the classical fidelity that is achieved without any entangled resources . hence , the nonclassical states introduced by gsp operations on coherent and thermal states are not resourceful for cv teleportation . this proves that not all two - mode entangled states generated under gsp operations are useful for cv information protocols . we show that this is due to the fact that gsp operations do not inject any nonclassicality in quadrature or epr correlations , thus rendering these states useless for cv information protocols . the results obtained may have interesting ramifications on noisy quantum channels . such channels can be modelled by a linear characteristic function of a low intensity thermal state and an entangled two - mode squeezed channel . for the gsp operations considered in our study , and restrictive optimizations under the bk protocol , the average fidelity of teleportation with a squeezed channel is enhanced while that with a noisy thermal state is reduced . this could lead to interesting interplay between nonclassicality and noise in determining the overall teleportation fidelity . the experimental advances in the generation of photon - added and photon - subtracted field states ensure that the advantages of non - gaussian operations will be put to further applications in the future . in the light of such developments the importance of theoretical studies on non - gaussian states is highly relevant . hsd thanks university grants commission , government of india for support under the senior research fellowship scheme . ac thanks serb , department of science and technology , government of india .

this shows that nonclassical optical states generated using the above operations on classical coherent and thermal state inputs are not resourceful for cv teleportation . this investigation could prove useful in efficient implementation of noisy non - gaussian channels , formed by linear operations , in future teleportation protocols .

we investigate the states generated in continuous variable ( cv ) optical fields on operating them with a number - conserving operator of the type , formed by the generalised superposition of products of field annihilation ( ) and creation ( ) operators , with . such an operator is experimentally realizable and can be suitably manipulated to generate nonclassical optical states when applied on single- and two - mode coherent , thermal , and squeezed input states . at low intensities , these nonclassical states can interact with a secondary mode via a linear optical device to generate two - mode discrete entangled states , which can serve as a resource in quantum information protocols . the advantage of these operations are tested by applying the generated entangled states as quantum channels in cv quantum teleportation , under the braunstein and kimble protocol . we observe that , under these operations , while the average fidelity of cv teleportation is enhanced for the nonclassical channel formed using input squeezed states , it remains at the classical threshold for input coherent and thermal states . this is due to the fact that though these operations can introduce discrete entanglement in all input states , it enhances the einstein - podolosky - rosen ( epr ) correlations only in the nonclassical squeezed state inputs , leading to an advantage in cv teleportation . this shows that nonclassical optical states generated using the above operations on classical coherent and thermal state inputs are not resourceful for cv teleportation . this investigation could prove useful in efficient implementation of noisy non - gaussian channels , formed by linear operations , in future teleportation protocols . ( some figures may appear in colour only in the online journal ) _ keywords _ : continuous variable system , non - gaussian operation , entanglement , quantum teleportation , epr correlation

astro-ph0702383

i

this study has been motivated by the apparent lack of a non - wkb analysis of alfvn waves in a multi - fluid solar wind with differentially flowing ions . to be more specific , this study is concerned with the propagation of dissipationless , hydromagnetic ( angular frequency @xmath10 well below ion gyro - frequencies ) , purely toroidal alfvn waves that propagate in a background 3-fluid solar wind comprised of electrons , protons and alpha particles . azimuthal symmetry is assumed throughout . no assumption has been made that the wavelength is small compared with the spatial scales at which the background flow parameters vary . the wave behavior at a given @xmath10 is governed by equation ( [ num_eqs ] ) , which is derived from the general transport equations in the five - moment approximation . the alfvnic point , where the combined alfvn mach number @xmath0 ( cf . eq.([def_mt2 ] ) ) , is a singular point of equation ( [ num_eqs ] ) and a regularity condition has to be imposed . for the other boundary condition , we impose a velocity amplitude of 10 @xmath176 at the coronal base ( 1 @xmath5 ) . for the given background model of a realistic low - latitude fast solar wind , equation ( [ num_eqs ] ) is integrated numerically for three representative angular frequencies @xmath1 , @xmath2 and @xmath3 @xmath6 to yield the radial distribution of the wave energy and energy flux densities as well as the wave - induced acceleration exerted on ion species . the first conclusion concerns the applicability of the wkb approximation . between 1 @xmath5 and 1 au , the numerical solutions show substantial deviation from the wkb expectations . even for the relatively high frequency @xmath1 @xmath6 , a wkb - like behavior can be seen only in regions where @xmath7 @xmath5 . in the low - frequency case @xmath8 @xmath6 , the computed profiles of wave - related parameters show a spatial dependence that is distinct from the wkb one , the deviation being particularly pronounced in interplanetary space . in the inner corona @xmath9 @xmath5 , the computed ion velocity fluctuations are considerably smaller than the wkb expectations in all cases , as is the computed wave - induced acceleration exerted on protons or alpha particles . as for the wave energy and energy flux densities , they can be enhanced or depleted compared with the wkb results , depending on @xmath10 . the second conclusion is concerned with how the wave acceleration may alter the background flow parameters . in reference to fig.[fig_ucorr ] , it is found that with the current choice of base wave amplitude , the wave acceleration has little effect on the force balance for protons or alpha particles in the corona . that is , one has to invoke processes other than the non - wkb wave acceleration to accelerate the ions out of the gravitational potential well of the sun . however , at large distances beyond the alfvnic point , low - frequency waves may play an important role in the ion dynamics , with the net effect being to equalize the speeds of the two ion species considered . strictly speaking , the separation of the flow into fluctuations and a time - independent background implies that the waves are linear . however , one may have noticed that the wave amplitude @xmath246 at 1 au for @xmath8 s@xmath4 @xmath6 is substantially larger than the background poloidal magnetic field strength ( cf . fig.[fig_ampltd]a ) . that the transverse magnetic field dominates the poloidal one demands a careful examination of the nonlinear effects other than the wave - induced acceleration . in particular , one needs to look at the generation of secondary waves and structures by the primary alfvn waves through the source terms in the momentum equation . as discussed by @xcite , in the case of ideal mhd these source terms decrease sufficiently fast with radial distance asymptotically . consequently , the first - order wave amplitudes are valid provided that the amplitude imposed at the coronal base is sufficiently small . the basic picture is expected to be the same even if a second ion species is included , although a similar discussion in the 3-fluid framework will be complicated by the richness of wave modes due to the differential proton - alpha streaming ( e.g. , * ? ? ? as has been mentioned in the introduction , alfvn waves are dissipated in some way , and this dissipation of the primary waves should be described self - consistently . a possibility to do this is to perform a full elssser analysis extended to the multi - fluid case , and to express the dissipation in terms of the amplitudes of counter - propagating waves . we note that this already complicated issue will become even trickier considering the necessity to apportion the dissipated wave energy among different species . in closing , we note that the low - frequency waves may also be important for outflows from stars other than the sun . for instance , in the radiatively driven stellar winds , these waves will provide a further channel of momentum exchange between passive ions and line - absorbing ions in addition to the coulomb friction . this possibility was first pointed out by @xcite in connection with the effects of stellar rotation . due to the clear resemblance between the low - frequency alfvn waves and stellar rotation ( cf . section [ sec_zero_freq ] ) , their discussion also applies to the case where the star persistently emits alfvn waves with frequencies lower than the critical one defined by equation ( [ def_omegac ] ) . consequently , the mass loss rate may be significantly altered . a quantitative study of this effect is beyond the scope of the present paper though . this research is supported by a pparc rolling grant to the university of wales aberystwyth . we thank shadia rifai habbal for her careful reading of the first draft , and hui - nan zheng for helpful discussions .

the propagation of dissipationless , hydromagnetic , purely toroidal alfvn waves in a realistic background three - fluid solar wind with axial symmetry and differential proton - alpha flow is investigated . the short wavelength wkb approximation is not invoked . instead , the equations that govern the wave transport are derived from standard multi - fluid equations in the five - moment approximation . the alfvnic point , where the combined poloidal alfvn mach number , is found to be a singular point for the wave equation , which is then numerically solved for three representative angular frequencies , and rad s with a fixed wave amplitude of 10 km s imposed at the coronal base ( 1 ) . the wave energy and energy flux densities as well as wave - induced ion acceleration are computed and compared with those derived in the wkb limit . between 1 and 1 au , the numerical solutions show substantial deviation from the wkb expectations . even for the relatively high frequency , a wkb - like behavior can be seen only in regions . in the low - frequency case , the computed profiles of wave - related parameters show a spatial dependence distinct from the wkb one , the deviation being particularly pronounced in interplanetary space . in the inner corona , the computed ion velocity fluctuations are considerably smaller than the wkb expectations in all cases , as is the computed wave - induced acceleration exerted on protons or alpha particles . as for the wave energy and energy flux densities , they can be enhanced or depleted compared with the wkb results , depending on . with the chosen base wave amplitude , the wave acceleration has negligible effect on the ion force balance in the corona . hence processes other than the non - wkb wave acceleration are needed to accelerate the ions out of the gravitational potential well of the sun . however , at large distances beyond the alfvnic point , the low - frequency waves can play an important role in the ion dynamics , with the net effect being to equalize the speeds of the two ion species considered .

the propagation of dissipationless , hydromagnetic , purely toroidal alfvn waves in a realistic background three - fluid solar wind with axial symmetry and differential proton - alpha flow is investigated . the short wavelength wkb approximation is not invoked . instead , the equations that govern the wave transport are derived from standard multi - fluid equations in the five - moment approximation . the alfvnic point , where the combined poloidal alfvn mach number , is found to be a singular point for the wave equation , which is then numerically solved for three representative angular frequencies , and rad s with a fixed wave amplitude of 10 km s imposed at the coronal base ( 1 ) . the wave energy and energy flux densities as well as wave - induced ion acceleration are computed and compared with those derived in the wkb limit . between 1 and 1 au , the numerical solutions show substantial deviation from the wkb expectations . even for the relatively high frequency , a wkb - like behavior can be seen only in regions . in the low - frequency case , the computed profiles of wave - related parameters show a spatial dependence distinct from the wkb one , the deviation being particularly pronounced in interplanetary space . in the inner corona , the computed ion velocity fluctuations are considerably smaller than the wkb expectations in all cases , as is the computed wave - induced acceleration exerted on protons or alpha particles . as for the wave energy and energy flux densities , they can be enhanced or depleted compared with the wkb results , depending on . with the chosen base wave amplitude , the wave acceleration has negligible effect on the ion force balance in the corona . hence processes other than the non - wkb wave acceleration are needed to accelerate the ions out of the gravitational potential well of the sun . however , at large distances beyond the alfvnic point , the low - frequency waves can play an important role in the ion dynamics , with the net effect being to equalize the speeds of the two ion species considered .

1602.02815

i

we consider the random vandermonde matrix @xmath2 , whose @xmath3-th entry is @xmath4 , where @xmath5 are independent with haar measure distribution on the unit circle . these have been studied in @xcite , @xcite , @xcite and @xcite and are of interest for applications in finance , signal array processing , wireless communications and biology ( see @xcite for references ) . in @xcite , ryan and debbah show that asymptotic moments of @xmath6 , ( namely , the limits @xmath7 where @xmath8 is the expectation and @xmath9 is the normalized trace on matrix algebras ) , exist and are given by sums of volumes of certain polytopes . they also compute some of these asymptotic moments . in @xcite , tucci and whiting show among other things that the asymptotic moments are given by @xmath10 for a unique measure @xmath11 on @xmath12 with unbounded support . ( this uses the stieltjes solution to the moment problem and a theorem of carleman for the former , see p. 76 of @xcite . ) further results are proved in @xcite and @xcite . g. tucci asked @xcite whether @xmath2 is asymptotically r - diagonal with respect to the expectation of the trace . in this paper , we answer tucci s question negatively , but show that @xmath2 has an asymptotic @xmath0-distribution as @xmath13 , which is in fact the @xmath0-distribution of an element that is r - diagonal over the c@xmath14-algebra @xmath1 $ ] . to be precise , we show that , for all @xmath15 and all @xmath16 , @xmath17 exists and we describe this limiting @xmath0-moment using the notion of @xmath1$]-valued r - diagonality . usual ( or scalar - valued ) r - diagonal elements are very natural in free probability theory , and have been much studied ; they were introduced by nica and speicher in @xcite . the algebra - valued version was introduced by niady and speicher in @xcite and has been further studied in @xcite . we will give the definition from @xcite , which is an easy reformulation of one of the characterizations in @xcite . the setting for algebra - valued r - diagonal elements is a @xmath18-valued @xmath0-noncommutative probability space @xmath19 , where @xmath20 is a unital inclusion of unital @xmath0-algebras and @xmath21 is a conditional expectation , namely , a @xmath18-bimodular unital projection . [ def : maxaltptn ] given @xmath15 and @xmath22 , we define the _ maximal alternating interval partition _ @xmath23 to be the interval partition of @xmath24 whose blocks are the maximal interval subsets @xmath25 of @xmath24 such that if @xmath26 and @xmath27 , then @xmath28 . for example , if @xmath29 , then @xmath30 . [ def : rdiag ] an element @xmath31 is _ @xmath18-valued r - diagonal _ if for every integer @xmath32 and every @xmath33 we have @xmath34 ( namely , odd alternating moments vanish ) and , for every integer @xmath35 , every @xmath36 and every choice of @xmath37 , we have @xmath38 where in each of the three products above , the terms are taken in order of increasing indices . note that the @xmath18-valued r - diagonality condition determines all of the @xmath18-valued @xmath0-moments @xmath39 for @xmath15 , @xmath40 and arbitrary @xmath16 , in terms of the alternating moments of even length , namely those when @xmath41 is even and @xmath28 for all @xmath42 . * contents : * the contents of the rest of the paper are as follows . in section [ sec : altmoms ] , we find asymptotics of diagonal entries of @xmath0-moments involving alternating @xmath2 and @xmath43 with certain deterministic diagonal matrices between . in section [ sec : rdiag ] , we prove our main result , characterizing arbitrary asymptotic @xmath0-moments of @xmath2 based on @xmath1$]-valued r - diagonality . in section [ sec : calcs ] , we prove results allowing the asymptotic alternating @xmath0-moments of @xmath2 found in section [ sec : altmoms ] to be computed in terms of certain integrals , we show that @xmath2 is not asymptotically scalar - valued r - diagonal , and we report the results of computations of certain @xmath1$]-valued cumulants of the asymptotic @xmath0-distribution of @xmath2 . ( details of these computations can be found in a mathematica @xcite file accompanying the arxived version of this paper . ) * notation : * on matrix algebras , @xmath44 is the normalized trace and @xmath45 is the usual trace . for partitions @xmath46 and @xmath47 of the same set , @xmath48 means their join in the lattice of all partitions of the set . we say that a set @xmath49 _ splits _ a partition @xmath50 if @xmath49 is the union of some of the blocks of @xmath50 . we write @xmath51 to mean that @xmath52 and @xmath53 are in the same block of @xmath50 . restriction _ of a partition @xmath50 to a set @xmath54 is the partition @xmath55 , and is denoted @xmath56 . if @xmath57 is a function with domain @xmath58 , then @xmath59 is the partition of @xmath58 so that @xmath60 and @xmath61 belong to the same block of @xmath59 if and only if @xmath62 . * acknowledgement : * the authors are grateful to gabriel tucci for helpful discussions about random vandermonde matrices at an early stage of this research .

appropriately normalized square random vandermonde matrices based on independent random variables with uniform distribution on the unit circle are studied . it is shown that as the matrix sizes increases without bound , with respect to the expectation of the trace there is an asymptotic-distribution , equal to that of a$]-valued r - diagonal element . research supported in part by nsf grant dms-1301604 . this work is included in the thesis of m. boedihardjo for partial fulfillment of the requirements to obtain a ph.d .

appropriately normalized square random vandermonde matrices based on independent random variables with uniform distribution on the unit circle are studied . it is shown that as the matrix sizes increases without bound , with respect to the expectation of the trace there is an asymptotic-distribution , equal to that of a$]-valued r - diagonal element . research supported in part by nsf grant dms-1301604 . this work is included in the thesis of m. boedihardjo for partial fulfillment of the requirements to obtain a ph.d . degree at texas a&m university ] research supported in part by nsf grant dms-1202660 . ]

math0411648

i

let @xmath0 be a complete riemannian manifold with infinite measure . the riesz transform @xmath15 on @xmath0 is the operator @xmath16 where @xmath17 is the positive laplace operator on @xmath0 . the riesz transform is always a bounded map from @xmath18 to @xmath19 . it is of interest to figure out the range of @xmath20 for which @xmath15 extends to a bounded map @xmath3 . equivalently , we can ask whether @xmath21it has been shown in @xcite that the riesz transform is bounded on @xmath9 for @xmath22 as soon as the manifold satisfies the doubling property as well as a natural heat kernel upper bound . the situation for @xmath10 is more complicated : there is some understanding of what happens in the more restricted class of manifolds satisfying upper and lower gaussian estimates for the heat kernel ( see @xcite , @xcite ) , and it is also known that the above more general assumptions do not imply the boundedness of the riesz transform for all @xmath23 . the counterexample is simply the connected sum of two copies of @xmath24 , where one easily sees that the riesz transform is unbounded for @xmath25 ( see @xcite ) , precisely because the boundedness for such @xmath20 would imply a lower gaussian heat kernel estimate on this manifold , which is known to be false . the first aim of the present article is to find out what happens in the remaining range @xmath26 , and to treat more generally by the same token manifolds with a finite number of euclidean ends . our second aim is to give , in a somewhat more general class of manifolds , a cohomological consequence of the boundedness of the riesz transform for some @xmath23 , which explains the unboundedness in the range @xmath27 in the examples just mentioned . on @xmath24 , it is a classical result in harmonic analysis that the riesz transform is bounded on @xmath9 for all @xmath28 . in this case , the kernel of the riesz transform is given by @xmath29 ( we shall use @xmath30 for a euclidean coordinate throughout this paper , while the prime denotes the ` right variable ' of a kernel @xmath31 ; also , @xmath32 denotes @xmath33 and we write @xmath34 for @xmath35 . ) it is useful to compactify @xmath24 to a compact manifold with boundary @xmath36 by adding a sphere at infinity , and using @xmath37 as a boundary defining function and @xmath38 . ] for it . if we consider this kernel of @xmath39 near the ` right boundary ' of @xmath40 , namely @xmath41 , where @xmath42 , we see that it has an expansion given by @xmath43 the leading power in this expansion is @xmath44 and the coefficient multiplying it is @xmath13 . this kernel , by itself , is not bounded on @xmath9 for @xmath5 because the decay of the kernel puts it only in @xmath45 , @xmath46 , as a function of @xmath47 with @xmath30 fixed , so it can only be boundedly paired with elements in @xmath9 for @xmath48 . however , when we apply a @xmath30-derivative , the leading term is killed ( since @xmath49 ) and the kernel of @xmath15 decays at one order better , namely @xmath50 . this allows pairing with elements of @xmath9 for any @xmath51 . let @xmath0 be a manifold with euclidean ends , and assume the number of ends is at least two . it is now relatively easy to explain why the riesz transform on @xmath0 is not bounded for @xmath5 . for simplicity we shall assume here that @xmath0 has exactly two euclidean ends . let us compactify @xmath0 to a compact manifold @xmath52 in the analogous way to @xmath36 above . the boundary of @xmath52 is then the disjoint union of two @xmath53-spheres , which we shall denote @xmath54 and @xmath55 . it turns out that the kernel of @xmath39 has a similar expansion at @xmath56 , of the form @xmath57 but it is no longer true that the leading term @xmath58 . rather , @xmath59 is the harmonic function on @xmath52 that equals @xmath13 on @xmath54 , and zero on @xmath55 . as a consequence , applying the derivative operator in the left variable @xmath30 does not make this leading term disappear , since @xmath60 . hence the kernel of @xmath15 only decays to order @xmath53 at the right boundary of @xmath61 , and therefore can only be paired boundedly with elements of @xmath9 for @xmath48 . in this paper we shall prove [ main ] let @xmath0 be a complete @xmath62 riemannian manifold of dimension @xmath63 which is the union of a compact part and a finite number of euclidean ends . then the riesz transform is bounded from @xmath64 to @xmath65 for @xmath4 , and is unbounded on @xmath9 for all other values of @xmath20 if the number of ends is at least two . our method is to analyze the kernel @xmath39 based on the formula @xmath66 since @xmath0 is a manifold which is conic at infinity , the laplacian @xmath17 on @xmath0 lies in the class of scattering differential operators @xcite and we can use methods from the scattering calculus to analyze the kernel of @xmath39 . we shall analyze the kernel of @xmath39 rather precisely and work out the leading term in the expansion at the right boundary . from this , it will be straightforward to analyze the kernel of @xmath15 and to prove the theorem . the plan of the paper is as follows . we briefly describe the scattering calculus in section [ scatt ] . in sections [ para ] [ rt ] we prove the theorem using the analysis of the resolvent of the laplacian on asymptotically conic spaces in @xcite as a model . we give some large time asymptotics on derivatives of the heat kernel on manifolds with euclidean ends in section [ heat ] . in section [ coh ] we change point of view and consider a much more general class of manifolds , namely complete manifolds @xmath0 of dimension @xmath11 satisfying the nash inequality and with a uniform upper bound @xmath12 on the volume of geodesic balls of radius @xmath67 . we _ assume _ that the riesz transform on @xmath0 is bounded on @xmath9 for some @xmath10 and give several geometric and topological consequences : a hodge - de rham interpretation of the @xmath9 cohomology of @xmath0 ( proposition [ hdr ] ) , injectivity of the map from @xmath14 to @xmath9 cohomology ( lemma [ inj ] ) and derive a contradiction if @xmath7 and @xmath0 has at least two ends ( corollary [ nb ] ) , thus generalizing the unboundedness part of theorem [ main ] for @xmath7 to this larger class of manifolds . in the final section we discuss our results in the context of previously known examples and pose some open problems .

let be a smooth riemannian manifold which is the union of a compact part and a finite number of euclidean ends , for some , each of which carries the standard metric . our main result is that the riesz transform on is bounded from for and unbounded for if there is more than one end . it follows from known results that in such a case the riesz transform on is bounded for and unbounded for ; the result is new for . we also give some heat kernel estimates on such manifolds . we then consider the implications of boundedness of the riesz transform in for some for a more general class of manifolds . assume that is a-dimensional complete manifold satisfying the nash inequality and with an upper bound on the volume growth of geodesic balls . we show that boundedness of the riesz transform on for some implies a hodge - de rham interpretation of the cohomology in degree , and that the map from to cohomology in this degree is injective .

let be a smooth riemannian manifold which is the union of a compact part and a finite number of euclidean ends , for some , each of which carries the standard metric . our main result is that the riesz transform on is bounded from for and unbounded for if there is more than one end . it follows from known results that in such a case the riesz transform on is bounded for and unbounded for ; the result is new for . we also give some heat kernel estimates on such manifolds . we then consider the implications of boundedness of the riesz transform in for some for a more general class of manifolds . assume that is a-dimensional complete manifold satisfying the nash inequality and with an upper bound on the volume growth of geodesic balls . we show that boundedness of the riesz transform on for some implies a hodge - de rham interpretation of the cohomology in degree , and that the map from to cohomology in this degree is injective .

cond-mat0210148

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in many materials , the symmetry of the superconducting order parameter is unconventional , i.e. not @xmath8-wave . in the high-@xmath10 cuprates , it is the singlet @xmath11-wave @xcite . there is experimental evidence that , in the quasi - one - dimensional ( q1d ) organic superconductors @xmath12 @xcite , the symmetry is triplet @xcite , most likely the @xmath0-wave @xcite , with the @xmath13 axis along the conducting chains . experiments indicate that @xmath14 has the triplet chiral @xmath9-wave pairing symmetry @xcite . the unconventional pairing symmetry typically results in formation of subgap andreev bound states @xcite on the surfaces of these superconductors @xcite . for @xmath1-wave cuprate superconductors , the midgap andreev states were predicted theoretically in ref . @xcite and observed experimentally as a zero - bias conductance peak in tunneling between normal metals and superconductors ( see review @xcite ) . for the q1d organic superconductors , the midgap states were theoretically predicted to exist at the edges perpendicular to the chains @xcite . in the chiral superconductor @xmath14 , the subgap surface states are expected to have a chiral energy dispersion @xcite . their contribution to tunneling is more complicated @xcite than a simple zero - bias conductance peak found for the midgap andreev states . various ways of observing electron edge states experimentally are discussed in ref . @xcite . when two unconventional superconductors are joined together in a josephson junction , their andreev surface states hybridize to form andreev bound states in the junction . these states play an important role in the josephson current through the junction @xcite . andreev bound states in high-@xmath10 junctions were reviewed in ref . the josephson effect between two q1d @xmath0-wave superconductors was studied in refs . andreev reflection @xcite at the interfaces between the a and b phases of superfluid @xmath15he was studied in ref . however , andreev bound states were not mentioned in this paper . in the present paper , we predict a new effect for josephson junctions between unconventional nonchiral superconductors , which we call the fractional ac josephson effect . suppose both superconductors forming a josephson junction have surface midgap states originally . this is the case for the butt - to - butt junction between two @xmath0-wave q1d superconductors , as shown in fig . [ fig : jj](a ) , and for the @xmath16 in - plane junction between two @xmath1-wave superconductors , as shown in fig . [ fig : d - wave](a ) . ( the two angles indicate the orientation of the junction line relative to the @xmath17 axes of each @xmath11 superconductor . ) we predict that the contribution of the hybridized andreev bound states produces a @xmath2-periodic relation between the supercurrent @xmath3 and the superconducting phase difference @xmath4 : @xmath5 @xcite . consequently , the ac josephson effect has the frequency @xmath6 , where @xmath18 is the electron charge , @xmath7 is the applied dc voltage , and @xmath19 is the planck constant . the predicted frequency is a half of the conventional josephson frequency @xmath20 originating from the conventional josephson relation @xmath21 with the period of @xmath22 . qualitatively , the predicted effect can be interpreted as follows . the josephson current across the two unconventional superconductors is carried by tunneling of _ single electrons _ ( rather than cooper pairs ) between the two resonant midgap states . thus , the cooper pair charge @xmath23 is replaced the single charge @xmath18 in the expression for the josephson frequency . this interpretation is also supported by the finding that , in the tunneling limit , the josephson current is proportional to the first power ( not square ) of the electron tunneling amplitude @xcite . possibilities for experimental observation of the fractional ac josephson effect are discussed in sec . [ sec : experiment ] . a summary of this work is published in the conference proceedings @xcite . the predicted current - phase relation @xmath5 is quite radical , because every textbook on superconductivity says that the josephson current must be @xmath22-periodic in the superconducting phase difference @xmath4 @xcite . to our knowledge , the only paper that discussed the @xmath2-periodic josephson effect is ref . @xcite by kitaev . he considered a highly idealized model of spinless fermions on a one - dimensional ( 1d ) lattice with superconducting pairing on the neighboring sites . the pairing potential in this case has the @xmath0-wave symmetry , and midgap states exist at the ends of the chain . they are described by the majorana fermions , which kitaev proposed to use for nonvolatile memory in quantum computing . he found that , when two such superconductors are brought in contact , the system is @xmath2-periodic in the phase difference between the superconductors . our results are in agreement with his work . however , we formulate the problem as an experimentally realistic josephson effect between known superconducting materials . for completeness , we also calculate the spectrum of andreev bound states and the josephson current between a singlet @xmath8-wave and a triplet @xmath24-wave superconductors , as well as between two chiral @xmath24-wave superconductors @xcite . in agreement with previous literature @xcite , we find that a josephson current is permitted between singlet and triplet superconductors , contrary to a common misconception that it is forbidden by the symmetry difference . however , we do not find the fractional josephson effect in these cases .

for certain orientations of josephson junctions between two-wave or two-wave superconductors , the subgap andreev bound states produce a-periodic relation between the josephson current and the phase difference : . consequently , the ac josephson current has the fractional frequency , where is the dc voltage . in the tunneling limit , the josephson current is proportional to the first power ( not square ) of the electron tunneling amplitude . thus , the josephson current between unconventional superconductors is carried by single electrons , rather than by cooper pairs . we also study junctions between singlet-wave and triplet-wave , as well as between chiral-wave superconductors .

for certain orientations of josephson junctions between two-wave or two-wave superconductors , the subgap andreev bound states produce a-periodic relation between the josephson current and the phase difference : . consequently , the ac josephson current has the fractional frequency , where is the dc voltage . in the tunneling limit , the josephson current is proportional to the first power ( not square ) of the electron tunneling amplitude . thus , the josephson current between unconventional superconductors is carried by single electrons , rather than by cooper pairs . the fractional ac josephson effect can be observed experimentally by measuring frequency spectrum of microwave radiation from the junction . we also study junctions between singlet-wave and triplet-wave , as well as between chiral-wave superconductors .

1007.2014

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cold atomic systems have provided an ideal playground for the experimental studies of the unitary evolution of thermally isolated quantum systems . @xcite apart from the experimental interest , studies of quantum evolution have shed light on some fundamental questions such as thermalization . @xcite a widely - studied scenario is the unitary evolution of a quantum state when the hamiltonian is suddenly changed a `` quantum quench '' , @xcite which has been the subject of many recent studies ( see refs . [ ] for a few examples ) . a challenging question , which has been addressed theoretically in one dimensional systems , is the evolution of the entanglement entropy following the quench . @xcite more generally , such studies are concerned with the fate of an out - of - equilibrium quantum state with a hamiltonian that changes with some time - dependent protocol . the case where the coupling constants are changed across a quantum phase transition is of special interest . in recent experiments with spinor condensates , for example , the formation of ferromagnetic domains was observed in a quench to a hamiltonian with a symmetry - breaking ferromagnetic ground state . @xcite even though the interactions after the quench favor a certain type of order , it is not at all obvious that the order should emerge out of equilibrium . since symmetry - breaking order has a local order parameter , the non - equilibrium state can support the formation of ordered domains . but what about quenches across a topological phase transition ? would any of the topological characteristics of the equilibrium phase show up in the non - equilibrium wave - function ? another interesting aspect of the non - equilibrium dynamics is the issue of thermalization and whether a large system can act as an effective heat bath for its subsystems . if thermalization occurs , due to the presence of some excess energy , the non - equilibrium state at long times should be in some sense _ close _ to a thermal state at a finite temperature , which implies volume scaling for the entanglement entropy . the qualitative discussions above motivate a detailed analysis of a quantum quench across a topological phase transition into the topological phase . we study the specific case of the kitaev toric code model @xcite with spin - polarized initial states . a related quantum quench problem with topologically ordered initial states was recently studied numerically in ref . we focus on the time evolution of the entanglement entropy because it is intimately related to topological order through the topological entanglement entropy . @xcite entanglement entropy is also related to thermalization since , as mentioned above , volume scaling of the entropy as opposed to the area law is generically expected of thermal states . we compute exactly the bipartite entanglement entropy as a function of time . this is an example where exact calculation can be done in 2 + 1d ( thus far , analytical results for the time - evolution of entanglement had focused on 1 + 1d systems ) . we show that the entanglement entropy respects the area law at all times and if one adds disorder to the coupling constants , the recurrences or revivals are suppressed at long times and the entanglement entropy per unit `` area '' ( boundary length ) @xmath0 equals @xmath1 in the thermodynamic limit when the initial polarization is in the @xmath2 or @xmath3 direction . we find the dependence of this saturation value on the initial state for an arbitrary direction of the initial magnetization . a new ingredient that comes in when considering these initial states is order - one corrections to the entanglement entropy from the convex and concave corners in the subsystem boundary . we find that the general form of the generated entanglement entropy is given by @xmath4 where @xmath0 is the perimeter of the subsystem and @xmath5 ( @xmath6 ) the number of convex ( concave ) corners in its boundary . the functions of time @xmath7 , @xmath8 and @xmath9 are independent of the subsystem geometry . from the form of the entanglement entropy above , we find that the topological entropy vanishes at all times . we study the effects of breaking the integrability in a perturbative approach . we identify the mechanism by which an integrability - breaking magnetic field can change the area law to the volume law as expected of thermalized states . the physical picture is that the area law survives at low orders in an expansion in the integrability - breaking field . going to higher orders however increases the thickness of a ring - like region around the subsystem boundary that contributes to the entanglement entropy . eventually at high enough orders , the ring will collapse onto itself making volume scaling possible . in the perturbative treatment , we explicitly find that the topological entanglement entropy remains zero at low orders . we expect that the excess energy and the finite density of defects should prevent the formation of any topological order in a sudden quench even if one breaks the integrability . the paper is organized as follows . in section [ sec : quenchesxz ] we discuss quantum quenches for spin - polarized initial states in the @xmath2 or @xmath3 direction . we calculate the entanglement entropy analytically and discuss the effects of disorder in the coupling constants . in section [ sec : corners ] , we study the role of the sharp corners in the subsystem boundary in the generation of entanglement by exactly calculating the second order renyi entropy for an arbitrary direction of the initial magnetization . we then discuss the effects of breaking the integrability , which we treat perturbatively , in section [ sec : non - integrable ] . we conclude the paper in section [ sec : conclusion ] .

we find that the area law survives at all times . adding disorder to the toric code couplings we argue that breaking the integrability with a small magnetic field could change the area law to a volume scaling as expected of thermalized states but is not sufficient for forming topological entanglement due to the presence of an excess energy and a finite density of defects .

we study quantum quenches in the two - dimensional kitaev toric code model and compute exactly the time - dependent entanglement entropy of the non - equilibrium wave - function evolving from a paramagnetic initial state with the toric code hamiltonian . we find that the area law survives at all times . adding disorder to the toric code couplings makes the entanglement entropy per unit boundary length saturate to disorder - independent values at long times and in the thermodynamic limit . there are order - one corrections to the area law from the corners in the subsystem boundary but the topological entropy remains zero at all times . we argue that breaking the integrability with a small magnetic field could change the area law to a volume scaling as expected of thermalized states but is not sufficient for forming topological entanglement due to the presence of an excess energy and a finite density of defects .

astro-ph9907342

i

the presence of dust in galaxies has a profound impact on observable characteristics such as their apparent uv / optical / near - ir luminosity , their spectral energy distribution , their recognizable level of star - formation activity , and their morphology . in addition , dust directly affects and often controls the physical conditions within the interstellar medium of galaxies and plays a major role in interstellar chemistry by providing the sites for the formation of interstellar molecular hydrogen and by regulating the interstellar radiation field . quantitative estimates of the dust mass responsible for the observed effects are needed in order to yield gas - to - dust ratios in galaxies of different types , essential if we are to understand the chemical evolution of galaxies over cosmological time scales . radiative transfer simulations often provide the most direct way to arrive at a quantitative assessment of the ways that lead to observed dust effects , provided such simulations are sufficiently realistic to apply to actual physical systems . all such simulations involve approximations . historically , these have ranged from the adoption of absorbing screen geometries ( @xcite , 1975 ) in analogy to the study of extinction of starlight in our galaxy , to the consideration of various geometries with embedded dust , including the effects of multiple scattering ( witt , thronson , & capuano 1992 , hereafter @xcite ; @xcite ) . according to @xcite , a galaxy may be looked upon as consisting of environments which are characterized by certain geometrical relations between the attenuating dust and the illuminating stars , for example , starburst regions may be approximated by regions occupied by luminous stars , surrounded on the outside by the remnants of molecular clouds from which the stars originated . quiescent parts of dusty disk galaxies may resemble systems in which stars and dust are fairly uniformly mixed , or , if one considers the same case at longer wavelengths where the dominant sources might be k - giants , a case where the scale height of sources is much larger than the scale height of the dust which is concentrated toward the center or central plane . as shown by @xcite , equal amounts of dust in these different configurations produce very different reddening and attenuation effects . for the analysis of effects resulting from changes in the inclination of disk galaxies , disk models with embedded dust have been developed , either in plane - parallel or doubly exponential geometry ( e.g. @xcite ; @xcite ; @xcite ; @xcite ) . all of the models mentioned so far consistently illustrate the fact that a certain quantity of embedded dust produces much smaller attenuation effects than a foreground screen made from the same amount of dust , and that the inclusion of multiple scattering reduces these effects even further by returning the scattered radiation to the optical radiation field , albeit with an altered spectral and directional distribution . an approximation in common among all the models mentioned above is the homogeneous nature of their assumed dust distributions , which are either constant or of a monotonically varying continuous variety . in the first paper in the present series ( witt & gordon 1996 , hereafter @xcite ) , we conducted an extensive exploration of the effects of clumpiness on the transport of radiation through a spherical system containing scattering dust and a single central source this study , together with the results of earlier work on transfer through clumpy media ( e.g. @xcite ; @xcite ; @xcite ) clearly revealed that the clumpy multi - phase structure of the interstellar medium ( ism ) leads to a significant reduction in the opacity produced by a given distribution and mass of interstellar dust . in addition , @xcite showed that the relationship between the effective optical depth of a clumpy distribution and that of an equivalent homogeneous distribution is non - linear ; this leads to an effective attenuation as a function of wavelength that differs from the opacity law intrinsic to the dust in the system . these conclusions have been further amplified in a recent investigation of the radiative transfer in the clumpy environment of young stellar objects by wolf , fischer , & pfau ( 1998 ) and general investigation of clumpy radiative transfer by vrosi & dwek ( 1999 ) . since clumpiness is a reality of the ism wherever it can be observed with sufficient spatial resolution , we are introducing it into the transfer of radiation in such galactic environments as investigated in @xcite now . a preliminary version of some aspects of this work appeared in gordon , calzetti , & witt ( 1997 ) . in addition to adding models with a clumpy two - phase structure , we have improved several other aspects of the original @xcite study . our knowledge of dust scattering properties in the uv has greatly improved since 1992 , and with some confidence we are now modeling the transfer for 15 ( out of a total of 25 ) bandpasses in the wavelength range from 1000 to 3000 , compared to two in @xcite . this improved uv coverage makes the current models particularly well suited for the analysis of starburst galaxies , both nearby and at high redshift , since these systems emit much of their stellar energy at uv wavelengths . furthermore , most previous multi - wavelength radiative transfer studies have assumed opacity functions and scattering properties representative of average milky way ( mw ) dust . even within the mw dust characteristics vary from one environment to another ( e.g. @xcite ) and already in the local group of galaxies there exists a considerable variety of opacity laws ( @xcite ; @xcite ; @xcite ) . in starburst galaxies , in particular , it has been shown ( @xcite ) that the opacity function intrinsic to the dust present there is much more similar to dust found typically in the bar of the small magellanic cloud ( smc ) . we therefore model all our galactic environments with both the average mw and smc bar dust . other radiative transfer studies which have included both mw and smc bar type dust are those detailed by gordon et al . ( 1997 ) , takagi , arimoto , & vansevicius ( 1999 ) , and ferrara et al . the models presented in the present paper are particularly well suited to analyze the reddening effects and the corresponding uv attenuation in lyman - break galaxies and galaxies seen in the hubble deep fields ( @xcite ; @xcite ; @xcite ; @xcite ; @xcite , @xcite ) . they are equally well usable for studying opacity effects in nearby dusty galaxies ( e.g. @xcite ; @xcite ; @xcite ; @xcite ) . the principal results from the current work are an extensive set of tables , accessible in the on - line version of this issue of the astrophysical journal or available by contacting the authors . we will present the details of the models in the following section 2 ; selected results will be summarized in graphical form in section 3 ; we will discuss the implications of these results for currently ongoing galaxy studies in section 4 , to be followed by a summary in section 5 .

extinction and scattering properties for two types of interstellar dust , similar to those found in the average diffuse medium of the milky way galaxy ( mw ) and the bar of the small magellanic cloud ( smc ) , are considered . the examination of the models concentrates on the study of uv / visual / near - ir reddening effects , the wavelength dependence of attenuation , and on the changes that arise from the transition from homogeneous to clumpy dust distributions in different star / dust geometries . this makes the assessment of the attenuation of the far - uv flux from starburst galaxies difficult , if only uv / visual / near - ir data are available .

we present and discuss the results of new multiple - scattering radiative transfer calculations for three representative types of galactic environments , filled with either homogeneous or two - phase clumpy dust distributions . extinction and scattering properties for two types of interstellar dust , similar to those found in the average diffuse medium of the milky way galaxy ( mw ) and the bar of the small magellanic cloud ( smc ) , are considered . the wavelength coverage extends from 1000 to 30,000 , with particular emphasis on the rest - frame uv . this makes these models especially applicable to starburst galaxies and lyman - break galaxy samples . the examination of the models concentrates on the study of uv / visual / near - ir reddening effects , the wavelength dependence of attenuation , and on the changes that arise from the transition from homogeneous to clumpy dust distributions in different star / dust geometries . embedded dust , especially when clumpy , leads to saturation at fairly low reddening values with correspondingly gray attenuation functions . this makes the assessment of the attenuation of the far - uv flux from starburst galaxies difficult , if only uv / visual / near - ir data are available . existing data for uv - selected starburst galaxies indicate a range of uv attenuation factors of 0150 . our models reproduce the `` calzetti attenuation law '' , provided one adopts smc - type dust and a clumpy shell - type dust distribution surrounding the starbursts . the average far - uv attenuation factor for the calzetti sample is found to be 7.4 . the only relatively reliable measure for the uv attenuation factor for single galaxies was found in the ratio of the integrated far - ir flux to the far - uv flux , measured near 1600 , requiring the measurement of the entire spectral energy distribution of galaxies .

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in this section we discuss which of our models with respect to geometry , optical depth , and dust type might best be used for the analysis of observations of different kinds of galaxies . in particular , we concentrate on dust attenuation studies of nearby starburst galaxies and lyman break galaxies . + + starburst galaxies exhibit a wide range of dustiness as evidenced by large variations in the uv spectral index @xmath39 , ratios of recombination line strengths , and ratios of far - ir to uv luminosities . the uv spectral index @xmath39 was defined by calzetti et al . ( 1994 ) through the relation @xmath40 in the range @xmath41 . by comparing the spectral energy distributions ( sed ) of more highly reddened starbursts with those of barely reddened starbursts , calzetti et al . ( 1994 ) derived the observed wavelength dependence of the dust attenuation in these systems . the attenuation function takes into account the return of scattered light into the integrated light of a galaxy and also reflects radiative transfer effects arising in the three - dimensional distributions of stars , gas , and dust in these galaxies . this observed attenuation function , further refined in calzetti ( 1997 ) , is referred to in the literature as the `` calzetti attenuation law '' or `` calzetti law '' . this attenuation due to internal dust must be clearly distinguished from the wavelength dependence of interstellar extinction , which is the attenuation due to absorption _ and _ scattering by a screen of dust located between a distant source and an observer . the principal characteristic of the `` calzetti law '' is the absence of a 2175 feature . gordon et al . ( 1997 ) showed that the `` calzetti law '' can be reproduced , if the radiative transfer in starburst galaxies is occurring in a medium with intrinsic dust properties closely resembling that of smc dust . also , the large range of observed reddenings , as measured by variations in the spectral index @xmath39 , appears to require efficient attenuation geometries such as provided by our shell or dusty geometries . in fig . [ fig_ext_cal ] we compare attenuation values derived from starburst galaxies by calzetti ( 1997 ) with our model attenuation functions . in order to facilitate this comparison , models and observations are renormalized to @xmath42 . in order to transform the values in table 5 of calzetti ( 1997 ) , we have used the result of calzetti ( 1997 ) that the stellar continuum suffers 40% the reddening that the gas suffers , i.e. @xmath43 . the data point capable of discriminating between different models most clearly is the one near @xmath44 , derived from the far - uv slope in the reddened seds of starbursts . no model with mw dust matches this data point . in addition , the lack of a 2175 feature in the observations compared to the prediction of a 2175 feature in the models with mw dust argues strongly against the presence of mw dust in starburst galaxies . this will be discussed further in section [ sec_bump ] . among smc dust models , the same point does discriminate between dust column densities and clearly favors the clumpy shell model for @xmath45 . as is apparent from fig . [ fig_ext_smc ] , such a model predicts an attenuation optical depth of about @xmath46 at @xmath44 , and , according to fig . [ fig_ebv_tauv ] , a color excess @xmath47 . an attenuation optical depth of 2.0 implies that the flux at @xmath44 has been reduced by a factor 7.4 on average in this uv - selected sample of starburst galaxies . we need to re - emphasize that there is no universal attenuation function and that the attenuation factor of 7.4 corresponds simply to the average of the sample of uv / optically - selected starbursts studied by calzetti et al . our average attenuation factor of 7.4 compares well with the luminosity - weighted mean absorption factor of 5.4 derived by meurer et al . ( 1999 ) for the same sample . we discuss the uv flux reduction factor and the uncertainties associated with its determination further in section [ sec_uv_atten ] . it came as an initial surprise during the iras mission that far - ir ultraluminous and by inference , very dust - rich , galaxies in most instances exhibited optical colors which were barely distinguishable from those of normal galaxies of similar population type . @xcite showed that this was due to the fact that , given embedded dust geometries , the optical colors were determined by the least attenuated stars , while the far - ir flux was due to the absorption of light from stars which contribute little or nothing to the optical flux . the present calculations were extended to dust column densities corresponding to @xmath48 instead of 15 in the case of @xcite . in fig . [ fig_ratio ] , we show the resulting ratios of the far - ir flux , integrated over all frequencies at which dust emission occurs , to the integrated uv / optical / near - ir stellar flux . we reproduce the most extreme observed ratios near 100 with the clumpy shell model of @xmath48 with a maximum reddening near 0.8 in @xmath20 and only slightly lower ratios with the homogeneous dusty models with a reddening less than 0.3 in @xmath20 . only the homogeneous shell , as expected for a simple screen , produces very large amounts of reddening of @xmath49 and @xmath50 for @xmath48 . the fact that most ir luminous galaxies appear to be relatively blue seems to indicate that clumpy dust structures prevail in most of them . this is also confirmed by the correlation between the ratio @xmath51 and the spectral index @xmath52 for different geometries and dust types , shown in fig . [ fig_uvratio ] . a major aim of studies of high - z starbursts ( or lyman - break galaxies ) is to determine the epoch of peak star formation in the history of the universe , if such a peak indeed exists . the outcome of such an investigation depends critically upon the corrections applied for dust attenuation in the rest - frame uv continuum spectrum of the observed galaxies , given that these systems contain substantial amounts of internal dust ( @xcite ; @xcite ; @xcite ; @xcite ; @xcite ) . in addition , the upcoming nasa galex mission is to produce about 100,000 uv galaxy spectra in order to probe the global history of star formation , and the observed uv spectral slope is be be related uniquely to the attenuation factor by which the uv flux has been reduced by dust internal to the galaxies . our figures [ fig_ext_mw ] and [ fig_ext_smc ] already indicated some of the problems to be expected in such an approach . the attenuation functions are geometry dependent and they become increasingly gray as the dust column density increases . this means that a heavily attenuated starburst may exhibit a steep uv slope in its sed , resembling that of a barely reddened galaxy , but show a greatly reduced uv flux , corresponding to a system with little star forming activity . the chances for underestimating the star formation rate in early epochs of the universe are therefore severe , if dust is abundant generally in the early galaxies . fortunately , our models provide an excellent set of tools with which to evaluate different approaches to the problem of determining the far - uv attenuation factor . in fig . [ fig_a1600]a we illustrate the computed attenuation factor at 1600 as a function of @xmath20 found for different model geometries and dust types . as anticipated above , the observation that most observed values of @xmath20 for lyman - break galaxies fall into the narrow range of 0.2 to 0.3 barely constrains the attenuation factor to the range 4 to 200 . this is not very useful as a constraint . in fig . [ fig_a1600]b we investigate the use of the spectral index @xmath39 as a tool to evaluate the attenuation factor . our radiative transfer models do not assume a specific energy distribution for the source spectrum . hence , we predict only the change in the spectral index @xmath39 which occurs as a result of the wavelength dependent attenuation . the galex program advocates this particular approach by suggesting that the change in the uv slope of the galaxies sed can be converted into information about the applicable attenuation factor . meurer et al . ( 1999 ) have taken the additional step of calibrating the correlation between the spectral index @xmath39 and the uv - attenuation , derived for nearby uv - selected starburst galaxies . in observed starburst spectra , this change in spectral index ranges from zero to 3 ( meurer et al.1997 ) . our fig . [ fig_a1600]b reveals that correlations between the spectral index change and the uv attenuation factor are extremely model dependent and even more dependent on the type of dust present in a given system . the calibration proposed by meurer et al . ( 1999 ) is shown in fig . [ fig_a1600]b as a solid black line . for this to be valid universally , one must assume that smc - type dust is present in all starburst galaxies and that shell - type geometries with various degrees of clumpiness are the prevailing star / dust geometries . even when restricting considerations to smc - type dust , the range of observed values of @xmath52 is consistent with attenuation factors in the range 0150 . as is evident from fig . [ fig_a1600]b , mw - type dust is not expected to produce positive values of @xmath52 . this is contrary to observations in starbursts , where such positive changes in the uv spectral index are seen ( meurer et al . however , mw - type dust will reveal its presence by the appearance of a 2175 feature . this has been seen in the heavily obscured starburst nucleus of m33 ( @xcite ) , which indicates that smc - type dust is not a universal characteristic of all starburst environments . however , the preference for smc - type dust in starburst galaxies is affirmed , when we compare values of @xmath53 flux ratios and corresponding values of @xmath52 from observations ( meurer et al . 1997 ) with our models in fig . [ fig_uvratio ] . for this calculation we assumed that the unattenuated source sed was given by a 1 or a 1000 myr constant star formation sed of fioc & rocca - volmerange ( 1999 ) . the observed data points clearly follow the trend set by the model for clumpy shell configurations with smc dust . this agreement would become even more convincing , were we to present models with different ratios of clump to interclump density , different clump size , and different filling factors , which is , however , beyond the scope of this present discussion . the demonstrated model dependence of the ratio of fir to f160bw flux suggests that the observed scatter in the data points is most likely real , as was concluded by meurer et al . ( 1999 ) also . the spread in the fir to f160bw ratio for a given value of @xmath52 corresponds to a factor of 10 uncertainty in the corresponding uv attenuation factor . we conclude , therfore , that the uv spectral slope is not a reliable indicator of the dust attenuation in a given galaxy . it is usable only , if a large sample of starburst galaxies with relatively uniform characteristics is being considered at once . in fig . [ fig_ratio_1600]a , we plot the ratio of dust - emitted ir flux to the integrated uv nir flux against the attenuation factor at 1600 . the model calculations assume two starbursts of different ages , one a 1 million year old constant star formation sed , the other a 1 billion year old constant star formation sed . we note that even this ratio does not yield a unique relation to the uv attenuation factor . in particular , clumpiness in a given dust distribution will reduce the attenuation at 1600 for a given value of the ratio of dust - emitted ir flux to the integrated uv nir flux , because clumpiness is associated with a much grayer attenuation function . this is particularly evident in shell - type geometries . variations in the age of the starburst and the associated changes in the uv nir sed affect the ratio as well , leading to a significant model dependence of the predicted attenuation factor at 1600 . by contrast , if we plot the ratio of integrated fir flux to the measured flux at 1600 against the attenuation factor at 1600 , as shown in fig . [ fig_ratio_1600]b , the model and age dependence practically vanish . we conclude , therefore , that the uv attenuation factor can be evaluated reliably for individual galaxies only , if a complete spectral survey of the fir emission of the galaxy is carried out and a flux measurement in the far - uv is obtained . gordon et al . ( 1997 ) showed that the absence of the 2175 extinction bump in the attenuation function of starbursts can not be explained by radiative transfer effects but requires the actual absence of the absorber giving rise to this feature . this is despite the fact that some weakening of the 2175 feature was seen in the attenuation curves ( fig . [ fig_ext_mw ] ) for embedded geometries involving mw dust and further weakening occurred when clumpiness was included . as was found by gordon et al . ( 1997 ) , the 2175 bump can be suppressed using radiative transfer effects , but at the expense of a gray extinction throughout the uv . thus , the existence of a substantial slope in the calzetti ( 1997 ) attenuation curve ( fig . [ fig_ext_cal ] ) implies that the dust in starburst galaxies must lack the absorbers which produce the 2175 bump . the dust in starbursts most closely resembles that found in the smc ( @xcite ) . recent modeling of this dust by zubko ( 1999 ) shows that such dust lacks the component normally introduced to produce the 2175 feature ( graphite ) , and that the overall size distribution of smc grains is shifted toward smaller sizes compared to mw dust . we find the color index ( @xmath54 ) to be particularly sensitive for distinguishing between the presence of smc dust and mw dust , one without the 2175 feature and the other with . in fig . [ fig_f170wf218w_bv ] , we show a color - color diagram of starburst data , which are compared to the colors of unreddened starburst models ( open symbols ) and to reddening lines produced by our models . these reddening lines are attached to different unreddened models to show them distinctly ; they may be shifted horizontally to fit the data . several facts emerge clearly : all starburst data appear on or below the line of unreddened burst models , i.e. they are reddened in the ( @xmath54 ) index . only the reddening lines for smc dust fall below the unreddened bursts , while all mw models fall above the unreddened bursts , where no data points are found . both the amount of reddening in the ( @xmath54 ) index and the distribution of data points in the color plane can best be fitted with a clumpy shell model with smc dust . we take this ( as did gordon et al . 1997 ) to be one of the strongest indications that nearby starbursts contain smc type dust and that the prevailing geometry is that of a clumpy shell model . this sensitive test might be applied to the rest - frame uv seds of high - redshift galaxies in general in order to test for the presence of the type dust ( mw or smc ) .

embedded dust , especially when clumpy , leads to saturation at fairly low reddening values with correspondingly gray attenuation functions . the average far - uv attenuation factor for the calzetti sample is found to be 7.4 . the only relatively reliable measure for the uv attenuation factor for single galaxies was found in the ratio of the integrated far - ir flux to the far - uv flux , measured near 1600 , requiring the measurement of the entire spectral energy distribution of galaxies .

we present and discuss the results of new multiple - scattering radiative transfer calculations for three representative types of galactic environments , filled with either homogeneous or two - phase clumpy dust distributions . extinction and scattering properties for two types of interstellar dust , similar to those found in the average diffuse medium of the milky way galaxy ( mw ) and the bar of the small magellanic cloud ( smc ) , are considered . the wavelength coverage extends from 1000 to 30,000 , with particular emphasis on the rest - frame uv . this makes these models especially applicable to starburst galaxies and lyman - break galaxy samples . the examination of the models concentrates on the study of uv / visual / near - ir reddening effects , the wavelength dependence of attenuation , and on the changes that arise from the transition from homogeneous to clumpy dust distributions in different star / dust geometries . embedded dust , especially when clumpy , leads to saturation at fairly low reddening values with correspondingly gray attenuation functions . this makes the assessment of the attenuation of the far - uv flux from starburst galaxies difficult , if only uv / visual / near - ir data are available . existing data for uv - selected starburst galaxies indicate a range of uv attenuation factors of 0150 . our models reproduce the `` calzetti attenuation law '' , provided one adopts smc - type dust and a clumpy shell - type dust distribution surrounding the starbursts . the average far - uv attenuation factor for the calzetti sample is found to be 7.4 . the only relatively reliable measure for the uv attenuation factor for single galaxies was found in the ratio of the integrated far - ir flux to the far - uv flux , measured near 1600 , requiring the measurement of the entire spectral energy distribution of galaxies .

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we have presented new multiple - scattering radiative transfer calculations for three representative types of galactic environments and two dust types , as found within the local group in the form of the average mw and smc type dust . both homogeneous and two - phase clumpy dust distributions have been explored over a large range of dust column densities , measured by @xmath55 . the full numerical details of the models are made available to the community via the authors , the authors www site , and eventually various national / international data centers . the environments examined include dusty , a fully mixed spherical distribution of dust and embedded stars ; shell , a dust - free star filled region , surrounded by a dust shell ; and cloudy , a mixed dust - star region surrounded by stars in a dust - free region on the outside . the models cover the wavelength range 1000 to 30000 with exceptionally close coverage of the rest - frame uv . this aspect makes these models particularly applicable to uv - selected starburst galaxies and lyman - break galaxies . we examined the models with respect to predicted reddening effects , attenuation functions , and the contribution of scattered light to the total flux as a function of wavelength . all model types except the homogeneous shell model exhibit reddening saturation effects . in particular , models that are likely representatives for starburst galaxies show values of @xmath20 not in excess of 0.3 , despite a large range of dust column density . reddening `` vectors '' in color - color diagrams are complex non - linear functions depending on the prevailing dust type and structure , as well as on the geometry . attenuation functions , which measure the wavelength - dependent reduction in the total stellar and scattered flux from a dusty galaxy , exhibit a trend toward increasing grayness with increasing dust column density . this trend is stronger in clumpy dust distributions than in homogeneous ones . no justification was found for the use of a universal attenuation function for the analysis of a large sample of galaxies . in particular , we found that the widely - employed `` calzetti law '' is most closely reproduced by our clumpy shell model with smc - type dust and a dust column density corresponding to @xmath31 . such a case corresponds to an attenuation optical depth in the uv of @xmath56 or a uv attenuation correction factor of 7.4 . the calzetti law is valid for statistical samples which have similar dust / star geometries as found in uv - selected starbursts and which have dust column densities within narrow limits . under no circumstances should it be used for the attenuation correction for single galaxies . when investigating various approaches to determining this attenuation factor in general , we found that the use of the color excess @xmath20 and the uv spectral index @xmath39 lead to results that depend strongly on dust type , dust distribution , and source - dust geometry . only the measurement of the @xmath57 flux ratio promises reasonable certainty for the determination of the uv attenuation correction factor in individual galaxies . this reaffirms the need for observations of starburst galaxies and lyman - break galaxies over the entire range of rest - wavelengths , particularly the fir , in addition to the uv . we further showed that observations can clearly discriminate between the presence of mw - type dust and smc - type dust through the use of a @xmath58 vs. @xmath59 color - color diagram . when applied to existing data on uv - selected nearby starburst galaxies , a consistent prevalence of smc dust is found . we gratefully acknowledge support from nasa grants nag 5 - 3367 and nagw-3168 to the university of toledo . constructive conversations with daniela calzetti , geoffrey clayton , and karl misselt are also gratefully acknowledged . berlind , a. a. , quillen , a. c. , pogge , r. w. , & sellgren , k. 1997 , , 114 , 107 bianchi , l. , clayton , g. c. , bohlin , r. c. , hutchings , j. b. , & massey , p. 1996 , , 471 , 203 boiss , p. 1990 , , 228 , 483 bruzual , a. g. , magris , g. , & calvet , n. 1988 , , 333 , 673 byun , y. i. freeman , k. c. , & kylafis , n. d. 1994 , 432 , 114 calzetti , d. 1997 , , 113,162 calzetti , d. , bohlin , r. c. , gordon , k. d. , witt , a. n. , bianchi , l. 1995 , , 446 , l97 calzetti , d. , kinney , a. l. , & storchi - bergmann , t. 1994 , , 429 , 582 cardelli , j. a. , clayton , g. c. , & mathis , j. s. 1989 , , 345 , 245 [ ccm ] corradi , r. l. m. , beckman , j. e. , & simonneau , e. 1996 , , 282 , 1005 di bartolomeo , a. , barbaro , g. , & perinotto , m. 1996 , in new light on galaxy evolution , iau symp . 171 , ed . r. bender and r. l. davies , kluwer acad . 363 dickinson , m. 1997 , in the hubble deep field , stsci symp . , eds . m. livio , s. m. fall , & p. madau , ( in press ) ferrara , a. , bianchi , s. , cimatti , a. , & giovanardi , c. 1999 , , in press ( astro - ph/9903078 ) fioc , m. & rocca - volmerange , b. , 1999 , in preparation fitzpatrick , e. l. 1999 , , 111,63 gordon , k. d. , calzetti , d. , & witt , a. n. 1997 , , 487 , 625 gordon , k. d. & clayton , g. c. 1998 , , 500 , 816 gordon , k. d. , witt , a. n. , carruthers , g. r. , christensen , s. a. , & dohne , b. c. 1994 , , 432 , 641 gordon , k. d. , hanson , m. m. , clayton , g. c. , rieke , g. h. , & misselt , k. a. 1999a , , 519 , 165 gordon , k. d. , witt , a. n. , & clayton , g. c. 1999b , in preparation heckman , t. m. 1998 , in the birth of galaxies : xth recontres de blois , ed . b. guiderdoni , in press henyey , l.g . & greenstein , j.l . 1941 , , 93 , 70 hobson , m. p. & scheuer , p. a. g. 1993 , , 264 , 145 holmberg , e. 1958 , medd . ser . 2 , no . 6 holmberg , e. 1975 , stars and stellar systems ix , univ . of chicago press , 123 hurwitz , m. 1994 , apj , 433 , 149 kim , s .- h . , martin , p. g. , & hendry , p. d. 1994 , , 422 , 164 kuchinski , l. e. , terndrup , d. m. , gordon , k. d. , & witt , a. n. 1998 , , 115 , 1438 larson , r. b. & tinsley , b. m. 1978 , , 219 , 46 lehtinen , k. & mattila , k. 1996 , , 309 , 570 lillie , c. f. , & witt a. n. 1976 , , 208 , 64 meurer , g. r. , heckman , t. m. , lehnert , m. d. , leitherer , c. , & lowenthal , j. 1997 , , 114 , 54 meurer , g. r. , heckman , t. m. , & calzetti , d. 1999 , , in press ( astro - ph/9903054 ) misselt , k. a. , clayton , g. c. , & gordon , k. d. 1999 , , 515 , 128 morgan , d. h. , nandy , k. , & thompson g. i. 1976 , , 177 , 531 natta , a. & panagia , n. 1984 , , 287 , 228 sawicki , m. & yee , h. k. c. 1998 , , 115 , 1329 sawicki , m. j. , lin , h. , & yee , h. k. c. 1997 , , 113 , 1 smith , d. a. , herter , t. , & haynes , m. p. 1998 , , 494 , 150 steidel , c. c. et al . 1999 , , in press ( astro - ph/9811399 ) takagi , t. , arimoto , n. , & vanseviius , v. 1999 , , in press ( astro - ph/9902219 ) toller , g. n. 1981 , phd thesis , state univ . of new york at stony brook vrosi , f. , & dwek , e. 1999 , , submitted witt , a. n. 1977 , , 35 , 1 witt , a. n. , friedmann , b. c. , sasseen , t. p. 1997 , , 481 , 809 witt , a. n. & gordon , k. d. 1996 , , 463 , 681 [ wg96 ] witt , a. n. & lillie , c. f. 1973 , , 25 , 397 witt , a. n. , lindell , r. s. , block , d. l. , & evans , r. 1994 , apj , 427 , 227 witt , a. n. , oliveri , m. v. , & schild , r. e. 1990 , , 99 , 888 witt , a. n. , petersohn , j. k. , bohlin , r. c. , oconnell , r. w. , roberts , m. s. , smith , a. m. , & stecher , t. p. 1992a , , 395 , l5 witt , a. n. , petersohn , j. k. , holberg , j. b. , murthy , j. , dring , a. , & henry , r. c. 1993 , , 410 , 714 witt , a. n. , thronson , h. a. , & capuano , j. m. 1992b , , 393 , 611 [ wtc ] witt , a. n. , walker , g. a. h. , bohlin , r. c. , & stecher , t. p. 1982 , , 261 , 492 wolf , s. , fischer , o. , & pfau , w. 1998 , , 340 , 103 zubko , v. g. 1999 , , in press

we present and discuss the results of new multiple - scattering radiative transfer calculations for three representative types of galactic environments , filled with either homogeneous or two - phase clumpy dust distributions . the wavelength coverage extends from 1000 to 30,000 , with particular emphasis on the rest - frame uv . this makes these models especially applicable to starburst galaxies and lyman - break galaxy samples . existing data for uv - selected starburst galaxies indicate a range of uv attenuation factors of 0150 . our models reproduce the `` calzetti attenuation law '' , provided one adopts smc - type dust and a clumpy shell - type dust distribution surrounding the starbursts .

we present and discuss the results of new multiple - scattering radiative transfer calculations for three representative types of galactic environments , filled with either homogeneous or two - phase clumpy dust distributions . extinction and scattering properties for two types of interstellar dust , similar to those found in the average diffuse medium of the milky way galaxy ( mw ) and the bar of the small magellanic cloud ( smc ) , are considered . the wavelength coverage extends from 1000 to 30,000 , with particular emphasis on the rest - frame uv . this makes these models especially applicable to starburst galaxies and lyman - break galaxy samples . the examination of the models concentrates on the study of uv / visual / near - ir reddening effects , the wavelength dependence of attenuation , and on the changes that arise from the transition from homogeneous to clumpy dust distributions in different star / dust geometries . embedded dust , especially when clumpy , leads to saturation at fairly low reddening values with correspondingly gray attenuation functions . this makes the assessment of the attenuation of the far - uv flux from starburst galaxies difficult , if only uv / visual / near - ir data are available . existing data for uv - selected starburst galaxies indicate a range of uv attenuation factors of 0150 . our models reproduce the `` calzetti attenuation law '' , provided one adopts smc - type dust and a clumpy shell - type dust distribution surrounding the starbursts . the average far - uv attenuation factor for the calzetti sample is found to be 7.4 . the only relatively reliable measure for the uv attenuation factor for single galaxies was found in the ratio of the integrated far - ir flux to the far - uv flux , measured near 1600 , requiring the measurement of the entire spectral energy distribution of galaxies .

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as mentioned in @xmath68 , per ob1 is unusual in that it is not associated with a giant molecular cloud . based on the results described in @xmath69 , we now find that per ob1 is unusual in at least two other respects . first , most of its members exhibit a bulk motion away from the galactic plane with those at larger heights moving faster ( on average ) away from the galactic plane . second , star formation has recently occurred ( and may still be occurring ) at unusually large heights of 280400 pc above the galactic plane . we now examine whether all of these features can be explained , and if so how , in the framework of current star formation models . star formation at the present epoch is thought to be relatively inefficient in converting molecular gas to stars , even more so in models that invoke spontaneous as opposed to triggered star formation . to explain the lack of a giant molecular cloud associated with per ob1 without invoking an extraordinarily effective dispersement or destruction mechanism , one would have to propose that the star formation in this association has been more efficient than normal in converting molecular gas to stars . this may , but is not necessarily required to , explain the unusually large stellar densities and masses of the @xmath0 and @xmath1 per double cluster . the high number density of stars and their resultant bipolar outflows , stellar winds , uv ionization , and/or supernova explosions would then be more effective also in sweeping away or destroying much of the remaining molecular gas . in a search for shells and supershells in the galaxy , @xcite identified a large shell of atomic hydrogen ( ) gas in the direction towards per ob1 . @xcite show that this shell occupies the same range in radial velocities as per ob1 , and forms a quasi - circular structure of size @xmath5@xmath70 pc centered at ( @xmath71)=(134@xmath72.5 , @xmath73.5 ) . the center of this shell therefore lies quite close to the locations of the @xmath0 and @xmath1 per double cluster . @xcite estimate a total mass of atomic gas in the shell of order @xmath74 m@xmath2 . they infer an an upper limit of 10 km s@xmath20 for the expansion velocity of the shell , and a kinetic energy for the shell of @xmath75 ergs . they also compute a minimum mechanical energy to blow the shell of @xmath76 ergs , compared with an energy released through stellar winds by all the known member b stars of @xmath77 ergs . thus , stellar winds from b stars alone in per ob1 is sufficient to blow the observed shell , let alone an additional energy from sources such as supernova explosions . we note that the total kinetic energy of the member stars due to their motion away from the galactic plane ( @xmath78 ergs ) adds insignificantly to the overall energetics . @xcite show from the _ iras _ 100-@xmath79 m image that emission from dust traces the inner border of the shell in the portion at large heights above the galactic plane ( any dust associated with the shell close to the galactic plane is confused with galactic dust ) . this dust feature can be seen as a nearly semi - circular arc in figure 2 of @xcite , extending to a galactic latitude of about @xmath80 at its largest height above the galactic plane . we speculate that this dust shell may have formed from the swept - up giant molecular cloud . we have checked the literature to see if the presumed hot bubble of gas responsible for sweeping up the abovementioned hi and dust shell is visible in x - rays . such x - ray emission is detectable in the rosat all sky survey ( rass ) @xcite from the orion - eridanus superbubble @xcite , which is powered by ori ob1 ( which contains approximately the same number of o stars as per ob 1 ) . this superbubble has approximately the same physical size as that enclosed by the hi shell associated with per ob1 . the kinematic energy of the orion - eridanus superbubble , as derived from its associated expanding shell , is about @xmath81 ergs @xcite , which is between one and two orders of magnitude larger than that of the presumed per ob1 superbubble . if the orion - eridanus superbubble was located at the distance of per ob1 , the count rate range of 3/4 kev band would be about 515 counts s@xmath20 . by comparison , the background count rate towards the presumed per ob1 superbubble is about 110 counts s@xmath20 . perhaps not surprisingly then , we did not find any significant x - ray emission from rass in 1/4 , 3/4 , and 1.5 kev bands towards the presumed per ob1 superbubble . we have searched the literature to find maps in molecular gas towards per ob1 . @xcite has mapped in co(1 - 0 ) the sky in the direction towards per ob1 at an angular resolution of 85 . compact and isolated co emission is detectable towards rmc1 , rmc2 , and rmc3 , but not towards rmc4 . if these sources are genuinely associated with the abovementioned remnant molecular clouds , the corresponding molecular gas mass is in these clouds @xmath5 8000 m@xmath2 . no co emission was detected towards rno6 , which has a molecular gas mass of @xmath5 400 m@xmath2 , consistent with the upper limit in sensitivity of the @xcite map . no co emission was detected towards the dust/ shell either ; assuming a co linewidth of 10 km s@xmath20 , the corresponding 3@xmath38 upper limit in molecular gas along this shell is @xmath82 m@xmath2 . if this estimate is accurate , the bulk of the molecular gas in this shell may therefore have been dissociated into atomic hydrogen gas . much of the star formation in the per ob1 association appears to have occurred in or within the vicinity of the @xmath0 and @xmath1 per double cluster . if so , then the observed increase ( on average ) in velocity with height ( acceleration ) away from the galactic plane may be a natural consequence of the dissolution of these clusters @xcite . over time , stars moving faster away from the double cluster would travel furthest from their initial locations , thus producing the observed linear increase in velocity with height above the galactic plane . although this model could explain the velocity pattern of the b main - sequence and supergiant stars , which can have ages up to @xmath5 10 myr of more , it can not easily explain the same velocity pattern observed for the o stars . the latter stars have ages of only a few millions years , much younger than the b stars in the @xmath0 and @xmath1 per double cluster ( @xmath5 13 myr ) , and could not have reached their present locations if traveling at their observed velocities from these clusters . this model also predicts that the member stars should form an approximately spherical distribution moving away from the @xmath0 and @xmath1 per double cluster , which is not seen ( c.f . fig . 2 ) . given that the molecular gas from which the stars in per ob1 formed appears to have been effectively swept outwards by the luminous stars in this association ( @xmath83 ) , we now consider whether the observed velocity dependence with height could simply be a reflection of stars forming in this swept - up gas . the situation envisaged is akin to that proposed in models of triggered star formation , in particular the scenario of cloud shuffling . cloud shuffling takes place on the periphery of an ob association where an over - pressured superbubble of accumulated stellar winds , supernova explosions , and/or ionized gas pushes and accelerates a giant molecular cloud outwards @xcite . such cloud shuffling is proposed to induce star formation , and also extend the lifetimes of molecular clouds by pushing them away from massive stars and their destructive effects . in the present case , the dust shell at the inner boundary of the shell presumably lies just beyond the expansion front of the superbubble associated with per ob1 . assuming typical physical conditions in ob associations , @xcite suggests that cloud shuffling can accelerate molecular gas by about 1 km s@xmath20 myr@xmath20 ( or equivalently 1 pc myr@xmath84 ) . let us assume that the @xmath0 and @xmath1 per double cluster was the original source of the superbubble ( with luminous stars formed later from the swept - up molecular gas adding to the energy of this superbubble ) , consistent with its location close to the center of the shell . the age of this double cluster is estimated to be @xmath513@xmath851 myr @xcite , allowing sufficient time for the molecular gas at the edge of the superbubble to be accelerated by over @xmath86 . this is the correct order of magnitude to produce , given the uncertainties involved in estimating the magnitude of the acceleration and its possible variation with time , the observed velocity dependence with height of the stars in per ob1 . the proposed scenario provides a natural explanation for the relatively large height of hd 15137 above the galactic plane , and its motion . @xcite suggest that both the massive stars hd 15137 and hd 14633 are runaway stars ejected from the open cluster ngc 654 in the perseus spiral arm . this suggestion , however , has a serious timescale problem , with inferred flight times for both stars that are longer than their ages @xcite . if hd 15137 is a member of per ob1 as proposed in @xmath87 , then in our proposed picture it formed close to its present location and inherited its relatively large velocity away from the galactic plane from its swept - up parent molecular cloud . note that the o star lying at the next highest galactic latitude , hd 15137 ( location as indicated in fig . 2 ) , has a comparably large proper motion away from the galactic plane . this explanation , however , can not be simply applied to hd 14633 , which we also proposed in @xmath87 to be a possible member of per ob1 . this star is located at a galactic latitude of @xmath88 , which is far beyond the presumed outer edge of the superbubble at a galactic latitude of about @xmath80 . the triggered formation of stars in the cloud - shuffling model naturally predicts an age gradient from the center of the superbubble , such that stars at larger radii have younger ages . if this model is applicable , the supergiant stars in per ob1 should therefore be closer to the @xmath0 and @xmath1 per double cluster ( the presumed center of the superbubble ) than the o stars . in figure 9 we plot the spatial distributions of o stars ( dotted lines ) and supergiant stars ( dashed lines ) proposed to be members of per ob1 from @xcite . using the kolmogorov - smirnov test @xcite , we find a @xmath89 probability that these two populations have different distributions in galactic height , such that the younger o tend to be located higher above the galactic plane than the older supergiant stars ( the visual impression given in fig . thus , there does seem to be a tendency , albeit only of marginally significance , for younger stars to be located at larger heights above the galactic plane . in the cloud shuffling model as applied to per ob1 , the relatively recent ( within the last @xmath51 myr ) formation of low- to intermediate - mass stars in remnant molecular clouds at unusually large heights above the galactic plane simply reflects the transport of molecular gas to such heights by the expanding superbubble . the dust and shells described in @xmath83 extend to galactic latitudes of about @xmath80 ( height @xmath5 450 pc above the galactic plane ) , and so the remnant molecular clouds described in @xmath90 lies in projection inside the superbubble . these clouds may actually comprise swept - up molecular gas located at the periphery of the superbubble . alternatively , they may comprise the densest condensations in the giant molecular cloud that were not completely swept up by the expanding superbubble . as mentioned in @xmath91 , all the rmcs have head - tail morphologies with their heads pointing towards the galactic plane rather than in the direction of any particular o star . these morphologies of these rmcs may therefore have been sculpted by the expanding superbubble rather than ionizing radiation from o stars .

we show from _ hipparcos _ data that the luminous members of this association exhibits a bulk motion away from the galactic plane , such that their average velocity increases with height above the galactic plane . the star - forming regions located at even larger heights above the galactic plane presumably correspond to more recent episodes of star formation at or near the periphery of this superbubble .

the per ob1 association , which contains the remarkable double cluster and per , is unusual in not having a giant molecular cloud in its vicinity . we show from _ hipparcos _ data that the luminous members of this association exhibits a bulk motion away from the galactic plane , such that their average velocity increases with height above the galactic plane . we find haebe and t tauri stars towards probable remnant molecular clouds associated with per ob1 . these star - forming regions lie well beyond the location of the luminous member stars at heights of 280400 pc above the galactic plane , far higher than that previously found for embedded clusters . we argue that the observed motion of the luminous member stars is most naturally explained if many formed from molecular gas pushed and accelerated outwards by an expanding superbubble driven presumably by stellar winds and perhaps also supernova explosions . a large shell of atomic hydrogen gas and dust that lies just beyond the remnant molecular clouds , believed to be driven by just such a superbubble , may comprise the swept - up remains of the parental giant molecular cloud from which this association formed . in support of this picture , we find a week trend for the younger o star members to lie at higher galactic latitudes than the older supergiant members . the star - forming regions located at even larger heights above the galactic plane presumably correspond to more recent episodes of star formation at or near the periphery of this superbubble .

