unconventional scaling theory for domain growth in the alternating bond glauber ising chain the domain growth after a quench is controlled by an exponent which generally has very broad universal properties the authors investigate the alternating bond ising chain with glauber dynamics and find that its growth exponent is universal even though the dynamical critical exponent z is non universal they show that usual scaling theory can be reformulated to account for the above findings

adm pade technique for the nonlinear lattice equations adm pade technique is a combination of adomian decomposition method adm and pade approximants we solve two nonlinear lattice equations using the technique which gives the approximate solution with higher accuracy and faster convergence rate than using adm alone bell shaped solitary solution of belov chaltikian bc lattice and kink shaped solitary solution of the nonlinear self dual network equations sdnes are presented comparisons are made between approximate solutions and exact solutions to illustrate the validity and the great potential of the technique

rational group decision making a random field ising model at t 0 abstract a modified version of a finite random field ising ferromagnetic model in an external magnetic field at zero temperature is presented to describe group decision making fields may have a non zero average a postulate of minimum inter individual conflicts is assumed interactions then produce a group polarization along one very choice which is however randomly selected a small external social pressure is shown to have a drastic effect on the polarization individual bias related to personal backgrounds cultural values and past experiences are introduced via quenched local competing fields they are shown to be instrumental in generating a larger spectrum of collective new choices beyond initial ones in particular compromise is found to results from the existence of individual competing bias conflict is shown to weaken group polarization the model yields new psychosociological insights about consensus and compromise in groups

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

dynamical critical behaviours of the ising spin chain swendsen wang and wolff algorithms we study the zero temperature ising chain evolving according to the swendsen wang dynamics we determine analytically the domain length distribution and various historical characteristics e g the density of unreacted domains is shown to scale with the average domain length as l with 3 2 for the q state potts model 1 q 1 we also compute the domain length distribution for the ising chain endowed with the zero temperature wolff dynamics

domain and hull enclosed area distributions in two dimensional coarsening abstract we obtain the exact distribution of the areas enclosed by domain boundaries hulls during the coarsening dynamics of a two dimensional nonconserved scalar field we prove that the number of hulls per unit area that enclose an area greater than a has the form n h a t 2 c a t where c 1 8 3 this result is also a demonstration of the validity of the dynamical scaling hypothesis in this system we also show that domain areas regions of aligned spins have a similar distribution

simple model for multiple choice collective decision making we describe a simple model of heterogeneous interacting agents making decisions between n 2 discrete choices for a special class of interactions our model is the mean field description of random field potts like models and is effectively solved by finding the extrema of the average energy e per agent in these cases by studying the propagation of decision changes via avalanches we argue that macroscopic dynamics is well captured by a gradient flow along e we focus on the permutation symmetric case where all n choices are on average the same and spontaneous symmetry breaking ssb arises purely from cooperative social interactions as examples we show that bimodal heterogeneity naturally provides a mechanism for the spontaneous formation of hierarchies between decisions and that ssb is a preferred instability to discontinuous phase transitions between two symmetric points beyond the mean field limit exponentially many stable equilibria emerge when we place this model on a graph of finite mean degree we conclude with speculation on decision making with persistent collective oscillations throughout the paper we emphasize analogies between methods of solution to our model and common intuition from diverse areas of physics including statistical physics and electromagnetism

coarsening in the q state potts model and the ising model with globally conserved magnetization we study the nonequilibrium dynamics of the q state potts model following a quench from the high temperature disordered phase to zero temperature the time dependent two point correlation functions of the order parameter field satisfy dynamic scaling with a length scale l t t 1 2 in particular the autocorrelation function decays as l t q we illustrate these properties by solving exactly the kinetic potts model in d 1 we then analyze a langevin equation of an appropriate field theory to compute these correlation functions for general q and d we establish a correspondence between the two point correlations of the q state potts model and those of a kinetic ising model evolving with a fixed magnetization 2 q 1 the dynamics of this ising model is solved exactly in the large q limit and in the limit of a large number of components n for the order parameter for general q and in any dimension we introduce a gaussian closure approximation and calculate within this approximation the scaling functions and the exponent q these are in good agreement with the direct numerical simulations of the potts model as well as the kinetic ising model with fixed magnetization we also discuss the existing and possible experimental realizations of these models

