phase ordering from off critical quenches and the measurement of the dynamic exponent lambda the ordering dynamics of a system with a nonconserved order parameter is considered following a quench into the ordered phase from high temperature the correlation of the order parameter field with its initial condition or more generally the correlation between the fields at different times involves the dynamic exponent lambda a non trivial exponent associated with the t 0 fixed point that drives phase ordering it is shown that lambda can be determined from the growth of the mean order parameter m t in a system which has a small but non zero mean order parameter m0 at t 0 since m t approximately m0l t lambda where l t approximately t1 2 is the characteristic length scale at time t the role of a weak external field h is also considered for h not 0 the growth of m t involves two power law terms m t approximately h at3 btlambda 2 for m0 0 with x 1 2 or 1 for a scalar or vector order parameter respectively the results are illustrated by the exact solution of the o n model at large n for general values of m0 and h

dynamic correlations in domain growth a 1 n expansion the authors consider the dynamics of the n component ginzburg landau model with nonconserved order parameter model a following a quench from a high temperature equilibrium state to zero temperature the two time correlation function of the order parameter field is found in the 1 n expansion to have the asymptotic scaling form ck t t t d2 t t lambda 2 f k2t k2t for t t with f 0 0 constant the form of the new exponent lambda which is a non trivial function of n and d was given explicitly to o 1 n in a recent letter the purpose of this study is to present a more detailed account of the calculation leading to the o 1 n form for lambda they also examine the role of thermal fluctuations in the ordered phase and the effect of long range initial correlations on the ordering process

growth of order in vector spin systems scaling and universality the growth of order in vector spin systems with nonconserved order parameter model a is considered following an instantaneous quench from infinite to zero temperature the results of numerical simulations in spatial dimension d 2 and spin dimension 2n5 are presented for n4 a scaling regime where a characteristic length scale l t emerges is entered for sufficiently long times with l t t12 the autocorrelation function a t decays with time as a t t d lambda 2 and the exponent lambda n agrees well with the predictions of the 1 n expansion the cases n 2 and 3 are more complicated due to the non trivial role played by topological singularities i e vortices n 2 and polyakov solitons n 3 for n4 universal amplitudes and scaling functions characterizing the energy relaxation and the equal time correlation function are identified it is argued that for d3 where an ordered phase exists at low temperature such universal quantities characterize the entire ordered phase

exact evaluation of the collapse phase boundary for two dimensional directed polymers the phase boundary of the collapsed phase for a directed polymer on a square lattice in the presence of an attractive wall and monomer monomer interactions is calculated exactly using transfer matrix techniques the position of the multicritical point is also identified

stochastic dynamics of invasion and fixation we study evolutionary game dynamics in finite populations we analyze an evolutionary process which we call pairwise comparison for which we adopt the ubiquitous fermi distribution function from statistical mechanics the inverse temperature in this process controls the intensity of selection leading to a unified framework for evolutionary dynamics at all intensities of selection from random drift to imitation dynamics we derive a simple closed formula that determines the feasibility of cooperation in finite populations whenever cooperation is modeled in terms of any symmetric two person game in contrast with previous results the present formula is valid at all intensities of selection and for any initial condition we investigate the evolutionary dynamics of cooperators in finite populations and study the interplay between intensity of selection and the remnants of interior fixed points in infinite populations as a function of a given initial number of cooperators showing how this interplay strongly affects the approach to fixation of a given trait in finite populations leading to counterintuitive results at different intensities of selection

transfer matrix study of the adsorption of a flexible self avoiding polymer chain in two dimensions the authors model the polymer as a self avoiding walk on a semi infinite square lattice with an energy contribution in from each step along the lattice boundary the critical adsorption temperature ta and the ordinary and special surface exponents of the walk above and at the adsorption temperature respectively are estimated with transfer matrix finite size scaling methods for the adsorption temperature they obtain exp in kta 2 041 or 0 002 and for the crossover and susceptibility exponents of the special transition phi sp 0 501 or 0 003 and gamma 1sp 1 454 or 0 004

