on tests for normality the problem of deciding whether a sample of a random field was generated by a gaussian distribution is considered based on extensions of large deviation estimates due to m d donsker and s r s varadhan 1985 a test that is optimal in a generalized neyman pearson sense is proposed this test turns out to depend on properties of the entropy of gaussian processes and does not depend on cumulant computations

the modified extended tanh function method for solving burgers type equations abstract by means of the modified extended tanh function metf method the multiple travelling wave solutions of some different kinds of nonlinear partial differential equations are presented and implemented in a computer algebraic system solutions for the nonlinear equations such as one dimensional burgers kdv burgers coupled burgers and two dimensional burgers equations are obtained precisely and so the efficiency of the method can be demonstrated

a general central limit theorem for fkg systems a central limit theorem is given which is applicable to not necessarily monotonic functions of random variables satisfying the fkg inequalities one consequence is convergence of the block spin scaling limit for the magnetization and energy densities jointly to the infinite temperature fixed point of independent gaussian blocks for a large class of ising ferromagnets whenever the susceptibility is finite another consequence is a central limit theorem for the density of thesurface of the infinite cluster in percolation models

a variational formula for the free energy of an interacting many particle system we consider n bosons in a box in r d with volume n rho under the influence of a mutually repellent pair potential the particle density p is an element of 0 infinity is kept fixed our main result is the identification of the limiting free energy f beta p at positive temperature 1 beta in terms of an explicit variational formula for any fixed rho if beta is sufficiently small and for any fixed beta if rho is sufficiently small the thermodynamic equilibrium is described by the symmetrized trace of e beta h n where h n denotes the corresponding hamilton operator the well known feynman kac formula reformulates this trace in terms of n interacting brownian bridges due to the symmetrization the bridges are organized in an ensemble of cycles of various lengths the novelty of our approach is a description in terms of a marked poisson point process whose marks are the cycles this allows for an asymptotic analysis of the system via a large deviations analysis of the stationary empirical field the resulting variational formula ranges over random shift invariant marked point fields and optimizes the sum of the interaction and the relative entropy with respect to the reference process in our proof of the lower bound for the free energy we drop all interaction involving infinitely long cycles and their possible presence is signalled by a loss of mass of the finitely long cycles in the variational formula in the proof of the upper bound we only keep the mass on the finitely long cycles we expect that the precise relationship between these two bounds lies at the heart of bose einstein condensation and intend to analyze it further in future

a new note on exact complex travelling wave solutions for 2 1 dimensional b type kadomtsev petviashvili equation abstract exact solutions of the 2 1 dimensional kadomtsev petviashvili by zhang huiqun zhang a note on exact complex travelling wave solutions for 2 1 dimensional b type kadomtsev petviashvili equation appl math comput 216 2010 2771 2777 are considered to look for new types of exact solutions travelling wave solutions of equation zhang has used the g g expansion method we demonstrate that there is the general solution for the reduction by zhang from the 2 1 dimensional kadomtsev petviashvili equation and all solutions by zhang are found as partial cases from the general solution

the equivalence of ensembles for classical systems of particles for systems of particles in classical phase space with standard hamiltonian we consider spatially averaged microcanonical gibbs distributions in finite boxes we show that infinite volume limits along suitable subsequences exist and are grand canonical gibbs measures on the way we establish a variational formula for the thermodynamic entropy density as well as a variational characterization of grand canonical gibbs measures

the extended tanh method for new solitons solutions for many forms of the fifth order kdv equations abstract the extended tanh method is used to derive new solitons solutions for several forms of the fifth order nonlinear kdv equation the forms include the lax sawada kotera sk sawada kotera parker dye skpd kaup kupershmidt kk kaup kupershmidt parker dye kkpd and the ito equations the criteria established in a m wazwaz abundant solitons solutions for several forms of the fifth order kdv equation by using the tanh method appl math comput in press doi 10 1016 j amc 2006 02 047 to build up reliable relations between the parameters of the equation are confirmed by using this new approach entirely new bell shaped solitons are determined