solitary waves of the regularized long wave equation abstract a finite element solution of the regularised long wave equation based on galerkin s method using cubic splines as element shape functions is set up a linear stability analysis shows the scheme to be unconditionally stable test problems including the migration and interaction of solitary waves are used to validate the method which is found to be accurate and efficient the three invariants of the motion are evaluated to determine the conservation properties of the algorithm the temporal evolution of a maxwellian initial pulse is then studied

statistical description of contact interacting brownian walkers on the line the distribution of interval lengths between brownian walkers on the line is investigated the walkers are independent until collision at collision the left walker disappears and the right walker survives with probability p this problem arises in the context of diffusion limited reactions and also in the scaling limit of the voter model a systematic expansion in correlation between neighbor intervals gives a series of approximations of increasing accuracy for the probability density functions of interval lengths the first approximation beyond mere statistical independence between successive intervals already gives excellent results as established by comparison with direct numerical simulations

solitary waves of the equal width wave equation a numerical solution of the equal width wave equation based on galerkin s method using cubic b spline finite elements is used to simulate the migration and interaction of solitary waves the interaction of two solitary waves is seen to cause the creation of a source for solitary waves usually these are of small magnitude but when the amplitudes of the two interacting waves are equal and opposite the source produces trains of solitary waves whose amplitudes are of the same order as those of the initiating waves the three invariants of the motion are evaluated to determine the conservation properties of the system finally the temporal evolution of a maxwellian initial pulse is studied for small ut uux uxxt 0 only positive waves are formed and the behaviour mimics that of the kdv and filw equations for larger values of d both positive and negative solitary waves are generated

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

scaling exponent for coarsening in a 1d q state system an exponent which characterises non equilibrium coarsening processes is calculated in a deterministic solvable model of coarsening for a 1d q state system we study how the fraction of sites p which have never changed their state scale with the characteristic domain length is defined by we propose a new model of coarsening that prevents correlations from developing between domains thereby ensuring tractability and an exact result for any q

application of the sinc method to a dynamic elasto plastic problem this paper presents the application of sinc bases to simulate numerically the dynamic behavior of a one dimensional elastoplastic problem the numerical methods that are traditionally employed to solve elastoplastic problems include finite difference finite element and spectral methods however more recently biorthogonal wavelet bases have been used to study the dynamic response of a uniaxial elasto plastic rod giovanni f naldi karsten urban paolo venini a wavelet galerkin method for elastoplasticity problems report 181 rwth aachen igpm and math modelling and scient computing vol 10 2000 in this paper the sinc galerkin method is used to solve the straight elasto plastic rod problem due to their exponential convergence rates and their need for a relatively fewer nodal points sinc based methods can significantly outperform traditional numerical methods j lund k l bowers sinc methods for quadrature and differential equations siam philadelphia 1992 however the potential of sinc based methods for solving elastoplasticity problems has not yet been explored the aim of this paper is to demonstrate the possible application of sinc methods through the numerical investigation of the unsteady one dimensional elastic plastic rod problem

statistical mechanics model for the emergence of consensus the statistical properties of pairwise majority voting over s alternatives are analyzed in an infinite random population we first compute the probability that the majority is transitive i e that if it prefers a to b to c then it prefers a to c and then study the case of an interacting population this is described by a constrained multicomponent random field ising model whose ferromagnetic phase describes the emergence of a strong transitive majority we derive the phase diagram which is characterized by a tricritical point and show that contrary to intuition it may be more likely for an interacting population to reach consensus on a number s of alternatives when s increases this effect is due to the constraint imposed by transitivity on voting behavior indeed if agents are allowed to express nontransitive votes the agents interaction may decrease considerably the probability of a transitive majority

exact exponent for the number of persistent spins in the zero temperature dynamics of the one dimensional potts model for the zero temperature glauber dynamics of theq state potts model the fractionr q t of spins which never flip up to timet decays like a power lawr q t t q when the initial condition is random by mapping the problem onto an exactly soluble one species coagulation model a a a or alternatively by transforming the problem into a free fermion model we obtain the exact expression of q for all values ofq the exponent q is in general irrational 3 0 53795082 4 0 63151575 with the exception ofq 2 andq for which 2 3 8 and 1

