on casimir operators of conformal galilei algebras in a previous work f alshammari p s isaac and i marquette j phys a math theor 51 065206 2018 we introduced an algorithm that utilises differential operator realisations to find polynomial casimir operators of lie algebras in this article we build on this work by applying the algorithm to several classes of finite dimensional conformal galilei algebras with central extension in these cases we highlight the utility of an algebra anti automorphism and give relevant details through key examples

the yang lee edge singularity in spin models on connected and non connected rings renormalization group arguments based on a 3 field theory lead us to expect a certain universal behavior for the density of partition function zeros in spin models with short range interaction such universality has been tested analytically and numerically in different d 1 and higher dimensional spin models in d 1 one finds usually the critical exponent 1 2 recently we have shown in the d 1 blume emery griffiths beg model on a periodic static lattice one ring that a new critical behavior with 2 3 can arise if we have a triple degeneracy of the transfer matrix eigenvalues here we define the d 1 beg model on a dynamic lattice consisting of connected and non connected rings non periodic lattice and check numerically that also in this case we have mostly 1 2 while the new value 2 3 can arise under the same conditions of the static lattice triple degeneracy which is a strong check of universality of the new value of we also show that although such conditions are necessary they are not sufficient to guarantee the new critical behavior

a new matrix method for the casimir operators of the lie algebras w mathfrak s mathfrak p n hbox mathbb r and i mathfrak s mathfrak p 2n hbox mathbb r a method is given to determine the casimir operators of the perfect lie algebras and the inhomogeneous lie algebras in terms of polynomials associated with a parametrized 2n 1 2n 1 matrix for the inhomogeneous symplectic algebras this matrix is shown to be associated to a faithful representation we further analyse the invariants for the extended schrodinger algebra in n 1 dimensions which arises naturally as a subalgebra of the method is extended to other classes of lie algebras and some applications to the missing label problem are given

generalized conformal pseudo galilean algebras and their casimir operators a generalization of the conformal galilei algebra with levi subalgebra isomorphic to is introduced and a virtual copy of the latter in the enveloping algebra of the extension is constructed explicit expressions for the casimir operators are obtained from the determinant of polynomial matrices for the central factor algebra an exact formula giving the number of invariants is obtained and a procedure to compute invariant functions that do not depend on the variables of the levi subalgebra is developed it is further shown that such solutions determine complete sets of invariants provided that the relation is satisfied

partition function zeros of the one dimensional potts model the recursive method the yang lee fisher and potts zeros of the one dimensional q state potts model are studied using the theory of dynamical systems an exact recurrence relation for the partition function is derived it is shown that zeros of the partition function may be associated with neutral fixed points of the recurrence relation further a general equation for zeros of the partition function is found and a classification of the yang lee fisher and potts zeros is given it is shown that the fisher zeros in a nonzero magnetic field are located on several lines in the complex temperature plane and that the number of these lines depends on the value of the magnetic field analytical expressions for the densities of the yang lee fisher and potts zeros are derived it is shown that densities of all types of zeros of the partition function are singular at the edge singularity points with the same critical exponent

exact results for the zeros of the partition function of the potts model on finite lattices the yang lee zeros of the q state potts model are investigated in one two and three dimensions analytical results derived from the transfer matrix for the one dimensional model reveal a systematic behavior of the locus of zeros as a function of q for 1 2 they lie outside the unit circle for finite temperature in the special case q 2 the zeros lie exactly on the unit circle as proved by lee and yang in two and three dimensions the zeros are calculated numerically and behave in the same way results are also presented for the critical line of the potts model in an external field as determined from the zeros of the partition function in the complex temperature plane

a differential operator realisation approach for constructing casimir operators of non semisimple lie algebras we introduce a search algorithm that utilises differential operator realisations to find polynomial casimir operators of lie algebras to demonstrate the algorithm we look at two classes of examples 1 the model filiform lie algebras and 2 the schrodinger lie algebras we find that an abstract form of dimensional analysis assists us in our algorithm and greatly reduces the complexity of the problem