0804.4520

i

the per ob1 association comprises the remarkable @xmath0 and @xmath1 per double cluster ( among the brightest and densest open clusters known ) , surrounded by luminous o / b and both early- and late - type supergiant stars . unlike virtually all other known ob associations in the galaxy , there is no known giant molecular cloud in the vicinity of per ob1 . we have gathered together the available information on the stellar population of per ob1 , primarily from the work by @xcite and @xcite . for those luminous early- and late - type stars included in the hipparcos astrometry mission , we have extracted measurements of their proper motions . we found that : we also searched for candidate intermediate - mass ( haebe ) and low - mass ( classical t tauri star ; ctts ) pre - main - sequence stars in per ob1 . we find a number of these candidate stars to be associated with four candidate remnant molecular clouds ( rmcs ) identified as dust clouds in _ iras _ 100-@xmath79 m images and optical nebulae in the 2nd digitized sky survey . all these rmcs are located high ( 280400 pc in projection ) above the galactic plane . from our spectroscopy of both candidate pre - main - sequence as well as main - sequence b a stars apparently associated with these rmcs , we : 1 . show that the distance moduli to the main - sequence b a stars are consistent with the rmcs being located in per ob1 2 . confirm that some of the candidate pre - main - sequence stars are indeed haebe stars and identify possible cttss , implying that there has been recent ( within the last 1 myr ) star formation at galactic heights far above the locations of known luminous members in per ob1 1 . point out that the large shell of atomic hydrogen ( ) gas ( mass @xmath5@xmath92 ) enclosing a slightly smaller shell of dust , studied by @xcite and which they propose to be created by a stellar - wind - blown superbubble from the @xmath0 and @xmath1 per double cluster and ob stars in per ob1 , likely comprises ( in part ) the swept - up remains of the giant molecular cloud from which per ob1 formed 2 . argue that if the observed motion of the luminous member stars is attributed to the dissolution of the @xmath0 and @xmath1 per double cluster ( at their outskirts ) , this can only explain the motion of the main - sequence b and late - type supergiant stars . the main - sequence o stars , which are much younger than the double cluster , would not have had sufficient time to reach their present locations high above the galactic plane if they originated from the close vicinity of the double cluster 3 . show that the observed motion of the luminous member stars is better explained in the cloud - shuffling model @xcite , in which the abovementioned superbubble pushes and accelerates the giant molecular cloud outwards and at the same time induces star formation at the dense cloud interface . this would naturally result in those stars forming locally in the compressed molecular gas to have increasingly large velocities away from galactic plane with height 4 . show that there is a weak trend for the younger o member stars to lie at higher galactic latitudes than the older late - type supergiant member stars , consistent with the simplest prediction of the cloud - shuffling but not cluster dissolution model 5 . suggest that the recent star formation in the remnant molecular clouds that we found at very large heights above the galactic plane , far above the locations of the luminous member stars , likely occurred in the swept - up molecular gas at the periphery of the superbubble , or in the densest condensations that were not entirely swept away by the expanding superbubble h .- lee thanks wen - ping chen for sharing observation time , wen - shan hsiao for helping spectral observations , rue - ron hsu and pin - gao gu for discussing , and the staff at the beijing astronomical observatory for their assistance during observing runs . we are grateful to the anonymous referee for constructive suggestions . this research makes use of data products from the two micron all sky survey , which is a joint project of the university of massachusetts and the infrared processing and analysis center / california institute of technology , funded by the national aeronautics and space administration and the national science foundation . this research made use of montage , funded by the national aeronautics and space administration s earth science technology office , computation technologies project , under cooperative agreement number ncc5 - 626 between nasa and the california institute of technology . montage is maintained by the nasa / ipac infrared science archive . this research made use of data products from the digitized sky surveys produced at the space telescope science institute . ambartsumian , v. a. 1947 , in stellar evolution and astrophysics , armenian acad . of sci . 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up spectroscopy . ] 100 @xmath55 image . locations of the rmcs identified in this work , as well as rno6 , are indicated . also indicated are the locations of main - sequence b or a stars ( blue ) used to estimate distances to the rmcs . the stars are numbered according to their identification numbers in table 4 . ] 130.900 & -3.441 & 8725 & 1.05 & 2.49 & 1.38 & 1.13 & hd 236894 & o8v & a , b + 131.479 & -2.433 & 9211 & 0.65 & -1.88 & 1.03 & 0.87 & hd 236915 & m2iab & b + 131.867 & -5.138 & 9017 & -0.85 & -3.01 & 1.46 & 1.33 & bd+55 441 & b1vpe & a + 132.691 & -2.588 & 9886 & -0.12 & -1.71 & 1.11 & 1.05 & hd 236947 & m2iab - ib & b + 132.742 & -1.700 & 10078 & 1.40 & -0.03 & 1.49 & 1.10 & hd 13036 & b0.5iii & a , b + 132.975 & -5.802 & 9523 & 0.77 & -5.80 & 1.00 & 1.02 & hd 12323 & on9v & a , b + 132.977 & -2.504 & 10060 & -0.13 & -0.26 & 1.00 & 0.98 & hd 13022 & o9.5ia & a , b + 132.981 & -2.880 & 9990 & -0.30 & -1.80 & 0.58 & 0.61 & hd 12953 & a1ia & a , b + 133.105 & -4.282 & 9826 & 0.72 & -3.10 & 1.12 & 0.98 & hd 12727 & b2iii & a + 133.173 & -6.153 & 9582 & 1.25 & -3.21 & 0.71 & 0.78 & hd 12401 & m4ib & b + 133.168 & -1.650 & 10323 & -0.30 & -1.28 & 1.49 & 1.10 & hd 13402 & b0.5ib & a , b + 133.174 & -3.334 & 10024 & -0.87 & -1.39 & 1.16 & 0.99 & hd 12993 & o6.5v & a , b + 133.270 & -4.170 & 9935 & -0.51 & -2.15 & 0.94 & 0.87 & hd 12856 & b0iiipe & a , b + 133.505 & -4.217 & 10055 & 0.72 & -2.47 & 1.09 & 0.98 & hd 13051 & b1ive & a + 133.565 & -2.549 & 10379 & 0.09 & -0.54 & 0.65 & 0.65 & hd 13476 & a3iab & a , b + 133.571 & -3.509 & 10227 & -0.14 & -1.92 & 0.66 & 0.61 & hd 13267 & b5ia & a , b + 133.888 & -2.882 & 10489 & -3.66 & 0.02 & 1.16 & 1.11 & hd 13658 & m1iab & b + 134.013 & -1.219 & 10904 & -0.90 & 0.50 & 1.69 & 1.43 & hd 14242 & m2iab & b + 134.030 & -4.924 & 10228 & 1.90 & -2.83 & 0.92 & 0.74 & hd 13268 & o7 : & a , b + 134.064 & -3.223 & 10527 & 0.90 & -2.15 & 1.03 & 0.90 & hd 13716 & b0.5iii & a , b + 134.130 & -1.931 & 10829 & 1.78 & -2.03 & 1.36 & 1.08 & hd 14142 & m2iab & b + 134.445 & -3.868 & 10624 & 0.23 & -2.39 & 0.77 & 0.69 & hd 13841 & b2ib & a , b + 134.448 & -3.840 & 10633 & -0.60 & -1.02 & 0.54 & 0.52 & hd 13854 & b1iab & a , b + 134.525 & -4.149 & 10615 & -0.51 & -2.68 & 0.86 & 0.81 & hd 13831 & b0iiie & a , b + 134.571 & -4.154 & 10641 & -0.85 & -1.85 & 0.68 & 0.66 & hd 13866 & b2ib & a , b + 134.649 & -4.891 & 10541 & 1.16 & -4.52 & 0.83 & 0.76 & hd 13745 & o9.7ii((n ) ) & a , b + 134.685 & -2.129 & 11093 & 3.21 & -2.09 & 1.98 & 1.71 & hd 14528 & m4ie & b + 134.705 & -5.589 & 10443 & -0.90 & -2.69 & 0.99 & 0.92 & hd 13621 & b0.5iii - iv((n ) ) & a + 134.705 & -3.665 & 10805 & 0.24 & -2.03 & 0.68 & 0.59 & hd 14134 & b3ia & a , b + 134.714 & -3.626 & 10816 & -0.64 & -1.76 & 0.66 & 0.59 & hd 14143 & b2ia & a , b + 134.792 & -2.861 & 10995 & 0.56 & -3.45 & 0.84 & 0.77 & hd 14404 & m2iab & b + 135.033 & -3.433 & 11020 & -0.50 & -2.13 & 0.61 & 0.57 & hd 14433 & a1ia & a , b + 135.058 & -1.678 & 11394 & 0.21 & -0.20 & 1.33 & 0.97 & hd 14947 & o5if+ & a , b + 135.120 & -3.247 & 11115 & -0.84 & -1.52 & 0.72 & 0.63 & hd 14542 & b8ia & a , b + 135.143 & -3.752 & 11018 & 1.46 & -2.86 & 0.99 & 0.84 & hd 14434 & o6.5 : & a , b + 135.155 & -3.385 & 11098 & -1.34 & -1.31 & 0.75 & 0.66 & hd 14535 & a2iab & a , b + 135.334 & -4.743 & 10926 & 0.10 & -1.02 & 0.79 & 0.63 & hd 14322 & b8ib & a , b + 135.381 & -4.815 & 10935 & 0.90 & -1.00 & 1.05 & 0.83 & hd 14331 & b0iii & a , b + 135.400 & -3.088 & 11284 & 2.05 & -1.52 & 1.32 & 1.36 & hd 14826 & m2iab & b + 135.488 & -2.795 & 11391 & 0.94 & -1.21 & 0.62 & 0.59 & hd 14956 & b2ia & a , b + 135.573 & -4.724 & 11060 & 0.76 & -0.99 & 0.66 & 0.54 & hd 14489 & a2iab & a , b + 135.683 & -3.866 & 11279 & -0.13 & -0.75 & 0.51 & 0.50 & hd 14818 & b2ia & a , b + 135.835 & -2.506 & 11625 & 0.07 & 0.58 & 0.68 & 0.63 & hd 15316 & a2ia & a , b + 136.119 & -2.524 & 11769 & 0.55 & 0.37 & 0.73 & 0.67 & hd 15497 & b6ia & a , b + 136.128 & -1.754 & 11953 & 0.73 & -0.30 & 1.21 & 0.98 & hd 15752 & b0iiin & a , b + 136.152 & -2.260 & 11841 & -0.92 & 0.24 & 1.01 & 0.90 & hd 15620 & b8iab & a , b + 136.323 & -0.371 & 12416 & -2.23 & -1.21 & 1.23 & 1.13 & bd+58 501 & m2iab & b + 136.351 & -3.293 & 11722 & 1.10 & -1.38 & 1.22 & 1.14 & hd 15450 & b1iiie & a + 136.385 & -2.587 & 11898 & 0.33 & -3.51 & 1.88 & 1.75 & hd 15690 & b2iab & a , b + 136.535 & -3.468 & 11782 & 0.34 & -1.86 & 1.37 & 1.30 & hd 15548 & b1v & a + 136.695 & -0.046 & 12750 & -0.06 & -0.04 & 0.74 & 0.67 & hd 16778 & a2ia & b + 137.159 & -4.660 & 11850 & 0.05 & -3.11 & 1.11 & 1.05 & hd 15642 & o9.5iii : n & a , b + 137.185 & -2.779 & 12302 & 1.33 & -3.09 & 0.86 & 0.86 & hd 236979 & m1iab & b + 137.351 & -1.300 & 12769 & -0.84 & -1.73 & 1.50 & 1.20 & hd 16808 & b0.5ib & a , b + 137.367 & -1.044 & 12840 & -0.58 & -1.36 & 1.27 & 1.09 & hd 236995 & a0ia & a , b + 137.532 & -7.507 & 11473 & 2.53 & -4.48 & 0.67 & 0.72 & hd 15137 & o9.5iii(n ) & c + 137.796 & -2.660 & 12676 & -0.65 & -4.71 & 1.04 & 1.14 & hd 16691 & o5f & a + 137.932 & -1.681 & 12972 & 1.01 & -1.89 & 0.94 & 0.93 & hd 17088 & b9ia & a , b + 138.022 & -1.701 & 13022 & 0.69 & -1.81 & 1.10 & 1.13 & hd 17145 & b8ia & a , b + 138.383 & -1.326 & 13290 & -0.36 & -1.51 & 1.61 & 1.46 & hd 237010 & m2iab & b + 138.537 & -2.110 & 13178 & -0.03 & -1.72 & 0.63 & 0.69 & hd 17378 & a5ia & a , b + 138.718 & -2.133 & 13262 & 1.21 & -5.23 & 1.01 & 1.03 & hd 237008 & m3iab & b + 138.930 & -2.081 & 13380 & 1.49 & -3.08 & 1.44 & 1.54 & hd 17638 & wc6 & c + 140.863 & -18.126 & 11099 & 3.13 & -6.05 & 0.87 & 0.69 & hd 14633 & on8v & c + [ table : members ] references(a ) @xcite ; ( b ) @xcite ; ( c ) this paper rrrrrr 0 @xmath94 & @xmath95 & @xmath96 & 0.72 & 0.66 & 2 + @xmath94 @xmath97 & 0.44 & @xmath98 & 0.42 & 0.35 & 11 + @xmath97 @xmath99 & 0.46 & @xmath100 & 0.26 & 0.24 & 18 + @xmath99 @xmath101 & 0.41 & @xmath102 & 0.24 & 0.22 & 16 + @xmath101 @xmath103 & 0.67 & @xmath104 & 0.28 & 0.25 & 11 + @xmath103 @xmath105 & 0.06 & @xmath106 & 0.68 & 0.64 & 3 + @xmath105 @xmath107 & 1.64 & @xmath108 & 0.71 & 0.78 & 1 + @xmath107 @xmath109 & 2.58 & @xmath110 & 0.67 & 0.72 & 1 + ......... + @xmath111 @xmath112 & 2.93 & @xmath113 & 0.87 & 0.69 & 1 + [ table : pm ] 1 & j01380790 + 5453463 & h@xmath114 & haebe ( a0 ) & around rmc1 + 2 & j01424061 + 5449135 & h(@xmath6652.5 ) & ctts & in rmc1 + 3 & j01433441 + 5451323 & h(@xmath666.1 ) & ctts & in rmc1 + 4 & j01435138 + 5526098 & h@xmath114 & haebe ( b3 ) & in rmc1 + 5 & j01494099 + 5341341 & & b ( b7v ) & with a reflection nebula in rmc2 + 6 & j01500456 + 5354007 & & b ( b3v ) & with a reflection nebula in rmc2 + 7 & j01501404 + 5341107 & h(@xmath6689.1 ) & ctts & in rmc2 + 8 & j01501546 + 5341350 & & a ( a2v ) & with a reflection nebula in rmc2 + 9 & j02151126 + 5519500 & h@xmath114 & haebe ( b8 ) & around rno 6 + 10 & j02220484 + 5038130 & & b ( b8v ) & with a reflection nebula in rmc3 + 11 & j02220662 + 5040013 & h(@xmath662.2 ) & wtts & in rmc3 + 12 & j02261522 + 5243131 & h(@xmath6616.1 ) & ctts & with a reflection nebula in rmc4 + 13 & j02262049 + 5244288 & h@xmath114 & haebe ( b6v ) & with a reflection nebula in rmc4 + [ table : spectra ]

the per ob1 association , which contains the remarkable double cluster and per , is unusual in not having a giant molecular cloud in its vicinity . we argue that the observed motion of the luminous member stars is most naturally explained if many formed from molecular gas pushed and accelerated outwards by an expanding superbubble driven presumably by stellar winds and perhaps also supernova explosions . a large shell of atomic hydrogen gas and dust that lies just beyond the remnant molecular clouds , believed to be driven by just such a superbubble , may comprise the swept - up remains of the parental giant molecular cloud from which this association formed . in support of this picture , we find a week trend for the younger o star members to lie at higher galactic latitudes than the older supergiant members .

the per ob1 association , which contains the remarkable double cluster and per , is unusual in not having a giant molecular cloud in its vicinity . we show from _ hipparcos _ data that the luminous members of this association exhibits a bulk motion away from the galactic plane , such that their average velocity increases with height above the galactic plane . we find haebe and t tauri stars towards probable remnant molecular clouds associated with per ob1 . these star - forming regions lie well beyond the location of the luminous member stars at heights of 280400 pc above the galactic plane , far higher than that previously found for embedded clusters . we argue that the observed motion of the luminous member stars is most naturally explained if many formed from molecular gas pushed and accelerated outwards by an expanding superbubble driven presumably by stellar winds and perhaps also supernova explosions . a large shell of atomic hydrogen gas and dust that lies just beyond the remnant molecular clouds , believed to be driven by just such a superbubble , may comprise the swept - up remains of the parental giant molecular cloud from which this association formed . in support of this picture , we find a week trend for the younger o star members to lie at higher galactic latitudes than the older supergiant members . the star - forming regions located at even larger heights above the galactic plane presumably correspond to more recent episodes of star formation at or near the periphery of this superbubble .

1008.2957

i

the epoch of reionization in hydrogen has become a topic of considerable interest ( barkana & loeb 2001 ; fan , carilli , & keating 2006 ; meiksin 2009 ; furlanetto et al . 2009 ) as a probe of the transition from neutral to ionized hydrogen in the intergalactic medium ( igm ) . this transition occurred somewhere between redshifts @xmath3 612 , marking the exit from the cosmic dark ages " , beginning at the time when the first stars and galaxies formed at redshifts @xmath24 ( tegmark et al . 1997 ; ricotti , gnedin , & shull 2002 ; trenti & shull 2010 ) . helium underwent similar reionization from to ( that is , from he@xmath25 to he@xmath26 ) at @xmath27 ( reimers et al . 1997 ; shull et al . 2004 ) , most likely mediated by the harder ( @xmath28 ev ) radiation from quasars and other active galactic nuclei ( agn ) . with a 4 ryd ionization potential , he@xmath29 is harder to ionize than h@xmath30 , and he@xmath26 recombines 56 times faster than h@xmath29 ( osterbrock & ferland 2006 ; fardal , giroux , & shull 1998 ) . for these reasons , and the fact that most hot stars lack strong 4 ryd continua , it is believed that agn are the primary agents of reionization . ionization models find that , owing to its resilience , he@xmath29 is much more abundant than h@xmath30 , with predicted column - density ratios @xmath31 n()/n ( ) @xmath32 50100 ( miralda - escud et al . 1996 ; fardal , giroux , & shull 1998 ) . determining when and how the universe was ionized has been an important question in cosmology for decades ( gunn & peterson 1965 ; sunyaev 1977 ) . although recent progress has led to quantitative constraints , we still do not know whether galaxies are the sole agents of hydrogen reionization , and the epoch of reionization remains uncertain . we _ do _ know that hydrogen reionization in the igm is complete by @xmath33 , based on the rapid evolution between redshifts @xmath34 and @xmath35 of ly@xmath2 gunn - peterson ( gp ) absorption from neutral hydrogen along lines of sight to qsos ( fan et al . 2002 ; gnedin 2004 ) . the optical depth of the cosmic microwave background ( komatsu et al . 2010 ) sets a @xmath36 constraint on instantaneous reionization at @xmath37 and a @xmath38 confidence interval of @xmath39 . a limit @xmath40 is set by the detection of ly@xmath2 emitters at @xmath41 ( major evolution in the observed luminosity function would be expected if neutral gas were present around the emitters ) . these observations are in line with @xmath42cdm simulations ( trac & cen 2007 ; cen 2003 ; gnedin 2004 ) and ionization - front ( i - front ) models ( venkatesan , tumlinson & shull 2003 ; bolton & haehnelt 2007 ; shull & venkatesan 2008 ) . the current data leave open several hydrogen ionization scenarios , some involving simple reionization at @xmath43 and others with more complex ionization histories that depend on the star - formation rate at @xmath44 and the transition from pop iii to pop ii stars . numerical models of the reionization process often follow the expansion and overlap of i - fronts , but the details are complicated by geometric uncertainties in the ionizing sources , higher recombination rates in denser gas , and radiative transfer of lyman continuum ( lyc ) photons . in particular , the gas is highly structured in both density and temperature . the reionization epoch ( @xmath45 ) and ionization processes are also poorly characterized . the thermal evolution of the igm includes many subtle effects , with degeneracies arising from fluctuations in density , temperature , and ionization fraction , as well as spectral hardness of the ionizing sources . previous estimates of @xmath21 were based on indirect measurements of temperature , ionization , and average optical depth of ly@xmath2 lines of , and on apparent shifts in / absorption - line ratios arising from changes in the 4-ryd continuum radiation field as was ionized to . early estimates of the igm temperature evolution and equation of state from line widths suggested a change at @xmath46 ( ricotti , gnedin , & shull 2000 ; schaye et al . theuns et al . ( 2002 ) analyzed the average optical depth of ( ) ly@xmath2 lines in 1061 quasar spectra , using low - resolution data from the sloan digital sky survey ( bernardi et al . 2003 ) . from a weak dip in @xmath47 at @xmath48 , these authors suggested that reionization started at redshift @xmath49 and lasted until @xmath50 . several recent studies with higher - resolution spectroscopic data have not confirmed the @xmath51 feature ( mcdonald et al . 2005 ; kim et al . faucher - giguere et al . ( 2008 ) found a feature in @xmath51 ( ) near @xmath52 , in a sample of 86 high - resolution , high - s / n quasar spectra taken with keck ( esi , hires ) and magellan ( mike ) . however , they question the reionization explanation of the depth and narrow redshift extent . they also note that at least three physical effects could produce a feature in in @xmath47 : changes in igm temperature , electron number density , and ionizing background . recent numerical simulations ( bolton et al . 2009 ; mcquinn et al . 2009 ; lidz et al . 2010 ) also question whether reionization is responsible for the proposed feature in @xmath47 at @xmath53 . the most direct estimates of reionization come from far - ultraviolet spectra of lyman-@xmath2 absorption toward high - redshift agn . because of strong galactic interstellar absorption in the lyman continuum , the @xmath54 line is only observable in the far ultraviolet , at redshifts @xmath55 when the line shifts longward of 912 . a small number of bright agn at @xmath3 2.93.3 have been observed with the _ hubble space telescope _ ( _ hst _ ) and the _ far ultraviolet spectroscopic explorer _ ( _ fuse _ ) . these data show moderate optical depths in the line , ranging up to @xmath56 , with a gradual recovery of transmission ( @xmath57 ) at @xmath8 . the best absorption data have been acquired toward three high - redshift agn : q0302@xmath1003 ( jakobsen et al . 1994 ; hogan , anderson , & rugers 1997 ; heap et al . 2000 ) ; and he 2347@xmath14342 ( reimers et al . 1997 ; kriss et al . 2001 ; smette et al . 2002 ; shull et al . 2004 ; zheng et al . 2004 ) ; and hs 1700@xmath586416 ( davidsen , kriss , & zheng 1996 ; fechner et al . 2006 ) . from an analysis of the optical - depth evolution in moderate - resolution fuse data toward he 2347@xmath14342 , shull et al . ( 2004 ) suggested that the reionization epoch of he@xmath29 occurred at @xmath59 . observations of with _ hst _ and _ fuse _ also constrain the thermodynamic state of the igm and the spectra of ionizing sources . for example , the high abundance ratio , n(he ii)/n(h i ) @xmath32 50100 , observed toward he 2347@xmath14342 and hs 1700@xmath586416 ( kriss et al . 2001 ; smette et al . 2002 ; shull et al . 2004 ; zheng et al . 2004 ; fechner et al . 2006 ) requires a soft ionizing radiation field , @xmath60 , with mean spectral index @xmath61 ( fardal et al . as observed in the qso rest - frame , the euv ( 12 ryd ) spectral indices of quasars exhibit a wide range ( telfer et al . 2002 ; scott et al . 2004 ) . more intriguing are the spectroscopic observations of and taken by _ fuse _ , the keck telescope , and the very large telescope ( vlt ) . kriss et al . ( 2001 ) and shull et al . ( 2004 ) report variations in @xmath62 over 210 mpc scales ( @xmath63 ) which imply spatial fluctuations in the radiation field at the ionization edges of ( 1 ryd ) and ( 4 ryd ) . most of these variations probably arise in the 4 ryd continuum , whose photons have greater penetrating power . these flux differences at 1 ryd and 4 ryd are then amplified by absorption and reprocessing by the igm ( haardt & madau 1996 ; fardal et al . 1998 ) . in this paper , we present new , high - quality , far - uv spectroscopic observations of intergalactic absorption toward he 2347@xmath14342 , using the cosmic origins spectrograph ( cos ) on _ hst _ ( green et al . 2010 ; osterman et al . this target is of considerable interest as a bright ( @xmath64 , @xmath65 ) continuum source , previously observed by the _ fuse _ , keck , and vlt spectrographs to study intergalactic ly@xmath2 absorption in both and . he 2347@xmath14342 is the first of three agn targets scheduled for cos guaranteed - time observations of the reionization epoch . the data were acquired with both the moderate - resolution g130 m grating ( @xmath66 , @xmath67 ) and the low - resolution g140l grating ( @xmath68 , @xmath69 ) . in the 303.78 line of , these wavelength bands allow us to probe redshifts down to @xmath70 ( g130 m ) and @xmath71 ( g140l ) . the cos data enable many improvements compared to previous studies . first , the high far - uv throughput of the cos / g130 m grating provides higher signal - to - noise ( s / n ) and better photometric accuracy . second , the low background of the cos detectors allows us to detect very weak flux - transmission through the igm , characterize low flux levels in absorption troughs , and probe regions of high optical depth , @xmath72 . finally , low - resolution g140l spectra ( 1000 - 2000 ) allow us to study the recovery of the optical depth at @xmath8 and characterize the continuum longward of the edge . in 2 we discuss the observations and data reduction techniques for both g130 m and g140l gratings . in 3 we display the fitted quasar continuum , @xmath73 , which we use to extrapolate below the edge at @xmath74 . from this continuum and the transmitted fluxes , we derive optical depths in the ly@xmath2 forest and analyze the fluctuating absorption . we observe minimal effects of local photoionization expected from proximity to this very luminous qso . in the ly@xmath2 forest at @xmath75 , we see narrow ( 25 , 1230 mpc of comoving radial distance ) windows of partial flux transmission , which we interpret as patchy reionization " , interspersed with broad absorption troughs ( 410 intervals , 2560 mpc ) with high optical depths , @xmath76 . at @xmath77 ( @xmath78 ) the mean opacity drops to @xmath79 , consistent with the overlap of the i - fronts . because is much more abundant than , its opacity through the cosmic web remains high . in 4 we summarize our observations and their implications for the reionization epoch . with reasonable assumptions about the physical state of the igm at @xmath80 , borne out by studies of and ly@xmath2-forest absorption and cosmological simulations , we can probe the reionization epoch down to fractional ionization @xmath81 in underdense regions ( @xmath82 ) relative to the mean baryon density of the cosmic web . this ionization level provides much greater sensitivity to conditions at @xmath83 than possible with at @xmath33 ( fan et al . coupled with galaxy surveys , cosmological simulations , and photoionization modeling , these uv spectra will help us understand the propagation and overlap of the helium ionization fronts .

we report ultraviolet spectra of the high - redshift ( ) quasar , he 2347 , taken by the cosmic origins spectrograph ( cos ) on the _ hubble space telescope _ ( _ hst _ ) . spectra in the g130 m ( medium - resolution , 11351440 ) and g140l ( low - resolution , 10302000 ) gratings exhibit patchy gunn - peterson absorption in the 303.78 ly line of he ii between 2.392.87 ( g140l ) and 2.742.90 ( g130 m ) . with cos , we obtain better spectral resolution , higher - s / n , and better determined backgrounds than previous studies , with sensitivity to abundance fractions in filaments of the cosmic web . the optical depths from cos are higher than those with the _ far ultraviolet spectroscopic explorer _ ( _ fuse _ ) and range from to , with a slow recovery in mean optical depth to at .

we report ultraviolet spectra of the high - redshift ( ) quasar , he 2347 , taken by the cosmic origins spectrograph ( cos ) on the _ hubble space telescope _ ( _ hst _ ) . spectra in the g130 m ( medium - resolution , 11351440 ) and g140l ( low - resolution , 10302000 ) gratings exhibit patchy gunn - peterson absorption in the 303.78 ly line of he ii between 2.392.87 ( g140l ) and 2.742.90 ( g130 m ) . with cos , we obtain better spectral resolution , higher - s / n , and better determined backgrounds than previous studies , with sensitivity to abundance fractions in filaments of the cosmic web . the optical depths from cos are higher than those with the _ far ultraviolet spectroscopic explorer _ ( _ fuse _ ) and range from to , with a slow recovery in mean optical depth to at . the / optical - depth ratio varies ( 10100 for , and 5500 for ) on scales ( 10.8 mpc in comoving radial distance at ) , with numerous flux - transmission windows between 11351186 . the absorption extends to 1186.26 ( ) , including associated absorbers with and minimal proximity effect " of flux transmission at the edge . we propose a qso systemic redshift , some higher than that derived from emission . three long troughs ( 410 or 2560 mpc comoving distance ) of strong absorption between are uncharacteristic of the intergalactic medium if reionized at . contrary to recent indirect estimates ( ) from optical depths , the epoch of reionization may extend to .

1008.2957

r

the systemic redshift of he 2347@xmath14342 is of interest , both to fix the expected location of the edge and to infer the metagalactic radiation field from the qso proximity effect ( dallaglio , wisotzki , & worseck 2008a , b ) . a significant puzzle for this sight line is the 6 offset between the extent of strong absorption ( out to 1186 ) and the expected edge ( 1180 ) based on an uncertain qso emission - line redshift . reimers et al . ( 1997 ) found @xmath154 , based on the weak @xmath19 emission line , while scannapieco et al . ( 2006 ) quoted @xmath155 with no error bar . emission - line redshifts were also measured with uves at the vlt / ut2 by dallaglio et al . ( 2008b ) , who quoted @xmath156 based on the + blend and assuming a rest wavelength @xmath157 for the blend . given the solar abundance ratio ( o / si)@xmath158 , this blend is probably dominated by three lines of , with a statistically weighted centroid at 1303.49 ( morton 2003 ) . in total , the blend consists of three lines decaying to the ground - state fine - structure levels of [ @xmath159 $ ] at 1302.17 , 1304.86 , 1306.03 and two lines of @xmath160 $ ] at 1304.37 and 1309.28 . dallaglio et al . ( 2008a ) measured the redshifts of the strongest emission lines to be @xmath161 ( ly@xmath2 ) and @xmath162 ( ) . however , there are well - known shifts in emission - line redshifts between the qso systemic redshift and the higher ionization lines " ( e.g. , ly@xmath2 , @xmath163977 , @xmath1631549 ) . for instance , 1000 - 3000 km s@xmath89 offsets are commonly seen in the emission - line spectra of agn ( espey et al . 1989 ; corbin 1990 ) . these issues provide systematic uncertainties in determining @xmath164 , either from the weak / blend or from higher ionization lines . thus , the precise qso systemic redshift remains uncertain . because of these problems with emission - line redshifts , we propose to use igm absorption to determine the qso redshift . we suggest that the qso systemic redshift is @xmath111 ( figure 4 ) based on the extent of the and absorption . this redshift is chosen as the midpoint between the centroid of the strong absorption feature seen in both and and the red edge of absorption . figure 4 provides an overview of the cos / g130 m spectrum from 11001190 , together with a blowup of the region from 1173 to the edge near 1186 . we see absorption extending well beyond the wavelengths ( 1180.21180.5 ) corresponding to the qso emission - line redshifts , @xmath165 and @xmath166 , suggested by reimers et al . ( 1997 ) and dallaglio et al . ( 2008b ) respectively . the absorption between 11811186 suggests that the qso actually lies at @xmath167 . interestingly , we see no ionization effects from proximity to the qso , a topic discussed further in section 3.6 . the absorption profile shows an absorption feature at 1186.5 , with optical depth @xmath168 , equivalent width 95 m , and fwhm = 0.14 . this may be proximate absorption or absorption from an intervening system . the spectrum near 1186.5 shows a clear flux minimum and recovery toward shorter wavelengths typical of weak absorption lines . a distinct absorber would appear as a broader shelf " on the side of the @xmath169 trough . we do not make a specific line identification for the feature . it does not seem to be low - redshift ly@xmath170 nor any of the usual igm metal - line systems ( danforth & shull 2008 ) . reimers et al . ( 1997 ) attribute the and absorption at @xmath171 to a multicomponent system of associated absorbers between 11811186 ( redshifts @xmath172 to @xmath173 ) . many of these systems have strong metal lines of , , and , and a few have anomalous ratios of and ly@xmath2 absorption . these observations suggest that the gas might be exposed to high fluxes of ionizing radiation and affected by nucleosynthetic anomalies in nuclear outflows . smette et al.(2002 ) and fechner et al . ( 2004 ) both noted evidence for line - locking " in and ( although the latter group found no statistical evidence compared to simulated line lists ) . line - locking occurs when two absorbers are separated by a velocity equal to the separation of the two doublet lines , resulting from radiation pressure on material physically near the qso ( weymann , carswell , & smith 1981 ) . these radiative forces will drive gas outward from the qso , whereas the redshifted associated absorbers would have infall velocity @xmath174 km s@xmath89 relative to the qso if @xmath175 . thus , our proposed redshift , @xmath176 , provides a more plausible explanation . the uncertainty in qso systemic redshift illustrates the need for infrared observations . unfortunately , the redshifted hydrogen balmer lines fall in difficult spectral bands ( h@xmath2 at 2.563 @xmath177 m , h@xmath170 at 1.898 @xmath177 m ) , as does the [ o ii ] @xmath178 doublet at 1.455 and 1.456 @xmath177 m . the forbidden lines of [ o iii ] @xmath179 occur at more promising wavelengths , 1.955 @xmath177 m and 1.936 @xmath177 m . thus , infrared spectroscopic searches for the [ o iii ] forbidden lines may offer the best opportunity to resolve the issue of @xmath180 . the standard gp optical - depth formula ( fan et al . 2006 ) for species ( @xmath181 = or ) is @xmath182 where @xmath183 @xmath184 hz is the integrated classical oscillator cross section , @xmath185 is the absorption oscillator strength for ly@xmath2 transitions of and at rest wavelengths @xmath186 and 303.78 , and @xmath187 is their number density ( @xmath188 ) . the hubble expansion parameter is @xmath189^{1/2}$ ] in a flat friedman cosmology ( @xmath190 ) . all cosmological parameters and the resulting coefficients are based on wmap-7 concordance values of cmb modeling from komatsu et al . ( 2010 ) , @xmath191 , @xmath192 , and @xmath193 , and hubble constant @xmath194 with @xmath195 . to set the ion densities @xmath187 , we define @xmath196 and @xmath197 as the abundance fractions of and , respectively . ( the quantity @xmath196 is often called the neutral fraction . ) the factors @xmath198 are the overdensities of h ( at @xmath33 ) and he ( at @xmath46 ) relative to the mean co - moving baryon density , @xmath199 g @xmath188 . with a primordial helium abundance @xmath200 by mass ( peimbert et al . 2007 ) and @xmath201 by number , this baryon density corresponds to and number densities , @xmath202 ^3 \ ; , \\ n_{\rm heii } & = & ( 1.01 \times 10^{-6}~{\rm cm}^{-3 } ) \ ; x_{\rm heii } \ ; \delta_{\rm he } \left [ \frac { ( 1+z)}{4 } \right ] ^3 \ ; . \end{aligned}\ ] ] in the high-@xmath203 limit , @xmath204 , we can express the hubble parameter as @xmath205^{3/2}$ ] scaled to the epoch @xmath46 relevant for the beginning of reionization . thus , the gunn - peterson optical depths for h i ( scaled to the @xmath206 epoch ) and he ii ( scaled to the @xmath207 epoch ) are : @xmath208 ^{3/2 } \ ; x_{\rm hi } \ ; \delta_{\rm h } \ ; , \\ \tau_{\rm heii } ( z ) & = & ( 3.55 \times 10 ^ 3 ) \left [ \frac { ( 1+z)}{4 } \right ] ^{3/2 } \ ; x_{\rm heii } \ ; \delta_{\rm heii } \ ; .\end{aligned}\ ] ] very small abundance fractions , @xmath209 and @xmath210 , will saturate the gunn - peterson ly@xmath2 absorption in and , with optical depths @xmath211 , even in under - dense regions with @xmath212 . it is primarily for this reason that the hydrogen reionization epoch is so difficult to measure in ly@xmath2 absorption at @xmath213 ( fan et al . . however , absorption at @xmath214 can probe 50100 times higher abundance fractions in @xmath197 . for the maximum observable values of optical depth ( @xmath215 ) and with typical densities in low - density filaments and voids , the intervals of high absorption at @xmath216 correspond to fractions , @xmath217 \left [ \frac { ( 1+z ) } { 3.8 } \right ] ^{-3/2 } \left [ \frac { \delta_{\rm he } } { 0.1 } \right ] ^{-1 } \ ; .\ ] ] these overdensities , @xmath218 , are appropriate for the low - column - density ( @xmath219 ) regions of the ly@xmath2 forest . figure 5 shows the optical depths for @xmath75 , using cos data from both g140l and g130 m and _ fuse_. to construct this figure , we reconstructed horizontal error bars " representing the redshift bins ( @xmath115 ) used in these papers . we used unpublished @xmath115 and uncertainties in optical depths @xmath114 from shull et al . ( 2004 ) . from zheng et al . ( 2004 ) , we used values of @xmath115 and @xmath114 from their figure 3 , with 25% uncertainties in @xmath114 . we find reasonable agreement with the _ fuse _ optical depths ( shull et al . 2004 ) down to @xmath220 , although some of the g140l fluxes are higher than those in the _ fuse _ extension to @xmath221 ( zheng et al . the smaller _ fuse _ optical depths may arise from uncertain background subtractions . defining the redshift ranges for these data points is difficult for optical depths that vary rapidly over @xmath222 . future cos spectra of fainter -gp targets ( often @xmath223 magnitude agn ) will have low s / n ratios and will probably not show the fluctuations in optical depths found here . at best , they will measure broad - band optical depths , @xmath224 . for he 2347@xmath14342 , we list below the and optical depths averaged over @xmath225 windows , together with the standard deviations of their distributions : * ( @xmath3 2.42.5 ) @xmath226 , @xmath227 * ( @xmath3 2.52.6 ) @xmath228 , @xmath229 * ( @xmath3 2.62.7 ) @xmath230 , @xmath231 there may be a slight trend to higher @xmath232 at lower redshifts , as we discuss in section 3.4 . considering the ratios of the broad - band averages , we find that @xmath233 rises from @xmath234 at @xmath235 to values @xmath236 at @xmath237 and @xmath238 at @xmath239 . despite the large spreads of the optical - depth distributions , the means are fairly well determined . figure 6 shows examples of the and ionization structures found in our cosmological simulations ( smith et al . 2010 ) , computed with ` enzo ` , an n - body , hydrodynamical code modified to compute time - dependent h and he ionization . one can see the projected topology of the cosmic web , the baryon overdensity , the ionization fractions of and at @xmath80 , and their ratio , @xmath240 . observationally , we measure the ratio of column densities , @xmath11 n()/n ( ) , which we approximate as @xmath241 . the factor of 4 arises from the larger frequency bandwidth , with the absorption - line cross section , @xmath242 , scaling as oscillator strength times wavelength . our igm simulations at @xmath243 show a mean value of the ionization ratio , @xmath244 , corresponding to @xmath245 for primordial he / h = 0.0823 by number . we have confirmed that a substantial amount of observable , with @xmath246 0.0010.01 , comes from ionized gas with @xmath247 ( much of it at @xmath248 ) and @xmath249 to @xmath250 . this gas is primarily confined to photoionized filaments in the cosmic web , with some contribution from collisional ionization ( at @xmath251 k ) . further analysis of these simulations will appear in a later paper . the and ly@xmath2-forest absorbers have traditionally been assumed to arise in photoionized gas , irradiated by metagalactic ionizing ( euv ) radiation of specific intensity @xmath252 , where @xmath181 refers to ( @xmath253 ev ) or ( @xmath254 ev ) . for these hydrogenic species , whose photoionization cross sections above threshold @xmath255 scale as @xmath256 , the photoionization rates @xmath257 . the parameters @xmath258 are local spectral indices of the ionizing background at 1 ryd and 4 ryd , respectively , and provide minor corrections to the photoionization rates . for typical metagalactic fluxes and igm densities during reionization , hydrogen and helium are mostly ionized , with fractions @xmath259 and @xmath260 . because the first ionization potentials of ( 13.6 ev ) and ( 24.58 ev ) are not greatly disparate , we expect the and ionization fronts to coincide for appropriate values of ionizing spectral index . for qso ionizing spectra of power - law form , the and ionization fronts , driven by the photon fluxes at 1 ryd and 4 ryd , respectively , will propagate at the same ( photon flux - limited ) velocity for a critical spectral index , @xmath261 corresponding to our adopted he / h abundance , @xmath262 . the agreement with the _ hst_-observed mean spectral index of agn at 12 ryd , @xmath263 ( telfer et al . 2002 ) , suggests that and ionization fronts normally propagate together . in photoionization equilibrium in regions of high ionization , @xmath264 and @xmath265 , the / abundance ratio is ( fardal et al . 1998 ; shull et al . 2004 ) , @xmath266 the numerical coefficient has been increased from 1.70 to 1.77 , reflecting an updated value of the primordial he / h abundance , @xmath262 , which we use as an approximation to @xmath267 . in this equation , @xmath268 , @xmath269 , @xmath270 , and @xmath271 are the case - a recombination rate coefficients and photoionization rates for and , and @xmath272 and @xmath273 are the specific intensities of the ionizing radiation field at 1 ryd and 4 ryd . the parameter @xmath274 is used to scale the temperature dependence of the case - a recombination rates over the range @xmath275 k to 20,000 k ( osterbrock & ferland 2006 ) : @xmath276 and @xmath277 . equation ( 8) is an approximation , which will break down when @xmath197 becomes significant . it also does not include the effects of collisional ionization of , which can become important in the shocked filaments of shocked gas at @xmath251 k , the so - called warm - hot intergalactic medium ( whim ) . as noted in figure 6 , our simulations suggest that some of the in shocked igm filaments may be collisionally ionized gas at @xmath251 k. however , the bulk of the is photoionized gas at @xmath278 k. ccccc mean ( @xmath232 ) & @xmath279 & @xmath280 & @xmath281 & @xmath282 + median ( @xmath232 ) & @xmath283 & @xmath284 & @xmath285&@xmath286 + mean ( @xmath287 ) & @xmath288 & @xmath289 & @xmath290 & @xmath291 + median ( @xmath287 ) & @xmath292 & @xmath293 & @xmath294 & @xmath293 + as shown in figures 2 and 4 , we have confirmed the presence of three long troughs with strong absorption ( @xmath72 ) and no detectable flux . these troughs have been noted previously ( reimers et al . 1997 ; smette et al . 2002 ; shull et al . 2004 ) , but the very low cos backgrounds allow us to better characterize their optical depth . we also detect numerous windows of flux transmission ( e.g. , at 1138 , 1139 , 1144 , 1154 , 1160 , 1174 , and 1179 see figure 2 ) . the g130 m data provide accurate boundaries in redshift . from those , we can determine their comoving radial sizes , using wmap-7 cosmological parameters : 1 . _ ( trough 1 ) _ @xmath295 ( 61 mpc ) , 2 . _ ( trough 2 ) _ @xmath296 ( 39 mpc ) , 3 . _ ( trough 3 ) _ @xmath297 ( 25 mpc ) . these dimensions , all much larger than 10 mpc , are incompatible with zones of photoionization around typical qsos . they are also unlikely to exist at the epoch following the overlap of expanding cosmological i - fronts . recent theoretical modeling has studied the statistics of troughs ( mcquinn et al . 2009 ; mcquinn 2009 ; furlanetto 2009a , b ; dixon & furlanetto 2009 ) . these studies examine large - scale fluctuations in the ly@xmath2 forest transmission , during and after reionization . a robust result is that long troughs of large optical depth , @xmath298 , can not be explained in models with a smoothly evolving ionizing radiation field ( furlanetto & dixon 2010 ) . furthermore , the observed 2560 mpc troughs of high opacity between @xmath299 can not be accommodated in standard reionization models unless reionization is delayed until @xmath8 . the absorption is therefore expected to be patchy at @xmath300 , as we have observed . it would be useful to conduct surveys ( worseck et al . 2007 ) of galaxies and qsos near the sight line at these trough redshifts to identify potential sources of ionization ( or lack thereof ) . as discussed in section 3.2 , the opacity greatly exceeds that of ; the ratio @xmath301 for typical conditions in an igm photoionized by qsos of low space density . thus , the propagation and overlap of i - fronts driven by ionizing continua will likely differ from those of hydrogen . the greater opacity means that filaments of the cosmic web still have @xmath302 at @xmath303 ( see figures 5 and 6 ) . thus , the topology of overlapping ionized zones probably differs from that of merging regions at @xmath206 . these theoretical results are explored in a later paper ( smith et al . 2010 ) using adaptive - mesh cosmological simulations with the ` enzo ` code . because reionization involves the stochastic propagation and overlap of ionization fronts ( i - fronts ) , one naturally expects variations in the abundances of and . the metagalactic flux of high - energy ( 4 ryd continuum ) radiation varies primarily because of the low space density of the dominant ionizing sources ( agn ) and varying attenuation through the igm . the variations in opacity can be especially large during reionization , because the 4 ryd continuum is strong near agn ( inside the i - fronts ) but heavily attenuated in the troughs , far from the agn and within the gaseous filaments of the cosmic web . figure 4 shows both and absorption , overlaid in redshift , illustrating the correspondence of flux - transmission windows with weak spots ( low absorption ) in the ly@xmath2 forest . the non - gaussian wings in the cos line - spread function ( lsf ) is most significant for weak absorbers , but we believe this is completely accounted for in the convolution of the data by the cos lsf . the resolving power ( @xmath304 ) of the cos lsf is more appropriately the effective gaussian resolving power ( green et al . the main difference in the convolved and unconvolved data in figure 4 is simply a degradation in resolution by a factor of 2.5 . the cos lsf contributes to a redistribution of flux in the narrowest lines , but this is accounted for with the non - gaussian lsf . the / ratio , @xmath241 , tracks the ratio of ionizing fluxes at 1 and 4 ryd ( see equation [ 8 ] ) . table 3 presents the mean and median values of @xmath232 in the g130 m and g140l data , and over various redshifts . in different columns , we present these statistics for the g140l and g130 m spectral regions , and for the region ( @xmath305 ) where the two gratings overlap . to calculate @xmath306 , we convolve the high - resolution vlt data with either the medium - resolution ( g130 m ) or low - resolution ( g140l ) cos line - spread functions , depending which dataset is representing at a particular redshift . the cos data are then smoothed by seven pixels ( @xmath307 resolution element ) and up - sampled to the finer vlt wavelength scale . optical depths @xmath308 and @xmath309 are calculated on a pixel - by - pixel basis . figures 7 and 8 show @xmath310 and @xmath311 and demonstrate that optical depth saturates in certain regions . over the range @xmath75 , 32% of pixels are saturated , but this fraction depends strongly on redshift and spectral resolution . in the low - resolution data at @xmath312 , we find that @xmath114 is almost always unsaturated . at @xmath313 , we see long absorption troughs in which 4045% of the pixels have @xmath314 . we computed mean and median values of @xmath232 using both saturated and unsaturated pixels . as the saturated pixel values for are entirely in the numerator , our average @xmath232 values are lower limits . using only unsaturated pixels reduces @xmath233 systematically by 10 - 20% at @xmath315 . correcting for larger true values of @xmath316 would increase the mean statistics . there is no change at @xmath317 . we confirm the fluctuations seen by _ fuse _ between @xmath318 ( kriss et al . 2001 ; shull et al . 2004 ) on small scales , @xmath319 . figures 7 and 8 show that @xmath232 fluctuates on scales down to @xmath222 at g140l resolution and @xmath320 at g130 m resolution . for reference , the redshift interval @xmath321 corresponds to a comoving radial distance of 10.8 mpc at @xmath14 . regions of hot gas ( @xmath251 k ) might appear as high-@xmath232 systems , in which is far more collisionally ionized than . however , the cos data also exhibit several instances of low-@xmath232 absorbers with @xmath322 . since @xmath241 , the low-@xmath232 systems appear primarily where the optical depth is large and optical depth small . if photoionized , these absorbers may be irradiated by very hard radiation fields , with large ratios of @xmath323 ( equation 8) , perhaps near an agn with a particularly flat euv spectral index , @xmath324 . several good examples of low@xmath232 absorbers appear at @xmath325 , 2.785 , 2.830 , 2.865 , and 2.904 . most of these systems have high @xmath326 , the exception being the absorber at @xmath327 in which both @xmath114 and @xmath326 are low , and their ratio poorly determined . for high-@xmath232 systems , the g130 m data exhibit regions with @xmath328 , typically in gas with large @xmath114 but low @xmath326 . extreme excursions in @xmath232 may arise from noise , and their detectable range depends on spectral resolution . we therefore take care to assess the range over which we can measure reliable optical depths . for ratios within the range @xmath11 10100 ( g140l ) and @xmath11 5500 ( g130 m ) , we believe nearly all the fluctuations are real . unfortunately , strong troughs of absorption at @xmath329 hinder our ability to measure @xmath114 for individual systems with the high - resolution g130 m . many of the @xmath232-fluctuations appear at @xmath8 , observed with the lower - resolution g140l . these small - scale @xmath232-variations have been the topic of numerous theoretical papers ( zuo 1992 ; fardal & shull 1993 ; fardal et al . 1998 ; bolton et al . 2005 , 2006 ) . the key focus of these papers is on fluctuations in the small numbers of agn within the characteristic attenuation length , corresponding to the @xmath330 sphere " at 4 ryd photon energy . because the opacity is so much larger than that of , one expects large variations in the ionizing flux , @xmath273 , on comoving scales of 2040 mpc at @xmath331 ( fardal et al . 1998 ; furlanetto 2009 ; dixon & furlanetto 2009 ) . a second important effect is that the observed low - redshift agn exhibit wide variations in their euv spectral indices ( telfer et al . 2002 ; scott et al . 2004 ) , which produce strong source variations in the flux ratio @xmath332 . finally , radiative transfer of the metagalactic ionizing radiation reprocesses the ionizing spectra , producing further variations ( fardal et al . what is now firmly established by the new cos data are the variations in @xmath232 on @xmath333 mpc comoving radial distance scales ( @xmath222 ) . it is surprising to note the sharpness of the edge at 1186.26 and the lack of any proximity effect near the qso . if ionizing radiation were escaping from the agn , the surrounding igm should be ionized within 510 mpc of the qso . the absorption extends @xmath334 beyond the previous qso redshift estimate , @xmath335 ( reimers et al . as discussed in section 3.1 , this dilemma is easily resolved by moving the quasar redshift to @xmath173 , an offset ( 1460 km s@xmath89 at @xmath336 ) that corresponds to 19.5 mpc comoving proper distance . however , the two proposed systemic redshifts , @xmath175 and 2.904 , raise several questions . does the qso lie inside an and cavity produced by its photoionizing radiation ? or , is the qso ionizing radiation absorbed by circumnuclear gas ? is there infalling gas near the agn that produces associated absorption with @xmath337 ? it is worth investigating these possibilities . for ( 1 ryd ) and ( 4-ryd ) ionizing - photon luminosities , @xmath338 and @xmath339 , what strmgren radii will this bright qso carve out ? these distances are obviously limiting cases , in ionization equilibrium , whereas one expects the ionization zones around the qso to involve time - dependent propagation of ionization fronts . indeed , the lack of a proximity effect could arise from this source just starting to burn its way out of the galactic nucleus . given the strength of the @xmath336 absorber , we will assume higher gas densities associated with the qso and scale to an overdensity ( @xmath340 ) at @xmath336 . the h and he densities are then : @xmath341 , @xmath342 , and @xmath343 . at @xmath344 k , @xmath345 and @xmath346 . a typical @xmath347 quasar produces a total of @xmath348 lyc photons s@xmath89 , but this qso is much brighter ( @xmath64 ) . extrapolation from 1200 down to the lyman limit ( 889.5 at @xmath176 ) shows that he 2347 - 4342 has an observed specific flux , @xmath349 erg @xmath105 s@xmath89 @xmath89 or @xmath350 erg @xmath105 s@xmath89 hz@xmath89 . from this flux and a luminosity distance , @xmath351 cm at @xmath173 , we estimate an ionizing photon luminosity of @xmath352 photons s@xmath89 in the 4-ryd continuum . scaling to @xmath353 , we estimate a strmgren radius , @xmath354 ^{1/3 } \nonumber \\ & \approx & ( 4~{\rm mpc } ) \left [ \frac { s_0^{{\rm ( he ) } } } { 10^{57}~{\rm s}^{-1 } } \right]^{1/3 } ( \delta_h/100)^{-2/3 } t_{4.3}^{0.255 } \ ; . \nonumber\end{aligned}\ ] ] a similar calculation , using the observed flux , @xmath355 erg @xmath105 s@xmath89 @xmath89 , at the redshifted ( 3561 ) edge , gives @xmath356 photons s@xmath89 and an strmgren radius of @xmath357 ^{1/3 } \nonumber \\ & \approx & ( 6~{\rm mpc } ) \left [ \frac { s_0^{{\rm ( h ) } } } { 5\times10^{57}~{\rm s}^{-1 } } \right]^{1/3 } ( \delta_h/100)^{-2/3 } t_{4.3}^{0.286 } \ ; . \nonumber\end{aligned}\ ] ] we note that the ratio of the extrapolated fluxes at the respective ionization limits is fairly small . in the qso rest - frame , @xmath358 , indicating a fairly hard ( flat ) power - law spectrum @xmath359 . these estimated strmgren radii are a substantial fraction of the proper distance of 19.5 mpc between the two proposed qso redshifts , @xmath173 and @xmath360 . even though the local ionization zone may not extend as far as these equilibrium strmgren radii , the expected proximity effect is minimally visible , except for a narrow feature with @xmath361% flux transmission at @xmath362 , just below the edge ( figure 4 ) . we conclude that ionizing radiation from this qso is strongly absorbed in the proximity of the nucleus , possibly by circumnuclear gas or by the strong absorber at @xmath65 . the photoionization cross sections for and above threshold are approximately @xmath363 and @xmath364 . thus , to absorb a substantial amount of the ionizing continua requires column densities @xmath365 ^3 \ ; \tau(e ) \nonumber \\ { \rm n}_{\rm heii } & = & ( 6.35 \times 10^{17}~{\rm cm}^{-2 } ) \left [ e/54.4~{\rm ev}\right ] ^3 \ ; \tau(e ) \end{aligned}\ ] ] for continuum optical depth @xmath366 at photon energy @xmath367 . for this very bright qso , the absence of a proximity effect indicates a significant attenuation of the 4 ryd continuum , with optical depth @xmath368 at mean photon energies 1.5 times the 54.4 ev threshold , or n@xmath369 . what are the observational consequences of such large column densities of ionized gas ? it has been suggested ( reimers et al . 1997 ) that resonance lines at 303.415 and 305.596 might be detectable , but we find no obvious candidates . it would be useful to search for signs of splittings of these lines , which are separated by 2.182 @xmath370 at @xmath65 . some of the associated absorbers have anomalously stronger than , suggesting that the gas is close to the qso with helium mostly fully ionized ( ) . more clues may come from the strong absorbers at @xmath371 ( 1184.71186.2 ) which would be closest to the qso if @xmath176 . this system has high optical depth in both and ( see figure 4 ) . very strong metal - line absorption is seen in with weaker absorption in , , and ( reimers et al . 1997 ; fechner et al . 2004 ) . by fitting higher lyman - series absorbers , fechner et al . ( 2004 ) found log n@xmath372 , while the metal - line absorbers gave log n@xmath373 , log n@xmath374 , and log n@xmath375 . they proposed that this absorber is exposed to the strongest and hardest radiation from the qso , and therefore may shield the other associated absorbers . however , their photoionization models gave log n@xmath376 , which is 100 times too small to provide the necessary absorption ( eq . [ 9 ] ) . the column is 10 times too small to shield the 1 ryd continuum . fox , bergeron , & petitjean ( 2008 ) obtained newer ( high s / n ) spectra on these metal - line absorbers at @xmath377 , 2.8972 , and 2.9041 . they found somewhat higher column densities of and and a slightly higher column density , @xmath378 in the @xmath379 absorber . this column is still insufficient to shield the qso s ionizing continuum . we conclude that no satisfactory explanation exists for the absence of a proximity effect around this very luminous qso , other than the possibility that it has only recently turned on ( within the last myr ) .

the / optical - depth ratio varies ( 10100 for , and 5500 for ) on scales ( 10.8 mpc in comoving radial distance at ) , with numerous flux - transmission windows between 11351186 . the absorption extends to 1186.26 ( ) , including associated absorbers with and minimal proximity effect " of flux transmission at the edge . we propose a qso systemic redshift , some higher than that derived from emission . contrary to recent indirect estimates ( ) from optical depths , the epoch of reionization may extend to .

we report ultraviolet spectra of the high - redshift ( ) quasar , he 2347 , taken by the cosmic origins spectrograph ( cos ) on the _ hubble space telescope _ ( _ hst _ ) . spectra in the g130 m ( medium - resolution , 11351440 ) and g140l ( low - resolution , 10302000 ) gratings exhibit patchy gunn - peterson absorption in the 303.78 ly line of he ii between 2.392.87 ( g140l ) and 2.742.90 ( g130 m ) . with cos , we obtain better spectral resolution , higher - s / n , and better determined backgrounds than previous studies , with sensitivity to abundance fractions in filaments of the cosmic web . the optical depths from cos are higher than those with the _ far ultraviolet spectroscopic explorer _ ( _ fuse _ ) and range from to , with a slow recovery in mean optical depth to at . the / optical - depth ratio varies ( 10100 for , and 5500 for ) on scales ( 10.8 mpc in comoving radial distance at ) , with numerous flux - transmission windows between 11351186 . the absorption extends to 1186.26 ( ) , including associated absorbers with and minimal proximity effect " of flux transmission at the edge . we propose a qso systemic redshift , some higher than that derived from emission . three long troughs ( 410 or 2560 mpc comoving distance ) of strong absorption between are uncharacteristic of the intergalactic medium if reionized at . contrary to recent indirect estimates ( ) from optical depths , the epoch of reionization may extend to .

1504.08273

i

dwarf spheroidals ( dsphs ) are very faint galaxies ( some of the recently discovered dsph satellites of milky way are the faintest known galaxies , @xcite ) which tend to cluster around large galaxies @xcite . among the 50 or so local group dsphs discovered so far , only two ( tucana and cetus ) are relatively isolated ; the rest are located in the vicinity of either milky way or m31 , and are believed to be their satellites . despite their dull appearances ( no ongoing star formation ; little or no interstellar medium ; @xcite ) , dsphs are fascinating objects largely due to the fact that they contain significant quantities of dark matter ( dm ) , and as such represent the smallest observed scale of dm clustering . state of the art cosmological simulations predict that large galaxies should contain many smaller sub - halos which have not had time to be completely destroyed by the tidal field of the host halo . dsphs are believed to represent at least some of this substructure @xcite . dsphs present two major challenges to the standard ( @xmath10cdm ) cosmological model . first , despite the recent advances on both theoretical and observational sides , there still appears to be a factor of a few discrepancy between the observed and predicted numbers of milky way satellites so called `` missing satellites problem '' @xcite . second , some indirect evidence ( such as the `` timing paradox '' for the five globular clusters of fornax dsphs ; @xcite ) suggests that dm distribution in dsphs has a flat core , which is in line with what is deduced for larger dwarf and low surface brightness galaxies @xcite , but is at odds with the results of many cosmological simulations , predicting central divergent dm cusps with the logarithmic slope @xmath11 @xcite . different theoretical mechanisms suggested to rectify this `` cusp core '' problem produce different velocity anisotropy profiles for stars . for example , our stellar feedback mechanism @xcite , where the dm cusp is flattened via gravitational heating from the interstellar gas sloshed around by supernovae , results in isotropic stellar cores . on the other hand , the dynamical friction mechanism of @xcite , where the cusp is heated by massive baryonic clumps passively spiraling in towards the galactic center , should produce noticeable central tangential anisotropy @xcite . constraining stellar anisotropy profiles in spheroidal galaxies can hence be a valuable indirect way of identifying the correct theoretical mechanism of dm core formation . @xcite was the first who deduced the presence of significant amounts of dm in a dsph ( draco ) , based on the measurements of the line - of - sight velocities of only three stars . since then , the number of stars in dsphs with known line - of - sight velocities has grown dramatically : recently published homogeneous datasets have up 2500 stars per galaxy ( for fornax ; @xcite ) . mass modeling of dsphs has dramatically improved as well : from simple global estimates based on the virial theorem @xcite , to spatial models with strong simplifying assumptions ( such as `` mass follows light '' ; @xcite ) , to more recent modeling efforts with fewer assumptions @xcite . the classical method of dsph mass modeling is to solve the spherical jeans equation for a range of models with different dm density profiles , and then to compare the predicted stellar line - of - sight velocity dispersion profiles with the observed ones using either @xmath12 or maximum likelihood techniques to find the best models . the spherical symmetry assumption is reasonably accurate given the spheroidal appearances of dsphs ( ellipticity @xmath13 is usually @xmath14 or less ) , absence of disk - like structures , and negligible rotation in these systems @xcite . to solve the spherical jeans equation ( that is , to derive the stellar velocity dispersion as a function of radius ) , one has to specify two functions : total ( dm @xmath15 stars ) density , and stellar velocity anisotropy ( @xmath16 ) profiles . to reduce the dimensionality of the problem , one usually assumes a certain shape of the @xmath16 radial profile either a constant , or the osipkov - merritt profile ( purely isotropic at the center , purely radially anisotropic in the infinity ; @xcite ) . there are no reasons to believe that stellar anisotropy is constant in dsphs . for example , simple dynamical models which start with an initially non - equilibrium stellar configuration inside the dm halo ( `` cold collapse '' , @xcite , and `` hot collapse '' , @xcite ) tend to produce the stellar velocity isotropy at the center and a variable degree of radial anisotropy in the outskirts of the relaxed stellar body . as already mentioned , the central parts of dwarf galaxies can be significantly affected by dense and violent baryons , which may either randomize stellar velocities @xcite or induce a significant tangential anisotropy @xcite . on the observational side , dsphs are known to be non - homogeneous objects , with younger , more metal - rich and kinematically colder star populations concentrated towards the center @xcite ; it would be strange if the stellar velocity anisotropy would be the same across these different populations of stars . given the expectation that @xmath16 is not constant across a dsph and that the important properties of dsphs ( such as the central logarithmic slope of the dm density ) are strongly degenerate with respect to the unknown stellar velocity anisotropy @xcite , proper mass modeling of dsphs has to include radially variable stellar anisotropy . to the best of my knowledge , the only example of a full - fledged jeans mass modeling of dsphs with variable @xmath16 is the work by @xcite . here i outline the main differences of my approach with that of @xcite . 1 . in this paper , i carry out mass modeling of the limited number ( five ; carina , fornax , leo i , sculptor , and sextans ) of galactic dsphs with the highest quality , homogeneous data : large ( @xmath17 stars ) homogeneous datasets of stellar line - of - sight velocities @xcite and accurate stellar surface brightness profiles derived in a homogeneous manner in this paper . this is in contrast to the work of @xcite , who analyzed a much larger set of local group dsphs , with heterogeneously derived data and a wide range of data quality . i employ a `` brute force '' optimization while searching for the best fitting models . this approach generated a wealth of statistical data , which can be used for testing a variety of different hypotheses about the distribution of stars and dm in dsphs . the data are available online . the `` brute force '' approach coupled with a flexible dsph model allowed me to find the dsph parameters which the jeans analysis can constrain very well . specifically , i found that the total enclosed mass in a dsph can be constrained to a high accuracy ( two - sigma uncertainty as good as @xmath1815% , for fornax ) at a certain radius , which is different for different dwarfs . this information can be valuable for matching the galactic dsphs to the predictions of cosmological simulations . similarly , i derived tight constraints on the local dm density at a certain radius ( unique for each galaxy ) , which can be used in the research aimed at detecting dm in dsphs via its annihilation signal . 4 . unlike @xcite , i properly account for the self - gravity of stars . this can be important for dsphs with dense stellar cores ( e.g. sculptor ) . i use an advanced ( with the variance due to random locations of stars within one radial bin removed ; see [ good ] ) @xmath12 model fitting approach . unlike @xcite , who employed a maximum likelihood technique , my approach is insensitive to the ( unknown ) shape of the line - of - sight star velocity probability distribution function ( pdf ) . i had two main goals for this paper . first , i wanted to find out which ( if any ) dsph parameters can be meaningfully constrained via the classical , jeans mass modeling approach , if such an analysis is pushed to the extreme ( large homogeneous observational datasets of stellar line - of - sight velocities ; a very flexible galactic model ; careful numerical analysis consuming a significant @xmath19 cpu hours in my case amount of supercomputing time ; a `` brute force '' optimization which ensures that no hidden `` valleys '' and local and global minima in the multi - dimensional likelihood manifold are missed ) . the second goal was to generate high - quality data which can be used to dramatically reduce computational time ( by restricting the model parameter space to be explored ) in future post - jeans ( analyzing the full shape of the stellar velocity pdf ) mass modeling efforts which will be the subject of paper ii in this series . as the dynamical state of the outer parts of dsphs is still a matter of debate ( specifically , some authors , e.g. @xcite , argue that the observed outskirts of these galaxies are undergoing a severe tidal disruption and hence are not in dynamic equilibrium , which would invalidate the jeans analysis for those parts ; but see @xcite for the opposite example ) , in the present study i put the main emphasis on recovering the _ inner _ structure of dsphs . unfortunately , the most interesting aspect of the inner structure of these galaxies the `` dm cusp or core '' question can not be addressed via the jeans analysis alone , as the central logarithmic slope of the dm density profile @xmath20 is known to be degenerate in this method . this follows from the properties of the spherical jeans equation @xcite , and is clearly visible even in the mass modeling with a constant stellar anisotropy @xcite . in this paper i obtain a more general result that @xmath21 is completely unconstrained by the jeans analysis not only at the center ( @xmath22 ) , but also at any other radius @xmath23 within the stellar body of the dwarf . this paper is organized as follows . section [ model ] describes the dsph model . section [ obs_data ] discusses the observational data ( stellar line - of - sight velocities and stellar surface brightness profiles ) . section [ fitting ] gives a detailed description of my @xmath12 optimization technique . section [ results ] presents the main results of this study . the conclusions are presented in section [ conclusions ] .

using a flexible galactic model with variable stellar velocity anisotropy , i apply the classical jeans mass modeling approach to the five dwarf spheroidal galaxies with the largest homogeneous datasets of stellar line - of - sight velocities ( between 330 and 2500 stars per galaxy ) carina , fornax , leo i , sculptor , and sextans . local dm density has the tightest constraints at smaller ( and also unique for each galaxy ) radii .

using a flexible galactic model with variable stellar velocity anisotropy , i apply the classical jeans mass modeling approach to the five dwarf spheroidal galaxies with the largest homogeneous datasets of stellar line - of - sight velocities ( between 330 and 2500 stars per galaxy ) carina , fornax , leo i , sculptor , and sextans . i carry out an exhaustive model parameter search , assigning absolute probabilities to each parameter combination . my main finding is that there is a well defined radius ( unique for each galaxy ) where the jeans analysis constraints on the enclosed mass are tightest , and are much better than the constraints at previously suggested radii ( e.g. 300 pc ) . for carina , fornax , leo i , sculptor , and sextans the enclosed dm mass is ( at 410 pc ) , ( at 925 pc ) , ( at 390 pc ) , ( at 435 pc ) , and ( at 1035 pc ) , respectively ( two - sigma uncertainties ; in m units ) . local dm density has the tightest constraints at smaller ( and also unique for each galaxy ) radii . the largest central dm density constraint is for sculptor : pc ( at two - sigma level ) . i show that the dm density logarithmic slope is totally unconstrained by the jeans analysis at all the radii probed by the data ( and not just at the center , as was demonstrated before ) . stellar velocity anisotropy has only very weak constraints . in particular , pure central tangential anisotropy is ruled out at better than two sigma level for three dwarfs , and the data are consistent with the global stellar velocity isotropy for all the five galaxies .

1504.08273

c

i carried out the classical jeans mass modeling of the five dwarf spheroidal galaxies with the highest quality observational data carina , fornax , leo i , sculptor , and sextans . my primary goal was to push the analysis to its limits , by developing a flexible enough galactic model ( with variable stellar velocity anisotropy ) , refining the traditional @xmath12 fitting algorithm , and investing a significant amount ( @xmath19 cpu hours ) of supercomputing time to carry out an exhaustive model parameter optimization . the main results of this study are as follows . * my galactic model with the six free parameters ( @xmath41 , @xmath42 , @xmath20 , @xmath35 , @xmath36 , and @xmath38 ) gives a good description of the observational data : the normalized @xmath12 for the differences between the model and observed velocity dispersion profiles are close to a unity , which is consistent with the deviations being purely due to the observational errors . * i show that the jeans mass modeling approach ( even with high quality data and modeling ) can not place meaningful constraints on most galactic parameters , including the central dm density logarithmic slope ( @xmath20 ) , dm halo scaling radius ( @xmath41 ) and density ( @xmath42 ) , and central stellar velocity anisotropy ( @xmath35 ) . moreover , i show that the local dm density logarithmic slope , @xmath202 , is unconstrained at all the radii probed by the data . as a consequence , one must resort to much more computationally expensive post - jeans mass modeling techniques ( which deal with the full probability distribution function for stellar line - of - sight velocities , and not just the dispersion ) to be able to solve the `` cusp core '' issue for dsphs , or to identify theoretical mechanisms responsible for flattening dm cusps in dwarf galaxies ( by constraining the stellar velocity anisotropy profiles ) . * my most important finding is that there is a certain radius ( @xmath152 ; different for each galaxy ) where jeans mass modeling provides the tightest constraints on the enclosed mass in dsphs . for carina , fornax , leo i , sculptor , and sextans my two - sigma constraints for the enclosed dm mass are @xmath203 m@xmath6 ( at 409 pc ) , @xmath204 m@xmath6 ( at 924 pc ) , @xmath205 m@xmath6 ( at 389 pc ) , @xmath206 m@xmath6 ( at 435 pc ) , and @xmath207 m@xmath6 ( at 1034 pc ) , respectively . these constraints are much tighter than the constraints at the previously suggested `` good '' radii 300 pc , 600 pc , and the half - light radius . the tight constraints can be very valuable for placing the dsphs in the proper cosmological context . * i also derive useful constraints on the local dm density . similarly to the enclosed mass , each galaxy has a certain radius ( @xmath155 ) where my jeans analysis places the tightest constraints on this quantity . for example , i show that in sculptor @xmath208 @xmath8 pc@xmath9 ( two - sigma interval ) at 256 pc from its center . also , the analysis produced useful minimum central dm density ( @xmath139 ) constraints ( the largest one is for sculptor : @xmath7 @xmath8 pc@xmath9 ) . these constraints can be used in projects aimed at detecting dm in dsphs via its annihilation signal . * i show that stellar anisotropy profiles are very poorly constrained in jeans mass modeling . the only useful results here are that the pure central tangential anisotropy is excluded at better than two - sigma level for three out of the five dsphs , and that the data are consistent with the global stellar velocity isotropy for all the five dwarfs . * a significant advantage of the exhaustive search through the multi - dimensional model parameter space employed in this study , with all the intermediate results stored and available online , is that the results can be used for many other projects . most importantly , this analysis can be used as the first preliminary step ( which eliminates a vast majority of models which are incompatible with the data ) in post - jeans mass modeling projects ( which model the full pdf for the stellar line - of - sight velocities ) the subject of my paper ii in this series . the latter approach should be able to overcome most of the degeneracies present in jeans mass modeling ( as exposed in the current work ) , hopefully settling once and for all whether dsphs have flat dm cores . the simulations reported in this paper were carried out on facilities of the shared hierarchical academic research computing network ( sharcnet : www.sharcnet.ca ) . this research was supported in part by sharcnet . aaronson , m. 1983 , , 266 , l11 an , j. h. , & evans , n. w. 2006 , , 642 , 752 baes , m. , & van hese , e. 2007 , , 471 , 419 binney , j. , & tremaine , s. 1987 , galactic dynamics ( princeton : princeton univ . press ) burkert , a. 1995 , , 447 , l25 coleman , m. g. , da costa , g. s. , & bland - hawthorn , j. 2005 , , 130 , 1065 coleman , m. g. , da costa , g. s. , bland - hawthorn , j. , & freeman , k. c. 2005 , , 129 , 1443 de blok , w. j. g. , & bosma , a. 2002 , , 385 , 816 el - zant , a. , shlosman , i. , & hoffman , y. 2001 , , 560 , 636 gentile , g. , burkert , a. , salucci , p. , klein , u. , & walter , f. 2005 , , 634 , l145 goerdt , t. , moore , b. , read , j. i. , stadel , j. , & zemp , m. 2006 , , 368 , 1073 irwin , m. , & hatzidimitriou , d. 1995 , , 277 , 1354 king , i. 1962 , , 67 , 471 lora , v. , snchez - salcedo , f. j. , raga , a. c. , & esquivel , a. 2009 , , 699 , l113 majewski , s. r. , ostheimer , j. c. , patterson , r. j. , kunkel , w. e. , johnston , k. v. , & geisler , d. 2000 , , 119 , 760 marchesini , d. , donghia , e. , chincarini , g. , firmani , c. , conconi , p. , molinari , e. , & zacchei , a. 2002 , , 575 , 801 martin , n. f. , ibata , r. a. , chapman , s. c. , irwin , m. , & lewis , g. f. 2007 , , 380 , 281 mashchenko , s. , & sills , a. 2004 , , 605 , l121 mashchenko , s. , & sills , a. 2005 , , 619 , 243 mashchenko , s. , sills , a. , & couchman , h. m. 2006 , , 640 , 252 mashchenko , s. , couchman , h. m. p. , & wadsley , j. 2006 , , 442 , 539 mashchenko , s. , wadsley , j. , & couchman , h. m. p. 2008 , science , 319 , 174 mateo , m. l. 1998 , , 36 , 435 mateo , m. , olszewski , e. w. , pryor , c. , welch , d. l. , & fischer , p. 1993 , , 105 , 510 mateo , m. , olszewski , e. w. , vogt , s. s. , & keane , m. j. 1998 , , 116 , 2315 mateo , m. , olszewski , e. w. , & walker , m. g. 2008 , , 675 , 201 merritt , d. 1985 , , 90 , 1027 moore , b. , ghigna , s. , governato , f. , lake , g. , quinn , t. , stadel , j. , & tozzi , p. 1999 , , 524 , l19 muoz , r. r. , et al . 2006 , , 649 , 201 navarro , j. f. , frenk , c. s. , & white , s. d. m. 1997 , , 490 , 493 odenkirchen , m. , et al . 2001 , , 122 , 2538 osipkov , l. p. 1979 , pisma astron . , 5 , 77 press , w. h. , teukolsky , s. a. , vetterling , w. t. , & flannery , b. p. 1992 , cambridge : university press , |c1992 , 2nd ed . , sgall , m. , ibata , r. a. , irwin , m. j. , martin , n. f. , & chapman , s. 2007 , , 375 , 831 srsic , j. l. 1963 , boletin de la asociacion argentina de astronomia la plata argentina , 6 , 41 smoli , v. , zucker , d. b. , bell , e. f. , coleman , m. g. , rix , h. w. , schinnerer , e. , ivezi , . , & kniazev , a. 2007 , , 134 , 1901 strigari , l. e. , bullock , j. s. , kaplinghat , m. , diemand , j. , kuhlen , m. , & madau , p. 2007 , , 669 , 676 strigari , l. e. , bullock , j. s. , kaplinghat , m. , simon , j. d. , geha , m. , willman , b. , & walker , m. g. 2008 , , 454 , 1096 tolstoy , e. , et al . 2004 , , 617 , l119 tonini , c. , lapi , a. , & salucci , p. 2006 , , 649 , 591 van den bosch , f. c. , & swaters , r. a. 2001 , , 325 , 1017 walker , m. g. , mateo , m. , olszewski , e. w. , gnedin , o. y. , wang , x. , sen , b. , & woodroofe , m. 2007 , , 667 , l53 walker , m. g. , mateo , m. , & olszewski , e. w. 2009 , , 137 , 3100 walker , m. g. , mateo , m. , olszewski , e. w. , sen , b. , & woodroofe , m. 2009 , , 137 , 3109 walker , m. g. , mateo , m. , olszewski , e. w. , pearrubia , j. , wyn evans , n. , & gilmore , g. 2009 , , 704 , 1274 wolf , j , et al . 2009 , , submitted ( arxiv:0908.2995 )

i carry out an exhaustive model parameter search , assigning absolute probabilities to each parameter combination . my main finding is that there is a well defined radius ( unique for each galaxy ) where the jeans analysis constraints on the enclosed mass are tightest , and are much better than the constraints at previously suggested radii ( e.g. 300 pc ) . for carina , fornax , leo i , sculptor , and sextans the enclosed dm mass is ( at 410 pc ) , ( at 925 pc ) , ( at 390 pc ) , ( at 435 pc ) , and ( at 1035 pc ) , respectively ( two - sigma uncertainties ; in m units ) . the largest central dm density constraint is for sculptor : pc ( at two - sigma level ) . i show that the dm density logarithmic slope is totally unconstrained by the jeans analysis at all the radii probed by the data ( and not just at the center , as was demonstrated before ) . in particular , pure central tangential anisotropy is ruled out at better than two sigma level for three dwarfs , and the data are consistent with the global stellar velocity isotropy for all the five galaxies .

using a flexible galactic model with variable stellar velocity anisotropy , i apply the classical jeans mass modeling approach to the five dwarf spheroidal galaxies with the largest homogeneous datasets of stellar line - of - sight velocities ( between 330 and 2500 stars per galaxy ) carina , fornax , leo i , sculptor , and sextans . i carry out an exhaustive model parameter search , assigning absolute probabilities to each parameter combination . my main finding is that there is a well defined radius ( unique for each galaxy ) where the jeans analysis constraints on the enclosed mass are tightest , and are much better than the constraints at previously suggested radii ( e.g. 300 pc ) . for carina , fornax , leo i , sculptor , and sextans the enclosed dm mass is ( at 410 pc ) , ( at 925 pc ) , ( at 390 pc ) , ( at 435 pc ) , and ( at 1035 pc ) , respectively ( two - sigma uncertainties ; in m units ) . local dm density has the tightest constraints at smaller ( and also unique for each galaxy ) radii . the largest central dm density constraint is for sculptor : pc ( at two - sigma level ) . i show that the dm density logarithmic slope is totally unconstrained by the jeans analysis at all the radii probed by the data ( and not just at the center , as was demonstrated before ) . stellar velocity anisotropy has only very weak constraints . in particular , pure central tangential anisotropy is ruled out at better than two sigma level for three dwarfs , and the data are consistent with the global stellar velocity isotropy for all the five galaxies .