quenched asymptotics of the ground state energy of random schrodinger operators with scaled gibbsian potentials this article describes the almost sure infinite volume asymptotics of the ground state energy of random schrodinger operators with scaled gibbsian potentials the random potential is obtained by distributing soft obstacles according to an infinite volume grand canonical tempered gibbs measure with a superstable pair interaction there is no restriction on the strength of the pair interaction it may be taken e g at a critical point the potential is scaled with the box size in a critical way i e the scale is determined by the typical size of large deviations in the gibbsian cloud the almost sure infinite volume asymptotics of the ground state energy is described in terms of two equivalent deterministic variational principles involving only thermodynamic quantities the qualitative behaviour of the ground state energy asymptotics is analysed depending on the dimension and on the holder exponents of the free energy density it is identified which cases lead to a phase transition of the asymptotic behaviour of the ground state energy

modified extended tanh function method and its applications to nonlinear equations new exact travelling wave solutions for the generalized shallow water wave equation the improved boussinesq equation and the coupled system for the approximate equations for water waves are found using a modified extended tanh function method the obtained results include rational periodic singular and solitary wave solutions

new solitary wave solutions to the modified forms of degasperis procesi and camassa holm equations abstract in this work we establish new solitary wave solutions to the modified forms of degasperis procesi and camassa holm equations unlike the standard degasperis procesi and camassa holm equations where multi peakon solutions arise the modified forms cause a change in the characteristic of these solutions and change it to bell shaped solitons periodic and complex solutions the extended tanh method the rational hyperbolic functions method and the rational exponential functions method are employed to reveal these new solutions

local microscopic behavior for 2d coulomb gases the study of two dimensional coulomb gases lies at the interface of statistical physics and non hermitian random matrix theory in this paper we give a large deviation principle ldp for the empirical fields obtained under the canonical gibbs measure by zooming around a point in the bulk of the equilibrium measure up to the finest averaging scale n 1 2 varepsilon the rate function is given by the sum of the renormalized energy of serfaty et al weighted by the inverse temperature and of the specific relative entropy we deduce a local law which quantifies the convergence of the empirical measures of the particles to the equilibrium measure up to the finest scale

green s function evaluation for three dimensional exponentially graded elasticity the numerical implementation of the green s function for an isotropic exponentially graded three dimensional elastic solid is reported the formulas for the nonsingular lq grading term rq in this green s function originally deduced by martin et al emph proc r soc lond a 458 1931 1947 2000 are quite complicated and a small error in one of the formulas is corrected the evaluation of the fundamental solution is tested by employing indirect boundary integral formulation using a galerkin approximation to solve several problems having analytic solutions the numerical results indicate that the green s function formulas and their evaluation are correct

the theory of large deviations from boltzmann s 1877 calculation to equilibrium macrostates in 2d turbulence abstract after presenting some basic ideas in the theory of large deviations this paper applies the theory to a number of problems in statistical mechanics these include deriving the form of the gibbs state for a discrete ideal gas describing probabilistically the phase transition in the curie weiss model of a ferromagnet and deriving variational formulas that describe the equilibrium macrostates in models of two dimensional turbulence a general approach to the large deviation analysis of models in statistical mechanics is also formulated

existence of gibbsian point processes with geometry dependent interactions we establish the existence of stationary gibbsian point processes for interactions that act on hyperedges between the points for example such interactions can depend on delaunay edges or triangles cliques of voronoi cells or clusters of k nearest neighbors the classical case of pair interactions is also included the basic tools are an entropy bound and stationarity

integration of singular enrichment functions in the generalized extended finite element method for three dimensional problems a mapping method is developed to integrate weak singularities which result from enrichment functions in the generalized extended finite element method the integration scheme is applicable to 2d and 3d problems including arbitrarily shaped triangles and tetrahedra implementation of the proposed scheme in existing codes is straightforward numerical examples for 2d and 3d problems demonstrate the accuracy and convergence properties of the technique copyright 2008 john wiley sons ltd

new solitary wave solutions to the kuramoto sivashinsky and the kawahara equations abstract in this work the kuramoto sivashinsky equation and the kawahara equation are studied the tanh method and the extended tanh method are used for analytic treatment for these two equations by means of these methods new solitary wave solutions are determined for each equation the two approaches are reliable and manageable

