singular continuous spectrum for palindromic schrodinger operators we give new examples of discrete schrodinger operators with potentials taking finitely many values that have purely singular continuous spectrum if the hullx of the potential is strictly ergodic then the existence of just one potentialx inx for which the operator has no eigenvalues implies that there is a generic set inx for which the operator has purely singular continuous spectrum a sufficient condition for the existence of such anx is that there is az x that contains arbitrarily long palindromes thus we can define a large class of primitive substitutions for which the operators are purely singularly continuous for a generic subset inx the class includes well known substitutions like fibonacci thue morse period doubling binary non pisot and ternary non pisot we also show that the operator has no absolutely continuous spectrum for allx x ifx derives from a primitive substitution for potentials defined by circle maps x n 1 j 0 n we show that the operator has purely singular continuous spectrum for a generic subset inx for all irrational and every half open intervalj

mathematical problems in the coupled linear theory of bone poroelasticity this paper concerns with the quasi static coupled linear theory of bone poroelasticity for materials with double porosity and some basic results of the classical theories of elasticity and thermoelasticity are generalized the system of equations of this theory is based on the equilibrium equations conservation of fluid mass the effective stress concept and darcy s law for material with double porosity the green s formulas in the considered theory are obtained the formulas of somigliana type integral representations of regular vector and regular classical solutions are presented the uniqueness theorems for classical solutions of the internal and external boundary value problems bvps are proved the single layer double layer and volume potentials are constructed and their basic properties are established finally the existence theorems for classical solutions of the bvps are proved by means of the potential method boundary integral method and the theory of singular integral equations

exponential stability to localized type iii thermoelasticity abstract this paper investigates the system proposed by a wave equation and a heat equation of type iii in one part of the domain a wave equation and a heat equation of type ii in another part of the domain coupled in a certain pattern in this paper we prove the exponential stability of the solutions under suitable conditions for the thermal conductivity and coupling term

random geometric graphs we analyze graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present the critical connectivity is found numerically by examining the size of the largest cluster we derive an analytical expression for the cluster coefficient which shows that the graphs are distinctly different from standard random graphs even for infinite dimensionality insights relevant for graph bipartitioning are included

recurrence of the eigenstates of a schrodinger operator with automatic potential we consider the schrodinger eigenvalue problem in the discrete case with a potential assuming two values distributed according to the automatic sequence of prouhet thue morse we show that there are no localized states and that the generalized eigenvectors are recurrent on a geometrical set stemming from the hierarchical nature of the potential

the spectrum of a quasiperiodic schrodinger operator the spectrum h of the tight binding fibonacci hamiltonian hmn m n 1 m 1 n m n v n v n chi omega 3 omega 2 n 1 1 is the golden number is shown to coincide with the dynamical spectrum the set on which an infinite subsequence of traces of transfer matrices is bounded the point spectrum is absent for any and h is a cantor set for 4 combining this with casdagli s earlier result one finds that the spectrum is singular continuous for 16

general decay for a porous thermoelastic system with memory the case of equal speeds abstract in this paper we consider a one dimensional system with porous elasticity in the presence of a visco porous dissipation and a macrotemperature effect we establish a general decay result of which the exponential and the polynomial results of soufyane 2008 10 are merely special cases

localization problem in one dimension mapping and escape a one dimensional schr odinger equation in a discontinuous quasiperiodic potential is reduced to a recursion relation for transfer matrices and then to one for traces of these matrices when the potential is periodic the bandwidth goes to zero as an algebraic function of the period with a critical index which depends upon the potential strength this critical index is also evaluated as the solution to an escape rate problem for the recursion relations

