random catalytic reaction networks abstract we study networks that are a generalization of replicator or lotka volterra equations they model the dynamics of a population of object types whose binary interactions determine the specific type of interaction product such a system always reduces its dimension to a subset that contains production pathways for all of its members the network equation can be rewritten at a level of collectives in terms of two basic interaction patterns replicator sets and cyclic transformation pathways among sets although the system contains well known cases that exhibit very complicated dynamics the generic behavior of randomly generated systems is found numerically to be extremely robust convergence to a globally stable rest point it is easy to tailor networks that display replicator interactions where the replicators are entire self sustaining subsystems rather than structureless units a numerical scan of random systems highlights the special properties of elementary replicators they reduce the effective interconnectedness of the system resulting in enhanced competition and strong correlations between the concentrations

manifestation of crossover from rmt fluctuation to poisson fluctuation in bse sensex a prototype of financial systems abstract we use the nearest neighbour spacing distribution nnsd of random matrix theory rmt as a tool to identify the type of spectral fluctuations of matrix ensemble constructed using high frequency bse sensex values nnsd shows wigner distribution for ensemble formed with detrended index values the detrended raw index values has the universal properties of the gaussian orthogonal ensemble of random matrices in contrast nnsd shows poisson distribution for ensemble formed using log transformed return of the index values which is corroborated by computation of the number variance we have also shown the intermediate transitions connecting rmt and poissonian fluctuations applying nnsd on the data sets generated using power transformation on the return index values log transformation is obtained in the asymptotic limit of the power transformation this gradual changes in the spectral fluctuations from rmt to poissonian type is reminiscent of localization theory results obtained in simulated experiments on the contrary the bse sensex values approximately 2 million data for a period of 2006 2010 has been taken as a prototype of real systems representing an emerging economy of the world

poincare husimi representation of eigenstates in quantum billiards for the representation of eigenstates on a poincare section at the boundary of a billiard different variants have been proposed we compare these poincare husimi functions discuss their properties and based on this select one particularly suited definition for the mean behavior of these poincare husimi functions an asymptotic expression is derived including a uniform approximation we establish the relation between the poincare husimi functions and the husimi function in phase space from which a direct physical interpretation follows using this a quantum ergodicity theorem for the poincare husimi functions in the case of ergodic systems is shown

phase transitions in open quantum systems we consider the behavior of open quantum systems through the dependence of the coupling to one decay channel by introducing the coupling parameter ensuremath alpha which is proportional to the average degree of overlapping under critical conditions a reorganization of the spectrum takes place that creates a bifurcation of the time scales with respect to the lifetimes of the resonance states we derive analytically the conditions under which the reorganization process can be understood as a second order phase transition and illustrate our results by numerical investigations the conditions are fulfilled e g for a uniform picket fence level distribution with equal coupling of the states to the continuum energy dependencies within the system are included we consider also the case of an unfolded gaussian orthogonal ensemble and of a spectrum bounded from below in all these cases the reorganization of the spectrum occurs at the critical value ensuremath alpha mathrm crit of the control parameter globally over the whole energy range of the spectrum all states act cooperatively

positive solutions of nonlinear m point boundary value problems on time scales in this paper by using fixed point theorems in a cone and the associated green s function we study the existence of at least two and three positive solutions to the m point boundary value problem bvp on time scales u d t f t u t 0 email protected 0 1 t bu 0 email protected d 0 0 u 1 email protected email protected iu e i m 3 where t is a time scale email protected c l d 0 1 x 0 0 b email protected 0 a email protected 0 for i 1 2 m 2 and e i satisfy 0 e 1 e 2 e m 2 r 1

fredholm method for scars a new quasiclassical formula for scars is obtained by using the fredholm method we show that it can be expanded into a formula obtained earlier by agam and fishman the derivation is simple and direct it is also more rigorous and more general than that of agam and fishman it also clarifies the remarkable process of resurgence relating the high order terms based on long orbits to the weyl term whose origin is the zero length orbits

scattering reflection and impedance of waves in chaotic and disordered systems with absorption we review recent progress in analysing wave scattering in systems with both intrinsic chaos and or disorder and internal losses when the scattering matrix is no longer unitary by mapping the problem onto a nonlinear supersymmetric model we are able to derive closed form analytic expressions for the distribution of reflection probability in a generic disordered system one of the most important properties resulting from such an analysis is statistical independence between the phase and the modulus of the reflection amplitude in every perfectly open channel the developed theory has far reaching consequences for many quantities of interest including local green functions and time delays in particular we point out the role played by absorption as a sensitive indicator of mechanisms behind the anderson localization transition we also provide a random matrix based analysis of s matrix and impedance correlations for various symmetry classes as well as the distribution of transmitted power for systems with broken time reversal invariance completing previous works on the subject the results can be applied in particular to the experimentally accessible impedance and reflection in a microwave or an ultrasonic cavity attached to a system of antennas