entropy for translation invariant random cluster measures we study translation invariant random cluster measures with techniques from large deviation theory and convex analysis in particular we prove a large deviation principle with rate function given by a specific entropy and a dobrushinlanfordruelle variational principle that characterizes translation invariant random cluster measures as the solutions of the variational equation for free energy consequences of these theorems include inequalities for edge and cluster densities of translationinvariant random cluster measures 1 introduction the random cluster model was introduced around 1972 by fortuin and kasteleyn 18 as a family of models that contains the bernoulli bond percolation model the ising model and the q state potts models as special cases it has developed into an important and very successful tool for studying the ising and potts models our paper focuses on the properties of the random cluster measures themselves our starting point is grimmett s 23 development of elements of a thermodynamic formalism for this model beginning with a definition of infinite volume random cluster measures in terms of a dlr dobrushinlanfordruelle equation just as for gibbsian systems natural next questions concern the validity of large deviation principles and variational characterizations of infinite volume measures these questions we answer in the present paper and derive some consequences here is a brief overview of the dlr approach of 23 the random cluster measures of interest live on the graph formed by putting edges between nearest neighbor vertices of the d dimensional hypercubic lattice d the edge that connects two vertices x and y that are l 1 distance one apart is

hydrodynamical limit for a hamiltonian system with weak noise starting from a general hamiltonian system with superstable pairwise potential we construct a stochastic dynamics by adding a noise term which exchanges the momenta of nearby particles we prolve that in the scaling limit the time conserved quantities energy momenta and density satisfy the euler equation of conservation laws up to a fixed timet provided that the euler equation has a smooth solution with a given initial data up to timet the strength of the noise term is chosen to be very small but nonvanishing so that it disappears in the scaling limit

boundary discretization based on the residual energy using the sgbem abstract the paper has as objective the estimation of the error in the structural analysis performed by using the displacement approach of the symmetric galerkin boundary element method sgbem and suggests a strategy able to reduce this error through an appropriate change of the boundary discretization the body characterized by a domain and a boundary is embedded inside a complementary unlimited domain bounded by a boundary in such new condition it is possible to perform a separate valuation of the strain energies in the two subdomains through the computation of the work defined generalized obtained as the product among nodal and weighted quantities on the actual boundary and on the complementary boundary in order to reduce the error in the analysis phases the scattered energy has been computed as generalized work in each boundary element of and an adequate node number has been introduced inside the boundary elements where this generalized work is higher this strategy made in a recursive way has shown effectiveness whether in the convergence proofs of some mechanical and kinematical quantities or in computing the percentage error obtained as ratio between the scattered work in and the total work both expressed in terms of generalized quantities

large deviations for the empirical field of a gibbs measure on applique le principe de contraction pour obtenir un principe de grande deviation pour la distribution des distributions empiriques on donne une description detaillee de la fonction de taux resultante

r local delaunay inhibition model unlike in the classical framework of gibbs point processes usually acting on the complete graph in the context of nearest neighbour gibbs point processes the nonnegativeness of the interaction functions do not ensure the local stability property this paper introduces domain wise but not pointwise inhibition stationary gibbs models based on some tailor made delaunay subgraphs all of them are subgraphs of the r local delaunay graph defined as the delaunay subgraph specifically not containing the edges of delaunay triangles with circumscribed circles of radii greater than some large positive real value r the usual relative compactness criterion for point processes needed for the existence result is directly derived from the ruelle bound of the correlation functions furthermore assuming only the nonnegativeness of the energy function we have managed to prove the existence of the existence of r local delaunay stationary gibbs states based on nonnegative interaction functions thanks to the use of the compactness of sublevel sets of the relative entropy

note on same result of different ansatz based on extended tanh function method for nonlinear models the same result of different ansatz based on extended tanh function method for nonlinear models is firstly reported as an example we obtain eleven kinds of variable separation solutions of variable coefficient boiti leon pempinelli system based on the extended tanh function method by considering three different ansatz namely positive power form ansatz positive and negative power symmetric ansatz and radical sign combined ansatz by careful analysis we find that these seemly independent variable separation solutions are essentially same from this perspective different ansatz are not really effective to construct so called new solutions therefore we should check carefully solutions obtained by the same method with different ansatz and avoid casually asserting these essentially same new solutions

