duality relations for asymmetric exclusion processes we derive duality relations for a class ofu q su 2 symmetric stochastic processes including among others the asymmetric exclusion process in one dimension like the known duality relations for symmetric hopping processes these relations express certainm point correlation functions inn particle systems n m in terms of sums of correlation functions of the same system but with onlym particles for the totally asymmetric case we obtain exact expressions for some boundary density correlation functions the dynamical exponent for these correlators isz 2 which is different from the dynamical exponent for bulk density correlations which is known to bez 3 2

iterated function system and ruelle operator abstract we consider a generalized iterated function system where the weights are variable functions by using the ruelle operator and a dynamical system consideration we prove that if the system is contractive and the weights are strictly positive functions and satisfy the dini condition then there exists a unique eigenmeasure corresponding to the ruelle operator on the attractor if in addition the maps are conformal and satisfy the open set condition then we prove that they satisfy the strong open set condition and by using this we can give a description of the l p scaling spectrum and the multifractal structure of the eigenmeasure the work extends some results of proc london math soc 73 1996 105 154 adv appl math 19 1997 486 513 j statist phys 86 1997 233 275 indiana univ math j 42 1993 367 411

higher order accurate time step integration algorithms by post integration techniques in this paper a framework to construct higher order accurate time step integration algorithms based on the post integration techniques is presented the prescribed initial conditions are naturally incorporated in the formulations and can be strongly or weakly enforced the algorithmic parameters are chosen such that unconditionally a stable higher order accurate time step integration algorithms with controllable numerical dissipation can be constructed for linear problems besides it is shown that the order of accuracy for non linear problems is maintained through the relationship between the present formulation and the runge kutta method the second order differential equations are also considered numerical examples are given to illustrate the validity of the present formulation copyright 2001 john wiley sons ltd

vector valued ruelle operators abstract the scalar ruelle operators have been extensively studied both in dynamical systems and iterated function systems and the ruelle perron frobenius theorem for scalar ruelle operator was well known we mainly set up a vector analogue theory in this paper

high order hierarchical a and l stable integration methods numerical integration of stiff first order systems of differential equations is considered it is shown how a c continuous polynomial time discretization in conjunction with a weighted residual method can be used to derive methods corresponding to the diagonal and first subdiagonal pade approximants in this manner a stable schemes of order 2k and l stable schemes of order 2k l are obtained at least for k 4 the methods are hierarchical in the sense that a scheme with a given accuracy embraces the equations of all lower order methods that have the same stability type

effect of detachments in asymmetric simple exclusion processes asymmetric simple exclusion processes are important for understanding low dimensional multi particle dynamic phenomena the effect of irreversible detachments of particles on dynamics of asymmetric simple exclusion processes is studied using analytical and computer simulation techniques in the simplest model where particles can only detach from a single site in the bulk of the system a theory is presented and used to calculate explicitly phase diagrams and particle density profiles the complexity of the phase behavior is discussed in terms of a recent domain wall theory for driven lattice systems the theoretical results qualitatively and quantitatively agree with computer monte carlo simulations

shape functions for mixed p version finite elements in the time domain abstract the advantages of mixed formulations are well known in that they simplify the form of the governing equations and can lead to potentially significant savings in computational effort for given accuracy likewise the p version of the finite element method is known to offer savings in computational effort for some problems in this paper shape functions for a mixed p version finite element formulation in the time domain are developed these shape functions produce a high percentage of zeros in certain coefficient matrices the mixed formulation in time used here is based on a weak form of hamilton s extended principle the present formulation allows for accurate and efficient solution of time domain problems the accuracy and power of this formulation are shown for initial value problems such as time marching and for directly obtaining the periodic response of linear systems the method is shown to yield a family of accurate unconditionally stable algorithms for initial value problems based on a simple linear oscillator

shocks in the asymmetric simple exclusion process in a discrete time update we study the dynamics of a shock distribution as an initial state for a one dimensional asymmetric simple exclusion process with sub lattice parallel update the time evolution of the shock distribution can be calculated exactly if the two initial densities of the shock satisfy a special relation which results from its uq su 2 symmetry the resulting distribution is a linear combination of shock measures the motion of the shock position can be interpreted as if it would perform a biased discrete time random walk with hopping rules related to that of a single particle in the exclusion process the shock diffusion constant and the shock velocity are calculated exactly we obtain simple expressions for these quantities in terms of the shock densities and currents which we argue to be valid for any pair of shock densities