separating the regular and irregular energy levels and their statistics in a hamiltonian system with mixed classical dynamics we look at the high lying eigenstates from the 10001 to the 13000 in the robnik billiard defined as a quadratic conformal map of the unit disk with the shape parameter lambda 0 15 all the 3000 eigenstates have been numerically calculated and examined in the configuration space and in the phase space which in comparison with the classical phase space enabled a clear cut classification of energy levels into regular and irregular this is the first successful separation of energy levels based on purely dynamical rather than special geometrical symmetry properties we calculate the fractional measure of regular levels as rho 1 0 365 or 0 01 which is in remarkable agreement with the classical estimate rho 1 0 360 or 0 001 this finding confirms the percival s 1973 classification scheme the assumption in berry robnik 1984 theory and the rigorous result by lazutkin 1981 1991 the regular levels obey the poissonian statistics quite well whereas the irregular sequence exhibits the fractional power law level repulsion and globally brody like statistics with beta 0 286 or 0 001 this is due to the strong localization of irregular eigenstates in the classically chaotic regions therefore in the entire spectrum we see that the berry robnik regime is not yet fully established so that the level spacing distribution is correctly captured by the berry robnik brody distribution

quantum scars of classical closed orbits in phase space the way in which quantum eigenstates are influenced by the closed orbits of a chaotic classical system is analysed in phase space x q p through the spectral wigner function w x e this is a sum over wigner functions of eigenstates within a range of energy e in the classical limit w is concentrated on the energy surface and smoothly distributed over it closed orbits provide oscillatory corrections scars for which explicit semiclassical formulae are calculated each scar is a fringe pattern decorating the orbit as x moves off the energy surface the fringes form an airy pattern with spacing of order h as x moves off the closed orbit the fringes form a complex gaussian with spacing h

existence results for n point boundary value problem of second order ordinary differential equations abstract this study concerns the existence of positive solutions to the boundary value problem u a t f u 0 t 0 1 u 0 i 1 n 2 b i u i u 1 i 1 n 2 a i u i where i 0 1 with 0 1 2 n 2 1 a i b i 0 with 0 i 1 n 2 a i 1 and i 1 n 2 b i 1 by applying the krasnoselskii s fixed point theorem in banach spaces some sufficient conditions guaranteeing the existence of at least one positive solution or at least two positive solutions are established for the above general n point boundary value problem

semiclassical theory of flexural vibrations of plates we study the biharmonic equation of flexural vibrations of elastic plates by a semiclassical method that can easily be generalized for other models of wave propagation three terms of the asymptotic number of levels for plates with smooth boundaries are derived and the trace formula for the density of states is obtained the main difference between this formula and the gutzwiller trace formula for billiards is the existence of a specific phase factor obtained while reflecting from the boundary six hundred eigenvalues of a clamped stadium plate are obtained by a specially developed numerical algorithm and the trace formula is assessed looking at its fourier transform an extra contribution occurs for a free plate due to the existence of boundary modes

supporting random wave models a quantum mechanical approach we show how two point correlation functions recently derived within non isotropic random wave models can be obtained in the appropriate limit in terms of the exact green function of the quantum system since no statistical model is required for this derivation this shows that taking the wavefunctions as gaussian processes is the only assumption of those models we also show how for clean systems the two point correlation function based on an energy average defines a gaussian theory which substantially reduces the spurious contributions coming from the normalization problem

a scattering approach to the quantization of hamiltonians in two dimensions application to the wedge billiard we extend the scattering approach to quantize general hamiltonian systems in two dimensions and demonstrate it for the wedge billiard the resulting energy levels are given by the zeros of a secular equation the corresponding wavefunctions may also be constructed we verify analytically that this quantization condition is exact in the case of the integrable wedges this method has been applied successfully to computing numerically a few thousand levels for various values of the angle using these data we can check the gutzwiller trace formula and other semiclassical relations involving the scattering matrix and periodic orbits for which we find excellent agreement

solvability of a three point nonlinear boundary value problem for a second order ordinary differential equation in case f x u u ps x p x u pjx u with pk 0 l 4 r locally integrable the boundary value problem l lt 1 2 was studied by kiguradze and lomtatidze i the purpose of this paper is to obtain existence and uniqueness theorems for the boundary value problem 1 1 t 1 2 under natural conditions on f using degree theoretic arguments we note that if u is a solution of 1 1 1 2 then there exists at least one 5 e q l such that u c 0 accordingly the boundary value problem

s matrix poles for chaotic quantum systems as eigenvalues of complex symmetric random matrices from isolated to overlapping resonances we study complex eigenvalues of large symmetric random matrices of the form where both and are real symmetric is a random gaussian and is such that when when the model can be used to describe the universal statistics of s matrix poles resonances in the complex energy plane we derive the ensuing distribution of the resonance widths which generalizes the well known distribution to the case of overlapping resonances we also consider a different class of almost real matrices when is random and uncorrelated with

the existence of countably many positive solutions for nonlinear singular m point boundary value problems on time scales in this paper by introducing a new operator improving and generating a p laplace operator for some p 1 we study the existence of countably many positive solutions for nonlinear boundary value pr