complete equivalence of the gibbs ensembles for one dimensional markov systems we show the equivalence of the gibbs ensembles at the level of measures for one dimensional markov systems with arbitrary boundary conditions that is the limit of the microcanonical gibbs ensemble is a gibbs measure with an interaction depending on the microcanonical constraint in fact the usual microcanonical condition is replaced by the sharper constraint that all type frequencies of neighboring spins including the boundary spins are fixed when conditioning on a set of different frequencies of neighboring spins compatible with physical quantities like energy density we get the usual microcanonical ensemble we show that the limit is a gibbs measure for a nearest neighbor potential depending on the pair measure which maximizes the entropy on the given set of pair measures for this we show the large deviation property of the pair empirical measure for arbitrary boundary conditions we establish analogous results for finite range potentials

exact solutions to the two dimensional korteweg de vries burgers equation two methods are described for obtaining exact travelling monotone shock wave solutions to the two dimensional korteweg de vries burgers equation they are compared with two methods that have been reported recently by other authors

direct evaluation of hypersingular galerkin surface integrals a direct algorithm for evaluating hypersingular integrals arising in a three dimensional galerkin boundary integral analysis is presented the singular integrals are defined as limits to the boundary and by integrating two of the four dimensions analytically the coincident integral is shown to be divergent however the divergent terms can be explicitly calculated and shown to cancel with corresponding singularities in the adjacent edge integrals a single analytic integration is employed for the edge and vertex singular integrals this is sufficient to display the divergent term in the edge adjacent integral and to show that the vertex integral is finite by explicitly identifying the divergent quantities we can compute the hypersingular integral without recourse to stokes s theorem or the hadamard finite part the algorithms are developed in the context of a linear element approximation for the laplace equation but are expected to be generally applicable as an example the algorithms are applied to solve a thermal problem in an exponentially graded material

galton watson trees with vanishing martingale limit we show that an infinite galton watson tree conditioned on its martingale limit being smaller than varepsilon agrees up to generation k with a regular mu ary tree where mu is the essential minimum of the offspring distribution and the random variable k is strongly concentrated near an explicit deterministic function growing like a multiple of log 1 varepsilon more precisely we show that if mu ge 2 then with high probability as varepsilon downarrow 0 k takes exactly one or two values this shows in particular that the conditioned trees converge to the regular mu ary tree providing an example of entropic repulsion where the limit has vanishing entropy our proofs are based on recent results on the left tail behaviour of the martingale limit obtained by fleischmann and wachtel 11

the extended tanh method for abundant solitary wave solutions of nonlinear wave equations the extended tanh method is used to establish abundant solitary wave solutions of nonlinear wave equations the obtained solutions include solitons kinks and plane periodic solutions the study is an extension to the remarkable development by malfliet 1 the extended tanh method presents a wider applicability for handling nonlinear wave equations

boundary element solution of heat convection diffusion problems abstract a boundary element method is described in detail for the solution of two dimensional steady state convective heat diffusion problems in homogeneous and isotropic media with both linear and nonlinear boundary conditions through an exponential variable transformation the introduction of fundamental solutions and the use of green s theorem the problem is reduced to one involving values of temperature and or heat flux in the form of an integral only along the boundary the integral is solved numerically for three examples two of them have linear boundary conditions and their numerical results are compared with the corresponding analytical solutions the other has a nonlinear boundary condition due to heat radiation and an iterative procedure is applied to obtain the numerical solution the fictitious source formulation leading to the boundary element solution of the same problems is discussed as an alternative the extension of the method to formulate transient and or three dimensional convective heat diffusion problems is also described and the relevant fundamental solutions are given finally the exponential variable transformation is applied to construct a functional of variational principle which leads to developing a finite element formulation of the problems with a banded symmetric stiffness matrix

exact travelling wave solutions for the generalized nonlinear schrodinger gnls equation with a source by extended tanh coth sine cosine and exp function methods the capability of extended tanh coth sine cosine and exp function methods as alternative approaches to obtain the analytic solution of different types of applied differential equations in engineering mathematics has been revealed in this study the generalized nonlinear schrodinger gnls equation is solved by three different methods to obtain the single soliton solutions for the equation the extended tanh coth and sine cosine methods are used furthermore for this nonlinear evolution equation the exp function method is applied to derive various travelling wave solution results show that while the first two procedures easily provide a concise solution the exp function method provides a powerful mathematical means for solving nonlinear evolution equations in mathematical physics