critical points for finite fibonacci chains of point delta interactions and orthogonal polynomials for a one dimensional schrodinger operator with a finite number n of point delta interactions with a common intensity the parameters are the intensity the n 1 intercenter distances and the mass critical points are points in the parameters space of the hamiltonian where one bound state appears or disappears the study of critical points for hamiltonians with point delta interactions arranged along a fibonacci chain is shown to be closely related to the study of the so called fibonacci operator a discrete one dimensional schrodinger type operator which occurs in the context of tight binding hamiltonians these critical points are the zeros of orthogonal polynomials previously studied in the context of special diatomic linear chains with elastic nearest neighbor interaction properties of the zeros location asymptotic behavior gaps are investigated the perturbation series from the solvable periodic case is determined the measure which yields orthogonality is investigated numerically from the zeros it is shown that the transmission coefficient at zero energy can be expressed in terms of the orthogonal polynomials and their associated polynomials in particular it is shown that when the number of point delta interactions is equal to a fibonacci number minus 1 i e when the intervals between point delta interactions form a palindrome all the fibonacci chains at critical points are completely transparent at zero energy

on the theory of thermoelasticity with microtemperatures abstract this paper studies the linear theory of thermoelastic materials with inner structure whose particles in addition to the classical displacement and temperature fields possess microtemperatures we discuss uniqueness results within the context of the dynamic boundary value problems under very mild assumptions upon the thermoelastic profile we also establish the relations describing the partition of the total energy in terms of the cesaro means of various types of component energies

remarks on the spectral properties of tight binding and kronig penney models with substitution sequences we comment on some recent investigations on the electronic properties of models associated with the thue morse chain point out that their conclusions contradict rigorously proven theorems and indicate some of the sources of these misinterpretations we briefly review and explain the current status of mathematical results in this field and discuss some conjectures and open problems

dynamical system related to quasiperiodic schrodinger equations in one dimension a dynamical map is obtained from a class of quasiperiodic discrete schrodinger equations in one dimension which include the fibonacci system the potentials are constant except for steps at special points

growth and uniqueness in thermoelasticity a uniqueness theorem is proved for two theories of thermoelasticity capable of admitting finite speed thermal waves the theories having been proposed by green naghdi uniqueness is proved under

on the hausdorff dimension of the spectrum of the thue morse hamiltonian we show that the hausdorff dimension of the spectrum of the thue morse hamiltonian has a common positive lower bound for all coupling

on kicked systems modulated along the thue morse sequence we give necessary conditions for the fourier transform of the time evolution operator of kicked systems modulated along the thue morse sequence to present dirac s delta functions the case of two level systems is analysed in detail and it is found based on the trace map and numerical investigations that generically its time evolution has no quasi periodic component

absence of localisation in the almost mathieu equation the author considers the discrete schrodinger operator on z with the potential lambda cos 2 pi alpha n theta this one dimensional model occurs in the study of an electron in a two dimensional periodic potential with a uniform magnetic field first it is proved that for every alpha and for lambda 2 this operator has no eigenvalue i e localised state furthermore at lambda 2 the eigenvalues if they exist belong to the set where the lyapunov exponent vanishes and the associated eigenvectors at in l2 z but are not summable

a re examination of the basic postulates of thermomechanics this paper is mainly concerned with a re examination of the basic postulates and the consequent procedure for the construction of the constitutive equations of material behaviour in thermomechanics however the implication of the basic postulates and the significance of the related procedure for the development of the constitutive equations is also illustrated in some detail in the context of flow of heat in a rigid solid with particular reference to the propagation of thermal waves at finite speed more specifically after briefly examining the nature of the basic equations of motion for a system of particles within the scope of the classical newtonian mechanics the basic postulates of the purely mechanical theory for a continuum including its specialization for a rigid body is re examined this includes some differences from the usual procedure on the subject next thermal variables are introduced and after observing a useful analogy between the thermal and mechanical variables a discussion of a theory of heat or a purely thermal theory is provided which differs from the usual development in the classical thermodynamics a detailed application of the latter development is then made to the problem of heat flow in a stationary rigid solid using several different and well motivated constitutive equations special cases of these include linearized theories of the classical heat flow by conduction and of heat flow transmitted as thermal waves the remainder of the paper is concerned with thermal mechanical theory of deformable media along with discussions of a number of related issues on the subject