1212.1306

c

we have performed global 3d mhd simulations of turbulent accretion disks which start from fully equilibrium mhd initial conditions . the local linear theory of the mri is used as a predictor of the growth of magnetic field perturbations in the global simulations . additional tests have also been performed to compare results obtained from global simulations using a number of different numerical algorithms and resolutions to the linear growth estimates . our main findings are : a. the growth of magnetic field perturbations in the global simulations shows good agreement with the linear mri growth estimates during approximately the first orbit of the disk . subsequently , the overwhelming influence of non - linear motions , which may be due either to the onset of turbulence or to secondary instabilities , saturates the _ local _ growth . b. the saturated state is found to be independent of the initially excited mri mode , showing that once the disk has expelled the initial net flux field and settled into quasi - periodic oscillations in the toroidal magnetic flux , the dynamo cycle regulates the global saturation stress level . furthermore , time - averaged measures of quasi - steady turbulence are found to be in agreement with previous work . in particular , the time averaged stress , @xmath181 . c. we find @xmath178 for global stratified simulations with 12.5 cells/@xmath32 in the @xmath35 direction , which is in good agreement with value found from high resolution , stratified , shearing - box simulations . higher @xmath35 resolution in the simulation ( at least @xmath182 cells/@xmath32 ) is required to maintain stronger radial and vertical magnetic field , and consequently a larger @xmath168 . d. from the numerical algorithms that we tested , the choice of reconstruction order or limiter does not significantly alter the resulting linear mri growth rate . convergence with resolution ( for the linear mri growth tests ) is found for resolutions of roughly @xmath1cells per scaleheight ( in the vertical direction ) . however , above all , a higher azimuthal resolution contributes to a much better agreement with linear growth estimates , supporting the push for low cell aspect ratio ( close to one ) in global accretion disk simulations . we thank the referee for a particularly useful report which helped to significantly improve the paper . this research was supported under the australian research council s discovery projects funding scheme ( project number dp1096417 ) . e. r. p thanks the arc for funding through this project . this work was supported by the nci facility at the anu and by the ivec facility at the pawsey centre , perth , wa . 67 natexlab#1#1 , s. a. , & hawley , j. f. 1991 , , 376 , 214 . 1992 , , 400 , 610 . 1998 , reviews of modern physics , 70 , 1 , d. s. , & meyer , c. 2010 , arxiv:1003.0018v1 , k. , armitage , p. j. , & simon , j. b. 2011 , , 416 , 361 , g. , cattaneo , f. , ferrari , a. , mignone , a. , & rossi , p. 2011 , , 739 , 82 , g. , mignone , a. , cattaneo , f. , rossi , p. , & ferrari , a. 2008 , , 487 , 1 , a. 2005 , an , 326 , 787 , a. , nordlund , a. , stein , r. f. , & torkelsson , u. 1995 , , 446 , 741 , s. 1960 , , 46 , 253 , p. , & sekora , m. d. 2008 , , 227 , 7069 , p. , & woodward , p. r. 1984 , , 54 , 174 , j. l. , bicknell , g. v. , sutherland , r. s. , & bland - hawthorn , j. 2008 , , 674 , 157 , s. w. , stone , j. m. , & pessah , m. e. 2010 , , 713 , 52 , m. , dzyurkevich , n. , klahr , h. , & mignone , a. 2010 , , 516 , a26 , m. , dzyurkevich , n. , klahr , h. , turner , n. , & henning , t. 2012 , , 744 , 144 , m. , dzyurkevich , n. , klahr , h. , turner , n. j. , & henning , t. 2011 , , 735 , 122 , s. , & nelson , r. p. 2006 , , 457 , 343 . 2009 , , 496 , 597 , s. , & papaloizou , j. 2007 , , 476 , 1113 , t. a. , & stone , j. m. 2008 , , 227 , 4123 , p. , & lynden - bell , d. 1965 , , 130 , 125 , j. , & xu , g. 1994 , , 432 , 213 , o. 2010 , , 405 , 41 , x. , & gammie , c. f. 2011 , , 728 , 130 , x. , gammie , c. f. , simon , j. b. , & johnson , b. m. 2009 , , 694 , 1010 , j. f. 2000 , , 528 , 462 , j. f. , & balbus , s. a. 1991 , , 376 , 223 , j. f. , gammie , c. f. , & balbus , s. a. 1995 , , 440 , 742 . 1996 , , 464 , 690 , j. f. , guan , x. , & krolik , j. h. 2011 , , 738 , 84 , j. f. , & krolik , j. h. 2002 , , 566 , 164 , h. n. , lesaffre , p. , & balbus , s. a. 2009 , , 394 , 715 , g. , & longaretti , p .- y . 2007 , , 378 , 1471 , d. , & pringle , j. e. 1974 , , 168 , 603 , w. , johansen , a. , klahr , h. , & piskunov , n. 2008 , , 479 , 883 , j. c. , tchekhovskoy , a. , & blandford , r. d. 2012 , , 423 , 3083 , a. , bodo , g. , massaglia , s. , matsakos , t. , tesileanu , o. , zanni , c. , & ferrari , a. 2007 , , 170 , 228 , a. , flock , m. , stute , m. , kolb , s. m. , & muscianisi , g. 2012 , , 545 , 152 , k. a. , & stone , j. m. 2000 , , 534 , 398 , t. , & kusano , k. 2005 , , 208 , 315 , s. c. , krolik , j. h. , & hawley , j. f. 2010 , , 711 , 959 , s. m. , reynolds , c. s. , miller , m. c. , & sorathia , k. a. 2011 , , 736 , 107 , b. , & wiita , p. j. 1980 , , 88 , 23 , j. c. b. , & terquem , c. 1997 , , 287 , 771 , m. e. 2010 , , 716 , 1012 , m. e. , chan , c .- k . , & psaltis , d. 2007 , , 668 , l51 , m. e. , & goodman , j. 2009 , , 698 , l72 , w. h. , flannery , b. p. , & teukolsky , s. a. 1986 , numerical recipes . the art of scientific computing , ed . press , w. h. , flannery , b. p. , & teukolsky , s. a. , o. , & umurhan , o. m. 2008 , , 481 , 21 , w. j. , greenough , j. a. , & kamm , j. r. 2007 , , 225 , 1827 , m. m. , ustyugova , g. v. , koldoba , a. v. , & lovelace , r. v. e. 2012 , , 421 , 63 , t. , inutsuka , s .- i . , turner , n. j. , & stone , j. m. 2004 , , 605 , 321 , r. , mckinney , j. c. , narayan , r. , tchekhovskoy , a. , gammie , c. f. , & mcclintock , j. e. 2008 , , 687 , l25 , n. i. , & sunyaev , r. a. 1973 , , 24 , 337 , j. , krolik , j. h. , & hirose , s. 2010 , , 708 , 1716 , j. b. , beckwith , k. , & armitage , p. j. 2012 , , 422 , 2685 , j. b. , hawley , j. f. , & beckwith , k. 2009 , , 690 , 974 . 2011 , , 730 , 94 , k. a. , reynolds , c. s. , & armitage , p. j. 2010 , , 712 , 1241 , k. a. , reynolds , c. s. , stone , j. m. , & beckwith , k. 2012 , , 749 , 189 , j. m. , hawley , j. f. , gammie , c. f. , & balbus , s. a. 1996 , , 463 , 656 , j. m. , & pringle , j. e. 2001 , , 322 , 461 , c. , & papaloizou , j. c. b. 1996 , , 279 , 767 , c. a. , & pringle , j. e. 1992 , , 259 , 604 , e. p. 1959 , , 36 , 1398 , e. t. 2009 , , 696 , 1021

global three dimensional magnetohydrodynamic ( mhd ) simulations of turbulent accretion disks are presented which start from fully equilibrium initial conditions in which the magnetic forces are accounted for and the induction equation is satisfied . the local linear theory of the magnetorotational instability ( mri ) is used as a predictor of the growth of magnetic field perturbations in the global simulations . the saturated state is found to be independent of the initially excited mri mode , showing that once the disk has expelled the initially net flux field and settled into quasi - periodic oscillations in the toroidal magnetic flux , the dynamo cycle regulates the global saturation stress level . furthermore , time - averaged measures of converged turbulence , such as the ratio of magnetic energies , are found to be in agreement with previous works . in particular , the globally averaged stress normalized to the gas pressure , , with notably higher values achieved for simulations with higher azimuthal resolution . supplementary tests are performed using different numerical algorithms and resolutions . convergence with resolution during the initial linear mri growth phase is found forcells per scaleheight ( in the vertical direction ) .

global three dimensional magnetohydrodynamic ( mhd ) simulations of turbulent accretion disks are presented which start from fully equilibrium initial conditions in which the magnetic forces are accounted for and the induction equation is satisfied . the local linear theory of the magnetorotational instability ( mri ) is used as a predictor of the growth of magnetic field perturbations in the global simulations . the linear growth estimates and global simulations diverge when non - linear motions - perhaps triggered by the onset of turbulence - upset the velocity perturbations used to excite the mri . the saturated state is found to be independent of the initially excited mri mode , showing that once the disk has expelled the initially net flux field and settled into quasi - periodic oscillations in the toroidal magnetic flux , the dynamo cycle regulates the global saturation stress level . furthermore , time - averaged measures of converged turbulence , such as the ratio of magnetic energies , are found to be in agreement with previous works . in particular , the globally averaged stress normalized to the gas pressure , , with notably higher values achieved for simulations with higher azimuthal resolution . supplementary tests are performed using different numerical algorithms and resolutions . convergence with resolution during the initial linear mri growth phase is found forcells per scaleheight ( in the vertical direction ) . [ firstpage ]

nucl-th0307035

i

in this work we have calculated the in - medium @xmath298 cross section within the opem taking into account the exchange pion collectivity , vertex corrections by the contact nuclear interactions and the effective masses of the nucleon and @xmath8 resonance . \(i ) we have observed that even without the effective mass modifications the cross section decreases with the nuclear matter density at high densities if one takes into account the in - medium @xmath8 width and includes the @xmath299 lindhard function in the calculations ( fig . [ fig : sigma_vs_rho ] ) . \(ii ) inclusion of the effective mass modifications for the nucleons and @xmath8 s leads to an additional strong reduction of the cross section . \(iii ) the fopi data @xcite on the total pion multiplicity from the systems ca+ca , ru+ru and au+au at 0.400 , 1.000 and 1.500 a gev seem to require a dropping effective mass with the baryon density ( nl2 version of the rmf model ) in combination with the universal value of 0.6 for all the landau - migdal parameters in the spin - isospin channel . we note that this still depends somewhat on the size of the @xmath8-spreading width used ( 80 mev @xmath300 @xcite ) . more precise data on the total pion multiplicity are needed in order to better select the model for the density dependence of the dirac effective masses of the baryons . the effect of the medium modifications of the @xmath293 cross sections on the pion multiplicity depends also on the assumption about other channels of the pion production / absorption in nn collisions , most importantly , on the @xmath67-wave direct channel @xmath301 . including the effective mass modifications in the @xmath302 channel _ only _ , does not lead to strong enough reduction of the observed pion multiplicity , since then more pions are produced in the @xmath67-wave channel . the in - medium modifications of the higher resonance cross sections do not influence the pion production at 1 - 2 a gev collision energy sensitively : other particles like @xmath303 and @xmath304 mesons are , probably , more sensitive to higher resonance in - medium modifications . the calculations with the in - medium modified cross sections slightly underpredict the low transverse mass @xmath294 yield at midrapidity for c+c collisions at 0.8 and 1.0 a gev ( fig . [ fig : dmtpi_cc_new ] ) . this implies , that with decreasing mass number of the colliding system the in - medium corrections disappear faster than in our model . the reason could be a strong nonequilibrium momentum distribution at the beginning of collision : instead of one fermi sphere there are two nonoverlapping fermi spheres , which is not taken into account in our calculation of the effective mass . indeed , the nonequilibrium momentum distribution reduces the scalar density , and , therefore , increases the effective mass . this effect is expected to be stronger for lighter systems , since smaller baryon density is reached in this case . another open problem is the general tendency of the transport models to overpredict pion multiplicity in heavy colliding systems at ags energies ( c.f . this problem can not be solved by just density modifications of the resonance production / absorption cross sections , since most pions are produced by the string mechanism here . in - medium modifications of the fritiof model , thus , could help to solve this problem . numerous stimulating discussions with m. post and dr . l. alvarez - ruso are gratefully acknowledged . the authors are grateful to markus post for the reading of the manuscript before publication , critical comments and suggestions and to luis alvarez - ruso for pointing out ref . @xcite which has influenced our results .

we present calculations of the cross section in nuclear matter within the one - pion exchange model taking into account pion collectivity , vertex renormalization by the contact nuclear interactions and dirac effective masses of the baryons due to coupling with the scalar field . introducing the dirac effective masses leads to an in - medium reduction of the cross section . the experimental data on pion multiplicities from the collisions of ca+ca , ru+ru and au+au at a gev are well described by buu calculations with the in - medium cross section .

we present calculations of the cross section in nuclear matter within the one - pion exchange model taking into account pion collectivity , vertex renormalization by the contact nuclear interactions and dirac effective masses of the baryons due to coupling with the scalar field . introducing the dirac effective masses leads to an in - medium reduction of the cross section . the experimental data on pion multiplicities from the collisions of ca+ca , ru+ru and au+au at a gev are well described by buu calculations with the in - medium cross section .

gr-qc0510111

i

there is growing concern in the numerical relativity community about the accuracy that can be achieved as robust implementations of the einstein equations become available . as has been discussed a number of times , the simulation of strongly gravitating astrophysical systems in 3d requires the stable and accurate handling of a large range of time and length scales @xcite . in the context of finite difference schemes , increasing resolution by using more grid points in a uniform grid quickly becomes prohibitively expensive , particularly with multiple spatial dimensions . two ways of achieving better accuracy include ( i ) the use of higher order methods for derivative approximations and time integration , and ( ii ) the use of a grid hierarchy which adapts to provide resolution only where and when needed , so called _ adaptive mesh refinement _ ( amr ) . both strategies have been adopted by the community largely following two independent paths . on one hand higher derivative operators are being introduced @xcite and on the other amr techniques within a second order accurate implementation have been adopted for over a decade @xcite . ( for recent efforts implementing second order amr / fmr see for instance @xcite/@xcite ) one key reason behind these independent developments lies in the complications encountered when implementing amr techniques , especially related to the way the ( artificial ) interface boundaries are treated . special care must be taken when dealing with the conditions at these boundaries , in particular how derivative operators should be modified near them . in the case of second order accurate implementations , there is little ambiguity on what these modifications can be as they need only be done at interface points . for higher order implementations , the strategy is far less clear . however , there are strong reasons to combine amr and implementations of higher orders . for instance , although higher order operators ( be they within finite difference , finite elements or spectral approximations ) do in principle provide an approximation with errors which are considerably smaller , they do so only if the underlying solution involved is well resolved by the adopted grid . certainly , the required grid can be anticipated for linear problems but this is hardly the case in non - linear ones where finer features induced by the non - linear nature of the problem can appear during the evolution . hence , an adaptive gridding mechanism which reacts to the solution itself is crucial . the combination of amr with higher order operators then provides lower errors for a given grid while being able to react to unanticipated features in the solution in addition to providing a more efficient use of computational resources. in order to combine these techniques , one must face how to treat the derivative operators near boundaries , and how to deal with the artificial boundaries themselves . a clean way to approach this problem is to consider operators satisfying summation by parts ( sbp ) which have recently been incorporated successfully in strongly / symmetric hyperbolic systems in numerical relativity @xcite . these techniques guarantee that a large set of problems can be implemented stably . having stability of the unigrid evolution , however , is not sufficient to guarantee a fully discrete energy estimate for an amr implementation . the analysis of the time integration , in particular how different grids communicate with each other to provide boundary conditions , becomes quite involved . nevertheless , one can argue strongly for adopting as a starting point an implementation in which a semi - discrete estimate is guaranteed since a necessary condition for an amr implementation to be stable is that its unigrid version be stable . as discussed in the literature , the latter is guaranteed when employing runge kutta operators of orders higher than 2 @xcite ( in conjunction with suitable boundary conditions ) . we thus adopt a strategy where spatial derivative operators satisfying sbp , along with runge kutta time integrators , are employed on all levels of the amr hierarchy . this choice , of course , does not dictate the treatment of the interface boundaries , and we consider various options for this treatment . for instance , in the standard berger oliger strategy , the solution obtained at a parent grid is employed to define boundary conditions for the child grid . leaving the stability issue aside for a moment , an immediate observation is that when employing a two - level implementation , this strategy can not generically give better accuracy than second order if boundary values are obtained by linear interpolation in time of the parent grid values . additionally , the definition of all field values via interpolation without regard for their propagation features is a likely source of inconsistencies making stability a delicate issue . in this work we examine alternative treatments of grid boundaries and derivative operators to deal with these issues . we pay particular attention to the stability of the system by effectively implementing a toy model problem within a fixed two - grid hierarchy and analyzing the spectrum of the overall update operator . these studies demonstrate that implementations with accuracy orders greater than two , employing the standard berger oliger scheme have unstable modes . furthermore , related schemes share this unfortunate feature . this instability can be remedied , with some caveats , with the addition of dissipation though at the expense of larger errors in the approximation . additionally , we observe that a simple modification of the standard strategy yields a stable scheme without requiring the addition of dissipation , albeit at additional computational cost . in this new strategy , a child grid effectively never requires boundary points from a parent . this can be achieved if the solution at level @xmath0 is obtained by integrating using the past domain of dependence of the child grid only . at first sight this is more computationally demanding as it requires the area of the child grid at level @xmath1 to be larger than that at @xmath0 so that the intersection of the numerical domain of dependence of the solution at the level @xmath0 is completely contained in the refined region at level @xmath1 . this is achieved simply by defining an ` extended ' child grid at level @xmath1 and discarding a buffer zone at level @xmath0 . as we will see later in appendix [ sec : cost ] , this extra cost need not be relevant at all , as for a given target error , a coarser base grid treated this way might be comparable to a finer base grid treated with the standard berger oliger scheme plus the addition of dissipation . this work is divided as follows . in section [ sec : technique ] , we detail different boundary treatments and describe our method to assess their stability properties . in section [ sec : tests ] , we present one and three dimensional tests which illustrate the behavior observed . section [ sec : conclusion ] concludes with some final comments , and we defer to appendix [ sec : cost ] the discussion of the cost associated with 2nd vs. 4th order implementations .

efforts to achieve better accuracy in numerical relativity have so far focused either on implementing second order accurate adaptive mesh refinement or on defining higher order accurate differences and update schemes . here , we argue for the combination , that is a higher order accurate adaptive scheme . this combines the power that adaptive gridding techniques provide to resolve fine scales ( in addition to a more efficient use of resources ) together with the higher accuracy furnished by higher order schemes when the solution is adequately resolved . to define a convenient higher order adaptive mesh refinement scheme

efforts to achieve better accuracy in numerical relativity have so far focused either on implementing second order accurate adaptive mesh refinement or on defining higher order accurate differences and update schemes . here , we argue for the combination , that is a higher order accurate adaptive scheme . this combines the power that adaptive gridding techniques provide to resolve fine scales ( in addition to a more efficient use of resources ) together with the higher accuracy furnished by higher order schemes when the solution is adequately resolved . to define a convenient higher order adaptive mesh refinement scheme , we discuss a few different modifications of the standard , second order accurate approach of berger and oliger . applying each of these methods to a simple model problem , we find these options have unstable modes . however , a novel approach to dealing with the grid boundaries introduced by the adaptivity appears stable and quite promising for the use of high order operators within an adaptive framework .

1407.6695

i

a primary activity of the lhc program is the exploration of the properties of the higgs boson , which was discovered over two years ago by the atlas and cms collaborations @xcite . currently , only couplings to gauge bosons and third - generation fermions are measured directly @xcite . the couplings that are fixed through the well - measured diboson decays of the higgs are determined at the @xmath14@xmath15 level . no deviations from the predictions of the standard model ( sm ) have been observed . while the possibility of measuring the higgs - boson couplings to muons at the high - luminosity lhc ( hl - lhc ) has been studied @xcite , the couplings of the higgs boson to first- and second - generation quarks are _ terra incognita_. they are only weakly constrained by the inclusive higgs - boson production cross sections , yet they can deviate significantly from their sm values in numerous theories of new physics . it was long thought to be impossible to measure these couplings , owing to the severe experimental difficulties that are inherent in reconstructing the signal and isolating it from the background . recent work has demonstrated that there is hope to determine the yukawa couplings of first- and second - generation quarks at future runs of the lhc . much of this renewed interest has arisen because of the realization that exclusive decays of the higgs boson to vector mesons can probe its couplings to light quarks . the resulting final states are relatively clean experimentally , and the theoretical predictions are also under control . the first manifestation of this idea was the discovery that decays of the higgs boson to an @xmath0-wave vector quarkonium plus a photon ( @xmath16 ) provide opportunities to determine the @xmath17 and @xmath18 couplings @xcite . [ here , @xmath19(@xmath20 ) and @xmath21(@xmath22 ) denote a charm ( bottom ) quark and charm ( bottom ) antiquark . ] while the @xmath17 coupling might be probed at the lhc by making use of charm - tagging techniques @xcite , its phase must be determined through processes that involve quantum interference effects , such as the decay @xmath23 . it is our intention in this paper to refine the theoretical prediction for the @xmath16 processes , where @xmath24 or @xmath4 , with @xmath5 . these modes feature clean experimental signatures in which a high - transverse - momentum lepton pair recoils against a photon . they proceed through two distinct mechanisms : * in the _ direct process _ , the higgs boson decays into a heavy quark - antiquark ( @xmath25 ) pair , one of which radiates a photon before forming a quarkonium with the other element of the pair . * in the _ indirect process _ , the higgs boson decays through a top - quark loop or a vector - boson loop to a @xmath26 and a @xmath27 ( virtual photon ) . the @xmath27 then decays into a vector quarkonium . the feynman diagrams for the direct amplitude for @xmath16 at order @xmath28 . the shaded blob represents the quarkonium wave function . the momenta that are adjacent to the heavy - quark lines are defined in the text . ] the feynman diagram for the indirect amplitude for @xmath16 . the hatched circle represents top - quark or @xmath29-boson loops , and the shaded blob represents the quarkonium wave function . ] the feynman diagrams for the direct and indirect processes are shown in figs . [ figure : direct ] and [ figure : indirect ] , respectively . it is the quantum interference between these two processes that provides phase information about the @xmath17 and @xmath18 couplings . the interference is destructive . in the case of the decay to the @xmath30 , the destructive interference is nearly complete , and so the rate is very sensitive to the @xmath18 coupling . the indirect decay amplitudes are determined at percent - level accuracy . the partial amplitude for the higgs - boson decay to @xmath31 can be inferred from calculations of the @xmath32 rate @xcite . the coupling of the quarkonium to a virtual photon is known from the decay rate of the quarkonium to a lepton pair . the largest theoretical uncertainty in the direct amplitude for @xmath33 and , consequently , in the decay rate , arises from uncalculated relativistic corrections . these corrections take into account the relative motion of the @xmath34 and @xmath35 in the quarkonium . they are nominally of order @xmath1 , where @xmath2 is the rms velocity of the @xmath34 or @xmath35 in the quarkonium rest frame . @xmath36 for the @xmath3 and @xmath37 for the @xmath30 . in this paper , we compute order-@xmath1 corrections and some order-@xmath38 corrections to the direct amplitudes for the processes @xmath23 and @xmath39 , where @xmath6 is the strong coupling . we also include some corrections involving leading logarithms of @xmath7 that are of order @xmath1 and of higher orders in @xmath6 . ( here , @xmath8 is the higgs - boson mass and @xmath9 is the heavy - quark mass . ) the remainder of this paper is organized as follows : in sec . [ sec : nrqcd ] , we use the methods of nonrelativistic qcd ( nrqcd ) factorization @xcite to compute the relativistic corrections to @xmath16 . these corrections can also be computed , in the limit @xmath40 , where @xmath41 is the quarkonium mass , by making use of light - cone methods @xcite . we carry out the light - cone calculation of the relativistic corrections in sec . [ sec : light - cone ] . the light - cone computation allows us to take advantage of existing calculations of corrections of next - to - leading order in @xmath6 and is a convenient framework in which to compute logarithms of @xmath7 . we give numerical results for the decay rates in sec . [ sec : numerical ] and summarize our findings in sec . [ sec : summary ] .

we improve the theoretical predictions for the decays of the higgs boson to an-wave vector quarkonium plus a photon by calculating the relativistic correction of order , where is the heavy - quark velocity in the quarkonium rest frame . these refinements reduce the theoretical uncertainties in the direct - production amplitudes for and by approximately a factor of 3 and open the door to improved determinations at the lhc of the higgs - boson yukawa couplings to the charm and bottom quarks .

we improve the theoretical predictions for the decays of the higgs boson to an-wave vector quarkonium plus a photon by calculating the relativistic correction of order , where is the heavy - quark velocity in the quarkonium rest frame . our numerical results are given for the and channels , with . the numerical results include a previously calculated correction of order and summations , to all orders in , of leading logarithms of , where is the higgs - boson mass and is the heavy - quark mass . these qcd corrections apply to the contribution of leading order in and to part of the order- correction . for the remainder of the order- correction , we sum leading logarithms of through order . these refinements reduce the theoretical uncertainties in the direct - production amplitudes for and by approximately a factor of 3 and open the door to improved determinations at the lhc of the higgs - boson yukawa couplings to the charm and bottom quarks .

0805.3646

i

the muon - spin rotation ( @xmath0sr ) technique is one of the most powerful and unique tool to study the internal magnetic field distribution @xmath7 associated with the vortex lattice in type - ii superconductors ( see , e.g. refs . ) . in the vortex state for an applied magnetic field @xmath8 , or @xmath9 ( @xmath5 and @xmath10 are the first critical field and the magnetic induction in a sample , respectively ) @xcite the energy of the surface , separating normal and superconducting fractions of the sample becomes negative and the field penetrates the sample in the form of quantized flux lines , called vortices each of them containing an elementary flux quantum ( @xmath11 wb ) @xcite . in the case of small pinning these vortices arrange themselves in a regular vortex lattice called a flux - line lattice ( fll ) @xcite . the distribution of the internal magnetic fields @xmath7 inside the superconducting sample in the vortex state is uniquely determined by two characteristic lengths , the magnetic field penetration depth @xmath1 and the coherence length @xmath2 . from @xmath0sr experiments @xmath7 profiles are obtained by performing a fourier transformation of the @xmath0sr time spectra . there are different approaches to analyze @xmath0sr data . generally , the magnetic field penetration depth @xmath1 is determined from the second moment @xmath12 of the internal field distribution @xmath7 @xcite . for an isotropic extreme type - ii superconductor ( @xmath13 ) it was shown that @xmath14 @xcite . the more advanced approaches that allow to obtain not only @xmath1 , but also the coherence length @xmath2 , require a theoretical model for the spatial variation of the internal magnetic field @xmath15 ( @xmath16 is spatial coordinate ) . an essential requirement of the model is that it must account for the finite size of the vortex cores . so far , the internal magnetic field distribution @xmath7 measured by @xmath0sr was analyzed assuming analytical models for @xmath15 based on london and ginzburg - landau ( gl ) theories . the london theory provides the simplest approach to model the fll . since london theory does not account for the finite size of the vortex cores , a cutoff factor derived from gl theory must be inserted into the analytical london expression for @xmath15 to correct for the divergence of @xmath15 in the vortex core @xcite . the gl theory has the spatial dependence of the order parameter build in and thus provides a phenomenological description of the magnetic field profile in the vortex core region . abrikosov @xcite predicted the vortex core state from a periodic solution of the gl equations near the second critical field @xmath17 and provided an approximate analytical solution of these equations for an isolated vortex for fields of the order of @xmath5 . clem @xcite proposed a variational method to solve the gl equations that was further extended by hao _ a simplified version of this model for @xmath18 was developed by yaouanc _ @xcite , and is often used in the literature @xcite . the london and the gl models were widely applied to determine values of @xmath1 and @xmath2 from measured @xmath0sr time spectra taken in the mixed state of type - ii superconductors @xcite . we should emphasize , however , that despite of the broad usage , the limits of validity of these models and the reliability of the parameters extracted from the fits are not much discussed in the literature . the main purpose of the present paper is to address these basic questions . the paper is divided into two parts . in the first part we briefly describe the models often used for the analysis of @xmath0sr spectra : the london model with gaussian cutoff ( lg model ) , the modified london model ( ml model ) , and the analytical ginzburg - landau model ( agl model ) . these models are compared with the most precise model based on the iterative method for solving the ginzburg - landau equations developed recently by brandt @xcite , the so called numerical ginzburg - landau model ( ngl model ) . @xmath7 profiles for various sets of @xmath1 , @xmath2 , and magnetic field @xmath10 were first simulated by means of the ngl model and then analyzed within the framework of the lg , ml , and agl model . for further discussions , it is convenient to define the reduced magnetic field @xmath19 . it was found that the ml model can be used _ only _ for low magnetic fields ( @xmath20 ) , while both the agl and the lg model yield reliable results almost in the _ whole _ magnetic field range . however , the values of @xmath1 and @xmath2 obtained by means of the agl and the lg model deviate systematically from the initial parameters used for the simulated @xmath7 profiles for magnetic fields in the range @xmath21 . it was also shown that for @xmath22 the @xmath7 profiles do not depend on the coherence length @xmath2 . in the second part of the paper we present a systematic analysis of simulated @xmath0sr time spectra ( with typical statistics used in real @xmath0sr experiments ) by means of the lg model . in the whole field range ( @xmath23 ) and for any values of the ginzburg - landau parameter @xmath24 there is a strong correlation between the values of @xmath1 and @xmath2 determined from the fit . this implies that an analysis of @xmath0sr data using this approach , without taking into account these correlations , may lead to substantial errors in the determination of the absolute values of @xmath1 and @xmath2 , and even may result in unphysical dependencies of @xmath1 and @xmath2 on magnetic field and temperature . in addition , the second moment method applied to a multiple gaussian fit was tested in order to check how reliably the penetration depth @xmath1 can be determined by this method . in particular , the influence of the number of gaussians used in the multi - gaussian fit on the quality of the fit was investigated . for typical statistics used in the experiment and practically in the whole field range ( @xmath25 ) , the second moment method applied to a multi - gaussian fit may provide correct values for @xmath1 within a few percent . the paper is organized as follows : in sec . ii various theoretical models used to analyze @xmath0sr data are briefly described . the dependence of the magnetic field distribution @xmath7 on @xmath1 , @xmath2 , @xmath26 , and the gaussian smearing parameter @xmath27 , as calculated within the lg model , is discussed in sec . iii . in sec . iv we compare the results obtained by means of the models described in sec . ii for the case of an extreme type - ii superconductor ( @xmath28 ) . v comprises the studies of the simulated @xmath0sr data . the simulated @xmath0sr spectra were analyzed by means of the various models described in sec . ii in order to search for possible correlations between the parameters , such as @xmath1 , @xmath2 , and @xmath27 . the conclusions follow in sec . vi .

a detailed analysis of muon - spin rotation (sr ) spectra in the vortex state of type - ii superconductors using different theoretical models is presented . analytical approximations of the london and ginzburg - landau ( gl ) models , as well as an exact solution of the gl model were used . the limits of the validity of these models and the reliability to extract parameters such as the magnetic penetration depth and the coherence length from the experimentalsr spectra were investigated . the analysis of the simulatedsr spectra showed that at high magnetic fields there is a strong correlation between obtained and for any value of the ginzburg - landau parameter . the smaller the applied magnetic field is , the smaller is the possibility to find the correct value of . it was found that for extreme type - ii superconductors and low magnetic fields , the fitted value of is practically independent of . the second - moment method frequently used to analyzesr spectra by means of a multi - component gaussian fit , generally yields reliable values of in the whole range of applied fields ( and are the first and second critical fields , respectively ) .

a detailed analysis of muon - spin rotation (sr ) spectra in the vortex state of type - ii superconductors using different theoretical models is presented . analytical approximations of the london and ginzburg - landau ( gl ) models , as well as an exact solution of the gl model were used . the limits of the validity of these models and the reliability to extract parameters such as the magnetic penetration depth and the coherence length from the experimentalsr spectra were investigated . the analysis of the simulatedsr spectra showed that at high magnetic fields there is a strong correlation between obtained and for any value of the ginzburg - landau parameter . the smaller the applied magnetic field is , the smaller is the possibility to find the correct value of . a simultaneous determination of and without any restrictions is very problematic , independent of the model used to describe the vortex state . it was found that for extreme type - ii superconductors and low magnetic fields , the fitted value of is practically independent of . the second - moment method frequently used to analyzesr spectra by means of a multi - component gaussian fit , generally yields reliable values of in the whole range of applied fields ( and are the first and second critical fields , respectively ) . these results are also relevant for the interpretation of small - angle neutron scattering ( sans ) experiments of the vortex state in type - ii superconductors .

0707.4182

i

observational cosmology has recently witnessed a tremendous increase in proficiency in the identification of galaxies at the earliest cosmic epochs . thanks in large part to the availability of large - format mosaic ccds well - suited for wide - field imaging and spectroscopic multiplexing , we are now transitioning from exotic , single detections of high - redshift galaxies ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) to the assembly of statistically robust samples spanning the earliest accessible redshifts . robust samples of this kind are necessary for understanding the systematics of selection criteria , and of the spatial distribution of the galaxies themselves . deficiencies in such understanding are the main source of uncertainty in inferred luminosity functions and universal star formation rates , which in turn are the keys to understanding the cosmic history of star formation , galaxy assembly and evolution , and even the early ionization history of the igm ( e.g. , * ? ? ? * ; * ? ? ? . searches for high - redshift galaxies typically follow the by - now familiar strategy of targeting redshifted emission at increasing wavelengths with narrow - band imaging in windows of low night - sky emission ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , or by photometric selection in broad - band imaging of the redshifted lyman break ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? these two techniques are complementary ; searches at typical sensitivities can identify galaxies with uv - continua too faint to be detected by the lyman break method , but such surveys only select that fraction of galaxies with strong line emission . the large area lyman alpha ( lala ) survey @xcite has recently identified in deep narrow - band imaging a large sample of -emitting galaxies at redshifts @xmath0 @xcite , @xmath13 @xcite , and @xmath10 @xcite . in @xcite ( paper i ) , we reported on the spectroscopic confirmation with the w. m. keck observatory s low resolution imaging spectrometer ( lris ; * ? ? ? * ) of 17 -emitting galaxies selected in the lala @xmath2 survey . the resulting sample of confirmed emission lines showed large equivalent widths ( median @xmath14 ) but narrow velocity widths ( fwhm @xmath15 km s@xmath16 ) , indicating that the emission in these sources derives from star formation , not from agn activity . models of star formation in the early universe predict that a small fraction of -emitting galaxies at @xmath0 may be nascent , metal - free objects ( e.g. , * ? ? ? * ) , and indeed we found with 90% confidence that 3 to 5 of the confirmed sources exceed the maximum equivalent width predicted for normal stellar populations . however , we did not detect the emission expected to be characteristic of primordial star formation . specifically , the flux in a composite of the 11 highest resolution spectra in the keck / lris sample was formally consistent with zero , with a 2@xmath17 ( 3@xmath17 ) upper limit of 13% ( 20% ) of the flux in the line . in other words , though these galaxies may be young , they show no evidence of being truly primitive , population iii objects . we have recently more than quadrupled our catalog of spectroscopically - confirmed -emitting galaxies at @xmath0 with a spectroscopic campaign using the w. m. keck observatory s deep imaging multi - object spectrograp ( deimos ; * ? ? ? * ) , targeting candidates selected from the lala survey . together with the detections presented in paper i ( and accounting for minor overlap in the samples ) , the 59 -emitters confirmed with keck / deimos bring the total catalog to 73 spectroscopically confirmed @xmath0 -emitting galaxies in the @xmath3 degrees@xmath4 imaged by lala . in this paper , we utilize these additional confirmations to update the results of paper i , and to construct a luminosity function of @xmath0 emission lines for comparison to luminosity functions spanning @xmath18 . we describe our imaging and spectroscopic observations in [ observations ] , and we summarize the results of the spectroscopic campaign in [ results ] . in [ discussion ] , we investigate the distribution of the lines in equivalent width , we construct luminosity functions for our sample and for several extant samples , and we discuss the implications of the luminosity functions for the relationship between -emitters and lyman - break galaxies ( lbgs ) , and for the history of reionization . throughout this paper we adopt a @xmath19-cosmology with @xmath20 and @xmath21 , and @xmath22 km s@xmath16 mpc@xmath16 @xcite . at @xmath23 , such a universe is 1.3 gyr old , the lookback time is 90.2% of the total age of the universe , and an angular size of 10 corresponds to 6.61 comoving kpc .

we present a catalog of 59 -emitting galaxies spectroscopically confirmed in a campaign of keck / deimos follow - up observations to candidates selected in the large area lyman alpha ( lala ) narrow - band imaging survey . we targeted 97 candidates for spectroscopic follow - up ; by accounting for the variety of conditions under which we performed spectroscopy , we estimate a selection reliability of . together with our previous sample of keck / lris confirmations , as with the keck / lris sample , we find that a non - negligible fraction of the confirmed lines have rest - frame equivalent widths ( ) which exceed the maximum predicted for normal stellar populations : 17% 31% ( 93% confidence ) of the detected galaxies show , and 12% 27% ( 90% confidence ) show . we construct a luminosity function of emission lines for comparison to luminosity functions spanning .

we present a catalog of 59 -emitting galaxies spectroscopically confirmed in a campaign of keck / deimos follow - up observations to candidates selected in the large area lyman alpha ( lala ) narrow - band imaging survey . we targeted 97 candidates for spectroscopic follow - up ; by accounting for the variety of conditions under which we performed spectroscopy , we estimate a selection reliability of . together with our previous sample of keck / lris confirmations , the 59 sources confirmed herein bring the total catalog to 73 spectroscopically confirmed -emitting galaxies in the degrees covered by the lala imaging . as with the keck / lris sample , we find that a non - negligible fraction of the confirmed lines have rest - frame equivalent widths ( ) which exceed the maximum predicted for normal stellar populations : 17% 31% ( 93% confidence ) of the detected galaxies show , and 12% 27% ( 90% confidence ) show . we construct a luminosity function of emission lines for comparison to luminosity functions spanning . we find no significant evidence for luminosity function evolution from to . this result supports the conclusion that the intergalactic medium remains largely reionized from the local universe out to . it is somewhat at odds with the pronounced drop in the cosmic star formation rate density recently measured between and in continuum - selected lyman - break galaxies , and therefore potentially sheds light on the relationship between the two populations .

0707.4182

c

together with the observations presented in paper i ( and accounting for minor overlap in the samples ) , the 59 -emitters confirmed herein bring the total catalog of spectroscopically confirmed @xmath0 -emitting galaxies to 73 objects in the @xmath3 degrees@xmath4 surveyed by the lala imaging . we now update the characteristics of this population as they were estimated in paper i by investigating the distribution of the total sample in equivalent width . we then construct a @xmath0 luminosity function , carefully accounting for survey incompleteness and for spectroscopic sensitivity , and we compare the result to luminosity functions spanning @xmath7 . as in paper i , we determine the rest - frame equivalent widths directly from the spectra according to @xmath98 , where @xmath99 is the flux in the emission line and @xmath100 is the measured red - side continuum flux density . the resulting equivalent width distribution is plotted in figure [ ew_hist ] , together with the equivalent widths measured in paper i. before interpreting this distribution , one should be cautioned that the determination is very sensitive to uncertainty in the measured continuum . since the continuum estimate enters into the denominator of the expression for , the characteristically small continuum values and their large fractional uncertainties cause significant scatter in the measurement , and the resulting error is neither gaussian nor symmetric about the measured value . especially problematic is the fact that the largest values of are also the least certain . detailed discussions of the uncertainties in measuring in high - redshift -emitters , along with the complicating effects of dust content , gas kinematics , and intergalactic absorption , are given in @xcite and in paper i. with these caveats in mind , we rigorously treated the error bars on the equivalent width estimates , and we restricted the analysis to sources with red - side continuum signal - to - noise ratios @xmath101 . to determine the equivalent width error bars , we first associated each measured line flux @xmath102 with a gaussian probability density function ( pdf ) centered on @xmath103 with width @xmath104 ; we proceeded similarly for the measured continuum fluxes . we then generated a grid of line flux versus continuum flux on which each node has an associated equivalent width and is assigned a weight given by the probability distribution on each of its flux axes . next we collapsed the grid into a histogram of equivalent widths , adding the weight from each grid point to the appropriate equivalent width bin . the result is a non - gaussian pdf @xmath105 for which @xmath106 is the probability of observing in the interval @xmath107 . the error bars @xmath108 and @xmath109 are then @xmath110 confidence intervals determined by integrating over the probability density functions @xmath111 . they are symmetric in probability density - space in the sense that @xmath112 . we find the resulting distribution to be broadly consistent with the equivalent widths presented in @xcite for @xmath113 and in @xcite for @xmath114 . while the majority of sources can be understood as comparatively young ( 1 to 10 myr ) galaxies with salpeter initial mass functions ( imfs ) , a non - negligible fraction exceeds the largest rest - frame equivalent widths expected from such stellar populations . @xcite use a salpeter initial mass function , an upper mass cutoff of 120 @xmath115 , and a metallicity of 1/20th solar to find maximum equivalent widths of 300 , 150 , and 100 for stellar populations of ages @xmath116 , @xmath117 , and @xmath118 years , respectively . adopting a correction factor of 0.64 as an upper limit to the effect of igm absorption on the measurement of in spectroscopy effectively reduces these upper limits to 190 , 100 , and 60 (see discussion in paper i ) . owing to the lower metallicity used in their models , the pre - igm - corrected values of @xcite are slightly higher than the canonical limiting rest - frame equivalent width of 240 given by @xcite . using the ensemble of @xmath111 described above , we find that 12% 27% ( 90% confidence ) of the galaxies in this sample show @xmath6 , and 17% 31% ( 93% confidence ) show @xmath5 . both results are nearly identical to the values given in paper i. on the simplest interpretation , these galaxies are required to be very young ( age @xmath119 years ) , or to have imfs skewed in favor of the production of massive stars . the possibility that agns in our sample are producing stronger - than - expected emission seems unlikely due to the comparatively narrow velocity widths of the lines and to the absence of the high - ionization state uv emission lines symptomatic of agn activity . moreover , deep ( @xmath120 ks ) _ chandra_/acis imaging of lala @xmath0 candidates in both botes @xcite and in cetus @xcite resulted in x - ray non - detections to an average 3@xmath17 limiting luminosity of @xmath121 erg s@xmath16 . this limit is roughly an order of magnitude fainter than what is typically observed for even the heavily obscured , type ii agns ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . by comparing the upper limit on the typical x - ray to luminosity ratio for the galaxy sample to the observed values of this ratio for quasar and seyfert galaxy samples , @xcite and @xcite conclude that agn account for @xmath122 of the galaxy sample . in figure [ lumfuncfig ] , we present an empirical cumulative line luminosity function computed for our sample at @xmath123 and compare this to luminosity functions computed for several other samples spanning @xmath7 . the cumulative luminosity function gives for each line luminosity @xmath124 the total number density of lines brighter than @xmath124 . the comparison samples are drawn from spectroscopic follow - up of narrow - band surveys with roughly comparable flux limits and candidate - selection criteria ( except where noted , below ) . we do not include non - spectroscopic -emitter luminosity functions ( e.g. , * ? ? ? * ) among the comparison samples . in each case , we converted the reported line fluxes to line luminosities using a @xmath19-cosmology with @xmath125 and @xmath126 , and @xmath22 km s@xmath16 mpc@xmath16 , and we made a minimal attempt to account for incompleteness sources as measured in narrow - band imaging , rather than line fluxes as measured in spectroscopy . as such , we adopt the conversion given in @xcite to estimate from . ] . specifically , the volume from which -emitting candidates were selected by their narrow - band excess is simply defined by the solid angle covered by the narrow - band imaging and the redshift range allowed by the narrow - band filter . however , the _ effective _ volume surveyed by the spectroscopic follow - up is smaller than the imaging survey volume by a factor of @xmath127 , where is the total number of -emitting candidates discovered in the imaging , and is the number of candidates actually targeted for spectroscopy . we estimated the uncertainties in the cumulative luminosity functions with monte carlo simulations . assuming the errors in the line fluxes are gaussian , we created synthetic data sets by drawing randomly from the gaussian flux pdfs for each object in each sample . the result for each sample was then a distribution of cumulative luminosity functions , which may be used to define upper and lower confidence intervals . figure [ lumfuncfig ] depicts 95% confidence intervals ; where more than one survey is plotted , just the confidence intervals for the survey with the largest range in line fluxes is depicted . no strong evolution is readily evident in the cumulative luminosity functions between @xmath11 and @xmath12 . the only significant scatter between luminosity functions occurs between the various @xmath11 surveys , and that scatter likely finds its origin in differences in the manner in which the experiments were performed . foremost , the area surveyed by the @xcite effort is comparatively small : just 25 arcmin@xmath4 in each of two fields ( hdf and ssa 22 ) , as opposed to 300 arcmin@xmath4 in @xcite and 132 arcmin@xmath4 in @xcite . @xcite note that the number counts in their hdf field appears to be 2.5 times richer in narrow - band excess objects than their ssa 22 field , highlighting the susceptibility of small survey areas to cosmic variance . separately , as noted by @xcite , the @xcite data may comparatively under - represent the density of -emitters due to their more stringent equivalent width criterion of @xmath128 , as opposed to @xmath129 in @xcite and effectively @xmath130 in @xcite . we now perform a more rigorous measurement of the @xmath132 luminosity function using a modified version of the @xmath131 method ( e.g. , * ? ? ? * ; * ? ? ? * ) . for each galaxy , is the volume over which of a given luminosity could be located and still be detected by our survey ; the luminosity function is then the sum of the inverse volumes of all galaxies in the given luminosity bins . our modifications to the @xmath133 method account for incompleteness in two senses . first , not every galaxy candidate identified in imaging was targeted in follow - up spectroscopy . following @xcite , figure [ completeness ] shows the fraction of narrow - band selected candidate -emitters which were targeted for spectroscopy as a function of flux in the band in which the candidate was detected . we label this _ a priori _ completeness function ; the candidate flux can be roughly estimated from the flux in the narrow - band with @xmath134 , where @xmath135 is the width of the narrow - band filter and is the flux of the candidate in the @xmath41-band . second , even if a candidate -emitter was selected for spectroscopy , its inclusion in the luminosity function depends on the detection and identification of the line . our spectroscopic sensitivity to emission as a function of flux and redshift is shown in figure [ spec_sens ] ; we label this function . as discussed in section [ sensitivity_sec ] , can be interpreted as the probability that a putative emission line of a given flux and a given redshift would have been detected in our spectroscopic campaign . in the presence of these selection effects , the available volume for a galaxy with emission of flux is @xmath136 where the comoving volume element in a solid angle @xmath137 and redshift interval @xmath138 is the familiar @xmath139 with @xmath140 in equation [ eq_vmax ] , @xmath141 is the solid angle covered by the lala survey , and is the line flux for the source in question if it were located at redshift @xmath48 . the lower limit of integration @xmath142 is set by the lowest wavelength at which could be detected by our narrow - band filters , corresponding to @xmath143 . the upper limit of integration @xmath144 is set in one of two ways . if the luminosity for a source is bright enough that the line remains above the survey flux limit out to the highest redshift accessible by our filter set , then @xmath144 is simply equal to the upper redshift limit for the survey , @xmath145 . for fainter sources , @xmath144 is taken to be the redshift at which the flux falls below the survey flux limit ; in this case , @xmath146 . having computed for each galaxy , we may compute the differential luminosity function @xmath147 , the number density of galaxies per logarithmic interval in luminosity . in a given luminosity bin of width @xmath148 centered on @xmath149 , this is given by @xmath150 here , the index @xmath151 denotes the luminosity bin and @xmath152 denotes the galaxies within the bin , where the galaxies summed in a given bin are selected by their luminosities according to @xmath153 finally , the uncertainty in the luminosity function may be estimated with @xmath154 = \frac{1}{\delta \log l } \left [ \sum_j \left ( \frac{1}{{\mbox{$v_{\mbox{\tiny max}}$}}_{,j } } \right ) ^2 \right ] ^{1/2 } \ ; . \label{variance}\ ] ] in figure [ difflumfuncfig ] , we present the resulting differential luminosity function at @xmath0 . we also fit the data with a schechter function . if @xmath155 is the comoving number density of galaxies with luminosities in the range @xmath156 , then the corresponding schechter function is @xmath157 where @xmath158 is the normalization , @xmath159 is the characteristic break luminosity , and @xmath160 sets the slope at the faint end . this is related to the number density of galaxies in _ logarithmic _ intervals by @xmath161 and it is this function which we fit to our data . as in @xcite , because the binned data points are few , we choose to fix @xmath162 so as to fit with only two free parameters , @xmath158 and @xmath159 . this choice fits well with the luminosity distribution of both lbgs and -emitters at @xmath163 @xcite . we find best - fit luminosity function paramters @xmath164erg s@xmath16 and @xmath165 mpc@xmath166 ( or equivalently , @xmath167 and @xmath168 ) . the error bars on @xmath159 and @xmath158 are the @xmath110 formal errors computed from the covariance matrix in the nonlinear least - squares fit , scaled by the measured value of @xmath169 . that is , @xmath170 , and similarly for @xmath171 @xcite . our @xmath132 sample provides one of the best measured luminosity functions to date . we can study redshift evolution of the luminosity function by comparing to results from the literature . recognizing that the uncertainties in @xmath159 and @xmath158 are strongly correlated , we examine not only the individual parameters but also the product @xmath172 , which is proportional to luminosity density , and which generally has smaller uncertainties than the individual parameters . for our sample , @xmath173 . at lower redshift , there is a @xmath174 lf by @xcite , who fit all three parameters . they find @xmath175 , @xmath176 , and @xmath177 , whence @xmath178 . at the high redshift end , we compare to lfs at @xmath179 by @xcite and @xcite , and at @xmath180 by @xcite and @xcite , all derived by fixing the faint end slope @xmath181 and fitting @xmath159 and @xmath158 . at @xmath179 , the lfs are similar to our @xmath23 result : @xcite find @xmath182 , @xmath183 , and @xmath184 , while @xcite find ( for their combined spectroscopic + photometric sample ) @xmath182 , @xmath185 , and @xmath186 . at @xmath180 , @xcite find @xmath187 , @xmath188 , and @xmath189 , while @xcite find @xmath190 , @xmath191 , and @xmath192 . the obvious differences between the lfs at each redshift may be caused by any combination of ( a ) simple uncertainty in deriving the lf from modest sized samples ; ( b ) field - to - field variations in galaxy density ; or ( c ) differences in the methods used to derive schechter function parameters , and in part to local variations in galaxy density . the @xcite and @xcite lfs are derived from larger total samples , but from a single survey field , while the @xcite lfs are based on a combination of several older , smaller samples from a few widely separated fields . regardless , if we take the difference between these various @xmath193 lfs as an empirical indication of total present uncertainties , the @xmath132 lf derived in the present paper supports a roughly constant luminosity density over the range @xmath194 . it is interesting to compare this result to the evolution of the rest - uv luminosity density and cosmic star formation rate density ( sfrd ) derived from lbgs over the same redshift range . estimates of the @xmath9 sfrd based on the great observatories origins deep survey / advanced camera for surveys ( goods / acs ; * ? ? ? * ) and the hubble ultra deep field @xcite show a factor of 1.56 drop between @xmath11 and @xmath12 @xcite . what does this mean for the -selected galaxies ? @xcite report that -selection with an equivalent width criterion typical of narrow - band surveys would return 20% 25% of their @xmath163 lbgs . if -emitters are merely a subset of the lbg population which happen to have been detected during a stage of strong production , than we would expect the luminosity density to decline beyond @xmath195 , in step with the global star formation rate density . integrating the luminosity functions discussed in section [ difflumfunc ] shows no compelling evidence for such a decline . though a modest decline can not be firmly ruled out , we may nontheless speculate that the -emitters as a population are evolving differently from the lbgs . the bolometric luminosities of galaxies are typically lower than lyman break galaxies , and provide a hint that they are less massive . detailed spectral energy distribution fitting @xcite bears out this preliminary inference , showing typical masses of @xmath196 and ages @xmath197 to @xmath118 years . the correlation strengths of galaxies and lbgs are similar @xcite , indicating similar masses of haloes . from the expected halo mass one can predict volume number density of emitters . comparing the expected and observed number densities implies a duty cycle of -emission in the range 6% 50% @xcite . a similar duty cycle , 7.5% - 15% , is inferred from stellar population modelling of the photomeric sample @xcite . the spectroscopic observations of the @xmath198 quasars yielded the first detections of the long - awaited gunn - peterson trough , implying at least the end of reionization at @xmath199 @xcite . subsequently , the _ wilkinson microwave anisotropy probe _ ( wmap ) identified a large amplitude signal in the temperature - polarization maps of the cosmic microwave background @xcite indicating a large optical depth to thomson scattering and favoring reionization instead at @xmath200 . the wmap results are not necessarily inconsistent with those of the quasar gunn - peterson troughs . only a small neutral fraction ( @xmath201 ) is required to produce the gunn - peterson effect , so one plausible scenario is that reionization may have been an extended event , beginning early but not completing until @xmath199 . alternatively , a variety of theoretical models now suggest that reionization occurred twice , first at @xmath202 with the onset of zero - metallicity population iii stars , and then again by massive population ii stars formed after a partial recombination ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? high - redshift -emitting galaxies offer another perspective on this issue , as the visibility of emission should be a sensitive function of the igm neutral fraction ( e.g. , * ? ? ? * ; * ? ? ? @xcite and @xcite present first attempts to exploit this fact by comparing luminosity functions of -emitters at @xmath114 and @xmath203 . they find no measurable evolution between these epochs , from which they infer that the igm remains largely reionized from the local universe out to @xmath10 ( but see * ? ? ? @xcite , applying the same test , find possible evidence for observed lf differences between @xmath180 and @xmath204 at the factor of 2 level . they suggest neutral gas at @xmath205 as the explanation , though @xcite argue that the observations could equally well be explained by the ongoing growth of cosmic structure from @xmath179 to @xmath180 . by using the galaxy sample from @xcite , @xcite showed that at least 30% of the igm by volume is ionized at @xmath205 . this is corroborated by dark gap statistics in gp troughs @xcite . all the tests of reionization assume that there is no intrinsic evolution in the luminosity functions between @xmath180 and 6.5 . in this paper we show that there is little evolution in luminosity function from @xmath206 to @xmath207 , thus strengthening the conclusion that the igm is not substantially neutral at @xmath179 . significantly , the related question of _ what _ is responsible for reionization remains at large . it has long been recognized that agn at early epochs are insufficient , owing to their rapid decline in space density at high redshift ( e.g. , * ? ? ? * ; * ? ? ? based on their analysis of the udf , @xcite conclude that the cosmic sfr in directly observed @xmath199 lbgs was roughly five times too low to reionize the universe . @xcite and @xcite argue that the ionizing photon budget is sufficient provided one accounts for sample incompleteness using a sufficiently steep slope at the faint end of the luminosity function . @xcite argue that the ionizing flux density may be very inhomogeneous due to large scale structure , as seen in galaxies in the hubble ultra deep field , and that the directly observed galaxies at @xmath9 do produce sufficient photons for reionization in overdense regions . we estimate that the contribution to the cosmic sfr from -emitters at this epoch is lower than that of the lbgs ( @xmath208 @xmath115 yr@xmath16 mpc@xmath209 , as compared to @xmath210 @xmath115 yr@xmath16 mpc@xmath209 ) when integrated over the same limits . consequently , though high - redshift -emitters are proving to be a useful probe of the history of reionization , they are evidently not its cause . while extinction corrections could occasionally be large @xcite and could modify this conclusion , most well studied galaxies have very modest extinction @xcite . when we compare the luminosity function of -emitters at @xmath211 to luminosity functions for similarly assembled samples spanning @xmath7 , we find no evidence for evolution over these epochs . this result bolsters the conclusion by @xcite and @xcite that the igm remains largely reionized from the local universe out to @xmath10 . however , it is somewhat at odds with the factor of 1.56 drop in the cosmic star formation rate density measured by @xcite between @xmath11 and @xmath12 in lyman - break galaxies selected in the exceptional imaging of the udf . it seems that these two populations emitters and lyman break galaxies follow different evolutionary histories . the disentanglement of this issue will likely rely on extensive followup observations of large samples , so that we can study the continuum and absorption lines of many galaxies , and conversely the properties of the break - selected galaxies . this work benefited greatly from conversations with m. cooper , s. mccarthy , t. robishaw , and j. simon , as well as from the careful commentary of the anonymous referee . in addition , we are humbly indebted to the expert staff of w. m. keck observatory for their assistance in obtaining the data herein . it is a pleasure to thank p. amico , j. lyke , and especially g. wirth for their invaluable assistance during observing runs . we thank f. valdes for writing the `` deitab '' package , which aids in deimos data processing . finally , we wish to acknowledge the significant cultural role that the summit of mauna kea plays within the indigenous hawaiian community ; we are fortunate to have the opportunity to conduct observations from this mountain . this material is based upon work supported by aura through the national science foundation under aura cooperative agreement ast 0132798 as amended . the work of d. s. was carried out at the jet propulsion laboratory , california institute of technology , under contract with nasa . a. d. and b. j. acknowledge support from noao , which is operated by the association of universities for research in astronomy , inc . , under cooperative agreement with the national science foundation ( nsf ) . h. s. gratefully acknowledges nsf grant ast 95 - 28536 and its successors for supporting much of the research presented herein . this work made use of nasa s astrophysics data system abstract service . llcllcll j020418.2@xmath25050748 & 4.449 & 2.55 @xmath212 0.87 & @xmath213 & 6.8 @xmath212 1.7 & 230 & -0.040 @xmath212 0.026 & -0.018 @xmath212 0.049 + j020423.2@xmath25050647 & 4.449 & 3.25 @xmath212 1.07 & @xmath214 & 5.7 @xmath212 1.0 & 160 & -0.003 @xmath212 0.026 & 0.014 @xmath212 0.034 + j020425.5@xmath25045610 & 4.461 & 3.72 @xmath212 1.22 & @xmath215 & 7.2 @xmath212 1.0 & 260 & 0.002 @xmath212 0.025 & 0.026 @xmath212 0.031 + j020425.7@xmath25045810 & 4.387 & 1.98 @xmath212 0.68 & @xmath216 & 4.1 @xmath212 0.6 & @xmath217 200 & -0.035 @xmath212 0.052 & 0.021 @xmath212 0.057 + j020427.4@xmath25050045 & 4.390 & 1.47 @xmath212 0.54 & @xmath218 & 5.4 @xmath212 2.8 & 140 & -0.010 @xmath212 0.018 & -0.011 @xmath212 0.019 + j020428.5@xmath25045924 & 4.390 & 3.57 @xmath212 1.27 & @xmath219 & 11.0 @xmath212 2.8 & 460 & -0.008 @xmath212 0.032 & 0.019 @xmath212 0.033 + j020429.8@xmath25050251 & 4.460 & 1.39 @xmath212 0.52 & @xmath220 & 7.1 @xmath212 2.2 & 250 & -0.124 @xmath212 0.070 & 0.012 @xmath212 0.077 + j020432.3@xmath25045519 & 4.360 & 3.13 @xmath212 1.04 & @xmath221 & 4.2 @xmath212 1.3 & @xmath217 210 & -0.003 @xmath212 0.023 & -0.009 @xmath212 0.022 + j142434.9@xmath24352833 & 4.423 & 1.13 @xmath212 0.46 & @xmath222 & 6.8 @xmath212 1.1 & 230 & 0.037 @xmath212 0.077 & 0.117 @xmath212 0.073 + j142436.0@xmath24352600 & 4.464 & 1.81 @xmath212 0.72 & @xmath223 & 5.0 @xmath212 0.2 & 100 & 0.016 @xmath212 0.022 & 0.128 @xmath212 0.025 + j142438.4@xmath24352339 & 4.526 & 3.21 @xmath212 1.28 & @xmath224 & 7.0 @xmath212 0.5 & 240 & 0.175 @xmath212 0.036 & 0.336 @xmath212 0.061 + j142445.2@xmath24352920 & 4.509 & 1.21 @xmath212 0.49 & @xmath225 & 9.5 @xmath212 1.5 & 370 & 0.106 @xmath212 0.041 & 0.350 @xmath212 0.049 + j142445.3@xmath24352450 & 4.475 & 2.47 @xmath212 0.99 & @xmath226 & 5.6 @xmath212 0.3 & 150 & -0.056 @xmath212 0.043 & -0.009 @xmath212 0.065 + j142445.4@xmath24352859 & 4.514 & 0.98 @xmath212 0.40 & @xmath227 & 8.2 @xmath212 2.0 & 310 & 0.174 @xmath212 0.040 & 0.447 @xmath212 0.052 + j142450.1@xmath24353000 & 4.507 & 4.32 @xmath212 1.73 & @xmath228 & 8.2 @xmath212 0.6 & 310 & -0.010 @xmath212 0.050 & 0.141 @xmath212 0.063 + j142452.4@xmath24352613 & 4.411 & 1.97 @xmath212 0.79 & @xmath229 & 6.5 @xmath212 0.6 & 210 & 0.051 @xmath212 0.038 & 0.054 @xmath212 0.047 + j142458.6@xmath24353558 & 4.522 & 2.02 @xmath212 1.06 & @xmath230 & 5.6 @xmath212 0.5 & 150 & -0.026 @xmath212 0.078 & -0.006 @xmath212 0.116 + j142459.8@xmath24353927 & 4.482 & 1.98 @xmath212 1.05 & @xmath231 & 5.0 @xmath212 0.5 & 100 & 0.030 @xmath212 0.041 & -0.009 @xmath212 0.049 + j142501.7@xmath24353652 & 4.496 & 1.38 @xmath212 0.78 & @xmath232 & 6.4 @xmath212 2.0 & 200 & 0.073 @xmath212 0.100 & 0.088 @xmath212 0.140 + j142502.8@xmath24353017 & 4.476 & 0.75 @xmath212 0.31 & @xmath233 & 5.6 @xmath212 0.9 & 150 & 0.052 @xmath212 0.034 & 0.016 @xmath212 0.042 + j142503.4@xmath24353222 & 4.489 & 0.66 @xmath212 0.28 & @xmath234 & 4.1 @xmath212 2.2 & @xmath217 200 & 0.113 @xmath212 0.037 & 0.086 @xmath212 0.044 + j142506.4@xmath24353819 & 4.446 & 8.11 @xmath212 4.26 & @xmath235 & 7.0 @xmath212 0.3 & 250 & 0.008 @xmath212 0.054 & 0.037 @xmath212 0.065 + j142508.3@xmath24353952 & 4.511 & 2.59 @xmath212 1.36 & @xmath236 & 8.6 @xmath212 0.6 & 330 & -0.019 @xmath212 0.038 & 0.040 @xmath212 0.048 + j142508.7@xmath24353200 & 4.478 & 2.41 @xmath212 0.96 & @xmath237 & 6.0 @xmath212 0.4 & 180 & 0.032 @xmath212 0.040 & -0.010 @xmath212 0.049 + j142512.0@xmath24353913 & 4.451 & 1.13 @xmath212 0.60 & @xmath238 & 4.1 @xmath212 1.4 & @xmath217 200 & 0.063 @xmath212 0.040 & 0.000 @xmath212 0.050 + j142512.7@xmath24353755 & 4.434 & 2.96 @xmath212 1.56 & @xmath239 & 6.1 @xmath212 0.6 & 190 & 0.201 @xmath212 0.040 & 0.235 @xmath212 0.053 + j142518.0@xmath24353415 & 4.408 & 5.37 @xmath212 2.15 & @xmath240 & 8.7 @xmath212 0.8 & 340 & 0.150 @xmath212 0.062 & 0.370 @xmath212 0.072 + j142522.4@xmath24353553 & 4.519 & 1.79 @xmath212 0.72 & @xmath241 & 7.4 @xmath212 0.6 & 260 & 0.011 @xmath212 0.046 & 0.126 @xmath212 0.053 + j142525.9@xmath24352349 & 4.471 & 3.27 @xmath212 1.34 & @xmath242 & 7.0 @xmath212 0.7 & 240 & 0.072 @xmath212 0.048 & 0.267 @xmath212 0.057 + j142526.2@xmath24352531 & 4.464 & 2.76 @xmath212 1.13 & @xmath243 & 6.2 @xmath212 0.4 & 190 & 0.067 @xmath212 0.050 & 0.087 @xmath212 0.054 + j142531.8@xmath24352652 & 4.482 & 0.94 @xmath212 0.40 & @xmath244 & 7.4 @xmath212 1.5 & 270 & 0.034 @xmath212 0.035 & 0.140 @xmath212 0.041 + j142532.9@xmath24353013 & 4.534 & 5.49 @xmath212 1.00 & @xmath245 & 7.1 @xmath212 0.3 & 250 & 0.005 @xmath212 0.015 & 0.075 @xmath212 0.018 + j142535.2@xmath24352743 & 4.449 & 6.23 @xmath212 2.54 & @xmath246 & 6.0 @xmath212 0.2 & 180 & 0.001 @xmath212 0.048 & 0.106 @xmath212 0.057 + j142539.5@xmath24353902 & 4.432 & 1.52 @xmath212 0.67 & @xmath247 & 4.0 @xmath212 1.6 & @xmath217 200 & 0.049 @xmath212 0.019 & 0.017 @xmath212 0.022 + j142541.7@xmath24353351 & 4.409 & 3.24 @xmath212 1.34 & @xmath248 & 5.4 @xmath212 0.8 & 130 & -0.042 @xmath212 0.045 & 0.080 @xmath212 0.050 + j142542.0@xmath24352557 & 4.393 & 1.05 @xmath212 0.44 & @xmath249 & 6.4 @xmath212 1.4 & 210 & 0.028 @xmath212 0.033 & 0.092 @xmath212 0.042 + j142542.6@xmath24352626 & 4.450 & 1.49 @xmath212 0.62 & @xmath250 & 7.5 @xmath212 0.9 & 270 & 0.101 @xmath212 0.043 & 0.215 @xmath212 0.059 + j142544.5@xmath24354325 & 4.533 & 2.84 @xmath212 1.20 & @xmath251 & 7.4 @xmath212 1.1 & 260 & 0.002 @xmath212 0.018 & 0.059 @xmath212 0.030 + j142546.8@xmath24354315 & 4.443 & 0.72 @xmath212 0.33 & @xmath252 & 6.3 @xmath212 1.5 & 200 & 0.012 @xmath212 0.016 & 0.049 @xmath212 0.022 + j142547.8@xmath24354200 & 4.539 & 1.11 @xmath212 0.48 & @xmath253 & 4.9 @xmath212 0.8 & 90 & 0.029 @xmath212 0.017 & 0.007 @xmath212 0.024 + j142548.4@xmath24352740 & 4.546 & 1.21 @xmath212 0.50 & @xmath230 & 5.4 @xmath212 0.7 & 130 & -0.058 @xmath212 0.038 & 0.004 @xmath212 0.067 + j142555.4@xmath24353039 & 4.423 & 10.31 @xmath212 1.88 & @xmath254 & 10.8 @xmath212 0.6 & 450 & 0.025 @xmath212 0.015 & 0.049 @xmath212 0.023 + j142556.7@xmath24354234 & 4.425 & 2.26 @xmath212 0.96 & @xmath255 & 4.8 @xmath212 0.6 & 80 & -0.019 @xmath212 0.020 & 0.032 @xmath212 0.022 + j142556.8@xmath24354215 & 4.426 & 2.85 @xmath212 1.20 & @xmath256 & 5.8 @xmath212 0.7 & 170 & 0.021 @xmath212 0.020 & 0.047 @xmath212 0.022 + j142559.8@xmath24353513 & 4.394 & 1.39 @xmath212 0.28 & @xmath257 & 5.6 @xmath212 0.6 & 160 & 0.005 @xmath212 0.013 & 0.023 @xmath212 0.014 + j142559.8@xmath24353748 & 4.420 & 4.95 @xmath212 0.91 & @xmath258 & 7.0 @xmath212 0.5 & 240 & 0.109 @xmath212 0.018 & 0.240 @xmath212 0.019 + j142601.3@xmath24353618 & 4.475 & 1.41 @xmath212 0.27 & @xmath259 & 5.0 @xmath212 0.4 & 100 & -0.013 @xmath212 0.011 & -0.003 @xmath212 0.013 + j142602.0@xmath24354554 & 4.473 & 1.83 @xmath212 0.78 & @xmath260 & 4.8 @xmath212 0.7 & 70 & -0.003 @xmath212 0.019 & 0.058 @xmath212 0.025 + j142612.2@xmath24353541 & 4.418 & 1.90 @xmath212 0.36 & @xmath261 & 6.3 @xmath212 0.5 & 200 & 0.082 @xmath212 0.013 & 0.002 @xmath212 0.017 + j142624.4@xmath24353832 & 4.460 & 2.46 @xmath212 0.46 & @xmath262 & 5.4 @xmath212 0.5 & 140 & -0.012 @xmath212 0.017 & 0.021 @xmath212 0.022 + j142627.5@xmath24353717 & 4.488 & 2.11 @xmath212 0.43 & @xmath263 & 6.5 @xmath212 2.4 & 210 & 0.044 @xmath212 0.025 & 0.135 @xmath212 0.051 + j142628.5@xmath24353809 & 4.409 & 3.82 @xmath212 0.71 & @xmath264 & 6.4 @xmath212 0.4 & 210 & -0.038 @xmath212 0.029 & -0.011 @xmath212 0.041 + j142653.5@xmath24353356 & 4.494 & 2.12 @xmath212 0.77 & @xmath265 & 7.8 @xmath212 1.8 & 280 & -0.016 @xmath212 0.015 & 0.040 @xmath212 0.017 + j142658.8@xmath24353144 & 4.495 & 2.16 @xmath212 0.79 & @xmath266 & 6.3 @xmath212 1.0 & 200 & -0.019 @xmath212 0.015 & 0.191 @xmath212 0.018 + j142706.3@xmath24353224 & 4.480 & 0.99 @xmath212 0.38 & @xmath267 & 5.0 @xmath212 1.6 & 100 & 0.021 @xmath212 0.014 & 0.027 @xmath212 0.018 + j142709.1@xmath24352738 & 4.407 & 1.77 @xmath212 0.65 & @xmath268 & 8.4 @xmath212 1.4 & 320 & 0.039 @xmath212 0.014 & 0.056 @xmath212 0.017 + j142709.2@xmath24352409 & 4.520 & 1.62 @xmath212 0.59 & @xmath269 & 5.8 @xmath212 1.2 & 170 & 0.029 @xmath212 0.015 & 0.008 @xmath212 0.022 + j142709.8@xmath24352641 & 4.405 & 1.78 @xmath212 0.66 & @xmath270 & 6.0 @xmath212 0.8 & 180 & 0.023 @xmath212 0.017 & 0.027 @xmath212 0.021 + j142712.2@xmath24353029 & 4.380 & 2.35 @xmath212 0.86 & @xmath271 & 4.3 @xmath212 2.4 & @xmath217 200 & 0.035 @xmath212 0.017 & 0.076 @xmath212 0.021 + [ table_spec_prop ]

the 59 sources confirmed herein bring the total catalog to 73 spectroscopically confirmed -emitting galaxies in the degrees covered by the lala imaging . we find no significant evidence for luminosity function evolution from to . this result supports the conclusion that the intergalactic medium remains largely reionized from the local universe out to . it is somewhat at odds with the pronounced drop in the cosmic star formation rate density recently measured between and in continuum - selected lyman - break galaxies , and therefore potentially sheds light on the relationship between the two populations .

we present a catalog of 59 -emitting galaxies spectroscopically confirmed in a campaign of keck / deimos follow - up observations to candidates selected in the large area lyman alpha ( lala ) narrow - band imaging survey . we targeted 97 candidates for spectroscopic follow - up ; by accounting for the variety of conditions under which we performed spectroscopy , we estimate a selection reliability of . together with our previous sample of keck / lris confirmations , the 59 sources confirmed herein bring the total catalog to 73 spectroscopically confirmed -emitting galaxies in the degrees covered by the lala imaging . as with the keck / lris sample , we find that a non - negligible fraction of the confirmed lines have rest - frame equivalent widths ( ) which exceed the maximum predicted for normal stellar populations : 17% 31% ( 93% confidence ) of the detected galaxies show , and 12% 27% ( 90% confidence ) show . we construct a luminosity function of emission lines for comparison to luminosity functions spanning . we find no significant evidence for luminosity function evolution from to . this result supports the conclusion that the intergalactic medium remains largely reionized from the local universe out to . it is somewhat at odds with the pronounced drop in the cosmic star formation rate density recently measured between and in continuum - selected lyman - break galaxies , and therefore potentially sheds light on the relationship between the two populations .

0910.4279

c

the herschel atlas is the largest open - time key project that will be carried out with the herschel space observatory . it will survey 510 square degrees of the extragalactic sky , four times larger than all the other herschel surveys combined , in five far - infrared and submillimetre bands . we have described the survey , the complementary multi - wavelength datasets that will be combined with the herschel data , and the six major science programmes we plan to undertake . using new models based on a submillimetre survey of nearby galaxies , we have presented predictions of the properties of the sources that will be detected by the h - atlas . we intend to release the h - atlas data maps and catalogues to the astronomical community in a series of data releases . the first of these will be in may 2010 . we thank the uk science and technology facilities council and the italian space agency ( asi contract i/016/07/0 cofis ) for funding . this research has made use of the nasa / ipac extragalactic database ( ned ) , which is operated by the jet propulsion laboratory , california institute of technology , under contract with the national aeronautics and space administration . amblard , a. and cooray , a. 2007 , , 670 , 903 baldry , i. et al . 2009 , , submitted balogh , m. et al . 2004 , , 348 , 1355 bartelmann , m. 2001 , , 370 , 754 . , , 388 , 732 baugh , c. et al , 2005 , , 356 , 1191 beelen , a. et al . 2006 , , 642 , 694 bendo , g. et al . 2003 , , 125 , 2361 bertoldi , f. et al . 2007 , , 172 , 132 bregman , j.n . , snider , b.a . , grego , l. & cox , c.v . 1998 , , 499 , 670 browne , i. 2003 , , 341 , 13 cantalup , c. , borrill , j. , jaffe , a. , kisner , t. & stompor , r. 2009 , astro - ph 0906.1775 cole , s. et al . 2000 , , 319 , 168 . coleman , g.d . , wu , c .- c . and weedman , d.w . 1980 , , 43 , 393 colless , m. et al . 2001 , , 328 , 1039 coppin , k. et al . 2006 , , 372 , 1621 davies , j. & burstein , d. 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the herschel atlas is the largest open - time key project that will be carried out on the herschel space observatory . it will survey 510 square degrees of the extragalactic sky , four times larger than all the other herschel surveys combined , in five far - infrared and submillimetre bands . we describe the survey , the complementary multi - wavelength datasets that will be combined with the herschel data , and the six major science programmes we are undertaking . using new models based on a previous submillimetre survey of galaxies , we present predictions of the properties of the atlas sources in other wavebands .

the herschel atlas is the largest open - time key project that will be carried out on the herschel space observatory . it will survey 510 square degrees of the extragalactic sky , four times larger than all the other herschel surveys combined , in five far - infrared and submillimetre bands . we describe the survey , the complementary multi - wavelength datasets that will be combined with the herschel data , and the six major science programmes we are undertaking . using new models based on a previous submillimetre survey of galaxies , we present predictions of the properties of the atlas sources in other wavebands .

hep-ph0605285

i

we have studied in detail the possibility to describe the neutrino masses and mixing angles in the context of split supersymmetric scenarios where the sfermions and/or higgses are very heavy . we have considered all relevant contributions to the neutrino mass matrix up to one - loop level coming from the r - parity violating interactions , showing the importance of the higgs one - loop corrections in the case of partial split susy , where only the sfermions are very heavy . we have found new contributions in the context of the minimal supersymmetric su(5 ) which can help us to generate the neutrino masses in agreement with the experiments in the split susy scenario . the work of m.a.d . was partly founded by conicyt grant 1060629 and conicyt and banco mundial grant `` anillo centro de estudios subatmicos '' . the work of p.f.p . has been supported by _ fundao para a cincia e a tecnologia _ ( fct , portugal ) through the project cftp , pocti - sfa-2 - 777 and a fellowship under project pocti / fnu/44409/2002 . also p.f.p . has been supported in part by the u.s . department of energy contract no . de - fg02 - 08er41531 and in part by the wisconsin alumni research foundation . we would like to thank e. j. chun and g. senjanovi for a discussion . p. f. p thanks the instituto de fisica corpuscular ( ific ) in valencia for hospitality . the work by c. m. was partly supported by conicyt fellowship , and by alfa - ec in the framework of helen program . c. m. would like to thank cern for their hospitality .

we investigate the possibility to generate neutrino masses in the context of split supersymmetric scenarios where all sfermions are very heavy . all relevant contributions coming from the r - parity violating terms to the neutrino mass matrix up to one - loop level are computed , showing the importance of the higgs one - loop corrections .

we investigate the possibility to generate neutrino masses in the context of split supersymmetric scenarios where all sfermions are very heavy . all relevant contributions coming from the r - parity violating terms to the neutrino mass matrix up to one - loop level are computed , showing the importance of the higgs one - loop corrections . we conclude that it is not possible to generate all neutrino masses and mixings in split susy with bilinear r - parity violating interactions . in the case of partial split susy the one - loop higgs contributions are enough to generate the neutrino masses and mixings in agreement with the experiment . in the context of minimal susy su(5 ) we find new contributions which help us to generate neutrino masses in the case of split susy .

1410.5912

i

it is important to investigate the relationships between the power sources of galaxies ( i.e. , active galactic nuclei ( agn ) and/or starbursts ) and the chemical properties of the surrounding dense interstellar medium in order to study the effects on molecular abundances and to probe the power source with molecular line observations . chemical properties , especially , have been expected to be powerful astrophysical tools for the study of galaxies , because the molecular line observations of different galaxies allow us to study the effects of these different physical properties / activities on the molecular medium . in fact , some groups have suggested that it is possible to diagnose power sources in dusty galaxies using molecular line ratios in nearby galaxies ( e.g. , kohno et al . 2001 , 2008 ; usero et al . 2004 ; kohno 2005 ; imanishi et al . 2007 ; krips et al . 2008 ; izumi et al . 2013 ) . for example , elevated hcn emission with respect to co and/or hco@xmath8 has often been detected toward agns ( e.g. , kohno et al . 1996 , 2003 ) , where it is expected to be the imprint of either strong x - ray irradiation / ionization ( e.g. garca - burillo et al . 2010 ) and/or a high - temperature environment caused by agn activity ( e.g. , harada et al . 2010 ; izumi et al . 2013 ) . on the other hand , we reported no significant differences in the relative abundances of the carbon containing molecules c@xmath9h and cyclic - c@xmath7h@xmath9 between one of the nearest galaxies with an agn , ngc 1068 , and the prototypical starburst galaxy , ngc 253 . it was concluded that these basic carbon - containing molecules are insensitive to agns and/or these molecules exist in a cold gas away from an agn ( nakajima et al . 2011 ) . systematic unbiased scans ( i.e. molecular line survey observations ) are the most effective method not only for complete understanding of chemical compositions in representative sources , but also for probing interstellar medium and star formation . over the last 10 years or so , millimeter / sub - millimeter observing systems with very high sensitivity , wide frequency range , and high velocity resolution have been put to use in a number of telescopes ( e.g. carter et al . 2012 ; nakajima et al . 2008 ; 2013a ) . with these , we can also obtain higher quality line survey observations of millimeter / sub - millimeter molecular lines toward nearby galaxies as well as galactic sources . to date , several line surveys have been reported towards the center of ngc 1068 using single dish telescopes ( snell et al . 2011 ; costagliola et al . 2011 ; kamenetzky et al . 2011 ; spinoglio et al . 2012 ; aladro et al . 2013 ; nakajima et al . for example , aladro et al . ( 2013 ) compared their results with ngc 253 , and they suggested that ngc 1068 has a different chemical composition from those of starburst galaxies . they discussed that ch@xmath7cch is not detected in ngc 1068 , yet cn , sio , hco@xmath8 , and hcn are detected and enhanced . although the chemical environment of ngc 1068 has become clearer thanks to these line survey observations , contamination from starbursts associated with inner spiral arms / ring ( @xmath1030@xmath11 ) could be a problem , if we consider the sizes of the observing beams ( 15@xmath1170@xmath11 ) in these single dish telescopes . on the other hand , interferometric imaging of the circumnuclear disk ( cnd ) gives clean measurements of spectral lines , but the observed lines are limited to major species such as @xmath12co ( @xmath2 = 10 , 21 and 32 ) , @xmath0co ( @xmath2 = 10 , 21 and 32 ) , c@xmath1o ( @xmath2 = 10 and 21 ) , hcn ( @xmath2 = 10 and 32 ) , hco@xmath8 ( @xmath2 = 10 , 32 and 43 ) , cs ( @xmath2 = 21 ) , cn ( @xmath3 = 21 ) , and sio ( @xmath2 = 21 ) ( e.g. planesas et al . 1991 ; kaneko et al . 1992 ; jackson et al . 1993 ; tacconi et al . 1994 , 1997 ; helfer and blitz 1995 ; papadopoulos et al . 1996 ; schinnerer et al . 2000 ; kohno et al . 2008 ; garca - burillo et al . 2010 ; krips et al . 2011 ; tsai et al . 2012 ) due to the limitation in sensitivity of the existing pre - alma ( atacama large millimeter / sub - millimeter array ) interferometers . although it is important to estimate the physical properties , such as temperature and density and so on , only one transition has been observed except for co , hcn and hco@xmath8 . in this situation , we proposed to observe several interesting molecules sensitively with alma in the 96100 ghz and 108111 ghz ( 3-mm ) regions for lower excitation lines ( takano et al . 2014 , hereafter paper-1 ) and also 327.5330.5 ghz and 338.5342.5 ghz ( 0.8-mm ) regions for higher excitation lines . these frequency regions are rich in molecules , including typical shock / dust related species and the co isotopologues . our aim has been to focus on the effects of strong x - ray and starburst on shock and/or dust related molecules , ch@xmath7oh , so , hnco , and ch@xmath7cn , which are well observed in galactic sources to study chemical and physical conditions . our observational results with alma will be compared with observations in galactic sources , model calculations , and laboratory experiments to study formation and destruction mechanisms of the above molecules . the complex organic molecules ch@xmath7oh and ch@xmath7cn are thought to be efficiently produced on dust ( e.g. watanabe and kouchi 2002 , takano et al . 1995 ) and subsequently desorbed into gas - phase ( garrod et al . 2008 ) , while hnco is also thought to be produced at least partially on dust ( quan et al . 2010 ) . the radical so is thought to have an enhanced abundance in shocked regions ( leen and graff 1988 ) . however , the abundances and chemical processes forming and destroying these molecules are not well understood in galaxies with active galactic nuclei . from our observations in the two frequency bands with alma , rotational temperatures and column densities can be obtained using intensities of two transitions . the field of view of the 0.8-mm observations is about 18@xmath11 , which means that only the cnd region can be covered with one pointing in ngc 1068 . therefore , we additionally observe a part of the starburst ring at the offset position from the center , so that distributions and abundances of molecules in the starburst environment as well as the cnd can be studied . this comparison will enable us to further study the impact of agns on the surrounding dense interstellar medium . in paper-1 , we have presented the distributions of detected molecules in the 3-mm band , such as @xmath0co , c@xmath1o , @xmath0cn , cs , so , hnco , hc@xmath7n , ch@xmath7oh , ch@xmath7cn , and discussed the implications of diversity . the main results of paper-1 are that the molecular distributions are reflections of both physical and chemical properties . in this paper , we report a high - resolution imaging study of molecular lines in the 0.8-mm band toward ngc 1068 observed with alma , and also the calculation of the fractional abundances of shock / dust related molecules based on not only the observations in 0.8-mm band but also on the earlier 3-mm band results from paper-1 . even in its early science operation phase , alma was already powerful enough to simultaneously observe four high - excitation molecular lines ( @xmath0co and c@xmath1o @xmath2 = 32 , cn @xmath3 = 32 and cs @xmath2 = 76 ) in the 0.8-mm band , uncovering a wide variety of molecular line distributions . we describe our observations and data reduction in section 2 , and present the images and spectra of the observed molecular lines and also estimated physical properties of individual molecules in section 3 . in section 4 , we discuss relationships among the molecular abundances toward the cnd and starburst ring in ngc 1068 , and galactic sources such as hot cores , cold cores , and shocked clouds . throughout the paper , we assume that the distance of ngc 1068 is 14.4 mpc ( tully 1988 ; bland - hawthorn et al . 1997 ) ; at this distance , 1@xmath11 corresponds to 72 pc .

we present 0.8-mm band molecular images and spectra obtained with the atacama large millimeter / submillimeter array ( alma ) toward one of the nearest galaxies with an active galactic nucleus ( agn ) , ngc 1068 . we find that the abundances of shock - related molecules are more similar to abundances in hot cores and/or shocked clouds than to cold cores .

we present 0.8-mm band molecular images and spectra obtained with the atacama large millimeter / submillimeter array ( alma ) toward one of the nearest galaxies with an active galactic nucleus ( agn ) , ngc 1068 . distributions of co isotopic species (co and co ) = 32 , cn = 32 and cs = 76 are observed toward the circumnuclear disk ( cnd ) and a part of the starburst ring with an angular resolution of. 1. . the physical properties of these molecules and shock - related molecules such as hnco , chcn , so , and choh detected in the 3-mm band were estimated using rotation diagrams under the assumption of local thermodynamic equilibrium . the rotational temperatures of the co isotopic species and the shock - related molecules in the cnd are , respectively , 1422 k and upper limits of 2040 k. although the column densities of the co isotopic species in the cnd are only from one - fifth to one - third of that in the starburst ring , those of the shock - related molecules are enhanced by a factor of 310 in the cnd . we also discuss the chemistry of each species , and compare the fractional abundances in the cnd and starburst ring with those of galactic sources such as cold cores , hot cores , and shocked molecular clouds in order to study the overall characteristics . we find that the abundances of shock - related molecules are more similar to abundances in hot cores and/or shocked clouds than to cold cores . the cnd hosts relatively complex molecules , which are often associated with shocked molecular clouds or hot cores . because a high x - ray flux can dissociate these molecules , they must also reside in regions shielded from x - rays .