large deviations and the maximum entropy principle for marked point random fields we establish large deviation principles for the stationary and the individual empirical fields of poisson and certain interacting random fields of marked point particles in d the underlying topologies are induced by a class of not necessarily bounded local functions and thus finer than the usual weak topologies our methods yield further that the limiting behaviour of conditional poisson distributions as well as certain distributions of gibbsian type is governed by the maximum entropy principle we also discuss various applications and examples

large deviations for gibbs random fields a large deviation principle for gibbs random fields on zd is proven and a corresponding large deviations proof of the gibbs variational formula is given a generalization of the lanford theory of large deviations is also obtained

self similarity of brownian motion and a large deviation principle for random fields on a binary tree using self similarity of brownian motion and its representation as a product measure on a binary tree we construct a random sequence of probability measures which converges to the distribution of the brownian bridge we establish a large deviation principle for random fields on a binary tree this leads to a class of probability measures with a certain self similarity property the same construction can be carried out forc 0 1 valued processes and we can describe for instance ac 0 1 valued ornstein uhlenbeck process as a large deviation of brownian sheet

symmetric weak form integral equation method for three dimensional fracture analysis a symmetric galerkin boundary element method is developed for the analysis of linearly elastic isotropic three dimensional solids containing fractures the formulation is based upon a weak form displacement integral equation and a weak form traction integral equation recently developed by li and mear 1997 these integral equations are only weakly singular and their validity requires only that the boundary displacement data be continuous hence allowing standard co elements to be employed as part of the numerical implementation a special crack tip element is developed which has a novel feature in that there exist degrees of freedom associated with the nodes at the crack front as a result a higher degree of approximation is achieved for the relevant displacement data on the crack and further the stress intensity factors are obtained directly in terms of the crack front nodal data various examples are treated for cracks in unbounded domains and for cracks in finite domains including both embedded and surface breaking cracks and it is demonstrated that highly accurate results can be achieved using relatively coarse meshes

entropy limit theorems and variational principles for disordered lattice systems we study infinite volume limits and gibbs states of disordered lattice systems with bounded and continuous potentials our main tools are a generalization of relative entropy for random reference measures and a large deviation theory for nonstationary independent processes we find that many familiar results of invariant potentials such as large deviation theorems variational principles and equivalence of ensembles continue to hold for disordered models with suitably modified statements

large deviations and the equivalence of ensembles for gibbsian particle systems with superstable interaction for gibbsian systems of particles inr d we investigate large deviations of the translation invariant empirical fields in increasing boxes the particle interaction is given by a superstable regular pair potential the large deviation principle is established for systems with free or periodic boundary conditions and under a stronger stability hypothesis on the potential for systems with tempered boundary conditions and for tempered infinite volume gibbs measures as a by product we obtain the gibbs variational formula for the pressure we also prove the asymptotic equivalence of microcanonical and grand canonical gibbs distributions and establish a variational expression for the thermodynamic entropy density

observations on the tanh coth expansion method for finding solutions to nonlinear evolution equations abstract the tanh coth expansion method for finding solitary travelling wave solutions to nonlinear evolution equations has been used extensively in the literature it is a natural extension to the basic tanh function expansion method which was developed in the 1990s it usually delivers three types of solution namely a tanh function expansion a coth function expansion and a tanh coth expansion it is known that for every tanh function expansion solution there is a corresponding coth function expansion solution it is shown that there is a tanh coth expansion solution that is merely a disguised version of the coth solution in many papers such tanh coth solutions are erroneously claimed to be new however other tanh coth solutions may be delivered that are genuinely new in the sense that they would not be delivered via the basic tanh function method similar remarks apply to tan cot and tan cot expansion solutions

on hypersingular surface integrals in the symmetric galerkin boundary element method application to heat conduction in exponentially graded materials a symmetric galerkin formulation and implementation for heat conduction in a three dimensional functionally graded material is presented the green s function of the graded problem in which the thermal conductivity varies exponentially in one co ordinate is used to develop a boundary only formulation without any domain discretization the main task is the evaluation of hypersingular and singular integrals which is carried out using a direct limit to the boundary approach however due to complexity of the green s function for graded materials the usual direct limit procedures have to be modified incorporating taylor expansions to obtain expressions that can be integrated analytically several test examples are provided to verify the numerical implementation the results of test calculations are in good agreement with exact solutions and corresponding finite element method simulations copyright 2004 john wiley sons ltd