model of cluster growth and phase separation exact results in one dimension we present exact results for a lattice model of cluster growth in one dimension the growth mechanism involves interface hopping and pairwise annihilation supplemented by spontaneous creation of the stable phase 1 regions by overturning the unstable phase 1 spins with probabilityp for cluster coarsening at phase coexistence p 0 the conventional structure factor scaling applies in this limit our model falls in the class of diffusion limited reactions a a inert the 1 cluster size grows diffusively t and the two point correlation function obeys scaling however forp 0 i e for the dynamics of formation of stable phase from unstable phase we find that structure factor scaling breaks down the length scale associated with the size of the growing 1 clusters reflects only the short distance properties of the two point correlations

autocorrelation functions for phase separation in ternary mixtures we present numerical and analytical results for the autocorrelation functions which characterize domain growth in ternary mixtures the numerical results are obtained from monte carlo simulations of the spin 1 blume emery griffiths model with spin exchange kinetics further we model the autocorrelation functions using an approach based on the continuous time random walk formalism the aging property of these functions is related to the time dependence of the domain size distribution our analytical results are found to be in good agreement with the numerical data

stable spins in the zero temperature spinodal decomposition of 2d potts models we present the results of zero temperature monte carlo simulations of the q state potts model on a square lattice with either four or eight neighbors and for the triangular lattice with six neighbors in agreement with previous works we observe that the domain growth process gets blocked for the nearest neighbor square lattice when q is large enough whereas for the eight neighbor square lattice and for the triangular lattice no blocking is observed our simulations indicate that the number of spins which never flipped from the beginning of the simulation up to time t follows a power law as a function of the energy even in the case of blocking the exponent of this power law varies from less than 1 2 for the ising case q 2 to 2 for q o0 and seems to be universal the effect of blocking on this exponent is invisible at least up to q 7

exponents appearing in the zero temperature dynamics of the 1d potts model for the glauber dynamics of the one dimensional q state potts model at zero temperature the fraction of spins which have never flipped up to time t decreases as t theta q where the exponent theta q varies continuously with q the calculation of the q dependence of this exponent can be reduced to the study of a simple reaction diffusion model using finite size scaling this allows one to obtain accurate estimates of b q for all values of q one can also show that for 1 1 epsilon the expansion of theta y is given by theta 1 2 pi epsilon o epsilon 2

solitary wave solutions for the general kdv equation by adomian decomposition method in recent publications chaos solitons fractals 12 2001 2283 int j appl math 3 4 2000 361 we have dealt with the numerical solutions of the korteweg de vries kdv and modified korteweg de vries mkdv equations we extend this study to a more general nonlinear equation which is the general korteweg de vries gkdv equation in which the previous studies is a special case of it the method applied here is adomian decomposition method which has been developed by george adomian solving frontier problems of physics the decomposition method kluwer academic publishers boston ma 1994 numerical examples are tested to illustrate the pertinent feature of the proposed algorithm

linearly implicit approximate factorization exponential methods for multi dimensional reaction diffusion equations abstract linearly implicit approximate factorization methods are used to reduce the solution of multi dimensional reaction diffusion equations to a sequence of two point boundary value problems in ordinary differential equations which are solved analytically in a piecewise manner it is shown that depending on the allocation of the transient diffusion and reaction terms to the second order ordinary differential operators several families of piecewise exponential methods can be obtained when only diffusion is included a quadratic analytical solution is obtained whereas if transient and diffusion diffusion and reaction and transient diffusion and reaction terms are included piecewise exponential methods result it is shown that exponential methods that only account for reaction and diffusion in the differential operator may result in ill conditioned systems of algebraic equation whereas if diffusion transient and reaction are included ill conditioning is avoided if the time step is sufficiently small it is also shown that the most robust exponential method is that that accounts for transient and diffusion terms in the differential operator and this method provides solutions in good accord with those of a linearly implicit approximate factorization technique which employs a three point second order accurate discretization of the diffusion terms it is also shown that a hybrid exponential method that solves the transient reaction and diffusion terms at odd time levels and the transient and diffusion terms at even time levels also provides very accurate solutions