weighting parameters for unconditionally stable higher order accurate time step integration algorithms part 2 second order equations in this paper unconditionally stable higher order accurate time step integration algorithms suitable for linear second order differential equations based on the weighted residual method are presented the second order equations are manipulated directly as in part 1 of this paper instead of specifying the weighting functions the weighting parameters are used to control the algorithm characteristics the algorithms are at least nth order accurate if the numerical solution for displacement is approximated by a polynomial of degree n 1 with n undetermined coefficients by choosing the weighting parameters carefully the order of accuracy can be improved the generalized pade approximations for the second order equations are considered the ultimate spectral radius is an algorithmic parameter by relating the approximate solutions to the equivalent formulations presented in part 1 of this paper the required weighting parameters are found explicitly any set of linearly independent functions can be used to construct the corresponding weighting functions from the weighting parameters the stabilizing weighting functions for the weighted residual method are found explicitly to ensure higher order accuracy in the general solution the accuracy of the particular solution due to excitation is also examined copyright 1999 john wiley sons ltd

vector valued submarkov operators and recurrent iterated function systems abstract we consider a recurrent ifs with place dependent transition weights by using the quasi compact operator theory and the spectral theory of positive operators the eigen problem of the given system is studied this is the vector analogue of fan and lau s results 1999 j math anal appl 231 319 344

a time integration algorithm for linear transient analysis based on the reproducing kernel method in this paper a new algorithm based on the reproducing kernel method is presented for linear transient analysis using very large time steps in the conventional time integration methods the required accuracy is always achieved by either decreasing the size of time steps or increasing the order of approximations the proposed method however does not require a restriction on the size of the time step the required approximating functions for integration of governing equations are determined using the concept of reproduction of the solution within each time step a recurrence relationship is obtained through solving the governing equation by the point collocation based reproducing kernel method within the time step in collocation points the values of external excitation can be obtained either through the approximation between the values at the beginning and the end of each time step or assigning the exact values of the external force hence one advantage of this new method is the independency of the sampling rates of external excitation from the size of the time step the proposed method is applied for solving first and second order differential equations and advantages of the method are illustrated through a number of numerical examples

computational algorithms for transient analysis the burden of weight and consequences towards formalizing discrete numerically assigned dna algorithmic markers wp family abstract different from the way we have been looking in the past at developments encompassing modal type and a wide class of step by step time stepping approaches for transient and dynamic field problems and significantly different from the way these have been developed and described in standard text books over the years this paper outlines the theoretical ideas and basis towards providing a generalized methodology and formulations leading to integral and a wide class of integration operators for the resulting solution of these transient equation systems it is herein postulated that integral operators and a wide class of integration operators pertain to and emanate from the same family with the burden which is being carried by a virtual field or weighted function field specifically introduced for the time discretization is strictly enacted in a mathematically consistent manner so as to first permit obtaining the adjoint operator of the original semi discretized equation system subsequently the selection or burden carried by the virtual or weighted function fields originally introduced to facilitate the time discretization process determines the formal development and outcome of exact integral operators approximate integral operators and a wide class of integration operators thus the present developments not only serve as a prelude towards the formal developments for exact integral operators but also demonstrate that the resulting approximate integral operators and a wide class of integration operators and known methods are simply subsets of the generalizations of a standardized w p family and emanate from the principles presented herein the burden of weight and the resulting consequences towards subsequently enabling a formal basis for the selection of discrete numerically assigned dna algorimmic markers to particularly identitfy a wide class of algorithms is described for transient field problems and dynamic field problems respectively

vector valued ruelle operator with weakly contractive ifs abstract the vector valued ruelle operator defined by contractive iterated function systems ifs was discussed by the author y l ye vector valued ruelle operator j math anal appl 299 2004 341 356 in this paper we consider vector valued ruelle operators defined by weakly contractive ifs and a vector valued analogue of the ruelle perron frobenius theorem for the scalar ruelle operator is set up our theorem gives a sufficient condition for the vector valued ruelle operator to be quasi compact under this sufficient condition we prove that the rate of convergence of the iterated operators is exponential