1410.5912

c

we observed the seyfert 2 galaxy ngc 1068 with the 0.8-mm band in the cnd and starburst ring during the alma early science program . the analyses were carried out with our data obtained at 3-mm band ( paper-1 ) . the main results of this work are summarized in the following list . we successfully observed images of @xmath0co ( @xmath2=32 ) , c@xmath1o ( @xmath2=32 ) , cn ( @xmath3=32 ) , and cs ( @xmath2=76 ) with an angular resolution of @xmath41.@xmath53 @xmath6 1.@xmath52 . @xmath0co and cn were detected in both of the cnd and starburst ring , while cs was only detected in the cnd . c@xmath1o was not significantly detected toward the cnd , but is relatively strong in the starburst ring . 2 . at present , some molecules have been found to be separated into eastern and western knots in the cnd with interferometric observations , and similar distributions of @xmath0co ( @xmath2=32 ) , cn ( @xmath3=32 ) and cs ( @xmath2=76 ) are found in our observations for the first time . we have determined rotation diagrams of observed molecules in the 3-mm band ( paper-1 ) and 0.8-mm band ( this work ) toward the cnd and the southwest position in the starburst ring . the rotational temperatures and column densities have been calculated from these diagrams . @xmath0co and c@xmath1o molecules trace cold gas ( @xmath50 10 k ) in the starburst ring and a little warmer gas ( 14.221.5 k ) in the cnd . although the column densities of the co isotopic species in the cnd are only one - third of that in the starburst ring , those of the shock / dust related molecules are enhanced by a factor of 34 in the cnd under the assumption of the same @xmath29 in the cnd and starburst ring . if the @xmath29 in the cnd is higher than the starburst ring , the column density of the shock related molecules , such as hnco , ch@xmath7cn , so , and ch@xmath7oh in the cnd are much larger than that in the starburst ring . the difference of the distributions between @xmath0co and c@xmath1o is unexplained by only a difference of excitation conditions , because the abundance ratio of these species is not sensitive to the molecular gas temperature and density . the column density ratios of @xmath0co / c@xmath1o in the cnd and the starburst ring are @xmath46 under the assumption that @xmath29 = 30 k for c@xmath1o and @xmath43 , respectively . the amount of c@xmath1o in the cnd is smaller than that in the starburst ring as compared with that of @xmath0co . this feature is possibly the result of differences in isotopic ratios and/or the effect of isotope - selective photodissociation . we found an especially large enhancement of cn in the cnd . specifically , the column density in the cnd is a factor of 2050 larger than that in the starburst ring . cn is one of the key molecules to study an x - ray dominated region ( xdr ) , as mentioned in theoretical studies ( e.g. meijerink et al . 2007 ; harada et al . 2013 ) . moreover the fractional abundance derived in the cnd is closer to the value in xdrs and in the shocked region l1157(b1 ) , but higher than that of cold cores or , especially , hot cores . since a high x - ray luminosity from the agn is seen , the high abundance of cn seen in the cnd can be explained by xdrs . therefore , the enhancement of column density and abundance of cn in the cnd may be the effects of extreme physical conditions such as those in xdrs . we discuss the chemistry of each species , and compare the observed abundances in the cnd and starburst ring with those of galactic sources such as cold cores , hot cores , and shocked molecular clouds in order to study the overall characteristics . as a result , the cnd of ngc 1068 seems to be chemically very rich . the cnd hosts relatively complex molecules , which are often associated with shocked molecular clouds or hot cores . because a high x - ray flux can dissociate these molecules , they must also reside in regions shielded from x - rays . this paper makes use of the following alma data : ads / jao.alma#2011.0.00061.s . alma is a partnership of eso ( representing its member states ) , nsf ( usa ) and nins ( japan ) , together with nrc ( canada ) and nsc and asiaa ( taiwan ) , in cooperation with the republic of chile . the joint alma observatory is operated by eso , aui / nrao and naoj . we thank the alma staff , especially akiko kawamura , for their supports . e. h. wishes to acknowledge the support of the national science foundation ( us ) for his astrochemistry program . he also acknowledges support from the nasa exobiology and evolutionary biology program through a subcontract from rensselaer polytechnic institute . kohno , k. , matsushita , s. , vila - vilar , b. , okumura , s. k. , shibatsuka , t. , okiura , m. , ishizuki , s. , & kawabe , r. 2001 , in asp conf . ser . , 249 , the central kiloparsec of starburst and agn : the la palma connection , ed . j. h. knapen et al . ( san francisco : asp ) , 672 mcmullin , j. p. , waters , b. , schiebel , d. , young , w. , & golap , k. 2007 , in asp conf . 376 , astronomical data analysis software and systems xvi , ed . r. a. shaw , f. hill , & d. j. bell ( san francisco , ca : asp ) , 127 nakajima , t. , takano , s. , kohno , k. , & line survey team 2013b , in asp conf . 476 , new trends in radio astronomy in the alma era : the 30th anniversary of nobeyama radio observatory , ed . r. kawabe , n. kuno , & s. yamamoto ( san francisco , ca : asp ) , 299 lc parameter & value + observation date & 28 nov 2011 + number of antennas & 14 + observing time ( min ) & 71.4 + bandpass calibrator & j0423 - 013 + flux calibrator & callisto + phase calibrator & j0339 - 017 + rms noise ( mjy beam@xmath14 ) & ( cnd / starburst ring ) + spw0 & 8.614.3/9.013.6 + spw1 & 5.46.6/5.47.6 + spw2 & 3.24.5/3.33.7 + spw3 & 3.54.0/3.64.5 + synthesized beam & ( major @xmath6 minor , p.a . ) + & 1.@xmath529@xmath61.@xmath523 , 2.@xmath893 + llllllll frequency & molecule & transition & @xmath90/k & peak flux & @xmath91 & line width & integrated flux + ( ghz ) & & & ( k ) & ( jy beam@xmath14 ) & ( km s@xmath14 ) & ( km s@xmath14 ) & ( jy beam@xmath14 km s@xmath14 ) + 329.330546 & c@xmath1o & @xmath2 = 32 & 31.76 & 0.02@xmath280.01 & 1106@xmath2820 & 173@xmath2847 & 4.59@xmath281.16 + 329.66437 & hnco & @xmath36 = 15@xmath3714@xmath38 & 126.69 & & & & @xmath500.97 ( 1@xmath27 ) + 330.587960 & @xmath0co & @xmath2 = 32 & 31.64 & 0.13@xmath280.01 & 1102@xmath284 & 178@xmath289 & 25.49@xmath281.26 + 331.071548 & ch@xmath7cn & @xmath41 = 18@xmath4217@xmath42 & 151.09 & & & & @xmath500.83 ( 1@xmath27 ) + 340.031567 & cn & @xmath3 = 32 , @xmath2 = 5/2 - 3/2 & 32.66 & 0.165@xmath280.004 & 1049@xmath288 & 272@xmath2835 & 47.67@xmath284.38 + 340.247874 & cn & @xmath3 = 32 , @xmath2 = 7/2 - 5/2 & 32.69 & 0.19@xmath280.01 & 1171@xmath287 & 308@xmath2815 & 62.83@xmath282.52 + 340.714350 & so & @xmath51 = 7@xmath526@xmath53 & 81.31 & & & & @xmath500.76 ( 1@xmath27 ) + 342.729781 & ch@xmath7oh & @xmath36 = 13@xmath3913@xmath40-+ & 232.49 & & & & @xmath500.49 ( 1@xmath27 ) + 342.882866 & cs & @xmath2 = 76 & 65.88 & 0.046@xmath280.004 & 1109@xmath287 & 183@xmath2817 & 8.88@xmath280.76 + llllllll frequency & molecule & transition & @xmath90/k & peak flux & @xmath91 & line width & integrated flux + ( ghz ) & & & ( k ) & ( jy beam@xmath14 ) & ( km s@xmath14 ) & ( km s@xmath14 ) & ( jy beam@xmath14 km s@xmath14 ) + 329.330546 & c@xmath1o & @xmath2 = 32 & 31.76 & 0.20@xmath280.02 & 1216@xmath281 & 28@xmath283 & 6.02@xmath280.50 + 329.66437 & hnco & @xmath36 = 15@xmath3714@xmath38 & 126.69 & & & & @xmath500.75 ( 1@xmath27 ) + 330.587960 & @xmath0co & @xmath2 = 32 & 31.64 & 0.53@xmath280.02 & 1216@xmath281 & 40@xmath282 & 22.30@xmath280.80 + 331.071548 & ch@xmath7cn & @xmath41 = 18@xmath4217@xmath42 & 151.09 & & & & @xmath500.41 ( 1@xmath27 ) + 340.031567 & cn & @xmath3 = 32 , @xmath2 = 5/2 - 3/2 & 32.66 & & & & @xmath500.27 ( 1@xmath27 ) + 340.247874 & cn & @xmath3 = 32 , @xmath2 = 7/2 - 5/2 & 32.69 & 0.05@xmath280.01 & 1212@xmath283 & 42@xmath286 & 2.41@xmath280.34 + 340.714350 & so & @xmath51 = 7@xmath526@xmath53 & 81.31 & & & & @xmath500.27 ( 1@xmath27 ) + 342.729781 & ch@xmath7oh & @xmath36 = 13@xmath3913@xmath40-+ & 232.49 & & & & @xmath500.31 ( 1@xmath27 ) + 342.882866 & cs & @xmath2 = 76 & 65.88 & & & & @xmath500.31 ( 1@xmath27 ) + lccccc & & & + molecule & @xmath29 & @xmath30 & & @xmath29 & @xmath30 + & ( k ) & ( @xmath610@xmath54 @xmath33 ) & & ( k ) & ( @xmath610@xmath92@xmath33 ) + c@xmath1o & & & & 8.0@xmath280.5 & 167@xmath93 + @xmath0co & 21.5@xmath94 & 147@xmath95 & & 8.5@xmath280.2 & 521@xmath96 + cs & 13.1@xmath280.3 & 2.7@xmath97 & & & + hc@xmath7n & 22 & 0.9 & & 18 & 0.1 + lccccccccccc & & & + molecule & 5(k ) & 10(k ) & 15(k ) & 30(k ) & 45(k ) & & 5(k ) & 10(k ) & 15(k ) & 30(k ) & 45(k ) + c@xmath1o & 901.9 & 69.8 & 35.4 & 24.0 & 25.1 & & & & & & + hnco & 1.2 & 0.5 & 0.4 & 0.5 & 0.6 & & 0.3 & 0.1 & 0.1 & 0.1 & 0.2 + ch@xmath7cn & 0.2 & 0.08 & 0.07 & 0.09 & 0.1 & & & & & & + cn & 38.4 & 2.9 & 1.5 & 1.0 & 1.0 & & 0.8 & 0.06 & 0.03 & 0.02 & 0.02 + so & 1.2 & 1.1 & 1.4 & 2.4 & 3.6 & & 0.2 & 0.2 & 0.2 & 0.4 & 0.6 + ch@xmath7oh & 2.4 & 2.5 & 3.0 & 5.4 & 8.5 & & 1.8 & 1.9 & 2.3 & 3.5 & 5.7 + cs & & & & & & & 0.4 & 0.4 & 0.5 & 0.7 & 1.0 + lccccc molecular line & component & @xmath23 & @xmath24 & integrated flux & flux ratio + & & ( @xmath11 ) & ( @xmath11 ) & ( jy beam@xmath14 km s@xmath14 ) & ( e - knot / w - knot ) + @xmath0co ( @xmath2=32 ) & e - knot & + 0.7 & 0.0 & 16.8@xmath280.6 & + & w - knot & -1.8 & + 0.5 & 7.7@xmath280.7 & 2.2@xmath280.2 + cn ( @xmath3=32 ) & e - knot & + 0.6 & -0.1 & 59.8@xmath283.3 & + & w - knot & -1.7 & + 0.8 & 26.2@xmath283.8 & 2.3@xmath280.4 + cs ( @xmath2=76 ) & e - knot & + 0.6 & -0.2 & 7.3@xmath280.5 & + & w - knot & -1.8 & + 0.4 & 2.1@xmath280.4 & 3.5@xmath280.7 + lcccccc species & cnd & starburst ring & cold core & & shocked cloud + & ( ngc 1068 ) & ( ngc 1068 ) & ( tmc-1 ) & ( sgr b2(n ) ) & ( afgl2591 ) & ( l1157(b1 ) ) + hnco & 0.7@xmath98(-8 ) & 0.4@xmath99(-9 ) & 5.7@xmath280.4(-10 ) & 5.6(-10)(halo ) & & 1.1@xmath280.7(-8 ) + & & & & 1.2(-8)(core ) & & + ch@xmath65cn & 1.1@xmath100(-9 ) & & 6(-10 ) & 2.2(-7)(core ) & & 0.7@xmath280.4(-9 ) + cn & 0.5@xmath101(-7 ) & 0.2@xmath102(-9 ) & 5(-9 ) & & 7.0@xmath280.7(-12 ) & 1.6(-7 ) + so & 1.6@xmath103(-8 ) & 7.7@xmath280.0(-10 ) & 2(-9 ) & 2(-8)(halo ) & 1(-8 ) & 2.5(-7 ) + ch@xmath65oh & 3.4@xmath104(-8 ) & 7.3@xmath105(-9 ) & 3(-9 ) & 3.4(-9)(halo ) & @xmath1062(-8 ) & 1.2@xmath283.4(-5 ) + & & & & 1.7(-6)(core ) & & + cs & 3.7@xmath103(-8 ) & 1.5@xmath107(-9 ) & 4(-9 ) & & 2(-8 ) & 1.9(-7 ) + hc@xmath65n & 1.2(-8 ) & 3.8(-10 ) & 2(-8 ) & 5(-9)(halo ) & 7(-9 ) & 1.0(-8 ) + & & & & 1(-7)(core ) & & +

distributions of co isotopic species (co and co ) = 32 , cn = 32 and cs = 76 are observed toward the circumnuclear disk ( cnd ) and a part of the starburst ring with an angular resolution of. 1. . the physical properties of these molecules and shock - related molecules such as hnco , chcn , so , and choh detected in the 3-mm band were estimated using rotation diagrams under the assumption of local thermodynamic equilibrium . the rotational temperatures of the co isotopic species and the shock - related molecules in the cnd are , respectively , 1422 k and upper limits of 2040 k. although the column densities of the co isotopic species in the cnd are only from one - fifth to one - third of that in the starburst ring , those of the shock - related molecules are enhanced by a factor of 310 in the cnd . we also discuss the chemistry of each species , and compare the fractional abundances in the cnd and starburst ring with those of galactic sources such as cold cores , hot cores , and shocked molecular clouds in order to study the overall characteristics .

we present 0.8-mm band molecular images and spectra obtained with the atacama large millimeter / submillimeter array ( alma ) toward one of the nearest galaxies with an active galactic nucleus ( agn ) , ngc 1068 . distributions of co isotopic species (co and co ) = 32 , cn = 32 and cs = 76 are observed toward the circumnuclear disk ( cnd ) and a part of the starburst ring with an angular resolution of. 1. . the physical properties of these molecules and shock - related molecules such as hnco , chcn , so , and choh detected in the 3-mm band were estimated using rotation diagrams under the assumption of local thermodynamic equilibrium . the rotational temperatures of the co isotopic species and the shock - related molecules in the cnd are , respectively , 1422 k and upper limits of 2040 k. although the column densities of the co isotopic species in the cnd are only from one - fifth to one - third of that in the starburst ring , those of the shock - related molecules are enhanced by a factor of 310 in the cnd . we also discuss the chemistry of each species , and compare the fractional abundances in the cnd and starburst ring with those of galactic sources such as cold cores , hot cores , and shocked molecular clouds in order to study the overall characteristics . we find that the abundances of shock - related molecules are more similar to abundances in hot cores and/or shocked clouds than to cold cores . the cnd hosts relatively complex molecules , which are often associated with shocked molecular clouds or hot cores . because a high x - ray flux can dissociate these molecules , they must also reside in regions shielded from x - rays .

1210.5409

i

the universal features of a large class of one - dimensional quantum models , exhibiting gapless excitations with linear spectrum , are successfully described @xcite by the tomonaga - luttinger ( tl ) liquid theory @xcite-@xcite . this theory applies to various systems , including nanowire junctions and carbon nanotubes , which are available nowadays in experiment @xcite-@xcite . for this reason the study of non - equilibrium phenomena in the tl liquid phase attracts recently much attention @xcite-@xcite . a typical non - equilibrium setup , considered in the literature , is the junction of two or more semi - infinite leads with electrons at different temperatures and/or chemical potentials . the junction is an interval of finite length @xmath5 , where the electrons injected from the leads interact among themselves . this interaction drives the system away from equilibrium . differently from the equilibrium tl liquid on the line , the non - equilibrium model defined in this way , is not exactly solvable . nevertheless , it is extensively studied @xcite-@xcite by various methods , including linear response theory , bosonization combined with the non - equilibrium keldish formalism and perturbation theory . one of the main goals of the present paper is to explore the possibility to construct and analyze an alternative _ exactly solvable _ model for a non - equilibrium tl junction . since the universal features of such a system are expected to manifest themselves in the critical ( scale invariant ) limit , it is natural to shrink the domain of the non - equilibrium interaction to a point , taking @xmath6 . for a complete description of the critical regime it is essential to take into account all point - like interactions , which ensure a unitary time evolution of the system . these interactions can be parametrized by a scattering matrix @xmath0 localized in the junction point , as shown in the multi - terminal setup displayed in fig.[fig1 ] . ( 600,120)(40,250 ) and @xmath7 semi - infinite leads , connected at infinity to thermal reservoirs with temperatures @xmath8 and chemical potentials @xmath9.,title="fig : " ] each lead contains a tl liquid , which at infinity is in contact with a heat reservoir with ( inverse ) temperature @xmath8 and chemical potential @xmath9 . our first step below is to show that there exists a non - equilibrium steady state ( ness ) , which describes the tl configuration in fig.[fig1 ] . this state is characterized by non - trivial time independent electric and heat currents , flowing in the leads . the scattering matrix @xmath0 is implemented by imposing specific boundary conditions at the junction . it turns out that the boundary conditions , which describe the splitting of the electric steady current in the junction , lead to an exactly solvable problem . in fact , we establish the operator solution in this case and investigate the relative non - equilibrium correlation functions in the ness representation . the tl theory has been introduced originally @xcite-@xcite for describing fermion systems . it has been understood later on @xcite-@xcite that the fermion tl liquid is actually an element of a more general family of _ anyon _ tl liquids , which obey abelian braid statistics . in this paper we explore the general anyon tl liquid , obtaining the conventional fermionic and bosonic ones as a special cases . from the two - point anyon correlation functions we extract the ness distribution of the tl anyon excitations . in momentum space this non - equilibrium distribution is a _ nested convolution _ of equilibrium distributions at different temperatures and chemical potentials . as expected , the convolution depends on the scattering matrix @xmath0 , which drives the system away from equilibrium . we investigate also the ness correlators of the electric and energy currents , describing in detail the charge and heat transport in the junction . the zero - frequency noise power is deduced from the two - point current - current correlation function , whose exact expression in terms of hypergeometric functions is established . we prove the breakdown of time reversal invariance as well . the paper has the following structure . in the next section we construct non - equilibrium chiral fields in a ness on a star graph modeling the junction . we derive here the non - equilibrium casimir energy and the heat current and compare the latter with the conformal field theory result . in section 3 we develop a non - equilibrium finite temperature operator bosonization procedure . we also establish the operator solution , subject to the current splitting boundary condition at the junction . we show that this condition covers two different physical situations , corresponding to a junction with and without charge dissipation . the non - equilibrium correlation functions are investigated in section 4 , where the anyon ness distributions are derived . the charge and heat transport as well as the noise are also studied there . section 5 provides a concise outlook of the paper and contains some general observations . the appendix collects some results about the asymptotic properties of the anyon ness correlators .

the boundary condition at the junction is fixed by an orthogonal matrix , which describes the splitting of the electric current among the leads . we develop a non - equilibrium bosonization procedure and compute some basic correlation functions . luttinger liquids with general anyon statistics are considered . both the charge and heat transport are studied . the exact current - current correlation function is derived and the zero - frequency noise power is determined . l s 1_1 o * v * * luttinger liquid in non - equilibrium + steady state * + mihail mintchev and paul sorba + 1.5 truecm _ istituto nazionale di fisica nucleare and dipartimento di fisica delluniversit di pisa , largo pontecorvo 3 , 56127 pisa , italy + _

we propose and investigate an exactly solvable model of non - equilibrium luttinger liquid on a star graph , modeling a multi - terminal quantum wire junction . the boundary condition at the junction is fixed by an orthogonal matrix , which describes the splitting of the electric current among the leads . the system is driven away from equilibrium by connecting the leads to heat baths at different temperatures and chemical potentials . the associated non - equilibrium steady state depends on and is explicitly constructed . in this context we develop a non - equilibrium bosonization procedure and compute some basic correlation functions . luttinger liquids with general anyon statistics are considered . the relative momentum distribution away from equilibrium turns out to be the convolution of equilibrium anyon distributions at different temperatures . both the charge and heat transport are studied . the exact current - current correlation function is derived and the zero - frequency noise power is determined . l s 1_1 o * v * * luttinger liquid in non - equilibrium + steady state * + mihail mintchev and paul sorba + 1.5 truecm _ istituto nazionale di fisica nucleare and dipartimento di fisica delluniversit di pisa , largo pontecorvo 3 , 56127 pisa , italy + _ laboratoire de physique thorique dannecy - le - vieux , cnrs , + 9 , chemin de bellevue , bp 110 , f-74941 annecy - le - vieux cedex , france

1210.5409

c

in this paper we constructed and investigated an exactly solvable model of a non - equilibrium luttinger junction . the basic points of our approach are : ( i ) : : a scale invariant point - like interaction , which is described by a scattering matrix @xmath0 and drives the system away from equilibrium ; ( ii ) : : a representation generated by a ness @xmath259 , which encodes the point - like interaction in the chiral fields @xmath27 ; ( iii ) : : an exact operator solution of the tl model ( in terms of @xmath27 ) on a star graph with the current splitting boundary condition in the vertex ; ( iv ) : : an extension of the conventional fermion luttinger liquid to anyon statistics . combining these ingredients , we derived the basic correlation functions in the state @xmath259 . the essential characteristic features of these functions are : ( a ) : : the non - equilibrium two - point anyon correlations are products of @xmath0-dependent powers of equilibrium correlations at the temperatures and chemical potentials of the heat baths , connected to the leads ; ( b ) : : accordingly , the corresponding momentum space distribution is the convolution of equilibrium anyon distributions at different temperatures and chemical potentials ; ( c ) : : the fourier transform of the leading terms in the large distance expansion of the anyon correlations gives cauchy - lorentz distributions , which after convolution reproduce themselves with appropriate width and median ; ( d ) : : in the critical limit one has a @xmath92 conformal field theory with @xmath0-dependent anomalous dimensions , which are explicitly derived ; ( e ) : : the expected breakdown of time reversal invariance is manifest in the current - current correlator . we investigated in detail the energy and charge transport in the junction for all values of the statistical parameter . the energy is conserved for @xmath175 , which covers both possibilities of a junction without and with electric charge dissipation . in the latter case we determined the exact expression for the charge flow leaving or entering the junction . the connected current - current correlation is a linear combination of hypergeometric functions . the associated zero - frequency noise power depends linearly on the temperatures . our investigation above has been focused essentially on the critical properties of anyon luttinger liquids away from equilibrium . it will be interesting to study the noncritical aspects as well . the generalization of the results of this paper beyond the luttinger liquid paradigm , when the nonlinearity of the dispersion relation becomes essential , is also a challenging open problem . we thank b. douot and i. safi for an inspiring discussion , which stimulated our interest in non - equilibrium luttinger liquids . would like also to thank the laboratoire de physique thorique dannecy - le - vieux for the kind hospitality during the preparation of the manuscript .

we propose and investigate an exactly solvable model of non - equilibrium luttinger liquid on a star graph , modeling a multi - terminal quantum wire junction . the system is driven away from equilibrium by connecting the leads to heat baths at different temperatures and chemical potentials . the associated non - equilibrium steady state depends on and is explicitly constructed . in this context the relative momentum distribution away from equilibrium turns out to be the convolution of equilibrium anyon distributions at different temperatures . laboratoire de physique thorique dannecy - le - vieux , cnrs , + 9 , chemin de bellevue , bp 110 , f-74941 annecy - le - vieux cedex , france

we propose and investigate an exactly solvable model of non - equilibrium luttinger liquid on a star graph , modeling a multi - terminal quantum wire junction . the boundary condition at the junction is fixed by an orthogonal matrix , which describes the splitting of the electric current among the leads . the system is driven away from equilibrium by connecting the leads to heat baths at different temperatures and chemical potentials . the associated non - equilibrium steady state depends on and is explicitly constructed . in this context we develop a non - equilibrium bosonization procedure and compute some basic correlation functions . luttinger liquids with general anyon statistics are considered . the relative momentum distribution away from equilibrium turns out to be the convolution of equilibrium anyon distributions at different temperatures . both the charge and heat transport are studied . the exact current - current correlation function is derived and the zero - frequency noise power is determined . l s 1_1 o * v * * luttinger liquid in non - equilibrium + steady state * + mihail mintchev and paul sorba + 1.5 truecm _ istituto nazionale di fisica nucleare and dipartimento di fisica delluniversit di pisa , largo pontecorvo 3 , 56127 pisa , italy + _ laboratoire de physique thorique dannecy - le - vieux , cnrs , + 9 , chemin de bellevue , bp 110 , f-74941 annecy - le - vieux cedex , france

astro-ph0202175

i

the value of equipping telescopes with a large field of view has been recognised for some time . in 1986 the royal astronomical society report `` review of scientific priorities for uk astronomical research 19902000 '' @xcite put a wide - field multi - object spectroscopic facility at the top of its priority list for new projects . subsequently the uk large telescope panel recommended that a wide - field survey facility be pursued in tandem with an 8 metre telescope project . the general scientific case for a wide - field spectroscopic facility on a 4 m telescope was two - fold : to provide spectra for large samples of objects found in the multi - colour imaging surveys from the uk , eso and oschin ( palomar ) schmidt telescopes ; and to generate targets for the coming generation of 8 - 10 m optical telescopes . the biggest specific science driver was to obtain redshifts of tens or even hundreds of thousands of galaxies and quasars , to elucidate the three - dimensional structure and evolution of the universe . other major projects required spectra for large samples of stars , to determine their kinematics and composition and hence the dynamical and chemical history of our galaxy ; for similar studies of the magellanic clouds ; and for detailed studies of star clusters and clusters of galaxies . one possibility was to provide a multi - fibre upgrade to the 3.9 metre anglo - australian telescope ( aat ) . this was particularly advantageous for two reasons . firstly , the optical design of the telescope ( a hyperboloidal primary mirror and relatively slow f - ratio of f/3.3 at prime focus ) enabled a wide field of 2 to be achieved using a large but straightforward optical corrector . secondly , the anglo - australian observatory ( aao ) already had extensive experience with multi - object fibre spectroscopy . this dates from the pioneering days of optical fibres and its brass plug - plate system focap @xcite and more recently the fully automated autofib fibre positioner system @xcite . at the end of 1988 the aat board ( aatb ) commissioned a full design study of a wide - field fibre - optic spectroscopic facility for the aat @xcite . following further detailed investigations into cost and budgets , and in the expectation of some additional funding from both the australian and uk governments , the aatb gave its approval to begin the two - degree field ( or 2df ) project in march 1990 . initially the direct budget allocated was a$2.25 m ( for components and certain specific tasks which could not be done in - house ) and it was expected to take 4 - 5 years to complete . since the project would dominate the aao s activities for several years , a project management committee was established with several external expert members . in developing the 2df facility the aao wished to build on the techniques already used for the fully automated autofib instrument in use at the cassegrain focus of the aat . since 2df would offer almost an order of magnitude increase in multiplex advantage over autofib and would be located at the more challenging prime focus , several technical problems had to be solved before final approval was given for commencement of the project . the technical problems were addressed in the initial design study reports and covered areas such as the accuracy required of the robotic positioner , the design of the fibre retraction systems , location and design of the fibre spectrographs and the requirement for a double fieldplate system to maximise observing time . the mechanical constraints were eased by the strength and rigidity of the telescope tube structure and the size of the dome , which meant that a large instrument could be housed at prime focus without clearance and flexure problems . commissioning of the 2df facility began with the new prime focus corrector in the latter part of 1993 . the instrument was officially declared open at a ceremony on 1995 november 20 , and the first spectroscopic data were obtained in mid-1996 . the facility began to provide scheduled scientific observations in september 1997 with almost full functionality . the project ran about 40 per cent over the original time estimate and 20 per cent over budget ( these two are linked , in that 2df could have been completed sooner had more funds been available ) . the effective total cost was subsequently estimated to have been about a$8 m , including all staff costs and overheads . the bulk of the design and construction work was eventually done in - house using the aao s facilities in sydney and coonabarabran , partly because many aspects involved innovative design features which could not be easily specified or contracted out , and partly to contain costs . progress reports describing the evolution of the design of 2df have been published @xcite and project updates have featured regularly in the quarterly aao newsletter . in this paper we provide a full technical description of the 2df facility and its performance . section [ overview ] gives an overview of the instrumentation and its relationship to other multiple object fibre spectroscopy systems . in section [ components ] , a detailed description of the individual components of the 2df facility is given . operation of the 2df facility is covered in section [ operations ] and actual performance is detailed in section [ performance ] . sections [ science ] and [ future ] describe the range of projects being done with 2df and some scientific possibilities for the future . up to date technical information and signal to noise calculators are available on the 2df www pages ( http://www.aao.gov.au/2df/ ) .

the 2df ( two - degree field ) facility at the prime focus of the anglo - australian telescope provides multiple object spectroscopy over a field of view . the 2df facility began routine observations in 1997 . 2df has achieved its initial astronomical goals . we also briefly review its scientific applications and possible future developments .

the 2df ( two - degree field ) facility at the prime focus of the anglo - australian telescope provides multiple object spectroscopy over a field of view . up to 400 target fibres can be independently positioned by a complex robot . two spectrographs provide spectra with resolutions of between 500 and 2000 , over wavelength ranges of 440 nm and 110 nm respectively . the 2df facility began routine observations in 1997 . 2df was designed primarily for galaxy redshift surveys and has a number of innovative features . the large corrector lens incorporates an atmospheric dispersion compensator , essential for wide wavelength coverage with small diameter fibres . the instrument has two full sets of fibres on separate field plates , so that re - configuring can be done in parallel with observing . the robot positioner places one fibre every 6 seconds , to a precision of 0.3 arcsec ( 20 ) over the full field . all components of 2df , including the spectrographs , are mounted on a 5-m diameter telescope top - end ring for ease of handling and to keep the optical fibres short in order to maximise uv throughput . there is a pipeline data reduction system which allows each data set to be fully analysed while the next field is being observed . 2df has achieved its initial astronomical goals . the redshift surveys obtain spectra at the rate of 2500 galaxies per night , yielding a total of about 200,000 objects in the first four years . typically a b galaxy gives a spectrum with signal to noise ratio of better than 10 per pixel in less than an hour ; redshifts are derived for about 95 per cent of all galaxies , with 99 per cent reliability or better . total system throughput is about 5 per cent . the failure rate of the positioner and fibre system is about 1:10,000 moves or once every few nights and recovery time is usually short . in this paper we provide the historical background to the 2df facility , the design philosophy , a full technical description and a summary of the performance of the instrument . we also briefly review its scientific applications and possible future developments . [ firstpage ] instrumentation : spectrographs techniques : spectroscopic surveys galaxies : distances and redshifts large - scale structure of universe

1506.02540

i

the mathematical theory for the spread of infectious diseases has a long history and is by now quite rich ( e.g. , @xcite ) . one of the more common type of disease models is called sir ( susceptible @xmath1 infective @xmath1 recovered ) meaning that individuals are at first susceptible . if infected ( by someone ) they immediately become infectious ( being able to spread the disease onwards ) . after some time an infectious individual recovers , which also means that the individual is immune to further infection from the disease . such models were originally studied for populations assuming homogeneous mixing , but during the last few decades considerable effort has been put into analysing epidemic models in communities which are not homogeneously mixing but instead may be described using some type of social structure , such as a community of households ( e.g. @xcite ) or a random network describing possible contacts ( e.g. @xcite ) . the vast majority of papers devoted to these type of problems assume a fixed community and community structure . in the current paper we treat the situation where the population is dynamic in the sense that people die and new individuals are born , or more precisely immigrate into the population . further , we assume that there is also importation of infectious individuals ( randomly in time according to a homogeneous poisson process ) , implying that the disease never vanishes forever . in order to facilitate analytical progress we consider only the case of a homogeneously mixing community , which in network terminology corresponds to treating the complete network . models for recurrent epidemics go back to the deterministic formulations of @xcite and @xcite . a stochastic treatment was given first in the pioneering work of @xcite , who considered an sir model with importation of both susceptibles and infectives , but without disease - unrelated deaths . an alternative model , with disease - unrelated deaths but no importation of infectives , has been studied extensively ( e.g. @xcite and the references therein ) . interest often centres on the time to extinction of infection and the closely - related problem of the critical community size for an infection to persist in a population . we consider a markovian sir epidemic with demography and importation of infectives , in which infectious individuals infect new individuals at constant rate and the infectious period is exponentially distributed . we study limit properties of the epidemic when the average population size @xmath0 tends to infinity . our focus lies on the case where the limit is taken keeping the basic reproduction number @xmath3 ( i.e. the average number of susceptibles infected by a single infective in an otherwise fully susceptible population of size @xmath0 ) and the immigration rate of infectives fixed , whereas the quotient of the average infectious period and the average lifetime tends to 0 faster than @xmath4 . for many infectious diseases this quotient typically lies between @xmath8 and @xmath9 , hence supporting this asymptotic regime , but in the discussion we treat other asymptotic regimes briefly . under the above asymptotic regime , all epidemic outbreaks are short , having duration that tends to @xmath10 in probability as @xmath11 further , as @xmath11 , epidemic outbreaks are either minor , having size of order @xmath12 , or major , having size of exact order @xmath13 . it follows that , as @xmath11 , the behaviour of the three - dimensional process describing the evolution of the fraction of the population that are susceptible , infective and recovered , is encapsulated in a one - dimensional regenerative process @xmath6 , describing the limiting fraction of the population that are susceptible . during each cycle , the process @xmath7 makes one down jump , corresponding to the occurrence of a major outbreak , and except for this increases deterministically , as minor outbreaks have no effect on @xmath14 in the limit as @xmath11 . ( here , @xmath15 , where , for @xmath16 , @xmath17 with @xmath18 being the number of susceptible individuals in the population at time @xmath19 . ) note that @xmath14 does not converge weakly to @xmath7 in the skorohod topology since the sample paths of @xmath7 are almost surely discontinuous but those of @xmath14 almost surely contain only jumps of size @xmath20 , so are close to being continuous . thus to obtain rigorous convergence results , we consider two processes , @xmath21 and @xmath22 , which coincide with @xmath14 , except during major outbreaks during which they sandwich @xmath14 , and prove that both @xmath21 and @xmath22 converge weakly to @xmath7 in the skorohod topology ( theorem [ wconv ] ) . it then follows that certain functionals of @xmath14 converge weakly to corresponding functionals of @xmath7 ( corollary [ convfunct ] ) . the paper is structured as follows . in section [ modelmain ] , we define the model and the limiting regenerative process , give an intuitive explanation of why @xmath7 approximates @xmath14 for large @xmath0 and present the main convergence results . in section [ s - properties ] , we derive some properties of the limiting regenerative process : the jump size distribution , the associated renewal time distribution and the stationary distribution . in section [ illustrations ] , we present simulations supporting the convergence result and illustrating various features of the limiting process . in section [ proofs ] , we prove the main results . we end in section [ disc ] with a discussion summarising our results and also exploring briefly additional questions , such as other asymptotic regimes .

consider a large uniformly mixing dynamic population , which has constant birth rate and exponentially distributed lifetimes , with mean population size . a markovian sir ( susceptible infective recovered ) infectious disease , having importation of infectives , taking place in this population is analysed . the main situation treated is where , keeping the basic reproduction number as well as the importation rate of infectives fixed , but assuming that the quotient of the average infectious period and the average lifetime tends to 0 faster than . it is shown that , as , the behaviour of the 3-dimensional process describing the evolution of the fraction of the population that are susceptible , infective and recovered , is encapsulated in a 1-dimensional regenerative process describing the limiting fraction of the population that are susceptible . properties of the process , including the jump size and stationary distributions , are determined .

consider a large uniformly mixing dynamic population , which has constant birth rate and exponentially distributed lifetimes , with mean population size . a markovian sir ( susceptible infective recovered ) infectious disease , having importation of infectives , taking place in this population is analysed . the main situation treated is where , keeping the basic reproduction number as well as the importation rate of infectives fixed , but assuming that the quotient of the average infectious period and the average lifetime tends to 0 faster than . it is shown that , as , the behaviour of the 3-dimensional process describing the evolution of the fraction of the population that are susceptible , infective and recovered , is encapsulated in a 1-dimensional regenerative process describing the limiting fraction of the population that are susceptible . the process grows deterministically , except at one random time point per regenerative cycle , where it jumps down by a size that is completely determined by the waiting time since the previous jump . properties of the process , including the jump size and stationary distributions , are determined .

hep-ph9211304

i

effective low energy hamiltonians for non leptonic weak decays of hadrons are usually written as linear combinations of four quark operators . the coefficients of these operators , the wilson coefficient functions , can be calculated in the renormalization group improved perturbation theory , as long as the normalization scale @xmath7 is not too low . the size of these coefficients depends on @xmath7 through the qcd effective coupling constant and on the anomalous dimensions of the operators in question . since the operators generally mix under renormalization , one deals with anomalous dimension matrices rather than with single anomalous dimensions . in the case of the @xmath2 hamiltonian , relevant for instance for the @xmath8 rule and the ratio @xmath9 , there are ten operators @xmath10 which have to be considered . consequently one deals with a @xmath11 anomalous dimension matrix . the ten operators in question can be divided into three classes : * current current operators @xmath12 originating in the usual w exchange and subsequent qcd corrections , * qcd penguin operators @xmath13 originating in qcd penguin diagrams , and * electroweak penguin operators @xmath14 originating in the photon penguin diagrams . explicit expressions for these operators are given in eq . ( [ eq:2.1 ] ) . because of the presence of electroweak penguin operators a consistent analysis must involve anomalous dimensions resulting from both strong and electromagnetic interactions . working to first order in @xmath15 but to all orders in @xmath16 the following anomalous dimension matrix is needed for the leading and next to leading logarithmic approximation for the wilson coefficient functions , @xmath17 in the leading logarithmic approximation only the one loop matrices @xmath18 and @xmath19 have to be considered . inclusion of next to leading corrections requires the evaluation of the two loop matrices @xmath20 and @xmath21 . in addition some one loop finite terms are needed . what is known in the literature are the matrices @xmath18 and @xmath19 @xcite@xcite and a @xmath22 submatrix of @xmath20 involving the current current operators @xmath23 and @xmath24 @xcite . the purpose of the present and a subsequent paper is to complete the evaluation of the matrix @xmath20 and to calculate @xmath21 . together with certain one loop finite terms this will allow the extension of the phenomenology of non leptonic @xmath2 transitions beyond leading logarithms . the results for the @xmath25 submatrix of @xmath20 involving current current and qcd penguin operators together with some phenomenological implications have already been presented by us in ref . @xcite . in the present paper we give the details of these two loop calculations and generalize them to the full matrix @xmath20 . the matrix @xmath21 is considered in a subsequent publication @xcite . in particular , we present the results for an arbitrary number of colours , @xmath26 , which is useful for the applications of the @xmath27 expansion . the phenomenological implications of these new results will be discussed in ref . @xcite . the calculation of the matrices @xmath20 and @xmath21 is very tedious . it involves a large number of two loop diagrams which make the use of an algebraic computer program almost mandatory .- algebra tracer , written in mathematica @xcite , which we extensively used during the calculation , has been developed by two of us @xcite and is available from the authors . ] moreover one has to deal with several subtleties which are absent in the calculations of @xmath18 and @xmath19 . first of all , the two loop anomalous dimensions depend on the renormalization scheme for operators and the treatment of @xmath5 in @xmath28 space time dimensions . it is known for instance on the basis of ref . @xcite , that the @xmath29 submatrix of @xmath20 involving @xmath30 and @xmath24 calculated in the ndr scheme ( naive dimensional regularization with anticommuting @xmath5 ) differs substantially from the one obtained in the hv scheme ( non anticommuting @xmath5 @xcite ) . the same feature is found for the full matrices @xmath20 and @xmath21 . the important point is that the difference between @xmath31 calculated in two different schemes is on general grounds entirely given in terms of @xmath32 and the finite parts of one loop diagrams calculated in the two schemes in question . this relation is very useful for checking the compatibility of two loop calculations performed in different renormalization schemes and plays an important role in demonstrating the scheme independence of physical quantities . it is given in eq . ( [ eq:2.12 ] ) . another subtle point is the dependence of the two loop anomalous dimensions obtained in the ndr scheme on whether a given operator has been put in colour singlet or colour non singlet form such as @xmath33 in @xmath34 dimensions @xmath24 and @xmath35 would be equivalent by means of fierz transformation . their one loop anomalous dimensions are the same . again the two loop anomalous dimensions for these two forms of operators can on general grounds be related to each other by calculating one loop diagrams . this feature turns out to be fortunate in that it offers one way to deal with dangerous closed fermion loops involving odd numbers of @xmath5 in two loop diagrams . the latter are known to be ambiguous in the case of the ndr scheme . indeed , as we will demonstrate explicitly in section 5 and in ref . @xcite , it is possible by using different forms of the operators and the relation mentioned above , to express all diagrams with closed fermion loops in terms of diagrams not containing such loops . in this way , consistent calculations of @xmath20 and @xmath21 can be performed in the ndr scheme and compared with the one obtained in the hv scheme , free of @xmath5 problems . the following sections constitute the calculation of @xmath20 and a detailed discussion of the subtle points mentioned above . in ref . @xcite , the methods developed here are generalized to include photon exchanges and are used to calculate @xmath21 . our paper is organized as follows : in section 2 , we give a list of the ten operators in question , and we classify the one and two loop diagrams into current current and penguin diagrams . we also discuss the basic formalism necessary for the calculation of @xmath20 . in section 3 , we recall the matrix @xmath18 , and we calculate the finite terms of one loop diagrams in the ndr and hv scheme . in section 4 , the calculations and results for two loop current current diagrams are presented . in section 5 , an analogous presentation is given for two loop penguin diagrams . in section 6 , we combine the results of the previous sections to obtain @xmath20 in ndr and hv schemes . we discuss various properties of this matrix , in particular its large-@xmath26 limit . section 7 contains a brief summary of our paper . in appendices a and b explicit expressions for the elements of the @xmath0 matrices @xmath18 and @xmath20 for an arbitrary number of colours ( @xmath26 ) and flavours ( @xmath36 ) are given . in appendix c the corresponding results for @xmath20 in the case of @xmath37 are presented .

we calculate the two the calculation is performed in two schemes for : the dimensional regularization scheme with anticommuting ( ndr ) , and in the t hooft veltman scheme . we demonstrate how a direct calculation of diagrams involving in closed fermion loops can be avoided thus allowing a consistent calculation in the ndr scheme . artcustom.sty , a4wide.sty , a4.sty : required style files except epsf.sty . epsf.sty is of any use only in connection with the rokicki dvips converter . a4wide.sty uses this particular version of a4.sty ( with the later separately available at this bulletin board although i do nt know whether the two are compatible ) . theo . physics t31,| internet : d-8046 garching , frg . > > > 2ladmqcd.tex < < < snip snip snip snip snip snip snip snip

we calculate the two loop anomalous dimension matrix involving current current operators , qcd penguin operators , and electroweak penguin operators especially relevant for weak non leptonic decays , but also important for decays . the calculation is performed in two schemes for : the dimensional regularization scheme with anticommuting ( ndr ) , and in the t hooft veltman scheme . we demonstrate how a direct calculation of diagrams involving in closed fermion loops can be avoided thus allowing a consistent calculation in the ndr scheme . the compatibility of the results obtained in the two schemes considered is verified and the properties of the resulting matrices are discussed . the two loop corrections are found to be substantial . the two loop anomalous dimension matrix , required for a consistent inclusion of electroweak penguin operators , is presented in a subsequent publication . remarks : below you find the * latex source * of our recent paper . the accompanying figures ( in postscript ) are distributed separately in an uuencoded compressed tar - file as required by the rules for postscript files on this bulletin board . the latex distribution is wrapped up in a single file with `` snip '' lines delimiting the individual files . the corresponding file names are indicated in the line `` > > > < filename < < < '' just above the leading `` snip '' lines . the * full * distribution consists of the following files : latex part ( this file ) : 2ladmqcd.tex : latex source of the paper . artcustom.sty , a4wide.sty , a4.sty : required style files except epsf.sty . epsf.sty is of any use only in connection with the rokicki dvips converter . a4wide.sty uses this particular version of a4.sty ( with the later separately available at this bulletin board although i do nt know whether the two are compatible ) . postscript part ( distributed separately ) : fig1qcd.ps , fig2qcd.ps , fig3qcd.ps , fig4qcd.ps , fig5qcd.ps , fig6qcd.ps , fig7qcd.ps : postscript files read in by `` 2ladmqcd.tex '' via epsf.sty provided with the rokicki dvips dvi - to - postscript converter . if you do nt have the rokicki dvips you should comment out the relevant epsf - commands in `` 2ladmqcd.tex '' . best regards , markus lautenbacher markus e. lautenbacher , | phone : + 49/89/3209 - 2387 technical university munich , | fax : + 49/89/32092296 physics dept .- theo . physics t31,| internet : d-8046 garching , frg . lauten@feynman.t30.physik.tu-muenchen.de > > > 2ladmqcd.tex < < < snip snip snip snip snip snip snip snip

hep-ph9211304

i

we have presented the details and the explicit results of the calculation of the two loop anomalous dimension matrix @xmath284 involving current - current , qcd - penguin and electroweak - penguin operators . performing the calculation in two schemes for @xmath5 , ndr and hv , we have verified the compatibility of the anomalous dimension matrices obtained in these two schemes . we have shown how the use of two different operator bases allows to avoid a direct calculation of penguin diagrams with closed fermion loops . this enabled us to find in an unambiguous way the two loop anomalous dimensions in the simplest dimensional regularization scheme , the one with anticommuting @xmath5 . the results of this paper generalize our earlier paper @xcite where electroweak penguin operators have not been taken into account . the two loop anomalous dimensions matrix presented for the first time in ref . @xcite and generalized in section 6 of the present paper will play a central role in any analysis of non - leptonic decays of hadrons which goes beyond the leading logarithmic approximation . a consistent next - to - leading order analysis involving electroweak penguin operators requires the calculation of @xmath21 , i.e. the two loop anomalous dimension matrix @xmath297 . a detailed account of this calculation is given in @xcite . the full renormalization group analysis with the anomalous dimension matrix of eq . ( [ eq:1.1 ] ) will be presented soon in ref . there the numerical values for the wilson coefficient functions @xmath298 of the operators @xmath285 including next - to - leading order corrections can be found . * acknowledgement * we would like to thank many colleagues for a continuous encouragement during this calculations . one of us ( a.j.b . ) would like to thank bill bardeen and david broadhurst for very interesting discussions . m.e.l . is grateful to stefan herrlich for a copy of his program feynd for drawing the feynman diagrams in the figures and to gerhard buchalla for stimulating discussions . 10 and b. w. lee , ( 1974 ) 108 . and l. maiani , ( 1974 ) 351 . , v. i. zakharov , and m. a. shifman , ( 1977 ) 670 . and m. b. wise , ( 1979 ) 2392 . and r. d. peccei , ( 1980 ) 289 . and m. b. wise , ( 1984 ) 245 . and j .- grard , ( 1987 ) 156 . , ( 1987 ) 551 . , ( 1989 ) 33 . and l. randall , ( 1989 ) 221 , erratum * 235b * ( 1990 ) 412 . , a. j. buras , and m. k. harlander , ( 1990 ) 313 . , g. curci , g. martinelli , and s. petrarca , ( 1981 ) 461 . and p. h. weisz , ( 1990 ) 66 . , m. jamin , m. e. lautenbacher , and p. h. weisz , ( 1992 ) 69 ; addendum ibid . _ nucl . _ * b375 * ( 1992 ) 501 . , m. jamin , and m. e. lautenbacher , two loop anomalous dimension matrix for @xmath2 weak non - leptonic decays ii : @xmath299 , . , m. jamin , and m. e. lautenbacher , effective hamiltonians for @xmath2 and @xmath3 non - leptonic decays beyond leading logarithms in the presence for electroweak penguins , . , , addison - wesley publishing company inc . , 1991 . and m. e. lautenbacher , . and m. veltman , ( 1972 ) 189 . and d. maison , ( 1977 ) 11 , 39 , 55 . , ( 1981 ) 384 . , a. j. buras , and j .- grard , ( 1986 ) 133 . , a. j. buras , and j .- grard , ( 1987 ) 787 . and b. grinstein , ( 1991 ) 239 . and e. de rafael , ( 1991 ) 311 . and zuber , ( 1975 ) 467 , 482 , 3159 . and b. w. lee , ( 1976 ) 160 . and j. a. dixon , ( 1978 ) 1113 ( 1983 ) 349 . , ( 1981 ) 189 . , d. kreimer , and k. schilcher , ( 1992 ) 503 .

loop anomalous dimension matrix involving current current operators , qcd penguin operators , and electroweak penguin operators especially relevant for weak non leptonic decays , but also important for decays . the two loop anomalous dimension matrix , required for a consistent inclusion of electroweak penguin operators , is presented in a subsequent publication . remarks : below you find the * latex source * of our recent paper . best regards , markus lautenbacher markus e. lautenbacher , | phone : + 49/89/3209 - 2387 technical university munich , | fax : + 49/89/32092296 physics dept .-

we calculate the two loop anomalous dimension matrix involving current current operators , qcd penguin operators , and electroweak penguin operators especially relevant for weak non leptonic decays , but also important for decays . the calculation is performed in two schemes for : the dimensional regularization scheme with anticommuting ( ndr ) , and in the t hooft veltman scheme . we demonstrate how a direct calculation of diagrams involving in closed fermion loops can be avoided thus allowing a consistent calculation in the ndr scheme . the compatibility of the results obtained in the two schemes considered is verified and the properties of the resulting matrices are discussed . the two loop corrections are found to be substantial . the two loop anomalous dimension matrix , required for a consistent inclusion of electroweak penguin operators , is presented in a subsequent publication . remarks : below you find the * latex source * of our recent paper . the accompanying figures ( in postscript ) are distributed separately in an uuencoded compressed tar - file as required by the rules for postscript files on this bulletin board . the latex distribution is wrapped up in a single file with `` snip '' lines delimiting the individual files . the corresponding file names are indicated in the line `` > > > < filename < < < '' just above the leading `` snip '' lines . the * full * distribution consists of the following files : latex part ( this file ) : 2ladmqcd.tex : latex source of the paper . artcustom.sty , a4wide.sty , a4.sty : required style files except epsf.sty . epsf.sty is of any use only in connection with the rokicki dvips converter . a4wide.sty uses this particular version of a4.sty ( with the later separately available at this bulletin board although i do nt know whether the two are compatible ) . postscript part ( distributed separately ) : fig1qcd.ps , fig2qcd.ps , fig3qcd.ps , fig4qcd.ps , fig5qcd.ps , fig6qcd.ps , fig7qcd.ps : postscript files read in by `` 2ladmqcd.tex '' via epsf.sty provided with the rokicki dvips dvi - to - postscript converter . if you do nt have the rokicki dvips you should comment out the relevant epsf - commands in `` 2ladmqcd.tex '' . best regards , markus lautenbacher markus e. lautenbacher , | phone : + 49/89/3209 - 2387 technical university munich , | fax : + 49/89/32092296 physics dept .- theo . physics t31,| internet : d-8046 garching , frg . lauten@feynman.t30.physik.tu-muenchen.de > > > 2ladmqcd.tex < < < snip snip snip snip snip snip snip snip

1010.4504

i

the covariance graph ( aka bi - directed graph ) of a probability distribution @xmath0 is the undirected graph @xmath1 where two nodes are adjacent iff their corresponding random variables are marginally dependent in @xmath0 . covariance graphs were introduced in @xcite to represent independence models . since then , they have received considerable attention . see , for instance , @xcite . the works @xcite are particularly important for the interpretation of covariance graphs in terms of independencies . specifically , these works introduce a graphical criterion for reading independencies from the covariance graph @xmath1 of a probability distribution @xmath0 , under the assumption that @xmath0 satisfies the graphoid properties and composition . in this paper , we show that @xmath1 can also be used to read dependencies holding in @xmath0 . specifically , we present a graphical criterion for reading dependencies from @xmath1 under the assumption that @xmath0 satisfies the graphoid properties , weak transitivity and composition . we also prove that our graphical criterion is sound and complete . here , complete means that it is able to read all the dependencies in @xmath0 that can be derived by applying the graphoid properties , weak transitivity and composition to the dependencies used in the construction of @xmath1 and the independencies obtained from @xmath1 . we also show that there exist important families of probability distributions that satisfy the graphoid properties , weak transitivity and composition . these include , for instance , all the regular gaussian probability distributions . note that this paper would be unnecessary if @xmath0 satifies all and only the independencies that can be read from @xmath1 via the graphical criterion in @xcite , i.e. @xmath0 is faithful to @xmath1 . we will see that one can not safely assume faithfulness in general . therefore , one is only entitled to assume that @xmath0 satifies all ( but not necessarily only ) the independencies that can be read from @xmath1 via the graphical criterion in @xcite , i.e. @xmath0 is markov wrt @xmath1 . this is actually the reason of being of this paper . two previous works that somehow address the problem of reading dependencies off covariance graphs are @xcite . these works propose to determine whether two random variables @xmath2 and @xmath3 are dependent given some other random variables @xmath4 by , first , constructing the covariance graph of the conditional probability distribution given @xmath4 of any set of random variables that includes @xmath2 and @xmath3 and , then , checking if the nodes corresponding to @xmath2 and @xmath3 are adjacent in the covariance graph constructed . therefore , these works construct multiple covariance graphs , one for each conditional probability distribution of interest , from which only the dependencies used in their construction are read . the work presented in this paper is radically different : we only construct the covariance graph of the probability distribution at hand and read from it many more dependencies than those used in its construction . while this is the first work where a sound and complete graphical criterion for reading dependencies off covariance graphs is developed , it is worth mentioning that there already exist sound and complete graphical criteria for reading dependencies off other graphical models . for instance , there exists a sound and complete graphical criterion for reading dependencies off the concentration graph ( aka minimal undirected independence map or markov network ) of a probability distribution that satisfies the graphoid properties @xcite , or the graphoid properties and weak transitivity @xcite . as a matter of fact , the graphical criterion that we present in this paper is dual to the one in @xcite . there also exists a sound and complete graphical criterion for reading dependencies off the bayesian network ( aka minimal directed independence map ) of a probability distribution that satisfies the graphoid properties @xcite , the graphoid properties and weak transitivity @xcite , or the graphoid properties and weak transitivity and composition @xcite . in the last two references , the bayesian networks are restricted to be polytrees . note that @xcite address a related but not more general problem than the one in this paper , since neither concentration graphs nor bayesian networks include covariance graphs . related more general problems than the one studied in this paper have been recently addressed , though . for instance , a method to read dependencies from multivariate regression graphs , which include covariance graphs , is proposed in @xcite . the author also presents necessary and sufficient conditions for the method to be sound . these conditions are the same as the ones considered in this paper , namely the graphoid properties plus weak transitivity and composition . unlike in this paper , no proof of completeness of the method proposed appears in @xcite . another related more general work is @xcite , where the author shows how summary graphs , which include covariance graphs , can help to detect which dependencies remain undistorted and which do not after marginalization and/or conditioning in a probability distribution generated over a so - called parent graph . it should be pointed out that that the probability distribution is generated over a parent graph implies that it satisfies the same conditions as the ones considered in this paper ( * ? ? ? * proposition 3 ) . again , unlike in this paper , the completeness question is not addressed in @xcite . finally , it should be noted that @xcite make use of the graphical criterion presented in @xcite for reading independencies from loopless mixed graphs , which include multivariate regression graphs , summary graphs and parent graphs . this criterion is sound and complete in certain sense , given that the graphoid properties and composition hold ( * ? ? ? * theorem 3 ) . these conditions are , in fact , not only sufficient but necessary too ( * ? ? ? * section 6.3 ) . we think that the work presented in this paper can be of great interest for the artificial intelligence community . graphs are one of the most commonly used metaphors for representing knowledge because they appeal to human intuition @xcite . furthermore , graphs are parsimonious models because they trade off accuracy for simplicity . consider , for instance , representing the independence model induced by a probability distribution as a graph . though this graph is typically less accurate than the probability distribution ( the graph may not represent all the ( in)dependencies and those that are represented are not quantified ) , it also requires less space to be stored and less time to be communicated than the probability distribution , which may be desirable features in some applications . thus , it seems sensible developing tools for reasoning with graphs . our graphical criterion is one such a tool : as the graphical criterion in @xcite makes the discovery of independencies amenable to human reasoning by enabling to read independencies off a covariance graph @xmath1 without numerical calculation , so does our graphical criterion with respect to the discovery of dependencies . there are fields where discovering dependencies is more important than discovering independencies @xcite . it is in these fields where we believe that our graphical criterion has greater potential . in bioinformatics , for instance , the nodes of @xmath1 may represent ( the expression levels of ) some genes under study . bioinformaticians are typically more interested in discovering gene dependencies than independencies , because the former provide contexts in which the expression level of some genes is informative about that of some other genes , which may lead to hypothesize dependencies , functional relations , causal relations , the effects of manipulation experiments , etc . see , for instance , @xcite for an application of covariance graphs to bioinformatics under the name of relevance networks . the rest of the paper is organized as follows . we start by reviewing some concepts in section [ sec : preliminaries ] . we show in section [ sec : wtc ] that assuming the graphoid properties , weak transitivity and composition is not too restrictive . we prove in section [ sec : indep ] that the existing graphical criterion for reading independencies from covariance graphs is complete in certain sense . this result , in addition to being important in its own , is important for reading as many dependencies as possible from covariance graphs . we introduce in section [ sec : dep ] our graphical criterion for reading dependencies from covariance graphs and prove that it is sound and complete in certain sense . finally , we close with some discussion in section [ sec : discussion ] .

the covariance graph ( aka bi - directed graph ) of a probability distribution is the undirected graph where two nodes are adjacent iff their corresponding random variables are marginally dependent in . implies that their corresponding random variables are marginally independent in . this difference in the definition is important in this paper . ] in this paper , we present a graphical criterion for reading dependencies from , under the assumption that satisfies the graphoid properties as well as weak transitivity and composition . for instance , all the regular gaussian probability distributions satisfy them .

the covariance graph ( aka bi - directed graph ) of a probability distribution is the undirected graph where two nodes are adjacent iff their corresponding random variables are marginally dependent in . implies that their corresponding random variables are marginally independent in . this difference in the definition is important in this paper . ] in this paper , we present a graphical criterion for reading dependencies from , under the assumption that satisfies the graphoid properties as well as weak transitivity and composition . we prove that the graphical criterion is sound and complete in certain sense . we argue that our assumptions are not too restrictive . for instance , all the regular gaussian probability distributions satisfy them .

0905.0020

i

after many years of preparation , interferometric gravitational wave ( gw ) detectors have now begun an era of long - duration observing . the three detectors of the laser interferometer gravitational - wave observatory ( ligo ) @xcite reached their design sensitivity levels in 2005 and began a `` science run '' that collected data through late 2007 . this run is called `` s5 '' since it followed a sequence of four shorter science runs that began in 2002 . the german / british geo600 detector @xcite joined the s5 run in january 2006 , and the italian / french virgo detector @xcite began its first science run ( denoted vsr1 ) in may 2007 , overlapping the last @xmath3 months of the s5 run . the data collected by these detectors provide the best opportunity yet to identify a gw signal though detection is still far from certain and is a baseline for future coordinated data collection with upgraded detectors . gravitational waves in the frequency band of ligo and the other ground - based detectors may be produced by a variety of astrophysical processes @xcite . see for example @xcite for inspiralling compact binaries , @xcite for spinning neutron stars , @xcite for binary mergers , and @xcite for core - collapse supernovae . the gw waveform emitted by a compact binary system during the inspiral phase can be calculated accurately in many cases , allowing searches with optimal matched filtering ; see , for example , @xcite . the waveform from the subsequent merger of two black holes is being modeled with ever - increasing success using numerical relativity calculations , but is highly dependent on physical parameters and the properties of strong - field gravity . the uncertainties for the waveforms of other transient sources are even larger . it is thus desirable to explore more generic search algorithms capable of detecting a wide range of short - duration gw signals from poorly - modeled sources such as stellar core collapse to a neutron star or black hole or unanticipated sources . as gw detectors extend the sensitivity frontier , it is important to not rely too heavily on assumptions about source astrophysics or about the true nature of strong - field gravity , and to search as broadly as possible . in this paper , we report on a search for gw `` burst '' signals in the ligo data that were collected during the first 12 months of the s5 science run . a search for gw bursts in the remainder of the s5 data set , along with the virgo vsr1 data , will be published jointly by the lsc and virgo collaborations at a later date . the gw burst signals targeted are assumed to have signal power within ligo s frequency band and durations shorter than @xmath41s , but are otherwise arbitrary . this analysis , like most of our previously published searches for gw bursts , focuses on low frequencies in this case 64hz to 2000hz where the detectors are the most sensitive . a dedicated search for bursts above 2000hz is presented in a companion paper @xcite . interferometric gw detectors collect stable , high - sensitivity ( `` science mode '' ) data typically for several hours at a time , with interruptions due to adverse environmental conditions , maintenance , diagnostics , and the need to occasionally regain the `` locked '' state of the servo controls . in this analysis we searched the data at all times when two or more ligo detectors were operating , a departure from the all - sky gw burst searches from earlier science runs @xcite , which required coincidence among three ( or more ) detectors . in this paper , the term `` network '' is used to describe a set of detectors operating in science mode at a given time . a network may include any combination of the hanford 4 km ( h1 ) and 2 km ( h2 ) detectors , the livingston 4 km ( l1 ) detector and geo600 . because the geo600 detector was significantly less sensitive than ligo during the s5 run ( a factor of 3 at 1000hz , and almost two orders of magnitude at 100hz ) , we do not use its data in the initial search but reserve it for evaluating any event candidates found in the ligo data . this paper presents results from three different `` analysis pipelines '' , each representing a complete search . while the pipelines analyzed the data independently , they began with a common selection of good - quality data and applied a common set of vetoes to reject identifiable artifacts . each pipeline was tuned to maximize the sensitivity to simulated gw signals while maintaining a fixed , low false alarm rate . the tuning of the pipelines , the choice of good data and the decision on the veto procedure were made before looking at potential candidates . no gw signal candidates were identified by any of the analysis pipelines with the chosen thresholds . in order to interpret this non - detection , we evaluate the sensitivity of each pipeline for simulated signals of various morphologies , randomly distributed over the sky and over time . as expected , there are some sensitivity differences among the pipelines , although the sensitivities rarely differ by more than a factor of 2 ( see section [ sec : simulations ] ) and no single pipeline performs best for all of the simulated signals considered . we combine the results of the pipelines to calculate upper limits on the rate of gw bursts as a function of signal morphology and strength . the rest of the paper is organized as follows : after specifying the periods of data , forming the first year of the s5 science run in sec . [ sec : ligos5run ] , sec . [ sec : s5detectors ] describes the state of the detectors during that period . section iv summarizes the elements of this gw burst search which are common to all of the analysis pipelines . the analysis pipelines themselves are detailed in sec . [ sec : algorithms ] and appendices c , d and e. section [ sec : tuning ] describes how each pipeline is tuned , while sec . [ sec : simulations ] presents the sensitivity curves for simulated signals and sec . [ sec : systematics ] describes the systematic errors in these sensitivity curves . the results of the search are given in sec . [ sec : results ] , and some discussion including estimates of the astrophysical reach for burst candidates in sec . [ sec : summaries ] .

we present the results obtained from an all - sky search for gravitational - wave ( gw ) bursts in the 642000hz frequency range in data collected by the ligo detectors during the first year ( november 2005 november 2006 ) of their fifth science run.the total analyzed livetime was 268.6 days . multiple hierarchical data analysis methods were invoked in this search .

we present the results obtained from an all - sky search for gravitational - wave ( gw ) bursts in the 642000hz frequency range in data collected by the ligo detectors during the first year ( november 2005 november 2006 ) of their fifth science run.the total analyzed livetime was 268.6 days . multiple hierarchical data analysis methods were invoked in this search . the overall sensitivity expressed in terms of the root - sum - square ( rss ) strain amplitude for gravitational - wave bursts with various morphologies was in the range of to a few . no gw signals were observed and a frequentist upper limit of 3.75 events per year on the rate of strong gw bursts was placed at the 90% confidence level . as in our previous searches , we also combined this rate limit with the detection efficiency for selected waveform morphologies to obtain event rate versus strength exclusion curves . in sensitivity , these exclusion curves are the most stringent to date .

cond-mat0505420

i

interactions between localized defects which are mediated by the continuum they are embedded in , play an important role in many areas of physics . typical examples are the rkky interaction between spins in a fermi liquid or the interaction between vortices in superfluids . in the present work , we discuss interactions between impurities in 1d quantum liquids . this study is motivated by the recent realization of strongly interacting `` atomic quantum wires '' with ultracold gases of both bosonic @xcite and fermionic atoms @xcite and the proposal @xcite , that single atoms in optical traps which are embedded in a superfluid reservoir allow to realize an atomic analog of a quantum dot with a tunable coupling to the environment . such quantum dots may be used to store qubits , which , under certain conditions , can be completely decoupled from their environment . arrays of these dots thus appear as ideal candidates for quantum information processing . it is therefore of considerable interest to study the induced interactions of such dots , mediated by the environment they are embedded in . similar questions arise also for quantum dots in solid state realizations , e.g. in carbon nanotubes @xcite , where the interaction is mediated by electrons in the intervening wire . quite generally , for both bosons and fermions , the low energy properties of a gapless 1d quantum liquid are described by the so called luttinger liquid ( ll ) phenomenology @xcite : the effective theory is a hydrodynamic energy functional characterized by the velocity of sound @xmath0 and the luttinger interaction parameter @xmath1 . in particular , for fermions , @xmath2 corresponds to the non - interacting case , while @xmath3 for repulsion . for repulsive bosons , in turn , one has @xmath4 , with @xmath5 in the limit of weak interactions , where a gross - pitaevskii or bogoliubov approximation applies . as shown by kane and fisher @xcite ( see also @xcite for a recent discussion ) , the interaction of a single impurity with a ll depends crucially on the value of @xmath1 : for @xmath4 , the impurity is irrelevant for the low energy properties . a 1d bose liquid is therefore effectively superfluid , although there is no true condensate @xcite . for @xmath3 the impurity changes the ground state of the liquid in a non - perturbative way , effectively cutting it into two disconnected parts . in this case , we will see that the induced interaction between two impurities is essentially a casimir - like effect . indeed , at low energies , two impurities at distance @xmath6 define a box with reflecting boundary conditions for the phonon modes of the quantum liquid , which leads to an attractive casimir interaction energy proportional to @xmath7 with @xmath0 the sound velocity . the case @xmath2 is marginal and corresponds to a non - interacting fermi gas in 1d or - equivalently - , a system of hard core bosons , the tonks - girardeau gas @xcite . in the following we will study the interactions mediated by the 1d quantum liquid between two impurities for the various cases , including fermions with spin . we focus our analysis on the case of _ static _ impurities , while the situation of a slow time dependence , relevant for atomic quantum dots , where the interactions depend on the internal states is only discussed qualitatively at the end of the paper .

the friedel oscillations of the interacting system are replaced , at long distances , by a universal casimir - type interaction which depends only on the sound velocity and decays inversely with the separation . the casimir - type interaction between localized perturbations embedded in a fermionic environment gives rise to a long range coupling between quantum dots in ultracold fermi gases , opening a novel alternative to couple qubits with neutral atoms .

we discuss the effective interactions between two localized perturbations in one - dimensional ( 1d ) quantum liquids . for non - interacting fermions , the interactions exhibit friedel oscillations , giving rise to a rkky - type interaction familiar from impurity spins in metals . in the interacting case , at low energies , a luttinger liquid description applies . in the case of repulsive fermions , the friedel oscillations of the interacting system are replaced , at long distances , by a universal casimir - type interaction which depends only on the sound velocity and decays inversely with the separation . the casimir - type interaction between localized perturbations embedded in a fermionic environment gives rise to a long range coupling between quantum dots in ultracold fermi gases , opening a novel alternative to couple qubits with neutral atoms . we also briefly discuss the case of bosonic quantum liquids in which the interaction between weak impurities turns out to be short ranged , decaying exponentially on the scale of the healing length .

astro-ph0309292

i

the spin down luminosity of a rotating pulsar powers the emission of an associated synchrotron nebula by driving an initially poynting flux - dominated wind ( the poynting - to - matter energy flux ratio is @xmath4 ) that flows along the open magnetic field lines . the density of the outflowing matter is enhanced by pair - creating cascades near the source and the resulting number density is sufficiently large to screen the electric field along the flow and provide the necessary charge and current densities for ideal magnetohydrodynamics ( mhd ) to hold . at a distance @xmath5 cm specifically for the crab the ram pressure of the wind equals the total nebula pressure and the wind terminates in a standing shock @xcite . the `` wisps '' ( which appear at distance @xmath6 from the center ) are an observational signature of the coupling between the fast pulsar wind and the slowly expanding nebula @xcite . by applying ideal mhd in the nebula , the matching shock conditions require that the pulsar wind has become completely matter - dominated at the position of the shock ; the @xmath2 function should be as low as @xmath7 just upstream of the termination shock ( kennel & coroniti 1984a , b ) , and the question arises as to how this transition from high to low values of @xmath2 can happen , the so - called @xmath2 problem . we note , however , that the very existence of the shock has been questioned by @xcite , who argues that no shock is necessary and that the observed emission is created by current dissipation in a poynting flux - dominated wind . furthermore , even if a shock indeed terminates the pulsar wind , abandoning the axisymmetry or the ideal mhd in the nebula results in undetermined @xmath8 @xcite . even so , @xmath8 could in general be small , and the interpretation of the wisps as ion driven compressions @xcite , as well as the fitting of the observed nebula emission @xcite , provide additional support for the value @xmath9 . the crab - pulsar / nebula is the first and most analyzed object of this kind . recent x - ray observations have shown that there exist other objects with common characteristics [ e.g. , the vela pulsar @xcite , the nebulae associated with psr b1509 - 58 @xcite , and psr b1957 + 20 @xcite ] . the study of approximately monopole magnetic field geometries that are extremely inefficient accelerators gave the impression to the community that ideal mhd is in general unable to solve the @xmath2 problem , and many authors refer to the `` @xmath2 parameter '' and not to the `` @xmath2 _ function _ '' . moreover , several alternative ( non - ideal mhd ) attempts ( see , e.g. , @xcite for a review ) gave unsatisfactory results , and the puzzle remains unsolved for almost three decades . however , there are in the literature @xmath10 self - similar , ideal mhd solutions that start with @xmath4 near the origin of the flow and reach @xmath11 ( @xcite ; @xcite ) , or even more efficient accelerators with @xmath12 @xcite , or @xmath13 @xcite . ( actually , @xmath10 self - similar are the only for the present known _ exact _ solutions of relativistic mhd in the sense that they satisfy the momentum equation in both directions : along the flow _ and _ in the transfield direction . ) we note in this connection that the main acceleration mechanism is not the centrifugal , but the _ magnetic_. the former may be important in the sub - alfvnic regime of a disk - wind and results in poloidal velocity of the order of the initial keplerian speed , while the latter caused by the magnetic pressure - gradient force results in much higher velocity that depends on the initial poynting - to - mass flux ratio @xmath14 . employing the @xmath2 function we may write @xmath15 , thus the maximum final lorentz factor is attained in solutions with @xmath16 . in this paper we show that ideal mhd can account for the full acceleration from @xmath17 to @xmath18 , _ if _ the boundary condition @xmath19 at the base of the ideal mhd accelerating regime is satisfied ( here @xmath20 is the poloidal current , @xmath21 the poloidal magnetic flux function , and @xmath22 the field angular velocity ) . the transfield force - balance equation is the most important in determining the acceleration by means of controlling the field line shape and consequently how fast the quantity @xmath23 decreases ( here @xmath24 is the cylindrical distance and @xmath25 the poloidal magnetic field ) . in the main part of the acceleration the transfield component of the electromagnetic force equals the poloidal centrifugal force that is proportional to the curvature of the poloidal field lines @xmath26 . if this is still the case after the end of the acceleration in the far - asymptotic regime where @xmath27 the electromagnetic force exactly vanishes yielding the solvability condition at infinity ( @xcite ; @xcite ) . however , if during the acceleration phase sufficiently small @xmath2 values are reached , the azimuthal centrifugal force the other part of the inertial force becomes important . in this regime it is the difference between poloidal and azimuthal centrifugal forces that equals the much smaller electromagnetic force in the transfield direction , and no solvability condition can be derived . we organize the paper as follows . in [ mhd ] we present the ideal mhd formalism focusing on the super - alfvnic asymptotic regime where the puzzling transition from @xmath28 to @xmath29 happens . in [ zss ] we derive a novel @xmath30 self - similar class of solutions describing the polar region of the wind and present the results of the integration . in [ genanalysis ] we analyze the asymptotic shape of the flow in relation to the acceleration , demonstrating that the same results are expected in non - self - similar cases as well . in [ equatorialwind ] we discuss the problem of the pulsar magnetosphere , pointing out the problems that the force - free picture faces , and suggesting qualitatively a scenario that seems plausible for creating an equatorial wind with the appropriate conditions for efficient acceleration from high to low-@xmath2 values satisfied . a summary follows in [ conclusions ] .

using relativistic , steady , axisymmetric , ideal magnetohydrodynamics ( mhd ) we analyze the super - alfvnic regime of a pulsar wind by means of solving the momentum equation along the flow as well as in the transfield direction . employing a self - similar model , we demonstrate that ideal mhd can account for the full acceleration from high ( ) to low ( ) values of , the poynting - to - matter energy flux ratio . we discuss the kind of the boundary conditions near the base of the ideal mhd regime that are necessary in order to have the required transition from high to low in realistic distances , and argue that this is a likely case for an equatorial wind . examining the mhd asymptotics in general

using relativistic , steady , axisymmetric , ideal magnetohydrodynamics ( mhd ) we analyze the super - alfvnic regime of a pulsar wind by means of solving the momentum equation along the flow as well as in the transfield direction . employing a self - similar model , we demonstrate that ideal mhd can account for the full acceleration from high ( ) to low ( ) values of , the poynting - to - matter energy flux ratio . the solutions also show a transition from a current - carrying to a return - current regime , partly satisfying the current - closure condition . we discuss the kind of the boundary conditions near the base of the ideal mhd regime that are necessary in order to have the required transition from high to low in realistic distances , and argue that this is a likely case for an equatorial wind . examining the mhd asymptotics in general , we extend the analysis of heyvaerts & norman and chiueh , li , & begelman by including two new elements : classes of quasi - conical and parabolic field line shapes that do not preclude an efficient and much faster than logarithmic acceleration , and the transition after which the centrifugal forces ( poloidal and azimuthal ) are the dominant terms in the transfield force - balance equation .

