spectral statistics for unitary transfer matrices of binary graphs quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits it is proposed here to generalize this approach by considering arbitrary directed graphs with unitary transfer matrices an exponentially increasing contribution to the form factor is identified when performing a diagonal summation over periodic orbit degeneracy classes a special class of graphs so called binary graphs is studied in more detail for these the conditions for periodic orbit pairs to be correlated including correlations due to the unitarity of the transfer matrix can be given explicitly using combinatorial techniques it is possible to perform the summation over correlated periodic orbit pair contributions to the form factor for some low dimensional cases gradual convergence towards random matrix results is observed when increasing the number of vertices of the binary graphs

finite dimensional lie algebras of order f f lie algebras are natural generalizations of lie algebras f 1 and lie superalgebras f 2 when f 2 not many finite dimensional examples are known in this article we construct finite dimensional f lie algebras f 2 by an inductive process starting from lie algebras and lie superalgebras matrix realizations of f lie algebras constructed in this way from su n sp 2n so n and sl n m osp 2 m are given we obtain nontrivial extensions of the poincare algebra by inonu wigner contraction of certain f lie algebras with f 2

spectral decomposition of the renyi map the authors construct a generalized spectral decomposition of the frobenius perron operator of the general beta adic renyi map using a general iterative operator method applicable in principle to any mixing dynamical system they also explicitly define appropriate rigged hilbert spaces which provide mathematical meaning to the formally obtained spectral decomposition the explicit construction of the eigenvalues and eigenvectors allows one to show that the essential spectral radius of the frobenius perron operator decreases as the smoothness of the domain increases the reason for the change of the spectrum from the unit disk to isolated eigenvalues is the existence of coherent states of the frobenius perron operator which are not infinitely differentiable

computer assisted bounds for the rate of decay of correlations the rate of decay of correlations quantitatively describes the rate at which a chaotic system mixes the state space we present a new rigorous method to estimate a bound for this rate of mixing the technique may be implemented on a computer and is applicable to both multidimensional expanding and hyperbolic systems the bounds produced are significantly less conservative than current rigorous bounds in some situations it is possible to approximate resonant eigenfunctions and to strengthen our bound to an estimate of the decay rate order of convergence results are stated

filiform lie algebras of order 3 the aim of this work is to generalize a very important type of lie algebras and superalgebras i e filiform lie super algebras into the theory of lie algebras of order f thus the concept of filiform lie algebras of order f is obtained in particular for f 3 it has been proved that by using infinitesimal deformations of the associated model elementary lie algebra it can be obtained families of filiform elementary lie algebras of order 3 analogously as that occurs into the theory of lie algebras m vergne cohomologie des algebres de lie nilpotentes application a l etude de la variete des algebres de lie nilpotentes bull soc math france 98 81 116 1970 also we give the dimension using an adaptation of the sl 2 c module method and a basis of such infinitesimal deformations in some generic cases

a global attractor for the elastic waveguide model in rn abstract this paper studies the longtime behavior of solutions to the elastic waveguide model in r n u t t u u t t 2 u u t u t u g x u f x it proves that when the space dimension n 5 under rather mild conditions on g and f the related solution semigroup possesses in phase space with low regularity x h 2 h 1 h 2 h with 0 1 a global attractor which is connected

the viscous cahn hilliard equation with inertial term abstract we consider a hyperbolic relaxation of the viscous cahn hilliard equation this equation describes the early stages of spinodal decomposition in certain glasses we establish the existence of families of exponential attractors and inertial manifolds which are continuous at any parameter of viscosity 0 continuity properties of the global attractors are also examined

optimal decay rate of solutions for cahn hilliard equation with inertial term in multi dimensions abstract the cauchy problem of the cahn hilliard equation with inertial term is considered based on green s function method together with energy estimates we get the global in time existence and optimal decay rate of solutions furthermore the viscous case is investigated in the last section