exact domain wall theory for deterministic tasep with parallel update we develop an exact domain wall theory dwt for the totally asymmetric exclusion process tasep with parallel update and deterministic p 1 bulk motion remarkably the dynamics of this system can be described by the motion of a domain wall not only on the coarse grained level but also exactly on the microscopic scale for arbitrary system size all properties of this tasep not only stationary but also time dependent are shown to follow from the solution of a bivariate master equation whose variables are not only the position but also the velocity of the domain wall in the continuum limit this exactly soluble model then allows us to perform a first principle derivation of a fokker planck equation for the position of the wall

weighting parameters for time step integration algorithms with predetermined coefficients in this paper the effect of using the predetermined coefficients in constructing time step integration algorithms is investigated both first and second order equations are considered the approximate solution is assumed to be in a form of polynomial in the time domain it can be related to the truncated taylor s series expansion of the exact solution therefore some of the coefficients can be predetermined from the known initial conditions if there are m predetermined coefficients and r unknown coefficients in the approximate solution the unknowns can be solved by the weighted residual method the weighting parameter method is used to investigate the resultant algorithm characteristics it is shown that the formulation is consistent with a minimum order of accuracy m r the maximum order of accuracy achievable is m 2r unconditionally stable algorithms exist if m r for first order equations and m 1 r for second order equations hence the dahlquist s theorem is generalized algorithms equivalent to the pade approximations and unconditionally stable algorithms equivalent to the generalized pade approximations are constructed the corresponding weighting parameters and weighting functions for the pade and generalized pade approximations are given explicitly copyright 2000 john wiley sons ltd

time dependent correlation functions in a one dimensional asymmetric exclusion process we study a one dimensional anisotropic exclusion process describing particles injected at the origin moving to the right on a chain of l sites and being removed at the right boundary we construct the steady state and compute the density profile exact expressions for all equal time n point density correlation functions and the time dependent two point function in the steady state as functions of the injection and absorption rates we determine the phase diagram of the model and compare our results with predictions from dynamical scaling and discuss some conjectures for other exclusion models

propagation dispersion equation a propagation dispersion equation is derived for the first passage distribution function of a particle moving on a substrate with time delays the equation is obtained as the hydrodynamic limit of the first visit equation an exact microscopic finite difference equation describing the motion of a particle on a lattice whose sites operate as time delayers the propagation dispersion equation should be contrasted with the advection diffusion equation or the classical fokker planck equation as it describes a dispersion process in time instead of diffusion in space with a drift expressed by a propagation speed with non zero bounded values the temporal dispersion coefficient is shown to exhibit a form analogous to taylor s dispersivity physical systems where the propagation dispersion equation applies are discussed

stochastic models of interacting systems interacting particle systems is by now a mature area of probability theory but one that is still very active we begin this paper by explaining how models from this area arise in fields such as physics and biology we turn then to a discussion of both older and more recent results about them concentrating on contact processes voter models and exclusion processes these processes are among the most studied in the field and have the virtue of relative simplicity in their description which permits us to address the fundamental issues about their behavior without dealing with the extra complications that models from specific areas of application would require

exact shock measures and steady state selection in a driven diffusive system with two conserved densities we study driven 1d lattice gas models with two types of particles and nearest neighbor hopping we find the most general case when there is a shock solution with a product measure which has a density profile of a step function for both densities the position of the shock performs a biased random walk we calculate the microscopic hopping rates of the shock we also construct the hydrodynamic limit of the model and solve the resulting hyperbolic system of conservation laws in case of open boundaries the selected steady state is given in terms of the boundary densities

exact shock profile for the asep with sublattice parallel update we analytically study the one dimensional asymmetric simple exclusion process with open boundaries under sublattice parallel updating scheme we investigate the stationary state properties of this model conditioned on finding a given particle number in the system recent numerical investigations have shown that the model possesses three different phases in this case using a matrix product method we calculate both the exact canonical partition function and also density profiles of the particles in each phase application of the yang lee theory reveals that the model undergoes two second order phase transitions at critical points these results confirm the correctness of our previous numerical studies

matrix product states of three families of one dimensional interacting particle systems abstract the steady states of three families of one dimensional non equilibrium models with open boundaries first proposed in n j phys 5 2003 145 1 are studied using a matrix product formalism it is shown that their associated quadratic algebras have two dimensional representations provided that the transition rates lie on specific manifolds of parameters exact expressions for the correlation functions of each model have also been obtained we have also studied the steady state properties of one of these models first introduced in j phys a math gen a 36 2003 74 with more details by introducing a canonical ensemble we calculate the canonical partition function of this model exactly using the yang lee theory of phase transitions we spot a second order phase transition from a power law to a jammed phase the density profile of particles in each phase has also been studied a simple generalization of this model in which both the left and the right boundaries are open has also been introduced it is shown that double shock structures may evolve in the system under certain conditions