gray isometries for finite chain rings and a nonlinear ternary 36 3 sup 12 15 code using tensor product constructions for the first order generalized reed muller codes we extend the well established concept of the gray isometry between z sub 4 spl delta sub l and z sub 2 sup 2 spl delta sub h to the context of finite chain rings our approach covers previous results by carlet see ibid vol 44 p 1543 7 1998 constantinescu see probl pered inform vol 33 no 3 p 22 8 1997 and ph d dissertation tech univ munchen munchen germany 1995 nechaev et al see proc ieee int symp information theory and its applications p 31 4 1996 and overlaps with heise et al see proc acct 6 pskov russia p 123 9 1998 and honold et al see proc acct 6 pskov russia p 135 41 1998 applying the gray isometry on z sub 9 we obtain a previously unknown nonlinear ternary 36 3 sup 12 15 code

z p sup k 1 linear codes we characterize codes over z sub p which are the gray images of 1 p sup k cyclic codes or cyclic codes over z p sup k l k spl ges 1 a necessary and sufficient condition for the gray image of a z p sup 2 linear 1 p cyclic code to be linear is given in many cases this yields an explicit description of the gray image of a linear 1 p cyclic code over z p sup 2 of length relatively prime to p linear cyclic codes over z p sup 2 whose gray images are linear cyclic codes over z sub p have been characterized some generalizations of these results to the case of z p sup k 1 where k spl ges 2 are also obtained

phase ordering dynamics of a vector order parameter mazenko s theory of phase ordering dynamics is generalized to an n component nonconserved vector order parameter the scaling functions for the equal time and two time correlation functions are calculated as well as the exponent characterizing the decay of autocorrelations the equal time correlation function is numerically quite close to that recently calculated by bray and puri 1991 and by toyoki 1991 and exhibits the same power law tail in its fourier transform the time dependent structure factor

domain growth properties of a two dimensional kinetic ising model the domain growth properties of the two dimensional single spin flip kinetic ising model with a metropolis type transition function and checkerboard updating are investigated numerically with quenches from the high temperature phase to temperatures in the ordered phase and to tc measuring the structure factor s 0 t varies as t2x and the autocorrelation function a t varies as t lambda x as a function of time the effect of deterministic dynamics at t 0 with x 1 0 is followed throughout the ordered phase at t tc tnot approximately tc crossover from x 1 0 to x 0 5 is shown to occur with increasing time and even at t tc the scaling exponents are still discernibly dependent on time lambda however is found to be unaffected in the whole temperature range

new exponent for dynamic correlations in domain growth the dynamics of the n component ginzburg landau model with non conserved order parameter model a are considered following a quench to zero temperature the correlation function of the order parameter field is found in the 1 n expansion to have the asymptotic scaling form ck t t t d2 t t lambda 2 f k2t k2t for t t with f 0 0 constant the new exponent lambda is calculated to o 1 n for general space dimension d and has a non trivial dependence on n and d

the embedding e0 and the spectrum dependent r matrix for q f4 the explicit embedding forms of e0 for the minimal representations of the quantum f4 e6 and e7 are obtained in this paper in terms of jimbo s method the spectrum dependent r matrices both trigonometric and rational for those representations are computed

repeated root cyclic codes in the theory of cyclic codes it is common practice to require that n q 1 where n is the word length and f sub q is the alphabet it is shown that the even weight subcodes of the shortened binary hamming codes form a sequence of repeated root cyclic codes that are optimal in nearly all other cases one does not find good cyclic codes by dropping the usual restriction that n and q must be relatively prime this statement is based on an analysis for lengths up to 100 a theorem shows why this was to be expected but it also leads to low complexity decoding methods this is an advantage especially for the codes that are not much worse than corresponding codes of odd length it is demonstrated that a binary cyclic code of length 2n n odd can be obtained from two cyclic codes of length n by the well known mod u mod u v mod construction this leads to an infinite sequence of optimal cyclic codes with distance 4 furthermore it is shown that low complexity decoding methods can be used for these codes the structure theorem generalizes to other characteristics and to other lengths some comparisons of the methods using earlier examples are given

rare event statistics in reaction diffusion systems we present an efficient method to calculate probabilities of large deviations from the typical behavior rare events in reaction diffusion systems this method is based on a semiclassical treatment of an underlying quantum hamiltonian encoding the system s evolution to this end we formulate the corresponding canonical dynamical system and investigate its phase portrait this method is presented for a number of pedagogical examples