1402.4813

i

how do coefficients of a wave - function change at continuous quantum phase transitions ? in a given basis , this question can be addressed by monitoring the behavior of ( inverse ) participation ratios , which have a long history _ e.g. _ in localization physics @xcite . more recently , the study of related quantities such as shannon - rnyi entropies ( which quantify the localization of the wave - function in a given basis ) in _ many - body _ problems has revealed an intriguing aspect : subleading terms in the finite - size scaling of these quantities appear to carry universal information , characteristic of the physics contained in the ground - state wave - function@xcite . for instance , they can characterize the presence of broken continuous or discrete symmetry breaking in the ground - state , as well as information on the universality class of continuous phase transitions . most previous studies@xcite on this topic focused on one - dimensional quantum systems , where both analytical and numerical studies are easiest . in particular , dealing with the exponentially growing size of the hilbert space of many - body problems , while maintaining a large enough total system size to study finite - size dependence , is a hurdle to surmount . recently , we have introduced in ref . convenient numerical methods to study the shannon - rnyi entropies of many - body systems through a quantum monte carlo ( qmc ) sampling of the ground - state wave function . this method allows studies of much larger systems than previously accessible in numerical calculations , which is necessary for the analysis of universal behavior at continuous quantum phase transitions where physical correlation lengths diverge . here , we will study this problem for a non - trivial , yet well - understood quantum phase transition in two - dimensional quantum magnetism : the transition between a nel antiferromagnet and a quantum paramagnet in two @xmath8 quantum spin heisenberg models with varying antiferromagnetic couplings , namely two - dimensional coupled dimers and plaquettes ( see fig . [ fig : lattices ] ) . the variation of the ratio of two exchange couplings @xmath9 allows to couple isolated paramagnetic units ( at @xmath10 ) to form a two - dimensional antiferromagnet ( at @xmath11 ) which spontaneously breaks @xmath2 symmetry at zero temperature . a quantum critical point at @xmath12 in the 3d @xmath1 universality class@xcite separates the quantum disordered and nel ordered phases . the first part of the paper ( sec . [ sec : sr ] ) is devoted to the study of the behavior of subleading terms in the sr entropies of the ground - state of heisenberg magnets . given a density matrix @xmath13 , the sr entropies are defined as : @xmath14 where @xmath15 are states of the computational basis in which sr entropies are calculated . note that the choice of the natural logarithm ( base @xmath16 ) fixes the units of sr entropies to `` nats '' . we will first consider in sec . [ sec : srfull ] the sr entropy of the full system composed of @xmath17 interacting @xmath18 spins on a square lattice , that is choosing @xmath19 in eq . to be the full density matrix @xmath20 of the ground state @xmath21 . sr entropies are generally found to have a leading behavior which is extensive@xcite @xmath22 where the pre - factor @xmath23 ( for spin @xmath0 systems ) depends on details of the model ( @xmath24 in that case ) . in the @xmath7 basis considered throughout this work , we naturally expect @xmath25 to be ` small ' in the nel phase , and ` large ' in the quantum disordered phase . this is easily understood by considering the limit @xmath26 , where @xmath27 . here , latexmath:[$\max(\rho_{ii})=\max_{i } maximal coefficient of the groundstate wave - function expanded in the @xmath7 basis . for antiferromagnetic systems , this is the coefficient of the nel state @xmath29 , which is expected to be much larger in the antiferromagnetically ordered phase than in the disordered phase . in the antiferromagnetic phase , the groundstate spontaneously breaks the continuous @xmath2 symmetry and our previous work @xcite showed that this is reflected in a subleading logarithmic correction : @xmath30 . in the disordered phase , no symmetry is broken and the subleading term is in general a universal constant ( expected to be zero in the paramagnetic phase discussed in this paper ) . for this first part of the paper ( sec . [ sec : sr ] ) , we will consider the case @xmath26 essentially for practical purposes . indeed , @xmath31 is simpler to obtain numerically ( within our qmc simulations ) and more importantly , the leading term prefactor @xmath32 is smaller ( @xmath33 for all finite @xmath34 ) which ensures that we can reach larger system sizes . despite these facts , simulations of the sr entropy of full two dimensional systems are limited to relatively small sizes ( up to @xmath35 ) close to the quantum phase transition , as the prefactor @xmath32 is still quite large in this region ( see also the discussion in appendix [ sec : mc ] ) . to circumvent this , we next consider in sec . [ sec : srline ] the scaling of the sr entropy of a subsystem , composed of a single line of size @xmath3 ( the geometry of the subsystem is defined in fig . [ fig : lattices ] ) embedded in a periodic @xmath4 torus . subsystem sr entropies are defined in analogy to eq . ( [ eq : sr - entropies ] ) , except that we now consider the _ reduced _ density matrix @xmath36 of a subsystem @xmath37 which is obtained by performing a partial trace over the rest of the system @xmath38 : @xmath39 with @xmath40 , _ i.e. _ where the basis state @xmath41 is a tensor product state of subsystems basis states @xmath42 and @xmath43 . the rationale for choosing a line shaped subsystem is two - fold : first , we physically expect that the sr entropy of the line also contains the information about antiferromagnetic ordering ( since for instance the correlation function @xmath44 along the line is defined in terms of diagonal elements of the reduced density matrix ) . second , the sr entropy of the line has a leading term @xmath45 , and therefore takes much smaller values than for the full - system sr entropy for the same value of @xmath3 ( @xmath3 scaling versus @xmath46 scaling ) . this leads to a better accuracy and allows to reach much larger linear sizes @xmath3 in our qmc simulations . our results indicate that the sr entropy of the line also shows a sub - leading @xmath47 term in the nel phase , and a constant term in the disordered phase which turns out to vanish ( see below ) . quite interestingly , the subleading term right at the quantum phase transition is a constant @xmath48 , which appears to be identical ( within error bars ) for the two models studied . this suggest that this constant is characteristic of the 3d @xmath1 universality class to which both quantum phase transitions belong . further simulations of the finite - temperature ordering phase transition of the simple cubic @xmath8 heisenberg model ( also in the same @xmath1 universality class ) support this conjecture for antiferromagnetic interactions . we also expect a universal value @xmath49 for the full system , even though the limited accuracy ( due to the large value of @xmath32 ) of our simulations does not allow to prove this . for the verification of the universality of @xmath50 , we have first performed extensive calculations of the spin stiffness in order to extract the best estimate for the value of the transition temperature , @xmath51 , in agreement with ref . . the sr entropies are global averages of all coefficients of the wave - function and their scaling with the ( sub- ) system size thus capture correctly phases and phase transitions . it is interesting to ask whether _ each individual _ coefficient ( or reduced density matrix diagonal element in the case of subsystems ) also `` sees '' the quantum phase transition when @xmath52 is varied this independently of their scaling with system size , as exemplified with the maximal diagonal entry of the ( reduced ) density matrix , governing @xmath31 ( @xmath53 ) . motivated by this question , we study in the second part of the paper ( sec . [ sec : ps ] ) the behavior of each diagonal element of the reduced density matrix @xmath54 for a line subsystem across the transition . in analogy with the entanglement spectrum @xcite , we define the `` participation spectrum '' as the set of pseudo - energies @xmath55 . the participation spectrum develops into well - defined bands , which can be classified according to the magnetization and the number of ferromagnetic domain - walls separating segments having different nel line configurations ( @xmath56 or @xmath57 . identifying the lowest - lying states in this spectrum allows to understand the quantum phase transition in terms of an effective repulsion between such domain - walls . even though the participation spectra appear to differ at first glance in the quantum disordered phases of the two studied models , we find that this can be understood easily by classifying states according to the number of strong or weak domain walls ( this notion is dictated by the local physics of one of the two models considered ) . a striking outcome of this analysis is that _ all _ individual levels ( even corresponding to assumedly irrelevant states such as the fully polarized state ) harbor signs of the quantum phase transition , as exemplified for instance by an inflection point ( with respect to @xmath52 ) for almost all @xmath58 . we analyze this in detail for the most probable state . another interesting sign of the quantum phase transition is revealed by the study of the finite - size behavior of the width of the lowest - lying bands . we will finally conclude in sec . [ sec : conclusion ] on the implications of our results while the appendices contain specific details of the qmc procedure used ( appendix [ sec : mc ] ) , as well as exact results in the limit of @xmath59 for reference ( appendix [ sec : exact ] ) . let us begin our paper ( sec . [ sec : model ] ) by providing useful details on the models studied as well as on the finite - size scaling analysis .

universal features in the scalings of shannon - rnyi entropies of many - body groundstates are studied for interacting spin- systems across ( 2 + 1 ) dimensional critical points , using quantum monte carlo simulations on dimerized and plaquettized heisenberg models on the square lattice . considering both full systems and line shaped subsystems , symmetry breaking on the nel ordered side of the transition is characterized by the presence of a logarithmic term in the scaling of shannon - rnyi entropies , which is absent in the disordered gapped phase . additionally , the phases and phase transition can be detected in several features of the participation spectrum , consisting of the diagonal elements of the reduced density matrix of the line subsystem . in particular the nel ordering transition can be simply understood in the basis by a confinement mechanism of ferromagnetic domain walls .

universal features in the scalings of shannon - rnyi entropies of many - body groundstates are studied for interacting spin- systems across ( 2 + 1 ) dimensional critical points , using quantum monte carlo simulations on dimerized and plaquettized heisenberg models on the square lattice . considering both full systems and line shaped subsystems , symmetry breaking on the nel ordered side of the transition is characterized by the presence of a logarithmic term in the scaling of shannon - rnyi entropies , which is absent in the disordered gapped phase . such a difference in the scalings allows to capture the quantum critical point using shannon - rnyi entropies for line shaped subsystems of length embedded in tori , as the smaller subsystem entropies are numerically accessible to much higher precision than for the full system . most interestingly , at the quantum phase transition an additive subleading constant emerges in the critical scaling of the line shannon - rnyi entropy . this number appears to be universal for 3d criticality , as confirmed for the finite - temperature transition in the 3d antiferromagnetic spin- heisenberg model . additionally , the phases and phase transition can be detected in several features of the participation spectrum , consisting of the diagonal elements of the reduced density matrix of the line subsystem . in particular the nel ordering transition can be simply understood in the basis by a confinement mechanism of ferromagnetic domain walls .

1606.04889

i

on september 14 , 2015 the advanced ligo interferometer ( aligo ) detected the event gw150914 , which has been interpreted as the first direct observation of gravitational waves ( gws ) from the inspiral and merger of a pair of black holes ( bhs ; * ? ? ? * ) . the event gw150914 was produced by two bhs with masses of @xmath4 and @xmath5 ( in the source frame ) , at a redshift @xmath6 assuming standard cosmology @xcite . the detection of the gravitational - wave signal of gw150914 has provided the first direct evidence that black holes with mass @xmath7 exist and that they can reside in binary systems . assuming that the source - frame binary bh merger rate is constant within the volume in which gw150914 could have been detected , and that gw150914 is representative of the underlying binary bh population , the bh - bh merger rate is inferred to be @xmath8 in the comoving frame @xcite . @xcite reviews various channels for the formation of bh binaries that can coalesce within a hubble time thus becoming potentially detectable by aligo . these include dynamical formation in dense stellar environments ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , and isolated binary evolution ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? while most of the former literature focused on bh binaries forming in globular clusters ( gcs ) , little attention has been devoted to the formation of such binaries in nuclear star clusters ( nscs ) . yet nscs have total stellar masses that are comparable to the whole stellar mass of the gc system for the galaxy , at least in the milky way , and are the densest and most massive star clusters observed in the local universe ( e.g. , * ? ? ? * ; * ? ? ? * ) , representing therefore a natural environment where dynamical processes can efficiently lead to the formation of bh binaries . in this paper we consider the dynamical formation scenario , and explore the contribution to the bh binary merger rate from nscs . in a stellar cluster , stellar mass bhs formed from the death of massive stars , quickly segregate to the center through dynamical friction @xcite . in these high - density environments , bhs can efficiently interact with each other and dynamically form new binaries . such binaries will subsequently harden through three - body interactions @xcite . via such dynamical processes , gcs can produce a significant population of bh binaries that , after being ejected from the cluster , will be able to merge in the local universe ( e.g. , * ? ? ? over the last years our understanding of the evolution of bhs in star clusters has improved considerably thanks to numerical efforts ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) . however , the role of nscs and their contribution to the bh binary merger rate in the local universe remains quite obscure . as discussed in what follows , nscs differ from lower mass gcs in at least three important ways , each of these can significantly enhance the bh merger rate and affect the properties of the merging binaries in nscs . \(i ) _ nscs retain most of their bhs_. while natal kicks can easily eject bhs from gcs , the natal kick magnitudes are unlikely to be large enough to eject a considerable number of bhs from nscs given the large escape speed in these latter systems . whether dynamically formed bh binaries will merge , and whether the merger will occur inside the cluster also depends on the cluster escape speed . the low escape speed ( @xmath9 ) from low mass clusters ( @xmath10 ) , implies that most bh binaries are ejected early after their formation with an orbital semi - major axis which is typically too large for gw emission to become efficient and drive the merger of the binary in one hubble time . the vast majority of dynamically formed bh binaries in gcs are also kicked out before merging , but they are able to merge in the local universe ( e.g. , * ? ? ? * ) . as argued by @xcite given that nscs have escape speeds that are several times those of globulars , they can retain most of their bh binaries . moreover , as we show below , even when accounting for the recoil kick due to anisotropic emission of gw radiation a large fraction of merger products is likely to be retained inside nscs . \(ii ) _ nscs contain young stellar populations . _ the common finding emerging from spectroscopic surveys is that nscs are characterized by complex star formation histories with a mixture of morphological components and different stellar populations spanning a wide range of characteristic ages ( from 10 myr to 10 gyr ) and metallicities @xcite . this implies that unlike gcs , nscs can still form fresh bhs and bh binaries at the present time . the presence of significant additional gas not found in old globular clusters could also result in differences in the black hole mass distribution , as well as the dynamics of the underlying black hole population @xcite . \(iii ) _ nscs reside at the center of galaxies . _ therefore , unlike gcs , nscs are not isolated . in time , newly formed star clusters could migrate by dynamical friction from the galaxy into the nsc itself replenishing bhs that have been kicked out by three - body processes or by gw recoil kicks . the orbital decay of massive star clusters through dynamical friction constitutes an additional source which can repopulate the bh binary population in the nuclei of galaxies @xcite . in this paper we study the dynamical formation of bh binary mergers in nscs , with particular focus on nscs which do not host a central massive black hole ( mbh ) which we define here as bhs having a mass of @xmath11 . our cluster models are based on a semi - analytical approach which describes the formation and evolution of bh binaries in static cluster models . although necessarily approximated , these models are shown to give reasonable results when compared to recent monte carlo models of massive gcs @xcite and previous bh binary merger rate estimates from nscs @xcite . we stress that although the mbh occupation fraction in nscs is largely unconstrained observationally , it has been long recognized that some nscs do not have mbhs ( e.g. , * ? ? ? * ; * ? ? ? we note that nscs with mbhs are very different , dynamically , than nscs without . if a mbh is present the velocity dispersion keeps growing towards the mbh , which means that no binary will be hard all the way to the center . here we make use of the semi - analytical galaxy formation models presented in @xcite to predict the occupation fraction of mbhs in nscs and the nsc initial mass function , which combined with the results of our cluster models allows an estimate of the aligo detection rate and properties of bh mergers forming in nscs . our results suggest that the bh merger event rate from nscs is substantial , with several tens of events per year detectable with aligo . in addition , we propose a new dynamical pathway to the formation of high mass bh binary mergers similar to gw150914 . this merger path is exclusive to nscs and to the most massive gcs . due to their large escape speeds , such massive clusters can keep a large fraction of their bh merger remnants while also evolving rapidly enough that the holes can sink back to the central regions where they can form a new binary , which will subsequently harden and merge . we find that this process can repeat several times and produce bh mergers of several tens of solar masses and up to a few hundreds of solar masses , without the need of invoking extremely low metallicity environments . the paper is organized as follows . in sections [ 3rec ] we discuss the processes leading to the formation and merger of bh binaries in the high density cores of gcs and nscs , focusing on the processes that can lead to the full ejection of bhs . in section [ sam ] we describe our semi - analytical approach and derive the expected merger rate of bh binaries in nscs . in section [ disc ] we discuss the implications of our results including the aligo detection rate and the contribution to the bh merger rate from nscs hosting central mbhs . finally , we summarize the main results of our study in section [ summ ] .

motivated by the recent detection of gravitational waves from the black hole binary merger gw150914 , we study the dynamical evolution of ( stellar mass ) black holes in galactic nuclei where massive star clusters reside . with masses of and sizes of only a few parsecs , nuclear star clusters are the densest stellar systems observed in the local universe and represent a robust environment where black hole binaries can dynamically form , harden and merge . we show that due to their large escape speeds , nuclear star clusters can retain a large fraction of their merger remnants . successive mergers can then lead to significant growth and produce black hole mergers of several tens of solar masses similar to gw150914 and up to a few hundreds of solar masses , without the need of invoking extremely low metallicity environments . we use a semi - analytical approach to describe the dynamics of black holes in massive star clusters . our models give a black hole binary merger rate of from nuclear star clusters , implying up to a few tens of possible detections per year with advanced ligo .

motivated by the recent detection of gravitational waves from the black hole binary merger gw150914 , we study the dynamical evolution of ( stellar mass ) black holes in galactic nuclei where massive star clusters reside . with masses of and sizes of only a few parsecs , nuclear star clusters are the densest stellar systems observed in the local universe and represent a robust environment where black hole binaries can dynamically form , harden and merge . we show that due to their large escape speeds , nuclear star clusters can retain a large fraction of their merger remnants . successive mergers can then lead to significant growth and produce black hole mergers of several tens of solar masses similar to gw150914 and up to a few hundreds of solar masses , without the need of invoking extremely low metallicity environments . we use a semi - analytical approach to describe the dynamics of black holes in massive star clusters . our models give a black hole binary merger rate of from nuclear star clusters , implying up to a few tens of possible detections per year with advanced ligo . moreover , we find a local merger rate of for high mass black hole binaries similar to gw150914 ; a merger rate comparable to that of similar binaries assembled dynamically in globular clusters . finally , we show that if all black holes receive high natal kicks , , then nuclear star clusters will dominate the local merger rate of binary black holes compared to either globular clusters or isolated binary evolution . # 1 # 1

astro-ph0203188

r

figure [ fig : comp ] shows a plot comparing the heliocentric radial velocities derived from our new optical rotation curves with the values derived from global spectra by fouqu et al . ( 1990 ) and matthews et al . overall the agreement is excellent . this agreement suggests that most extreme late - type spirals seem to have well - defined centers in spite of their often diffuse stellar disks and shallow central potentials . consequently , this can offer an additional means of distinguishing extreme late - type spirals from true irregular galaxies . in our sample we have only 6 instances where we see a discrepancy of more than @xmath210 between the radial velocities derived from optical versus radio measurements . because of the small formal measurement errors on both the optical and radial velocities ( @xmath2910 and @xmath295 , respectively ) , it is possible that in at least some of these cases , these discrepencies may a consequence of true offsets between the centroid of the global profile and the center of the galaxy defined by the optical continuum . similar offsets have been reported in other moderate - to - low - mass , late - type spirals ( colin & athanassoula 1981 ; minniti , olszewski , & reike 1993 ; rownd , dickey , & helou 1994 ) . in 4 of the 6 galaxies where @xmath30 and @xmath31 differ by more than 10 , asymmetries are observed in the global profiles ( see figure [ fig : pv ] ; section [ asymm ] ) . together these two trends may hint that these could be galaxies where the stellar disk is in libration about the minimum of the or dark matter potential ( kornreich et al . 1998 ; see also levine & sparke 1998 ; noordermeer , sparke , & levine 2001 ) . levine & sparke ( 1998 ) and noordermeer et al . ( 2001 ) have shown through numerical simulations and modelling that such configurations can reproduce the lopsidedness observed in many extreme late - type spirals ( see also below ) . nonetheless , as we discuss below , approximately one - third of our sample appears to exhibit kinematic lopsideness , hence in the majority of lopsided galaxies , the peak of the stellar density correlates surprisingly well with the centroid of the global profile . the centroid of the global profile thus generally seems to be a good indicator of the location of the minimum of the disk potential , even in most asymmetric galaxies . this would seem to argue that the overall potential of the galaxies ( established mainly by the dark matter halo in the small systems considered here ) are symmetric on large scales , even in cases where asymmetries in the visible matter or velocity field are observed ( cf . rix & zaritsky 1995 ; jog 1999 ) . the position - velocity ( p - v ) curves derived from our final spectra are presented in figure [ fig : pv ] . when available , we plot next to the h@xmath1 p - v curves the corresponding high resolution global spectra from matthews et al . parameters measured from the optical data , including systemic velocities and the peak measured rotational velocities , are presented in table 2 along with photometric and global parameters from the literature . from figure [ fig : pv ] and table 2 it can be seen that among the galaxies where @xmath32 ( i.e. , cases where the galaxy s major axis and the spectrograph slit were well - aligned ) , the disk rotation velocities measured in the plane of the sky from our new optical data ( @xmath33 ) agree to within measurement errors with those derived from global data ( @xmath34 ) about half of the time . in the remaining cases , regions were not observable to sufficiently large radii to reach the peak of the rotation curves in our longslit measurements of these optically faint galaxies . for the 15 galaxies in our sample with @xmath35 and @xmath32 , we derived deprojected rotation curves along the disk major axis ( figure [ fig : rc ] ) . the disks were assumed to be in circular rotation , and the measured heliocentric radial velocities at each point were projected onto the plane of the galaxy using the relations given by rubin , ford , & thonnard ( 1980 ) to correct for disk inclination and small position angle misalignments . in cases where the systemic velocities derived from global spectra differed from our new optically derived values , we used whichever value minimized the asymmetry of the folded rotation curve . distances for the galaxies were adopted from mg97 . we see from figures [ fig : pv ] & [ fig : rc ] that most of our sample galaxies show a leisurely rise in rotational velocity with increasing radius , and many have rotation profiles that continue to rise to the last measured point . similar rotation curve shapes are frequently seen among the extreme late - type spiral rotation curves measured by other workers using the h@xmath1 emission line ( e.g. , goad & roberts 1981 ; karachentsev 1991 ; makarov , burenkov , & tyurina 1999 ; swaters 1999 ; dalcanton & bernstein 2000 ; mcgaugh , rubin , & de blok 2001 ) and have become well - established as the hallmark of small , dark matter - dominated disk galaxies . these are in stark contrast to giant spirals , where rotation curves typically rise rapidly to @xmath36 within the inner portion of the stellar disk ( cf . casertano & van gorkom 1991 ) . in 3 of the most extreme cases ( eso 418 - 008 ; eso 504 - 017 ; eso 440 - 049 ) , we can partially attribute the shallow velocity gradients in our observed p - v plots to position angle misalignments between the spectrograph slit and the galaxy major axis ( @xmath37 ; see table 1 ) . however , in all other instances , the slow rise of the rotation velocity as a function of @xmath38 appears to be real , and thus be indicative of low matter densities within the inner disks of these galaxies . for example , eso 358 - 060 has a particularly shallow rotation curve in spite of being nearly edge - on ( @xmath39=85@xmath40 ) . this galaxy has a very low deprojected central surface brightness [ @xmath4125.5 mag arcsec@xmath8 ] and would likely be nearly invisible if seen close to face - on in an optical broadband survey image . as demonstrated by matthews & wood ( 2001 ) , such a shallow rotation curve can not be explained solely by projection effects or internal extinction , even in edge - on systems . in only a few of our sample galaxies do we see a clear turnover or flattening of the optical p - v curve on both the approaching and receding sides : eso 482 - 005 , eso 504 - 025 , eso 440 - 049 , eso 443 - 079 . these galaxies are some of the `` earlier '' hubble type objects in our sample ( sc - sd ) , and include some of the sample galaxies with the most clearly - defined spiral structure . in some other cases , we see an apparent turnover on only one side of the p - v curve ( eso358 - 020 ; eso 425 - 008 ; eso 438 - 005 ; eso 380 - 025 ; eso 508 - 034 ; eso 444 - 033 ; see also section [ asymm ] ) . we find that even in instances where a turnover or flattening is seen , our observed p - v curves rarely extend significantly beyond this turnover . moreover , while the sc - scd galaxies in our sample seem more prone to exhibiting flattening of their p - v curves , we otherwise see no absolute correlation between hubble type , galaxy morphology , or luminosity and the p - v or rotation curve shape in our sample . for example , eso 504 - 025 and eso 358 - 020 both have @xmath43 - 17.5 and @xmath44 , but have very different inner rotation curve shapes and amplitudes . at the same time , we also see cases where optically rather dissimilar galaxies ( e.g. , eso 380 - 025 and eso 508 - 034 ) have similar rotation curve shapes and amplitudes . these rotation curves signatures may hold important clues as to the evolutionary histories of these galaxies for example , the possibility that morphological tranformations may occur in late - type disk galaxies as a result of viscous evolution , interactions , or tidally - induced starbursts ( e.g. , gallagher & matthews 2001 ; noguchi 2001 ; matthews & uson 2002 ) . rotation curves that do not flatten within the optical galaxy imply that the bulk of the stellar disk is in solid body rotation . it has long been known that such rotation curves are common in gas - rich dirr galaxies ( e.g. , carignan & freeman 1988 ; carignan & puche 1990 ; ct et al . 1991 ; casertano & van gorkom 1991 ; ct , carignan , & freeman 2000 ) . however , while most such galaxies are still predominantly rotationally supported , many of the dirrs with apparent solid - body rotation curves also have single - peaked global spectra , implying that solid body rotation persists to the outermost observable regions of the gas disk ( e.g. , skillman 1996 ) . in contrast , most of the galaxies in our sample have _ double - peaked _ global profiles ( figure [ fig : pv ] ; see also fouqu et al . 1990 ; matthews et al . 1998 ) , which in turn implies that the outer rotation curve contains a flat or relatively flat region ( cf . giovanelli & haynes 1988 ) , although it may lie outside the stellar disk . data will clearly be needed to trace this portion of the disk rotation profiles in our present sample . it is evident from figures [ fig : pv ] & [ fig : rc ] that asymmetries are the rule rather than the exception for our extreme late - type spiral rotation profiles . many of the p - v plots and rotation curves show significant differences in their radial extents on the approaching and receding sides . often , the amplitudes of the two sides of the rotation curves also differ ( sometimes by tens of kilometers per second ) , and in some cases , the rotation curves show differing velocity gradients on the two sides of the galaxy . although there is frequently some uncertainty in defining the center of any given rotation curve , our sample nonetheless appears to contain some galaxies where the velocity differences between the approaching and receding sides are greater than 20% , in contrast to swaters et al . ( 1999 ) , who suggested that perhaps such significant ( kinematic ) asymmetries may not exist . based on statistical studies of high - quality global data , richter & sancisi ( 1994 ) and haynes ( 1998 ) found that profile asymmetries occur in approximately 50% of normal spirals . matthews et al . ( 1998 ) explored the frequency of profile asymmetries in extreme late - type spirals and found that the frequency of lopsidedness may be even higher among small late - type spirals than among giant galaxies . unfortunately , from asymmetries in the global profiles alone , it is not possible to assess whether these asymmetries arise from asymmetric gas distributions ( e.g. as a result of accretion events ; rix & zaritsky 1995 ; zaritsky & rix 1997 ) or from true kinematic lopsidedness , which in turn may indicate lopsidedness in the overall galaxy potential ( e.g. , schoenmakers , franx , & de zeeuw 1997 ; levine & sparke 1998 ; jog 1999 ) . our new optical spectra allow us to obtain additional insight into this question . six of the 17 galaxies in the present sample for which matthews et al . ( 1998 ) obtained high precision global profiles were catagorized by matthews et al . as having strong asymmetries ( eso 358 - 020 , eso 422 - 005 ; eso 502 - 016 ; eso 504 - 017 ; eso 380 - 025 ; eso 444 - 033 ) . in 5 out of 6 of these cases , we find the optical rotation curve to have a greater amplitude on the same side as the `` excess '' in the global profile . several of these cases also exhibit different velocity gradients on the approaching and receding sides of the disk . this latter effect is particularly pronounced in eso 422 - 005 and eso 444 - 033 . this suggests that these asymmetries result from true lopsidedness in the disk kinematics rather than non - symmetric matter densities ( see swaters et al . 1999 ; noordermeer et al . 2001 ) . among the 11 remaining galaxies in our sample whose profiles were analyzed by matthews et al . and not classified as strongly asymmetric , we see a significant rotation curve _ amplitude _ asymmetry in only one other case ( eso 358 - 015 ) , and a significant difference in the rates at which the two sides of the rotation curve rise in only eso 358 - 015 and eso 359 - 029 . strong asymmetries in the global profiles therefore appear to be good , although not perfect , predictors of lopsidedness in the disk kinematics . as noted above , we see additional galaxies in our sample whose rotation curves show asymmetries in terms of their _ extents _ on the two sides of the disk ( e.g. , eso 305 - 009 , eso 425 - 008 , eso 438 - 005 ) . however , in these latter cases , it is possible that these asymmetries arise from asymmetric matter distributions as opposed to true lopsided kinematics . we conclude that the results from our small sample are consistent with at least one - third of extreme late - type spirals exhibiting true kinematic asymmetries ( see also swaters et al . 1999 ) , and hence possibly asymmetries in their overall potentials ( but see section [ voptcomp ] ) and with approximately 50% of extreme late - type spirals exhibiting either kinematic _ or _ structural asymmetries . since all of the objects in our sample are field spirals , generally lying on the peripheries of loose groups or associations ( gallagher , littleton , & matthews 1995 ) , it would seem unlikely that the lopsided natures of all of our sample galaxies are exclusively the result of very recent interactions with other galaxies , although there may be some exceptions ( e.g. , matthews & uson 2002 ) . although asymmetries are common among disk galaxies covering a wide range of masses and luminosities ( e.g. , baldwin , lynden - bell , & sancisi 1980 ; richter & sancisi 1994 ; haynes et al . 1998 ) , our new data , and the findings of matthews et al . ( 1998 ) , hint that they are equally , or perhaps more common in low - mass spirals . indeed , based on the models of noordermeer et al . ( 2001 ) , pronounced asymmetries are more persistent in galaxy systems where the dark matter halo strongly dominates the potential , as is expected in typical extreme late - type spirals ( see also levine & sparke 1998 ) . using models with a disk lying off - center in a dark halo , noordermeer et al . produced model rotation curves whose shapes were very similar to some of those seen in the present sample , i.e. , showing differing slopes on the approaching and receding sides , and flattening of the rotation profile on one side only . swaters et al . ( 1999 ) noted similar signatures in the rotation curves of the two asymmetric extreme late - type spirals that they analyzed . five of the extreme late - type spirals in the present sample were noted by mg97 to possess a compact , semi - stellar nucleus ( eso 359 - 029 ; eso 358 - 015 ; eso 305 - 009 ; eso 504 - 025 ; eso 505 - 013 ; see also figure [ fig : elts ] ) . the nucleus of eso 359 - 029 was subsequently observed with the planetary camera 2 on the _ hubble space telescope _ and demonstrated by matthews et al . ( 1999 ) to be a true compact star cluster nucleus analogous to those at the centers of many brighter galaxies . subsequently , one additional galaxy in our sample ( eso 418 - 008 ) has also been found to possess a compact star cluster nucleus based on _ hst _ imaging ( bker et al . 2002 ; windhorst et al . although the formation mechanism for these compact nuclei at the centers of such diffuse galaxies with shallow central potentials remains a mystery , these types of `` naked '' nuclei are now known to be commonplace at the centers of late - type , pure disk spirals ( see also van den bergh 1995 ; phillips et al . 1996 ; bker et al . 2001,2002 ) . in our present sample , in five of the cases where the presence of a compact nuclear feature is seen in the ccd images of mg97 , we also see a signature of this nucleus in our spectroscopic data i.e . the p - v curves exhibit reversals , breaks , or disturbances near the location of the nucleus ( see figure [ fig : pv ] ) . this strongly suggests that in all of these cases , these nuclei are compact , massive star clusters rather than simply small nuclear regions . if we assume that the ionized gas surrounding these nuclei is in keplerian rotation , we can make very rough estimates of their masses from our present data @xmath45 , where @xmath46 is the gravitational constant , @xmath38 is the galactocentric distance along the major axis , and @xmath47 is the orbital semi - amplitude of the material orbiting the nucleus in the reference frame of the disk , after correction for inclination . because the velocity and spatial resolution of our data are rather coarse relative to the amplitudes and spatial extents of these central rotation curve features , and because it is unclear whether the nuclear disk material will share the same inclination as the main disk of the galaxy , these calculations are necessarily very crude . nonetheless , we estimate nuclear masses @xmath48 , comparable to the masses of low - luminosity star cluster nuclei derived for other late - type spirals [ e.g. , m33 : @xmath49 ( kormendy & mcclure 1993 ) ; ngc 4449 : @xmath50 ( bker et al . 2001 ) ; ic 342 : @xmath51 ( bker , van der marel , & vacca 1999 ) ] . as a final note , we draw attention to the fact that some of the nuclei in our present sample appear to be offset from the dynamical centers of the galaxies as defined by either the optical continuum and/or the centroid of the global profile ( see also the appendix ) . the frequent displacement of compact nuclei from the dynamical centers of galaxies has been discussed previously by miller & smith ( 1992 ; see also levine & sparke 1998 ) and may offer an important clue to the formation mechanism of the nuclei . higher resolution spectroscopy of more extensive samples of these types of nuclei is clearly desirable in order to better understand their natures , to improve these mass estimates , and to help us understand their dynamical relationships to the surrounding disk material .

the p - v curves show significant asymmetries in shape , extent , and/or amplitude on the approaching and receding sides of the disk . at least 6 of the galaxies in our sample possess semi - stellar nuclei that appear to be compact nuclear star clusters ; in 5 of these cases we see kinematic signatures in the p - v curves at the location of the nucleus .

we present optical longslit spectroscopic observations of 21 low - luminosity , extreme late - type spiral galaxies . our sample is comprised of sc - sm local supercluster spirals with moderate - to - low optical surface brightnesses and with luminosities at the low end for spiral disk galaxies ( ) . for each galaxy we have measured high spatial resolution position - velocity ( p - v ) curves using the h emission line , and for 15 of the galaxies we also derive major axis rotation curves . in% of our sample , the p - v curves show significant asymmetries in shape , extent , and/or amplitude on the approaching and receding sides of the disk . a number of the p - v curves are still rising to the last measured point , or reach a clear turnover on only one side . in most instances we find good agreement between the kinematic centers of extreme late - type spirals as defined by the global emission profile and by their optical continuum , although in a few cases we see evidence of possible real offsets . in spite of their shallow central gravitational potentials , at least 6 of the galaxies in our sample possess semi - stellar nuclei that appear to be compact nuclear star clusters ; in 5 of these cases we see kinematic signatures in the p - v curves at the location of the nucleus . finally , we find that like giant spirals , our sample galaxies have higher specific angular momenta than predicted by current cold dark matter models . 0.5 cm

astro-ph0203188

c

we have presented new optical longslit kinematic measurements for 21 low - luminosity , extreme late - type spiral galaxies using the h@xmath1 emission line . we have derived position - velocity ( p - v ) curves for all 21 galaxies , as well as deprojected major axis rotation curves for 15 of the objects . to facilitate future synthesis with rotation curve measurements , we have also made all of our p - v data available in electronic format . most of the extreme late - type spirals in our sample exhibit slowly rising , nearly linear p - v curves throughout a significant fraction of their stellar disks . many of the p - v curves continue to rise to the last measured point in the optical galaxy , implying low central matter densities . the disks of these galaxies appear to follow the trend between specific angular momentum and rotational velocity seen in giant spirals , suggesting that the angular momenta of disks are not closely tied to the details of their structures or star formation histories , and are intrinsically larger than predicted by current cold dark matter models . a significant fraction of our measured optical p - v curves are not symmetric , and our observations are consistent with @xmath250% of extreme late - type spirals possessing kinematic and/or structural asymmetries . in some cases , this may also be manifested as an offset between the @xmath57 values measured from global spectra and that measured from the optical data , although in most cases those values show excellent agreement . we find that lopsided global profiles appear to be a good , although not a perfect predictor of kinematic asymmetries in extreme late - type spiral disks . five of the extreme late - type spirals in our sample possess compact , semi - stellar nuclei that produce kinematic signatures in the galaxy rotation curves . rough mass estimates help to confirm that these are massive , highly compact star nuclei star clusters analogous to those seen in brighter galaxies . such nuclei appear to be a common feature of extreme late - type spiral galaxies in spite of their apparently weak central gravitational potentials . we are grateful to the late r. schommer as well as the ctio staff for their assistance with the rc spectrograph observations . ldm completed a portion of this work while supported by a clay fellowship from the harvard - smithsonian center for astrophysics . jsg thanks the university of wisconsin graduate school and for their partial support of this research . baldwin , j. e. , lynden - bell , d. , & sancisi , r. 1980 , mnras , 193 , 313 blais - ouellette , s. , carignan , c. , amran , p. , & ct , s. 1999 , aj , 118 , 2123 bker , t. , laine , s. , van der marel , r. p. , sarzi , m. , rix , h .- w . , ho , l. c. , & shields , j. c. 2002 , aj , in press ( astro - ph/0112086 ) bker , t. , van der marel , r. p. , mazzuca , l. , rix , h .- w . , rudnick , g. , ho , l. c. , & shields , j. c. 2001 , aj , 121 , 1473 bker , t. , van der marel , r. p. , & vacca , w. d. 1999 , aj , 118 , 831 bosma , a. , van der hulst , j. m. , & athanassoula , e. 1988 , a&a , 198 , 100 carignan , c. & freeman , k. c. 1988 , apj , 347 , 760 carignan , c. & puche , d. 1990 , aj , 100 , 641 carignan , c. , sancisi , r. , & van albada t. s. 1988 , aj , 95 , 37 casertano s. & van gorkom j. h. 1991 , aj , 101 , 1231 colin , j. & athanassoula , e. 1981 , a&a , 97 , 63 ct , s. , carignan , c. , & sancisi , r. 1991 , aj , 102 , 904 ct , s. , carignan , c. , & freeman , k. c. 2000 , aj , 120 , 3027 dalcanton , j. j. & bernstein , r. a. 2000 , in dynamics of galaxies : from the early universe to the present , ed . by f. combes , g. a. mamon , and v. charmandaris , ( san franciso : asp ) , 161 de blok , w. j. g. , mcgaugh , s. s. , bosma , a. , & rubin , v. c. 2001 , apj , 552 , l23 de blok , w. j. g. , mcgaugh , s. s. , & van der hulst , j. m. 1996 , mnras , 283 , 18 efstathiou , g. 2000 , mnras , 317 , 697 fall , s. m. & efstathiou , g. 1980 , mnras , 193 , 189 fouqu , p. , bottinelli , l. , durand , n. , gouguenheim , l. , & paturel , g. 1990 , a&as , 86 , 473 gallagher , j. s. , littleton , j. e. , & matthews , l. d. 1995 , aj , 109 , 2003 gallagher , j. s. & matthews , l. d. 2001 , in modes of star formation and the origin of field star populations , ed . by e. grebel & w. brandner , ( san francisco : asp ) , in press giovanelli , r. , & haynes , m. p. 1988 , in galactic and extragalactic radio astronomy , edited by g. l. verschuur and k. i. kellermann ( new york : springer - verlag ) , 526 goad , j. w. & roberts , m. s. 1981 , apj , 250 , 79 haynes , m. p. , van zee , l. , hogg , d. e. , roberts , m. s. , & maddalena , r. j. 1998 , aj , 115 , 62 iliev , i. t. , shapiro , p. r. 2001 , apj , 546 , l5 jobin , m. & carignan , c. 1990 , aj , 100 , 648 jog , c. j. 1999 , apj , 522 , 661 karachentsev , i. d. 1991 , sov . , 17 , 206 kormendy , j. & mcclure , r. d. 1993 , aj , 105 , 1793 kornreich , d. a. , haynes , m. p. , & lovelace , r. v. e. 1998 , aj , 116 , 2263 kravtsov , a. v. , klypin , a. a , bullock , j. s. , & primack , j. r. 1998 , apj , 502 , 48 levine , s. e. & sparke , l. s. 1998 , apj , 496 , l13 martimbeau , n. , carignan , c. , & roy , j .- 1994 , aj , 107 , 543 makarov , d. i. , burenkov , a. n. , & tyurina , n. v. 1999 , astron . , 25 , 706 massey , p. , valdes , f. , & barnes , j. 1992 , a user s guide to reducing slit spectra with iraf ( http://iraf.noao.edu/docs/spectra.html ) matthews , l. d. 2000 , aj , 120 , 1764 matthews , l. d. et al . 1999 , aj , 118 , 208 matthews , l. d. & gallagher , j. s. 1997 , aj , 114 , 1899 ( mg97 ) matthews , l. d. & uson , j. m. 2002 , in seeing through the dust : the detection of and the exploration of the ism in galaxies , ed . by r. taylor , t. landecker , & t. willis ( san francisco : asp ) , in press matthews , l. d. , van driel , w. , & gallagher , j. s. 1998 , aj , 116 , 1169 matthews , l. d. & wood , k. 2001 , apj , 548 , 150 2001 mcgaugh , s. s. & de blok , w. j. g. 1998 , apj , 499 , 41 mcgaugh , s. s. , rubin , v. c. , & de blok , w. j. g. 2001 , aj , 122 , 2381 meurer , g. r. , carignan , c. , beaulieu , s. f. , & freeman , k. c. 1996 , aj , 111 , 1551 miller , r. h. & smith , b. f. 1992 , apj , 393 , 508 minniti , d. , olszewski , e. w. , & rieke , m. 1993 , apj , 410 , l79 navarro , j. f. , frenk , c. s. , & white , s. d. m. 1995 , mnras , 275 , 56 navarro , j. f. & steinmetz , m. 2000 , apj , 538 , 477 noguchi , m. 2001 , apj , 555 , 289 noordermeer , e. , sparke , l. s. , & levine , s. e. 2001 , mnras , 328 , 1064 osterbrock , d. e. , fulbright , j. p. , martel , a. r. , keane , m. j. , & trager , s. c. 1996 , pasp , 108 , 277 phillips , a. c. , illingworth , g. d. , mackenty , j. w. , & franx , m. 1996 , aj , 111 , 1566 richter , o .- g . & sancisi , r. 1994 , a&a , 290 , 9 rix , h .- w . & zaritsky , d. 1995 , apj , 447 , 118 rownd , b. k. , dickey , j. m. , & helou , g. 1994 , aj , 108 , 1638 rubin , v. c. , ford , w. k. jr . , & thonnard , n. 1980 , apj , 238 , 471 schoenmakers , r. h. m. , franx , m. , & de zeeuw , p. t. 1997 , mnras , 292 , 349 silk , j. 2001 , mnras , 324 , 313 skillman , e. d. 1996 in the minnesota lectures on extragalactic neutral hydrogen , asp conference series , vol . 106 , ed . by e. d. skillman ( san francisco : asp ) , 208 swaters , r. a. 1999 , ph.d . thesis , university of groningen swaters , r. a. , madore , b. f. , & trewhella , m. 2000 , apj , 531 , l107 swaters , r. a. , schoenmakers , r. h. m. , sancisi r. , & van albada t.s . 1999 , mnras , 304 , 330 van den bergh , s. 1995 , aj , 110 , 613 van den bosch , f. c. , burkert , a. , & swaters , r. a. 2001 , mnras , 326 , 1205 van den bosch , f. c. , robertson , b. e. , dalcanton , j. j. , & de blok , w. j. g. 2000 , aj , 119 , 1579 van der hulst , j. m. , skillman , e. d. , smith , t. r. , bothun , g. d. , mcgaugh s. s. , & de blok w. j. g. 1993 , 106 , 548 windhorst , r. a. et al . 2002 , submitted to apjs zaritsky , d. & rix , h .- w . 1997 , apj , 477 , 118 llccccccc eso418 - 008 & sbdm & 03 29 28 & -30 22 54 & 2 & 1500 & 0 & 140@xmath58 & 40 eso482 - 005 & sbd & 03 30 52 & -24 18 06 & 2 & 1800 & 79 & 80 & 1 eso358 - 015 & sdm & 03 31 10 & -34 58 30 & 2 & 2000 & 16 & 180 & 16 eso358 - 020 & sbdm & 03 32 58 & -32 48 18 & 2 & 1500 & 165 & 167 & 2 eso358 - 060 & sm & 03 43 18 & -35 43 30 & 2 & 2000 & 102 & 102 & 0 eso359 - 029 & sdm & 04 10 56 & -33 07 42 & 2 & 2000 & 20 & 20 & 5 eso422 - 005 & sdm & 04 50 07 & -28 40 30 & 1 & 1000 & 35 & 15 & 20 eso305 - 009 & sabc & 05 06 26 & -38 22 30 & 2 & 2000 & 90 & 63@xmath58 & 27 eso425 - 008 & sbm : & 06 04 38 & -27 52 18 & 2 & 1800 & 80 & 80 & 0 am0605 - 341 & sbdm & 06 05 31 & -34 11 49 & 1 & 750 & 90 & 90 & 0 eso502 - 016 & sbd & 11 02 48 & -26 21 18 & 1 & 1200 & 82 & 79 & 3 eso438 - 005 & sd & 11 06 33 & -28 06 00 & 2 & 2000 & 62 & 60 & 2 eso504 - 010 & sbdm & 11 40 32 & -23 09 18 & 1 & 1200 & 14 & 15 & 1 eso504 - 017 & scd / bcd & 11 46 15 & -27 06 00 & 1 & 500 & 60 & 103 & 43@xmath59 eso504 - 025 & sd & 11 51 18 & -27 04 18 & 2 & 1800 & 30 & 20 & 10 eso440 - 049 & sc & 12 02 59 & -31 08 42 & 2 & 1800 & 0 & 60 & 60 eso505 - 013 & sabc & 12 03 33 & -22 34 18 & 1 & 900 & 135 & 45 & 90@xmath59 eso380 - 025 & sbdm & 12 21 56 & -35 07 54 & 1 & 1000 & 15 & 13 & 2 eso443 - 079 & sabd & 13 07 38 & -27 42 18 & 2 & 2000 & 0 & 180 & 0 eso508 - 034 & spec & 13 14 13 & -25 04 24 & 1 & 900 & 132 & 129 & 3 eso444 - 033 & sbdm & 13 23 16 & -31 52 12 & 1 & 1000 & 89 & 88 & 1 lcccrrrcrrc eso418 - 008 & 1.91 & @xmath6017.4 & 55.0 & 153.5 & 125.0 & 1188.9 & 0.64 & 79.6 & 1193.4 & 1 eso482 - 005 & 2.60 & @xmath6017.0 & 81.3 & 170.8 & 153.7 & 1914.2 & 1.54 & 178.1 & 1918.4 & 1 eso358 - 015 & 1.53 & @xmath6016.3 & 46.7 & 100.2 & 67.8 & 1402.9 & 0.59 & 98.8 & 1386.4 & 1 eso358 - 020 & 1.93 & @xmath6017.7 & 37.1 & 117.7 & 98.1 & 1754.2 & 0.35 & 64.8 & 1762.2 & 1 eso358 - 060 & 2.24 & @xmath6014.3 & 85.1 & 82.0 & 54.0 & 801.2 & 1.03 & 61.2 & 794.4 & 1 eso359 - 029 & 1.92 & @xmath6015.8 & 56.4 & 141.1 & 134.2 & 872.6 & 0.68 & 140.8 & 866.3 & 1 eso422 - 005 & 1.70 & @xmath6016.7 & 41.7 & 126.2 & 99.0 & 1460.9 & 0.73 & 65.3 & 1481.3 & 1 eso305 - 009 & 4.63 & @xmath6017.2 & 52.9 & 129.8 & 113.1 & 1018.8 & 1.56 & 112.4 & 999.4 & 1 eso425 - 008 & 1.20 & @xmath6014.1 & 78.8 & 106.5 & 91.3 & 1475.5 & 0.57 & 94.3 & 1473.9 & 1 am0605 - 341 & 1.27 & @xmath6015.4 & 26.0 & 124.2 & 95.3 & 775.2 & 0.44 & 55.8 & 768.9 & 1 eso502 - 016 & 2.46 & @xmath6017.2 & 67.1 & 155.0 & 102.8 & 1511.0 & 0.85 & 106.7 & 1540.3 & 1 eso438 - 005 & 3.40 & @xmath6016.7 & 80.0 & 163.9 & 145.5 & 1499.4 & 1.86 & 145.9 & 1497.2 & 1 eso504 - 010 & 1.44 & @xmath6016.2 & 67.2 & 145 & 127 & 1932 & 0.64 & 118.3 & 1940.8 & 2 eso504 - 017 & 1.10 & @xmath6018.0 & 30.8 & 220.1 & 169.3 & 1888.3 & 0.55 & 123.2 & 1891.5 & 1 eso504 - 025 & 2.42 & @xmath6017.2 & 39.9 & 137 & 118 & 1637 & 1.06 & 105.2 & 1631.6 & 2 eso440 - 049 & 2.22 & @xmath6018.5 & 32.0 & 151 & 131 & 2264 & 0.78 & 54.5 & 2273.0 & 2 eso505 - 013 & 2.96 & @xmath6018.8 & 18.3 & 132.2 & 117.3 & 1726.1 & 1.62 & 82.6 & 1719.4 & 1 eso380 - 025 & 1.63 & @xmath6018.6 & 76.9 & 180.6 & 163.9 & 2788.1 & 0.84 & 186.1 & 2799.2 & 1 eso443 - 079 & 2.18 & @xmath6017.2 & 72.8 & 157.7 & 136.3 & 2124.4 & 1.16 & 132.5 & 2127.8 & 1 eso508 - 034 & 1.53 & @xmath6017.5 & 64.6 & 167 & 150 & 1910 & 0.79 & 162.2 & 1911.5 & 2 eso444 - 033 & 2.03 & @xmath6017.9 & 74.3 & 169.0 & 147.0 & 2428.2 & 0.92 & 182.9 & 2408.7 & 1 lccc eso482 - 005 & 70.5 & 2003.0 & 18.5 & 68.1 & 2001.5 & 19.4 & 65.7 & 1997.5 & 17.9 & 53.3 & 1977.6 & 15.4 & 51.2 & 1987.1 & 10.1 & 49.0 & 1994.7 & 8.2 & 46.9 & 1990.7 & 8.2 & 44.8 & 1984.0 & 7.8 & 42.4 & 1979.8 & 7.5 & 40.3 & 1978.5 & 9.0 & 37.8 & 1984.2 & 10.4 & 36.0 & 1984.8 & 14.0 & 34.2 & 1987.3 & 12.7 & 31.8 & 1979.9 & 5.6 & 29.4 & 1990.1 & 3.5 & 27.6 & 1987.6 & 3.3 & 25.7 & 1987.3 & 3.3 & 23.0 & 1977.8 & 5.1 & 20.3 & 1974.2 & 6.2 & 17.2 & 1972.8 & 7.5 & 14.2 & 1966.4 & 8.2 & 11.2 & 1960.1 & 6.8 & 8.5 & 1955.5 & 7.1 & 5.1 & 1946.4 & 6.7 & 2.4 & 1929.8 & 5.0 & -0.5 & 1918.4 & 4.8 & -2.9 & 1914.9 & 4.9 & -6.3 & 1902.8 & 6.7 & -9.0 & 1885.9 & 7.8 & -12.0 & 1869.0 & 8.6 & -15.0 & 1861.7 & 11.8 & -17.5 & 1859.2 & 13.7 & -23.8 & 1868.3 & 12.1 & -26.2 & 1869.2 & 12.2 & -29.0 & 1867.5 & 12.9 & -31.7 & 1857.8 & 16.1 & -59.8 & 1824.9 & 13.5 & -63.2 & 1832.7 & 11.7 & -66.2 & 1837.1 & 10.9 & -68.9 & 1846.7 & 16.2 & -75.3 & 1831.8 & 19.2 & -77.7 & 1836.5 & 18.8

we present optical longslit spectroscopic observations of 21 low - luminosity , extreme late - type spiral galaxies . we have measured high spatial resolution position - velocity ( p - v ) curves using the h emission line , and for 15 of the galaxies we also derive major axis rotation curves . in% of our sample , finally , we find that like giant spirals , our sample galaxies have higher specific angular momenta than predicted by current cold dark matter models . 0.5 cm

we present optical longslit spectroscopic observations of 21 low - luminosity , extreme late - type spiral galaxies . our sample is comprised of sc - sm local supercluster spirals with moderate - to - low optical surface brightnesses and with luminosities at the low end for spiral disk galaxies ( ) . for each galaxy we have measured high spatial resolution position - velocity ( p - v ) curves using the h emission line , and for 15 of the galaxies we also derive major axis rotation curves . in% of our sample , the p - v curves show significant asymmetries in shape , extent , and/or amplitude on the approaching and receding sides of the disk . a number of the p - v curves are still rising to the last measured point , or reach a clear turnover on only one side . in most instances we find good agreement between the kinematic centers of extreme late - type spirals as defined by the global emission profile and by their optical continuum , although in a few cases we see evidence of possible real offsets . in spite of their shallow central gravitational potentials , at least 6 of the galaxies in our sample possess semi - stellar nuclei that appear to be compact nuclear star clusters ; in 5 of these cases we see kinematic signatures in the p - v curves at the location of the nucleus . finally , we find that like giant spirals , our sample galaxies have higher specific angular momenta than predicted by current cold dark matter models . 0.5 cm

hep-ph0303184

i

scattering processes have played a crucial role in establishing the fundamental interactions of nature . they represent the most important source of information on short - distance physics . with increasing energy , multiparticle events are becoming more and more dominant . thus , in testing various aspects of qcd , the high - energy scattering processes , both exclusive and inclusive , in which the total number of particles ( partons ) in the initial and final states is @xmath5 , have recently become increasingly important . owing to the well - known fact that the lo predictions in perturbative qcd ( pqcd ) do not have much predictive power , the inclusion of higher - order corrections is essential for many reasons . in general , higher - order corrections have a stabilizing effect , reducing the dependence of the lo predictions on the renormalization and factorization scales and the renormalization scheme . therefore , to achieve a complete confrontation between theoretical predictions and experimental data , it is very important to know the size of radiative corrections to the lo predictions . obtaining radiative corrections requires the evaluation of one - loop integrals arising from the feynman diagram approach . with the increasing complexity of the process under consideration , the calculation of radiative corrections becomes more and more tedious . therefore , it is extremely useful to have an algorithmic procedure for these calculations , which is computerizable and leads to results which can be easily and safely evaluated numerically . the case of feynman integrals with massless internal lines is of special interest , because one often deals with either really massless particles ( gluons ) or particles whose masses can be neglected in high@xmath0energy processes ( quarks ) . owing to the fact that these integrals contain ir divergences ( both soft and collinear ) , they need to be evaluated in an arbitrary number of space - time dimensions . as it is well known , in calculating feynman diagrams mainly three difficulties arise : tensor decomposition of integrals , reduction of scalar integrals to several basic scalar integrals and the evaluation of a set of basic scalar integrals . considerable progress has recently been made in developing efficient approaches for calculating one@xmath0loop feynman integrals with a large number ( @xmath5 ) of external lines @xcite . various approaches have been proposed for reducing the dimensionally regulated ( @xmath5)@xmath0point tensor integrals to a linear combination of @xmath1 and lower@xmath0point scalar integrals multiplied by tensor structures made from the metric tensor @xmath6 and external momenta @xcite . it has also been shown that the general @xmath7point scalar one@xmath0loop integral can recursively be represented as a linear combination of @xmath8@xmath0point integrals provided the external momenta are kept in four dimensions @xcite . consequently , all scalar integrals occurring in the computation of an arbitrary one@xmath0loop @xmath9@xmath0point integral can be reduced to a sum over a set of basic scalar box @xmath10 integrals with rational coefficients depending on the external momenta and the dimensionality of space@xmath0time . despite , the considerable progress , the developed methods still can not be applied to all cases of practical interest . the problem is related to vanishing of various relevant kinematic determinants . as far as the calculation of one - loop @xmath11-point massless integrals is concerned , the most complete and systematic method is presented in @xcite . it does not , however , apply to all cases of practical interest . namely , being obtained for the non - exceptional external momenta it can not be , for example , applied to the integrals in which the set of external momenta contains subsets comprised of two or three collinear on - shell momenta . the integrals of this type arise when performing the leading - twist nlo analysis of hadronic exclusive processes at large@xmath0momentum transfer in pqcd . with no restrictions regarding the external kinematics , in this paper we formulate an efficient , systematic and completely general method for reducing an arbitrary one@xmath0loop @xmath1point massless integral to a set of basic integrals . although the method is presented for massless case , the generalization on massive case is straightforward . the main difference between the massive and massless cases manifests itself in the basic set of integrals , which in former case is far more complex . among the one@xmath0loop faynman integrals there exist both massive and massless integrals for which the existing reduction methods break down . the massless integrals belonging to this category are of more practical interest at the moment , so in this paper we concentrate on massless case . the paper is organized as follows . section 2 is devoted to introducing notation and to some preliminary considerations . in sec . 3 , for the sake of completenes , we briefly review a tensor decomposition method for @xmath1point tensor integrals which was originally obtained in ref . @xcite . in sec . 4 we present a procedure for reducing one@xmath0loop @xmath12@xmath0point massless scalar integrals with generic @xmath13@xmath0dimensional external momenta to a fundamental set of integrals . since the method is closely related to the one given in @xcite , similarities and differences between the two are pointed out . being derived with no restrictions to the external momenta , the method is completely general and applicable for arbitrary kinematics . section 5 contains considerations regarding the fundamental set of integrals which is comprised of eight integrals . section 6 is devoted to some concluding remarks . in the appendix a we give explicit expressions for the relevant basic massless box integrals in @xmath2 space@xmath0time dimensions . these integrals constitute a subset of the fundamental set of scalar integrals . as an illustration of the tensor decomposition and scalar reduction methods , in the appendix b we evaluate an one@xmath0loop 6@xmath0point feynman diagram with massless internal lines , contributing to the nlo hard@xmath0scattering amplitude for @xmath14 exclusive reaction at large momentum transfer in pqcd .

being derived with no restrictions regarding the external momenta , the method is completely general and applicable for arbitrary kinematics . in particular , it applies to the integrals in which the set of external momenta contains subsets comprised of two or more collinear momenta , which are unavoidable when calculating oneloop contributions to the hardscattering amplitude for exclusive hadronic processes at large momentum transfer in pqcd .

we present a systematic method for reducing an arbitrary onelooppoint massless feynman integral with generic 4dimensional momenta to a set comprised of eight fundamental scalar integrals : six box integrals in , a triangle integral in , and a general twopoint integral in space time dimensions . all the divergences present in the original integral are contained in the general twopoint integral and associated coefficients . the problem of vanishing of the kinematic determinants has been solved in an elegant and transparent manner . being derived with no restrictions regarding the external momenta , the method is completely general and applicable for arbitrary kinematics . in particular , it applies to the integrals in which the set of external momenta contains subsets comprised of two or more collinear momenta , which are unavoidable when calculating oneloop contributions to the hardscattering amplitude for exclusive hadronic processes at large momentum transfer in pqcd . the iterative structure makes it easy to implement the formalism in an algebraic computer program . irbth/03 * * reduction method for dimensionally regulated one - loop n - point feynman integrals * + g. duplani ' c and b. nii ' c + _ theoretical physics division , rudjer bokovi institute , p.o . box 180 , hr-10002 zagreb , croatia _ + *

hep-ph0303184

c

in this work we have considered one@xmath0loop scalar and tensor feynman integrals with an arbitrary number of external lines which are relevant for construction of multi@xmath0parton one@xmath0loop amplitudes in massless field theories . main result of this paper is a scalar reduction approach by which an arbitrary @xmath1point scalar one@xmath0loop integral can be reqursively represented as a linear combination of eight basic scalar integrals with rational coefficients depending on the external momenta and the dimensionality of space@xmath0time , provided the external momenta are kept in four dimensions . the problem of vanishing of the kinematic determinants , which is a reflection of very complex singularity structure of these integrals , has been solved in an elegant and transparent manner . namely , the approach has been taken according to which instead of solving the general system of linear equations given in ( [ f25 ] ) , and then finding the limit , which sometimes does nt exists , of the obtained solution corresponding to a given singular kinematic situation , we first obtain and then solve the system of equations appropriate to the situation being considered . our method has been derived without any restrictions regarding the external momenta . as such , it is completely general and applicable for arbitrary kinematics . in particular , it applies to the integrals in which the set of external momenta contains subsets comprised of two or more collinear momenta . this kind of integrals are encountered when performing leading@xmath0twist nlo pqcd analysis of the hadronic exclusive processes at large@xmath0momentum@xmath0transfer . trough the tensor decomposition and scalar reduction presented , any massless one - loop feynman integral with generic 4-dimensional momenta can be expressed as a linear combination of a fundamental set of scalar integrals : six box integrals in @xmath2 , a triangle integral in @xmath3 , and a general two@xmath0point integral . all the divergences present in the original integral are contained in the general two - point integral and associated coefficients . in conclusion , the computation of ir divergent one@xmath0loop integrals for arbitrary number of external lines can be mastered with the reduction formulas presented above . the iterative structure makes it easy to implement the formalism in algebraic computer program . with this work all the conceptual problems concerning the construction of multi@xmath0parton one@xmath0loop amplitudes are thus solved .

we present a systematic method for reducing an arbitrary onelooppoint massless feynman integral with generic 4dimensional momenta to a set comprised of eight fundamental scalar integrals : six box integrals in , a triangle integral in , and a general twopoint integral in space time dimensions . all the divergences present in the original integral are contained in the general twopoint integral and associated coefficients . the problem of vanishing of the kinematic determinants has been solved in an elegant and transparent manner . the iterative structure makes it easy to implement the formalism in an algebraic computer program .

we present a systematic method for reducing an arbitrary onelooppoint massless feynman integral with generic 4dimensional momenta to a set comprised of eight fundamental scalar integrals : six box integrals in , a triangle integral in , and a general twopoint integral in space time dimensions . all the divergences present in the original integral are contained in the general twopoint integral and associated coefficients . the problem of vanishing of the kinematic determinants has been solved in an elegant and transparent manner . being derived with no restrictions regarding the external momenta , the method is completely general and applicable for arbitrary kinematics . in particular , it applies to the integrals in which the set of external momenta contains subsets comprised of two or more collinear momenta , which are unavoidable when calculating oneloop contributions to the hardscattering amplitude for exclusive hadronic processes at large momentum transfer in pqcd . the iterative structure makes it easy to implement the formalism in an algebraic computer program . irbth/03 * * reduction method for dimensionally regulated one - loop n - point feynman integrals * + g. duplani ' c and b. nii ' c + _ theoretical physics division , rudjer bokovi institute , p.o . box 180 , hr-10002 zagreb , croatia _ + *

1608.06448

i

atomic and molecular ultracold gases offer many advantages for studying quantum phenomena , especially within the realm of many - body physics , due to the high degree of tunability of inter - atomic interactions @xcite . in particular , dipolar quantum gases of atoms and molecules have received much attention in recent years , as the anisotropic and long - range nature of the magnetic or electric dipole - dipole interaction ( ddi ) gives rise to a rich spectrum of novel properties in such systems @xcite . such systems include those made up of ultracold atoms , as well as those consisting of heteronuclear molecules with large dipole - dipole interactions . furthermore , in the recent theoretical and experimental research @xcite a novel kind of strongly dipolar quantum gas was introduced . these are weakly bound polar molecules produced from atoms with large magnetic dipole moments , such as erbium and other lanthanides . these molecules can have a very large magnetic moment , which amounts to twice that of its individual atoms @xcite . in 2005 an anisotropic deformation of the expanding dipolar bosonic chromium condensate due to ddi was observed @xcite . in the recent experiment @xcite , also the rosensweig instability was detected in a @xmath0dy bose - einstein condensate , which represents a quantum ferrofluid due to the large atomic magnetic dipole moments . namely , after a sudden decrease of the scattering length , the dipolar quantum gas creates self - ordered surface structures in form of droplet crystals , which can only be understood by taking into account ddi @xcite and the corresponding quantum fluctuations @xcite . for dipolar fermi gases it was predicted that the long - range and anisotropic ddi leads in equilibrium to an anisotropic deformation of the fermi surface from a sphere to an ellipsoid @xcite . a recent time - of - flight ( tof ) expansion experiment has now unambiguously detected such an ellipsoidal fermi surface ( fs ) deformation in a dipolar quantum gas of fermionic erbium atoms , which turns out to be of the order of a few percent @xcite . within the hartree - fock mean - field theory for a many - body system , first - order contributions of ddi to the total energy of the system taken into account are in terms of both the hartree direct interaction and the fock exchange interaction @xcite . in the case of a fermi gas with isotropic interaction , the hartree and the fock interactions cancel out @xcite , thus leading to a spherically symmetric fs . but in the case of a fermi gas with anisotropic ddi the hartree term gives rise to a distortion in real space @xcite , whereas the fock term gives rise to a distortion in momentum space , i.e. , to an ellipsoidal deformation of the fermi sphere . note in this context that the fock exchange term in dipolar fermi gases is the consequence of a combined effect of the ddi and the pauli exclusion principle . in the current experimentally relevant range of dipolar interactions the theory beyond hartree - fock , where the total energy is determined up to second - order in the ddi , yields only small differences , which can not yet be resolved experimentally . therefore , the hartree - fock mean - field approximation yields already quantitatively accurate results for present - day experiments @xcite . the investigations of collective oscillations and tof dynamics of dipolar fermi gases have so far focused on either the collisionless ( cl ) regime @xcite , where collisions can be neglected , or on the hydrodynamic ( hd ) regime @xcite , where collisions occur so often that local equilibrium can be assumed . the recent paper of wchtler _ et al . _ @xcite studied even the behavior of collective oscillations when the system undergoes a crossover from one regime to the other . motivated by the experimental observation of the ellipsoidal fs deformation in the tof experiment @xcite , we continue here the analytical analysis along the lines of reference @xcite and investigate in detail the expansion dynamics for the collisional regime , which represents the transition zone between the limiting cl and hd regimes . we also extend previous approaches based on the relaxation - time approximation by introducing a self - consistently determined relaxation time , and study how this quantitatively affects the tof dynamics . the paper is structured as follows . in section [ sec : amdfg ] we introduce our notation and summarize recent experiments on atomic and molecular dipolar fermi gases . in section [ sec : ge ] we analyze the global equilibrium of the system by minimizing the hartree - fock total energy in order to obtain the thomas - fermi radii and momenta . afterwards , in order to study the dynamics , in section [ sec : bve ] we follow reference @xcite and introduce the boltzmann - vlasov equation for dipolar fermi gases as well as an approximative solution , which is based on a suitable rescaling ansatz for the equilibrium wigner function . in section [ sec : tof ] we study in detail the tof expansion dynamics of an initially trapped fermi gas . to this end we present our analytical and numerical results of the tof analysis all the way from the collisionless to the hydrodynamic regime and reveal how the expanding cloud bears the signature of the underlying ddi . finally , section [ sec : con ] gathers our concluding remarks and gives an outlook for future research .

a recent time - of - flight ( tof ) expansion experiment with polarized fermionic erbium atoms measured a fermi surface deformation from a sphere to an ellipsoid due to dipole - dipole interaction , thus confirming previous theoretical predictions . here we perform a systematic study of the ground - state properties and tof dynamics for trapped dipolar fermi gases from the collisionless to the hydrodynamic regime at zero temperature . to this end

a recent time - of - flight ( tof ) expansion experiment with polarized fermionic erbium atoms measured a fermi surface deformation from a sphere to an ellipsoid due to dipole - dipole interaction , thus confirming previous theoretical predictions . here we perform a systematic study of the ground - state properties and tof dynamics for trapped dipolar fermi gases from the collisionless to the hydrodynamic regime at zero temperature . to this end we solve analytically the underlying boltzmann - vlasov equation within the relaxation - time approximation in the vicinity of equilibrium by using a suitable rescaling of the equilibrium distribution . the resulting ordinary differential equations for the respective scaling parameters are then solved numerically for experimentally realistic parameters and relaxation times that correspond to the collisionless , collisional , and hydrodynamic regime . the equations for the collisional regime are first solved in the approximation of a fixed relaxation time , and then this approach is extended to include a self - consistent determination of the relaxation time . the presented analytical and numerical results are relevant for a detailed quantitative understanding of ongoing experiments and the design of future experiments with ultracold fermionic dipolar atoms and molecules . in particular , the obtained results are relevant for systems with strong dipole - dipole interaction , which turn out to affect significantly the aspect ratios during the tof expansion . _ keywords _ : ultracold fermi gas , dipolar interaction , boltzmann - vlasov equation

1108.2719

i

m dwarfs are main sequence stars whose spectra display bands of tio and other molecules such as cah , vo , feh , and crh @xcite . the high molecular opacities are the result of a cool atmosphere with effective temperatures in the range 2400k-3700k @xcite . observed orbital motion of astrometric binaries @xcite show that m dwarfs have masses ranging from @xmath50.5 m@xmath6 all the way down to the hydrogen - burning limit ( @xmath50.075 m@xmath6 ) . m dwarfs have relatively small sizes , with radii roughly proportional to their masses . recent measurements of eclipsing systems @xcite indicate a roughly linear relationship between masses and radii , with a 0.4 m@xmath6 ( 0.1 m@xmath6 ) m dwarf having a radius of 0.4 r@xmath6 ( 0.15 r@xmath6 ) . by number , m dwarfs form the bulk of the stars in our galaxy . the census of stars within 33 parsecs of the sun @xcite shows m dwarfs outnumbering all other hydrogen - burning objects by a factor of three to one . because of their low mass - to - light ratio , m dwarfs contribute only a small fraction of the light emission in galaxies , but they may be the dominant baryonic component in at least some galaxies @xcite . in recent years there has been an increasing interest in m dwarfs due to the discovery that they too host exoplanets . as of january 2011 , 25% of the 41 doppler - confirmed planets with @xmath730m@xmath8 are orbiting m dwarfs . the geneva / harps planet search team reports that @xmath930% of low - mass stars harbor planets with masses @xmath030@xmath10 on orbits shorter than 50 d @xcite and preliminary _ kepler _ results suggest that m dwarfs host just as many , if not more , super - earths and neptunes as solar - mass stars @xcite . exoplanet candidates have been identified by _ kepler _ in stars having colors consistent with m dwarfs @xcite , despite the fact that very few m dwarfs are being targeted by the mission @xcite . large exoplanet surveys have now started to monitor sizable numbers of m dwarfs , such as the m2k program which is targeting some 1,600 m dwarfs for radial velocity monitoring @xcite , and the mearth project @xcite which is designed to detect exoplanet transits in nearby late - type m dwarfs . the two principal methods of exoplanet detection , doppler measurement of radial velocity ( rv ) and photometric detection of transits , are more sensitive to planets around stars of lower mass . for a given planet mass and orbital period , rv amplitude scales as @xmath11 . in contrast to late - type m stars , the vast majority of early m dwarfs are not rapid rotators or chromospherically active ( w@xmath12 ) @xcite and are thus amenable to these search techniques . in fact , inactive k and early m stars have weaker p - mode oscillations and lower doppler noise ( `` jitter '' ) than their f or g counterparts @xcite . photometric transit depth scales approximately as @xmath13 for planets of similar size . because of their significantly smaller radii , m dwarfs display deeper transits which do not require high precision photometry for detection , as they do for g stars @xcite . another method of planet detection is high - contrast imaging at infrared wavelengths where a ( giant ) planet is self - luminous @xcite . m dwarf systems present a much more favorable planet / star contrast ratio compared to solar - mass stars , due to the significantly lower luminosity of m dwarfs . young systems are of particular interest because the luminosity of giant planets is predicted to be orders of magnitude higher at ages of @xmath14 yr @xcite providing a more favorable contrast , even as the host star itself is moderately more luminous at this younger age . young solar mass stars can be identified by their enhanced rotation , dynamo activity , and chromospheric emission @xcite , although the trend for late m stars for which the mechanism of dynamo operation is thought to be different is less clear @xcite . another challenge for this approach is the apparent rarity of giant planets on long - period orbits around solar - mass stars @xcite combined with the paucity of giant planets around m dwarfs compared to g dwarfs @xcite . it is also possible that young giant planets may be less luminous and more difficult to detect than previously predicted @xcite . low luminosity m dwarfs are also attractive targets because planets within their diminutive habitable zones are easier to detect @xcite . the correlation between high metallicity and the presence of giant planets found among solar - mass stars @xcite has been recently extended to m dwarf stars @xcite , and metal - rich m dwarfs , if they can be identified @xcite , would be especially propitious targets for planet searches . despite the attractiveness of m dwarfs for exoplanet surveys , there still is no systematic , all - sky census of these objects to a useful limiting magnitude . part of the problem is that the low - mass m dwarfs are stars of relatively low luminosities ( m@xmath15 ) . all but the closest m dwarfs are too faint ( v@xmath912 ) to be part of the _ hipparcos _ catalog @xcite , which means that existing m dwarf samples are selected from proper motion catalogs with fainter magnitude limits . these include the tycho-2 catalogue @xcite , which extends the hipparcos catalog a few magnitudes fainter , and also the older and deeper luyten half second ( lhs ) and new luyten two - tenths ( nltt ) catalogs @xcite which were the primary source material for the well - known _ catalog of nearby stars _ @xcite . newer and more complete proper motion catalogs , such as the lspm - north @xcite have the potential to expand the list of available m dwarf targets . in this paper , we present the first all - sky catalog of bright ( j@xmath010 ) m dwarfs . the sample is extracted from the all - sky superblink proper motion catalog of stars with @xmath140 mas yr@xmath2 , an extension of lspm - north currently in development . the selection method is detailed in 2 . the catalog itself is presented in 3 . the completeness of the catalog is evaluated in 4 . conclusions follow in 5 .

we present an all - sky catalog of m dwarf stars with apparent infrared magnitude j . these bright m dwarfs are all prime targets for exoplanet surveys using the doppler radial velocity or transit methods ; the combination of low - mass and bright apparent magnitude should make possible the detection of earth - size planets on short - period orbits using currently available techniques .

we present an all - sky catalog of m dwarf stars with apparent infrared magnitude j . the 8,889 stars are selected from the ongoing superblink survey of stars with proper motion mas yr , supplemented on the bright end with the tycho-2 catalog . completeness tests which account for kinematic ( proper motion ) bias suggest that our catalog represents of the estimated m dwarfs with j expected to populate the entire sky . our catalog is , however , significantly more complete for the northern sky (% ) than it is for the south (% ) . stars are identified as cool , red m dwarfs from a combination of optical and infrared color cuts , and are distinguished from background m giants and highly - reddened stars using either existing parallax measurements or , if such measurements are lacking , on their location in an optical - to - infrared reduced proper motion diagram . these bright m dwarfs are all prime targets for exoplanet surveys using the doppler radial velocity or transit methods ; the combination of low - mass and bright apparent magnitude should make possible the detection of earth - size planets on short - period orbits using currently available techniques . parallax measurements , when available , and photometric distance estimates are provided for all stars , and these place most systems within 60 parsecs of the sun . spectral type estimated from v - j color shows that most of the stars range from k7 to m4 , with only a few late m dwarfs , all within 20 pc . proximity to the sun also makes these stars good targets for high - resolution exoplanet imaging searches , especially if younger objects can be identified on the basis of x - ray or uv excess . for that purpose , we include x - ray flux from rosat and fuv / nuv ultraviolet magnitudes from galex for all stars for which a counterpart can be identified in those catalogs . additional photometric data include optical magnitudes from digitized sky survey plates , and infrared magnitudes from 2mass .