the partition function zeros in the one dimensional q state potts model the zeros of the partition function in the one dimensional q state potts model with arbitrary and continuous q or 0 have been studied using a transfer matrix the location of zeros and the yang lee edge singularity have been analysed and two different regimes corresponding to q 1 and q 1 have been observed a duality relation has also been derived which relates the zeros in the complex field plane to those in the complex temperature plane

thin fisher zeros various authors have suggested that the loci of partition function zeros can profitably be regarded as phase boundaries in the complex temperature or field planes we obtain the fisher zeros for ising and potts models on non planar thin regular random graphs using this approach and note that the locus of fisher zeros on a bethe lattice is identical to the corresponding random graph since the number of states q appears as a parameter in the potts solution the limiting locus of chromatic zeros is also accessible

density of yang lee zeros for the ising ferromagnet the densities of yang lee zeros for the ising ferromagnet on the l x l square lattice are evaluated from the exact grand partition functions l 3 approximately 16 the properties of the density of yang lee zeros are discussed as a function of temperature t and system size l the three different classes of phase transitions for the ising ferromagnet first order phase transition second order phase transition and yang lee edge singularity are clearly distinguished by estimating the magnetic scaling exponent yh from the densities of zeros for finite size systems the divergence of the density of zeros at yang lee edge in high temperatures yang lee edge singularity which has been detected only by the series expansion until now for the square lattice ising ferromagnet is obtained from the finite size data the identification of the orders of phase transitions in small systems is also discussed using the density of yang lee zeros

a new barrier to the existence of moving kinks in frenkel kontorova lattices an explanation is offered for an observed lower bound on the wave speed of travelling kinks in frenkel kontorova lattices kinks exist at discrete wavespeeds within a parameter regime where there is a resonance with linear waves phonons however they fail to exist even in this codimension one sense whenever there is more than one phonon branch in the dispersion relation inside such bands only quasi kinks with nondecaying oscillatory tails are possible the results are presented for a discrete sine gordon lattice with an onsite potential that has a tunable amount of anharmonicity novel numerical methods are used to trace kinks with topological charge q 1 and 2 in three parameters representing the propagation speed lattice discreteness and anharmonicity although none of the analysis is presented as rigorous mathematics numerical results suggest that the bound on allowable wavespeeds is sharp the results also explain why the vanishing at discrete values of anharmonicity of the peierls nabarro barrier between stationary kinks as discovered by savin et al does not lead to bifurcation of kinks with small wave speed 2003 elsevier b v all rights reserved

kinematical lie algebras via deformation theory we present a deformation theory approach to the classification of kinematical lie algebras in 3 1 dimensions and present calculations leading to the classifications of all deformations of the static kinematical lie algebra and of its universal central extension up to isomorphism in addition we determine which of these lie algebras admit an invariant symmetric inner product among the new results we find some deformations of the centrally extended static kinematical lie algebra which are extensions but not central of deformations of the static kinematical lie algebra this paper lays the groundwork for two companion papers which present similar classifications in dimension d 1 for all d 4 and in dimension 2 1 we present a deformation theory approach to the classification of kinematical lie algebras in 3 1 dimensions and present calculations leading to the classifications of all deformations of the static kinematical lie algebra and of its universal central extension up to isomorphism in addition we determine which of these lie algebras admit an invariant symmetric inner product among the new results we find some deformations of the centrally extended static kinematical lie algebra which are extensions but not central of deformations of the static kinematical lie algebra this paper lays the groundwork for two companion papers which present similar classifications in dimension d 1 for all d 4 and in dimension 2 1

nonrelativistic conformal groups ii further developments and physical applications the finite dimensional conformal groups associated with the galilei and oscillating or expanding newton hooke space time manifolds was characterized by the present authors in a recent work three isomorphic group families one for each nonrelativistic kinematics were obtained whose members are labeled by a half integer number l since the action of these groups on their corresponding space time manifolds is only local a linearization is introduced here such that the corresponding action is well defined everywhere in particular the l 1 conformal cases that can be obtained by contraction from the well known minkowskian conformal group are treated in more detail as an application of physical interest the conformal invariance of the galilean electromagnetism is studied in order to achieve it the pertinent local representations of the galilean conformal algebras are derived