dynamic correlations in phase ordering the 1 n expansion reconsidered the ordering dynamics of a system with a non conserved order parameter is considered following a quench into the ordered phase from high temperature newman and bray 1990 have set up an expansion in powers of 1 n for the o n model to obtain correlation functions and the two time exponent lambda but their calculation contains a simplifying assumption which is incorrect tight upper and lower bounds for lambda are obtained as a function of the space dimension d these bounds exclude the result of newman and bray although the dependence of lambda on d is qualitatively very similar comparison with simulations shows that the first order 1 n calculation does not agree with numerical results as well as previously thought

the z sub 4 linearity of kerdock preparata goethals and related codes certain notorious nonlinear binary codes contain more codewords than any known linear code these include the codes constructed by nordstrom robinson 1967 kerdock 1972 preparata 1968 goethals 1974 and delsarte goethals 1975 it is shown here that all these codes can be very simply constructed as binary images under the gray map of linear codes over z sub 4 the integers mod 4 although this requires a slight modification of the preparata and goethals codes the construction implies that all these binary codes are distance invariant duality in the z sub 4 domain implies that the binary images have dual weight distributions the kerdock and preparata codes are duals over z sub 4 and the nordstrom robinson code is self dual which explains why their weight distributions are dual to each other the kerdock and preparata codes are z sub 4 analogues of first order reed muller and extended hamming codes respectively all these codes are extended cyclic codes over z sub 4 which greatly simplifies encoding and decoding an algebraic hard decision decoding algorithm is given for the preparata code and a hadamard transform soft decision decoding algorithm for the i kerdock code binary first and second order reed muller codes are also linear over z sub 4 but extended hamming codes of length n spl ges 32 and the golay code are not using z sub 4 linearity a new family of distance regular graphs are constructed on the cosets of the preparata code

binary images of cyclic codes over z sub 4 we determine all linear cyclic codes over z sub 4 of odd length whose gray images are linear codes or equivalently whose nechaev gray 1989 image are linear cyclic codes or are linear cyclic codes

non equilibrium dynamics of the ising model for t less than equal totc the growth of order in ising models with nonconserved order parameter is considered for quenches to final temperatures tf 0 and tf tc the results of numerical simulations in spatial dimension d 2 are presented in all cases a scaling regime is entered for sufficiently long times where the characteristic length scale is the domain size l t approximately t12 for tf 0 and the nonequilibrium correlation length xi t approximately t1z for tf tc the equal time correlation function has the expected scaling forms f r l t and r d 2 eta fc r xi t for tf 0 and tc respectively the scaling function fc x has interesting short distance behaviour which is elucidated using scaling arguments and by in and 1 n expansions the t 0 scaling function f x depends on whether the spin correlations present in the initial conditions are of long or short range as does the exponent which describes the decay of the autocorrelation function a t si t si o approximately l t results for a quench from the equilibrium critical state to tf 0 are consistent with theoretical predictions

universality class for domain growth in random magnets a 2d ising model with random ferromagnetic bonds is studied by monte carlo simulation following a quench from t infinity to t tc the domain size grows as l t approximately in t to x at late times the data are consistent with the theoretical prediction chi 4 the exponent defined by si 0 si t approximately l t and the scaling functions for the spatial correlations are very close to those of the pure system suggesting that pure and random systems belong to the same universality class

coevolutionary dynamics from finite to infinite populations traditionally frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes only recently have stochastic processes been introduced to study evolutionary dynamics in finite populations however the relationship between deterministic and stochastic approaches remained unclear here we solve this problem by explicitly considering large populations in particular we identify different microscopic stochastic processes that lead to the standard or the adjusted replicator dynamics moreover differences on the individual level can lead to qualitatively different dynamics in asymmetric conflicts and depending on the population size can even invert the direction of the evolutionary process

some ternary and quaternary codes and associated sphere packings tables of good ternary and quaternary codes are presented and they are used in the construction of dense sphere packings results include 1 tables of the best ternary and quaternary constacyclic codes including cyclic codes up to block length 50 2 a class of optimal n 2 codes over gf q 3 the u v w mod 2u v mod u construction a new ternary code construction technique that can be used to construct the ternary reed muller codes and others and 4 tables of linear ternary and quaternary codes obtained by modifying and combining various codes here and in the literature packings are generated in even dimensions up to 100 using these codes and a sphere packing construction in dimensions 36 and 60 new record densities appear to have been achieved