1108.2719

m

the superblink proper motion survey is an all - sky search for stars with large proper motions based on a re - analysis of images from the digitized sky surveys ( dss ) using a specialized image - differencing algorithm and software . the basic search method is described in @xcite . quality control procedures , including cross - correlation with other catalogs and the compilation of astrometric and photometric results , is discussed at length in @xcite . stringent quality control procedures , including visual confirmation of most objects , guarantees a very low level of false detections . the survey has a fixed , low proper motion threshold of @xmath16 mas yr@xmath2 . new stars with very large proper motions ( @xmath17 mas yr@xmath2 ) discovered in the survey have been published in @xcite , @xcite , @xcite , and @xcite . a complete list of northern stars with proper motions @xmath18 mas yr@xmath2 was published in @xcite ; a similar list covering the southern sky has been completed and is available from the authors . those complete lists incorporate data from the hipparcos and tycho-2 catalogs at the bright end , and the catalogs are estimated to be @xmath19 complete to a visual magnitude @xmath20 , and extend to @xmath21 . the completeness is significantly higher at high galactic latitudes , where field crowding is less of an issue . dense fields at low galactic latitudes have a lower completeness due to faint stars often being lost to non - linearity in the crowded areas of photographic plates ; saturation also prevents the detection of proper motion sources in the extended glare ( up to several arc minutes ) of extremely bright stars ( e.g. vega , sirius , canopus ) . as of july 2011 , the full superblink catalog ( stars with proper motions @xmath16 mas yr@xmath2 ) comprised 2,270,481 objects , with the most extensive sky coverage north of decl.=-20@xmath22 . the catalog was complete for the northern sky ( decl.@xmath90@xmath22 ) , but the survey was still in progress for large parts of the southern sky . the southern survey was however complete for stars with proper motions @xmath18 mas yr@xmath2 . this version of the superblink catalog is the one used here . the use of a proper motion catalog is a convenient way to identify nearby stars in general , and m dwarfs in particular , because proper motion - selected samples discriminate against distant background sources including m giants that would otherwise significantly contaminate a sample of cool stars selected by color alone . however , proper motion selection carries its own inherent bias : stars with small velocities in the plane of the sky tend not to be detected in proper motion surveys , depending on the distance to the source . nearby , slow - moving stars can be included by lowering the proper motion limit of the sample , but this has the effect of increasing the contamination from background sources . there is a fine balance to achieve in adjusting the proper motion threshold , which would ideally have the sample incorporate the largest possible fraction of stars up to a specified distance , minimizing the kinematic bias , while at the same time limiting the contamination from background objects . the superblink catalog , with a proper motion limit @xmath16 mas yr@xmath2 , achieves such a balance for stars located within 100 parsecs of the sun . this can be demonstrated with an analysis of proper motion in the _ hipparcos _ catalog . figure 1 shows the fraction of hipparcos stars at a given distance from the sun which have proper motions @xmath18 mas yr@xmath2 and @xmath16 mas yr@xmath2 . the former value is the proper motion limit of the lspm - north and south catalogs ( which is also the approximate proper motion limit of the nltt catalog and , by extension , the catalog of nearby stars ) , while the latter is the proper motion limit of the extended superblink catalog . the diagram shows that operating with a proper motion limit of @xmath18 mas yr@xmath2 will only detect half the stars at 40pc and very few stars ( only those with very large components of motion ) at 100pc . however a sample with a proper motion limit @xmath16 mas yr@xmath2 will include @xmath595% of the stars at 40pc and @xmath570% of the stars at 100pc . background giant stars , on the other hand , tend to have small proper motions , which exclude them from the superblink catalog . figure 2 shows the distribution of proper motions for red giant stars in the hipparcos catalog , selected with the color and absolute magnitude cuts @xmath231.0 , @xmath243.0 . the bulk of the giants have proper motions below the superblink threshold . this particular subset of giants , because it is from the hipparcos catalog , also represents the nearest red giants to the sun , since they all have magnitudes @xmath25 . more distant giants would have even smaller proper motions , and would also be excluded from our sample . figure 3 shows the distribution of optical - to - infrared @xmath26 colors for a subset of m dwarfs with spectral classification from the sloan digital sky survey database @xcite . infrared @xmath27 magnitudes are from 2mass , while @xmath28 magnitudes are the superblink visual magnitudes , estimated from palomar sky survey photographic plate measurements as described in @xcite . the subset includes all stars in sdss which have counterparts in the superblink proper motion catalog . for this subset of nearby m dwarfs , @xmath26 color ranges from @xmath29 at subtype m0 , to @xmath30 at subtype m9 . we adopt an m dwarf color - cut of @xmath31 , which is expected to include most stars of subtype m0 and later , at the expense of some contamination from late - k stars . in addition , we select stars that are bright enough to be monitored by current and planned doppler radial velocity instruments . stars as faint as @xmath32 are routinely monitored using the high resolution spectrometer ( hires ) on the 10 m keck i telescope , e.g. @xcite , and fainter but highly meritorious stars with transiting planets , e.g. gj 1214 @xcite , have been observed . m dwarf stars are brighter in the near - infrared , and future high - resolution spectrometers should be able to detect planets around stars as faint as @xmath33 . anticipating such developments , we select stars with @xmath34 , which also includes all m dwarfs with @xmath35 . to summarize , we select bright m dwarfs among high proper motion stars ( @xmath16 mas yr@xmath2 ) in the superblink catalog using these color / magnitude cuts : @xmath36 figure 4 shows the full magnitude - color distribution of superblink stars , and the region targeted by our selection . out of 2,270,481 stars in the superblink catalog , our color and magnitude cuts select 10,659 bright red stars . this we use as our initial sample to identify bright m dwarfs . the sky distribution of the color - selected stars is shown in figure 5 . separate plots show the stars listed in the tycho-2 and hipparcos catalogs ( top ) , stars from the superblink catalog which are not listed in tycho-2 or hipparcos _ and _ have proper motions @xmath1 150 mas yr@xmath2 ( center ) , and finally stars from the superblink catalog not listed in tycho-2 or hipparcos _ and _ with proper motions 40 mas yr@xmath37 150 mas yr@xmath2 ( bottom ) . the subsample from the tycho-2 and hipparcos catalogs includes 3,319 of the brighter stars , spread over the entire sky . their distribution shows a slight overdensity in the direction of the galactic bulge , which is likely due to the larger number of red giants found in that part of the sky . the very high proper motion ( @xmath1 150 mas yr@xmath2 ) subsample from superblink includes 4,398 stars , and extends uniformly over the entire sky . the moderately high proper motion ( 40 mas yr@xmath37 150 mas yr@xmath2 ) subsample from superblink includes 2,941 stars , and clearly suffers from incompleteness in the southern hemisphere ; the subsample also displays an overdensity around ( @xmath38,@xmath39)@xmath5(80,+20 ) which is associated with the nearby hyades cluster . giant stars constitute the main source of contaminant in the sample . indeed , an excess of red sources in the apparent magnitude range @xmath40 ( see figure 4 ) points to a modest population of very red m giants in the superblink catalog ( probably including agb stars ) . while these giants are only a tiny fraction of the full superblink catalog , they are systematically selected in our initial color / magnitude cut . to eliminate these giants from our sample we apply three selection criteria . the first is based on evaluation of absolute magnitudes , and is used on stars with existing parallax data . the second method identifies giants from their location in a reduced proper motion diagram , and is used for stars for which there are no existing parallax measurements . a third method selects for m dwarfs based on @xmath41 and @xmath42 colors , further eliminating giants and interlopers with bad optical and/or infrared photometry . we searched the literature to find astrometric parallaxes for stars in our subsample of m dwarf candidates . parallaxes for 1,622 stars were recovered from the updated version of the hipparcos catalog @xcite . ground - based astrometric parallaxes were additionally recovered for 10 stars in @xcite , 46 stars in @xcite , 15 stars in @xcite , 6 stars in @xcite , 3 stars in @xcite , 1 star in @xcite , 2 stars in @xcite , 18 stars in @xcite , 4 stars in @xcite , 14 stars in @xcite , 15 stars in @xcite , 3 stars in @xcite , and 3 stars in @xcite . whenever parallaxes were found for one star in more than one bibliographical source , we adopted the most recent measurement , following the order above . the numbers quoted above refer to incremental additions to the list of parallaxes . in addition , we found parallaxes for 3 stars in the sky2000 master catalog , version 4 @xcite , and for 315 more from the nstars database . in all cases we only retained parallax measurements with errors @xmath020% . the final tally comprises a total of 2,080 stars with astrometric parallaxes . from the parallax @xmath43 we calculate absolute visual magnitudes using : @xmath44 the resulting hertzsprung - russel ( h - r ) diagram is displayed in figure 6 . the stars populate two very distinct loci . the more luminous group includes all m giants and the less luminous group consists of all the m dwarfs . for stars with @xmath29 , the giants are typically 7 - 8 magnitudes more luminous than the dwarfs . the difference in luminosity only increases at redder colors , with the reddest giants almost 20 magnitudes more luminous than dwarfs of similar @xmath26 color . from the absolute magnitude @xmath45 and optical - to - infrared color @xmath26 , we define the following criterion for a star to be considered an m dwarf : @xmath46 this cut identifies 561 stars as most likely to be red giants . the remaining 1,519 objects are identified as m dwarfs . we emphasize that this selection works only for the @xmath47 stars in our initial sample for which astrometric parallax measurements are available . note that the color - magnitude relationship for the m dwarfs in our sample closely follows : @xmath48 which implies that we are eliminating stars that are more than 4.5 magnitudes overluminous compared to the average m dwarf of the same color . this cut could possibly eliminate some very young m dwarfs , which tend to be overluminous in an optical - to - infrared color - magnitude diagram @xcite . indeed a number of stars with parallaxes appear to be a few magnitudes over - luminous compared to average field stars . however a close examination of figure 6 indicates that our magnitude cut would , in the worst case , eliminate only a handful of objects that could have been overluminous dwarfs . for stars without parallax measurements , it is possible to identify giants based on their location in a reduced proper motion diagram . the reduced proper motion is defined as : @xmath49 a quantity which is analogous to the absolute magnitude @xmath45 ( eq.3 ) except that the proper motion @xmath50 is substituted for the parallax @xmath43 . the two quantities are mathematically connected , with : @xmath51 where @xmath52 is the projected motion in the plane of the sky , i.e. the transverse velocity , here expressed in km s@xmath2 . this means that the reduced proper motion diagram is basically an h - r diagram where the ordinates are modulated by the individual components of transverse velocities . just as in the h - r diagram , m giants and m dwarfs tend to occupy distinct loci , with the giants all having relatively low values of @xmath53 and clustering in the upper part of the diagram . we demonstrate this in the upper panel of figure 7 , which shows the reduced proper motion diagram of the stars in our sample for which there are parallax measurements . stars identified as giants based on their parallax are plotted in red , dwarfs are plotted in black . we define a demarcation line which separates stars of the two groups quite well . from this , we postulate that m dwarfs can be separated from giants following this criterion : @xmath54 because the reduced proper motion depends on both absolute magnitude _ and _ transverse velocity , our selection may eliminate some main sequence m dwarfs if their transverse motion is small . based on equations 5 and 7 , we see that stars on the mean main sequence will be eliminated if their transverse velocity @xmath55 km s@xmath2 . given that the velocity dispersion for stars in the solar neighborhood is @xmath540 km s@xmath2 @xcite , our adopted criterion will exclude relatively few m dwarfs . conversely , giants with large transverse velocities will also have large values of @xmath53 which may place them beyond the limit defined in equation 8 . among the parallax - confirmed giants , we find 4 stars which fall within our defined reduced proper motion cut for m dwarfs . one of the stars has a inferred transverse velocity @xmath56 km s@xmath2 based on its hipparcos parallax and proper motion . however the other three stars have suspiciously faint absolute magnitudes ( 4.5@xmath575.0 ) for m giants , and may instead be m dwarfs with erroneous ( underestimated ) parallaxes measurements . the reduced proper motion diagram of stars with no parallax measurements is shown in the bottom panel of figure 7 . of the 8,580 stars with proper motions but no parallax measurements , we identify 626 as probable m giants , and those are eliminated from the sample . the remaining 7,954 stars are retained as m dwarf candidates . this leaves 9,473 stars , with or without parallax , on the list of m bright m dwarf candidates . a significant number of sources are found to have very red colors ( @xmath585 ) and reduced proper motion in the range typical for dwarf stars ( @xmath5912 ) and yet fall above the line we defined as the giant - dwarf boundary . a close examination of their infrared colors shows that most of these stars fall outside the normal range for m dwarfs ( see below ) and are likely either stars with erroneous ( overestimated ) v magnitudes , or distant f - g - k stars with large components of reddening . most of these stars are eliminated after the infrared cuts described below . giant stars are notable for having infrared colors different from the m dwarfs , most apparent in a [ ( @xmath41),(@xmath60 ) ] color - color diagram . this has been known since @xcite . dwarf stars have comparatively bluer @xmath41 colors than giants . this is due to opacity differences , mostly from molecular bands of h@xmath61o , which yield significantly higher @xmath62-band and @xmath63-band opacities in m dwarfs @xcite . figure 8 shows the [ ( @xmath41),(@xmath60 ) ] color - color distribution for the stars in our initial sample . stars with parallax measurements are shown in the upper panel , stars without parallax in the lower panel . in both panels , all objects we have identified as probable giants , based on either absolute magnitude ( 2.4.1 ) or reduced proper motion(2.4.2 ) , are plotted in red . the remaining m dwarf candidates are plotted in black . the giants are clearly segregated from the dwarfs along j - h , although there is a small overlap between the two groups . in fact m dwarfs appear to be confined to a relatively compact region around @xmath64 and @xmath65 . a small number of alleged m dwarfs fall outside the cluster ; some have red @xmath41 colors more consistent with the m giants , and indeed they most probably are . other stars have bluer colors which are more typical of f - g - k stars ; we suspect these probably are more massive main sequence stars which made it into our sample probably due to an overestimated photographic magnitude @xmath28 , which would also overestimate the @xmath26 color term , bringing them into the m star subsample . in order to eliminate these leftover misidentified m giants and misclassified f - g - k stars , we further restrict our m dwarf selection to the region in [ ( @xmath41),(@xmath60 ) ] diagram bounded by : @xmath66 among stars with trigonometric parallaxes , we find that 97 of the m dwarf candidates ( black dots in figure 8 upper panel ) fall outside the limits of the region defined above . we conclude that these stars likely have significant errors in their estimated optical or infrared magnitudes , and we exclude them from our census of m dwarfs . among stars with no parallax measurements identified as probable m dwarfs from the reduced proper motion cut ( black dots in figure 8) , we find 487 which fall outside the defined m dwarf boundaries ; these stars are eliminated as well . some of the stars have color consistent with f - g - k main sequence stars ( 0@xmath670.2 , 0.1@xmath680.6 ) and most likely made the initial @xmath582.7 color cut due to an underestimated v magnitude . other excluded sources have @xmath690.7 , and are either giants or distant main sequence stars with large reddening . after these cuts , we are left with a list of 8,889 probable bright m dwarfs , which we retain for building our catalog . among the giants confirmed through parallax ( stars plotted in red in the upper panel of figure 8) a small number fall within the selection box for m dwarfs . specifically , 66 of the 561 giants fall within the region defined by equations 9 - 13 . this means that jhk color cuts alone are susceptible to contamination by background giants . this makes the reduced proper motion selection critical in minimizing giant contamination . note that only 4 of the 561 giants have reduced proper motions within the limit defined for m dwarfs , which increases our confidence that giant contamination in our catalog is negligible . the reduced proper motion cut , on the other hand , may be eliminating bona fide m dwarfs , as mentioned in 2.4.2 above . the lower panel in figure 8 show evidence for this , as 160 of the 626 stars excluded after the reduced proper motion cut ( plotted in red ) do fall within the m dwarf box . overall this suggests that our adopted selection criteria places more of an emphasis on avoiding contamination by giants , at the expense of some incompleteness in the m dwarf targets . from the numbers above , we predict that @xmath70100 m dwarfs might be missing from our catalog because they fail the reduced proper motion cut . in addition , we note that stars identified as giants based on parallax data ( figure 8 top panel , red dots ) and stars excluded from the reduced proper motion cuts ( figure 8 bottom panel , red dots ) show significantly different distributions in @xmath41/@xmath60 color - color space . one average the parallax giants tend to have bluer @xmath42 colors . we suggest that this is due to the fact that most red giants with @xmath140 mas yr@xmath2 are bright enough to have parallaxes from the hipparcos catalog , and that the reduced proper motion cut for stars with no parallax essentially serves to exclude stars with large components of reddening , which are expected to have redder @xmath42 colors than the giants . lllrrrrrrrc pm i00001@xmath716943 & & & & 0.028531 & 69.717117 & 0.136 & 0.136 & -0.002 & & + pm i00003@xmath720802s & & & & 0.087698 & -8.037146 & 0.100 & 0.029 & -0.096 & & + pm i00005@xmath720533 & & & & 0.144895 & -5.551960 & 0.193 & 0.181 & 0.067 & & + pm i00006@xmath711829 & & tyc 1181 - 1683 - 1 & & 0.163528 & 18.488850 & 0.387 & 0.335 & 0.195 & & + pm i00007@xmath711624 & & & & 0.195877 & 16.402805 & 0.125 & 0.013 & -0.125 & & + pm i00007@xmath723510 & & & & 0.195306 & -35.168343 & 0.316 & 0.312 & -0.048 & & + pm i00007@xmath726243 & & & & 0.189068 & -62.728802 & 0.199 & 0.166 & -0.110 & & + pm i00012@xmath711358s & & tyc 600 - 1507 - 2 & & 0.303578 & 13.972055 & 0.147 & 0.025 & 0.144 & 24.9@xmath731.0 & va95 + pm i00014@xmath714724 & & & gj 1293 & 0.371546 & 47.414665 & 0.172 & 0.171 & -0.008 & & + pm i00014@xmath721656 & hip 112 & tyc 5838 - 784 - 1 & & 0.357633 & -16.948410 & 0.393 & 0.299 & -0.255 & 31.4@xmath734.2 & vl07 + pm i00015@xmath720814 & & & & 0.399365 & -8.244875 & 0.124 & 0.097 & -0.077 & & + pm i00016@xmath723258 & & & & 0.408577 & -32.978249 & 0.238 & 0.238 & 0.005 & & + pm i00016@xmath727613 & & & & 0.408879 & -76.230522 & 0.188 & 0.188 & 0.008 & & + pm i00017@xmath723528 & & & & 0.433436 & -35.476082 & 0.502 & 0.502 & -0.023 & & + pm i00024@xmath710440 & & & & 0.613839 & 4.668418 & 0.122 & 0.058 & 0.105 & & + pm i00024@xmath724601 & hip 191 & tyc 8022 - 637 - 1 & & 0.612922 & -46.028893 & 0.194 & 0.192 & -0.022 & 23.0@xmath734.4 & vl07 + pm i00025@xmath726324 & & & & 0.639251 & -63.401974 & 0.822 & -0.488 & -0.661 & & + pm i00026@xmath713821 & & & & 0.667151 & 38.362587 & 0.075 & -0.073 & -0.020 & & + pm i00026@xmath721123 & & & & 0.654399 & -11.393147 & 0.584 & -0.413 & -0.413 & & + pm i00026@xmath723919 & & & & 0.654961 & -39.320053 & 0.200 & 0.199 & 0.023 & & +

the 8,889 stars are selected from the ongoing superblink survey of stars with proper motion mas yr , supplemented on the bright end with the tycho-2 catalog . our catalog is , however , significantly more complete for the northern sky (% ) than it is for the south (% ) . stars are identified as cool , red m dwarfs from a combination of optical and infrared color cuts , and are distinguished from background m giants and highly - reddened stars using either existing parallax measurements or , if such measurements are lacking , on their location in an optical - to - infrared reduced proper motion diagram . spectral type estimated from v - j color shows that most of the stars range from k7 to m4 , with only a few late m dwarfs , all within 20 pc . additional photometric data include optical magnitudes from digitized sky survey plates , and infrared magnitudes from 2mass .

we present an all - sky catalog of m dwarf stars with apparent infrared magnitude j . the 8,889 stars are selected from the ongoing superblink survey of stars with proper motion mas yr , supplemented on the bright end with the tycho-2 catalog . completeness tests which account for kinematic ( proper motion ) bias suggest that our catalog represents of the estimated m dwarfs with j expected to populate the entire sky . our catalog is , however , significantly more complete for the northern sky (% ) than it is for the south (% ) . stars are identified as cool , red m dwarfs from a combination of optical and infrared color cuts , and are distinguished from background m giants and highly - reddened stars using either existing parallax measurements or , if such measurements are lacking , on their location in an optical - to - infrared reduced proper motion diagram . these bright m dwarfs are all prime targets for exoplanet surveys using the doppler radial velocity or transit methods ; the combination of low - mass and bright apparent magnitude should make possible the detection of earth - size planets on short - period orbits using currently available techniques . parallax measurements , when available , and photometric distance estimates are provided for all stars , and these place most systems within 60 parsecs of the sun . spectral type estimated from v - j color shows that most of the stars range from k7 to m4 , with only a few late m dwarfs , all within 20 pc . proximity to the sun also makes these stars good targets for high - resolution exoplanet imaging searches , especially if younger objects can be identified on the basis of x - ray or uv excess . for that purpose , we include x - ray flux from rosat and fuv / nuv ultraviolet magnitudes from galex for all stars for which a counterpart can be identified in those catalogs . additional photometric data include optical magnitudes from digitized sky survey plates , and infrared magnitudes from 2mass .

1510.02860

i

a ballistic atom pump is a system containing two or more reservoirs of neutral atoms or molecules and a junction connecting them containing a time - dependent potential . `` ballistic '' means that atoms move through the pump as independent particles . the theoretical description may be given by classical , semiclassical , or quantum theories . atom statistics may be bose , fermi , or boltzmann . we intend that the definition of `` ballistic atom pumps '' be interpreted broadly ( however , systems having intrinsically many - body phenomena such as viscosity should not be called `` ballistic ; '' if there are interactions among the particles , these interactions can be described by an average single - particle potential ) . particle transport is an ongoing topic of interest in a variety of systems from solid state circuitry to microfluidic devices to futuristic atomtronic components . since the advent of laser cooling , precise control and manipulation of neutral ultracold atoms has attracted attention to atomic systems that can mimic more challenging systems . one such phenomenon in electronic solid - state systems describes electronic transport through mesojunctions @xcite having time - dependent potential barriers , a phenomenon often called `` quantum pumping''@xcite . the choice of potential likewise emulates the turnstile quantum pump usually studied in mesoscopic electronics @xcite . although quantum pumping has been theorized for decades @xcite , there has only recently been an experimental realization of such a system due to the challenges of overcoming capacitive coupling and rectification effects in electronic systems @xcite . recent proposals have suggested bypassing these difficulties by simulating a quantum pump in a system of neutral cold atoms @xcite . neutral atom transport is also becoming increasingly important in its own right due to the ongoing development of atomtronics , which seeks to replicate critical tools of electronics in neutral atoms . analogues of batteries , diodes , transistors , and recently hysteresis @xcite have been explored in ultracold neutral atom systems . the motivation behind such devices is multifarious . unlike their electronic counterparts , these systems allow scientists to study analogous tools in well - controlled and idealized environments like optical lattices . additionally , long coherence times provide unique opportunities for quantum state preparation , storage , and readout , making atomtronic devices a serious competitor as a basis for quantum computers @xcite . finally , neutral atoms present degrees of freedom not available in their electronic counterparts , such as bosons , fermions , and scalable interactions . in this paper , we present a detailed study of the classical and quantum features of a ballistic atom pump which has potential applications such as a battery , diode , or rectifier in atomtronic circuits . the pumps we consider in this paper have two reservoirs and a pump which is effectively one - dimensional , so the hamiltonian is @xmath0 we choose @xmath1 to consist of two repulsive barriers oscillating with the same frequency @xmath2 , but not necessarily with the same amplitude or phase . we study rectangular barriers ( easiest theoretically ) and gaussian barriers ( easiest experimentally using optical forces ) . the questions we address are : can such systems pump atoms preferentially from one side to the other without an external bias , such as a difference in chemical potentials in the reservoirs ? in particular , can we make an atom `` diode '' that will allow atoms to pass through the pump in only one direction ? in order to understand the quantum features of such a pump , it is necessary to develop a clear understanding of classical scattering by a pair of oscillating potential barriers that function as a turnstile pump . we begin with a precise specification of the models we study . then we consider simple asymmetric pumps that rectify net particle transport , which we call `` particle diodes '' because they allow transport in only one direction for certain ranges of initial particle energy . these diodes have one barrier fixed and one oscillating barrier . then we consider pumps that are symmetric in the sense that the two barriers are identical , but their oscillations are not in phase with each other . we prove a symmetry theorem which shows that such pumps can give no net particle pumping if the behavior of the particles is classical and the initial phase - space distribution is uniform in both reservoirs . however , if the phase - space distribution is not uniform , then such pumps can produce net particle transport in either direction . we also show that if the two potential barriers are separated by a modest distance , atoms can get stuck in a `` complex '' or resonance zone between them , and the system is a nice model of chaotic transport @xcite . ( in a separate paper @xcite we have provided a topological description of this chaotic transport ) . the relationships among classical , semiclassical , and quantum descriptions for transport past a single oscillating gaussian barrier were discussed in detail in @xcite . consider the case that atoms enter the pump from one side with fixed momentum @xmath3 and kinetic energy @xmath4 . in the quantum description , because the barriers are oscillating with a fixed frequency , floquet theory tells us that after passing through the pump , the spectrum of transmitted energies is a set of narrow peaks at energies @xmath5 , where @xmath6 is an integer . the heights of these peaks can be computed numerically by solving the schroedinger equation , but in general no patterns are visible in those heights . in the classical description ( again assuming that particles enter with a fixed initial momentum @xmath3 but a range of positions @xmath7 ) , then the final momentum @xmath8 is a bounded periodic function of the initial position @xmath7 , @xmath9 . the upper and lower bounds of the range of this function define the classically allowed region . inside this classically allowed region , provided that @xmath10 is continuous , there must be an even number of trajectories leading to each final momentum . the distribution of final momenta is a smooth function except at extrema of @xmath10 , where the distribution has an integrable singularity . one finds that the floquet peaks obtained in the quantum description are large primarily in the classically allowed region , with small spillover past the boundaries ( momentum - space tunneling ) . still the heights of peaks are incomprehensible . finally , in semiclassical theory , for each final momentum one sums over the initial positions that give trajectories leading to that final momentum , and incorporates phases for each such orbit ( momentum - space action plus maslov indices ) . summing over one cycle of @xmath11 produces a smooth function , and the relative heights of the floquet peaks are discrete values of it . summing over many cycles of @xmath11 causes the peaks seen in the quantum description to emerge , with good agreement between the two methods ( see figs . [ gaussrects ] and [ gauss2osc ] ) . we show a few representative calculations of each type in this paper , but we concentrate on the classical description , with the understanding that semiclassical calculations can be carried out when desired , and that the semiclassical description agrees well with the quantum description .

we examine a classically - chaotic system consisting of two reservoirs of particles connected by a channel containing oscillating potential - energy barriers . we investigate whether such a system can preferentially pump particles from one reservoir to the other , a process often called `` quantum pumping . '' then we examine systems having symmetric barriers . we study the system classically , semiclassically , and quantum mechanically , and find that the quantum description can not be fully understood without the insight gained from classical and semiclassical analysis .

we examine a classically - chaotic system consisting of two reservoirs of particles connected by a channel containing oscillating potential - energy barriers . we investigate whether such a system can preferentially pump particles from one reservoir to the other , a process often called `` quantum pumping . '' we show how to make a `` particle diode '' which under specified conditions permits net particle pumping in only one direction . then we examine systems having symmetric barriers . we find that if all initial particle energies are considered , a system with symmetric barriers can not preferentially pump particles . however , if only finite initial energy bands are considered , the system can create net particle transport in either direction . we study the system classically , semiclassically , and quantum mechanically , and find that the quantum description can not be fully understood without the insight gained from classical and semiclassical analysis . = 1

1103.1910

i

_ shards _ were introduced in @xcite as a way to understand lattice congruences of the weak order on a finite coxeter group . they are defined in terms of the geometry of the associated simplicial hyperplane arrangement . the collection @xmath1 of arbitrary intersections of shards studied in @xcite , forms a lattice under reverse containment . this lattice is called the _ shard intersection order_. surprisingly , @xmath1 was found to be in bijection with the elements of the finite coxeter group @xmath0 , and thus the shard intersection order defines a new lattice structure on @xmath0 . this lattice is graded and contains the @xmath0-noncrossing partition lattice nc(@xmath0 ) as a sublattice . indeed , for any coxeter element , the subposet induced by @xmath2-sortable elements @xcite is a sublattice isomorphic to nc(@xmath0 ) . a formula for calculating the mbius numbers of lower intervals was given in @xcite , but overall the structure of the shard intersection order is not yet well - understood . + in this paper we consider the most classical coxeter group , the symmetric group , whose associated hyperplane arrangement is the braid arrangement . in section [ sectshard ] , we give necessary background information on hyperplane arrangements and the general construction of shards . we then specifically describe shards and shard intersections in the symmetric group . throughout the paper , no prior knowledge of coxeter groups will be assumed . following a suggestion from aguiar @xcite , in section [ sectpermpre ] we characterize shard intersections of type @xmath3 by realizing them combinatorially as certain pre - orders , which we call _ permutation pre - orders_. in section [ sectintord ] , we realize the shard intersection order as an order on the permutation pre - orders and use this realization to determine properties of the order , including an el - labeling . finally , in section [ sectnon ] we characterize _ noncrossing pre - orders _ , which correspond to @xmath2-sortable permutations .

the shard intersection order is a new lattice structure on a finite coxeter group which encodes the geometry of the reflection arrangement and the lattice theory of the weak order . in the case where is the symmetric group , we characterize shard intersections as certain pre - orders which we call permutation pre - orders . we use this combinatorial characterization to determine properties of the shard intersection order . in particular , we give an el - labeling .

the shard intersection order is a new lattice structure on a finite coxeter group which encodes the geometry of the reflection arrangement and the lattice theory of the weak order . in the case where is the symmetric group , we characterize shard intersections as certain pre - orders which we call permutation pre - orders . we use this combinatorial characterization to determine properties of the shard intersection order . in particular , we give an el - labeling .

0905.4784

i

it is now generally accepted that accretion of circumstellar disk material onto the surface of classical t tauri stars ( cttss ) is controlled by strong stellar magnetic fields ( e.g. see review by bouvier et al . cttss represent class ii sources in the classification system defined by lada ( 1987 ) . the definition is based on a gradually falling spectral energy distribution ( sed ) beyond @xmath1 m . this sed shape is believed to arise from a geometrically thin , optically thick accretion disk containing a high concentration of submicron sized dust grains ( e.g. bertout et al . 1988 ) . at some level , the final mass of these forming stars is determined by how much of this disk material accretes onto the central star . additionally , it is within the disks around these low mass pre - main sequence stars that solar systems similar to our own form . it is critical to understand how the central young star interacts with and disperses its disk in order to understand star , and particularly planet , formation . the class i sources defined by lada ( 1987 ) represent one of the earliest stages of star formation and are identified by a rising sed . these sources are deeply embedded within molecular clouds and are very faint or undetectable at optical wavelengths because of a thick envelope of circumstellar dust . it has been commonly thought that class i objects represent an earlier evolutionary stage relative to class ii sources , with the paradigm emerging that class i sources are young protostars near the end of their bulk mass accretion phase . this paradigm is bolstered by the very weak photospheric absorption features in near infrared ( ir ) spectra of these objects ( e.g. casali & matthews 1992 ; greene & lada 1996 , 2000 ) . the lack of absorption lines was interpreted by these authors as the result of strong veiling produced by emission originating in a vigorously accreting circumstellar disk which is being fed by an infalling envelope . this emission is reprocessed by the dusty envelope which results in both the observed featureless continuum and the rising sed . as the accretion rate in the disk weakens and the thick circumstellar envelope either accretes onto the star plus disk system or is disrupted by strong outflows , it is generally thought that class i objects evolve into class ii sources . this general paradigm has been recently challenged by white & hillenbrand ( 2004 ) who find no strong differences in the properties of the central stellar source between a sample of optically selected class i and class ii sources in taurus . on the other hand , doppmann et al . ( 2005 ) argue that the white & hillenbrand ( 2004 ) results are biased by their optical selection of these class i young stellar objects ( ysos ) . doppmann et al . ( 2005 ) perform an extensive ir study of class i ysos in several star forming regions and conclude that , while there is a fair amount of spread in the stellar and accretion properties of these objects , the general paradigm of class i sources representing an earlier , higher accretion rate phase of stellar evolution relative to class ii sources is borne out ( see also prato et al . 2009 ) . some of the confusion and disagreement over the true nature of the class i ysos may be due to variability . it has been suggested that the bulk of a star s final mass is accreted through episodic events where the accretion rate through the disk increases by a factor of @xmath2 for some period of time ( e.g. , hartmann 1998 ) . these episodes of rapid disk accretion may be what we recognize as fu orionis events ( hartmann & kenyon 1996 ) , with these events occuring more frequently during the class i stage . as a result , class i objects should display a large range of accretion behavior , with some objects accreting at close to typical ctts rates , while others are accreting much more rapidly than this . qualitatively , such a picture matches the range of behavior found in these sources in recent studies ( doppmann et al . 2005 , white et al . 2007 , prato et al . 2009 ) . since class i ysos are often rapidly accreting material , the question arises as to how this process occurs . there is substantial evidence to show that fu ori outbursts are the result of very rapid disk accretion ( for a review see hartmann & kenyon 1996 ) . the evidence also suggests that when these objects are not in outburst , accretion onto the central protostar occurs through a disk with infalling material from the envelope piling up in the disk ( e.g. bell 1993 ) . such a scenario can explain the apparent low luminosity of some class i sources relative to what is expected if the infalling material from the envelope were to land initially on the central object ( kenyon et al . 1993 , 1994 ) . these observations of fu ori and lower luminosity class i ysos suggest that accretion onto the central source occurs primarily through a disk whether a particular yso is in a high or low accretion state . for the class ii sources ( cttss ) this accretion process appears to be well described by the magnetospheric accretion paradigm ( see bouvier et al . 2007 for a review ) , but it is currently unclear to what extent this model is appropriate for class i protostars . the magnetospheric accretion model is successful at explaining a number of obsverations of cttss . a key question in the study of these stars is to understand how they can accrete large amounts of disk material with high specific angular momentum , yet maintain rotation rates that are observed to be relatively slow ( e.g. hartmann & stauffer 1989 , edwards et al . this problem is solved in current magnetospheric accretion models by having the stellar magnetic field truncate the inner disk , typically near the corotation radius , and channel the disk material onto the stellar surface , most often at high stellar latitude . the angular momentum of the accreting material is either transferred back to the disk ( e.g. , knigl 1991 ; cameron & campbell 1993 ; shu et al . 1994 ) or is carried away by some sort of accretion powered stellar wind ( e.g. , matt & pudritz 2005 ) . greene and lada ( 2002 ) analyzed the stellar parameters and mass accretion rate of the class i source oph irs 43 and showed that these were consistent with magnetospheric accretion models provided the magnetic field on this source is on a order a kg in strength . covey et al . ( 2005 ) analyzed the rotational properties of class i sources and found that while they are rotating more rapidly than cttss on average , they are not rotating at breakup velocities . these observations could be interpreted in the standard magnetospheric accretion paradigm if the accretion rates of class i sources are larger on average than those of cttss . magnetospheric accretion naturally requires a strong stellar magnetic field . several ttss have now been observed to have strong surface magnetic fields ( basri et al . 1992 ; guenther et al . 1999 ; johns krull 2007 ; johns krull et al . 1999b , 2004 ; yang et al . 2005 , 2008 ) , and strong magnetic fields have been observed in the formation region of the emission line at 5876 ( johns krull et al . 1999a ; valenti & johns krull 2004 ; symington et al . 2005 ; donati et al . 2007 , 2008 ) , which is believed to be produced in a shock near the stellar surface as the disk material impacts the star ( beristain , edwards , & kwan 2001 ) . while a considerable amount is now known about the magnetic field properties of class ii ysos , almost nothing is known directly about the magnetic field properties of class i sources . while not a class i source , fu ori has recently shown evidence for a magnetic field in its disk , revealed through high resolution spectropolarimetry ( donati et al . 2005 ) ; however , there are currently no observations of magnetic fields on the surface of a class i protostar . this is in part due to their faintness and the need for substantial observing time on @xmath3 m class telescopes equipped with high resolution near ir spectrometers in order to obtain the necessary data . in order to begin to address the magnetic field properties of class i sources , we have begun an observational program to survey the magnetic field properties of several class i ysos in the @xmath4-ophiuchi star forming region . here , we report on our first field detection on the class i source wl 17 ( 2mass j16270677 - 2438149 , iso - oph 103 ) . this source has a rising ir sed ( wilking et al . 1989 ) with a spectral index of @xmath5 over the 2 24 @xmath6 m region ( evans et al . wl 17 has been detected in x - rays ( imanishi et al . 2001 ; ozawa et al . 2005 ) suggesting the star is magnetically active . the temperature ( @xmath7@xmath8 k ) and luminosity ( @xmath9 ) of wl 17 ( doppmann et al . 2005 ) give it a mass of @xmath10 and an age @xmath11 years using the tracks of siess et al . ( 2000 ) . in this paper , we look for zeeman broadening of k - band lines in high resolution spectra of wl 17 to diagnose its magnetic field properties . magnetic broadening is easiest to detect when other sources of line broadening are minimized , and the small rotation velocity of wl 17 ( @xmath12sin@xmath13 km s@xmath14 ; doppmann et al . 2005 ) is a great advantage for this work . muzerolle et al . ( 1998 ) derive an accretion luminosity of @xmath15 based on the br-@xmath16 line luminosity measurements of greene and lada ( 1996 ) . this accretion luminosity implies a mass accretion rate of @xmath17 yr@xmath14 using equation ( 8) of gullbring et al . ( 1998 ) with the disk truncation radius assumed to be at @xmath18 . while there are reasons to be concerned about this mass accretion rate estimate ( which are discussed in 4 ) , such a truncation radius implies a stellar field of about a kilogauss . detecting and measuring that field is the goal of the current work . in 2 we describe our observations and data reduction . the magnetic field analysis is described in 3 . in 4 we give a discussion of our results , and 5 summarizes our findings .

strong stellar magnetic fields are believed to truncate the inner accretion disks around young stars , redirecting the accreting material to the high latitude regions of the stellar surface . in the past few years , observations of strong stellar fields on t tauri currently , nothing is known about the magnetic field properties of younger , more embedded class i young stellar objects ( ysos ) . it is believed that protostars accrete much of their final mass during the class i phase , but the physics governing this process remains poorly understood . here , we use high resolution near infrared spectra obtained with nirspec on keck and with phoenix on gemini south to measure the magnetic field properties of the class i protostar wl 17 . we find clear signatures of a strong stellar magnetic field .

strong stellar magnetic fields are believed to truncate the inner accretion disks around young stars , redirecting the accreting material to the high latitude regions of the stellar surface . in the past few years , observations of strong stellar fields on t tauri stars with field strengths in general agreement with the predictions of magnetospheric accretion theory have bolstered this picture . currently , nothing is known about the magnetic field properties of younger , more embedded class i young stellar objects ( ysos ) . it is believed that protostars accrete much of their final mass during the class i phase , but the physics governing this process remains poorly understood . here , we use high resolution near infrared spectra obtained with nirspec on keck and with phoenix on gemini south to measure the magnetic field properties of the class i protostar wl 17 . we find clear signatures of a strong stellar magnetic field . analysis of this data suggests a surface average field strength of kg on wl 17 . we present our field measurements and discuss how they fit with the general model of magnetospheric accretion in young stars .

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quantum annealing ( qa ) , the quantum counterpart of simulated annealing , is an approach for harnessing quantum mechanical effects in searching the energy landscapes of classical np - hard optimization problems @xcite . the development of a quantum annealer by _ d - wave systems _ @xcite has initiated a great deal of theoretical and experimental research into the usefulness of the qa approach and its potential supremacy over classical algorithms @xcite . in recent years , the research community has focused mainly on searching for a useful area of application where qa demonstrates a scaling advantage over classical algorithms . although there is evidence that the d - wave quantum annealer exhibits quantum means of energy landscape exploration such as tunnelling @xcite and entanglement @xcite , the efforts to identify an application for which the device is able to outperform classical optimization have not yet been conclusive . the highlight of the search for potential quantum supremacy is the recent study by google @xcite on an artificially crafted weak strong cluster problem showing that quantum approaches using either the d - wave 2x ( dw2x ) quantum annealer or quantum monte carlo simulation scale significantly better than simulated annealing . the primary difficulty in demonstrating a quantum scaling advantage on useful optimization problems can be attributed to the architecture of the quantum annealer . the quantum annealer is designed to find the ground state of ising hamiltonians with pair - wise interactions on a fixed sparse graph called `` chimera '' . although the majority of optimization problems across various disciplines can be translated into ising problems , their formulations usually have connectivity different from that specified by the chimera s structure . minor embedding ( me ) is a technique for mapping such _ non - native _ problems to the hardware , where several physical qubits encode one logical qubit @xcite . due to the me overhead , embedded problems are suboptimal for determining a scaling advantage @xcite . however , the analysis of the quantum annealer s performance on these problems is critical for the design of future hardware architectures and the setting of various programming parameters . examples of studies on parametrized families of hard embedded problems include the sherrington kirkpatrick model with random @xmath0 couplings , which is directly related to the graph partitioning problem @xcite , operational navigation and scheduling problems @xcite , the job - shop scheduling problem @xcite , the multi - period portfolio optimization problem @xcite , and the graph isomorphism problem @xcite . in this paper , we report on the performance of the dw2x and discuss efficient programming guidelines for the problem of measuring similarity among small molecules that are modelled as labelled graphs . to determine the similarity between two molecular graphs while accounting for noise , a relaxation of the maximum weighted independent set problem , known as maximum weighted co-@xmath1-plex problem , is formulated such that it is consistent with the hardware s architecture . previous studies of non - native problems were conducted using randomly generated instances . to the best of our knowledge , our work is the first to examine the performance of a quantum annealer on real instances of problems in the context of molecular similarity . encoding and decoding are challenges specific to solving non - native problems on a quantum annealer . encoding includes two problems : topological embedding and parameter setting . in the former , the mapping between each logical qubit and a set of connected physical qubits is determined . in the latter , the strength of internal couplings ( among physical qubits corresponding to the same logical qubit ) is set , and the logical local fields and coupling values are distributed among the physical qubits and couplers . it is well known that both topological embedding and parameter setting problems have a significant impact on the efficiency of a quantum annealer @xcite . decoding refers to the process of inferring the solution of each logical qubit from the retrieved solutions of the corresponding physical qubits . an important consequence of the limited available precision @xcite and the existence of errors @xcite of the quantum annealer is that the physical qubits representing a logical qubit might be assign to different values . classical post - processing techniques are often used to assign the right value to the logical qubit . in this paper , we review current approaches for encoding and decoding non - native problems and provide alternatives to the current suboptimal practices , which require substantial computational time . the rest of the paper is organized as follows . in section [ sec : molecular_similarity ] , we define the molecular similarity problem . in section [ sec : quantum_annealing ] , a background on qa is presented and a novel formulation of the molecular similarity problem amenable to qa is developed . different challenges of solving an embedded problem on the hardware architecture are then discussed . detailed experimental results are presented in section [ sec : experimental_results ] . we conclude and discuss future work in section [ sec : conclusion ] . supplementary information is presented in the appendix .

considerable progress has been made in the development of a physical quantum annealer , motivating the study of methods to enhance the efficiency of such a solver . in this work , we present a quantum annealing approach to measure similarity among molecular structures . the authors would like to thank clemens adolphs , hamed karimi , anna levit , dominic marchand , and arman zaribafiyan for useful discussions , robyn foerster for valuable support , and marko bucyk for editorial help . we thank helmut katzgraber for reviewing the manuscript .

quantum annealing is a promising technique which leverages quantum mechanics to solve hard optimization problems . considerable progress has been made in the development of a physical quantum annealer , motivating the study of methods to enhance the efficiency of such a solver . in this work , we present a quantum annealing approach to measure similarity among molecular structures . implementing real - world problems on a quantum annealer is challenging due to hardware limitations such as sparse connectivity , intrinsic control error , and limited precision . in order to overcome the limited connectivity , a problem must be reformulated using minor - embedding techniques . using a real data set , we investigate the performance of a quantum annealer in solving the molecular similarity problem . we provide experimental evidence that common practices for embedding can be replaced by new alternatives which mitigate some of the hardware limitations and enhance its performance . common practices for embedding include minimizing either the number of qubits or the chain length , and determining the strength of ferromagnetic couplers empirically . we show that current criteria for selecting an embedding do not improve the hardware s performance for the molecular similarity problem . furthermore , we use a theoretical approach to determine the strength of ferromagnetic couplers . such an approach removes the computational burden of the current empirical approaches , and also results in hardware solutions that can benefit from simple local classical improvement . although our results are limited to the problems considered here , they can be generalized to guide future benchmarking studies . this research was supported by 1qbit . the authors would like to thank clemens adolphs , hamed karimi , anna levit , dominic marchand , and arman zaribafiyan for useful discussions , robyn foerster for valuable support , and marko bucyk for editorial help . we thank helmut katzgraber for reviewing the manuscript . we also acknowledge the support of the universities space research association ( usra ) quantum artificial intelligence laboratory research opportunity program .

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in this work , we have studied the performance of a quantum annealer in solving instances of the molecular similarity problem utilizing a real data set . the effective use of a quantum annealer presents many challenges . here , we focused on challenges derived from encoding and decoding real - world problems . we addressed the challenges present in both aspects of encoding , that is , embedding and parameter setting , and demonstrated how a careful encoding strategy helps to improve the performance of the dw2x device . in particular , our results emphasized the importance of the embedding selection problem . for some instances , we observed that two different embedding representations of the same original problem yield very different success probabilities . commonly , this difference is attributed to various properties of embedding , for example , the number of qubits used . however , we have shown that none of the commonly observed embedding properties correlate with the hardware s performance . in this work , we have incorporated an empirical method that selects the embedding that maximizes the success probability . we have also observed that the performance of the quantum annealer is less sensitive to the choice of embedding when increasing the size of the original problem . this result is expected since a minor - embedding heuristic will successfully find a larger number of distinct embeddings if the size of the problem to be embedded is significantly smaller than the size of the chip . thus , we expect that the poor performance of embedded problems with a size as large as the size of the current chip should improve in a next - generation quantum annealer . we have also shown that using a theoretical , rather than empirical , approach to select the parameters in the embedding can have significant advantages . besides eliminating the impractical experimental penalty optimization , a theoretical parameter - setting approach ensures an accurate representation of the logical ising hamiltonian , and as a consequence reduces the probability of broken qubits . of particular importance is the overall boosting of the hardware s performance , which benefits from an improved scaling factor over the empirical approach . another important question we have addressed is the selection of a decoding technique . for our problem set , we have found that a simple local decoding technique is effective . this is mainly a consequence of the reduced connectivity of broken logical qubits . specifically , we have shown that fufrther improvement in the hardware performance can be achieved if we use majority vote to fix the broken solutions and subsequently apply a greedy descent post - processing technique . whereas our experimental conclusions are restricted to the specific type of problem studied here , the results provide useful insight for future non - native benchmarking studies . in future work , we will address some of the questions still open regarding the effective implementation of a problem embedded into a quantum annealer . of practical importance is gaining a better understanding of which properties correlate to the performance of the quantum annealer . one possible research direction could be to study the quality of the physical qubits and couplers in the chip . an alternative direction could be to study whether the properties defining the hardness of spin glass problems have an impact on the hardware s performance . after having determined an optimal encoding , we will address the problem of determining the optimal annealing time . 10 e.s . giuseppe , t. erio , j. phys . gen . * 39 * , r393 ( 2006 ) e. farhi , j. goldstone , s. gutmann , j. lapan , a. lundgren , d. preda , science * 292 * , 472 ( 2001 ) m.w . johnson , m.h.s . amin , s. gildert , t. lanting , f. hamze , n. dickson , r. harris , a.j . berkley , j. johansson , p. bunyk , e.m . chapple , c. enderud , j.p . hilton , k. karimi , e. ladizinsky , n. ladizinsky , t. oh , i. perminov , c. rich , m.c . thom , e. tolkacheva , c.j.s . truncik , s. uchaikin , j. wang , b. wilson , g. rose , nature * 473 * , 194 ( 2011 ) v.s . denchev , s. boixo , s.v . isakov , n. ding , r. babbush , v. smelyanskiy , j. martinis , h. neven , phys . x * 6 * , 031015 ( 2016 ) i. hen , j. job , t. albash , t.f . rnnow , m. troyer , d.a . lidar , phys . a * 92 * , 042325 ( 2015 ) d. venturelli , s. mandr , s. knysh , b. ogorman , r. biswas , v. smelyanskiy , phys . x * 5 * , 031040 ( 2015 ) w. vinci , t. albash , g. paz - silva , i. hen , d.a . lidar , phys . a * 92 * , 042310 ( 2015 ) h.g . katzgraber , f. hamze , z. zhu , a.j . ochoa , h. munoz - bauza , phys . x * 5 * , 031026 ( 2015 ) z. zhu , a.j . ochoa , s. schnabel , f. hamze , h.g . katzgraber , phys . a * 93 * , 012317 ( 2016 ) a. perdomo - ortiz , b. ogorman , j. fluegemann , r. biswas , v.n . smelyanskiy , sci . rep . * 6 * ( 2016 ) . : 10.1038/srep18628 s. boixo , v.n . smelyanskiy , a. shabani , s.v . isakov , m. dykman , v.s . denchev , m.h . amin , a.y . smirnov , m. mohseni , h. neven , nat . commun . * 7 * ( 2016 ) . : 10.1038/ncomms10327 t. lanting , a.j . przybysz , a.y . smirnov , f.m . spedalieri , m.h . amin , a.j . berkley , r. harris , f. altomare , s. boixo , p. bunyk , n. dickson , c. enderud , j.p . hilton , e. hoskinson , m.w . johnson , e. ladizinsky , n. ladizinsky , r. neufeld , t. oh , i. perminov , c. rich , m.c . thom , e. tolkacheva , s. uchaikin , a.b . wilson , g. rose , phys . x * 4 * , 021041 ( 2014 ) j. cai , w.g . macready , a. roy , arxiv preprint arxiv:1406.2741 ( 2014 ) v. choi , quantum . inf . process . * 10 * , 343 ( 2011 ) s. mandr , z. zhu , w. wang , a. perdomo - 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a problem must be reformulated using minor - embedding techniques . using a real data set , we investigate the performance of a quantum annealer in solving the molecular similarity problem . although our results are limited to the problems considered here , they can be generalized to guide future benchmarking studies . we also acknowledge the support of the universities space research association ( usra ) quantum artificial intelligence laboratory research opportunity program .

quantum annealing is a promising technique which leverages quantum mechanics to solve hard optimization problems . considerable progress has been made in the development of a physical quantum annealer , motivating the study of methods to enhance the efficiency of such a solver . in this work , we present a quantum annealing approach to measure similarity among molecular structures . implementing real - world problems on a quantum annealer is challenging due to hardware limitations such as sparse connectivity , intrinsic control error , and limited precision . in order to overcome the limited connectivity , a problem must be reformulated using minor - embedding techniques . using a real data set , we investigate the performance of a quantum annealer in solving the molecular similarity problem . we provide experimental evidence that common practices for embedding can be replaced by new alternatives which mitigate some of the hardware limitations and enhance its performance . common practices for embedding include minimizing either the number of qubits or the chain length , and determining the strength of ferromagnetic couplers empirically . we show that current criteria for selecting an embedding do not improve the hardware s performance for the molecular similarity problem . furthermore , we use a theoretical approach to determine the strength of ferromagnetic couplers . such an approach removes the computational burden of the current empirical approaches , and also results in hardware solutions that can benefit from simple local classical improvement . although our results are limited to the problems considered here , they can be generalized to guide future benchmarking studies . this research was supported by 1qbit . the authors would like to thank clemens adolphs , hamed karimi , anna levit , dominic marchand , and arman zaribafiyan for useful discussions , robyn foerster for valuable support , and marko bucyk for editorial help . we thank helmut katzgraber for reviewing the manuscript . we also acknowledge the support of the universities space research association ( usra ) quantum artificial intelligence laboratory research opportunity program .

cs0702033

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let @xmath0 be a finite alphabet of size @xmath1 viewed as an additive group mod @xmath1 . consider the set @xmath2 of vectors of dimension @xmath3 over @xmath0 . a vector @xmath4 will be written as a concatenation of @xmath5 blocks of length @xmath6 each , @xmath7 for a given vector @xmath4 let @xmath8 be the number of @xmath6-blocks of @xmath4 whose rightmost nonzero entry is in the @xmath9th position counting from the beginning of the block . the @xmath6-vector @xmath10 will be called the _ shape _ of @xmath4 . for two vectors @xmath11 let us write @xmath12 if @xmath13 . a shape vector @xmath10 defines a partition of a number @xmath14 into a sum of @xmath6 parts . let @xmath15 be the set of all such partitions . for brevity we write @xmath16 let @xmath17 be a vector of shape @xmath18 . define a weight function ( norm ) on @xmath2 by setting @xmath19 and let @xmath20 denote the metric induced by this norm . we call the function @xmath21 the _ ordered weight_. the ordered weight was first introduced by niederreiter @xcite in his study of low - discrepancy point sets . later , rosenbloom and tsfasman @xcite independently defined the weight @xmath22 ( more precisely , the weight @xmath23 defined below ) , calling it the @xmath24-metric , and studied codes in @xmath2 with respect to it . the set @xmath2 together with this metric will be called the _ ordered hamming space _ ( the _ nrt space _ ) and denoted by @xmath25 . unless specified otherwise , below by distance ( weight ) we mean the ordered distance ( weight ) for some fixed value of @xmath6 . note that the case @xmath26 corresponds to the usual hamming distance on @xmath27 . an @xmath28 _ ordered code _ @xmath29 is an arbitrary subset of @xmath30 vectors in @xmath2 such that the ordered distance between any two distinct vectors in @xmath31 is @xmath32 or more . if @xmath0 is a finite field and @xmath31 is a linear code of dimension @xmath33 , we refer to it as an @xmath34 $ ] code . to define ordered orthogonal arrays , let us call a subset of coordinates @xmath35 _ left - adjusted _ if with any coordinate @xmath36 in the @xmath9th block it also contains all the coordinates @xmath37 of the same block . a subset @xmath38 is called a @xmath39 _ ordered orthogonal array _ ( ooa ) of strength @xmath40 if its projection on any left - adjusted set of @xmath40 coordinates contains all the @xmath41 rows an equal number , say @xmath42 , of times . the parameter @xmath42 is called the _ index _ of @xmath43 . it follows that @xmath44 . if @xmath31 is a linear @xmath34 $ ] code then the code orthogonal to it with respect to the dot product is a @xmath45 linear ooa of index @xmath46 if @xmath0 is equipped with the structure of an additive group , then one can construct _ additive _ ooas . if @xmath0 is a finite field , it is possible to construct linear ooas . ooas ( also called hypercubic designs ) were introduced in lawrence @xcite and mullen and schmid @xcite as a combinatorial equivalent of point sets suitable for numerical integration over the cube . informally this link can be described as follows . let @xmath47^n$ ] be a unit cube , let @xmath48 be a continuous function of bounded variation and let @xmath49 be a set of @xmath50 points in @xmath51 called a net . it is known that the error of quasi - monte carlo integration @xmath52 can be bounded above by @xmath53 where @xmath54 is the total variation of @xmath48 on @xmath55 and @xmath56 is the discrepancy factor of the net . the parameter @xmath56 measures the deviation of the net from a uniformly distributed set of points . the study of uniformly distributed point sets was initiated by h. weyl and e. hlawka . @xcite developed the notions described above and gave the first constructions of nets with bounded factor @xmath58 the study of nearly uniform point sets was taken up in niederreiter @xcite which put forward the notion of @xmath59-nets and derived a bound on @xmath56 via its parameters . we refer to @xcite for detailed background and more references for @xmath59-nets and in particular , to the literature on their constructions . the following theorem relates ooas and @xmath59-nets . below we use its statement as a definition of a @xmath59-net . [ thm : tms ] ( lawrence @xcite , mullen and schmid @xcite ) . there exists a @xmath59-net if and only if there exists an @xmath60 ooa of index @xmath41 and size @xmath61 independently of this line of work , rosenbloom and tsfasman @xcite considered codes in the ordered hamming space and derived bounds on their size . it became clear shortly after their work that ooas and ordered codes are dual types of objects in the sense of delsarte s algebraic theory of coding . this link opened up an avenue for applications of coding - theoretic methods to the study of @xmath59-nets and motivated the study of ordered codes and ooas independently of these applications . in particular , martin @xcite has constructed an association scheme that describes the combinatorics of the space @xmath62 , formulated the linear programming bound ( lp bound ) , outlined a construction of orthogonal polynomials that describe the eigenvalues of the scheme and derived plotkin and rao bounds on ooas via linear programming . much attention was also devoted to relations between the weight enumerators of linear codes and their duals in the ordered hamming space and its generalizations . in particular , a macwilliams theorem for the nrt space was derived by martin @xcite , see also skriganov @xcite , dougherty and skriganov @xcite . bierbrauer @xcite studied coding constructions of @xmath59-nets and bounds for them including the lp bound . apart from the combinatorial context , ordered codes arise in a number of applied problems such as recent algebraic list decoding algorithms of reed - solomon codes @xcite , a study of linear complexity of sequences @xcite , and in a problem in communication theory @xcite . in this paper , we derive several new bounds on ooas and ordered codes . we begin with a bassalygo - elias bound on codes which improves the known upper bounds on their size . however , the bulk of our results are devoted to code bounds using the approach via association schemes and linear programming . we begin with a study of the eigenvalues of the ordered hamming scheme , an association scheme that describes the combinatorics of the space @xmath63 the approach that we follow relies on the orthogonality relation of the eigenvalues . this enables us to identify the eigenvalues as multivariate generalizations of the well - known krawtchouk polynomials , i.e. , a family of real polynomials of @xmath6 discrete variables orthogonal on @xmath64 with respect to the weight given by the multinomial probability distribution . this is the subject of section [ sect : ac ] . turning to bounds , in sect . [ sect : lpb ] we derive a new universal estimate of the size of ordered codes and ooas with a given distance ( strength ) . the asymptotic version of this estimate improves the other results in a certain range of rates . the final section is devoted to the case @xmath65 for which the bounds can be further improved relying on a direct approach . together with the space @xmath62 we will consider the space @xmath66 which differs from it in that the vectors are read `` from right to left . '' namely , for @xmath17 let @xmath67 where @xmath68 is the number of blocks @xmath69 such that @xmath70 and @xmath71 let @xmath72 where @xmath73 and let @xmath74 these metric spaces are identical to each other ; the reason for considering them both is that if we equip @xmath62 with the structure of an association scheme then its dual scheme in delsarte s sense gives rise to the space @xmath75 in particular , if @xmath0 is a finite field and @xmath31 is a linear code in @xmath62 then its dual code @xmath76 lives in @xmath75 we elaborate on this below . an easy combinatorial calculation shows that the number of vectors of shape @xmath18 in @xmath62 is given by @xmath77 and the number of vectors of weight @xmath32 equals to @xmath78 let @xmath79 and let @xmath80 satisfy the equation @xmath81 define the function @xmath82 in the case @xmath26 we write @xmath83 instead of @xmath84 , where @xmath85 let @xmath86 the asymptotic volume of the sphere in @xmath62 is given in the next lemma . [ lemma : vol ] @xcite ( a ) for @xmath87 , equation ( [ eq : z0 ] ) has a unique positive root @xmath88.$ ] + ( b ) let @xmath89 be fixed , @xmath90 then @xmath91

we derive new estimates of the size of codes and orthogonal arrays in the ordered hamming space ( the niederreiter - rosenbloom - tsfasman space ) . we also show that the eigenvalues of the ordered hamming scheme , the association scheme that describes the combinatorics of the space , are given by the multivariate krawtchouk polynomials , and establish some of their properties . dept . of electrical and computer engineering and institute for systems research , university of maryland , college park , md 20742 . email : ppurka@umd.edu . ]

we derive new estimates of the size of codes and orthogonal arrays in the ordered hamming space ( the niederreiter - rosenbloom - tsfasman space ) . we also show that the eigenvalues of the ordered hamming scheme , the association scheme that describes the combinatorics of the space , are given by the multivariate krawtchouk polynomials , and establish some of their properties . dept . of electrical and computer engineering and institute for systems research , university of maryland , college park , md 20742 , usa , and institute for problems of information transmission , russian academy of sciences , moscow , russia . email : abarg@umd.edu . ] dept . of electrical and computer engineering , university of maryland , college park , md 20742 . email : ppurka@umd.edu . ]

math0410132

i

the study of billiards on euclidean polygonal tables has benefitted greatly from the use of the theory of riemann surfaces . a classical unfolding process associates to each rational - angled polygonal table a riemann surface with holomorphic 1-form , see @xcite . using this , kerkhoff - masur - smillie @xcite showed that for almost every direction on a polygonal table , the billiard flow is ergodic . soon thereafter , veech @xcite identified a setting where the only non - ergodic directions are those of saddle connections ; these examples are identified by an associated group , the veech group , being a lattice fuchsian group . in @xcite , veech asked if in general these groups can be non - finitely generated . only recently have examples of infinitely generated veech groups been given @xcite , @xcite . here we study the geometry associated to some of these groups . the riemann moduli space @xmath0 is the space of smooth compact riemann surfaces of genus @xmath1 , up to biholomorphic equivalence . the holomorphic 1-forms on a riemann surface @xmath2 of genus @xmath1 form a @xmath1-dimensional complex vector space , @xmath3 . pairs @xmath4 with @xmath5 form a bundle @xmath6 ( of course , @xmath0 is not a manifold , but rather an orbifold , thus a fiber is @xmath7 ) . each pair @xmath4 ( with @xmath8 non - null ) identifies a translation structure on the real surface @xmath2 : local coordinates are defined by integration of @xmath8 . invoking the real structure of @xmath9 , there is a @xmath10-action on these translation surfaces : post - composition with the local coordinate functions . to each @xmath4 , there is thus a map from @xmath10 to @xmath0 , given by sending group elements to corresponding orbit elements . but , rotations act so as to leave the riemann surface @xmath2 fixed . thus there is an induced a map from @xmath11 to @xmath0 . with respect to the teichmller metric on @xmath0 , this map turns out to be an isometric immersion of the hyperbolic plane @xmath12 . the resulting image is called the _ teichmller complex geodesic _ determined by @xmath4 . we will denote this by @xmath13 . the @xmath10-stabilizer of @xmath4 induces a subgroup of the oriented isometry group of the hyperbolic plane . this induced group is the _ veech group _ , denoted @xmath14 . the teichmller complex geodesic is thus the image of the hyperbolic surface ( or possibly orbifold ) uniformized by the veech group ; the map between them is generically injective . we use this to show : [ thmgeometry ] for any genus @xmath15 , there exists a complex teichmller geodesic in the riemann moduli space @xmath0 that has infinitely many cusps and infinitely many infinite ends . we remind the reader of the definition and basic classification of ends of a hyperbolic surface below . informally , an _ end _ is a direction in which geodesics can leave compact subsets . finite volume hyperbolic surfaces can only have cusps as ends ; briefly , a _ cusp _ , or puncture , corresponds to a conformal punctured unit disk in the surface ( which can not be completed in the surface ) . an end of a hyperbolic surface which corresponds to a conformal non - trivial annulus is called a hole , or a flare . these two types of ends are called finite , an _ infinite end _ is an end which is not finite . we prove our main results using the approach of translation surfaces . in particular , in terms that we make precise below , whereas cusps always form a discrete set , we give examples such that any direction giving an infinite end is the limit of directions of inequivalent infinite ends . a translation surface @xmath16 is called a _ veech surface _ if @xmath17 is a lattice in @xmath18 ; the definition of a non - periodic connection point can be found in subsection [ sadparspecpts ] [ inffatboys ] let @xmath4 be a translation surface which is a finite ramified covering of a veech surface @xmath16 , with ramification above some non - periodic connection point and possibly the singularities of @xmath16 . then @xmath19 has infinitely many cusps and infinitely many infinite ends . choose a dirichlet fundamental domain for @xmath14 acting upon the hyperbolic plane @xmath20 ; this determines an infinite set @xmath21 of points in @xmath22 , each representing a distinct infinite end . the set @xmath21 has no isolated points . that @xmath14 , for @xmath4 as in theorem [ inffatboys ] , is infinitely generated is the main result of @xcite . for the @xmath4 of theorem [ inffatboys ] , the complicated geometry at infinity of @xmath19 is projected to a small sublocus of the riemann moduli space . [ thmbigcusp ] let @xmath23 be as in theorem [ inffatboys ] , and suppose that @xmath2 is of genus @xmath1 . then , there is a two - complex dimensional sublocus @xmath24 such that all ends of the complex teichmller geodesic generated by @xmath23 are contained in finitely many ends of @xmath25 . we prove theorem [ thmgeometry ] by restricting to the case where @xmath4 satisfies the hypotheses of theorem [ inffatboys ] an application of the riemann - hurwitz formula shows that we may assume that the corresponding @xmath16 be of genus two , we give explicit examples of such @xmath16 which admit non - periodic connection points in @xcite , it is now known @xcite , @xcite that the set of such examples is large the existence of infinitely many cusps is proven in [ manycusps ] , the existence of infinitely many infinite ends is proven in [ manyends ] , that every direction of an infinite end is the limit of distinct infinite end directions is also proven in [ manyends ] . we prove theorem [ thmbigcusp ] in [ locend ] . in 2 we give background material on translation surfaces and certain @xmath10-actions , in 3 we discuss projections of horocycles to the moduli space @xmath0 . the main results rest upon the elementary tools presented in 4 . that a hyperbolic surface uniformized by an infinitely generated fuchsian group of the first kind admits infinite ends can be deduced already from @xcite , theorem 16 . thus , the examples of infinitely generated veech group given by mcmullen @xcite must also have these . each of mcmullen s examples has its associated teichmller complex geodesics lying densely on a symmetric hilbert modular surface , all ends must lie in the finitely many ends of the hilbert modular surface . thus , if here also there are infinitely many infinite ends , then they may well show the geometry of the type we discuss here . it is a pleasure to thank f. dalbo , g. forni , and j. smillie for helpful discussions . in particular , we thank g. forni for his ideas which are reflected in [ projhoro ] . we thank a. eskin and others , see @xcite , for continued interest in these matters .

veech groups uniformize teichmller geodesic curves in riemann moduli space . recently , examples of infinitely generated veech groups have been given . we show that these can even have infinitely many cusps and infinitely many infinite ends . we further show that examples exist for which each direction of an infinite end is the limit of directions of inequivalent infinite ends .

veech groups uniformize teichmller geodesic curves in riemann moduli space . recently , examples of infinitely generated veech groups have been given . we show that these can even have infinitely many cusps and infinitely many infinite ends . we further show that examples exist for which each direction of an infinite end is the limit of directions of inequivalent infinite ends .

astro-ph0603198

i

deep irac mosaics identify infrared counterparts for 17 of 20 scuba galaxies in the cudss 14@xmath1 field . the recovery rate of scuba galaxies at 8.0 @xmath0 m is comparable to or better than that found in other counterpart surveys , once the likelihood of mistaken identifications is estimated ( three or fewer for the current work ) . for more than half of the sample , the most - likely 8.0 @xmath0 m counterpart is different than the _ k_-selected counterpart . multiband irac - mips seds allow one to identify and avoid unlikely candidates in the scuba beam ( e.g. , elliptical galaxies ) . this suggests that the mid - infrared regime in general ( and the irac 8.0 @xmath0 m band in particular ) offers a more reliable means than ground - based optical or near - infrared surveys for identifying the true counterparts to the high - redshift , dusty starforming galaxies detected in submillimeter surveys . on the basis of power - law fits to the infrared irac - mips seds we infer that five or possibly six of the counterparts are agn - dominated . the 8.0 @xmath0 m counterparts have redder infrared colors than the general population of irac - detected galaxies in the field . five counterparts have irac - mips seds that are fit well by red power laws and are likely to be agn - dominated . one more is fit well by a slightly blue power - law and may also harbor an active nucleus . four of these six objects are detected in x - ray observations , lending further support to the agn hypothesis . the remaining counterparts are likely to be dominated by starburst emission . this work is based on observations made with the _ spitzer space telescope _ , which is operated by the jet propulsion laboratory , california institute of technology under nasa contract 1407 . support for this work was provided by nasa through contract number 1256790 issued by jpl / caltech . we are grateful to the anonymous referee , whose comments and suggestions greatly improved the clarity and presentation of this work . iraf is distributed by the national optical astronomy observatories , which are operated by the association of universities for research in astronomy , inc . , under cooperative agreement with the national science foundation . facilities : . lcrrrrrccll @xmath7314.1 & & 40.7 & 44.8 & 32.5 & 41.1 & 191 & 14 17 40.22 & 52 29 06.5 & 1.07(0.28 ) & 0.11 + @xmath7314.2 & a & 38.5 & 45.0 & 41.5 & 27.0 & 150 & 14 17 51.33 & 52 30 24.9 & 6.55 & 0.18 + 14.2 & b & 2.0 & 3.3 & 5.5 & 8.6 & @xmath74 & 14 17 51.93 & 52 30 30.8 & 2.12 & 0.45 + @xmath7314.3 & & 35.0 & 41.0 & 48.6 & 48.4 & 408 & 14 18 00.58 & 52 28 21.3 & 0.87(2.32 ) & 0.078 + @xmath7314.4 & a & 2.7 & 3.6 & 5.2 & 27.2 & 239 & 14 17 43.43 & 52 28 05.8 & 8.71 & 0.18 + 14.4 & b & 52.8 & 49.2 & 40.7 & 40.9 & & 14 17 42.41 & 52 28 11.6 & 9.07 & 0.11 + 14.4 & c & 7.4 & 8.7 & 9.5 & 6.2 & @xmath74 & 14 17 43.80 & 52 28 16.8 & 4.71 & 0.52 + 14.6 & & 1.8 & 1.8 & @xmath75 & 5.5 & @xmath74 & 14 17 57.02 & 52 29 14.7 & 8.50 & 0.51 + 14.7 & a & 8.4 & 10.6 & 11.7 & 12.9 & @xmath74 & 14 18 00.95 & 52 29 50.0 & 1.68 & 0.35 + @xmath7314.7 & b & 5.3 & 10.6 & 20.2 & 51.3 & 150 & 14 18 01.15 & 52 29 42.0 & 7.02 & 0.071 + @xmath7314.8 & a & 21.4 & 24.5 & 24.7 & 15.3 & 275 & 14 18 02.01 & 52 30 16.3 & 6.43 & 0.31 + 14.8 & b & 5.4 & 5.6 & 4.9 & 2.9 & @xmath74 & 14 18 02.70 & 52 30 10.4 & 5.25 & 0.76 + @xmath7314.10 & a & 50.1 & 48.4 & 34.8 & 38.3 & 307 & 14 18 03.00 & 52 29 33.2 & 9.81 & 0.12 + 14.10 & b & 4.3 & 3.2 & @xmath75 & @xmath76 & @xmath74 & 14 18 03.98 & 52 29 40.6 & 2.20 & 0.86 + 14.11 & a & 153.6 & 99.5 & 66.7 & 36.0 & @xmath74 & 14 17 46.89 & 52 32 36.1 & 2.69 & 0.13 + 14.11 & b & 225.3 & 140.8 & 92.7 & 50.3 & @xmath74 & 14 17 47.32 & 52 32 42.1 & 4.60 & 0.075 + @xmath7314.12 & a & 3.7 & 5.7 & @xmath75 & 8.0 & 80 & 14 18 04.70 & 52 28 56.0 & 5.48 & 0.47 + 14.12 & b & 3.1 & 4.2 & @xmath75 & 18.3 & @xmath74 & 14 18 05.69 & 52 29 03.3 & 8.60 & 0.33 + @xmath7314.13 & & 580.1 & 981.7 & 1448.5 & 2225.5 & 5646 & 14 17 41.88 & 52 28 23.5 & 0.67(6.46 ) & 0.0013 + 14.14 & a & 9.9 & 8.3 & 3.4 & 6.2 & @xmath74 & 14 18 09.06 & 52 31 00.5 & 4.78 & 0.52 + @xmath7314.14 & b & 9.4 & 10.7 & 7.8 & 6.9 & 120 & 14 18 08.21 & 52 31 08.1 & 6.16 & 0.50 + 14.15 & a & 30.8 & 26.7 & 19.7 & 17.1 & 103 & 14 17 29.87 & 52 28 21.5 & 5.83 & 0.28 + @xmath7314.15 & b & 7.4 & 10.8 & 15.3 & 12.1 & 93 & 14 17 28.44 & 52 28 19.8 & 7.90 & 0.37 + @xmath7314.17 & & 47.1 & 47.0 & 34.6 & 77.0 & 266 & 14 17 24.44 & 52 30 46.1 & 9.48 & 0.049 + @xmath7314.18 & & 159.7 & 138.1 & 143.0 & 164.7 & 1078 & 14 17 42.11 & 52 30 25.7 & 0.61(1.51 ) & 0.029 + @xmath7314.19 & & 15.3 & 20.6 & 21.1 & 25.2 & 84.0 & 14 18 11.26 & 52 30 12.3 & 2.33(8.59 ) & 0.20 + @xmath7314.20 & & 18.5 & 21.2 & 18.6 & 13.9 & @xmath74 & 14 17 50.51 & 52 30 55.2 & 8.87 & 0.34 + 14.22 & a & 29.2 & 28.1 & 19.6 & 19.1 & @xmath74 & 14 17 55.08 & 52 32 08.4 & 7.91 & 0.25 + @xmath7314.22 & b & 72.1 & 66.7 & 49.1 & 50.3 & 500 & 14 17 56.80 & 52 31 57.8 & 9.94 & 0.075 + @xmath7314.23 & a & 31.7 & 43.4 & 47.1 & 34.0 & 529 & 14 17 46.21 & 52 33 22.2 & 1.97 & 0.14 + 14.23 & b & 21.4 & 17.5 & 20.1 & 20.1 & @xmath74 & 14 17 46.68 & 52 33 29.6 & 6.60 & 0.24 lcccccccccc 14.1 & 27.17@xmath770.32 & 26.60@xmath770.12 & 26.28@xmath770.11 & 26.6@xmath770.1 & 24.71@xmath770.05 & 24.79@xmath770.34 & 21.18@xmath770.05 & + 14.2a & 28.0@xmath770.6 & 25.9@xmath770.1 & 26.64@xmath770.07 & 24.94@xmath770.06 & 25.0@xmath770.05 & & 21.4@xmath770.1 & + 14.3 & 24.71@xmath770.06 & 24.55@xmath770.05 & 24.06@xmath770.05 & 24.97@xmath770.06 & 23.20@xmath770.05 & 22.78@xmath770.05 & 21.23@xmath770.05 & + 14.4a & 22.71@xmath770.05 & 22.60@xmath770.05 & 22.70@xmath770.05 & 21.74@xmath770.02 & 22.37@xmath770.05 & @xmath78 & @xmath79 & + 14.7b & 24.53@xmath770.06 & 23.64@xmath770.05 & 23.41@xmath770.05 & 23.5@xmath770.05 & 23.49@xmath770.05 & & 22.5@xmath770.2 & + 14.8a & 25.93@xmath770.13 & 25.48@xmath770.05 & 24.96@xmath770.05 & 25.0@xmath770.1 & 24.58@xmath770.05 & 24.24@xmath770.20 & 21.5@xmath770.1 & + 14.10a & 27.29@xmath770.34 & 26.74@xmath770.13 & 27.01@xmath770.23 & 25.7@xmath770.1 & 24.65@xmath770.05 & 23.83@xmath770.14 & 20.8@xmath770.1 & + 14.12a & @xmath80 & @xmath81 & 27.60@xmath770.37 & 26.4@xmath770.2 & 25.54@xmath770.09 & @xmath78 & @xmath82 & + 14.13 & 23.93@xmath770.05 & 23.73@xmath770.05 & 22.90@xmath770.05 & 22.02@xmath770.02 & 20.86@xmath770.05 & 20.39@xmath770.05 & 18.5@xmath770.1 & 1.150 + 14.14b & 24.80@xmath770.07 & 24.32@xmath770.02 & 24.02@xmath770.02 & 23.76@xmath770.07 & 23.53@xmath770.02 & 22.99@xmath770.11 & 22.0@xmath770.2 & + 14.15b & @xmath80 & @xmath81 & @xmath83 & @xmath84 & 25.13@xmath770.06 & & @xmath85 & + 14.17 & 23.84@xmath770.05 & 23.11@xmath770.05 & 22.29@xmath770.05 & 21.69@xmath770.02 & 21.13@xmath770.05 & 21.00@xmath770.05 & 19.7@xmath770.1 & + 14.18 & 22.97@xmath770.05 & 22.57@xmath770.05 & 21.99@xmath770.05 & 21.36@xmath770.02 & 20.61@xmath770.05 & 20.56@xmath770.05 & 19.7@xmath770.1 & 0.661 + 14.19 & 26.57@xmath770.19 & 24.95@xmath770.03 & 24.36@xmath770.03 & 24.1@xmath770.04 & 24.08@xmath770.05 & 24.10@xmath770.18 & 21.7@xmath770.1 & + 14.20 & @xmath80 & @xmath81 & @xmath83 & 27.7@xmath86 & 25.63@xmath770.65 & 25.83@xmath770.88 & 21.6@xmath770.1 & + 14.22b & @xmath80 & @xmath81 & @xmath83 & 24.83@xmath770.07 & 23.55@xmath770.1 & & 20.19@xmath770.1 & + 14.23a & @xmath80 & 26.75@xmath770.15 & 26.57@xmath770.16 & 27.7@xmath770.6 & 25.09@xmath770.07 & 25.53@xmath770.67 & 20.9@xmath770.2 & lrrrrrrr 8 @xmath0 m galaxies & 726 & @xmath87 & @xmath88 & @xmath89 & @xmath90 & @xmath91 + 8 @xmath0 m counterparts & 17 & @xmath92 & @xmath93 & @xmath94 & @xmath95 & @xmath96 + counterparts subsample & 7 & @xmath97 & @xmath93 & @xmath94 & @xmath98 & @xmath99

we argue that 8.0 m selection offers a better means for identifying counterparts to submillimeter galaxies than near - infrared or optical selection . based on the panchromatic seds , power - law fits to the seds suggest that five objects in the 8.0 m - selected counterpart sample harbor dominant agns ; a sixth object is identified as a possible agn . the 3.6 - 8.0 m colors of the infrared - selected counterparts are significantly redder than the general irac galaxy population in the cudss 14 field .

we identify 17 possible 8.0 m - selected counterparts to the submillimeter galaxies in the cudss 14 field , derived from deep imaging carried out with the irac and mips instruments aboard the _ spitzer space telescope_. ten of the 17 counterparts are not the same as those previously identified at shorter wavelengths . we argue that 8.0 m selection offers a better means for identifying counterparts to submillimeter galaxies than near - infrared or optical selection . based on the panchromatic seds , most counterparts appear to be powered by ongoing star formation . power - law fits to the seds suggest that five objects in the 8.0 m - selected counterpart sample harbor dominant agns ; a sixth object is identified as a possible agn . the 3.6 - 8.0 m colors of the infrared - selected counterparts are significantly redder than the general irac galaxy population in the cudss 14 field .

hep-ph9709214

i

when a high - energy electron emits a soft photon via bremsstrahlung , the process occurs over a rather long distance , known as the formation length . if anything happens to an electron or a photon while traveling this distance , the emission can be disrupted . landau and pomeranchuk were the first who showed that if the formation length of bremsstrahlung becomes comparable to the distance over which a multiple scattering becomes important , the bremsstrahlung will be suppressed @xcite . migdal @xcite , @xcite developed a quantitative theory of this phenomenon . side by side with the multiple scattering of emitting electron one has to take into account also an influence of a medium on radiated electromagnetic field . since long distances are essential in the problem under consideration this can be done by introducing dielectric constant @xmath0 . this effect leads also to suppression of the soft photon emission ( ter - mikaelian effect , see in @xcite ) . a clear qualitative analysis of different mechanisms of suppression is presented in @xcite,@xcite . more simple derivation of the migdal s results is given in @xcite . the next step in a quantitative theory of lpm effect was made in @xcite . this theory is based on the quasiclassical operator method in qed developed by authors @xcite , @xcite . one of the basic equations ( obtained with use of kinetic equations describing a motion of electron in a medium in the presence of external field ) is the schrdinger equation in external field with imaginary potential ( eq.(3.3),@xcite ) . the same equation ( without external field ) was rederived recently in @xcite . the last derivation is based on the approach results of which is coincide basically with the operator quasiclassical method . in @xcite a new calculation approach is developed where multiple scattering is described with the path integral treatment . new activity with the theory of lpm effect is connected with a very successful series of experiments @xcite - @xcite performed at slac during last years ( see in this connection @xcite ) . in these experiments the cross section of bremsstrahlung of soft photons with energy from 200 kev to 500 mev from electrons with energy 8 gev and 25 gev is measured with an accuracy of the order of a few percent . both lpm and dielectric suppression is observed and investigated . these experiments are the challenge for the theory since in all the mentioned papers calculations are performed to logarithmic accuracy which is not enough for description of the new experiment . the contribution of the coulomb corrections ( at least for heavy elements ) is larger then experimental errors and these corrections should be taken into account . in the present paper we calculated the cross section of bremsstrahlung process with term @xmath1 , where @xmath2 is characteristic logarithm of the problem , and with the coulomb corrections taken into account ( section 2 and appendix a ) . this cross section is valid for very high energies when the lpm effect manifest itself for a photon energy of the order of an energy of the initial electron . in the photon energy region , where the lpm effect is `` turned off '' , our cross section gives the exact bethe - heitler cross section ( within power accuracy ) with coulomb corrections . this important feature was absent in the previous calculations . the polarization of a medium is incorporated into this approach ( section 3 ) . the considerable contribution into the soft part of the investigated in the experiment spectrum of radiation gives a photon emission on the boundaries of a target . we calculated this contribution taking into account the multiple scattering and polarization of a medium for the case when a target is much thicker than the formation length of the radiation ( section 4 ) . in section 5 we considered a case when a target is much thinner than the formation length . in this case the cross section has multiplicative form ( probability of radiation times cross section of scattering for the given impact parameter ) . in section 6 a case of an intermediate thickness of a target ( between cases of a thick and a thin target ) is analyzed , polarization of a medium is not included . in section 7 a qualitative picture of a spectral curve ( an effective thickness of a target , position of a minimum ) is discussed . in section 8 we compare the theoretical curve for the intensity spectrum with the data . although agreement between experiment and theory is rather satisfactory , an additional analysis should be done to obtain information about an accuracy of agreement between experimental data and theory .

bremsstrahlung of photons from highly relativistic electrons is investigated . the cross section of the processes , which is suppressed due to a multiple scattering of an emitting electron in dense media ( lpm effect ) and due to photon interaction with electrons of a medium , is calculated with an accuracy up to `` next to leading logarithm '' and with the coulomb corrections taken into account . making allowances for a multiple scattering and a polarization of a medium an analysis of radiation on a target boundary is carried out . interrelation with the recent experiment is discussed .