analytical approximations and pade approximants for volterra s population model in this paper an analytic approximation for volterra s model for population growth of a species in a closed system is presented the nonlinear integro differential model includes an integral term that characterizes accumulated toxicity on the species in addition to the terms of the logistic equation the series solution method and the decomposition method are implemented independently to the model and to a related ode the pade approximants that often show superior performance over series approximations are effectively used in the analysis to capture the essential behavior of the population u t of identical individuals

multistable binary decision making on networks we propose a simple model for a binary decision making process on a graph motivated by modeling social decision making with cooperative individuals the model is similar to a random field ising model or fiber bundle model but with key differences on heterogeneous networks for many types of disorder and interactions between the nodes we predict discontinuous phase transitions with mean field theory which are largely independent of network structure we show how these phase transitions can also be understood by studying microscopic avalanches and describe how network structure enhances fluctuations in the distribution of avalanches we suggest theoretically the existence of a glassy spectrum of equilibria associated with a typical phase even on infinite graphs so long as the first moment of the degree distribution is finite this behavior implies that the model is robust against noise below a certain scale and also that phase transitions can switch from discontinuous to continuous on networks with too few edges numerical simulations suggest that our theory is accurate

phase transitions in the coloring of random graphs we consider the problem of coloring the vertices of a large sparse random graph with a given number of colors so that no adjacent vertices have the same color using the cavity method we present a detailed and systematic analytical study of the space of proper colorings solutions we show that for a fixed number of colors and as the average vertex degree number of constraints increases the set of solutions undergoes several phase transitions similar to those observed in the mean field theory of glasses first at the clustering transition the entropically dominant part of the phase space decomposes into an exponential number of pure states so that beyond this transition a uniform sampling of solutions becomes hard afterward the space of solutions condenses over a finite number of the largest states and consequently the total entropy of solutions becomes smaller than the annealed one another transition takes place when in all the entropically dominant states a finite fraction of nodes freezes so that each of these nodes is allowed a single color in all the solutions inside the state eventually above the coloring threshold no more solutions are available

universal scaling function for domain growth in the glauber ising chain the equal time correlation function is calculated at t 0 for the one dimensional ising model with glauber dynamics random initial conditions appropriate to a sudden quench from non zero temperature are imposed averaging over initial conditions yields the scaling form c r t f r2 t the scaling function is given by f x integral 01 dy pi y 1 y 1 2 exp x 4y and is universal i e independent of the probability distribution for the initial conditions

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

solitary wave solutions of the improved kdv equation by vim the variational iteration method vim is applied to solve numerically the improved korteweg de vries equation ikdv a correction function is constructed with a general lagrange multiplier that can be identified optimally via the variational theory this technique provides a sequence of functions with easily computable components that converge rapidly to the exact solution of the ikdv equation propagation of single interaction of two and three solitary waves and also birth of solitons have been discussed three invariants of motion have been evaluated to determine the conservation properties of the problem this procedure is promising for solving other nonlinear equations

comparison study between restrictive taylor restrictive pade approximations and adomian decomposition method for the solitary wave solution of the general kdv equation some accurate finite difference sophisticated methods for solving initial boundary value problem for partial differential equations gives its exact solution with certain values of the mesh sizes of space and time as done h n a ismail on the convergence of the restrictive pade approximation to the exact solutions of ibvp of parabolic and hyperbolic types appl math comput accepted h n a ismail g s e salem on the convergence of the restrictive taylor approximation to the exact solutions of ibvp for parabolic hyperbolic convection diffusion and kdv equations appl math comput in press the restrictive pade and restrictive taylor approximations are very promising methods in recent publications h n a ismail k r raslan g s e salem solitary wave solutions for the general kdv equation by adomian decomposition method 28th international conference for statistics and computer science and its applications cairo appl math comput june accepted a m wazwaz construction of solitary wave solutions and rational solutions for the kdv equation by adomian decomposition method chaos soliton fract 12 2001 2283 2293 a m wazwaz solitary wave solutions for the modified kdv equation by adomian decomposition method int j appl math 3 4 2000 361 368 we have dealt with the numerical solutions of the korteweg de vries kdv and modified korteweg de vries mkdv equations we extend this study to a more general nonlinear equation which is the general korteweg de vries gkdv equation the method applied here is adomian decomposition method which has been developed by george adomian solving frontier problems of physics the decomposition method kluwer academic publishers boston ma 1994 restrictive taylor and restrictive pade approximations numerical examples are tested to illustrate the pertinent feature of the proposed algorithms