nonzero solutions of hammerstein integral equations with discontinuous kernels using the theory of fixed point index we establish new results for the existence of nonzero solutions of integral equations of the form u t gk t s f s u s ds where g is a compact set in rn and k changes sign so positive solutions may not exist f satisfies caratheodory conditions and k may be discontinuous we apply our results to prove the existence of nontrivial solutions of some nonlocal boundary value problems

on the ensemble variance of reverberation room transmission functions the effect of spectral rigidity abstract the modal statistics of the gaussian orthogonal ensemble of large random symmetric matrices are applied to reverberation room acoustics these statistics are found to predict spectral fluctuations which are weaker than those predicted by the assumption of modal independence and are also in better agreement with observations

classical wave experiments on chaotic scattering we review recent research on the transport properties of classical waves through chaotic systems with special emphasis on microwaves and sound waves inasmuch as these experiments use antennas or transducers to couple waves into or out of the systems scattering theory has to be applied for a quantitative interpretation of the measurements most experiments concentrate on tests of predictions from random matrix theory and the random plane wave approximation in all studied examples a quantitative agreement between experiment and theory is achieved to this end it is necessary however to take absorption and imperfect coupling into account concepts that were ignored in most previous theoretical investigations classical phase space signatures of scattering are being examined in a small number of experiments

experimental investigation of wigner s reaction matrix for irregular graphs with absorption we use tetrahedral microwave networks consisting of coaxial cables and attenuators connected by t joints to make an experimental study of wigner s reaction k matrix for irregular graphs in the presence of absorption from measurements of the scattering matrix s for each realization of the microwave network we obtain distributions of the imaginary and real parts of k our experimental results are in good agreement with theoretical predictions

survey of the eigenfunctions of a billiard system between integrability and chaos we study numerically the eigenfunctions and their wigner phase space distributions of the two dimensional billiard system defined by the quadratic conformal image of the unit disk as introduced by robnik 1983 this system is a generic kam system and displays a transition from integrability to almost ergodicity as the billiard shape changes we clearly identify two classes of states the regular ones associated with integrable regions and the irregular states supported on classically chaotic regions whilst the mixed type states were not found in support of percival s conjecture 1973 we confirm the existence of extremely intense scars in the classically chaotic regions and demonstrate their association with classical periodic orbits three classes of scars are revealed one orbit scars many orbit one family scars of statistically similar orbits in the homoclinic neighbourhood and many orbit many family scars we argue that it is impossible to find an a priori semiclassical theory of individual eigenstates but do not deny the usefulness of general semiclassical arguments in analysing the collective and statistical properties of eigenstates

green s function estimation using secondary sources in a shallow water environment this work provides a new way to measure the green s function between two points in an acoustic channel without emitting a pulse by any of the two points the green s function between a and b is obtained from a set of secondary sources in the guide by averaging either the correlation or the convolution of the signals received in a and b a theoretical approach based on mode propagation in a monochromatic regime is presented results are then extended to the time domain estimation of the green s function is performed numerically in a range independent and a range dependent environment application to discreet acoustic communications is discussed

phase transition in random catalytic networks the notion of auto catalytic networks has become a cornerstone in understanding the possibility of a sudden dramatic increase of diversity in biological evolution as well as in the evolution of social and economical systems here we study catalytic random networks with respect to the final outcome diversity of products we show that an analytical treatment of this long standing problem is possible by mapping the problem onto a set of nonlinear recurrence equations the solution of these equations shows a crucial dependence of the final number of products on the initial number of products and the density of catalytic production rules for a fixed density of rules we can demonstrate the existence of a phase transition from a practically unpopulated regime to a fully populated and diverse one the order parameter is the number of final products we are able to fully understand the origin of this phase transition as a crossover from one set of solutions from a quadratic equation to the other we observe a remarkable similarity of the solution of the system and the pvt diagrams in standard thermodynamics

existence of multiple positive solutions for m point boundary value problems in banach spaces this paper deals with the positive solutions of m point nonlinear boundary value problem in banach spaces by using the fixed point theorem of strict set contractions some sufficient conditions for the existence of at least one or two positive solutions to m point boundary value problem in banach spaces are obtained an example illustrating the main results is given

distribution of nearest distances between nodal points for the berry function in two dimensions according to berry a wave chaotic state may be viewed as a superposition of monochromatic plane waves with random phases and amplitudes here we consider the distribution of nodal points associated with this state using the property that both the real and imaginary parts of the wave function are random gaussian fields we analyze the correlation function and densities of the nodal points using two approaches the poisson and bernoulli we derive the distribution of nearest neighbor separations furthermore the distribution functions for nodal points with specific chirality are found comparison is made with results from numerical calculations for the berry wave function

the existence of countably many positive solutions for nonlinear singular m point boundary value problems on the half line in this paper by introducing a new operator improving and generating a p laplace operator for some p 1 we study the existence of countably many positive solutions for nonlinear boundary value problems on the half line f u a t f u t 0 0r is the increasing homeomorphism and positive homomorphism and f 0 0 we show the sufficient conditions for the existence of countably many positive solutions by using the fixed point index theory and a new fixed point theorem in cones