bremsstrahlung of photons from highly relativistic electrons is investigated . the cross section of the processes , which is suppressed due to a multiple scattering of an emitting electron in dense media ( lpm effect ) and due to photon interaction with electrons of a medium , is calculated with an accuracy up to `` next to leading logarithm '' and with the coulomb corrections taken into account . making allowances for a multiple scattering and a polarization of a medium an analysis of radiation on a target boundary is carried out . the method of consideration of radiation in a thin target under influence of the lpm effect is developed . interrelation with the recent experiment is discussed . = 14.4 cm = -1 cm # 1 .25 cm .5 cm budker institute of nuclear physics , 630090 novosibirsk , russia 2.0 cm

math0408170

i

let @xmath17 be a prime number , @xmath0 a number field , and @xmath18 a finite set of places of @xmath0 . let @xmath19 be the compositum of all extensions of @xmath0 ( in a fixed algebraic closure @xmath20 ) which are unramified outside @xmath18 , and put @xmath21 for its galois group . these _ arithmetic fundamental groups _ play a very important role in number theory . algebraic geometry provides the most fruitful known source of information concerning these groups . namely , given a smooth projective variety @xmath22 , the @xmath17-adic tale cohomology groups of @xmath23 are finite - dimensional vector spaces over @xmath24 equipped with an action of @xmath25 where @xmath18 consists of the primes of bad reduction for @xmath22 together with the primes of @xmath0 of residue characteristic @xmath17 . the richness of this action can be judged , for example , by the intimate relationships between algebraic geometry and the theory of automorphic forms which it mediates . for this and many other reasons , it would be difficult to overstate the importance of these @xmath17-adic galois representations . nonetheless , linear @xmath17-adic groups simply form too restrictive a class of groups to capture _ all _ galois - theoretic information , and some important conjectures in the subject , notably the fontaine - mazur conjecture @xcite ( to mention only one , see the discussion in section [ sec : conjectures ] ) , point specifically toward the kind of information inside arithmetic fundamental groups which can not be captured by finite - dimensional @xmath17-adic representations . in this work , we discuss a method for studying finitely ramified extensions of number fields via _ arithmetic dynamical systems on _ @xmath26 . at least conjecturally , this method provides a vista on a part of @xmath25 invisible to @xmath17-adic representations . we now sketch the construction , which is quite elementary . let @xmath0 be a perfect field , and suppose @xmath27 $ ] is a polynomial of degree @xmath28 such that its derivative @xmath29 is not identically @xmath30 in @xmath31 $ ] . for each @xmath32 , let @xmath33 be the @xmath7-fold iterate of @xmath8 , i.e. @xmath34 and @xmath35 for @xmath32 . let @xmath1 be a parameter for @xmath36 with function field @xmath2 . we are interested in the tower of branched covers of @xmath37 given by @xmath38,\ ] ] as well as extensions of @xmath0 obtained by adjoining roots of its specializations at arbitrary @xmath39 . the variable - separated polynomial @xmath12 is clearly absolutely irreducible ( since it is linear in @xmath1 ) and of degree @xmath40 in @xmath41 $ ] ; it is separable over @xmath9 by the assumption that @xmath29 is not identically 0 . fix an algebraic closure @xmath42 of @xmath9 , and let @xmath20 be the algebraic closure of @xmath0 determined by this choice , i.e. the subfield of @xmath11 consisting of elements algebraic over @xmath0 . for @xmath32 , let @xmath43 be the set of roots in @xmath11 of @xmath12 ; it has cardinality @xmath40 . we denote by @xmath44 the @xmath45-regular rooted tree whose vertex set is @xmath46 , and whose edges connect @xmath47 to @xmath48 exactly when @xmath49 ; its root ( at ground level ) is @xmath1 . let us choose and fix an _ end _ @xmath50 of this tree ; in other words , we have @xmath51 and @xmath52 for @xmath13 . for each @xmath13 , we consider the field @xmath53/(\ph_n)$ ] and its galois closure @xmath54 over @xmath9 . let @xmath55 be the integral closure of @xmath56 $ ] in @xmath57 . corresponding to each @xmath58 , we may fix compatible _ specialization maps _ @xmath59 with image @xmath60 , a normal extension field of @xmath0 and put @xmath61 for the correspoding compatible system of roots of @xmath62 . we denote by @xmath63 the image of the restriction of @xmath64 to @xmath65 . we refer the reader to subsection [ subsec : specialization ] for more details , but we should emphasize here that @xmath62 is not necessarily irreducible over @xmath0 ; hence , although @xmath60 depends only on @xmath66 and @xmath67 , the isomorphism class of @xmath63 depends _ a priori _ on the choice of @xmath68 as well as on the choice of compatible @xmath64 . also , the galois closure of @xmath69 is contained in , but possibly distinct from , @xmath60 . nonetheless , unless stated otherwise , @xmath68 and @xmath67 are arbitrary but fixed , and in this case we will usually not decorate @xmath63 with @xmath68 and occasionally we may write simply @xmath70 instead of @xmath71 . taking the compositum over all @xmath13 , we obtain the _ iterated extension _ @xmath72 attached to @xmath8 , with galois closure @xmath73 over @xmath9 . similarly for each @xmath74 , we obtain a specialized iterated extension @xmath75 with galois closure over @xmath0 contained in @xmath76 . we put @xmath77 for the _ iterated monodromy group _ of @xmath8 and for @xmath39 , we denote by @xmath78 its specialization at @xmath67 . the group @xmath79 has a natural and faithful action on the tree @xmath44 , hence comes equipped with a rooted tree representation @xmath80 . for more on rooted trees and iterated monodromy groups ( in a more general context , in fact ) , see nekrashevych @xcite as well as bartholdi - grigorchuk - nekrashevych @xcite . since we are interested in finitely ramified towers ( meaning those where only finitely many places of the base field are ramified ) , we need to answer the following question : which polynomials @xmath8 have the property that the corresponding iterated tower @xmath81 , as well as all of its specialziations @xmath82 , are finitely ramified ? we first recall some standard terminology from polynomial dynamics . we say that @xmath83 is _ periodic _ for @xmath8 if @xmath84 for some @xmath13 . moreover , @xmath85 is _ preperiodic _ for @xmath8 if for some @xmath86 , @xmath87 is periodic for @xmath8 ; equivalently , @xmath88 is preperiodic for @xmath8 means that @xmath89 , i.e. the orbit of @xmath88 under the iterates of @xmath8 , is a finite set . we put @xmath90 for the set of affine _ ramification _ and _ branch _ points , respectively . the elements of @xmath91 and @xmath92 are also the _ critical points _ , respectively _ critical values _ of @xmath8 . the polynomial @xmath8 is called _ post - critically finite _ if every member of @xmath91 is a preperiodic point for @xmath8 . in other words , @xmath8 is post - critically finite exactly when the _ post - critical set _ @xmath93 , i.e. the union of the orbits of critical points under the iterates of @xmath8 , is a finite set . it has long been known that the post - critical set plays a crucial role in the dynamics of the polynomial . indeed , the class of dynamical systems corresponding to post - critically finite polynomials is a well - studied one , having gained prominence following a celebrated theorem of thurston ; see , for example , douady - hubbard @xcite , bielefed - fisher - hubbard @xcite , as well as the papers by poirier @xcite , pilgrim @xcite , and pakovich @xcite ; the latter two concern the connection with actions of @xmath94 on certain finite trees . our starting point is the following characterization of finitely ramified iterated extensions . [ thm:1 ] the iterated tower of function fields @xmath15 is finitely ramified if and only if @xmath8 is post - critically finite . if @xmath8 is post - critically finite , every specialization @xmath95 of this tower is finitely ramified . the first assertion of the theorem is clear geometrically since @xmath96 . the second assertion , however , is not a formal consequence of the first , since any element of @xmath0 is a unit in @xmath9 ; the proof we give for it proceeds via proposition [ prop : recur ] , where we calculate a recurrence for the discriminant of @xmath12 ( valid for an arbitrary polynomial @xmath8 ) , giving a more precise version of the theorem . the proof of proposition [ prop : recur ] rests on a riemann - hurwitz genus formula for polynomials @xcite . now let us return to the case of a number field @xmath0 . for each post - critically finite @xmath27 $ ] , and each @xmath97 , theorem [ thm:1 ] provides a surjection @xmath98 for an effectively determined finite set @xmath99 of places of @xmath0 ( see definition [ def : s ] and corollary [ cor : imr ] ) . we call @xmath100 the _ iterated monodromy representation _ attached to @xmath8 and @xmath67 . the study of automorphism groups of rooted trees is a relatively new and quite active topic in group theory ( see @xcite , @xcite , and @xcite ) . the structure of non - abelian subgroups of these automorphism groups appears to be quite different from that of linear @xmath17-adic groups ( see the papers just cited as well as bux - perez @xcite ) . the natural action of iterated monodromy groups on rooted trees leads us to the expectation that iterated monodromy representations @xmath100 attached to post - critically finite polynomials @xmath101 $ ] have the potential of revealing aspects of arithmetic fundamental groups which are not visible to @xmath17-adic representations ; see the discussion in section [ sec : conjectures ] as well as boston s preprint @xcite , where tree representations are suggested as the proper framework for studying finitely ramified tame extensions . since all finitely ramified @xmath17-adic galois representations with infinite image are expected , by a conjecture of fontaine and mazur , to be wildly ( even deeply ) ramified at some prime of residue characteristic @xmath17 , an immediate question is what can be said about the presence of wild ramification in specialized iterated extensions @xmath95 . experimentation leads to the expectation that generically the primes of residue characteristic dividing @xmath45 ramify deeply in @xmath95 . for example , if @xmath102 with @xmath103 and @xmath104 , then for all @xmath105 , the extensions @xmath95 are deeply ramified at all @xmath17 dividing @xmath45 . ( see , however , questions [ ques:1 ] and [ ques:2 ] in [ sec : conjectures ] ) . under an assumption of good reduction for @xmath8 , we prove a partial result toward this expectation , namely for integral @xmath67 , we estimate from below the power of @xmath17 dividing the discriminant of @xmath62 . to be precise , in [ sec : wild ] , we will prove the following theorem . [ thm : wild1 ] let @xmath0 be a number field . suppose @xmath27 $ ] is post - critically finite , has degree divisible by @xmath17 , and has good reduction at a valuation @xmath47 of residue characteristic @xmath17 , i.e. @xmath8 has @xmath47-integral coefficients with @xmath47-unital leading coefficient . then for any @xmath106 , @xmath107 assuming @xmath62 is @xmath0-irreducible for all @xmath7 , this estimate shows that the tower of rings @xmath108 $ ] , where @xmath109 is a compatible sequence of roots of @xmath62 , is wildly ramified at @xmath17 . note that @xmath108 $ ] is an _ order _ inside the maximal order of @xmath110 ; it is the discriminant of the latter which is our primary interest , but the theorem estimates the discriminant of the former . this is one sense in which the above theorem is only a partial answer to our question about wild ramification in iterated extensions . on the other hand , in section [ sec : quad ] , we illustrate with the tower corresponding to @xmath111 , the possibility that the orders @xmath112 $ ] ( for a large set of @xmath113 ) are maximal , giving examples of monogne number fields . the organization of this article is as follows . in [ sec : prelim ] , we outline some preliminary facts regarding post - critically finite polynomials , including a classification of the very simplest examples for each degree , namely those that are _ critically fixed _ ( every critical point is fixed , also known as _ conservative _ ) and _ simply ramified _ ( every non - trivial ramification index is @xmath114 ) . in [ sec : pcf ] and [ sec : wild ] , we prove theorems [ thm:1 ] [ thm : wild1 ] ) , respectively . in [ sec : decomposition ] , we describe the decomposition of unramified primes in iterated towers in terms of simple properties of certain finite graphs . in [ sec : quad ] , we study the quadratic case in more detail , obtaining a recursion for writing down post - critically finite quadratic polynomials , which give number fields of independent interest ; we also discuss the example @xmath115 in detail , proving monogenicity of certain number fields . finally , in [ sec : conjectures ] , we outline a number of questions and open problems . * acknowledgments . * work on this project began in june 2003 during visits by wa and cm to amherst supported partially by nsf grant dms-0226869 . a few months later , the preprint @xcite of v. nekrashevych was posted on ` arxiv.org ` ; in it , iterated monodromy groups from a more general perspective are studied . we learned from @xcite that the construction ( [ pn ] ) we had been studying had earlier been suggested by r. pink ( private communication ) . a special case also occurs in boston s preprint @xcite . cm thanks r. pink for a helpful conversation . cm and fh would like to thank e. bayer - fluckiger for financial support of their visits to epfl , lausanne in 2004 where a portion of this work was completed . we are grateful to r. benedetto and p. gunnells for useful discussions .

let be a number field , a parameter , , and $ ] a polynomial of degree . the polynomial $ ] , where is the-fold iterate of , is absolutely irreducible over ; we compute a recursion for its discriminant . let be the field obtained by adjoining to all roots ( in a fixed ) of for all ; its galois group is the iterated monodromy group of . the iterated extension is finitely ramified over if and only if is post - critically finite . we show that , moreover , for post - critically finite , every specialization of at is finitely ramified over , pointing to the possibility of studying galois groups of number fields with restricted ramification via tree representations associated to iterated monodromy groups of post - critically finite polynomials . we discuss the wildness of ramification in some of these representations , describe prime decomposition in terms of certain finite graphs , and also give some examples of monogne number fields that arise from the construction . + august 12 , 2004

let be a number field , a parameter , , and $ ] a polynomial of degree . the polynomial $ ] , where is the-fold iterate of , is absolutely irreducible over ; we compute a recursion for its discriminant . let be the field obtained by adjoining to all roots ( in a fixed ) of for all ; its galois group is the iterated monodromy group of . the iterated extension is finitely ramified over if and only if is post - critically finite . we show that , moreover , for post - critically finite , every specialization of at is finitely ramified over , pointing to the possibility of studying galois groups of number fields with restricted ramification via tree representations associated to iterated monodromy groups of post - critically finite polynomials . we discuss the wildness of ramification in some of these representations , describe prime decomposition in terms of certain finite graphs , and also give some examples of monogne number fields that arise from the construction . + august 12 , 2004

1501.01629

i

the density at which a particular molecular transition is excited has always been an interesting quantity for studies of molecular gas in the interstellar medium . two concepts have been developed , the critical density and the effective excitation density , to quantify the excitation density of a transition . a traditional approach in studying the critical density has been to consider the molecular rotational energy levels as a simple two level system . while this approach has pedagogical advantages , the interpretation of concepts , such as critical density , are oversimplified and incorrect . molecules are fundamentally multi - level systems with radiative and collisional processes between the levels ( figure 1 ) . it is almost never appropriate to approximate commonly observed dense gas tracers , such as hco@xmath3 , hcn , nh@xmath7 , n@xmath4h@xmath3 , etc . , as two level systems . therefore , in this tutorial , we eschew the two level approximation and consider the full multi - level nature of molecular excitation . it is assumed that the reader has a basic familiarity with statistical equilibrium , radiative transfer , and molecular spectroscopy . for a summary of radiative transfer techniques and molecular data used in those calculations , see van der tak ( 2011 ) and references therein . the purpose of this tutorial is to quantify and systematize the use of critical density and effective excitation density for dense gas molecular tracers . we shall use the excitation of two molecules , hco@xmath3 and nh@xmath7 , as examples throughout this tutorial . figure 1 shows the energy level structure for both molecules . hco@xmath3 is an abundant linear molecule with a simple @xmath9 electronic ground state meaning that there is zero net electronic spin and zero net electronic angular momentum that could interact with and split the rotational levels of the molecule . electric dipole selection rules limit transitions to @xmath10 . the @xmath2 ground state rotational transition is a millimeter transition at 89 ghz ( 3.3 mm ) and the frequency of rotational transitions progress linearly into the submillimeter part of the spectrum . nh@xmath7 is an abundant pyramidal symmetric top molecule with a simple @xmath11 electronic ground state also meaning that there is zero net electronic spin and zero net electronic angular momentum . the energy levels are designed by @xmath12 where @xmath13 is the total rotational angular momentum and @xmath14 is the projection of the angular momentum onto the nh@xmath7 symmetry axis . electric dipole transition do not allow the projected angular momentum to change ( @xmath15 ) . as a results , the energy level structure is usually organized in k - ladders with each k - ladder designated as either ortho ( @xmath14 = 0 , 3 , 6 , etc . ) or para ( @xmath14 = 1 , 2 , 4 , 5 , etc . ) due to the spin symmetry required to satisfy fermi - dirac statistics for each rotational energy level . the plane of three h atoms can tunnel from positions above and below the n atom resulting in inversion splitting of each rotational level ( with symmetry denoted by @xmath16 ) except for levels with @xmath17 for which half of the inversion levels are missing due to the pauli exclusion principle ( see townes & schwalow 1975 for a detailed explanation ) . electric dipole transitions are allowed between the inversion - split levels with different symmetries and these inversion transitions occur at wavelengths near 1.3 cm ( 24 ghz ) . since @xmath13 and @xmath14 do not change in a pure inversion transition , the shorthand notation @xmath18 has been adopted . as with hco@xmath3 , there are rotational transition with @xmath10 , but since nh@xmath7 is a lighter molecule than hco@xmath3 ( @xmath19 where i is the moment of inertia of the molecule measured from a coordinate system at the center - of - mass ) , the transitions occur at submillimeter and far - infrared wavelengths . thus , the lowest energy transitions of hco@xmath3 and nh@xmath7 cover a wide range of wavelengths from the centimeter to the far - infrared .

the optically thin critical densities and the effective excitation densities to produce a 1 k km / s ( or jy km / s ) spectral line are tabulated for 12 commonly observed dense gas molecular tracers . the dependence of the critical density and effective excitation density on physical assumptions ( i.e. gas kinetic temperature and molecular column density ) is analyzed .

the optically thin critical densities and the effective excitation densities to produce a 1 k km / s ( or jy km / s ) spectral line are tabulated for 12 commonly observed dense gas molecular tracers . the dependence of the critical density and effective excitation density on physical assumptions ( i.e. gas kinetic temperature and molecular column density ) is analyzed . critical densities for commonly observed dense gas transitions in molecular clouds ( i.e. hcn , hco , nh ) are typically orders of magnitude larger than effective excitation densities because the standard definitions of critical density do not account for radiative trapping and k km / s lines are typically produced when radiative rates out of the upper energy level of the transition are faster than collisional depopulation . the use of effective excitation density has a distinct advantage over the use of critical density in characterizing the differences in density traced by species such as nh , hco , nh , and hcn as well as their isotpologues ; but , the effective excitation density has the disadvantage that it is undefined for transitions when , for low molecular column densities , and for heavy molecules with complex spectra ( i.e. chcho ) .

1501.01629

i

in this tutorial , @xmath51 and are defined and their properties analyzed . the values for @xmath51 and are calculated for multiple transitions of 12 commonly observed dense molecular gas species in table 1 . inversely depends on the choice of column density and increases non - linearly as gas kinetic temperatures are lowered ( @xmath100 k ) . we have estimated the reference column density for difference species listed in table 1 from surveys of cores and clumps in the milky way . the quoted can be easily scaled to another column density using equation 13 . since the definition of is arbitrary ( the @xmath6 k km / s criteria ) and does not depend on a specific ratio of radiative rates to collisional depopulation rates ( c.f . @xmath34 for the definition of @xmath33 ) , it is seductive to use @xmath51 to characterize the density at which a transition is excited as it can be analytically calculated ; however , @xmath51 does not account for radiative trapping which can easily lower the effective critical density by more than an order of magnitude for commonly observed dense gas tracers such as hco@xmath3 @xmath2 , hcn @xmath2 , n@xmath4h@xmath3 @xmath2 , etc . the combination of @xmath122 and radiative trapping that generate a @xmath6 k km / s line lower by @xmath191 orders of magnitude relative to @xmath51 for many commonly observed millimeter and submillimeter lines . furthermore , can account for abundance or column density differences to better differentiate the excitation density of different species than @xmath51 ( i.e. hco@xmath3 vs. n@xmath4h@xmath3 or isotpologues vs. the main species ) . overall , the effective excitation density gives a better estimate of the range of densities at which a modest ( 1 k km / s ) molecular line can be observed ; however , use of @xmath94 has the disadvantages that an appropriate column density must be determined for the observations of interest and that it is not defined for all transitions ( in particular when @xmath8 ) and for all species ( e.g. hnco , ch@xmath7cho , etc . ) . @xmath51 and provide only rough estimates of the densities traced and should not be over - interpreted . more sophisticated tools such as the contribution function ( tafalla et al . 2006 ) may be used to determine the various contributions to the observed line profile along the line of sight ( see pavlyuchenkov et al . 2008 for a detailed analysis of these techniques ) . ultimately , if one wants to understand their observed spectra , radiative transfer modeling with publicly available codes are a fast and efficient way to determine the physical properties of a region .

the use of effective excitation density has a distinct advantage over the use of critical density in characterizing the differences in density traced by species such as nh , hco , nh , and hcn as well as their isotpologues ; but , the effective excitation density has the disadvantage that it is undefined for transitions when , for low molecular column densities , and for heavy molecules with complex spectra ( i.e. chcho ) .

the optically thin critical densities and the effective excitation densities to produce a 1 k km / s ( or jy km / s ) spectral line are tabulated for 12 commonly observed dense gas molecular tracers . the dependence of the critical density and effective excitation density on physical assumptions ( i.e. gas kinetic temperature and molecular column density ) is analyzed . critical densities for commonly observed dense gas transitions in molecular clouds ( i.e. hcn , hco , nh ) are typically orders of magnitude larger than effective excitation densities because the standard definitions of critical density do not account for radiative trapping and k km / s lines are typically produced when radiative rates out of the upper energy level of the transition are faster than collisional depopulation . the use of effective excitation density has a distinct advantage over the use of critical density in characterizing the differences in density traced by species such as nh , hco , nh , and hcn as well as their isotpologues ; but , the effective excitation density has the disadvantage that it is undefined for transitions when , for low molecular column densities , and for heavy molecules with complex spectra ( i.e. chcho ) .

1603.07354

i

two particle correlations in high - energy collisions have played significant role to unravel qcd novel phenomena @xcite . the recent discovery of the so - called ridge phenomenon , namely di - hadron collimation in the relative azimuthal angle @xmath0 between pairs at near - side @xmath1 ( and at away - side @xmath2 ) which extend to a large pseudorapidity separation between pairs @xmath3 , in high - multiplicity events selection in both proton - proton and proton(deuteron)-nucleus collisions at the lhc and rhic @xcite and more recently in @xmath4 collisions at rhic @xcite , triggered an on - going debate about the underlying dynamics of high - multiplicity events in small colliding systems . strikingly , such correlations when triggering on rare events with high multiplicities ( not present in minimum bias proton - proton collisions ) show great deal of similarity to that measured in semi peripheral nucleus - nucleus collisions @xcite . the observation of a ridge in high - multiplicity p+pb collisions @xcite was less surprising compared to the same effect in proton - proton ( p+p ) collisions @xcite , but it was unexpected that the strength of the correlation is almost as large as the ridge in heavy - ion collisions . the ridge - type structure in nucleus - nucleus ( a+a ) collisions at rhic and the lhc is fairly understood as a phenomenon related to hydrodynamical behavior of the quark - gluon - plasma , see for example refs.@xcite . however , it is still an outstanding problem to understand how ( and why ) a small system like the one produced in p+p collisions , an order of magnitude smaller than in heavy - ion collisions , exhibits a hydro type behavior @xcite . the initial - state color - glass - condensate ( cgc ) effective field theory approach provides an alternative description of the ridge effect in small colliding systems @xcite . within the initial - state cgc framework , it was shown that the ridge effect can arise from three rather different mechanisms : glasma graphs @xcite , local anisotropy of target fields @xcite and spatial variation of partonic density @xcite . in principle , all these three mechanisms can be relevant to understanding the true physical origin of the ridge in p+p(a ) collisions @xcite . note that it was recently shown that the calculation based on the glasma graphs @xcite can be understood in terms of bose enhancement of gluons in the hadronic wave - functions @xcite . a complete analysis of the observed ridge effect in p+p(a ) collisions which incorporates all above - mentioned contributions is still missing . for recent reviews on the ridge effect , see refs.@xcite . it is currently unknown whether the ridge is a universal phenomenon , for all different two - particle productions such as di - hadron , photon - jet , di - jet and di - photon production in p+p(a ) collisions , see ref.@xcite . in this paper , for the first time , we investigate whether based on the initial - state physics there is a ridge - type structure for prompt photon and jet pair production in high multiplicity p+p(a ) collisions at rhic and the lhc . we show near - side collimation of photon - jet production in p+p(a ) collisions strongly depends on the gluon saturation dynamics and such measurements can help to understand the true origin of ridge effect in high - multiplicity events . photons radiated in hard collisions not via hadronic decays are usually called prompt photon . there are advantages to studying prompt photon and jet pair production as compared to di - hadron ( and di - jet ) production . it is theoretically cleaner ; one avoids the difficulties involved with description of hadronization and possible initial - state - final - state interference effects which may be present for hadrons pair production . in particular , in the inclusive di - jet production at leading - order approximation , higher number of wilson lines , the weizscker - williams and the dipole gluon distributions are involved @xcite while in diffractive dis di - jet @xcite , photon - jet @xcite and prompt di - photon @xcite cross - sections , only dipole gluon distribution appears which is both experimentally and theoretically well - known , see for example refs.@xcite . moreover , in contrast to gluons , prompt photons do not scatter on the target gluon field , but rather decohere from the projectile wavefunction due to scatterings of the quarks . therefore , the underlying mechanism of prompt photon and quark pair production is quite different from two gluons ( and quark - gluon ) pair production , and such measurements can provide vital complementary information to address whether it is the initial or final state effects that play dominant role in formation of the ridge collimation in p+p(a ) collisions . note that the photon - hadron ( and photon - jet ) correlations have also been a very powerful probe of the in - medium parton energy loss in high - energy heavy - ion collisions @xcite . it was recently shown @xcite that the correlation of the back - to - back photon - hadron pair production in high - energy p+p and p+a collisions can be used to probe the gluon saturation at small - x region and to study the physics of cold nuclear matter in dense region . however , in the previous studies , photon - hadron correlations were only studied in a small kinematic window ( concentrating mostly in away - side correlations at @xmath5 ) in minimum bias ( or medium impact parameters ) collisions . here , we extend the previous cgc studies , and analysis in details photon - jet and photon - hadron pair correlations in p+p and p+a collisions at finite rapidity separations between prompt photon and jet @xmath6 for arbitrary azimuthal angle @xmath7 between the pairs in high multiplicity events . we show that due to gluon saturation dynamics the photon - jet pairs within forward rapidity separation about @xmath8 are collimated in the relative azimuthal angle between pairs at near - side @xmath9 at low transverse momenta of pairs in high multiplicity collisions . these ridge - like features are strikingly similar to the observed ridge effect for di - hadron correlations @xcite at rhic and the lhc . we provide various predictions for photon - jet correlations ( and the ridge ) which can be tested at rhic and the lhc . the asymmetric nature of photon - hadron ( and photon - jet ) production , and the fact that in semi - inclusive photon - hadron production , qcd and electromagnetic interactions are inextricably intertwined , make correlations very intriguing . we show that the hadronization of jet has non - trivial effects on the photon - jet correlations . this paper is organized as follows ; in sec . ii , we first provide a concise description of theoretical framework by introducing the main formulas for the calculation of the cross sections of photon - jet and photon - hadron pair production within the cgc approach . in sec . ii we also introduce the observables that we are interested to compute and our numerical setup . in sec . iii , we present our detailed results and predictions . we summarize our main results in sec .

we investigate long range rapidity correlations of pairs of prompt photon and jet in the color glass condensate ( cgc ) framework in proton - proton and proton - nucleus collisions at rhic and the lhc . we show that photon - jet correlations exhibit long - range azimuthal collimation at near - side for low transverse momenta of the produced photon and jet in high - multiplicity events . these ridge - like features are strikingly similar to the observed ridge effect for di - hadron correlations at rhic and the lhc . we show that correlations in the relative rapidity and the relative azimuthal angle between pairs of prompt photon and jet strongly depend on the gluon saturation dynamics at small - x kinematics and such measurements can help to understand the true origin of the observed di - hadron ridge in p+a collisions , and address whether the ridge is a universal phenomenon for all two particle correlations at high energy and high multiplicity events . we also investigate if there is a ridge - like structure for photon - hadron pair correlations at rhic and the lhc . we found that the hadronization of jet has non - trivial effects on the photon - jet correlations .

we investigate long range rapidity correlations of pairs of prompt photon and jet in the color glass condensate ( cgc ) framework in proton - proton and proton - nucleus collisions at rhic and the lhc . we show that photon - jet correlations exhibit long - range azimuthal collimation at near - side for low transverse momenta of the produced photon and jet in high - multiplicity events . these ridge - like features are strikingly similar to the observed ridge effect for di - hadron correlations at rhic and the lhc . we show that correlations in the relative rapidity and the relative azimuthal angle between pairs of prompt photon and jet strongly depend on the gluon saturation dynamics at small - x kinematics and such measurements can help to understand the true origin of the observed di - hadron ridge in p+a collisions , and address whether the ridge is a universal phenomenon for all two particle correlations at high energy and high multiplicity events . we also investigate if there is a ridge - like structure for photon - hadron pair correlations at rhic and the lhc . we found that the hadronization of jet has non - trivial effects on the photon - jet correlations .

1001.1107

i

the formation of roche lobe overflowing x - ray binaries ( xrbs ) with black hole ( bh ) accretors in galactic fields , involves the evolution of a primordial isolated binary of which at least one of the component stars is massive enough to form a bh . right before the supernova ( sn ) explosion that will create the bh , the binary orbit is assumed to be circular , due to tidal interactions and possible preceding mass - transfer ( mt ) episodes , and the spins of the two stars are assumed to be aligned with the orbital angular momentum at the formation of the binary . the subsequent sn explosion will change the orbital characteristics of the binary . if the sn explosion is symmetric , the mass lost from the binary will cause the orbit to expand and induce some eccentricity , however the bh spin axis will remain aligned with the orbital angular momentum . in contrast , if an asymmetric kick is imparted on the bh during its formation , the orientation of the orbit will also change and this in turn will cause a misalignment between the spin axis of the bh and the orbital angular momentum . through studies of the position and spatial velocity of radio pulsars in the galaxy , it has been established in the literature that neutron stars ( nss ) can receive large asymmetric sn kicks ( @xmath3 ) @xcite . on the other hand , the possibility of an asymmetric kick imparted to bhs remains still an open question . stellar bhs need to be in xrbs in order to be observable , and only for a handful of galactic bh xrbs there are accurate measurements of their position and spatial velocity . however , indirect bh kick observations indicate that low mass bh receive high asymmetric kicks , while high mass bhs low or no kicks @xcite . on the other hand , detailed theoretical modeling of the evolutionary history of two galactic bh xrbs ( groj1655 - 40 and xtej1118 + 480 ) showed that for the case of groj1655 - 40 a moderate asymmetric kick is possible , while in the case of xtej1118 + 480 an asymmetric kick larger than @xmath4 is necessary in order to explain the current properties of the system @xcite . unless the direction of this asymmetric kick during the formation of the bh is finely tuned to be on the orbital plane , it will induce a misalignment of the bh spin and the orbital angular momentum . in fact , two microquasar type galactic bh xrbs ( groj1655 - 40 and v4641 sgr ) have been observed with relativistic radio jets that are misaligned with respect to their orbital plane . this misalignment angle is estimated to be @xmath5 for groj1655 - 40 @xcite , and @xmath6 for v4641 sgr @xcite . assuming that the radio jet has the same direction as the spin of the bh , this misalignment angle can be translated to a tilt of the bh spin axis with respect to the orbital plane . in this letter we present population synthesis ( ps ) models of roche - lobe overflowing , galactic field bh xrbs , and study their bh spin - orbit misalignment and its their dependence on model parameters .

in black hole x - ray binaries , a misalignment between the spin axis of the black hole and the orbital angular momentum can occur during the supernova explosion that forms the compact object . in this letter we present population synthesis models of galactic black hole x - ray binaries , and study the probability density function of the misalignment angle , and its dependence on our model parameters . in our modeling the misalignment angle for x - ray binaries is the natal kick that the black hole may receive at its formation . however , large kicks tend to disrupt binaries , while small kicks allow the formation of xrbs and naturally select systems with small misalignment angles .

in black hole x - ray binaries , a misalignment between the spin axis of the black hole and the orbital angular momentum can occur during the supernova explosion that forms the compact object . in this letter we present population synthesis models of galactic black hole x - ray binaries , and study the probability density function of the misalignment angle , and its dependence on our model parameters . in our modeling , we also take into account the evolution of misalignment angle due to accretion of material onto the black hole during the x - ray binary phase . the major factor that sets the misalignment angle for x - ray binaries is the natal kick that the black hole may receive at its formation . however , large kicks tend to disrupt binaries , while small kicks allow the formation of xrbs and naturally select systems with small misalignment angles . our calculations predict that the majority ( ) of galactic field bh xrbs have rather small ( ) misalignment angles , while some systems may reach misalignment angles as high as and even higher . this results is robust among all population synthesis models . the assumption of small small misalignment angles is extensively used to observationally estimate black hole spin magnitudes , and for the first time we are able to confirm this assumption using detailed population synthesis calculations .

1204.1521

i

the very first picture of an inflationary multiverse scenario was proposed in ref . @xcite , in which it would seem that the author wanted to suggest a universe without the cosmological singularity problem using an interesting feature of self - reproducting or regenerating exponential expansion of the universe . a major development in this scenario was triggered by the discovery of the eternal inflationary scenario @xcite and a paradigm for string theory landscape @xcite . the eternal inflation is related to the expanding false vacuum solution with a positive cosmological constant , which in turn means that the inflation is eternal into the future . if the theory has multiple minima then the false vacuum state decays into the true vacuum state , i.e. the phase transition proceeded _ via _ the nucleation of a vacuum bubble . in this scenario the universe is situated within some bubble called a pocket universe @xcite having a certain value of the cosmological constant and the whole universes are referred to as multiverse . the description of self - reproduction including tunneling process and random walk was combined into a scenario called recycling universe @xcite . these scenarios seem to provide an escape from the question of the initial conditions of the universe , i.e. it seems to be eternal into the past . unfortunately , inflationary spacetimes can not be made complete in the past direction @xcite , even though the universe is eternal into the future . there are still interesting arguments on the beginning of the universe @xcite . the string theory landscape is a setting that involves a huge number of different metastable and stable vacua @xcite , originated from different choices of calabi - yau manifolds and generalized magnetic fluxes . the huge number of different vacua can be approximated by the potential of a scalar field . the important thing is the fact that , once the de sitter vacuum can exist , the inflationary expansion is eternal into the future and has the possibility of self - reproduction . on the other hand , there are theories of gauged @xmath1 , @xmath2 supergravity having de sitter(ds ) solution , in which all susys are spontaneously broken . it is well known that the ds solution corresponds to a m / sting theory solution with a non - compact @xmath3- or @xmath4-dimensional internal space , in which a small value of the cosmological constant stems from the @xmath5-form flux . the simplest representative of these kind of theories has a tachyonic potential with the ds maxima @xcite . the potential in the vicinity of the maximum reduces to a form having a quadratic term , that is not metastable but unstable . however , according to some authors , the time for collapse giving rise to the tachyonic potential can be much greater than the age of the universe for anthropic reasoning . if the curvature radius of the potential in the vicinity of the maximum is greater than that used in the above theory , then that will be all together different story . the supergravity analogue of the tachyonic potential could be constructed also by using an exact supergravity solution representing the @xmath6-@xmath7 system @xcite . from the above scenarios , the study of the possibility of the tunneling process for the potential with stable and metastable vacua , or even tachyonic behavior has acquired renewed interest . in the present paper , we will study the tunneling process under a simple tachyonic potential governed by a quartic term both without the quadratic term and with the term as a toy model . to obtain the general solution including the effect of the backreaction , we solve the coupled equations for the gravity and the scalar field simultaneously . although the model has a tachyonic potential , it might still be an useful example to show how the tunneling process occurs in various shapes of the potential provided by the above scenarios . a quantum particle can tunnel through a finite potential barrier _ via _ the so - called barrier penetration . this process can be described by the euclidean solution obeying appropriate boundary conditions . there exist two kinds of euclidean solutions describing quantum tunneling phenomena . one corresponds to an instanton solution representing a stable pseudoparticle configuration characterized by the existence of a nontrivial topological charge . it does not change even if we continuously deform the field , as long as the boundary conditions remain the same . the instanton solution corresponds to the minimum of the euclidean action to pass from the initial to final state @xcite . the solution , in case of a double well potential , describes a general shift in the ground state energy of the classical vacuum due to the presence of an additional potential well , then lifting the so - called classical degeneracy . the other is a bounce solution representing an unstable nontopological configuration that corresponds to a saddle point rather than a minimum of the euclidean action . the second derivative of the euclidean action around the bounce has one negative eigenvalue which leads to the imaginary part of the energy . the existence of the negative eigenvalue implies that the vacuum state is unstable , i.e. the state decays into other states @xcite . the euclidean solutions can also mediate phase transitions . the phase transition describes the sudden change of a physical system from one state to another . the transition are of two different types transition accompanied by temperature or zero temperature . the competition between the entropy and the energy terms in the thermodynamic potential cause thermal phase transitions in which dynamics is irrelevant . in the modern classification scheme , thermal phase transitions are divided into two broad categories either with a discontinuous jump in the first - order derivatives of the free energy or without it . a first - order phase transition is characterized by the discontinuity in the first derivative of the free energy and is associated with the existence of latent heat , whereas a @xmath8th - order phase transition is characterized by the continuity in the first derivative while there is a discontinuity in the @xmath8th - order derivative . a quantum phase transition describes a transition between different phases by quantum fluctuation , which occurs at zero temperature , unlike the case of a thermal phase transition which is governed by a thermal fluctuation @xcite . to simplify things , we consider an asymmetric double well potential to distinguish two different phase transitions at zero temperature . if the initial state is the metastable vacuum state and the tunneling occurs from that state to the other vacuum state , then the transition corresponds to a tunneling process @xcite . on the other hand , if the initial state is the local maxima of the potential and the field is rolling down to one vacuum state continuously rather than any discontinuous jump , then the transition corresponds to the rolling . however , one more channel exists as tunneling and that corresponds to the one without a barrier . in this kind of transition , the initial state on the top of a potential can tunnel to the other state rather than rolling down the potential @xcite . there are two different kind of transitions in this case . one is the tunneling without a barrier representing the tunneling from the local maximum of the potential to the vacuum state @xcite . recently , an analytic study on this type of solution was performed in @xcite . the other is a tunneling without a barrier representing the tunneling from the maximum of the potential to any arbitrary state . this case corresponds to the fubini instanton @xcite , where the tachyonic potential is employed . can we describe the rolling corresponding to the transition between the initial metastable vacuum state and the other final vacuum state ? this may look similar to a superfluid motion by the liquid helium . although to establish the phase transition corresponding to the superfluid motion is itself a very challenging problem , we concentrate on the fubini instantons in this work . the fubini instanton @xcite describes the decay of a vacuum state by the quantum phase transition instead of rolling down the tachyonic potential consisted of a quartic term only . on the other hand , one can consider a tachyonic potential consisted of a quadratic term only , the point @xmath9 is unstable . a small perturbation will cause it to roll down the hill of the potential . originally , it was fubini who introduced a fundamental scale of hadron phenomena by means of the dilatation noninvariant vacuum state in the framework of a scale invariant lagrangian field theory @xcite . however , the solution is a one - parameter family of instanton solutions representing a tunneling without a barrier as an interpolating solution from the maximum of the potential to any arbitrary state . the instanton solution was studied in a conformally invariant model , i.e. a fixed background was used and the effect of the backreaction by instantons was neglected @xcite . this is a good approximation , when the variation of the potential during the transition is much smaller than the maximum of the potential . the instanton has gained much interest now - a - days in the context of anti - de sitter(ads)/conformal field theory correspondence @xcite . the paper is organized as follows : in sec . 2 , we review the fubini instanton in the absence of gravity . we present numerical solutions including the euclidean energy density as an example and analyze the structure of the solution in the theory with a potential having only the quartic self - interaction term . we stress the fact that there is no such solutions with the potential containing both the quartic and the quadratic terms . in sec . 3 , we show that the instanton solutions exist in the curved space . we perform a numerical study to solve the coupled equations for the gravity and the scalar field simultaneously . we show that there exist numerical solutions without oscillation in the initial ads space in the potential with only the quartic term . we also show that there exist numerical solutions in the potential both with the quartic and the quadratic terms irrespective of the value of the cosmological constant , which is possible only when the gravity is switched on . in order to estimate the decay rate of the background state , we compute the action difference between that of the solution and the background obtained by numerical means . we present an oscillating numerical solutions in the potential with only the quartic term with various values of the cosmological constant . one type of these solutions has the structure with @xmath0 symmetry . we will discuss on the interpretation of the solutions with @xmath0 symmetry in the final section . we analyze the behavior of the solutions using the phase diagram method . in sec . 4 , to observe the dynamics of the solutions , we briefly sketch the causal structures of the solutions in the lorentzian spacetime . finally in sec . 5 , we summarize and discuss our results .

the fubini instanton describes the decay of a vacuum state under tunneling instead of rolling in the presence of a tachyonic potential . the tunneling occurs from the maximum of the potential , which is a vacuum state , to any arbitrary state , belonging to the tunneling without any barrier . the other has both the quartic and quadratic terms . one type of them has the structure with symmetry . this type of the solution is possible only in the de sitter background . we discuss on the interpretation of the solutions with symmetry . pacs numbers : 04.62.+v , 98.80.cq

we study fubini instantons of a self - gravitating scalar field . the fubini instanton describes the decay of a vacuum state under tunneling instead of rolling in the presence of a tachyonic potential . the tunneling occurs from the maximum of the potential , which is a vacuum state , to any arbitrary state , belonging to the tunneling without any barrier . we consider two different types of the tachyonic potential . one has only a quartic term . the other has both the quartic and quadratic terms . we show that , there exist several kinds of new o(4)-symmetric fubini instanton solution , which are possible only if gravity is taken into account . one type of them has the structure with symmetry . this type of the solution is possible only in the de sitter background . we discuss on the interpretation of the solutions with symmetry . pacs numbers : 04.62.+v , 98.80.cq

1407.3694

i

the problem of dynamic resource allocation in constrained queueing networks is fundamental to modern communication networks . this has long been the subject of significant research , where the @xcite of tassiulas and ephremides proposed the mw ( maximum weight ) scheduling algorithm of throughput - optimality . it has been also a powerful paradigm in cross - layer control and resource allocation @xcite . however , the algorithm can not be implemented in practice due to its high algorithmic complexity . been made since then for developing algorithms of lower complexity while maintaining the same performance guarantee . examples of such algorithms include greedy algorithms @xcite and random access algorithms @xcite . recently , there have been exciting progresses for the topic that even fully distributed random access algorithms based on csma ( carrier sense multiple access ) can achieve the desired high performance , i.e. , throughput - optimality , in wireless interference network models , e.g. , see @xcite . the main intuition underlying these results is that nodes in a network can adjust their csma parameters dynamically using local information such as queue - length so that they can simulate the mw algorithm asymptotically for throughput - optimality . however , it is known that the queue - based csma algorithms suffer from very poor delay performance . there have been also significant efforts formally addressing the limitation in the delay performance of the queue - based csma algorithms @xcite as well as designing better alternatives in delay under certain scenarios @xcite . in addition , another issue is that the throughput - optimality proof in @xcite is very sensitive to the underlying wireless network model . namely , it is not an easy task to design similar csma - like throughput - optimal algorithms in other network models since one has to reproduce painful , long and routine proof - arguments for throughput - optimality in each different model . the main goal of this paper is to resolve these issues of the recent queue - based csma algorithms by developing a general framework that can produce a variety of throughput - optimal and low - complexity scheduling algorithms , not to the underlying network models . design and analysis of resource allocation algorithms in constrained queueing networks have been of great interest for last four decades across various research communities , where the contention resolution protocols in multiple - access broadcast channels have been studied since the mid-1970s @xcite . the broadcast channels induce a special constraint in resources usages among queues ( i.e. , every queue contend with all other queues ) , and simple distributed contention resolution protocols gained much attention in the ages . it is the year 1992 that the seminal work by tassiulas and ephremides proposed a throughput - optimal algorithm , referred to as mw , for general resource constraints . its main appeal is that it does require only information on the current queue lengths ( and instantaneous service rates ) and does not rely on the knowledge of underlying system parameters . however , as we mentioned earlier , the mw algorithm suffers from the high implementation complexity , and a huge array of subsequent research has been made to develop algorithms with high performance guarantees and low - complexity . maximal scheduling or longest - queue - first algorithm are low - complexity alternatives to mw , but they achieve only some fraction of the maximal throughput region . parallel iterative matching @xcite and islip @xcite were shown to be 50% throughput - optimal @xcite . on the other hand , kumar et al . @xcite and dimakis and walrand @xcite identified sufficient conditions on the network topology for throughput - optimality . those conditions were further analyzed to obtain fractional throughput results about a class of wireless networks by joo et al . @xcite and leconte et al . these algorithms are generally not throughput - optimal and require multiple rounds of message exchanges between nodes . simpler or distributed implementations of mw has been also extensively studied in the literature . tassiulas @xcite provides linear - complexity versions of mw , called ` pick - and - compare ' , but it is known that they suffer from the bad delay performance . the works on this line also include a variant of mw by giaccone , prabhakar and shah @xcite and a gossip - based algorithm by modiano , shah and zussman @xcite . however , these algorithms are specific to certain network models and still require high information ( or message ) exchanges for each new scheduling decision . a few years ago , it was proven that even fully distributed queue - based random access algorithms based on csma with very little message passing can simulate the mw algorithm asymptotically and hence achieve throughput - optimality in wireless interference network models @xcite . however , the csma algorithms are known to suffer from the following two issues : the bad delay performance and the limited applicability to other network models . for the delay issue , bouman et al . @xcite formally established explicit lower bounds on the delay of queue - based random access algorithms . on the other hand , significant efforts have also been made to design csma algorithms with better delay performance , e.g. , see @xcite . the limited applicability issue is rather technical : it is a technically tedious task to design similar csma - like throughput - optimal algorithms in other network models since one has to reproduce painful , long and routine proof - arguments for analyzing ` time - varying ' markov chains in each different model , e.g. , see the buffered circuit switched network model @xcite . the main motivation of this paper is for resolving these issues and goes beyond csma - like algorithms for achieving high performance guarantees and low implementation complexity , not sensitive to the underlying network models . we develop a generic framework for designing throughput - optimal and low - complexity scheduling algorithms , where queue - based csma algorithms belong to it as special cases . under the framework , an algorithm updates current schedules via an interaction with a given oracle system that can generate a solution of a certain discrete optimization problem in a finite number of interactive queries . specifically , an algorithm maintains three parameters , ` schedule ' , ` weight ' and ` advice ' , at each time instance . the schedule and advice are kept being updated under interactions with the oracle system and the weight is decided by some function of current queue - size , which we call ` queue - length - function ' . therefore , the scheduling algorithm design is determined by ` which oracle is used ' and ` which queue - length - function is chosen ' . the oracle system can be designed through iterative optimization methods including the naive exhaustive search algorithm , the markov chain monte carlo ( e.g. , the glauber dynamics @xcite ) , the message - passing inference algorithms ( e.g. , the belief propagation @xcite ) and the linear / integer programming ( e.g. , the cutting - plane method @xcite ) . in this paper , we describe three oracle examples , the exhaustive search ( es ) , the markov chain monte carlo ( mcmc ) and the belief propagation ( bp ) in section [ sec : exam ] . in particular , the ` pick - and - compare ' algorithms @xcite and queue - based csma algorithms can be understood as such algorithms ( with minor modifications ) using es and mcmc oracles , respectively ( see section [ sec : exam ] ) . the scheduling complexity is decided by the number of operations required for an oracle processing a single query , which is typically very small , e.g. , es , mcmc and bp . we prove that given any oracle system , there exists a queue - length - function such that an algorithm using the oracle is throughput - optimal under general constrained queueing network models , which includes wireless network models , input - queued switch models , the buffered circuit switched network model , etc . in particular , we first show there exists a queue - length - function such that its value does not change too often ( i.e. , remains fixed for a long time ) and hence the mw optimization problem can be solved through ( enough ) interactions to the oracle , i.e. , the algorithm simulates mw and is throughput - optimal . this proof strategy is similar to those of @xcite in spirit . the main difference is that we force the queue - length - function value being ` rarely - varying ' in integers , while the authors in @xcite do it being ` slowly - varying ' in real numbers . due to such a difference , now we do not need to analyze ` time - varying ' algorithms ( e.g. , markov chains ) , i.e. , analysis when algorithm parameters are fixed is enough . this makes the proof much simpler and not sensitive to the given oracle and underlying network model . our strong theoretical statement provides a quite powerful paradigm for developing a variety of low - complexity scheduling algorithms of high performance . for example , our experimental results show that the delay performance of such an algorithm using the bp oracle is close to that of the mw algorithm , and it significantly outperforms csma algorithms ( see section [ sec : exp ] ) . moreover , one can also easily design other types of throughput - optimal algorithms , via designing various oracle systems , under a quite broad class of constrained queueing network models , without suffering from repeating tedious proofs sensitive to the underlying assumptions and setups . at a high level , we use the interactive oracle concept to provide a ` black - box ' tool for designing scheduling algorithms of high performance and low - complexity . this establishes a rigorous connection between iterative optimization methods and low - complexity scheduling algorithms , which we believe provides various future directions and new insights in both areas . in section [ sec : pre ] , we describe the constrained queueing network model of our interest and the performance metric ( i.e. , throughput - optimality ) for scheduling algorithms . section [ sec : main ] provides the main result of this paper , i.e. , our generic framework for designing a throughput - optimal and low - complexity scheduling algorithm which decides its current schedule via an interaction with an oracle system . in section [ sec : exam ] , we provide several examples of scheduling algorithms under the framework . section [ sec : pfmainthm ] provides the formal proof of the main result , and our experimental results are presented in section [ sec : exp ] .

since tassiulas and ephremides proposed the maximum weight scheduling algorithm of throughput - optimality for constrained queueing networks in 1992 , extensive research efforts have been made for resolving its high complexity issue under various directions . in this paper , we resolve the issue by developing a generic framework for designing throughput - optimal and low - complexity scheduling algorithms . under the framework , an algorithm updates current schedules via an interaction with a given oracle system that can generate a solution of a certain discrete optimization problem in a finite number of interactive queries . therefore , one can design a variety of scheduling under this framework by choosing different oracles , e.g. , the exhaustive search ( es ) , the markov chain monte carlo ( mcmc ) , the belief propagation ( bp ) and the cutting - plane ( cp ) algorithms . the complexity of the resulting algorithm is decided by the number of operations required for an oracle processing a single query , which is typically very small . somewhat surprisingly , we prove that an algorithm using any such oracle is throughput - optimal for general constrained queueing network models that arise in the context of emerging large - scale communication networks . in particular , the ` pick - and - compare ' algorithms developed by tassiulas in 1998 and recently developed queue - based csma algorithms can be also understood as special cases of such algorithms using es and mcmc oracles , respectively . to our best knowledge

since tassiulas and ephremides proposed the maximum weight scheduling algorithm of throughput - optimality for constrained queueing networks in 1992 , extensive research efforts have been made for resolving its high complexity issue under various directions . in this paper , we resolve the issue by developing a generic framework for designing throughput - optimal and low - complexity scheduling algorithms . under the framework , an algorithm updates current schedules via an interaction with a given oracle system that can generate a solution of a certain discrete optimization problem in a finite number of interactive queries . therefore , one can design a variety of scheduling under this framework by choosing different oracles , e.g. , the exhaustive search ( es ) , the markov chain monte carlo ( mcmc ) , the belief propagation ( bp ) and the cutting - plane ( cp ) algorithms . the complexity of the resulting algorithm is decided by the number of operations required for an oracle processing a single query , which is typically very small . somewhat surprisingly , we prove that an algorithm using any such oracle is throughput - optimal for general constrained queueing network models that arise in the context of emerging large - scale communication networks . in particular , the ` pick - and - compare ' algorithms developed by tassiulas in 1998 and recently developed queue - based csma algorithms can be also understood as special cases of such algorithms using es and mcmc oracles , respectively . to our best knowledge , our result is the first that establishes a rigorous connection between iterative optimization methods and low - complexity scheduling algorithms , which we believe provides various future directions and new insights in both areas .

1607.03286

i

the collection , @xmath9 , of closed subsets of a topological space @xmath10 , ordered by inclusion , forms a distributive complete lattice often referred to as the _ closed set lattice _ of @xmath10 . if a lattice @xmath11 is isomorphic to the closed set lattice of some topological space @xmath10 , we say that @xmath10 is a _ topological representation _ of @xmath11 . it is natural to ask : [ quest : first question ] which lattices have topological representations ? seymour papert was the first to characterize such lattices as those which are complete , distributive , and have a base consisting of irreducible elements , @xcite . we can also ask how much of the topological structure of a space is encoded in its closed set lattice . following wolfgang thron , @xcite , we say that two topological spaces @xmath10 and @xmath12 are _ lattice - equivalent _ if their closed - set lattices are order - isomorphic . clearly , homeomorphic spaces are lattice - equivalent , but the converse fails . this then leads us to : [ quest : second question ] which classes @xmath2 of topological spaces are such that any two lattice - equivalent spaces @xmath10 and @xmath13 are homeomorphic , i.e. : @xmath14 sober topological spaces are exactly those that can be fully reconstructed from their closed set lattices , @xcite ; therefore the class @xmath15 of sober spaces is a natural choice in answer to question [ quest : second question ] . furthermore , any topological space @xmath10 is lattice - equivalent to its sobrification @xmath16 and so it follows that @xmath2 can not contain a non - sober space @xmath10 and its sobrification @xmath16 at the same time , in other words , @xmath15 is a _ maximal _ choice for @xmath2 . the two questions above can also be asked in the context of a particular class of topological spaces . the ones we have in mind were introduced by dana scott , @xcite , and are known collectively as _ domains_. the characteristic feature of domains is that they carry a partial order and that their topology is completely determined by the order . more precisely , let @xmath0 be a poset and @xmath17 a subset of @xmath0 . one says that @xmath17 _ scott open _ , if ( i ) @xmath17 is an upper set , and ( ii ) @xmath17 is inaccessible by directed joins . the set @xmath18 of all scott opens of @xmath0 forms the _ scott topology _ on @xmath0 , and @xmath19 is called the _ scott space _ of @xmath0 . in what follows , for a poset @xmath0 , we write @xmath1 to always mean the lattice of scott - closed subsets of @xmath0 . we may now relativize our definitions to the context of scott spaces . we say that a lattice @xmath11 has a _ scott - topological representation _ if @xmath11 is isomorphic to @xmath1 for some poset @xmath0 , and ask : [ prob : first problem ] which lattices have scott - topological representations ? although some work has been done on this problem , @xcite , as of now it remains open . in the special case of _ continuous domains _ a very pleasing answer was given independently by jimmie lawson , @xcite , and rudolf - eberhardt hoffmann , @xcite . they showed that a lattice @xmath11 has a scott - topological representation @xmath1 for some continuous domain @xmath0 if and only if @xmath11 is completely distributive . in the order - theoretic context the second question reads as follows : [ prob : second problem ] which classes of posets @xmath2 satisfy the condition @xmath20 a class @xmath2 of posets is said to be _ @xmath4-faithful _ if the above condition holds ( @xcite[p . 2170 , remark 2 ] ) . the following classes of posets are known to be @xmath4-faithful : 1 . @xmath21 of complete semilattices , @xcite , containing in particular all complete lattices ; 2 . @xmath22 of dcpos whose scott topologies are sober , containing in particular @xmath23 , the class of all continuous dcpos . a _ dcpo - completion _ of a poset @xmath0 is a dcpo @xmath24 together with a scott - continuous mapping @xmath25 such that for any scott - continuous mapping @xmath26 into a dcpo @xmath27 there exists a unique scott - continuous mapping @xmath28 satisfying @xmath29 . it was shown in @xcite that the dcpo - completion , @xmath30 , of a poset @xmath0 always exists ; furthermore @xmath31 . hence the class , @xmath32 , of all posets is _ not _ @xmath4-faithful . indeed any class of posets that is strictly larger than @xmath8 , the class of dcpos , is not @xmath4-faithful . this means that we can restrict attention entirely to dcpos , in particular , it leads one to ask : ( @xcite , ( * ? ? ? * remark 2 ) ) [ prob : ho - zhao problem ] is @xmath8 @xmath4-faithful ? this question was dubbed the _ ho - zhao problem _ in @xcite . the authors of this paper claimed that the two dcpos @xmath33,\leq ) \text { and } \psi = ( \{[0,a ] \mid 0 < a \leq 1\},\subseteq)\ ] ] show that @xmath8 is not @xmath4-faithful . however , it is easy to see that @xmath34,\leq)$ ] so that @xmath35,\leq)$ ] . on the other hand , @xmath36,\leq)_\bot$ ] which is not isomorphic to @xmath37 . this failure is only to be expected as both @xmath38 and @xmath39 are continuous dcpos and we already noted that @xmath23 is @xmath4-faithful . this paper comprises two parts . in section [ sec : positive ] we present a positive result by introducing the class @xmath40 of _ dominated dcpos _ and showing it to be @xmath4-faithful . importantly , @xmath40 subsumes all currently known @xmath4-faithful classes listed above . in the second part ( sections [ sec : johnstones - countereg][sec : hoxi - structure ] ) we show that the answer to the ho - zhao problem is negative . we construct a dcpo @xmath41 which is not dominated , and derive from it a dominated dcpo @xmath42 so that @xmath43 but @xmath44 . the construction makes use of johnstone s famous example of a dcpo @xmath45 whose scott topology is not sober ( @xcite ) . to familiarize the reader with johnstone s dcpo @xmath45 , we revisit it in section [ sec : johnstones - countereg ] , highlighting its peculiarities . this prepares us for the counterexample @xmath41 , presented in section [ sec : hoxi - informal ] . for quick accessibility we keep the description of @xmath41 in section [ sec : hoxi - informal ] informal . intrepid readers who are keen to pursue the detailed construction of @xmath41 and how it works in answering the ho - zhao problem may then continue their odyssey into section [ sec : hoxi - structure ] . for notions from domain theory we refer the reader to @xcite .

given a poset , the set , , of all scott closed sets ordered by inclusion forms a complete lattice . this subcategory subsumes all currently known-faithful subcategories . with this new concept in mind , we construct the desired counterexample which relies heavily on johnstone s famous dcpo which is not sober in its scott topology .

given a poset , the set , , of all scott closed sets ordered by inclusion forms a complete lattice . a subcategory of ( the category of posets and scott - continuous maps ) is said to be-faithful if for any posets and in , implies . it is known that the category of all continuous dcpos and the category of bounded complete dcpos are-faithful , while is not . ho & zhao ( 2009 ) asked whether the category of dcpos is-faithful . in this paper , we answer this question in the negative by exhibiting a counterexample . to achieve this , we introduce a new subcategory of dcpos which is-faithful . this subcategory subsumes all currently known-faithful subcategories . with this new concept in mind , we construct the desired counterexample which relies heavily on johnstone s famous dcpo which is not sober in its scott topology .

1607.03286

r

a nonempty subset @xmath24 of a topological space @xmath46 is called _ irreducible _ if whenever @xmath47 for closed sets @xmath27 and @xmath48 , @xmath49 or @xmath50 follows . we say that @xmath24 is _ closed irreducible _ if it is closed and irreducible . the set of all closed irreducible subsets of @xmath10 is denoted by @xmath51 . two facts about irreducible sets will be important below : * if @xmath24 is irreducible then so is its topological closure . * the direct image of an irreducible set under a continuous function is again irreducible . in this paper we are exclusively interested in dcpos and the scott topology on them . when we say `` ( closed ) irreducible '' in this context we always mean ( closed ) irreducible with respect to the scott topology . it is a fact that every directed set in a dcpo is irreducible in this sense , while a set that is directed and closed is of course a principal ideal , that is , of the form @xmath52 . peter johnstone discovered in 1981 , @xcite , that a dcpo may have irreducible sets which are not directed , and closed irreducible sets which are not principal ideals ; we will discuss his famous example in section [ sec : johnstones - countereg ] and someone not familiar with it may want to have a look at it before reading on . given that we may view irreducible sets as a generalisation of directed sets , the following definition suggests itself : a dcpo @xmath53 is called _ strongly complete _ if every irreducible subset of @xmath54 has a supremum . in this case we also say that @xmath54 is an _ scpo_. a subset of an scpo is called _ strongly closed _ if it closed under the formation of suprema of irreducible subsets . note that despite this terminology , strongly complete partial orders are a long way from being complete in the sense of lattice theory . the basis of questions [ quest : first question ] and [ quest : second question ] in the introduction is the well - known ( dual ) adjunction between topological spaces and frames , which for our purposes is expressed more appropriately as a ( dual ) adjunction between topological spaces and coframes : @xmath55[r]{$\gamma:\mathbf{top}$}\ar@/^/[r]_\bot & \makebox[2em][l]{$\mathbf{cofrm}^{\mathrm{op}}:\mathrm{spec}$}\ar@/^/[l ] } \ ] ] here @xmath56 is the functor that assigns to a coframe its set of _ irreducible _ elements , that is , those elements @xmath57 for which @xmath58 implies @xmath59 or @xmath60 , topologized by closed sets @xmath61 . starting with a topological space @xmath46 we obtain the _ sobrification _ @xmath16 of @xmath10 by composing @xmath56 with @xmath4 . concretely , the points of @xmath16 are given by the closed irreducible subsets of @xmath10 and the topology is given by closed sets @xmath62 where @xmath63 . in order to present problems [ prob : first problem ] and [ prob : second problem ] in a similar fashion , it seems natural to replace @xmath64 with the category of _ dcpo spaces _ , i.e. , directed - complete partially ordered sets equipped with the scott topology . however , while we know that @xmath56 yields topological spaces which are dcpos in their specialisation order , it is _ not the case _ that the topology on @xmath65 equals the scott topology with respect to that order ; all we know is that every @xmath66 is scott - closed . rather than follow a topological route , therefore , we reduce the picture entirely to one concerning _ ordered sets_. to this end we restrict the adjunction above to the category @xmath67 of _ monotone convergence spaces _ ( * definition ii-3.12 ) ) on the topological side and compose it with the adjunction between monotone convergence spaces and dcpos @xmath68_\bot & \mathbf{mcs}:\mathrm{so}\ar@/^/[l ] } \ ] ] which assigns to a dcpo its scott space and to a space its set of points with the _ specialisation order_. we obtain a functor from @xmath8 to @xmath69 which assigns to a dcpo its coframe of scott - closed subsets and we re - use the symbol @xmath4 for it rather than writing @xmath70 . in the other direction , we assign to a coframe the _ ordered set _ of irreducible elements , where the order is inherited from the coframe . to emphasize the shift in perspective , we denote it with @xmath71 rather than @xmath56 or @xmath72 . it will also prove worthwhile to recall the action of @xmath71 on morphisms : if @xmath73 is a coframe homomorphism , then @xmath74 maps an irreducible element @xmath57 of @xmath75 to @xmath76 . altogether we obtain the following ( dual ) adjunction : @xmath55[r]{$\gamma:\mathbf{dcpo}$}\ar@/^/[r]_\bot & \makebox[2em][l]{$\mathbf{cofrm}^{\mathrm{op}}:{\mathrm{irr}}$}\ar@/^/[l ] } \ ] ] its unit @xmath77 maps an element @xmath78 of a dcpo @xmath54 to the principal downset @xmath52 , which is always closed and irreducible and hence an element of @xmath79 . the counit @xmath80 ( as a concrete map between coframes ) sends an element @xmath81 of a coframe @xmath11 to the set @xmath82 which is clearly closed under directed suprema , hence an element of @xmath83 . combining @xmath71 with @xmath4 yields a monad on @xmath8 which we denote with @xmath84 . concretely , it assigns to a dcpo @xmath54 the set @xmath85 of closed irreducible subsets ordered by inclusion . we call this structure the _ order sobrification of @xmath54_. if @xmath86 is a scott - continuous function between dcpos , and @xmath87 is a closed irreducible set , then @xmath88 is the scott closure of the direct image @xmath89 ( which is again irreducible as we noted at the beginning of this section ) . the monad unit is given by the unit of the adjunction and the multiplication @xmath90 maps a closed irreducible collection . ] of closed irreducible subsets to their union . we will see in section [ sec : hoxi - informal ] that this order - theoretic monad is _ not _ idempotent ; this is an important difference to its topological counterpart , the sobrification monad . the concrete description of @xmath91 as union allows us to conclude immediately : [ prop : scpo ] for any dcpo @xmath54 , @xmath85 is strongly complete . there is more to discover about our adjunction and the union operation : [ prop : union ] let @xmath54 be a dcpo . 1 . if @xmath27 a closed set of @xmath54 then @xmath92 . 2 . if @xmath93 is irreducible as a subset of @xmath85 then @xmath94 is irreducible as a subset of @xmath54 . if @xmath95 is scott - closed as a subset of @xmath85 then @xmath96 is scott - closed as a subset of @xmath54 . if @xmath27 is a closed set of @xmath54 then @xmath97 is strongly closed . \(1 ) this follows from the general description of the counit . \(2 ) assume we have @xmath98 with @xmath99 scott - closed subsets of @xmath54 . then @xmath100 by ( 1 ) and because every member of @xmath93 is irreducible . furthermore , @xmath97 and @xmath101 are scott - closed subsets of @xmath85 , so by assumption , one of them must cover the irreducible collection @xmath93 , say @xmath97 . it then follows that @xmath94 is contained in @xmath27 . \(3 ) this follows for categorical reasons because the union operation is the same as @xmath102 , but a direct proof is instructive for what follows : if @xmath103 is a directed subset of @xmath94 then each @xmath104 must belong to some @xmath105 . because each @xmath106 is a lower set of @xmath54 we have @xmath107 and because @xmath93 is a lower set of @xmath85 it follows that @xmath108 . the collection @xmath109 is directed and by assumption its supremum @xmath110{$\scriptstyle\uparrow$}}}}s$ ] belongs to @xmath93 as @xmath93 is scott - closed . if follows that @xmath111{$\scriptstyle\uparrow$}}}}s$ ] belongs to @xmath94 . \(4 ) let @xmath93 be an irreducible subset of @xmath97 . then by ( 2 ) we have that @xmath94 is irreducible . since @xmath94 is contained in the closed set @xmath27 , so is its closure @xmath24 . we know that @xmath24 is again irreducible and therefore this is the supremum of @xmath93 and it belongs to @xmath97 . strong closedness is crucial for the following result : [ lem : strong ] let @xmath54 be a dcpo and @xmath112 . 1 . @xmath113 . 2 . if @xmath95 is strongly closed then equality holds . the first statement is trivial by the definition of the counit @xmath114 . for the second , let @xmath24 be a closed irreducible subset of @xmath96 . we need to show that @xmath24 is an element of @xmath95 . every element @xmath78 of @xmath24 belongs to some @xmath115 . as we argued in part ( 3 ) of the preceding proof , it follows that for every @xmath116 , @xmath117 . we claim that the collection @xmath118 is irreducible as a subset of @xmath85 . this will finish our proof as we clearly have that @xmath24 is the supremum of @xmath93 and by assumption , @xmath95 is closed under forming suprema of irreducible subsets . so let @xmath93 be covered by two closed collections @xmath119 , in other words , every @xmath52 belongs to either @xmath120 or @xmath121 . it follows that each @xmath116 belongs to either @xmath122 or @xmath123 and these two sets are scott - closed by part ( 3 ) of the preceding proposition . because @xmath24 is irreducible , it is already covered by one of the two , and this implies that @xmath93 is covered by either @xmath120 or @xmath121 . we approach question [ prob : second problem ] via the monad @xmath84 . starting from the assumption @xmath124 we immediately infer @xmath125 and the question then becomes whether this isomorphism implies @xmath126 . our counterexample will demonstrate that in general the answer is `` no '' but in this section we will exhibit a new class @xmath40 of _ dominated dcpos _ for which the answer is positive , that is , we will show : @xmath127 before we do so , let us check that invoking the monad does not change the original question , in other words , the assumption @xmath128 is neither stronger nor weaker than @xmath124 : for arbitrary dcpos @xmath54 and @xmath129 , @xmath130 . the implication from right to left is trivial , so assume we are given an order isomorphism @xmath131 . the idea for an isomorphism @xmath132 from @xmath133 to @xmath134 is very simple : given @xmath135 we compute @xmath97 , the collection of all closed irreducible sets contained in @xmath27 . each of these can be replaced with its counterpart in @xmath129 via the given isomorphism @xmath136 . in @xmath129 , then , we simply take the union of the collection @xmath137 . using the maps that are provided to us by the adjunction , we can express @xmath132 as follows : @xmath138^{\varepsilon_{\gamma(d ) } } & \gamma({\widehat{d}})\ar[r]^{\gamma(i^{-1 } ) } & \gamma({\widehat{e}})\ar[r]^{\bigcup } & \gamma(e ) } \ ] ] for an inverse , we follow the same steps , starting at @xmath134 : @xmath139^{\varepsilon_{\gamma(e ) } } & \gamma({\widehat{e}})\ar[r]^{\gamma(i ) } & \gamma({\widehat{d}})\ar[r]^{\bigcup } & \gamma(d ) } \ ] ] in order to show that these are inverses of each other we use the fact that @xmath97 is _ strongly _ closed which we established in proposition [ prop : union](4 ) . since the concept of strong closure is purely order - theoretic we get that the direct image under @xmath136 is again strongly closed . this is crucial as it allows us to invoke lemma [ lem : strong](2 ) . the computation thus reads : @xmath140 the other composition , @xmath141 , simplifies in exactly the same way to the identity on @xmath134 , and since all maps involved are order - preserving , we have shown that the pair @xmath142 constitutes an order isomorphism between @xmath133 and @xmath134 . our new version of question [ prob : second problem ] requires us to infer @xmath126 from @xmath128 , and the most direct approach is to find a way to recognize _ purely order - theoretically _ inside @xmath85 those elements which correspond closed irreducible subsets of the form @xmath52 with @xmath143 . as our counterexample @xmath41 to the ho - zhao problem will show , this is not possible for general dcpos . the purpose of the present section is to exhibit a class of dcpos for which the direct approach works . given @xmath144 we write @xmath145 if there is @xmath116 such that @xmath146 . we write @xmath147 for the set @xmath148 . clearly , an element @xmath24 of @xmath85 is of the form @xmath52 if and only if @xmath149 holds , but this is not yet useful since the definition of @xmath150 makes explicit reference to the underlying dcpo @xmath54 . we can , however , record the following useful facts : let @xmath54 be a dcpo and @xmath87 closed and irreducible . 1 . @xmath151 2 . @xmath152 is irreducible as a subset of @xmath85 . the first statement is trivial because @xmath152 contains all principal ideals @xmath52 , @xmath116 . the proof of the second statement is essentially the same as that of lemma [ lem : strong ] . let @xmath54 be a strongly complete partial order and @xmath153 . we write @xmath154 if for all closed irreducible subsets @xmath24 of @xmath54 , @xmath155 implies @xmath156 . we say that @xmath143 is _ @xmath157-compact _ if @xmath158 , and denote the set of @xmath157-compact elements by @xmath159 . note that this is an _ intrinsic _ definition of a relation on @xmath54 without reference to any other structure . it is reminiscent of the way - below relation of domain theory but note that it is defined via _ closed _ irreducible sets . this choice has the following consequence , which is definitely not true for way - below : [ prop : prec - downset ] let @xmath54 be an scpo and @xmath143 . the set @xmath160 is scott - closed . let @xmath161 be a directed set of elements , each of which is @xmath157-below @xmath78 . we need to show that @xmath111{$\scriptstyle\uparrow$}}}}_{i\in i}a_i$ ] is also @xmath157-below @xmath78 . to this end let @xmath24 be a closed irreducible subset of @xmath54 with @xmath162 . since @xmath163 for all @xmath164 we have that every @xmath165 belongs to @xmath24 and because @xmath24 is closed , @xmath111{$\scriptstyle\uparrow$}}}}_{i\in i}a_i\in a$ ] follows . recall from proposition [ prop : scpo ] that @xmath85 is strongly complete for any dcpo @xmath54 , so on @xmath85 we can consider both @xmath150 and @xmath157 . we observe : @xmath145 implies @xmath166 for all @xmath167 . this holds because the supremum of a closed directed collection of closed irreducible subsets is given by union . our aim now is to give a condition for dcpos @xmath54 which guarantees the reverse implication . a dcpo @xmath54 is called _ dominated _ if for every closed irreducible subset @xmath24 of @xmath54 , the collection @xmath152 is scott - closed in @xmath85 . we are ready for the final technical step in our argument : a dcpo @xmath54 is dominated , if and only if @xmath166 implies @xmath145 for all @xmath167 . if : let @xmath168 . by assumption we have @xmath169 and in proposition [ prop : prec - downset ] we showed that the latter is always scott - closed . only if : let @xmath166 . we know that @xmath152 is irreducible and by assumption closed . we also know that @xmath151 so it must be the case that @xmath170 . we are ready to reap the benefits of our hard work . all of the following are now easy corollaries : for a dominated dcpo @xmath54 , the only @xmath157-compact elements of @xmath85 are the principal ideals @xmath52 , @xmath143 . also , the unit @xmath77 is an order isomorphism from @xmath54 to @xmath171 . let @xmath54 and @xmath129 be dominated dcpos . the following are equivalent : 1 . 2 . @xmath173 . 3 . @xmath174 . the class @xmath40 of dominated dcpos is @xmath4-faithful . let us now explore the reach of our result and exhibit some better known classes of dcpos which are subsumed by @xmath40 . [ prop : complete semilattice is dominated ] every scpo is dominated . if @xmath145 for closed irreducible subsets of an scpo , then by definition @xmath146 for some @xmath116 and hence @xmath175 . if @xmath176 is a directed family in @xmath152 , then @xmath111{$\scriptstyle\uparrow$}}}}_{i\in i}a_i\subseteq{\mathord{\downarrow}}{\mathop{\bigvee{}^{\,\makebox[0pt]{$\scriptstyle\uparrow$}}}}_{i\in i}(\bigvee a_i)$ ] , and the element @xmath111{$\scriptstyle\uparrow$}}}}_{i\in i}(\bigvee a_i)$ ] belongs to @xmath24 because @xmath24 is a scott - closed set . [ cor : all - dominated ] the following are all dominated : 1 . complete semilattices and complete lattices ; 2 . dcpos which are sober in their scott topologies ; 3 . @xmath85 for any dcpo @xmath54 . \(1 ) holds because complete semilattices have suprema for all bounded sets , which is all that is needed in the proof of the preceding proposition . \(2 ) holds because the only closed irreducible subsets of sober dcpos are principal ideals . \(3 ) holds because we showed in proposition [ prop : scpo ] that @xmath85 is always strongly complete . recall that a topological space is called _ coherent _ if the intersection of two compact saturated sets is again compact . it is called _ well - filtered _ if whenever @xmath177 is a filtered collection of compact saturated sets contained in an open @xmath178 , then some @xmath179 is contained in @xmath178 already . [ lem : ub(a ) is compact saturated ] let @xmath54 be a dcpo which is well - filtered and coherent in its scott topology . then for any @xmath180 , the set @xmath181 of upper bounds of @xmath24 is compact saturated . since @xmath182 , it is saturated . for any finite nonempty @xmath183 , @xmath184 is compact since @xmath54 is coherent . thus @xmath185 forms a filtered family of compact saturated sets whose intersection equals @xmath181 . if it is covered by a collection of open sets then by well - filteredness of @xmath54 some @xmath184 is covered already , but the latter is compact by coherence so a finite subcollection suffices to cover it . [ prop : filtered and coherent implies dominated ] every dcpo @xmath54 which is well - filtered and coherent in its scott topology is dominated . let @xmath176 be a directed family in @xmath152 . by the preceding proposition , the sets @xmath186 are compact saturated and form a filtered collection . suppose for the sake of contradiction that @xmath187 . since @xmath188 is scott open , by the well - filteredness of @xmath54 it follows that there exists @xmath189 such that @xmath190 . this contradicts the fact that every @xmath191 is bounded by an element of @xmath24 . at the juncture , the curious reader must be wondering why we have not yet given an example of a dcpo which is not dominated . now , as we showed , any dcpo whose scott topology is sober is dominated and so a non - dominated dcpo , if it exists , must be non - sober . peter johnstone , @xcite was the first to give an example of such a dcpo and it is thus natural to wonder whether it is dominated or not . in order to answer this question we explore his example @xmath45 in some detail in the next section . this will also help us to construct and study our counterexample to the ho - zhao conjecture .

a subcategory of ( the category of posets and scott - continuous maps ) is said to be-faithful if for any posets and in , implies . it is known that the category of all continuous dcpos and the category of bounded complete dcpos are-faithful , while is not . ho & zhao ( 2009 ) asked whether the category of dcpos is-faithful . in this paper , we answer this question in the negative by exhibiting a counterexample . to achieve this , we introduce a new subcategory of dcpos which is-faithful .

given a poset , the set , , of all scott closed sets ordered by inclusion forms a complete lattice . a subcategory of ( the category of posets and scott - continuous maps ) is said to be-faithful if for any posets and in , implies . it is known that the category of all continuous dcpos and the category of bounded complete dcpos are-faithful , while is not . ho & zhao ( 2009 ) asked whether the category of dcpos is-faithful . in this paper , we answer this question in the negative by exhibiting a counterexample . to achieve this , we introduce a new subcategory of dcpos which is-faithful . this subcategory subsumes all currently known-faithful subcategories . with this new concept in mind , we construct the desired counterexample which relies heavily on johnstone s famous dcpo which is not sober in its scott topology .

1508.01409

i

in various researches and scientific activities ranging from theoretical and simulation to technological approaches , surfaces and interfaces are ubiquitous . characterization of rough surfaces is necessary through the simulation and making stochastic field for further applications . the electromagnetic and mechanical as well as chemical features of rough surfaces and interfaces are affected by morphological evolution during growth or etching processes . subsequently , investigation of local ( geometrical ) and global ( topological ) properties of rough surfaces play crucial role in determining the behavior of a rough surfaces as elements and their impact on incident beam of ray @xcite . during various aspects and processes such as evaporation / condensation @xcite , surface diffusion during the growth , geophysical studies @xcite , kinetic roughening on a nearby surface @xcite , exotic growth processes @xcite and etc . , it is possible to form anisotropic rough surfaces . many important properties of rough surfaces such as friction , diffusivity of particles of surface , contact , and wear can be influenced by topography of the underlying surface such as anisotropy . propagation of cracks @xcite , formation of ripple patterns @xcite , turbulent flow @xcite , depinning in anisotropic media @xcite , elastic - plastic contact model @xcite , lubricant film flow @xcite , anderson localization in anisotropic random media @xcite , diffusion , transport @xcite , transmission @xcite , turbulent boundary layer @xcite , cosmic microwave background radiation @xcite and large scale structures in the cosmos @xcite are some phenomena affected by roughness and anisotropies . in addition , from machinery and workpiece processes , many associated parameters influence on morphology of constructed rough surfaces @xcite ( see @xcite for experimental setup ) . from experimental , theoretical as well as technological points of view , it is important to have a measure for anisotropy probe , which can exhibit different properties . in principle , to determine whether underlying rough surface is anisotropic or not , following questions must be answered : first of all , what is the degree of anisotropy ? , what is the direction of anisotropy ? and finally , what is the kind of anisotropy ? @xcite . in the presence of anisotropy , one can divide the anisotropies into two categories : anisotropy in scaling exponents and / with in correlation length scale @xcite . the applicability of fractal properties and scaling concepts have been considered in @xcite , but if there is no scaling behavior represented by underlying surface , therefor one can not find reliable results by implementation of mentioned method based on scaling behavior . many given rough surfaces , even without any scaling properties , have also anisotropic nature and it is important to provide a robust and feasible algorithm for characterization of probable anisotropy . especially , in stochastic rough interfaces , the anisotropic features could be screened by the random nature of the surface , and it can induce additional and/or spurious properties . for instance , in the growth of anisotropic organic thin films , or erosion and growth with incident angle , anisotropic recognition and determining the kinds of anisotropies are of interest . lateral ordering of nano - dots has been reported in many experiments @xcite . in many cases , the underlying order in the distribution of nano - dots is not directly observable without further analysis on the surface profile , such as fourier analysis with especial wavelet @xcite and curvelet analysis . also in cases , where nano - ripples form , the exact experimental parameters which lead to ripple formation can not be easily measured unless one is able to detect and track the formation of asymmetric ripples precisely . since usual methods to detect anisotropies , e.g. , fourier transform , have their numerical and technical limits , especially in situations , where having large number of samples to make a proper statistical ensemble not to be possible . however many researchers have tried to examine the anisotropic surfaces , but a little part of them has been devoted to give a quantitative measurements to quantify anisotropy @xcite . an extensive quantitative analysis has been done by zhao et . al . by means of diffraction from anisotropic rough surfaces e. vivo et . al . , used the so - called height power spectral density analysis to examine the scaling anisotropic rough surface @xcite . recently , g. guillemot et . al . , have introduced a so - called regularity parameter to quantify the degree of anisotropy @xcite . according to field theoretic renormalization , there is an extensive work done by b. schmittmann et . a trivial and well - known approach is calculating the height - height correlation function and check whether the roughness exponent is directionally dependent or not ? . even though , previous researches give a good approach to find the direction of anisotropy , but only in some cases a method to discriminate between various natures of anisotropy has been established . in this paper , by notion of anisotropic feature in surface erosion and self - affine rough surfaces , we introduce and apply crossing statistics as a benchmark of anisotropy measure . we show that this method makes a feasible measure to quantify the existence of anisotropy and to discriminate isotropic and anisotropic pattern in real space . it can be mounted on the experimental devices , such as atomic force microscopy and scanning tunnelling microscopy . for the first time , rice introduced level crossing statistics @xcite . after that this method has been improved and used to investigate up - crossing and down - crossing of a typical stochastic field . during the last decades , many researches have been done to examine @xmath10 and @xmath0dimensional stochastic processes from the level crossing point of view @xcite . some advantages of this approach are as follows : in many of previous researches with the same purpose , there is no well - defined approach to quantify the degree of probable anisotropy at different thresholds while in the crossing statistics method there is a systematic framework to examine anisotropic nature for various values of thresholds ( see section [ method ] ) . in addition , this method enables us to predict theoretical crossing statistics even in the presence of more complicated correlation function as well as probability density function of underlying fluctuation functions . in other words , the non - gaussianity of underlying stochastic fields can be characterized by using this method , simultaneously . in the presence of isotropy and homogeneity , by calculating crossing statistics in @xmath10d , one can determine extension of given results for quantifying @xmath0d and @xmath11d without doing statistical analysis , directly in higher dimensions since they are much more complicated and much more time consuming @xcite . as we will show , crossing statistics can offer a new measure for characteristics length scales for a riven thresholds . the rest of paper is organized as follows : in sec . [ surf ] we will give a brief explanation regarding the synthetic generation of isotropic and anisotropic rough surfaces . we implement crossing statistics to investigate the height fluctuation of isotropic and anisotropic rough surfaces in sec . [ method ] . simulations of isotropic and anisotropic rough surfaces and analysis based on crossing statistics by means of theoretical and numerical computations will be given in detail in sec . [ result ] . summary and conclusions are presented in sec .

the directional dependency of difference between computed results in mentioned directions are clarify . finally we systematically recognize the anisotropy direction at confidence interval using p - value approach . in order to distinguish between nature of anisotropies , after applying a typical method in determining the scaling exponents in both mentioned directions with respect to the recognized anisotropy direction using up - crossing statistics , the kind and the ratio of correlation length anisotropy are specified . our algorithm can be mounted with a simple software on various instruments for surface analysis , such as afm , stm and etc . * keywords * : crossing statistics , stochastic field , anisotropy , correlation length , scaling exponent .

we use crossing statistics and its generalization to determine the anisotropic direction imposed on a stochastic fields indimension . this approach enables us to examine not only the rotational invariance of morphology but also we can determine the gaussianity of underlying stochastic field in various dimensions . theoretical prediction of up - crossing statistics ( crossing with positive slope at a given threshold of height fluctuation ) , , and generalized roughness function , , for correlation length ( ) and / with scaling exponent ( ) anisotropies are calculated . the strategy to examine the anisotropy nature and to determine its direction is as follows : we consider a set of normal axes , and sign them ( parallel ) and ( normal ) with respect to unknown anisotropic direction . then we determine and in both directions . the directional dependency of difference between computed results in mentioned directions are clarify . finally we systematically recognize the anisotropy direction at confidence interval using p - value approach . in order to distinguish between nature of anisotropies , after applying a typical method in determining the scaling exponents in both mentioned directions with respect to the recognized anisotropy direction using up - crossing statistics , the kind and the ratio of correlation length anisotropy are specified . our algorithm can be mounted with a simple software on various instruments for surface analysis , such as afm , stm and etc . * keywords * : crossing statistics , stochastic field , anisotropy , correlation length , scaling exponent .