moving kinks and nanopterons in the nonlinear klein gordon lattice we study moving topological solitons kinks and antikinks in the nonlinear klein gordon chain these solitons are shown to exist with both monotonic non oscillating and oscillating asymptotics tails using the pseudo spectral method the anti kink solutions with oscillating background so called nanopterons are found as travelling waves of permanent profile propagating with constant velocity each of these solutions may be considered as a bound state of an anti kink with a background nonlinear periodic wave so that the wave pushes the anti kink over the peierls nabarro barrier the stability of these bound states is confirmed numerically travelling wave solutions of permanent profile are shown to exist depending on the convexity of the on site substrate potential the set of velocities at which the anti kinks with monotonic asymptotics propagate freely is calculated we also find moving non oscillating anti kink profiles with higher topological charges each of which appears to be the bound state of anti kinks with lower topological charge jq jd 1 2000 elsevier science b v all rights reserved

dynamical transitions between equilibria in a dissipative klein gordon lattice abstract we consider the energy landscape of a dissipative klein gordon lattice with a 4 on site potential our analysis is based on suitable energy arguments combined with a discrete version of the ojasiewicz inequality in order to justify the convergence to a single nontrivial equilibrium for all initial configurations of the lattice then global bifurcation theory is explored to illustrate that in the discrete regime all linear states lead to nonlinear generalizations of equilibrium states direct numerical simulations reveal the rich structure of the equilibrium set consisting of non trivial topological kink shaped interpolations between the adjacent minima of the on site potential and the wealth of dynamical convergence possibilities these dynamical evolution results also provide insight on the potential stability of the equilibrium branches and glimpses of the emerging global bifurcation structure elucidating the role of the interplay between discreteness nonlinearity and dissipation

a numerical method to compute exactly the partition function with application to z n theories in two dimensions i present a new method to exactly compute the partition function of a class of discrete models in arbitrary dimensions the time for the computation for ann state model on anl d lattice scales like n l d 1 nl d i show examples of the use of this method by computing the partition function of the 2d ising and 3 state potts models for maximum lattice sizes 10 10 and 8 8 respectively the critical exponentsv and and the critical temperature one obtains from these are very near the exactly known values the distribution of zeros of the partition function of the potts model leads to the conjecture that the ratio of the amplitudes of the specific heat below and above the critical temperature is unity

transfer matrix for the restricted canonical and microcanonical ensembles the numerical transfer matrix for the partition function of discrete lattice models is generalized to allow the calculation of the density of states ensuremath omega e and the restricted density of states ensuremath omega e m given ensuremath omega e m the partition function is expressed as a polynomial in the variables x mathit e mathrm ensuremath beta mathit h and y mathit e mathrm ensuremath mathrm ensuremath beta these algorithms are illustrated with calculations for the ising model on finite square lattices the zeros of the partition function are examined in both the complex x and y planes finite size scaling analysis of the zeros leads to very accurate estimates for the critical temperature and critical exponents

the partition function zeros of the anisotropic ising model with multisite interactions on a zigzag ladder abstract it is shown that the spin 1 2 anisotropic ising model with multisite interactions on a zigzag ladder may be mapped into the one dimensional spin 1 2 axial next nearest neighbor ising annni model with multisite interactions the partition function zeros of the annni model with multisite interactions are investigated a comprehensive analysis of the partition function zeros of the annni model with and without three site interactions on a zigzag ladder is done using the transfer matrix method analytical equations for the distribution of the partition function zeros in the complex magnetic field yang lee zeros and temperature fisher zeros planes are derived the yang lee and fisher zeros distributions are studied numerically for a variety of values of the model parameters the densities of the yang lee and fisher zeros are studied and the corresponding edge singularity exponents are calculated it is shown that the introduction of three site interaction terms in the annni model leads to a simpler distribution of the partition function zeros for example the yang lee zeros tend to a circular distribution when increasing by modulus the three site interactions term coefficient it is found that the yang lee and fisher edge singularity exponents are universal and equal to each other 1 2

finite size scaling of the density of zeros of the partition function in first and second order phase transitions the finite size scaling form for the density of zeros of the partition function in first and second order phase transitions is derived using the finite size scaling of the density of zeros the order of a phase transition can be easily determined and the order parameter calculated from finite size data we illustrate the scaling theory using exact values for the zeros of the partition function of the two dimensional ising model in the complex magnetic field plane