cohomology of 3 dimensional color lie algebras we develop the cohomology theory of color lie algebras due to scheunert zhang in a framework of non homogeneous quadratic koszul algebras in this approach the chevalley eilenberg complex of a color lie algebra becomes a standard koszul complex for its universal enveloping algebra providing a constructive method for computation of cohomology as an application we compute cohomologies with trivial coefficients of z 2 n graded 3 dimensional color lie algebras 2 c 2006 elsevier inc all rights reserved

towards a semiclassical theory of the quantum baker s map abstract we develop semiclassical 0 treatments of the quantum baker s map paying special attention to a the discrete and finite nature of its hilbert space and b the asymptotic analysis of the true quantum objects themselves new techniques are described at the theoretical level exact symbolic decomposition of the propagator and at the numerical level color graphics display of operators in the kirkwood representation both of which are of general interest for other quantized chaotic maps periodic orbit theory is tested numerically and we find that log corrections need to be included before an accurate calculation of the spectrum from periodic orbits can be achieved however the asymptotic analysis of the traces of the propagator reveals unexpected departures from standard semiclassical theory those anomalies which we compute explicitly in a few cases are traced ultimately to the discontinuity of the map and to the compactness of the phase space the analysis is far from complete but the results point towards the necessity of careful assessment of semiclassical folklore when applied to chaotic maps

uniqueness and stability of an inverse problem for a phase field model using data from one component we study an inverse problem of determining a spatial varying coefficient in a parabolic hyperbolic phase field model with the following observation data of only one component the order parameter in a subdomain w satisfying email protected email protected email protected along a sufficiently large time interval and at a suitable time over the whole spatial domain based on a carleman estimate for the parabolic hyperbolic phase field system we prove the lipschitz stability and uniqueness for this inverse problem

diffuse interface model for rapid phase transformations in nonequilibrium systems a thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and the space of fast variables we introduce finiteness of the heat and solute diffusive propagation at the finite speed of the interface advancing to describe transformations within the diffuse interface we use the phase field model which allows us to follow steep but smooth changes of phase within the width of the diffuse interface governing equations of the phase field model are derived for the hyperbolic model a model with memory and a model of nonlinear evolution of transformation within the diffuse interface the consistency of the model is proved by the verification of the validity of the condition of positive entropy production and by outcomes of the fluctuation dissipation theorem a comparison with existing sharp interface and diffuse interface versions of the model is given

convergence to equilibrium for a parabolic hyperbolic phase field system with dynamical boundary condition abstract this paper is concerned with the well posedness and the asymptotic behavior of solutions to the following parabolic hyperbolic phase field system 0 1 t 0 t t t 0 in 0 subject to the neumann boundary condition for 0 2 0 on 0 the dynamical boundary condition for 0 3 t 0 on 0 and the initial conditions 0 4 0 0 0 0 t 0 1 in where is a bounded domain in r 3 with smooth boundary is the outward normal direction to the boundary and is a real analytic function in this paper we first establish the existence and uniqueness of a global strong solution to 0 1 0 4 then we prove its convergence to an equilibrium as time goes to infinity and we provide an estimate of the convergence rate

global attractor for the generalized double dispersion equation abstract the paper studies the existence of global attractor for the generalized double dispersion equation arising in elastic waveguide model u t t u u t t 2 u u t g u f x the main result is concerned with nonlinearities g u with supercritical growth in that case we construct a subclass g of the limit solutions and show that it has a weak global attractor especially in non supercritical case the weak topology becomes strong the further regularity of the global attractor is obtained and the exponential attractor is established in natural energy space

unstable periodic orbits and semiclassical quantisation the bohr sommerfeld quantisation condition has a meaningful extension to classically chaotic systems whose periodic unstable orbits are isolated it provides a semiclassical euler factorisation for the functional determinant of the quantal hamiltonian in contrast to the hadamard infinite product over the eigenvalues by which the exact determinant is defined