detecting degree symmetries in networks the surrounding of a vertex in a network can be more or less symmetric we derive measures of a specific kind of symmetry of a vertex which we call degree symmetry the property that many paths going out from a vertex have overlapping degree sequences these measures are evaluated on artificial and real networks specifically we consider vertices in the human metabolic network we also measure the average degree symmetry coefficient for different classes of real world network we find that most studied examples are weakly positively degree symmetric the exceptions are an airport network having a negative degree symmetry coefficient and one mode projections of social affiliation networks that are rather strongly degree symmetric

recurrent versus diffusive dynamics for a kicked quantum system we study the dynamics of a two level quantum system subject to a time dependent kicking perturbation modulated along the thue morse sequence for a nontrivial set of the parameters the quantum autocorrelation function is explicitly calculated and splits into a purely recurrent and a purely diffusive part furthermore the diffusive part is directly related to the singular continuous correlation measure of the thue morse sequence

block variables for deterministic aperiodic sequences we use the concept of block variables to obtain a measure of order disorder for some one dimensional deterministic aperiodic sequences for the thue morse sequence the rudin shapiro sequence and the period doubling sequence it is possible to obtain analytical expressions in the limit of infinite sequences for the fibonacci sequence we present some analytical results which can be supported by numerical arguments it turns out that the block variables show a wide range of different behaviour some of them indicating that some of the considered sequences are more random than other however the method does not give any definite answer to the question of which sequence is more disordered than the other and in this sense the results obtained are negative we compare this with some other ways of measuring the amount of order disorder in such systems and there seems to be no direct correspondence between the measures

analysis for the strain gradient theory of porous thermoelasticity abstract in this paper we analyse a model involving a strain gradient thermoelastic rod with voids existence and uniqueness as well as an energy decay property are proved by means of the semigroup arguments the variational formulation is derived and then a fully discrete approximation is introduced by using the finite element method to approximate the spatial variable and the implicit euler scheme to discretize the time derivatives a stability result and a priori error estimates are obtained from which the linear convergence of the algorithm is deduced under suitable additional regularity conditions finally some numerical simulations are presented to demonstrate the accuracy of the algorithm and the behaviour of the solution

a new type of transition between critical and extended states in one dimension the author studies a tight binding model psi n 1 psi n 1 lambda nvn psi n e psi n where vn is a fibonacci array of two potentials and lambda n f 12 n alpha for alpha 1 2 this model is asymptotically equivalent at large n to a continuous schrodinger equation with an electric field f and a quasiperiodic potential he finds that for this value of alpha almost all states are changed from critical to extended states as the field strength is increased however some states still remain critical and coexist with most extended states he also discusses the result for other values of alpha

trace maps for arbitrary substitution sequences the authors prove the existence and show how to construct trace maps for products of 2 2 matrices generated by arbitrary substitution sequences the dimension of the underlying space of the trace map is lower than the one suggested recently by other authors

spectrum and extended states in a harmonic chain with controlled disorder effects of the thue morse symmetry along the lines of previous work we give the general framework together with a detailed and rigorous study of the spectrum and born von karman eigenstates of a 1d harmonic chain with controlled disorder determined by the thue morse sequence the spectrum is a cantor like set we prove numerically that its measure is zero and calculate its bouligand minkowski dimension box dimension we prove that the value of the ids on each of the gaps is 2k 1 3 2 p withk andp integers finally we also prove that points in a dense subset of the spectrum give rise to extended states an exceptional property due to the symmetry of the thue morse substitution which can have important applications to multilayered structures and we illustrate this situation

characterizing graph symmetries through quantum jensen shannon divergence in this paper we investigate the connection between quantum walks and graph symmetries we begin by designing an experiment that allows us to analyze the behavior of the quantum walks on the graph without causing the wave function collapse to achieve this we base our analysis on the recently introduced quantum jensen shannon divergence in particular we show that the quantum jensen shannon divergence between the evolution of two quantum walks with suitably defined initial states is maximum when the graph presents symmetries hence we assign to each pair of nodes of the graph a value of the divergence and we average over all pairs of nodes to characterize the degree of symmetry possessed by a graph