finite lattice extrapolation algorithms two algorithms for sequence extrapolation due to van den broeck and schwartz 1979 and bulirsch and stoer 1964 are reviewed and critically compared applications to three state and six state quantum chains and to the 2 1 d ising model show that the algorithm of bulirsch and stoer is superior in particular if only very few finite lattice data are available

virtual copies of semisimple lie algebras in enveloping algebras of semidirect products and casimir operators given a semidirect product g s r of semisimple lie algebras s and solvable algebras r we construct polynomial operators in the enveloping algebra u g of g that commute with r and transform like the generators of s up to a functional factor that turns out to be a casimir operator of r such operators are said to generate a virtual copy of s in u g and allow to compute the casimir operators of g in closed form using the classical formulae for the invariants of s the behavior of virtual copies with respect to contractions of lie algebras is analyzed applications to the class of hamilton algebras and their inhomogeneous extensions are given

translationally invariant discrete kinks from one dimensional maps for most discretizations of the phi4 theory the stationary kink can only be centered either on a lattice site or midway between two adjacent sites we search for exceptional discretizations that allow stationary kinks to be centered anywhere between the sites we show that this translational invariance of the kink implies the existence of an underlying one dimensional map phi n 1 f phi n a simple algorithm based on this observation generates three families of exceptional discretizations

high speed kinks in a generalized discrete phi 4 model we consider a generalized discrete ensuremath phi 4 model and demonstrate that it can support exact moving kink solutions in the form of tanh with an arbitrarily large velocity the constructed exact moving solutions are dependent on the specific value of the propagation velocity we demonstrate that in this class of models given a specific velocity the problem of finding the exact moving solution is integrable namely this problem originally expressed as a three point map can be reduced to a two point map from which the exact moving solutions can be derived iteratively it was also found that these high speed kinks can be stable and robust against perturbations introduced in the initial conditions

exact enumeration of hamiltonian circuits walks and chains in two and three dimensions we present an algorithm for enumerating exactly the number of hamiltonian chains on regular lattices in low dimensions by definition these are sets of k disjoint paths whose union visits each lattice vertex exactly once the well known hamiltonian circuits and walks appear as the special cases k 0 and k 1 respectively in two dimensions we enumerate chains on l l square lattices up to l 12 walks up to l 17 and circuits up to l 20 some results for three dimensions are also given using our data we extract several quantities of physical interest

on irreducible representations of the exotic conformal galilei algebra we investigate the representations of the exotic conformal galilei algebra this is done by explicitly constructing all singular vectors within the verma modules and then deducing irreducibility of the associated highest weight quotient modules a resulting classification of infinite dimensional irreducible modules is presented

exceptional discretizations of the sine gordon equation the method of one dimensional maps was recently introduced as a means of generating exceptional discretizations of the phi 4 theory i e discrete phi 4 models which support kinks centered at a continuous range of positions relative to the lattice in this paper we employ this method to obtain exceptional discretizations of the sine gordon equation i e exceptional frenkel kontorova chains we also use one dimensional maps to construct a discrete sine gordon equation supporting kinks which move with arbitrary velocities without emitting radiation

standard nearest neighbour discretizations of klein gordon models cannot preserve both energy and linear momentum we consider nonlinear klein gordon wave equations and illustrate that standard discretizations thereof involving nearest neighbours may preserve either standardly defined linear momentum or standardly defined total energy but not both this has a variety of intriguing implications for the non potential discretizations that preserve only the linear momentum such as the self accelerating or self decelerating motion of coherent structures such as discrete kinks in these nonlinear lattices

nonrelativistic conformal groups in this work a systematic study of finite dimensional nonrelativistic conformal groups is carried out under two complementary points of view first the conformal killing equation is solved to obtain a whole family of finite dimensional conformal algebras corresponding to each of the galilei and newton hooke kinematical groups some of their algebraic and geometrical properties are studied in a second step among the groups included in these families one can identify for example the contraction of the minkowski conformal group the analog for a nonrelativistic de sitter space or the nonextended schrodinger group