statistical analysis of scars in stadium billiard in this paper by using our improved plane wave decomposition method we study the scars in the eigenfunctions of the stadium billiard from a very low state to as high as about the 1 millionth state in the systematic searching for scars of various types we have used the approximate criterion based on the quantization of the classical action along the unstable periodic orbit supporting the scar we have analysed the profile of the integrated probability density along the orbit we found that the maximal integrated intensity of different types of scars scales in different way with the which confirms qualitatively and quantitatively the existing theories of scars such as that of bogomolny and robnik

robust and efficient solution of the drum problem via nystrom approximation of the fredholm determinant the drum problem finding the eigenvalues and eigenfunctions of the laplacian with dirichlet boundary condition has many applications yet remains challenging for general domains when high accuracy or high frequency is needed boundary integral equations are appealing for large scale problems yet certain difficulties have limited their use we introduce the following two ideas to remedy this 1 we solve the resulting nonlinear eigenvalue problem using boyd s method for analytic root finding applied to the fredholm determinant and we show that this is many times faster than the usual iterative minimization of a singular value 2 we fix the problem of spurious exterior resonances via a combined field representation this also provides the first robust boundary integral eigenvalue method for non simply connected domains we implement the new method in two dimensions using spectrally accurate nystrom product quadrature we prove exponential convergence of the determinant at roots for domains with

positive solutions of m point boundary value problems for higher order ordinary differential equations abstract in this paper we study m point boundary value problems for higher order ordinary differential equation y 2 n t f t y t y t y 2 n 1 t 0 t 1 y 2 i 0 0 y 2 i 1 j 1 m 2 k i j y 2 i j 0 i n 1 where f is allowed to change sign and 0 0 1 2 m 2 m 1 1 we show sufficient conditions for the existence of at least two positive solutions by applying a new fixed point theorem in cones and the associated green s function in particular the second positive solutions for the above problem is not concave

generalized berry conjecture and mode correlations in chaotic plates we consider a modification of the berry conjecture for eigenmode statistics in wave bearing systems the eigenmode correlator is conjectured to be proportional to the imaginary part of the green s function the generalization is applicable not only to scalar waves in the interior of homogeneous isotropic systems where the correlator is a bessel function but to arbitrary points of heterogeneous systems as well in view of recent experimental measurements expressions for the intensity correlator in chaotic plates are derived

statistics of nodal lines and points in chaotic quantum billiards perimeter corrections fluctuations curvature for real time reversal symmetric quantum billiards the mean length l of nodal line is calculated for the nth mode n 1 with wavenumber k using a gaussian random wave model adapted locally to satisfy dirichlet or neumann boundary conditions the leading term is of order k i e n and the first perimeter correction dominated by an unanticipated long range boundary effect is of order log k i e log n with the same sign negative for both boundary conditions the leading order state to state fluctuations l are of order log k for the curvature of nodal lines and 2 are of order k but 3 and higher moments diverge for complex e g aharonov bohm billiards the mean number n of nodal points phase singularities in the mode has a leading term of order k2 i e n the perimeter correction again a long range effect is of order klog k i e nlog n and positive notwithstanding nodal depletion near the boundary and the fluctuations n are of order k log k generalizations of the results for mixed robin boundary conditions are stated

experiments on elastomechanical wave functions in chaotic plates and their statistical features we measure the amplitude of the elastomechanical displacement at a fine grid of points on a free plate having the shape of a sinai stadium the obtained displacement field formally corresponds to a wave function in a quantum system while the distribution of the squared amplitudes agrees with the prediction of random matrix theory rmt there is a strong deviation of the spatial correlator from the standard prediction for quantum chaotic systems we show that this is due to the presence of two modes leading to a beating phenomenon we construct a proper extension of the spatial correlator within the framework of rmt

statistics of interior current distributions in two dimensional open chaotic billiards the probability current statistics of two dimensional open chaotic ballistic billiards is studied both analytically and numerically assuming that the real and imaginary parts of the scattering wave function are both random gaussian fields we find a universal distribution function for the interior probability current as a by product we recover previous analytic forms for wave function statistics the expressions bridge the entire region from goe to gue type statistics our analytic expressions are verified numerically by explicit quantum mechanical calculations of transport through a bunimovich billiard

towards a physics of evolution critical diversity dynamics at the edges of collapse and bursts of diversification systems governed by the standard mechanisms of biological or technological evolution are often described by catalytic evolution equations we study the structure of these equations and find an analogy with classical thermodynamic systems in particular we can demonstrate the existence of several distinct phases of evolutionary dynamics a phase of fast growing diversity one of stationary finite diversity and one of rapidly decaying diversity while the first two phases have been subject to previous work here we focus on the destructive aspects in particular the phase diagram of evolutionary dynamics the main message is that within a critical region massive loss of diversity can be triggered by very small external fluctuations we further propose a dynamical model of diversity which captures spontaneous creation and destruction processes fully respecting the phase diagrams of evolutionary systems the emergent time series show rich diversity dynamics including power laws as observed in actual economical data e g firm bankruptcy data we believe the present model presents a possibility to cast the famous qualitative picture of schumpeterian economic evolution into a quantifiable and testable framework