a new sinc galerkin method for convection diffusion equations with mixed boundary conditions abstract a new sinc galerkin method is developed for approximating the solution of convection diffusion equations with mixed boundary conditions on half infinite intervals the method avoids differentiation of the coefficients of the pde rendering it appropriate as a forward solver in an inverse coefficient problem the method has the advantage that no functions are appended to the sinc basis in the discretization an error analysis is included and it is shown that the error in the approximate solution is bounded in the infinity norm by the norm of the inverse of the coefficient matrix multiplied by a factor that decays exponentially with the size of the system we demonstrate the exponential convergence of the method on several test problems

the modified decomposition method and pade approximants for solving the thomas fermi equation in this paper we propose a new approach to develop a nonperturbative approximate solution for the thomas fermi equation this approach rests on the recently developed modification of the adomian decomposition method the initial slope of the thomas fermi potential y 0 is computed by converting the obtained series solution into several diagonal pade approximants the proposed scheme is presented in a general way so that it can be used in applied sciences

non trivial exponents in the zero temperature dynamics of the 1d ising and potts models we consider the glauber dynamics of the q state potts model in one dimension at zero temperature starting with a random initial configuration we measure the density r t of spins which have never flipped from the beginning of the simulation until time t we find that for large t the density r t has a power law decay left r t sim t theta right where the exponent theta varies with q our simulations lead to theta simeq 37 for q 2 theta simeq 53 for q 3 and theta longrightarrow 1 as q longrightarrow infty

finite size scaling of the time dependent structure factor in the one dimensional glauber model abstract we study the time dependent structure factor of the one dimensional glauber model upon instantaneous cooling results obtained earlier by reiss mazenko and widom and bray are linked together next finite size scaling in the limit of zero temperature long times small wave vectors and large systems is established the scaling function is compared with numerical simulation results obtained by vinals and jasnow in the case of a two dimensional glauber model quenched into the region of phase separation

numerical methods for nonlinear second order hyperbolic partial differential equations ii rothe s techniques for 1 d problems abstract two families of rothe s methods that are based on the discretization of the time variable and keeping the spatial one continuous for the solution of second order hyperbolic equations with damping and nonlinear source terms are presented the first family is based on time integration and results in a volterra integro differential equation which upon approximating certain time integrals can be written as an ordinary differential equation in space upon discretizing the spatial derivatives by means of finite difference formula this family results in nonlinear algebraic equations which contain exponential terms that depend on the time step and its accuracy is shown to be lower than that of an explicit second order accurate discretization in both space and time of second order hyperbolic equations the second family of methods is based on the discretization of the time derivatives and time linearization and results in linear ordinary differential equations in space upon freezing the coefficients of these equations one can integrate analytically the resulting linear ordinary differential equations to obtain piecewise exponential solutions which are continuous in space and three point finite difference equations which depend exponentially on the time step spatial grid size and the diffusion relaxation damping and reaction times the finite difference equations are shown to result in non diagonally dominant matrices unless the time step is smaller than the characteristic relaxation diffusion damping and reaction times to avoid this problem two rothe s techniques that do not account for the jacobian of the reaction terms in the ordinary differential operator are developed and it is shown that the rothe s techniques belonging to the second family are as accurate as the linearly implicit methods presented in part i provided that the relaxation time is smaller than the critical time and the solution does not oscillate in space when the relaxation time is greater than the critical one rothe s methods have been found to be less accurate than the finite difference techniques of part i the rothe s techniques belonging to the second family are generalized to systems of nonlinear second order hyperbolic equations and mixed systems of parabolic and second order hyperbolic partial differential equations

on the sinc galerkin method for triharmonic boundary value problems abstract a numerical scheme is developed to provide an approximate solution to the triharmonic boundary value problem based on the sinc inner product approximations a direct discretization of the triharmonic operator 3 reduces the problem to a generalized sylvester equation numerical examples illustrate the pertinent features of the sinc galerkin method where very accurate results are obtained even when singularities occur at the boundaries