normal form for travelling kinks in discrete klein gordon lattices abstract we study travelling kinks in the spatial discretizations of the nonlinear klein gordon equation which include the discrete 4 lattice and the discrete sine gordon lattice the differential advance delay equation for travelling kinks is reduced to the normal form a scalar fourth order differential equation near the quadruple zero eigenvalue we show numerically the non existence of monotonic kinks heteroclinic orbits between adjacent equilibrium points in the fourth order equation making generic assumptions on the reduced fourth order equation we prove the persistence of bounded solutions heteroclinic connections between periodic solutions near adjacent equilibrium points in the full differential advance delay equation with the technique of centre manifold reduction existence of multiple kinks in the discrete sine gordon equation is discussed in connection to recent numerical results of aigner et al a a aigner a r champneys v m rothos a new barrier to the existence of moving kinks in frenkel kontorova lattices physica d 186 2003 148 170 and results of our normal form analysis

fisher zeros of the q state potts model in the complex temperature plane for nonzero external magnetic field the microcanonical transfer matrix is used to study the distribution of the fisher zeros of the qg2 potts models in the complex temperature plane with nonzero external magnetic field h q unlike the ising model for h q ensuremath ne 0 which has only a nonphysical critical point the fisher edge singularity the qg2 potts models have physical critical points for h q l0 as well as the fisher edge singularities for h q g0 for h q l0 the crossover of the fisher zeros of the q state potts model into those of the q ensuremath 1 state potts model is discussed and the critical line of the three state potts ferromagnet is determined for h q g0 we investigate the edge singularity for finite lattices and compare our results with the high field low temperature series expansion of enting for 3l ql 6 we find that the specific heat magnetization susceptibility and the density of zeros diverge at the fisher edge singularity with exponents ensuremath alpha e ensuremath beta e and ensuremath gamma e which satisfy the scaling law ensuremath alpha e 2 ensuremath beta e ensuremath gamma e 2

on a class of discretizations of hamiltonian nonlinear partial differential equations abstract we present a new class of discretizations of partial differential equations pdes that preserve a momentum like integral of the motion this results in an effective translational invariance for the dynamical problem and the absence of a peierls nabarro barrier that is usually present in discretizations of hamiltonian pdes a general method to construct such discretizations for any nonlinearity is given and the properties of the resulting differential difference equations are analyzed in a number of different cases for nonlinear klein gordon as well for nonlinear schrodinger type systems while for the former nonintegrability of the dynamical problem is evident in the latter case numerical evidence suggests that the behavior is close to the one of integrable systems we also show how static solutions of the equations can be constructed for these discretizations and discuss the similarities and differences of the method with previously reported ones

generalized partition function zeros of 1d spin models and their critical behavior at edge singularities here we study the partition function zeros of the one dimensional blume emery griffiths model close to their edge singularities the model contains four couplings h j k including the magnetic field h and the ising coupling j we assume that only one of the three couplings j k is complex and the magnetic field is real the generalized zeros zi tend to form continuous curves on the complex z plane in the thermodynamic limit the linear density at the edges ze diverges usually with z z ze and 1 2 however as in the case of complex magnetic fields yang lee edge singularity if we have a triple degeneracy of the transfer matrix eigenvalues a new critical behavior with 2 3 can appear as we prove here explicitly for the cases where either or k is complex our proof applies for a general three state spin model with short range interactions the fisher zeros complex j are more involved in practice we have not been able to find an explicit example with 2 3 as far as the other couplings h k are kept as real numbers our results are supported by numerical computations of zeros we show that it is absolutely necessary to have a non vanishing magnetic field for a new critical behavior the appearance of 2 3 at the edge closest to the positive real axis indicates its possible relevance for tricritical phenomena in higher dimensional spin models

complex q zeros of the partition function of the potts model with long range interactions abstract the zeros of the partition function of the ferromagnetic q state potts model with long range interactions in the complex q plane are studied in the mean field case while preliminary numerical results are reported for the finite 1 d chains with power law decaying interactions in both cases at any fixed temperature the zeros lie on the arc shaped contours which cross the positive real axis at the value for which the given temperature is transition temperature for finite number of spins the positive real axis is free of zeros which approach to it in the thermodynamic limit the convergence exponent of the zero closest to the positive real q axis is found to have the same value as the temperature critical exponent 1