poincare and sl 2 algebras of order 3 in this paper we initiate a general classification for lie algebras of order 3 and we give all lie algebras of order 3 based on sl 2 c and iso 1 3 the poincare algebra in four dimensions we then set the basis of the theory of the deformations in the gerstenhaber sense and contractions for lie algebras of order 3

fractional supersymmetry and fth roots of representations a generalization of super lie algebras is presented it is then shown that all known examples of fractional supersymmetry can be understood in this formulation however the incorporation of three dimensional fractional supersymmetry in this framework needs some care the proposed solutions lead naturally to a formulation of a fractional supersymmetry starting from any representation d of any lie algebra g this involves taking the fth roots of d in an appropriate sense a fractional supersymmetry in any space time dimension is then possible this formalism finally leads to an infinite dimensional extension of g reducing to the centerless virasoro algebra when g sl 2 r

on the discrete frobenius perron operator of the bernoulli map we study the spectra of a finite dimensional frobenius perron operator matrix of the bernoulli map derived from phase space discretization the eigenvalues and right and left eigenvectors are analytically calculated which are closely related to periodic orbits on the partition points in the degenerate case jordan decomposition of the matrix is explicitly constructed except for the isolated eigenvalue 1 there is no definite limit with respect to eigenvalues when n the behaviour of the eigenvectors is discussed in the limit of large n

z3 graded algebras and the cubic root of the supersymmetry translations a generalization of supersymmetry is proposed based on z3 graded algebras introducing the objects whose ternary commutation relations contain the cubic roots of unity e2 i 3 e4 i 3 and 1 the operators whose trilinear combinations yield the supersymmetric translation generators can be constructed cubic matrices forming a ternary algebra are the generalization of pauli s matrices the general properties of z3 grading some other representations of such algebras and their possible pertinence with regard to the quark model are briefly discussed

attractors for the cahn hilliard equation with memory in 2d abstract we deal with the memory relaxation of the cahn hilliard equation proposed by rotstein et al as a model for the phenomenological description of phase transition which contains as a particular case the hyperbolic version of the equation due to the absence of viscosity effects existence and uniqueness of solutions are far from being trivial in space dimension n 1 this paper is devoted to the analysis of energy solutions for the 2d model after discussing the well posedness of the problem we study its long term dynamics and we prove the existence and regularity of the global attractor provided that the relaxation parameter of the memory kernel is small enough

the hyperbolic allen cahn equation exact solutions using the first integral method a general set of analytical solutions is obtained for the hyperbolic allen cahn equation the solutions are presented by i the class of continual solutions described by profiles for traveling waves of the order parameter and ii the class of singular solutions which exhibit unbounded discontinuity in the profile of the order parameter at the origin of the coordinate system it is shown that the solutions include the previous analytical results for the parabolic allen cahn equation as a limited class of functions in which the inertial effects are omitted

group theoretical foundations of fractional supersymmetry fractional supersymmetry denotes a generalization of supersymmetry which may be constructed using a single real generalized grassmann variable n 0 for arbitrary integer n 2 3 an explicit formula is given in the case of general n for the transformations that leave the theory invariant and it is shown that these transformations possess interesting group properties it is shown also that the two generalized derivatives that enter the theory have a geometric interpretation as generators of left and right transformations of the fractional supersymmetry group careful attention is paid to some technically important issues including differentiation that arise as a result of the peculiar nature of quantities such as

a semiclassical quantization of area preserving maps abstract a semiclassical path integral formalism is developed for a class of area preserving maps the quasi energy spectrum of these systems is represented as a sum over closed orbits in the manner of gutzwiller the method is illustrated with some numerical tests of the standard map

r adic one dimensional maps and the euler summation formula for the r adic one dimensional maps the author explicitly constructs the decaying eigenstates and adjoint eigenstates associated with the ruelle resonances it is shown that the eigenfunctions of the corresponding frobenius perron operator are the well known bernoulli polynomials the adjoint eigendistributions are obtained as derivatives of the dirac distributions at the end points of the unit interval the resulting expansion of the initial density in terms of the decaying eigenstates is given by the euler summation formula