quantum phase space structures in classically mixed systems a scattering approach the structure of quantum wavefunctions is discussed for a billiard system with mixed classical dynamics using a scattering formalism we introduce a husimi like distribution for s matrix eigenvectors at arbitrary wavenumbers k not necessarily eigenenergies of the system this constitutes probability density plots on the poincare surface of section at any k many eigenvectors are structured by classical objects such as invariant tori the intermediate layer between regular and chaotic motion and unstable periodic orbits scars we find that eigenvector structure is stable over significant energy ranges while the associated eigenphases increase linearly with k at a rate determined by the underlying classical objects additionally we observe that in the presence of time reversal symmetry eigenvectors scarred by non self retracing periodic orbits form doublets which are closely spaced in eigenphase our results provide a new perspective on the quantization of structured states quantization is determined by the linearly increasing eigenphases and occurs whenever an eigenphase is equal to while structure is encoded in the eigenvectors it is present at all energies and varies only slowly this allows one to predict many quantized eigenfunctions over an entire energy range by studying the eigenparameters of at a single intermediate energy and identifying the underlying classical objects

multiplicity of positive solutions for second order three point boundary value problems we study the multiplicity of positive solutions for the second order three point boundary value problem u h t f u 0 t 0 1 u 0 0 u u 1 where 0 1 0 1 the methods employed are fixed point index theorems and leray schauder degree and upper and lower solutions

positive solutions of a nonlinear three point boundary value problem in this paper by using the fixed point index theorems we study the existence of at least one or two positive solutions to the three point boundary value problem y t a t f y t 0 0 t 1 y 0 0 y 1 y where 0 1 0 1 as an application we also give some examples to demonstrate our results

adaptive evolution on a continuous lattice model in the current work we investigate the evolutionary dynamics of a spatially structured population model defined on a continuous lattice in the model individuals disperse at a constant rate v and competition is local and delimited by the competition radius r due to dispersal the neighborhood size number of individuals competing for reproduction fluctuates over time here we address how these new variables affect the adaptive process while the fixation probabilities of beneficial mutations are roughly the same as in a panmitic population for small fitness effects s a dependence on v and r becomes more evident for large s these quantities also strongly influence fixation times but their dependencies on s are well approximated by s ensuremath 1 2 which means that the speed of the genetic wave front is proportional to sqrt s most important is the observation that the model exhibits a dual behavior displaying a power law growth for the fixation rate and speed of adaptation with the beneficial mutation rate as observed in other spatially structured population models while simultaneously showing a nonsaturating behavior for the speed of adaptation with the population size n as in homogeneous populations

response variance prediction in the statistical energy analysis of built up systems in the statistical energy analysis sea of high frequency noise and vibration a complex engineering structure is represented as an assembly of subsystems the response of the system to external excitation is expressed in terms of the vibrational energy of each subsystem and these energies are found by employing the principle of power balance strictly the computed energy is an average taken over an ensemble of random structures and for many years there has been interest in extending the sea prediction to the variance of the energy a variance prediction method for a general built up structure is presented here closed form expressions for the variance are obtained in terms of the standard sea parameters and an additional set of parameters alpha k that describe the nature of the power input to each subsystem k and alpha ks that describe the nature of the coupling between subsystems k and s the theory is validated by comparison with monte carlo simulations of plate networks and structural acoustic systems

the relative variance of the transmission function of a reverberation room the transmission function of a reverberation room is defined to be the square of the modulus of the ratio of the reverberant field sound pressure to the volume velocity of the sound source the input impedance of a reverberation room is defined to be the ratio of the near field sound pressure to the volume velocity of the sound source lyon s formula for the relative variance of the transmission function is extended to cover the case when the transmission function is averaged over multiple source and receiver positions this extended formula reduces easily to lyon s formula for the relative variance of the real part of the input impedance and thus demonstrates the relationship which exists between the two formulae the above formulae are derived under the assumption that the modal frequencies are randomly distributed lyon also derived a formula for the relative variance of the real part of the input impedance when the modal frequencies tend to repel each other it is shown that this formula of lyon is in error and the correct formula is derived the formula for the relative variance of the transmission function is modified so that it will reduce to the formula for the relative variance of the real part of the input impedance derived under this assumption of modal frequency repulsion these formulae for the relative variance of the transmission function are compared with experimental values of relative variance there is reasonable agreement between these formulae and the experimental results the above formulae are extended to cover the case when the transmission function or the real part of the input impedance is averaged over a frequency band the formulae derived in this paper are important for predicting the precision of sound power measurements in a reverberation room

lossy chaotic electromagnetic reverberation chambers universal statistical behavior of the vectorial field the effective hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers the latter are commonly used in electromagnetic compatibility tests as a first step the distribution of wave intensities in chaotic systems with varying opening in the weak coupling limit for scalar quantum waves is derived by means of random matrix theory in this limit the only parameters are the modal overlap and the number of open channels using the extended effective hamiltonian we describe the intensity statistics of the vectorial electromagnetic eigenmodes of lossy reverberation chambers finally the typical quantity of interest in such chambers namely the distribution of the electromagnetic response is discussed by determining the distribution of the phase rigidity describing the coupling to the environment using random matrix numerical data we find good agreement between the theoretical prediction and numerical calculations of the response