kinematical lie algebras in 2 1 dimensions we classify kinematical lie algebras in dimension 2 1 this is approached via the classification of deformations of the static kinematical lie algebra in addition we determine which kinematical lie algebras admit invariant symmetric inner products

bifurcations of travelling wave solutions in the discrete nls equations abstract we study discrete nonlinear schrodinger nls equations which include the cubic nls lattice with on site interactions and the integrable ablowitz ladik lattice standing wave solutions are known to exist in the discrete nls equations outside of the finite spectral band we study travelling wave solutions which have nonlinear resonances with unbounded linear spectrum by using center manifold and normal form reductions we show that a continuous nls equation with the third order derivative term is a canonical normal form for the discrete nls equation near the zero dispersion limit bifurcations of travelling wave solutions near the zero dispersion limit are analyzed in the framework of the third order derivative nls equation we show that there exists a continuous two parameter family of single humped travelling wave solutions in the third order derivative nls equation when it is derived from the integrable ablowitz ladik lattice on the contrary there are no single humped solutions in the third order derivative nls equation when it is derived from the cubic nls equation with on site interactions nevertheless we show that there exists an infinite discrete set of one parameter families of double humped travelling wave solutions in the latter case our results are valid in the neighborhood of the zero dispersion point on the two parameter plane of travelling wave solutions

the partition function zeros for a potts model of helix coil transition with three site interactions abstract the partition function fisher zeros of the q state potts model with three site interactions on a zigzag ladder are studied by a transfer matrix approach this q state model is proposed as a description of helix coil transition in homopolymers the fisher zeros are exactly derived for arbitrary value of the system parameter q it is shown that there is only a quasi phase transition for all temperatures the dependence of the helix coil transition on solvent is analyzed using fisher zeros of the model the densities of the fisher zeros are singular at the edge singularity points and the critical exponent 1 2

the correlation length of the potts model at the first order transition point the authors consider the q state two dimensional potts model for q g i e in the first order phase transition regime following a scheme given by p martin 1991 the authors prove an identity between the spectra of the transfer matrices of the potts model and the transfer matrices connecting the diagonals of a 6 vertex model by using a bethe ansatz for the latter they obtain an exact expression for the correlation length of the potts model at the transition point

intertwining operators for l conformal galilei algebras and hierarchy of invariant equations the l conformal galilei algebra denoted by is a non semisimple lie algebra specified by a pair of parameters d l the algebra is regarded as a nonrelativistic analogue of the conformal algebra we derive hierarchies of partial differential equations which have invariance of the group generated by with a central extension as kinematical symmetry this is done by developing a representation theory such as verma modules singular vectors of and vector field representations for d 1 2

possible central extensions of non relativistic conformal algebras in 1 1 we investigate possibility of central extension for non relativistic conformal algebras in 1 1 dimension three different forms of charges can be suggested a trivial charge for temporal part of the algebra exists for all elements of l galilei algebra class in attempt to find a central extension as of conformal galilean algebra for other elements of the l galilei class possibility for such extension was excluded for integer and half integer elements of the class we can have an infinite extension of the generalized mass charge for the virasoro like extended algebra for finite algebras a regular charge inspired by schrodinger central extension is possible

yang lee zeros of the q state potts model on recursive lattices the yang lee zeros of the q state potts model on recursive lattices are studied for noninteger values of q considering one dimensional 1d lattice as a bethe lattice with coordination number equal to 2 the location of yang lee zeros of 1d ferromagnetic and antiferromagnetic potts models is completely analyzed in terms of neutral periodical points three different regimes for yang lee zeros are found for qg1 and 0lql1 an exact analytical formula for the equation of phase transition points is derived for the 1d case it is shown that yang lee zeros of the q state potts model on a bethe lattice are located on arcs of circles with the radius depending on q and temperature for qg1 complex magnetic field metastability regions are studied for the qg1 and 0lql1 cases the yang lee edge singularity exponents are calculated for both 1d and bethe lattice potts models the dynamics of metastability regions for different values of q is studied numerically