the tanh coth method for solitons and kink solutions for nonlinear parabolic equations abstract the tanh coth method is used to derive solitons and kink solutions for some of the well known nonlinear parabolic partial differential equations the equations include the fisher equation newell whithead equation allen cahn equation fitzhugh nagumo equation fisher s equation and the burgers fisher equation the new tanh coth approach provides abundant solitons and kink solutions in addition to the existing ones the power of this manageable method is confirmed

exact solutions for the nonlinear schrodinger equation with variable coefficients using the generalized extended tanh function the sine cosine and the exp function methods abstract in this article we find the exact traveling wave solutions of the generalized nonlinear schrodinger gnls equation with variable coefficients using three methods via the generalized extended tanh function method the sine cosine method and the exp function method the main objective of this article is to compare the efficiency of these methods by delivering the exact traveling wave solutions of the proposed nonlinear equation

large deviations and maximum entropy principle for interacting random fields on mathbb z d we present a new approach to the principle of large deviations for the empirical field of a gibbsian random field on the integer lattice zd this approach has two main features first we can replace the traditional weak topology by the finer topology of convergence of cylinder probabilities and thus obtain estimates which are finer and more widely applicable second we obtain as an immediate consequence a limit theorem for conditional distributions under conditions on the empirical field the limits being those predicted by the maximum entropy principle this result implies a general version of the equivalence of gibbs ensembles stating that every microcanonical limiting state is a grand canonical equilibrium state we also prove a converse to the last statement and discuss some applications 0 introduction as is well known the study of the asymptotic probabilities of large fluctuations of time averages or space averages away from the mean is based on two fundamental principles the principle of large deviations and the maximum entropy principle the former provides the exact rate of exponential decay of the fluctuation probabilities whereas the latter predicts the limiting conditional distribution under the condition that the fluctuations are large it is obvious that these principles are intimately related in this paper we investigate these principles in the case of interacting random fields on the integer lattice 7zd the setup is the following first we let e 4 be any measurable space we shall assume throughout that e a is standard borel but we shall avoid making any explicit topological assumptions on e so we do not assume that e is polish next we let s zd be the d dimensional integer lattice and q f e gas the associated product space in lattice models of statistical mechanics e is called the state space or single spin space and q f the configuration space we let j s f denote the set of all probability

microcanonical distributions for lattice gases in this article a large deviation principle cf theorem 1 3 for the empirical distribution functional is applied to prove a rather general version of boltzmann s principle cf theorem 3 5 for models with shift invariant finite range potentials the final section contains an application of these considerations to the two dimensional ising model at sub critical temperature

a galerkin symmetric boundary element method in elasticity formulation and implementation a symmetric boundary element method based on a weighted residual galerkin approach for elastoplastic analysis is revisited and its computer implementation for two dimensional homogeneous problems is described

a note on new travelling wave solutions to the ostrovsky equation in a recent paper by yasar e yasar new travelling wave solutions to the ostro vsky equation appl math comput 216 2010 3191 3194 new travelling wave solutions to the transformed reduced ostrovsky equation are presented in this note it is shown that some of these solutions are disguised versions of known solutions

a note on travelling wave solutions to lax s seventh order kdv equation ganji and abdollahzadeh d d ganji m abdollahzadeh appl math comput 206 2008 438 444 derived three supposedly new travelling wave solutions to lax s seventh order kdv equation each solution was obtained by a different method it is shown that any two of the solutions may be obtained trivially from the remaining solution furthermore it is noted that one of the solutions has been known for many years

the simple boundary element method for multiple cracks in functionally graded media governed by potential theory a three dimensional galerkin approach the simple boundary element method consists of recycling existing codes for homogeneous media to solve problems in non homogeneous media while maintaining a purely boundary only formulation within this scope this paper presents a simple galerkin boundary element method for multiple cracks in problems governed by potential theory in functionally graded media steady state heat conduction is investigated for thermal conductivity varying either parabolically exponentially or trigonometrically in one or more co ordinates a three dimensional implementation which merges the dual boundary integral equation technique with the galerkin approach is presented special emphasis is given to the treatment of crack surfaces and boundary conditions the test examples simulated with the present method are verified with finite element results using graded finite elements the numerical examples demonstrate the accuracy and efficiency of the present method especially when multiple interacting cracks are involved copyright 2005 john wiley sons ltd