on thermoelastic bodies with inner structure and microtemperatures abstract in the first part of this paper we present a linear theory of thermoelastic bodies with microstructure and microtemperatures which permits the transmission of heat as thermal waves at finite speed the theory is based on the entropy balance postulated by green and naghdi a e green p m naghdi a re examination of the basic postulates of thermomechanics proc r soc london a 432 1991 171 194 we consider bodies with microstructure whose microelements can stretch and contract independently of their translations then we establish existence and uniqueness results in the context of the dynamic theory

on the leading term and the degree of the polynomial trace mapping associated with a substitution using the trace mapping and the reduced trace mapping associated with a substitution one obtaines the spectral properties of one dimensional schrodinger operators of the formh v onl2 where is the discrete laplacian andv is a diagonal operator with elements derived from a substitution rule in particular the reduced trace mapping is closely related to the leading term of the original trace mapping in this paper the explicit expression of the leading term is given and its properties are discussed

emergence of symmetry in complex networks many real networks have been found to have a rich degree of symmetry which is a universal structural property of complex networks yet has been rarely studied so far one of the fascinating problems related to symmetry is exploration of the origin of symmetry in real networks for this purpose we summarized the statistics of local symmetric motifs that contribute to local symmetry of networks analysis of these statistics shows that the symmetry of complex networks is a consequence of similar linkage pattern which means that vertices with similar degrees tend to share common neighbors an improved version of the baraba i albert model integrating similar linkage pattern successfully reproduces the symmetry of real networks indicating that similar linkage pattern is the underlying ingredient that is responsible for the emergence of symmetry in complex networks

existence of only delocalized eigenstates in the electronic spectrum of the thue morse lattice abstract we present an analytical method for finding all the electronic eigenfunctions and eigenvalues of the aperiodic thue morse lattice we prove that this system supports only extended electronic states which is a very unusual behavior for this class of systems and so far as we know this is the only example of a quasiperiodic or aperiodic system in which critical or localized states are totally absent in the spectrum interestingly we observe that the symmetry of the lattice leads to the existence of degenerate eigenstates and all the eigenvalues excepting the four global band edges are doubly degenerate we show exactly that the landauer resistivity is zero for all the degenerate eigenvalues and it scales as l 2 l system size at the global band edges we also find that the localization length diverges in the limit of infinite system size

effective number of accessed nodes in complex networks the measurement called accessibility has been proposed as a means to quantify the efficiency of the communication between nodes in complex networks this article reports results regarding the properties of accessibility including its relationship with the average minimal time to visit all nodes reachable after h steps along a random walk starting from a source as well as the number of nodes that are visited after a finite period of time we characterize the relationship between accessibility and the average number of walks required in order to visit all reachable nodes the exploration time conjecture that the maximum accessibility implies the minimal exploration time and confirm the relationship between the accessibility values and the number of nodes visited after a basic time unit the latter relationship is investigated with respect to three types of dynamics traditional random walks self avoiding random walks and preferential random walks

unbounded trace orbits of thue morse hamiltonian it is well known that an energy is in the spectrum of fibonacci hamiltonian if and only if the corresponding trace orbit is bounded however it is not known whether the same result holds for the thue morse hamiltonian in this paper we give a negative answer to this question more precisely we construct two subsets sigma ii and sigma iii of the spectrum of the thue morse hamiltonian both of which are dense and uncountable such that each energy in sigma ii cup sigma iii corresponds to an unbounded trace orbit exact estimates on the norm of the transfer matrices are also obtained for these energies for e in sigma ii cup sigma iii the norms of the transfer matrices behave like begin aligned e c 1 gamma sqrt n le vert t n e vert le e c 2 gamma sqrt n end aligned however two types of energies are quite different in the sense that each energy in sigma ii is associated with a two sided pseudo localized state while each energy in sigma iii is associated with a one sided pseudo localized state the difference is also reflected by the local dimensions of the spectral measure the local dimension is 0 for energies in sigma ii and is larger than 1 for energies in sigma iii as a comparison we mention another known countable dense subset sigma i each energy in sigma i corresponds to an eventually constant trace map and the associated eigenvector is an extended state in summary the thue morse hamiltonian exhibits mixed spectral nature