time reversal symmetry in dynamical systems a survey abstract in this paper we survey the topic of time reversal symmetry in dynamical systems we begin with a brief discussion of the position of time reversal symmetry in physics after defining time reversal symmetry as it applies to dynamical systems we then introduce a major theme of our survey namely the relation of time reversible dynamical sytems to equivariant and hamiltonian dynamical systems we follow with a survey of the state of the art on the theory of reversible dynamical systems including results on symmetric periodic orbits local bifurcation theory homoclinic orbits and renormalization and scaling some areas of physics and mathematics in which reversible dynamical systems arise are discussed in an appendix we provide an extensive bibliography on the topic of time reversal symmetry in dynamical systems

self organized criticality and thermodynamic formalism we develop a thermodynamic formalism for a dissipative version of the zhang model of self organized criticality where a parameter allows us to tune the local energy dissipation by constructing a suitable markov partition we define gibbs measures in the sense of sinai ruelle and bowen partition functions and topological pressure allowing the analysis of probability distributions of avalanches we discuss the infinite size limit in this setting in particular we show that a lee yang phenomenon occurs in the conservative case this suggests new connections to classical critical phenomena

trace formulas for the casimir operators of the unextended schrodinger algebra s n using the contraction of the centrally extended schrodinger algebra s n onto the lie algebra s n r in combination with the newton identities associated with the characteristic polynomial of a matrix we derive explicit expressions for the casimir operators of the unextended schrodinger algebra s n in terms of trace operators it is shown that these operators can be defined independently of the contraction from which a direct method for the computation of the s n invariants is deduced

continuum limit of lattice approximation schemes boundary layer perturbation theory problems are inherently singular however it is known that discretizing the problem by introducing a lattice may convert such problems into regular perturbation problems the singular nature of boundary layer problems is then relegated to and hidden in the continuum limit the subtle limit in which the lattice spacing tends to zero if the lattice is introduced cavalierly then extrapolating to zero lattice spacing gives a sequence of extrapolants that at first approaches the correct limit and then veers off thereby revealing the asymptotic nature of such problems however discretizing the problem following the procedures described here yields lattice approximations that have a smooth and regular continuum limit these ideas are illustrated by three nonlinear ordinary differential equations the cubic equation that describes instantons an oscillator equation having a quadratic nonlinearity and the blasius equation

one parameter localized traveling waves in nonlinear schrodinger lattices we address the existence of traveling single humped localized solutions in the spatially discrete nonlinear schr nls equation a mathematical technique is developed for analysis of persistence of these solutions from a certain limit in which the dispersion relation of linear waves contains a triple zero the technique is based on using the implicit function theorem for solution of an appropriate differential advance delay equation in exponentially weighted spaces the resulting melnikov calculation relies on a number of assumptions on the spectrum of the linearization around the pulse which are checked numerically we apply the technique to the so called salerno model and the translationally invariant discrete nls equation with a cubic nonlinearity we show that the traveling solutions terminate in the salerno model whereas they generally persist in the translationally invariant nls lattice as a one parameter family of solutions these results are found to be in a close correspondence with numerical approximations of traveling solutions with zero radiation tails analysis of persistence also predicts the spectral stability of the one parameter family of traveling solutions under time evolution of the discrete nls equation c 2007 elsevier b v all rights reserved

origin of multikinks in dispersive nonlinear systems we develop em the first analytical theory of multikinks for strongly em dispersive nonlinear systems considering the examples of the weakly discrete sine gordon model and the generalized frenkel kontorova model with a piecewise parabolic potential we reveal that there are no 2 pi kinks for this model but there exist em discrete sets of 2 pi n kinks for all n 1 we also show their bifurcation structure in driven damped systems

discrete klein gordon models with static kinks free of the peierls nabarro potential for the nonlinear klein gordon type models we describe a general method of discretization in which the static kink can be placed anywhere with respect to the lattice these discrete models are therefore free of the peierls nabarro potential previously reported models of this type are shown to belong to a wider class of models derived by means of the proposed method a relevant physical consequence of our findings is the existence of a wide class of discrete klein gordon models where slow kinks practically do not experience the action of the peierls nabarro potential such kinks are not trapped by the lattice and they can be accelerated by even weak external fields