analytical integrations in 2d bem elasticity in the context of two dimensional linear elasticity this paper presents the closed form of the integrals that arise from both the standard collocation boundary element method and the symmetric galerkin boundary elementmethod adopting polynomial shape functions of arbitrary degree on straight elements finite part of hadamard cauchy principal values and lebesgue integrals are computed analytically working in a local coordinate system for the symmetric galerkin boundary element method a study on the singularity of the external integral is conducted and the outer weakly singular integral is analytically performed numerical tests are presented as a validation of the obtained results

large deviation principle for empirical fields of log and riesz gases we study a system of n particles with logarithmic coulomb or riesz pairwise interactions confined by an external potential we examine a microscopic quantity the tagged empirical field for which we prove a large deviation principle at speed n the rate function is the sum of an entropy term the specific relative entropy and an energy term the renormalized energy introduced in previous works coupled by the temperature we deduce a variational property of the sine beta processes which arise in random matrix theory we also give a next to leading order expansion of the free energy of the system proving the existence of the thermodynamic limit

a note on new kink shaped solutions and periodic wave solutions for the 2 1 dimensional sine gordon equation exact solutions of the nizhnik novikov veselov equation by li new kink shaped solutions and periodic wave solutions for the 2 1 dimensional sine gordon equation appl math comput 215 2009 3777 3781 are analyzed we have observed that fourteen solutions by li from 30 do not satisfy the equation the other 16 exact solutions by li can be found from the general solutions of the well known solution of the equation for the weierstrass elliptic function

the tanh coth method for new compactons and solitons solutions for the k n n and the k n 1 n 1 equations abstract the nonlinear k n n and the k n 1 n 1 equations are analytically studied the tanh coth method the rational hyperbolic functions method and the rational exponential function method are applied for this analytic study we show that these equations exhibit new compactons solitons and periodic solutions the change of the physical structure of the solutions is caused by variation of the exponents and the coefficients of the derivatives

large deviation principles for euclidean functionals and other nearly additive processes we prove a large deviation principle for a process indexed by cubes of the multidimensional integer lattice or euclidean space under approximate additivity and regularity hypotheses the rate function is the convex dual of the limiting logarithmic moment generating function in some applications the rate function can be expressed in terms of relative entropy the general result applies to processes in euclidean combinatorial optimization statistical mechanics and computational geometry examples include the length of the minimal tour the traveling salesman problem the length of the minimal matching graph the length of the minimal spanning tree the length of the k nearest neighbors graph and the free energy of a short range spin glass model

entropic repulsion of the lattice free field consider the massless free field on thed dimensional lattice d d 3 that is the centered gaussian field on open image in new window with covariances given by the green function of the simple random walk on d we show that the probability that all the spins are positive in a box of volumen d decays exponentially at a rate of ordernd 2 logn and compute explicitly the corresponding constant in terms of the capacity of the unit cube the result is extended to a class of transient random walks with transition functions in the domain of the normal and stable law

large deviations for ℤ d actions we establish large deviations bounds for translation invariant gibbs measures of multidimensional subshifts of finite type this generalizes fo and partially c o and b where only full shifts were considered our framework includes in particular the hard core lattice gas models which are outside of the scope of fo c o and b

analytical integrations of hypersingular kernel in 3d bem problems abstract for 3d symmetric galerkin boundary element method some results on the analytical integration of the hypersingular kernel in potential problems are presented here adopting linear shape functions inner integrations are performed both for the finite part of hadamard and for lebesgue integrals working in a local coordinate system a study on the singularity of the external integral is finally conducted

the meshless galerkin boundary node method for stokes problems in three dimensions the galerkin boundary node method gbnm is a boundary only meshless method that combines an equivalent variational formulation of boundary integral equations for governing equations and the moving least squares mls approximations for generating the trial and test functions in this approach boundary conditions can be implemented directly and easily despite of the fact that the mls shape functions lack the delta function property besides the resulting formulation inherits the symmetry and positive definiteness of the variational problems the gbnm is developed in this paper for solving three dimensional stationary incompressible stokes flows in primitive variables the numerical scheme is based on variational formulations for the first kind integral equations which are valid for both interior and exterior problems simultaneously a rigorous error analysis and convergence study of the method for both the velocity and the pressure is presented in sobolev spaces the capability of the method is also illustrated and assessed through some selected numerical examples copyright 2011 john wiley sons ltd