physics of evolution selection without fitness abstract traditionally evolution is seen as a process where from a pool of possible variations of a population e g biological species or industrial goods a few variations get selected which survive and proliferate whereas the others vanish survival probabilities and proliferation rates are typically associated with the fitness of particular variations in this paper we argue that the notion of fitness is an a posteriori concept in the sense that one can assign higher fitness to species that survive but one can generally not derive or predict fitness per se proliferation rates can be measured whereas fitness landscapes i e the inter dependence of proliferation rates cannot for this reason we think that in a physical theory of evolution such notions should be avoided in this spirit here we propose a random matrix model of evolution where selection mechanisms are encoded in interaction matrices of species thereby extending the previous work of ours by a control parameter describing suppressors in the system we are able to recover some key facts of evolution dynamics endogenously such as punctuated equilibrium i e the existence of intrinsic large extinction events and at the same time periods of dramatic diversification as known e g from the fossil record further we comment on two fundamental technical problems of a physics of evolution the non closedness of its phase space and the problem of co evolving boundary conditions apparent in all systems subject to evolution

several existence theorems of nonlinear m point boundary value problem for p laplacian dynamic equations on time scales abstract in this paper several existence theorems of positive solutions are established for nonlinear m point boundary value problem for p laplacian dynamic equations on time scales as an application an example to demonstrate our results is given the conditions we used in the paper are different from those in h r sun w t li positive solutions for nonlinear three point boundary value problems on time scales j math anal appl 299 2004 508 524 h r sun w t li positive solutions for nonlinear m point boundary value problems on time scales acta math sinica 49 2006 369 380 in chinese y wang c hou existence of multiple positive solutions for one dimensional p laplacian j math anal appl 315 2006 144 153 y wang w ge positive solutions for multipoint boundary value problems with one dimensional p laplacian nonlinear appl 66 6 2007 1246 1256

diabolical points in the spectra of triangles accidental degeneracies between energy levels e j and e j 1 of a real hamiltonian can occur generically in a family of hamiltonians labelled by at least two parameters x y energy level surfaces in e x y space have locally a double cone diabolo connection and we refer to the degeneracies themselves as diabolical points we studied the family of systems in which a particle moves freely within hard walled triangles vibrations of triangular membranes with x and y labelling two of the angles using an efficient green function technique to compute the levels we found several diabolical points for low lying levels as well as some symmetry degeneracies the lowest diabolical point occurred for levels 5 and 6 of the triangle 130 57 30 73 18 70 the conical structure was confirmed by noting that the normal derivative u of the wavefunction at a boundary point changed sign during a small circuit of the diabolical point the form of the variation of u around a circuit and the changing pattern of nodal lines of agreed with theoretical expectations an estimate of the total number of degeneracies n d j involving levels 1 through j based on the energy scaling of cone angles and the level spacing distribution gave n d j j 2 5 and our limited data support this prediction analytical theory confirmed that for thin triangles where our computational method is slow there are no degeneracies in the energy range studied

full characterization of a strange attractor chaotic dynamics in low dimensional replicator system abstract two chaotic attractors observed in lotka volterra equations of dimension n 3 are shown to represent two different cross sections of one and the same chaotic regime the strange attractor is studied in the equivalent four dimensional catalytic replicator network analytical expressions are derived for the lyapunov exponents of the flow in the centre of the chaotic regime the strange attractor was characterized by the lyapunov dimension dl 2 06 0 02 and the renyi fractal dimensions the set corresponding to the attractor represents a multifractal its singularity spectrum is computed one route in parameter space leading into the chaotic regime and crossing it was studied in detail it leads to a feigenbaum type cascade of bifurcations before the chaos is fully developed the dynamic system passes an internal crisis through a period two tangent bifurcation then a second sequence of period doubling bifurcations leading to another chaotic regime is observed which eventually ends in a crisis and then after a rather complicated periodic regime the attractor finally disappears trajectories in the intermediate periodic regime show transient chaotic bursts of intermittency type a series of one dimensional maps is derived from a properly chosen poincare cross section which illustrates structural changes in the attractor mutations are included in the catalytic replicator network and the changes in the dynamics observed are compared with the predictions of an approach based on perturbation theory the most striking result is the gradual disappearance of complex dynamics with increasing mutation rates the parameter space spanned by the mutation rate and selected parameters of the replication network is split in regions of complex periodic behaviour near the chaotic regime fractal boundaries of these regions are likely to occur but the data available do not allow definitive conclusions yet

universal statistics of the scattering coefficient of chaotic microwave cavities we consider the statistics of the scattering coefficient s of a chaotic microwave cavity coupled to a single port we remove the nonuniversal effects of the coupling from the experimental s data using the radiation impedance obtained directly from the experiments we thus obtain the normalized scattering coefficient whose probability density function pdf is predicted to be universal in that it depends only on the loss quality factor of the cavity we compare experimental pdfs of the normalized scattering coefficients with those obtained from random matrix theory rmt and find excellent agreement the results apply to scattering measurements on any wave chaotic system