formulation and analysis of variational methods for time integration of linear elastodynamics abstract a general framework for variational formulations of linear elastodynamics is introduced variational formulations which originate from the principle of minimum potential energy the hellinger reissner principle and the hu washizu principle are considered they are characterized by the weak enforcement of the velocity displacement relation and of the initial displacement and velocity special cases are obtained by a priori enforcement of these conditions the time integration algorithms obtained discretizing in the space and time domains are studied with reference to accuracy stability and high frequency behaviour it is shown that some of these algorithms are very competitive with respect to classical finite difference methods the only drawback of variational methods seems to be the large size of the set of simultaneous equations which they generate effective solution procedures aiming at minimizing both the storage and the computational effort will be discussed in a separate paper

complex time step newmark methods with controllable numerical dissipation in this paper unconditionally stable higher order accurate time step integration algorithms with controllable numerical dissipation are presented the algorithms are based on the newmark method with complex time steps the ultimate spectral radius the sub step locations j and the weighting factors j are the algorithmic parameters for an algorithm that is 2n 1 th order accurate the sub step locations which may be complex are shown to be the roots of an nth degree polynomial the polynomial is given explicitly in terms of n and the weighting factors are then obtained by solving a system of n simultaneous equations it is further shown that the order of accuracy is increased by one for the non dissipative algorithms with 1 the stability properties of the present algorithms are studied it is shown that if the ultimate spectral radius is set between 1 and 1 the eigenvalues of the numerical amplification matrix are complex with magnitude less than or equal to unity the algorithms are therefore unconditionally c stable when the ultimate spectral radius is set to 0 or 1 the algorithms are found to be equivalent to the first sub diagonal and diagonal pade approximations respectively the present algorithms are more general as the numerical dissipation is controllable and are very suitable for parallel computers the accuracy of the excitation responses is found to be enhanced by the present complex time step procedure to maintain high order accuracy the excitation may need some modifications 1998 john wiley sons ltd

temporal evolution of product shock measures in the totally asymmetric simple exclusion process with sublattice parallel update it is known that when the steady state of a one dimensional multispecies system which evolves via a random sequential updating mechanism is written in terms of a linear combination of bernoulli shock measures with random walk dynamics it can be equivalently expressed as a matrix product state in this case the quadratic algebra of the system always has a two dimensional matrix representation our investigations show that this equivalence exists at least for the systems with deterministic sublattice parallel update in this paper we consider the totally asymmetric simple exclusion process on a finite lattice with open boundaries and sublattice parallel update as an example

a unified set of single step asymptotic annihilation algorithms for structural dynamics when solving the equations of structural dynamics using direct time integration meth6ds algorithmic damping is useful in controlling spurious high frequency oscillations ideally an algorithm should possess asymptotic annihilation of the highfrequency response i e spurious oscillations in the high frequencies are eliminated after one time step in this paper a new class of asymptotic annihilation algorithms for structural dynamics is presented that possesses little numerical dissipation in the low frequency regime the algorithms are based upon using finite elements in time the displacement and velocity fields are interpolated independently using time discontinuous functions the equations of motion displacement velocity compatibility and the time continuity of displacement and velocity are satisfied weakly asymptotic annihilation is achieved by choosing the displacement and velocity fields to be of equal order algorithms of any desired order of temporal accuracy can be obtained by appropriate choice of the finite element interpolations in time an analysis of the proposed class of algorithms is given proving the asymptotic annihilation property and the spectral equivalence of the algorithms to the upper diagonal of the pad6 approximation table results from finite difference analyses are presented showing the spectral behavior of the algorithms as well as their dissipation and dispersion properties in the low frequency regime

time finite element methods for structural dynamics summary time finite element methods are developed for the equations of structural dynamics the approach employs the time discontinuous galerkin method and incorporates stabilizing terms having least squares form these enable a general convergence theorem to be proved in a norm stronger than the energy norm results are presented from finite difference analyses of the time discontinuous galerkin and least squares methods with various temporal interpolations and commonly used finite difference methods for structural dynamics these results show that for particular interpolations the time finite element method exhibits improved accuracy and stability