spectral properties of one dimensional schrodinger operators with potentials generated by substitutions we investigate one dimensional discrete schrodinger operators whose potentials are invariant under a substitution rule the spectral properties of these operators can be obtained from the analysis of a dynamical system called the trace map we give a careful derivation of these maps in the general case and exhibit some specific properties under an additional easily verifiable ypothesis concerning the structure of the trace map we present an analysis of their dynamical properties that allows us to prove that the spectrum of the underlying schrodinger operator is singular and supported on a set of zero lebesgue measure a condition allowing to exclude point spectrum is also given the application of our theorems is explained on a series of examples

a natural class of generalized fibonacci chains in this paper we propose a class of substitution rules that generate quasiperiodic chains sharing their typid properties with the quasiperiodic fibonacci chain for a subclass we explicitly con vct the atomic surface moreover scaling properties of the energy specmm are discussed in relation to the dynamics of trace maps

on uniqueness and continuous dependence in type iii thermoelasticity abstract this note is concerned with the linear and linearised type iii thermoelastic theory proposed by green and naghdi first the continuous dependence of the solutions upon the initial data and supply terms is established for noncentrosymmetric bodies then a uniqueness result for centrosymmetric materials is established

schrodinger operators with rudin shapiro potentials are not palindromic we prove a conjecture of a hof o knill and b simon commun math phys 174 149 159 1995 by showing that the rudin shapiro sequence is not palindromic i e does not contain arbitrarily long palindromes we prove actually this property for all paperfolding sequences and all rudin shapiro sequences deduced from paperfolding sequences as a consequence and as guessed by the above authors their method cannot be used for establishing that discrete schrodinger operators with rudin shapiro potentials have a purely singular continuous spectrum

discrete breathers in aperiodic diatomic fpu lattices with long range order this study presents various aspects of discrete breathers in diatomic fpu lattices with masses varying according to the aperiodic fibonacci and thue morse sequences we investigate the existence of time periodic breathers starting from the anti continuous limit and consider excitations of isolated light atoms hence obtaining the domain of unique existence for these breathers we also perform a linear stability analysis by studying the floquet operator the found exact solutions are used slightly perturbed as initial conditions for long time simulations of the breathers these breathers turn out to be robust finally we consider how initial excitations of two consecutive light atoms evolve depending on the properties of the phase space for the two atom system at the anti continuous limit we obtain different behaviour of these excitations especially we find that the aperiodic lattices can support localized excitations with a continuous frequency distribution for the timescales we consider while a periodic lattice is unable to these excitations are referred to as chaotic breathers c 2000 elsevier science b v all rights reserved

aperiodic and correlated disorder in xy chains exact results we study thermodynamic properties surface magnetization specific heat and susceptibility of xy quantum chains with coupling constants following arbitrary substitution sequences generalizing an exact renormalization group rg transformation originally formulated for ising quantum chains we obtain exact relevance criteria of harris luck type for this class of models for two letter substitution rules a detailed classification is given of sequences leading to irrelevant marginal or relevant aperiodic modulations we find that the relevance of the same aperiodic sequence of couplings in general will be different for xy and ising quantum chains by our method continuously varying critical exponents may be calculated exactly for arbitrary two letter substitution rules with marginal aperiodicity a number of examples are given including the period doubling three folding and precious mean chains we also discuss extensions of the renormalization approach to a special class of long range correlated random chains generated by random substitutions

strain gradient theory of chiral cosserat thermoelasticity without energy dissipation in this paper we use the green naghdi theory of thermomechanics of continua to derive a linear strain gradient theory of cosserat thermoelastic bodies the theory is capable of predicting a finite speed of heat propagation and leads to a symmetric conductivity tensor the constitutive equations for isotropic chiral thermoelastic materials are presented in this case in contrast with the classical cosserat thermoelasticity a thermal field produces a microrotation of the particles the thermal field is influenced by the displacement and microrotation fields even in the equilibrium theory existence and uniqueness results are established the theory is used to study the effects of a concentrated heat source in an unbounded homogeneous and isotropic chiral solid