random matrix theory and acoustic resonances in plates with an approximate symmetry we discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model an acoustic resonator like e g an aluminum plate may have an approximate symmetry we have measured the frequency spectrum and the widths for acoustic resonances in thin aluminum plates cut in the shape of the so called three leaf clover due to the mirror symmetry through the middle plane of the plate each resonance of the plate belongs to one of two mode classes and we show how to separate the modes into these two classes using their measured widths we compare the spectral statistics of each mode class with results for the gaussian orthogonal ensemble by cutting a slit of increasing depth on one face of the plate we gradually break the mirror symmetry and study the transition that takes place as the two classes are mixed presenting the spectral fluctuation statistics and the distribution of widths for the resonances we find that this transition is well described by the random matrix model

mean field approximation for two and three person prisoner s dilemmas abstract we consider the mean field approximation mfa to the system of interacting agents playing two and three person prisoner s dilemma games 2 pd and 3 pd the agents have three available strategies all c all d and a third one which we choose in various ways long time distribution of the strategies is compared for both games the latter game admits coexistence of larger number of strategies in the long run in the case of external pressure for cooperation more pressure is in general necessary for 3 pd than for 2 pd to guarantee cooperation for almost all initial compositions of the strategies results for different types of tit for tat strategies for 3 pd are discussed unlike the 2 pd case the more forgiving tit for tat strategy can survive in the long run in 3 pd

smoothed wave functions of chaotic quantum systems abstract it is shown that wave functions of quantum systems as 0 have an extra density near unstable periodic trajectories of the classical problem the averaged wave function square is represented as the sum over a finite number of periodic trajectories the contribution of each trajectory is expressed through the elements of the monodromy matrix of the trajectory the results are compared with the numerical calculations of the wave functions for the stadium billiard

evolutionary dynamics from a variational principle we demonstrate with a thought experiment that fitness based population dynamical approaches to evolution are not able to make quantitative falsifiable predictions about the long term behavior of some evolutionary systems a key characteristic of evolutionary systems is the ongoing endogenous production of new species these novel entities change the conditions for already existing species even darwin s demon a hypothetical entity with exact knowledge of the abundance of all species and their fitness functions at a given time could not prestate the impact of these novelties on established populations we argue that fitness is always a posteriori knowledge it measures but does not explain why a species has reproductive success or not to overcome these conceptual limitations a variational principle is proposed in a spin model like setup of evolutionary systems we derive a functional which is minimized under the most general evolutionary formulation of a dynamical system i e evolutionary trajectories causally emerge as a minimization of a functional this functional allows the derivation of analytic solutions of the asymptotic diversity for stochastic evolutionary systems within a mean field approximation we test these approximations by numerical simulations of the corresponding model and find good agreement in the position of phase transitions in diversity curves the model is further able to reproduce stylized facts of timeseries from several man made and natural evolutionary systems light will be thrown on how species and their fitness landscapes dynamically coevolve

dynamics of the eigen and the crow kimura models for molecular evolution we introduce an alternative way to study molecular evolution within well established hamilton jacobi formalism showing that for a broad class of fitness landscapes it is possible to derive dynamics analytically within the 1n accuracy where n is the genome length for a smooth and monotonic fitness function this approach gives two dynamical phases smooth dynamics and discontinuous dynamics the latter phase arises naturally with no explicite singular fitness function counterintuitively the hamilton jacobi method yields straightforward analytical results for the models that utilize fitness as a function of hamming distance from a reference genome sequence we also show the way in which this method gives dynamical phase structure for multipeak fitness

positive solutions of a nonlinear m point boundary value problem let ai 0 for i 1 m 3 and am 2 0 let i satisfy 0 1 2 m 2 1 and m 2i 1 ai i 1 we study the existence of positive solutions to the boundary value problem where a c 0 1 0 and f c 0 0 we show the existence of at least one positive solution if f is either superlinear or sublinear by applying a fixed point theorem in cones

fredholm methods for billiard eigenfunctions in the coherent state representation we obtain a semiclassical expression for the projector onto eigenfunctions by means of the fredholm theory we express the projector in the coherent state basis thus obtaining the semiclassical husimi representation of the stadium eigenfunctions which is written in terms of classical invariants periodic points their monodromy matrices and maslov indices

three positive solutions for second order m point boundary value problems for the second order m point boundary value problemu t f t u 0 0 0 i 1 2 m 2 0 x 1 x 2 x m 2 1 growth conditions are imposed on f which yield the existence of at least three positive solutions by using the leggett williams fixed point theorem the associated green s function for the m point boundary value problem is also given