1508.01409

m

as explained in the introduction , we are interested in finding a criterion to distinguish the isotropic and anisotropic rough surfaces , consequently , the crossing statistics method will be carried out in the @xmath0dimensional framework @xcite . this method has been used to examine cosmological stochastic fields and many aspects of it have been derived in @xcite . in order to make more sense for further usage , we summarize mentioned method with some modifications in the following steps : * step1 : definition of variables : * suppose that for a rough surface in 2d , height of the fluctuations is represented by @xmath50 at coordinate @xmath51 with resolution @xmath52 and size @xmath42 ( see fig . [ surface1 ] ) . it is not compulsory that the size of width and height of underlying rough surface to be same . for convenience , suppose that the origin of the coordinate system is located at the centre of rough surface . we assign height fluctuations by @xmath53 , where @xmath54 and @xmath55 demonstrate the coordinate position through the basis vectors namely , @xmath34 and @xmath56 , respectively . in this case we have @xmath57 for the square shape of rough surface . for 1d field as indicated in upper panel of fig . [ level11 ] , crossing points with positive slope at arbitrary threshold , @xmath58 , are so - called up - crossing indicated by @xmath59-symbols in this figure . here @xmath1 and @xmath22 are the value of surface height and variance of height fluctuations , respectively . we can extend this crossing statistics for 2d and 3d stochastic fields . for example for ( 2 + 1)d rough surface , the iso - height contours at given threshold represent crossing statistics for a ( 2 + 1)d surface , while for ( 3 + 1)d stochastic field , iso - density surfaces recognize crossing statistics in this dimension @xcite . according to mathematical framework introduced for crossing statistics , it is straightforward to demonstrate that crossing statistics in higher dimensions are proportional to crossing statistics in 1d slice of underlying field . in this paper we use the up - crossing statistics through a line taken in arbitrary direction as a criterion to pick up anisotropy imposed on a stochastic field in 2d . positive slope crossing at the level @xmath60 . ] sketch of joint probability density function of a typical fluctuation and its derivative with respect to corresponding dynamical parameter ( position ) in the level crossing theory . the shaded area indicates the total probability of finding crossing with positive slope at level @xmath61 . the symbol @xmath62 can be replaced for each direction . ] * step2 : preparing data sets : * we consider two categories of slices for height fluctuation in two separate and orthogonal directions labeled by @xmath18 and @xmath19 . it must point out that these two directions are produced by rotation counterclockwise with respect to the origin of coordinate through the angle @xmath33 . for @xmath63 the common axes to be retrieved . we indicate the @xmath10d fluctuations along these slices by @xmath64 and @xmath65 . here @xmath66 refers to the @xmath66th slice through the @xmath18 or @xmath19 directions . the size of these @xmath10d signals depend on the resolution and the direction of slicing of underlying rough surface . the upper panel of fig . [ level11 ] shows a schematic of @xmath10d slice of underlying rough surface . if @xmath67 to be invariant under eulerian rotation , consequently the statistical isotropy will be valid , and in this case each of mentioned slices belong to the so - called isotropic gibbs ensemble . for an isotropic and homogenous process , in long run , the up - crossing and down - crossing are statistically equivalent @xcite . here in this study , we only take up - crossing events in order to find a benchmark for anisotropy . * step3 : theoretical approach : * probability distribution function ( pdf ) of the height of rough surface is represented by @xmath68 and the corresponding conditional pdf is defined by @xmath69 , here @xmath70 . the gradient of the height can be written as : @xmath71 . for both direction @xmath18 and @xmath19 , we construct one dimensional fluctuations as @xmath72 , in which @xmath62 symbol can be replaced by @xmath18 and @xmath19 and @xmath73 runs from @xmath74 to @xmath75 , here @xmath75 is sample size as : @xmath76 . let @xmath77 denotes the number of up - crossing ( crossing with positive slope ) the height fluctuations at an arbitrary level @xmath1 . where the additional parameter @xmath78 corresponds to the angle between the direction of a fixed frame and positive axis of e.g. @xmath18 ( see fig . [ aniso surf ] for more details ) . for convenient , we set @xmath79 . the ensemble averaging for level crossing with positive slope is also given by : @xmath80 to evaluate the conditions of up - crossing , we consider a 1d interval with length @xmath52 started from position @xmath81 . the sample fluctuations , @xmath82 will intersect the level @xmath1 in direction @xmath83 if and only if two following necessary and sufficient conditions are satisfied ( see the lower panel of fig . [ level11 ] ) : @xmath84 and the slope of signal should be larger or at least equal to the slope of line which is plotted by using the point at the beginning of interval and point located at the level @xmath1 , namely : @xmath85 } { \delta}\le\eta_{\diamond}(\phi;n , m_1).\ ] ] for each slicing we set the mean value to zero . according to joint pdf of height fluctuations and its derivative @xmath86 , the region corresponding to @xmath87 and @xmath88 , in the plane ( @xmath89 ) is related to the probability of up - crossing in direction @xmath90 at level @xmath1 . in fig . [ proba ] , we have indicated the shaded volume corresponding to joint probability density function to satisfy the mentioned conditions @xcite . subsequently , the probability of having up - crossing in the interval @xmath52 is given by : @xmath91 here @xmath92 is step function . therefore , @xmath93 here @xmath94 has been marginalized over other component of @xmath95 vector ( hereafter we remove bar symbol for convenience ) and @xmath96 is the average of up - crossing at level @xmath97 or @xmath98 corresponds to wavelength of having an up - crossing at level @xmath1 through the direction @xmath99 , statistically . the most familiar form of eq . ( [ levelmain ] ) is @xmath100 . in addition , if @xmath101 as for homogeneous and isotropic gaussian field then eq . ( [ levelmain ] ) indicates that @xmath102 . from theoretical point of view , one can calculate up - crossing statistic using the functional form of joint pdf of relevant variables . in the case of multivariate gaussian joint pdf of relevant variables of rough surface , we have : @xmath103 where @xmath104 and @xmath105 is the inverse of the covariance matrix of underlying variables : @xmath106.\ ] ] each element of covariant matrix can be computed using power spectrum of underlying 2d rough surface , @xmath107 . we derived these element for @xmath108dimensional isotropic stochastic field in appendix . we suppose that @xmath109 , therefore , the analytical form of up - crossing statistics for isotropic rough surface for arbitrary slice ( eq . ( [ levelmain ] ) ) reads as ( see the appendix for more details ) : @xmath110 where @xmath22 and @xmath111 are spectral parameters defined in appendix . additional 2-factor in the denominator of eq . ( [ theory for nu gaussain ] ) in comparison to that of introduced in ref . @xcite is in fact due to the up - crossing enumeration rather than taking into account both up- and down - crossings . however , we wrote up - crossing statistics for gaussian stochastic field , but it is possible to rewrite it for general case as : @xmath112 here @xmath113 is dirac delta function . in addition to above definition for up - crossing , @xcite introduced another kind of crossing for which a condition is taken into account for perpendicular direction of up - crossing . in another word , the value of field in perpendicular of at each crossing point should be extrema . therefore the mathematical form of this circumstance is : @xmath114 the perturbation formula for eqs . ( [ theory for nu nongaussain ] ) up to @xmath115 has been given in ref . @xcite and for an isotropic gaussian field in @xmath0-d closed form of eq . ( [ theory for nu nongaussaincond ] ) has been indicated in @xcite . as we are going to use this method for probing anisotropy imposed on a typical 2d rough surface , we can rewrite up - crossing in arbitrary direction based on 1d power spectrum , @xmath116 , as @xcite @xmath117 where @xmath118 and 1d power spectrum is given by : @xmath119 for isotropic rough surface we have @xmath120 , consequently : @xmath121 . upper panel : simulated isotropic gaussian rough surface . middle panel : up - crossing analysis for the isotropic gaussian rough surface . lower panel is @xmath122 for isotropic gaussian rough surface . the red line represents the theoretical prediction and filled circles correspond to the numerical computation.,title="fig : " ] upper panel : simulated isotropic gaussian rough surface . middle panel : up - crossing analysis for the isotropic gaussian rough surface . lower panel is @xmath122 for isotropic gaussian rough surface . the red line represents the theoretical prediction and filled circles correspond to the numerical computation.,title="fig : " ] upper panel : simulated isotropic gaussian rough surface . middle panel : up - crossing analysis for the isotropic gaussian rough surface . lower panel is @xmath122 for isotropic gaussian rough surface . the red line represents the theoretical prediction and filled circles correspond to the numerical computation.,title="fig : " ] upper panel shows the up - crossing analysis for completely isotropic rough surface for two arbitrary directions . lower panel corresponds to @xmath123 as a function of level for anisotropic rough surface for two anisotropic directions.,title="fig : " ] upper panel shows the up - crossing analysis for completely isotropic rough surface for two arbitrary directions . lower panel corresponds to @xmath123 as a function of level for anisotropic rough surface for two anisotropic directions.,title="fig : " ] for gaussian anisotropic rough surface we use power spectrum given in eq . ( [ spectrumcoraniso ] ) belonging to correlation length anisotropic model . the up - crossing in direction @xmath62 is : @xmath124 therefore for anisotropic gaussian rough surface , the ratio of up - crossing in two anisotropic direction is @xmath125 representing the inverse ratio of corresponding correlation length scales . for scaling anisotropic model , power spectrum introduced in eq . ( [ spectrumexponent ] ) is implemented . the up - crossing in direction @xmath62 is : @xmath126 in this case we have : @xmath127 another useful parameter based on @xmath96 is introduced by : @xmath128 obviously , for @xmath129 the above quantity specifies the total number of up - crossing for height fluctuations with positive slope at all levels in direction @xmath62 . for a typical rough fluctuation , @xmath130 can be a criterion to recognize the roughness of processes . for a typical long - range correlated process , @xmath130 is smaller than the same just it ordering has been destroyed , while for anti - correlated data set @xmath130 is larger than that of for which its memories have been destroyed by shuffling method . for isotropic gaussian rough surface we have : @xmath131 for correlation length anisotropic gaussian surface , by using eqs . ( [ spectrumcoraniso ] ) and ( [ theory for nu gaussain ] ) , eq . ( [ ntq ] ) reads as : @xmath132 while for scaling exponent anisotropic gaussian surface , we consider power spectrum according to eq . ( [ spectrumexponent ] ) , therefore , eq . ( [ ntq ] ) becomes : @xmath133 the upper panel of fig . [ gff ] shows isotropic gaussian rough surface . the filled circle symbols in the middle panel of this figure correspond to the numerical computation of @xmath2 while the solid line is calculated by eq . ( [ theory for nu gaussain ] ) , which is the theoretical prediction for up - crossing as a function of @xmath1 . the generalized crossing statistics , @xmath122 , has been shown in lower panel . as we expect , our results do not depend on special direction . our results demonstrate that there exists a good consistency between numerical and theoretical prediction . upper panel : simulated anisotropic gaussian rough surface in which , its power spectrum is given by eq . ( [ spectrumcoraniso ] ) middle panel : up - crossing analysis for the correlation length anisotropic gaussian rough surface . lower panel is @xmath122 for the mentioned simulated rough surface . the red line represents the theoretical prediction and filled circles correspond to the numerical computation.,title="fig : " ] upper panel : simulated anisotropic gaussian rough surface in which , its power spectrum is given by eq . ( [ spectrumcoraniso ] ) middle panel : up - crossing analysis for the correlation length anisotropic gaussian rough surface . lower panel is @xmath122 for the mentioned simulated rough surface . the red line represents the theoretical prediction and filled circles correspond to the numerical computation.,title="fig : " ] upper panel : simulated anisotropic gaussian rough surface in which , its power spectrum is given by eq . ( [ spectrumcoraniso ] ) middle panel : up - crossing analysis for the correlation length anisotropic gaussian rough surface . lower panel is @xmath122 for the mentioned simulated rough surface . the red line represents the theoretical prediction and filled circles correspond to the numerical computation.,title="fig : " ] upper panel : synthetic anisotropic gaussian rough surface with correlation as well as scaling exponent anisotropies ( eq . ( [ spectrumexponent ] ) ) . middle panel : up - crossing analysis anisotropic gaussian rough surface . lower panel is @xmath122 for the mentioned simulated rough surface . the red line represents the theoretical prediction and filled circles correspond to the numerical computation.,title="fig : " ] upper panel : synthetic anisotropic gaussian rough surface with correlation as well as scaling exponent anisotropies ( eq . ( [ spectrumexponent ] ) ) . middle panel : up - crossing analysis anisotropic gaussian rough surface . lower panel is @xmath122 for the mentioned simulated rough surface . the red line represents the theoretical prediction and filled circles correspond to the numerical computation.,title="fig : " ] upper panel : synthetic anisotropic gaussian rough surface with correlation as well as scaling exponent anisotropies ( eq . ( [ spectrumexponent ] ) ) . middle panel : up - crossing analysis anisotropic gaussian rough surface . lower panel is @xmath122 for the mentioned simulated rough surface . the red line represents the theoretical prediction and filled circles correspond to the numerical computation.,title="fig : " ] in the following sections , we are going to derive the @xmath134 for height fluctuations in two distinct directions and then we try to find a robust criterion to distinguish the isotropic and anisotropic surfaces due to various growth mechanisms .

we use crossing statistics and its generalization to determine the anisotropic direction imposed on a stochastic fields indimension . this approach enables us to examine not only the rotational invariance of morphology but also we can determine the gaussianity of underlying stochastic field in various dimensions . theoretical prediction of up - crossing statistics ( crossing with positive slope at a given threshold of height fluctuation ) , , and generalized roughness function , , for correlation length ( ) and / with scaling exponent ( ) anisotropies are calculated . the strategy to examine the anisotropy nature and to determine its direction is as follows : we consider a set of normal axes , and sign them ( parallel ) and ( normal ) with respect to unknown anisotropic direction .

we use crossing statistics and its generalization to determine the anisotropic direction imposed on a stochastic fields indimension . this approach enables us to examine not only the rotational invariance of morphology but also we can determine the gaussianity of underlying stochastic field in various dimensions . theoretical prediction of up - crossing statistics ( crossing with positive slope at a given threshold of height fluctuation ) , , and generalized roughness function , , for correlation length ( ) and / with scaling exponent ( ) anisotropies are calculated . the strategy to examine the anisotropy nature and to determine its direction is as follows : we consider a set of normal axes , and sign them ( parallel ) and ( normal ) with respect to unknown anisotropic direction . then we determine and in both directions . the directional dependency of difference between computed results in mentioned directions are clarify . finally we systematically recognize the anisotropy direction at confidence interval using p - value approach . in order to distinguish between nature of anisotropies , after applying a typical method in determining the scaling exponents in both mentioned directions with respect to the recognized anisotropy direction using up - crossing statistics , the kind and the ratio of correlation length anisotropy are specified . our algorithm can be mounted with a simple software on various instruments for surface analysis , such as afm , stm and etc . * keywords * : crossing statistics , stochastic field , anisotropy , correlation length , scaling exponent .

1508.07183

c

we present a covariant study of the light isovector meson spectrum . via various comparisons of our calculated results for mass splittings to experimental data , we investigated the role and importance of the two characteristic features of the effective interaction used herein , which are the strength of the interaction s intermediate - momentum part represented by the parameter @xmath4 on the one hand , and the inverse effective range of the interaction represented by the parameter @xmath24 and easily visible as the peak position of the effective interaction in momentum space . at the beginning of the analysis we revisit the problem of isovector exotic vector states , which was already discussed previously @xcite and add an in - depth discussion of the situation , presenting also predictions for the lowest - lying @xmath0 states in the @xmath1 channel . then , in a step - by - step fashion , we investigate our results for radial , orbital , other , and pion - related isovector - meson mass splittings and their dependence on the two parameters in our model . the following conclusions may be drawn from our results : first , for most individual splittings in our investigation , the dependence on @xmath24 was more pronounced and important for a good match to experimental data than the one on @xmath4 in the sense that for the optimal @xmath24 region the dependence on @xmath4 was very small . second , since our rl - truncated approach somewhat simplifies the problem and ignores both nonresonant and resonant effects expected beyond rl , achieving a good fit to experimental light - meson data would not be a sign of an accurate description of the physics mechanisms behind those states . it is thus also unsurprising that fitting all available splittings does not provide the best match to the data . in order to find a better match , we select sets of splittings from each category in two steps and , in the end , combine them as such to arrive at an overall result . our general impression is that choosing a small but reliable set of splittings provides the best results . third , the pion emerges as a critical state for the fitting process in the sense that its mass is fixed in our study due to its protection via the axial - vector ward - takahashi identity . as a result , pion - related splittings appear to be substantially more important than others for achieving a reasonable match of our calculated results to experimental data . finally , regarding preferred parameter values from our investigations we find that @xmath24 values lower on our grid together with high @xmath4 values provide the best matching result . this means an inverse effective range of the model interaction of @xmath182 gev , which is at the upper end of the domain orginally investigated by maris and tandy @xcite , but with an increased overall strength of the interaction . this is different from our results obtained previously for heavy quarkonia @xcite , where the resulting inverse effective range was @xmath220 gev . this means that for our setup the important features of the effective interaction are shorter range in heavy quarkonia and longer range in the light - quark sector . in our analysis of the orbital angular momentum decomposition of the covariant bethe - salpeter wave functions , the ground states follow intuitive patterns . for excited states in the @xmath55 channel , concretely for excitations of the @xmath2 meson , our results for the @xmath190 show a predominant @xmath4-wave component , which is similar to results from lattice qcd and in contrast to a @xmath108 state in the quark model . quark model interpretations of the @xmath2 excitations in terms of hybrid admixtures are not contradicted , however , since such contributions are implicit in our approach . further insight is expected from upcoming studies of hadronic partial decay widths of these states . as an outlook we note that the possibilities of making the effective interaction more general and flexible have still not been exhausted and present the most promising path for making a study such as ours more successful in the present rl setup . steps beyond the current truncation are promising as well , with a clear emphasis on nonresonant corrections , in particular in the light - quark sector . we acknowledge helpful discussions with m. pak , c. popovici and r. williams .

we discuss splittings among as well as orbital angular momentum properties of various states in detail and analyze common features of mass splittings with regard to properties of the effective interaction . in particular , we predict the mass of exotic states , and identify orbital angular momentum content in the excitations of the meson . while the and its second excitation are predominantly-wave , the first excitation is predominantly-wave .

we investigate the light quarkonium spectrum using a covariant dyson - schwinger - bethe - salpeter - equation approach to qcd . we discuss splittings among as well as orbital angular momentum properties of various states in detail and analyze common features of mass splittings with regard to properties of the effective interaction . in particular , we predict the mass of exotic states , and identify orbital angular momentum content in the excitations of the meson . while the and its second excitation are predominantly-wave , the first excitation is predominantly-wave .

hep-ph9907319

i

signals from supersymmetry ( susy ) are important targets for particle physics experiments . these signals range from the direct discovery of supersymmetric particles at high energy colliders to indirect signals at lower energy experiments through measurements of flavor - changing processes , magnetic and electric dipole moments , and so on . the set of possible signals and the promise of individual experiments for susy searches depend strongly on what model of susy breaking is assumed . it is therefore important to understand the characteristic features and predictions of well - motivated susy breaking scenarios . probably the most well - known scenario is that of susy breaking in the supergravity framework , i.e. , `` gravity - mediated '' susy breaking . in this framework , susy breaking originates in a hidden sector and is transmitted to the observable sector though planck scale - suppressed operators . in particular , soft masses for squarks , sleptons , and higgs bosons are induced by direct khler interactions between hidden and observable sector fields . unfortunately , these khler interactions are not , in general , flavor - diagonal . squark and slepton mass matrices therefore typically have large flavor mixings , and these induce unacceptably large flavor - changing processes , such as @xmath6-@xmath7 mixing and @xmath8 @xcite . these difficulties , together commonly referred to as the susy flavor problem , may be avoided if the khler potential is somehow constrained to be flavor - diagonal . gauge - mediated susy breaking @xcite is one proposal for solving this problem . recently the mechanism of `` anomaly - mediated '' susy breaking has been proposed as a possibility for generating ( approximately ) flavor - diagonal squark and slepton mass matrices @xcite . in this scenario , susy is again broken in a hidden sector , but it is now transmitted to the observable sector dominantly via the super - weyl anomaly @xcite . gaugino and scalar masses are then related to the scale dependence of the gauge and matter kinetic functions . for first and second generation fields , whose yukawa couplings are negligible , wavefunction renormalization is almost completely determined by gauge interactions . their anomaly - mediated soft scalar masses are thus almost diagonal , and the susy flavor problem is solved . note that this solution requires that the anomaly - mediated terms be the dominant contributions to the susy breaking parameters . this possibility may be realized , for example , if susy breaking takes place in a different world , i.e. , on a brane different from the 3-brane of our world , and direct khler couplings are thereby suppressed @xcite . as will be discussed below , the expressions for anomaly - mediated susy breaking terms are scale - invariant . thus , they are completely determined by the known low energy gauge and yukawa couplings and an overall mass scale @xmath1 . anomaly - mediated susy breaking is therefore highly predictive , with fixed mass ratios motivating distinctive experimental signals , such as macroscopic tracks from highly degenerate wino - like lightest supersymmetric particles ( lsps ) @xcite . unfortunately , one such prediction , assuming minimal particle content , is that sleptons are tachyons . several possible solutions to this problem have already been proposed @xcite . we will adopt a phenomenological approach , first taken in ref . @xcite , and assume that the anomaly - mediated scalar masses are supplemented by an additional universal contribution @xmath9 . for large enough @xmath2 , the slepton squared masses are positive . along with the requirement of proper electroweak symmetry breaking , this defines the minimal anomaly - mediated model in terms of only 3 + 1 parameters : @xmath1 , @xmath2 , @xmath3 , and @xmath4 , where @xmath3 is the ratio of higgs vacuum expectation values ( vevs ) , and @xmath10 is the higgsino mass parameter . the simplicity of this model allows one to thoroughly examine all of parameter space . in this paper , we present a detailed study of the phenomenology of the minimal anomaly - mediated model . we begin in sec . [ sec : amsb ] with a brief discussion of the mechanism of anomaly - mediated susy breaking . in sec . [ sec : mam ] we review the tachyonic slepton problem and the universal @xmath2 `` solution , '' and present in detail the minimal anomaly - mediated model described above . the universal scalar mass @xmath2 breaks the simple scale invariance of expressions for soft terms . however , this breaking is rather minimal , in a sense to be explained , and the minimal anomaly - mediated model inherits several simple properties from the pure anomaly - mediated case . the naturalness of this model is examined in sec . [ sec : naturalness ] . we find that the minimal anomaly - mediated model exhibits a novel renormalization group ( rg ) `` focus point '' ( as opposed to fixed point ) behavior , which allows slepton and squark masses to be well above their usual naturalness bounds . the title `` supernatural supersymmetry '' derives from this feature and the envisioned other - worldly susy breaking . we then turn in sec . [ sec : highenergy ] to high - energy experimental implications . we explore the parameter space and find a variety of interesting features , including 3 possible lsp candidates : a degenerate triplet of winos , the lighter stau @xmath11 , and the tau sneutrino @xmath12 . the wino lsp scenario is realized in a large fraction of parameter space and has important new implications for both collider physics @xcite and cosmology @xcite . we find that naturalness and electroweak symmetry breaking favor light winos with the smallest possible mass splittings , i.e. , the ideal region of parameter space for wino searches and within the discovery reach of run ii of the tevatron . while anomaly - mediated models have the virtue that they predict very little flavor - changing in the first and second generations , they are not therefore automatically safe from all low - energy probes . in sec . [ sec : lowenergy ] we analyze several sensitive low - energy processes : @xmath5 , which probes flavor - changing in the third generation , and three important flavor-_conserving _ observables , the anomalous magnetic dipole moment of the muon , and the electric dipole moments of the electron and neutron . our conclusions and final remarks are collected in sec . [ sec : conclusions ] . in the appendix , we present expressions for anomaly - mediated susy breaking terms in a general supersymmetric theory and also the full flavor - dependent expressions for the specific case of the minimal anomaly - mediated model .

such a scenario is envisioned to arise when supersymmetry breaking takes place in another world , i.e. , on another brane . the renormalization group equations exhibit a novel `` focus point '' ( as opposed to fixed point ) behavior , which allows squark and slepton masses far above their usual naturalness bounds . we present the superparticle spectrum and highlight several implications for high energy colliders . three lightest supersymmetric particle ( lsp ) candidates exist : the wino , the stau , and the tau sneutrino . for the wino lsp scenario , light wino triplets with the smallest possible mass splittings are preferred ; such winos are within reach of run ii tevatron searches . finally , we study a variety of sensitive low energy probes , including , the anomalous magnetic moment of the muon , and the electric dipole moments of the electron and neutron . . suppl . * rep . astron . astrophys . * rev . nucl . . lett . mod .

we discuss the phenomenology of supersymmetric models in which supersymmetry breaking terms are induced by the super - weyl anomaly . such a scenario is envisioned to arise when supersymmetry breaking takes place in another world , i.e. , on another brane . we review the anomaly - mediated framework and study in detail the minimal anomaly - mediated model parametrized by only parameters : , , , and . the renormalization group equations exhibit a novel `` focus point '' ( as opposed to fixed point ) behavior , which allows squark and slepton masses far above their usual naturalness bounds . we present the superparticle spectrum and highlight several implications for high energy colliders . three lightest supersymmetric particle ( lsp ) candidates exist : the wino , the stau , and the tau sneutrino . for the wino lsp scenario , light wino triplets with the smallest possible mass splittings are preferred ; such winos are within reach of run ii tevatron searches . finally , we study a variety of sensitive low energy probes , including , the anomalous magnetic moment of the muon , and the electric dipole moments of the electron and neutron . # 1#2#3jhep * # 1 * , # 3 ( 19#2 ) # 1#2#3eur . phys . j. * c#1 * , # 3 ( 19#2 ) # 1#2#3nucl . phys . * b#1 * , # 3 ( 19#2 ) # 1#2#3nucl . phys . . suppl . * # 1 * , # 3 ( 19#2 ) # 1#2#3phys . lett . * b#1 * , # 3 ( 19#2 ) # 1#2#3phys . lett . * # 1b * , # 3 ( 19#2 ) # 1#2#3phys . rev . * d#1 * , # 3 ( 19#2 ) # 1#2#3phys . rev . lett . * # 1 * , # 3 ( 19#2 ) # 1#2#3phys . rep . * # 1 * , # 3 ( 19#2 ) # 1#2#3ann . rev . astron . astrophys . * # 1 * , # 3 ( 19#2 ) # 1#2#3ann . rev . nucl . part . sci . * # 1 * , # 3 ( 19#2 ) # 1#2#3mod . . lett . * a#1 * , # 3 ( 19#2 ) # 1#2#3zeit . fr physik * c#1 * , # 3 ( 19#2 ) # 1#2#3ap . j. * # 1 * , # 3 ( 19#2 ) # 1#2#3ann . phys . * # 1 * , # 3 ( 19#2 ) # 1#2#3rev . mod . phys . * # 1 * , # 3 ( 19#2 ) # 1#2#3comm . math . phys . * # 1 * , # 3 ( 19#2 ) epsf.tex ( # 1 width # 2)=#2

astro-ph0001501

c

we developed a continuous jet model for the radio outbursts of galactic microquasars . the model naturally explains the observed rather flat decaying lightcurves of these bursts as the signature of synchrotron radiation of relativistic particles accelerated by internal shocks in the conical jets . the comparatively long duration of the bursts implies that this model is a ` time - resolved ' version of the internal shock model proposed for grb ( rees & meszaros 1994 ) , though the synchrotron emission is produced at much lower frequencies . the gradual steepening of the radio spectrum is explained by a superposition of the radiation of different populations of relativistic particles with different ages . this spectrum of ages results from the shock traveling along the jet with older populations of accelerated particles left behind . we find that only a roughly constant rate of acceleration of relativistic particles followed by an exponential decay can explain the observed light curves for the strong outburst of grs 1915 + 105 in 1994 . we interpret this behaviour as the signature of two colliding shells of jet material , as in the internal shock model for grb . a consequence of this is the continued steepening of the lightcurves of a given outburst coupled with a decreasing flux ratio of the emission observed from the approaching to that from the receding jet side . the energy requirements of the continuous jet model for producing radio outbursts are similar to those of the plasmon model . however , much of the energy underlying the outbursts may be stored in the continuous jet while the passage of the internal shock only ` lights up ' the jet . this implies that the rate at which the energy of the outburst is supplied by the central engine to the jet is much lower than in the plasmon model . the occurrence of mini - bursts in microquasars with flat spectra up to infrared frequencies ( mirabel et al . 1998 ) and the observation of k - band emission in the jet a considerable distance away from the core ( sams et al . 1996 ) suggest different modes of jet production : ( i ) a stable ` mini - burst ' mode with relative little variation in the bulk jet speed and therefore also only weak internal shocks . ( ii ) a more variable outburst mode with strong variations in the jet speed and strong internal shocks ( see also fender 1999 ) . the weaker flavour internal shocks seem to produce flatter relativistic particle spectra extending to higher energy compared to the strong shocks . however , the total number of accelerated particles must be much larger in the strongly variable phase . we show that the properties of the continuous jets of microquasars should lead to strong shocks at their ends where they are in contact with the surrounding ism . this is consistent with the recent observations of the decelerating radio emission region of xte j1748 - 288 ( hjellming et al . 1999 ) and its persistence for 15 months after the start of the original outburst ( rupen , private communication ) . the shocked jet material may subsequently inflate a low density cavity around the jets similar to the radio lobes in extragalactic jet sources of type frii . this is observed in ss433 ( dubner et al . 1998 ) and may be in a few other microquasars . the absence of such shocks and radio lobes in grs 1915 + 105 may indicate that the jets in this source are young and/or that they recollimate because of the pressure of their environment . if this is the case then the detection of a non - thermal emission region in the more extended environment of grs 1915 + 105 ( rodrguez & mirabel 1998 ) may imply a recurrence time of the jet activity scale of @xmath171 years . many of the predictions of this model for microquasars can be tested observationally . however , to clearly distinguish between this model of continuous jets and the plasmon model it would be necessary to spatially resolve the superluminal emission regions during outbursts , preferentially at more than one radio frequency . additional support for the scenario of continuous jets may come from further high resolution observations of the cores of microquasars during quiescence . these should show at least some spatial extension of the radio emission along the jet axis as observed in cygnus x-1 ( fender et al . these observations can potentially provide us with valuable information on the properties of the jets which otherwise we can only study during strong outbursts when strong shocks pass through them .

we present a model for the radio outbursts of microquasars based on the assumption of quasi - continuous jet ejection . the observed comparatively flat decay light curves combined with gradually steepening spectral slopes are explained by a superposition of the radiation of the aging relativistic particle population left behind by the shocks . observations of ` mini - bursts ' with flat spectral slopes and of infrared emission far from the source centre suggest two different states of jet ejections : ( i ) a ` mini - burst ' mode with relatively stable jet production and weak radio emission with flat spectra and ( ii ) an outburst mode with strong variations in the jet bulk velocities coupled with strong radio emission with steeper spectra .

we present a model for the radio outbursts of microquasars based on the assumption of quasi - continuous jet ejection . the jets are ` lit up ' by shock fronts traveling along the jets during outbursts . the shocks accelerate relativistic particles which emit the observed synchrotron radiation . the observed comparatively flat decay light curves combined with gradually steepening spectral slopes are explained by a superposition of the radiation of the aging relativistic particle population left behind by the shocks . this scenario is the low energy , time - resolved equivalent to the internal shock model for grbs . we show that this model predicts energy contents of the radiating plasma similar to the plasmon model . at the same time , the jet model relaxes the severe requirements on the central source in terms of the rate at which this energy must be supplied to the jet . observations of ` mini - bursts ' with flat spectral slopes and of infrared emission far from the source centre suggest two different states of jet ejections : ( i ) a ` mini - burst ' mode with relatively stable jet production and weak radio emission with flat spectra and ( ii ) an outburst mode with strong variations in the jet bulk velocities coupled with strong radio emission with steeper spectra . we also show that the continuous jets in microquasars should terminate in strong shocks and possibly inflate radio lobes similar to extragalactic jet sources . we investigate the possibility of testing the predictions of this model with resolved radio observations . finally , we suggest that doppler - shifted x - ray iron lines , and possibly h - alpha lines , may be emitted by the jet flow of microquasars if thermal instabilities analogous to those in ss433 exist in their jets .

1512.01022

i

multilevel monte carlo ( mlmc ) methods pioneered by @xcite and @xcite are now standard for estimation of expectations of functionals of processes defined by stochastic differential equations ( sdes ) . while the mlmc techniques have origins in the integral operators @xcite and sdes @xcite , they can be applied also in other application domains , where estimates with gradually increasing accuracy are available ; see the recent review by @xcite and references therein . more recently , so - called debiasing techniques @xcite have attracted a lot of research activity ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ; * ? ? ? * ) , although similar ideas have been suggested much earlier in more specific contexts ( e.g. * ? ? ? * ; * ? ? ? * ; * ? ? ? these techniques are based on similar ideas as mlmc , but instead of optimal allocation of computational resources for minimising the error , the primary focus is in providing unbiased estimators . monte carlo inference is straightforward with independent unbiased samples , allowing to construct confidence intervals in a reliable way @xcite . debiasing techniques may also be employed within a stochastic approximation algorithm @xcite . in particular , in a stochastic gradient descent type algorithm @xcite relevant for instance in maximum likelihood inference @xcite , unbiased gradient estimate implies pure martingale noise , which is supported by a well - established theory ( e.g. * ? ? ? * ; * ? ? ? the debiasing techniques involve balancing with cost and variance , which often boils down to similar methods and conditions as those that are used with mlmc . the connection between mlmc and debiasing techniques has been pointed out earlier at least by @xcite , @xcite and @xcite , but this connection has not been fully explored yet . the purpose of this paper is to further clarify the connection of mlmc and debiasing techniques , within a general framework for unbiased estimators . many techniques for unbiased estimation other than those considered here have been suggested in the literature . for instance , there is a whole body of literature for ` perfect sampling ' by markov chains @xcite or with certain classes of sde models @xcite ; see also the recent monograph by @xcite and references therein . perfect sampling can be used to construct unbiased estimators , but the problem is generally more prestigious and often harder to implement . see also the recent article by @xcite for discussion of other related unbiased estimation techniques . the rest of the paper is organised as follows . the multilevel monte carlo and the previous debiasing methods are presented briefly in sections [ sec : mlmc ] and [ sec : unbiased ] , respectively . section [ sec : general ] introduces a new general unbiased scheme with an explicit expression for its variance ( theorem [ thm : general ] ) . the unbiased estimators suggested by @xcite and @xcite are reformulated as specific instances of this scheme , as well as an obvious ` hybrid ' scheme with mlmc and unbiased components ( example [ ex : hybrid - mlmc ] ) . new unbiased estimators are suggested in section [ sec : new ] . two of the new schemes , termed stratified and residual sampling estimators , have provably lower variance than simple averages of independent unbiased estimates ( proposition [ prop : consistency ] ) . because stratification is a well - known variance reduction technique , these estimators may be well - known , but they do not seem to be recorded in the literature yet . the first main finding of this paper is theorem [ thm : residual - eff ] which shows that the asymptotic variance of two of new schemes are asymptotically equal to that of mlmc under general conditions . this result suggests that unbiasedness can often be achieved with asymptotically negligible additional variance . the expected cost of the methods is discussed in section [ sec : cost ] . the new schemes appear even more appealing after seeing that the expected cost of mlmc and the unbiased schemes are also asymptotically equivalent ( proposition [ prop : mlmc - expected - cost ] ) and therefore the efficiency of an estimator with new schemes can be made arbitrarily close to mlmc ( corollary [ cor : batch - complexity ] ) . the limiting variance formulation in theorem [ thm : residual - eff ] leads into an easily applicable optimisation criteria for the sampling distribution related to the new estimators . section [ sec : stopping ] presents a further generalisation of the unbiased scheme , which accomodates further conditioning and dependent randomisation schemes based on stopping times . numerical experiments in section [ sec : numerical ] show how the efficiency bounds predicted by theory are attained in four examples , three of which were also studied by @xcite . the paper is concluded by a discussion about the implications of the findings in section [ sec : conclusions ] . some practical guidelines and possible future topics are discussed as well .

multilevel monte carlo ( mlmc ) and unbiased estimators recently proposed by mcleish ( _ monte carlo methods appl . _ , 2011 ) and rhee and glynn ( _ oper . _ , 2015 ) are closely related . new lower variance estimators are proposed , which are stratified versions of earlier unbiased schemes . under general conditions , essentially when mlmc admits the canonical square root monte carlo error rate , the proposed new schemes are shown to be asymptotically as efficient as mlmc , both in terms of variance and cost . the experiments demonstrate that the variance reduction provided by the new schemes can be substantial .

multilevel monte carlo ( mlmc ) and unbiased estimators recently proposed by mcleish ( _ monte carlo methods appl . _ , 2011 ) and rhee and glynn ( _ oper . res . _ , 2015 ) are closely related . this connection is elaborated by presenting a new general class of unbiased estimators , which admits previous debiasing schemes as special cases . new lower variance estimators are proposed , which are stratified versions of earlier unbiased schemes . under general conditions , essentially when mlmc admits the canonical square root monte carlo error rate , the proposed new schemes are shown to be asymptotically as efficient as mlmc , both in terms of variance and cost . the experiments demonstrate that the variance reduction provided by the new schemes can be substantial .

1512.06923

i

we work over an algebraically closed field @xmath2 of characteristic 2 . complex enriques surfaces with a finite group of automorphisms are completely classified into seven types . the main purpose of this paper is to determine which types of such enriques surfaces exist in characteristic 2 . recall that , over the complex numbers , a generic enriques surface has an infinite group of automorphisms ( barth and peters @xcite ) . on the other hand , fano @xcite gave an enriques surface with a finite group of automorphisms . later dolgachev @xcite gave another example of such enriques surfaces . then nikulin @xcite proposed a classification of such enriques surfaces in terms of the periods . finally the second author @xcite classified all complex enriques surfaces with a finite group of automorphisms , geometrically . there are seven types @xmath3 of such enriques surfaces . the enriques surfaces of type @xmath4 or @xmath5 form an irreducible one dimensional family , and each of the remaining types consists of a unique enriques surface . the first two types contain exactly twelve nonsingular rational curves , on the other hand , the remaining five types contain exactly twenty nonsingular rational curves . the enriques surface of type @xmath4 ( resp . of type @xmath6 ) is the example given by dolgachev ( resp . by fano ) . we call the dual graphs of all nonsingular rational curves on the enriques surface of type @xmath7 the dual graph of type @xmath7 ( @xmath8 ) . in positive characteristics , the classification problem of enriques surfaces with a finite group of automorphisms is still open . especially the case of characteristic 2 is most interesting . in the paper @xcite , bombieri and mumford classified enriques surfaces in characteristic 2 into three classes , namely , singular , classical and supersingular enriques surfaces . as in the case of characteristic @xmath9 , an enriques surface @xmath10 in characteristic 2 has a canonical double cover @xmath11 , which is a separable @xmath12-cover , a purely inseparable @xmath13- or @xmath14-cover according to @xmath10 being singular , classical or supersingular . the surface @xmath15 might have singularities , but it is @xmath16-like in the sense that its dualizing sheaf is trivial . in this paper we consider the following problem : _ does there exist an enriques surface in characteristic @xmath17 with a finite group of automorphisms whose dual graph of all nonsingular rational curves is of type @xmath18 or @xmath19 @xmath20 _ note that if enriques surface @xmath21 in any characteristic has the dual graph of type @xmath7 ( @xmath22 ) , then the automorphism group @xmath23 is finite by vinberg s criterion ( see proposition [ vinberg ] ) . we will prove the following table [ table1 ] : [ ] in table [ table1 ] , @xmath24 means the existence and @xmath25 means the non - existence of an enriques surface with the dual graph of type @xmath26 . in case of type @xmath27 , the construction of such enriques surfaces over the complex numbers works well in characteristic 2 ( theorems [ ithm ] , [ iithm ] , [ vithm ] ) . the most difficult and interesting case is of type @xmath6 . we give a 1-dimensional family of classical and supersingular enriques surfaces with a finite group of automorphisms whose dual graph is of type @xmath6 ( theorems [ main ] , [ main2 ] ) . we remark that this family is non - isotrivial ( theorem [ non - isotrivial ] ) . recently the authors @xcite gave a one dimensional family of classical and supersingular enriques surfaces which contain a remarkable forty divisors , by using a theory of rudakov and shafarevich @xcite on purely inseparable covers of surfaces . we employ here the same method to construct the above classical and supersingular enriques surfaces with the dual graph of type @xmath6 . it is known that there exist enriques surfaces in characteristic 2 with a finite group of automorphisms whose dual graphs of all nonsingular rational curves do not appear in the case of complex surfaces ( ekedahl and shepherd - barron@xcite , salomonsson@xcite ) . see remark [ extra ] . the remaining problem of the classification of enriques surfaces in characteristic 2 with a finite group of automorphisms is to determine such enriques surfaces appeared only in characteristic 2 . the plan of this paper is as follows . in section [ sec2 ] , we recall the known results on rudakov - shafarevich s theory on derivations , lattices and enriques surfaces . in section [ sec3 ] , we give a construction of a one dimensional family of classical and supersingular enriques surfaces with the dual graph of type @xmath28 . moreover we show the non - existence of singular enriques surfaces with the dual graph of type @xmath19 ( theorem [ non - existvii ] ) . in section [ sec4 ] , we discuss other cases , that is , the existence of singular enriques surfaces of type @xmath29 and the non - existence of other cases ( theorems [ ithm ] , [ non - existi ] , [ iithm ] , [ non - existii ] , [ vithm ] , [ non - existvi ] , [ non - existiii ] ) . in appendices a and b , we give two remarks . as appendix a , we show that the covering @xmath16 surface of any singular enriques surface has height @xmath30 . as appendix b , we show that for each singular enriques surface with the dual graph of type @xmath31 its canonical cover is isomorphic to the kummer surface of the product of two ordinary elliptic curves . * acknowledgement . * the authors thank igor dolgachev for valuable conversations . in particular all results in section [ sec4 ] were obtained by discussion with him in soeul and kyoto , 2014 . they thank him that he permits us to give these results in this paper . the authors also thank matthias schtt and hiroyuki ito for pointing out the non - existence of singular enriques surfaces with the dual graph of nonsingular rational curves of type @xmath28 .

complex enriques surfaces with a finite group of automorphisms are classified into seven types . in this paper , we determine which types of such enriques surfaces exist in characteristic 2 . in particular we give a one dimensional family of classical and supersingular enriques surfaces with the automorphism group isomorphic to the symmetric group of degree five .

complex enriques surfaces with a finite group of automorphisms are classified into seven types . in this paper , we determine which types of such enriques surfaces exist in characteristic 2 . in particular we give a one dimensional family of classical and supersingular enriques surfaces with the automorphism group isomorphic to the symmetric group of degree five .

1407.1724

c

in this paper we study new - physics ( np ) contributions to top - quark decay . such effects can be significant only for decays that are suppressed in the sm . here we focus on @xmath0 , whose sm amplitude involves the small element @xmath11 ( @xmath12 ) of the ckm matrix . allowing for all lorentz structures , there are ten possible dimension-6 np operators that can contribute to this decay . the goal is to find ways of detecting the presence of such np in @xmath14 . since the lhc produces top quarks copiously , it is an excellent place to search for signals of np in @xmath0 . however , the dominant mode for top - quark production is pair ( @xmath1 ) production via gluon fusion : @xmath165 . this makes it difficult to study @xmath14 on its own . in order to search for np in top decay , the full process @xmath2 must be analyzed . we consider only cp - conserving np , and find that there are two types of observables that can be used to reveal the presence of np in top decay . the first is an invariant mass - squared distribution involving two of the final - state particles in @xmath14 . there are three such distributions . the second is an angular correlation between the decay products of the @xmath3 and @xmath5 . this is related to the @xmath1 spin correlation . we consider the angular correlation between one of the final - state quarks in @xmath14 and the @xmath4 coming from the @xmath5 decay . there are three such correlations . the six observables depend on different combinations of the coefficients of the ten np operators . we compare the analytical expressions for the observables with the results of a numerical simulation of the lhc using . we find that the agreement between the two is excellent . this suggests that the measurement of these observables can indeed be used to extract some of the new - physics parameters . in the companion paper , @xcite , we demonstrate this explicitly by performing fits of such measurements . we also show how to deal with complications such as the background due to the @xmath19 coming from the @xmath5 decay . * acknowledgments * : the authors wish to thank the madgraph and feynrules teams for extensive discussions about madgraph and feynrules , respectively . the authors are also indebted to german valencia and howard baer for helpful discussions and to zach bethel and carl daudt for technical support . this work was financially supported by nserc of canada ( dl , ps ) . in addition , this work has been partially supported by anpcyt under grant no . pict - prh 2009 - 0054 and by conicet ( as ) . the work of sj and jm was supported by the u.s . national science foundation under grant phy1215785 . the work of kk was supported by the u.s . national science foundation under grants phy0900914 and phy1215785 . kk also acknowledges sabbatical support from taylor university .

in this paper we study new - physics contributions to the top - quark decay . we find six observables that can be used to reveal the presence of new physics in . three are invariant mass - squared distributions involving two of the final - state particles in the top decay , and three are angular correlations between the final - state quarks coming from the decay and the coming from the decay .

in this paper we study new - physics contributions to the top - quark decay . we search for ways of detecting such new physics via measurements at the lhc . as top quarks are mainly produced at the lhc in production via gluon fusion , we analyze the process . we find six observables that can be used to reveal the presence of new physics in . three are invariant mass - squared distributions involving two of the final - state particles in the top decay , and three are angular correlations between the final - state quarks coming from the decay and the coming from the decay . the angular correlations are related to the spin correlation .

1406.1196

i

this paper introduces a family of sorting maps on words that we call _ sweep maps_. in its simplest form , a sweep map @xmath1 uses coprime parameters @xmath2 and @xmath3 to associate a _ level _ @xmath4 to each letter @xmath5 in a word @xmath6 consisting of @xmath7 copies of the letter @xmath8 and @xmath9 copies of the letter @xmath10 . ( note that @xmath2 or @xmath3 may be negative . ) this assignment is done recursively : use the convention that @xmath11 ; for @xmath12 we set @xmath13 if @xmath14 and @xmath15 if @xmath16 . the word @xmath17 is then obtained by sorting the letters in @xmath18 according to level , starting with @xmath19 , then continuing with @xmath20 . figure [ fig : sweepmap1 ] provides an example of @xmath21 acting on the word @xmath22 . ( here we have identified @xmath18 with a lattice path in the plane : each @xmath8 corresponds to a unit - length north step , while each @xmath10 corresponds to a unit - length east step . ) surprisingly , even though sweep maps act by sorting , they are ( apparently ) bijective . the reader may find it useful to check this bijectivity by hand for @xmath23 acting on the set of all lattice paths from @xmath24 to @xmath25 . as detailed in conjecture [ conj : gen - sweep ] , bijectivity seems to hold even for the general sweep maps over arbitrary alphabets with arbitrary weights , described in section [ subsec : gen ] . the bijectivity of the general sweep maps appears to be a very subtle and difficult fact . the order in which the levels are traversed is a key ingredient to bijectivity . for example , in the case of @xmath26 , @xmath27 , if we scan levels in the order @xmath28 , both of the paths @xmath29 and @xmath30 map to @xmath31 . the sweep maps encode complex combinatorial information related to @xmath0-catalan numbers , the bergeron - garsia nabla operator , and other constructions arising in representation theory , algebraic geometry , and symmetric functions . researchers have discovered special cases of the sweep map in many different guises over the last fifteen years or so . one of the goals of this paper is to present a unifying framework for all of this work . in @xcite , loehr introduced bijections on @xmath32-dyck paths , as well as generalizations to lattice paths contained in certain trapezoids , that turn out to be special cases of the sweep map . the bijection in the case @xmath33 also appears in a paper of haglund and loehr @xcite and is foreshadowed by a counting argument in haglund s seminal paper on @xmath0-catalan numbers ( * ? ? ? * proof of thm . the inverse bijection in the case @xmath33 appears even earlier , where it was used by andrews et al . @xcite in their study of @xmath34-nilpotent @xmath35-ideals in the lie algebra @xmath36 . ( see also @xcite . ) more recently , special cases of the sweep map have arisen while studying lattice paths in squares @xcite ; partition statistics @xcite ; simultaneous core partitions @xcite ; and compactified jacobians @xcite . we discuss a number of these connections in more detail in section [ sec : alg - sweep ] . we suspect that to the typical mathematician , the most interesting question regarding the sweep maps is whether they are bijective ( as conjectured in conjecture [ conj : gen - sweep ] ) . for a researcher interested in the @xmath0-catalan numbers , however , of comparable interest is the connection between the sweep maps and statistics on lattice paths such as @xmath37 , @xmath38 and @xmath39 . since shortly after haiman s introduction of @xmath39 , it has been known that a `` zeta map '' takes @xmath39 to @xmath37 to @xmath38 . one point of view , then , is that rather than having three statistics on dyck paths , we have one statistic @xmath37 and a sweep map . many polynomials related to the @xmath0-catalan numbers can be defined using only an `` area '' and an appropriate sweep map . that these polynomials are jointly symmetric ( conjecturally ) supports the utility of this view ( see section [ sec : area - qtcat ] ) . the structure of this paper is as follows . section [ sec : basic ] introduces the necessary background on lattice paths . we then define sweep maps and present conjecture [ conj : gen - sweep ] on their bijectivity in section [ sec : intro - sweep ] . section [ sec : alg - sweep ] reviews various algorithms that have appeared in the literature that are equivalent to special cases of the sweep map , while section [ sec : invert - sweep ] describes how to invert these maps ( when known ) . finally , section [ sec : area - qtcat ] shows how the sweep maps may be used to give concise combinatorial formulas for the higher @xmath0-catalan numbers and related polynomials formed by applying the nabla operator to appropriate symmetric functions and then extracting the coefficient of @xmath40 . an extended abstract of this paper appears as @xcite .

the sweep maps give concise combinatorial formulas for the-catalan numbers , the higher-catalan numbers , the-square numbers , and many more general polynomials connected to the nabla operator and rational catalan combinatorics . we prove that many algorithms that have appeared in the literature ( including maps studied by andrews , egge , gorsky , haglund , hanusa , jones , killpatrick , krattenthaler , kremer , orsina , mazin , papi , vaill , and the present authors ) are all special cases of the sweep maps or their inverses . the sweep maps provide a very simple unifying framework for understanding all of these algorithms .

we define a family of maps on lattice paths , called _ sweep maps _ , that assign levels to each step in the path and sort steps according to their level . surprisingly , although sweep maps act by sorting , they appear to be bijective in general . the sweep maps give concise combinatorial formulas for the-catalan numbers , the higher-catalan numbers , the-square numbers , and many more general polynomials connected to the nabla operator and rational catalan combinatorics . we prove that many algorithms that have appeared in the literature ( including maps studied by andrews , egge , gorsky , haglund , hanusa , jones , killpatrick , krattenthaler , kremer , orsina , mazin , papi , vaill , and the present authors ) are all special cases of the sweep maps or their inverses . the sweep maps provide a very simple unifying framework for understanding all of these algorithms . we explain how inversion of the sweep map ( which is an open problem in general ) can be solved in known special cases by finding a `` bounce path '' for the lattice paths under consideration . we also define a generalized sweep map acting on words over arbitrary alphabets with arbitrary weights , which is also conjectured to be bijective .

1611.00422

c

in this paper , we have presented a detailed analysis of the photometric performance of gems / gsaoi using data obtained during its science verification phase . in particular , we have focused on developing the optimal strategies for obtaining precise stellar photometry from mcao images using science based metrics to quantify the success or otherwise of our approaches for crowded fields . our strategy is based on the well known technique of psf fitting , specifically with the daophot ii suite of programs , but modified to account for the challenges posed by mcao data , especially the significant temporal and spatial variation in the psf . efficient exploitation of mcao imaging in the nir is absolutely essential to the future of ground - based astronomy given the development of the next generation of oir telescopes , especially tmt and the e - elt . the following is a list of our primary conclusions : * mcao delivers a more uniform correction than classical ao over the moderately wide field of view . however , the shape of the psf can still vary significantly in a complex manner , both spatially and temporally ( i.e. , between exposures ; section [ sec : performance ] ) , as also found by @xcite . it is possible that some of this variation has been removed since gems has undergone several realignments of the optics , but residual variability is still expected . as a consequence , this should be reflected in the creation of the psf model by allowing it to have a high degree of spatial variability , and by treating all exposures independantly . * the mcao correction is applied on a scale equal to the `` control radius '' of the system . the majority of the spatial variability of the psf is found within this radius . we demonstrate that we obtain the most precise photometry when the radius of the psf model is set approximately equal to the control radius of the ao system ( section [ sec : psfrad ] ) . if the psf radius is considerably smaller than the control radius , part of the variable psf controlled by the mcao system is not measured , causing a systematic error dependent on the position of the stars . if the psf radius is much larger than the control radius , then the resulting model attempts to include the halo of the psf . this region is generally not varying and contains a fixed fraction of the flux in the psf , and can therefore be accounted for during the calibration procedure . if the psf model includes these outer regions , then the low flux levels mean that other features , including noise artifacts and faint stars , are included and identified as intrinsic features of the psf . this results in an incorrect psf model for these regions and a reduction in the precision of the photometry . * there is an appreciable improvement in photometric precision when the psf model is based on a second iteration of the derivation procedure , i.e. , derived from an image which has had non - psf stars subtracted ( section [ sec : psfclean ] ) . this practice is likely less important with sparse fields . * during the profile fitting , the sky flux under every star is measured interior to the psf radius . in exposures with a large fwhm , we have noticed that using an area significantly smaller than the psf radius increases the precision of the photometry ( section [ sec : psfsky ] ) . we postulate that this is because a larger sky region is more likely to have contamination from unidentified stars , leading to inaccuracies in the sky measurements . * simultaneous profile fitting of all the observations , such as is done with allframe , should be avoided because of the difficulty in finding the proper geometric transformation for the edges of some of the images . treating the images independently leads to more robust photometric / astrometric solutions ( section [ sec : psfindep ] ) . * calibration of mcao photometry is complex . standard star observations are insufficient to estimate the zeropoint since the zeropoint changes for each exposure as a result of the mcao correction . it is therefore advisable to match every exposure and chip independently to a reference catalog of the same field , that is itself calibrated to the nir 2mass system . the measurement of the zeropoints must account for the different spatial resolutions of the catalogs ( section [ sec : calibration ] ) . for gems / gsaoi , we do not measure a significant color term . the procedures described in this paper have allowed us to derive extremely deep and precise nir photometry for the globular cluster ngc 1851 . comparison to isochrones suggest remarkable agreement between our observational data and the theoretical expectations for the color and magnitude distribution of the stars ( from the main sequence knee , through the main sequence turn - off to the subgiant and giant branch ) given our understanding of the age , metallicity , and distance of this cluster as derived from optical data . when combined with optical hst acs data , the ( v - j ) and ( v - k@xmath0 ) cmds allow for the identification of the split subgiant branch ( already demonstrated for the k@xmath0 band in @xcite . with precision photometry and high quality psf modeling in hand , a future contribution will discuss the astrometric performance and precision of our data using a similar approach of the identification of science - based metrics . mcao is a key technology for the future of ground - based nir astronomy , especially as we approach the era of tmt and e - elt , where the large apertures will provide diffraction limits that will significantly surpass even the james webb space telescope . gems / gsaoi allows us to explore the utility of this technology for science observations and develop solutions to the new challenges that are encountered . for example , nfiraos , the mcao system on tmt @xcite , is still expected to present noticeable psf variability even though it will be considerably more uniform and stable than gems . the instrument will be thermally controlled , on a nasmyth platform , and equipped with internal calibration tools . the geometry of the system will also improve the quality of the correction thanks to the use of more laser guide stars , a larger overlapping of the volumes probed by the guide stars , and a smaller scientific field of view . a comparable fraction of the flux will still reside outside the control radius compared to gems , since the density of actuators on the deformable mirrors will be similar . our current analysis suggests that the photometric calibration of tmt observations of crowded fields will be a significant challenge . our present technique of using a calibrated reference catalog of the field would require relatively deep , relatively high spatial resolution photometry if we are to identify large numbers of stars in common with ultra - deep , ultra - high resolution imaging from tmt . by exploring and solving these issues now , before the new generation of mcao instruments are on - sky , we can expect to improve significantly their science return at first light . based on observations for the program gs-2012b - sv-406 ( p.i . : mcconnachie ) at the gemini observatory , which is operated by the association of universities for research in astronomy , inc . , under a cooperative agreement with the nsf on behalf of the gemini partnership : the national science foundation ( united states ) , the national research council ( canada ) , conicyt ( chile ) , ministerio de ciencia , tecnologa e innovacin productiva ( argentina ) , and ministrio da cincia , tecnologia e inovao ( brazil ) . ascenso , j. , neichel , b. , silva , m. , fusco , t. & garcia , p. 2015 , ao4elt 4 conference proceedings , 31540 bec , m. , rigaut , f. j. , galvez , r. , et al . 2008 , , 7015 , 701568 blank , r. , anglin , s. , beletic , j. w. , et al . 2012 , , 8453 , 845310 bono , g. , stetson , p. b. , vandenberg , d. a. , et al . 2010 , , 708 , l74 boyer , c. & ellerbroek , b. 2016 , , 9909 , 990908 carrasco , e. r. , edwards , m. l. , mcgregor , p. j. , et al . 2012 , , 8447 , 84470n carretta , e. , lucatello , s. , gratton , r. g. , bragaglia , a. & dorazi , v. 2011 , , 533 , a69 davies , r. & kasper , m. 2012 , , 50 , 305 diolaiti , e. , ciliegi , p. , abicca , r. , et al . 2016 , , 9909 , 99092d dotter , a. , chaboyer , b. , jevremovi , d. , et al . 2008 , , 178 , 89 ferraro , f. r. , dalessandro , e. , mucciarelli , a. , et al . 2009 , , 462 , 483 figer , d. f. , rauscher , b. j. , regan , m. w. , et al . 2004 , , 5167 , 270 finger , g. , dorn , r. , meyer , m. , et al . 2006 , , 6276 , 62760f fiorentino , g. , tolstoy , e. , diolaiti , e. , et al . 2011 , , 535 , a63 fowler , a. m. & gatley , i. 1990 , , 353 , l33 harris , w. e. 1996 , , 112 , 1487 herriot , g. , andersen , d. r. , atwood , j. , et al . 2014 , , 9148 , 914810 marchetti , e. , hubin , n. n. , fedrigo , e. , et al . 2003 , , 4839 , 317 massari , d. , fiorentino , g. , mcconnachie , a. , et al . 2016a , , 586 , a51 massari , d. , fiorentino , g. , mcconnachie , a. , et al . 2016b , , in press massari , d. , fiorentino , g. , tolstoy , e. , et al . 2016c , , 9909 , 99091 g moretti , a. , piotto , g. , arcidiacono , c. , et al . 2009 , , 493 , 539 mcgregor , p. j. , hart , j. , stevanovic , d. , et al . 2004 , , 5492 , 1033 milone , a. p. , bedin , l. r. , piotto , g. , et al . 2008 , , 673 , 241 neichel , b. , dorgeville , c. , callingham , j. , et al . 2013 , , 429 , 3522 neichel , b. , rigaut , f. j. , vidal , f. , et al . 2014 , , 440 , 1002 rigaut , f. j. & gendron , e. 1992 , , 261 , 677 rigaut , f. j. , neichel , b. , boccas , m. , et al . 2014 , , 437 , 2361 saracino , s. , dalessandro , e. , ferraro , f. r. , et al . 2015 , , 806 , 152 saracino , s. , dalessandro , e. , ferraro , f. r. , et al . 2016 , , in press sarajedini , a. , bedin , l. r. , chaboyer , b. , et al . 2007 , , 133 , 1658 stetson , p. b. 1987 , , 99 , 191 stetson , p. b. 1994 , , 106 , 250 stetson , p. b. & harris , w. e. 1988 , , 96 , 909 stetson , p. b. 1989 , the techniques of least squares and stellar photometry with ccds lectures at v escola avanada de astrofsica , aguas de so pedro , brazil turri , p. , mcconnachie , a. w. , stetson , p. b. , et al . 2015 , , 811 , l15 vandenberg , d. a. , brogaard , k. , leaman , r. & casagrande , l. 2013 , , 775 , 134 yuan , h. b. , liu , x. w. & xiang , m. s. 2013 , , 430 , 2188

we show that the psf produced by gems possesses significant spatial and temporal variability that must be accounted for during the photometric analysis by allowing the psf model a reasonably high degree of spatial variability and by treating all exposures independently . as with seeing - limited observations , we show that standard star observations are insufficient to provide accurate photometric calibration of mcao data . instead

we present a detailed discussion of how to obtain precise stellar photometry in crowded fields using images obtained with multi - conjugate adaptive optics ( mcao ) , with the intent of informing the scientific development of this key technology for the extremely large telescopes . we use deep j and k exposures of ngc 1851 obtained using the gemini multi - conjugate adaptive optics system ( gems ) on gemini south to quantify the performance of the system and to develop an optimal strategy for extracting precise stellar photometry from the images using well - known psf - fitting techniques . we judge the success of the various techniques we employ by using science - based metrics , particularly the width of the main sequence turn - off region . we also compare the gems photometry with the exquisite hst data of the same target in the visible . we show that the psf produced by gems possesses significant spatial and temporal variability that must be accounted for during the photometric analysis by allowing the psf model a reasonably high degree of spatial variability and by treating all exposures independently . as with seeing - limited observations , steps need to be taken to minimize contamination of the psf model and sky estimates from unidentified faint neighboring stars . we show that standard star observations are insufficient to provide accurate photometric calibration of mcao data . instead , we cross - match sources in our mcao observations to a calibrated seeing - limited catalog with a shallower depth but sufficient to include a large number of common sources . however , done in this way , it is critical to consider the different spatial resolutions of the two datasets by accounting for stars that are multiple sources in the mcao dataset but which appear as single sources in the seeing - limited catalog . we identify photometric calibration as a critical issue for next generation mcao systems such as those on tmt and the e - elt . our final cmds reach k , below the main sequence knee of this cluster , and theoretical isochrones provide remarkable agreement with the stellar locus in our data from the main sequence knee to the red giant branch .

physics0403048

i

clusters of heterogeneous materials show a much richer behavior than their homogeneous counterparts . in many bulk compounds , doping can significantly affect some global property , and alloying is a common way to tailor a completely new kind of material . at the mesoscale level , size is another complicating factor , giving rise to further changes with respect to the macroscopic object . to a large extent , most expectations of nanotechnology have been put into the electronic and catalytic properties of small atomic clusters . therefore , it should not be surprising that numerous theoretical studies of mixed clusters were devoted to bimetallic clusters . in particular , there has been a significant amount of work at the level of sophisticated electronic structure calculations,@xcite but these were often limited to small sizes due to the numerical effort involved . on a different scale of chemical complexity , many studies have been carried out using explicit , empirical force fields in order to investigate the segregation properties of these clusters . there are several driving forces toward mixing or segregation in binary systems : * the difference in atomic sizes ; * the difference in surface energies ; * minimization of the overall strain ; * the number of interactions between unlike atoms . these factors can often compete with each other . for instance , minimizing surface energies does usually not increase with the number of interactions between different atoms . also , even though this is not our prime interest here , it should be noted that kinetic factors can be crucial in this problem.@xcite in particular , vach and coworkers have found from experiments and simulations of mixed rare - gas clusters that some anomalous enrichment effects could be observed due to the growth by pick - up of these systems.@xcite very recently , radial segregation and layering have been observed in large ar / xe clusters formed in an adiabatic expansion by tchaplyguine _ et al._@xcite using photoelectron spectroscopy measurements . these data have also been theoretically interpreted by amar and smaby.@xcite fortunately , mixed rare - gas systems can be quite safely described using simple pairwise potentials such as the lennard - jones ( lj ) potential . more accurate potentials are of course also available , even though we will have no need for them in the present , mostly methodological work . hence they are much more convenient to study in a broad size range , not only for their structure but also their dynamics or thermodynamics . it is known from previous studies that the topography of the potential energy surfaces of homogeneous lj clusters can be very peculiar , as for the sizes 38 or 75.@xcite the multiple - funnel structure of these energy landscapes makes it especially hard to locate the most stable structures ( global minima ) or to simulate the finite - temperature behavior of these clusters in an ergodic way . the effects of mixing different rare - gas atoms on cluster structure and thermodynamics have been studied for the specific size 13 by frantz on the examples of ar kr mixtures@xcite as well as ne ar mixtures.@xcite fanourgakis _ have also investigated these latter compounds.@xcite a systematic work of ar xe mixed clusters of 13 and 19 atoms has been carried out by munro and coworkers,@xcite including some global optimization and monte carlo simulations . mixed clusters involving lighter species such as h@xmath1 and d@xmath1 have been investigated using path - integral monte carlo simulations ( pimc ) by chakravarty.@xcite more recently , sabo , doll and freeman reported a rather complete study of the energy landscapes@xciteand melting phase change@xcite in mixed ar ne clusters . in this work quantum delocalization and the effects of impurities on cluster properties were also accounted for using pimc techniques . the main conclusion of these studies is that atomic heterogeneity can be responsible for a drastic increase in complexity of the energy landscapes of rare - gas clusters . this complexity is manifested by numerous new low - lying minima in competitive funnels , characterized by the same overall geometrical arrangement but different permutations of unlike atoms . following jellinek and krissinel,@xcite we will refer to such isomers as `` homotops . '' the presence of several homotops on a given energy landscape often induces solid - solid transitions , which can be detected by some feature in the heat capacity,@xcite even though they can be washed out by quantum effects.@xcite as shown by munro _ et al._,@xcite the various funnels corresponding to different homotops of a same geometry are separated by significant energy barriers . this explains the difficulty or even failure of simulation methods to achieve ergodic sampling of these systems , albeit small.@xcite a similar situation is found in lennard - jones polymers,@xcite where a large number of isomers are based on the same geometrical arrangement , differing only in the path linking the monomers . beyond the actual rare - gases , binary lennard - jones compounds have been investigated in both the cluster and bulk regimes . clarke and coworkers looked at phase separation of small particles with equal compositions.@xcite based on monte carlo simulations , they sketched a phase diagram in the general structure of liquid clusters . bulk binary lennard - jones systems have been seen to provide relatively simple numerical models for glass formation.@xcite most often , the lj interactions in such studies have been tuned in a non - additive way in order to hinder crystallisation . in another related work , lee and coworkers@xcite have investigated the role of atomic size ratio in binary and ternary metallic alloys . interestingly , severaly links between the physics and chemistry of clusters and those of supercooled liquids and glasses have been established since the pioneering work by frank.@xcite the initial suggestion that the local order in simple liquids is not crystalline but icosahedral@xcite ( more generally polytetrahedral ) has since been verified experimentally@xcite and theoretically.@xcite from the clusters viewpoint , the favored finite - size structures of good model glassformers have been shown by doye and coworkers to be polytetrahedral.@xcite the 38-atom homogeneous lennard - jones cluster is known to show some glassy properties , especially slow relaxation to the ground state,@xcite due to the competition between two stable funnels on the energy landscape , corresponding to truncated octahedral and icosahedral shapes , respectively . due to entropic effects,@xcite a solid - solid transition occurs between the two funnels , at temperatures lower than the melting point . the crystal - like configuration of this cluster makes it a good candidate to further investigate the relationship between cluster structure and criteria for glassification . because homogeneous lj@xmath0 constitutes a relatively difficult task for global optimization algorithms , binary clusters of the same size can be expected to be much worse . in this paper , we propose a simple but efficient way to deal with the multiple new minima introduced by unlike atoms within a general monte carlo global minimization scheme . this algorithm will then be applied to the 38- and 55-atom cases , in mixtures of xe with either ar or kr atoms . in the next section , we present the method and test it on the simple cases of the 13- and 19-atom clusters . in sec . [ sec : res ] we give our results obtained at sizes 38 and 55 and we correlate them to the different glassforming abilities of the bulk mixtures . we finally conclude in sec . [ sec : ccl ] .

the method is applied to the more difficult case of the 38-atom cluster , for which the homogeneous clusters have a truncated octahedral shape . these trends are indeed also observed and further analysed on the 55-atom cluster . finally , we correlate the relative stability of cubic structures in these clusters to the glassforming character of the bulk mixtures .

the low - energy structures of mixed ar xe and kr xe lennard - jones clusters are investigated using a newly developed parallel monte carlo minimization algorithm with specific exchange moves between particles or trajectories . tests on the 13- and 19- atom clusters show a significant improvement over the conventional basin - hopping method , the average search length being reduced by more than one order of magnitude . the method is applied to the more difficult case of the 38-atom cluster , for which the homogeneous clusters have a truncated octahedral shape . it is found that alloys of dissimilar elements ( ar xe ) favor polytetrahedral geometries over octahedra due to the reduced strain penalty . conversely , octahedra are even more stable in kr xe alloys than in kr or xe , and they show a core - surface phase separation behavior . these trends are indeed also observed and further analysed on the 55-atom cluster . finally , we correlate the relative stability of cubic structures in these clusters to the glassforming character of the bulk mixtures .

0809.0253

i

observations of a wide variety of astronomical objects suggests the existence of magnetic fields in relativistic environments . there have been many studies of magnetic fields emanating from differentially rotating systems . some of them confine themselves to the non - relativistic regime in which the displacement currents can be neglected . even then few of them are analytic e.g. @xcite , @xcite , , @xcite , while most of them are computational e.g. @xcite , @xcite , @xcite . in the force - free case it was shown that the time evolution of the magnetic field arises solely from the time dependence of the boundary conditions so that the exact dynamical evolution can be calculated from the time dependent sequence of static models @xcite . those in turn can be derived from the energy principle . however , that simplification depends on both the force - free condition and the neglect of the displacement currents which is only valid when the velocities are much less than @xmath5 . relativistic problems are harder as that approximation is invalid , so most studies are purely computational e.g. @xcite , @xcite , @xcite , @xcite and @xcite or semi - analytical e.g. @xcite . despite this , @xcite was able to find an exact solution to the relativistic mhd problem of a point magnetic explosion . he derived a time dependent relativistic analogue of the grad - shafranov equation that governs axially symmetric force - free mhd by assuming that the radial coordinate and the time since the explosion only appear in the dimensionless combination @xmath6 . strictly speaking such equations are only valid when the length scale and @xmath7 the time scale of the region of the explosion are much smaller than @xmath8 and @xmath9 . the resulting prendergast equation is non - linear but becomes linear in a special case . it was this special case that prendergast studied in detail . however , he found that there are spherical nodes where the radial magnetic field is zero and these nodes occur before the highly relativistic regime @xmath10 is reached . this has the unfortunate consequence that magnetic field lines emanating from small @xmath8 turn back before they reach the extremely relativistic region where the displacement currents are very important . the field lines in that region are an appendage unattached to their origin . very similar effects are well known when one takes the analogous case , @xmath11 with @xmath12 constant , in non - relativistic mhd in spherical coordinates . when @xmath13 becomes large , the system gives way to oscillating solutions with a series of nodes . this difficulty occurs because @xmath14 has dimension @xmath15 and the field has to vary on this fixed length scale even at large r. at large distances there is too much current for unit field and the smaller scale is then reflected in the scale of oscillation . it is known that non - linear ansatzes for the non - relativistic grad - shafranov equation can avoid this , which we now recognise as a bad consequence of a mathematically simple linear approximation which is not generally justified in the physics of the problem . we shall therefore study the non - linear prendergast equation in all its glory ! we generalise the idea of force - free fields by considering a configuration where for each point there exists a lorentz frame in which the electric field is zero and the current is along the magnetic field . the force density @xmath16 in the frame fixed at the origin is then : @xmath17 where @xmath18 is the velocity of the moving frame . in this paper , we study such fields by solving the equation proposed by @xcite . however , before stepping to a solution , we extract as much information as possible about the fields that is independent of the detailed form of the solution . then we solve the equations semi - analytically as it impossible to achieve general analytical solutions . the solutions simplify in the non - relativistic limit and converge to those of @xcite . there are some other cases that are interesting and exactly soluble , namely the current - free magnetic dipole and the linear force - free field of prendergast . the introduction of currents in the system allows the existence of a toroidal component of the field at the cost of making analytical solutions much harder , however it is still possible to design analytical solutions for this structure .

the magnetic field expands uniformly either within a cone or in all directions and it is therefore accompanied by an electric field . in the highly conducting plasma the charges move to annul the electric field in the frame of the moving plasma . the solutions presented are analytical and semi - analytical .

following prendergast we study the relativistically expanding electromagnetic fields generated by an axisymmetric explosion of magnetic energy in a small volume . the magnetic field expands uniformly either within a cone or in all directions and it is therefore accompanied by an electric field . in the highly conducting plasma the charges move to annul the electric field in the frame of the moving plasma . the solutions presented are analytical and semi - analytical . we find that the time - scale for the winding up of the initial magnetic field is crucial , as short time - scales lead to strong radiant fields . assuming a magnetic field of emerging from a magnetosphere of we end with a jet when confined by a pressure environment that falls more slowly than . the jet carries energy of , which is mostly due to differential rotation at the base . [ firstpage ] stars : magnetic fields , pulsars , magnetars ,-ray bursts , radio galaxies , quasars

1602.05494

i

cluster algebras were introduced by fomin and zelevinsky in @xcite , and have since found applications across many types of mathematics . these are commutative subalgebras of @xmath0 generated by rational functions constructed using a certain combinatorial procedure starting from an initial seed which produces that seed s mutation class . in the same paper fomin and zelevinsky defined the exchange graph of a cluster algebra to better visualise the combinatorics of the mutation class . these graphs proved a useful tool in their classification of finite - type cluster algebras in @xcite where these algebras were shown to correspond to dynkin diagrams . cluster algebras were shown to be closely related to triangulations of surfaces by fomin , shapiro and thurston in @xcite , where a quiver is constructed from a given triangulation and quiver mutations correspond to flipping an edge in the triangulation . these quivers from surfaces play an important role in the classification of mutation - finite quivers , given by felikson , shapiro and tumarkin in @xcite , as all such quivers are mutation - finite and there are only 11 other exceptional mutation classes . in a similar fashion triangulations of orbifolds with orbifold points of order 2 were shown to correspond to mutation - finite diagrams by felikson , shapiro and tumarkin in @xcite . unfoldings of diagrams , introduced by felikson , shapiro and tumarkin in @xcite , then correspond to coverings of the orbifold by a triangulated surface , as shown in ( * ? ? ? * section 12 ) . cluster automorphisms were introduced by assem , schiffler and shramchenko in @xcite , for cluster algebras generated from quivers , as automorphisms of the cluster algebra taking clusters to clusters and acting as either the identity or the opposite function on quivers . these ideas were extended to cluster algebras generated from certain skew - symmetrizable matrices by chang and zhu in @xcite . the group of cluster automorphisms of a cluster algebra arising from the triangulation of a surface was shown to be isomorphic to the mapping class group of this surface by brstle and qiu in @xcite . in their paper on labelled seeds and global mutations @xcite , king and pressland showed that cluster automorphisms arise naturally when mutation classes are considered as orbits of labelled seeds under the action of a global mutation group @xmath1 . the group of cluster automorphisms is a subgroup of the automorphisms of these mutation classes , @xmath2 , which commute with this group action , and in fact for mutation - finite quivers these groups are isomorphic . we use the links between automorphisms of the exchange graph and the labelled exchange graph to prove that this group @xmath2 is isomorphic to the group of exchange graph automorphisms : for a labelled mutation class @xmath3 with mutation class @xmath4 and exchange graph @xmath5 @xmath6 therefore for mutation - finite quivers , such as those from triangulations of a surface , exchange graph automorphisms are cluster automorphisms . for a cluster algebra @xmath7 constructed from a mutation - finite quiver with exchange graph @xmath8 @xmath9 this result was proved in a different way by chang and zhu in @xcite who also proved an extension of this to skew - symmetrizable matrices of type @xmath10 and @xmath11 for @xmath12 . however for other skew - symmetrizable matrices it is not true that exchange graph automorphisms are cluster automorphisms . it can be shown that the group of cluster automorphisms is isomorphic to a subgroup of the group of exchange graph automorphisms but in general there exist graph automorphisms which do not correspond to cluster automorphisms . in order to generalise these results we introduce a marking on the exchange graph in such a way that any automorphism which fixes these markings does in fact correspond to a cluster automorphism . let @xmath13 be a seed where @xmath14 is a mutation - finite skew - symmetrizable matrix with cluster algebra @xmath7 and marked exchange graph @xmath15 then @xmath16 therefore the cluster automorphisms of any cluster algebra generated by mutation - finite skew - symmetrizable matrices can be studied using just the combinatorial properties of its marked exchange graph . a skew - symmetrizable matrix associated to a good orbifold with order 2 orbifold points can be unfolded to a skew - symmetric matrix associated to a surface which covers the orbifold . in this case we show that automorphisms of the marked exchange graph induce automorphisms of the unfolded exchange graph . given a skew - symmetrizable matrix @xmath14 which unfolds to a matrix @xmath17 , with corresponding marked exchange graphs @xmath18 and @xmath19 , @xmath20 we finish the paper with a conjecture generalising a result of brstle and qiu linking the tagged mapping class group of a surface with the cluster automorphisms of the corresponding surface cluster algebra . for a cluster algebra @xmath7 arising from the triangulation of an orbifold @xmath21 @xmath22 the structure of the paper is as follows : section [ sec : mut ] gives basic definitions of cluster algebras and mutations while section [ sec : exch ] looks at the exchange graph of a cluster algebra and includes proofs linking graph automorphisms and mutation class automorphisms . section [ sec : clauts ] recalls the definition of cluster automorphisms and various known results linking these to mutation class automorphisms and exchange graph automorphisms . the section ends by explaining how a maximal green sequence of an acyclic quiver can be used to construct a cluster automorphism . in section [ sec : exchauts ] we introduce the marked exchange graph which enables us to extend these results to cluster algebras from skew - symmetrizable matrices . we show that graph automorphisms fixing the marking are in one - to - one correspondence with cluster automorphisms . in section [ sec : unf ] we consider unfoldings of skew - symmetrizable matrices and show how the cluster automorphisms of a skew - symmetrizable cluster algebra induce cluster automorphisms of its unfolded cluster algebra . section [ sec : mcg ] looks at these ideas when the skew - symmetrizable cluster algebra is constructed from an orbifold and its unfolding gives a surface cluster algebra .

cluster automorphisms have been shown to have links to the mapping class groups of surfaces , maximal green sequences and to exchange graph automorphisms for skew - symmetric cluster algebras . in this paper we generalise these results to the skew - symmetrizable case by introducing a marking on the exchange graph . * keywords : * cluster algebra ; quiver mutation ; cluster automorphism ; exchange graph ; mapping class group .

cluster automorphisms have been shown to have links to the mapping class groups of surfaces , maximal green sequences and to exchange graph automorphisms for skew - symmetric cluster algebras . in this paper we generalise these results to the skew - symmetrizable case by introducing a marking on the exchange graph . many skew - symmetrizable matrices unfold to skew - symmetric matrices and we consider how cluster automorphisms behave under this unfolding with applications to coverings of orbifolds by surfaces . * keywords : * cluster algebra ; quiver mutation ; cluster automorphism ; exchange graph ; mapping class group .