some applications of thermodynamic formalism to manifolds with constant negative curvature the purpose of this article is to present a different approach to the analysis of the spectrum of a compact surface of constant negative curvature to explain our ideas we recall that there exists a highly successful theory for analyzing zeta functions for closed geodesics originated by a selberg the zeros for this zeta function identify the eigenvalues of the laplacian for the surface the main tool in this analysis is the selberg trace formula 7 there exists an approach having its roots in ergodic theory and statistical mechanics for analyzing zeta functions for geodesic and more general flows the principle here is quite different from that in the selberg approach the zeta function is some form of determinant of a family of perron frobenius type operators parameterized by the complex domain the zeta function behaves like a determinant in that zeros correspond to parameters for which the corresponding operator is not invertible 10 111 since both methods apply to surfaces of constant negative curvature this suggests that there is some mechanism involving a perron frobenius type operator characterizing the laplacian spectrum of the surface 161 oooi 8708 91 7 50

the spatial temporal lamellar structures in the confined ideal polymer blends we consider the formation of self organized spatial temporal oscillating structures in symmetric binary polymer blends confined by two flat walls an influence of these walls on the formation of the oscillating volume structures is studied this phenomenon is simulated by an initial boundary value problem for the conserved order parameter or the concentration of one of the components in a binary mixture under a special choice the dynamical puri binder s boundary conditions these structures look like the lamellar structures the behavior of the order parameter is described by the modified cahn hilliard equation which models so called the non fickian diffusion in the symmetric binary polymer blends the nonlinear dynamical boundary conditions correspond to the process of adsorption desorption on the walls as a result these nonlinear surface processes induce into the volume the spatial temporal asymptotically periodic structures of relaxation pre turbulent or turbulent type with finite countable or non countable points of discontinuities on the period correspondingly the frequency of oscillations on the period follows a power law for the relaxation type and increases exponentially in the other cases

asymptotic behavior of a nonisothermal viscous cahn hilliard equation with inertial term we consider a differential model describing nonisothermal fast phase separation processes taking place in a three dimensional bounded domain this model consists of a viscous cahn hilliard equation characterized by the presence of an inertial term tt being the order parameter which is linearly coupled with an evolution equation for the relative temperature the latter can be of hyperbolic type if the cattaneo maxwell heat conduction law is assumed the state variables and the chemical potential are subject to the homogeneous neumann boundary conditions we first provide conditions which ensure the well posedness of the initial and boundary value problem then we prove that the corresponding dynamical system is dissipative and possesses a global attractor moreover assuming that the nonlinear potential is real analytic we establish that each trajectory converges to a single steady state by using a suitable version of the eojasiewicz simon inequality we also obtain an estimate of the decay rate to equilibrium

a rule for quantizing chaos the authors find a real function delta e whose zeros approximate the quantum energy levels of a system with chaotic classical trajectories delta e is a finite sum over combinations of classical periodic orbits it is obtained from gutzwiller s infinite and divergent sum 1982 representing the spectral density in terms of periodic orbits by means of a resummation conjectured by analogy with a derivation of the riemann siegel formula for the riemann zeros they assess the practicality of the quantization condition

an efficient algorithm for solving the phase field crystal model we present and discuss the development of an unconditionally stable algorithm used to solve the evolution equations of the phase field crystal pfc model this algorithm allows for an arbitrarily large algorithmic time step as the basis for our analysis of the accuracy of this algorithm we determine an effective time step in fourier space we then compare our calculations with a set of representative numerical results and demonstrate that this algorithm is an effective approach for the study of the pfc models yielding a time step effectively 180 times larger than the euler algorithm for a representative set of material parameters as the pfc model is just a simple example of a wide class of density functional theories we expect this method will have wide applicability to modeling systems of considerable interest to the materials modeling communities