statistical properties of high lying chaotic eigenstates we study the statistical properties of the high lying chaotic eigenstates 200000 and above which are deep within the semiclassical regime the system we are analysing is the billiard system inside the region defined by the quadratic complex conformal map of the unit disk as introduced by robnik 1983 we are using heller s method of plane wave decomposition of the numerical eigenfunctions and perform extensive statistical analysis with the following conclusions i the local average probability density is in excellent agreement with the microcanonical assumption and all statistical properties are also in excellent agreement with the gaussian random model ii the autocorrelation function is found to be strongly direction dependent and only after averaging over all directions agrees well with berry s 1977 prediction iii although the scars of unstable classical periodic orbits in such an ergodic regime are expected to exist so far we have not found any around the 200000th state other than a scar like feature resembling the whispering gallery modes

an efficient fredholm method for the calculation of highly excited states of billiards a numerically efficient fredholm formulation of the billiard problem is presented the standard solution in the framework of the boundary integral method in terms of a search for roots of a secular determinant is reviewed first we next reformulate the singularity condition in terms of a flow in the space of an auxiliary one parameter family of eigenproblems and argue that the eigenvalues and eigenfunctions are analytic functions within a certain domain based on this analytic behavior we present a numerical algorithm to compute a range of billiard eigenvalues and associated eigenvectors by only two diagonalizations

the ensemble variance of random noise in a reverberation room the literature contains conflicting results for the ensemble relative variance of the intensity of a frequency band of random noise which has been passed through a reverberation room some theoretical and experimental results suggest that passing a band of noise through a reverberation room has no effect on its ensemble relative variance other theoretical and experimental results show that the ensemble relative variance is doubled this paper shows that the magnitude of the effect depends on the ratio of the integrating time of the detector to the integrating time of the reverberation room if this ratio is small the reverberation room has no effect if the ratio is large the ensemble relative variance is doubled this explains why conflicting results have appeared in the literature

interior dirichlet eigenvalue problem exterior neumann scattering problem and boundary element method for quantum billiards an explicit expression for the fredholm determinant d e appearing in the boundary element method for two dimensional quantum billiards is derived in terms of the interior dirichlet eigenenergies and exterior neumann scattering phase shifts not only in the semiclassical regime but also in all order of h bar d e admits the factorization into the interior and exterior contributions where the former has zeros at interior dirichlet eigenenergies and the latter at resonances of the neumann scattering a new aspect of the kac close quote s inverse problem is also discussed copyright ital 1997 ital the american physical society

wavefunctions expectation values and scars on poincare sections a scattering approach using the scattering approach to quantization we define an appropriate representation of the billiard wavefunction on the scattering poincar section the expectation values of smooth operators in terms of these poincar section wavefunctions are expressed as sums over periodic orbits a special operator is used to define scars on the section and the relation to scars in configuration space is discussed and demonstrated numerically

fast computation of high frequency dirichlet eigenmodes via spectral flow of the interior neumann to dirichlet map we present a new algorithm for numerical computation of large eigenvalues and associated eigenfunctions of the dirichlet laplacian in a smooth star shaped domain in d d 2 conventional boundary based methods require a root search in eigenfrequency k hence take o n3 effort per eigenpair found where n o kd 1 is the number of unknowns required to discretize the boundary our method is o n faster achieved by linearizing with respect to k the spectrum of a weighted interior neumann to dirichlet ntd operator for the helmholtz equation approximations to the square roots kj of all o n eigenvalues lying in k k where o 1 are found with o n3 effort we prove an error estimate with c independent of k we present a higher order variant with eigenvalue error scaling empirically as o 5 and eigenfunction error as o 3 the former improving upon the scaling method of vergini and saraceno for planar domains d 2 with an assumption of absence of spectral concentration we also prove rigorous error bounds that are close to those numerically observed for d 2 we compute robustly the spectrum of the ntd operator via potential theory nystrom discretization and the cayley transform at high frequencies 400 wavelengths across with eigenfrequency relative error 10 10 we show that the method is 103 times faster than standard ones based upon a root search 2014 wiley periodicals inc

positive solution for m point boundary value problems in this paper we investigate an m point boundary value problem with sign changing nonlinearity the existence of an interval of parameters which ensures the problem has at least one positive solution is determined by constructing available operator and combining the method of lower solution with the method of topology degree moreover the associated green s function for the above problem is also given

crossover from regular to irregular behavior in current flow through open billiards we discuss signatures of quantum chaos in terms of distributions of nodal points saddle points and streamlines for coherent electron transport through two dimensional billiards which are either nominally integrable or chaotic as typical examples of the two cases we select rectangular and sinai billiards we have numerically evaluted distribution functions for nearest distances between nodal points and found that there is a generic form for open chaotic billiards through which a net current is passed we have also evaluated the distribution functions for nodal points with specific vorticity winding number as well as for saddle points the distributions may be used as signatures of quantum chaos in open systems all distributions are well reproduced using random complex linear combinations of nearly monochromatic states in nominally closed billiards in the case of rectangular billiards with simple sharp cornered leads the distributions have characteristic features related to order among the nodal points a flaring or rounding of the contact regions may however induce a crossover to nodal point distributions and current flow typical for quantum chaos for an irregular arrangement of nodal points as for example in the sinai billiard the quantum flow lines become very complex and volatile recalling chaos among classical trajectories similarities with percolation are pointed out 2002 the american physical society