phase transition in continuum potts models we establish phase transitions for a class of continuum multi type particle systems with finite range repulsive pair interaction between particles of different type this proves an old conjecture of lebowitz and lieb a phase transition still occurs when we allow a background pair interaction between all particles which is superstable and has sufficiently short range of repulsion our approach involves a random cluster representation analogous to the fortuin kasteleyn representation of the potts model in the course of our argument we establish the existence of a percolation transition for gibbsian particle systems with random edges between the particles and also give an alternative proof for the existence of gibbs measures with supperstable interaction

hypersingular kernel integration in 3d galerkin boundary element method we consider cauchy singular and hypersingular boundary integral equations associated with 3d potential problems defined on polygonal domains whose solutions are approximated with a galerkin boundary element method related to a given triangulation of the boundary in particular for constant and linear shape functions the most frequently used basis functions we give explicit results of the analytical inner integrations and suggest suitable quadrature schemes to evaluate the outer integrals required to form the galerkin matrix elements these numerical indications are given after an analysis of the singularities arising in the whole integration process which is valid also for shape functions of higher degrees

a note on the uniqueness result for the inverse henderson problem the inverse henderson problem of statistical mechanics is the theoretical foundation for many bottom up coarse graining techniques for the numerical simulation of complex soft matter physics this inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles roughly stated it asks for the interaction potential given the equilibrium pair correlation function of the system in 1974 henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system here we provide a rigorous proof of a slightly more general version of the latter statement using georgii s variant of the gibbs variational principle the inverse henderson problem of statistical mechanics is the theoretical foundation for many bottom up coarse graining techniques for the numerical simulation of complex soft matter physics this inverse problem concerns classical particles in continuous space which interact according to a pair potential depending on the distance of the particles roughly stated it asks for the interaction potential given the equilibrium pair correlation function of the system in 1974 henderson proved that this potential is uniquely determined in a canonical ensemble and he claimed the same result for the thermodynamical limit of the physical system here we provide a rigorous proof of a slightly more general version of the latter statement using georgii s variant of the gibbs variational principle

the simple boundary element method for transient heat conduction in functionally graded materials abstract this paper presents a simple boundary element method for transient heat conduction in functionally graded materials which leads to a boundary only formulation without any domain discretization for a broad range of functional material variation quadratic exponential and trigonometric of thermal conductivity and specific heat the non homogeneous problem can be transformed into the standard homogeneous diffusion problem a three dimensional boundary element implementation using the laplace transform approach and the galerkin approximation is presented the time dependence is restored by numerically inverting the laplace transform by means of the stehfest algorithm a number of numerical examples demonstrate the efficiency of the method the results of the test examples are in excellent agreement with analytical solutions and finite element simulation results

darcy s flow with variable permeability a boundary integral solution a boundary integral equation method biem for darcy s flow with spatially varied permeability is developed the formulation requires that green s function be found for each given permeability variation for a few permeability functions in one and two dimensions which can be used to fit field permeability data closed form green s functions are obtained numerical examples are solved and verified

the tanh coth and the sine cosine methods for kinks solitons and periodic solutions for the pochhammer chree equations abstract in this paper the tanh coth method and the sine cosine method are used for a reliable treatment of the pochhammer chree equations which include a variety of models travelling wave solutions of distinct structures namely bell shaped solitons kink shaped solitons and periodic solutions are formally derived the two methods demonstrate power reliability and efficiency

crack tip interpolation revisited it is well known that the near tip displacement eld on a crack surface can be represented in a power series in the variable p r where r is the distance to the tip it is shown herein that the coecients of the linear terms on the two sides of the crack are equal equivalently the linear term in the crack opening displacement vanishes the proof is a completely general argument valid for an arbitrary e g multiple nonplanar crack conguration and applied boundary conditions moreover the argument holds for other equations such as laplace a limit procedure for calculating the surface stress in the form of a hypersingular boundary integral equation is employed to enforce the boundary conditions along the crack faces evaluation of the nite surface stress and examination of potentially singular terms lead to the result inclusion of this constraint in numerical calculations should result in a more accurate approximation of the displacement and stress elds in the tip region and thus a more accurate evaluation of stress intensity factors