negacyclic and cyclic codes over z sub 4 the negashift spl nu of z sub 4 sup n is defined as the permutation of z sub 4 sup n such that spl nu a sub 0 a sub 1 spl middot spl middot spl middot a sub i spl middot spl middot spl middot a sub n 1 a sub n 1 a sub 0 spl middot spl middot spl middot a sub i spl middot spl middot spl middot a sub n 2 and a negacyclic code of length n over z sub 4 is defined as a subset c of z sub 4 sup n such that spl nu c c we prove that the gray image of a linear negacyclic code over z sub 4 of length n is a binary distance invariant not necessary linear cyclic code we also prove that if n is odd then every binary code which is the gray image of a linear cyclic code over z sub 4 of length n is equivalent to a not necessary linear cyclic code and this equivalence is explicitely described this last result explains and generalizes the existence already known of versions of kerdock preparata and others codes as doubly extended cyclic codes furthermore we introduce a family of binary linear cyclic codes which are gray images of z sub 4 linear negacyclic codes

non conserved ordering kinetics abstract attempts are made to understand the relationship between the two analytic approaches to non conserved ordering kinetics one approach originates from the use of singular perturbation with respect to nonlinearity of the governing field equation another one focuses on the dynamics of topological defects recent progress in analytical and numerical investigations are briefly reviewed and the origin of complications found in some models of the vector order parameter is tentatively attributed to the interplay between phase and defect dynamics

exact results in the large system size limit for the dynamics of the chemical master equation a one dimensional chain of equations cme we found exact analytical expressions in large system size limit for the probability distribution including explicit expression for the dynamics of variance of distribution we also give the solution for some simple cases of the model with time dependent rates we derived the results of the van kampen method from the hje approach using a special ansatz using the van kampen method we give a system of ordinary differential equations odes to define the variance in a two dimensional case we performed numerics for the cme with stationary noise we give analytical criteria for the disappearance of bistability in the case of stationary noise in one dimensional cmes

phase separation by directional quenching and morphological transition abstract with the help of a two dimensional numerical simulation the time evolution of the phase separation of a mixture is studied for various types of quenching firstly the usual homogeneous types of quenching is briefly reviewed secondly the spatiotemporal inhomogeneous type of quenching is studied by setting the quench boundary which is the boundary between the stable phase and the unstable phase and shifting it with a constant velocity the time evolution of the domain morphologies are examined numerically three different types of domain morphologies are found one is irregular and is essentially equivalent to that produced by the homogeneous quench the other two are regular and are characteristic of the inhomogeneous quenching process one of the regular domain morphologies is parallel to the quench boundary on the average whereas the other regular one is perpendicular to the quench boundary the transition between the two regular morphologies is sharp

the analytical dynamics of the finite population evolution games abstract we study the dynamics of a finite number of replicators with different strategies in evolutionary games using the moment closure approximation for the master equation and the hamilton jacobi equation approach these methods give finite population corrections to the results of the replicator equation the model under investigation has two strategies n overall replicators with constant payoff matrix and the moran process as the update mechanism our results are compared with the results of the deterministic replicator equation and the results of numerical stochastic calculations

conservative dynamics phase ordering and stretched exponential decays the authors discuss the dynamics of an observable field related to a locally conserved field they show that for a model of phase ordering dynamics and for a variation of model c critical dynamics that the two time momentum space correlation function decays asymptotically as a stretched exponential they show that under some conditions the asymptotic behaviour is experimentally observable and argue that the non exponential behaviour is not a feature specific to these models but should rather apply for any observable coupled to a locally conserved field

infinitely many symmetries of the davey stewartson equation using a formal series symmetry method for the davey stewartson equation dse we find that there exist two sets of infinitely many formal series symmetries of the dse however different from the kadomtsev petviashvili equation kpe we failed to get infinitely many truncated symmetries only six truncated symmetries can be obtained simply from the formal series symmetries

phenomenological renormalisation of the self avoiding walk in two dimensions phenomenological renormalisation is used to calculate the exponent v and the connective constant of the self avoiding walk problem on a square lattice a transfer matrix technique is developed for the polymer problem the results indicate that flory s value v 0 75 is true in two dimensions to extremely high accuracy