hierarchical characterization of complex networks while the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node valuable information about the network topological properties can be obtained by considering further neighborhoods the current work considers the concept of virtual hierarchies established around each node and the respectively defined hierarchical node degree and clustering coefficient introduced in cond mat 0408076 complemented by new hierarchical measurements in order to obtain a powerful set of topological features of complex networks the interpretation of such measurements is discussed including an analytical study of the hierarchical node degree for random networks and the potential of the suggested measurements for the characterization of complex networks is illustrated with respect to simulations of random scale free and regular network models as well as real data airports proteins and word associations the enhanced characterization of the connectivity provided by the set of hierarchical measurements also allows the use of agglomerative clustering methods in order to obtain taxonomies of relationships between nodes in a network a possibility which is also illustrated in the current article

power law bounds on transfer matrices and quantum dynamics in one dimension ii abstract we establish quantum dynamical lower bounds for a number of discrete one dimensional schrodinger operators these dynamical bounds are derived from power law upper bounds on the norms of transfer matrices we develop further the approach from part i and study many examples particular focus is put on models with finitely or at most countably many exceptional energies for which one can prove power law bounds on transfer matrices the models discussed in this paper include substitution models sturmian models a hierarchical model the prime model and a class of moderately sparse potentials

walk entropies in graphs abstract entropies based on walks in graphs and in their line graphs are defined they are based on the summation over diagonal and off diagonal elements of the exponential of the adjacency matrix known as the network communicability the walk entropies are strongly related to the walk regularity of graphs and line graphs they are not biased by the graph size and have significantly better correlation with the inverse participation ratio of the eigenmodes of the adjacency matrix than other graph entropies a homogeneous weighting of the edges of the graph is used to simulate the effects of the temperature over the entropies defined in particular the walk entropy of graphs is non monotonic for regular but non walk regular graphs in contrast to non regular graphs

concentric network symmetry we developed a new node center symmetry measurement for complex networks the symmetry values were compared among six network models as well as four real world networks by using principal component analysis we obtained distinctive signatures of symmetry for each considered network quantification of symmetries in complex networks is typically done globally in terms of automorphisms extending previous methods to locally assess the symmetry of nodes is not straightforward here we present a new framework to quantify the symmetries around nodes which we call connectivity patterns we develop two topological transformations that allow a concise characterization of the different types of symmetry appearing on networks and apply these concepts to six network models namely the erd s renyi barabasi albert random geometric graph waxman voronoi and rewired voronoi real world networks namely the scientific areas of wikipedia the world wide airport network and the street networks of oldenburg and san joaquin are also analyzed in terms of the proposed symmetry measurements several interesting results emerge from this analysis including the high symmetry exhibited by the erd s renyi model additionally we found that the proposed measurements present low correlation with other traditional metrics such as node degree and betweenness centrality principal component analysis is used to combine all the results revealing that the concepts presented here have substantial potential to also characterize networks at a global scale we also provide a real world application to the financial market network

singular continuous electron spectrum for a class of circle sequences we derive substitution rules for a class of binary quasiperiodic sequences generated by circle maps whose rotation numbers are obtained from the precious means the nature of the electron spectra for the corresponding diatomic chains is studied in the nearest neighbour on site tight binding approximation using the transfer matrix technique by studying properties of the trace maps we find that the spectrum is purely singular continuous in most of the studied cases

repeller structure in a hierarchical model i topological properties the repeller associated with the renormalization dynamics of the spectral problem of a hierarchical tight binding schrodinger equation is studied analysis of escaping regions and of stable and unstable manifolds provide complementary descriptions of the recurrent set whose structure undergoes relevant changes when the growth rater of the potential barriers is modified the minimal region containing the repeller is determined and the mechanism originating a cantor set structure along the unstable manifold is revealed the repeller is continuous along the stable manifold forr 2 finally we show the existence of a pointlike component of the spectrum located at its upper extremum forr 1 and we present the associated wavefunctions