diffusion on self avoiding walk networks two properties of self avoiding walk networks constructed by connecting the nearest neighbour points of self avoiding walks on the square lattice are studied numerically the average end to end linear part of such networks is investigated and is found to be proportional to the length of the walk secondly random walks on this structure are studied and the associated spectral dimension of such networks is estimated to be 1 03 or 0 03 which implies that the effect of such connections affects the spectral dimension only weakly if at all

a fuzzy reliability assessment of basic events of fault trees through qualitative data processing abstract probabilistic approaches are common in the analysis of reliability of complex engineering systems however they require quantitative historical failure data for determining reliability characteristics in many real world areas such as e g nuclear engineering quantitative historical failure data are unavailable or become inadequate and only qualitative data such as expert opinions which are described in linguistic terms can be collected and then used to assess system reliability moreover experts are more comfortable justifying event failure likelihood using linguistic terms which capture uncertainties rather than by expressing judgments in a quantitative manner new techniques are therefore needed that will help construct models of reliability of complex engineering system without being confined to quantitative historical failure data the objective of this study is to develop a fuzzy reliability algorithm to effectively generate basic event failure probabilities without reliance on quantitative historical failure data through qualitative data processing the originality of this study comes with an introduction of linguistic values articulated in terms of component failure possibilities in order to qualitatively assess basic event failure possibilities treated as inputs of the proposed model and generate basic event failure probabilities as its outputs to demonstrate the feasibility and effectiveness of the proposed algorithm actual basic event failure probabilities collected from nuclear power plant operating experiences are compared with the failure probabilities generated by the algorithm the results demonstrate that the proposed fuzzy reliability algorithm arises as a suitable alternative for the probabilistic reliability approach when quantitative historical failure data are unavailable

configurational properties of dilute polymer solutions dimensionality and perturbation theory by using second order perturbation theory in the small parameter epsilon 4 d to 0 the author determines a specific value of the excluded volume parameter u equivalent to the fixed point value given by renormalisation group theory for this value of the excluded volume parameter each expansion series in epsilon can be summed to an exponential function the author thus studies the total number of configurations c the number of configurations returning to the origin u and the mean square end to end distance r2 of the polymer coil an interdimensional relationship developed by kosmas and freed 1978 is used to extrapolate the authors results to lower dimensions finally the author compares his results with those of previous theories and lattice enumerations discussing possible differences between the gaussian excluded volume model used by him and the self avoiding walk model close to dimensionality d 1

monte carlo studies of three dimensional two step restricted self avoiding walks two step restricted walk tsrw models are a class of restricted self avoiding walk saw where in addition to the self avoidance constraint certain restrictions are placed upon each pair of successive steps in this paper we explore the relationship between the restrictions and the scaling of the average size of walks in three dimensional models we use the pruned enriched rosenbluth method algorithm to perform monte carlo studies in five representative tsrw models in three dimensions the results present strong numerical evidence that all non trivial tsrw models in three dimensions have the same size scaling behaviour as unrestricted saws this is in contrast to two dimensions where several universality classes are accepted to exist in particular we find no rule analogous to the spiral walk of two dimensions

a fuzzy universal generating function based method for the reliability evaluation of series systems with performance sharing between adjacent units under parametric uncertainty abstract this paper considers fuzzy multi state systems msss with performance sharing between adjacent units in which each fuzzy multi state unit has a random performance and a random demand if the performance of a unit exceeds its individual demand performance demand its surplus performance can be transmitted to its adjacent unit that experiences performance deficiency performance

self avoiding polygons on the square l and manhattan lattices transfer matrix techniques are used to extend the self avoiding polygon generating function on the square lattice to terms in x46 corresponding to 46 step polygons these techniques are then extended to apply to directed square lattices such as the l and manhattan lattice and the self avoiding polygon generating function to x48 is found for these lattices series analysis confirms that the specific heat exponent alpha 1 2 for the self avoiding walk problem and gives the following estimates for the connective constants mu sq 2 638155 or 0 000025 mu l 1 5657 or 0 0019 and mu man 1 7328 or 0 0005 some evidence for a correction to scaling exponent delta approximately 0 84 is found from square lattice series

correction to scaling exponents and amplitudes for the correlation length of linear polymers in two dimensions we consider the scaling behaviour of the radius of gyration for a system of dilute linear polymers we focus on pn the mean square end to end distance of an n step self avoiding walk for which an additional two terms were recently calculated for the close packed triangular lattice combining several extrapolation methods we find that a consistent description of the scaling behaviour exists if and only if the correction to scaling exponent a is roughly half as large as commonly believed we conclude that all data ale consistent with the equation pn an2 1 b na c n where y a a 1 j2 abso 21 and c lo

the radius of gyration of a branch of a uniform star polymer the authors use monte carlo methods and perturbation calculations to study the mean square radius of gyration of a branch of a uniform star with excluded volume as a function of the number f of branches and of the number n of monomers per branch they show that the mean square radius of gyration s n f 2 scales like a f n2v f fixed n to infinity where the exponent is independent of f they estimate the amplitude ratios a f a 1 for various values of f and show that these ratios are lattice independent the amplitude ratio increases as f increases but the effect is small the numerical agreement between the two methods is good especially for small values of f

the scaling limit of self avoiding random walk in high dimensions the brydges spencer lace expansion is used to prove that the scaling limit of the finite dimensional distributions of self avoiding random walk in the d dimensional cubic lattice mathbb z d is gaussian if d is sufficiently large it is also shown that the critical exponent gamma for the number of self avoiding walks is equal to 1 if d is sufficiently large

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

lattice models of branched polymers statistics of uniform stars the authors investigate the statistical properties of uniform star polymers with f branches modelled on lattices in two and three dimensions it is shown that the growth constant exists and is equal to mu f where mu is the self avoiding walk limit the f dependence of the corresponding critical exponent gamma f is studied using exact enumeration and monte carlo techniques and the results are compared with the predictions of miyake and freed 1983 obtained using chain conformation space renormalisation group method

new exact exponents for two dimensional self avoiding walks the author establishes using standard coulomb gas methods the values of a new set of geometrical exponents that have been previously conjectured these exponents give for any p the number of configurations of p two dimensional self avoiding walks of the same length l which are attached by their ends

field theoretic and monte carlo analysis of the domb joyce model we present a field theoretic analysis of high precision monte carlo data for the domb joyce model on the sc lattice we vary the repulsion between two segments at the same point from zero random walk to infinity self avoiding walk eventually we even include a repulsion between segments at neighbour points to increase the excluded volume beyond that of self avoiding walks the data for the end to end distance the radius of gyration and the partition function clearly show the existence of two branches of universal behaviour these two branches can be identified with the weak and strong coupling branch of the renormalization group respectively a quantitative analysis shows the ability of the standard field theoretic approach to describe the data including the data for strong coupling i e renormalized coupling u greater than its fixed point value we conclude in contrast with some claims in the literature that the standard formalism of the renormalized field theory can be used even for strong coupling branch in addition exploiting the fast approach to asymptotic behaviour at the transition between weak and strong coupling we obtain very precise estimates for the critical exponents of self avoiding walks

position space renormalisation group for isolated polymer chains we develop a cell position space renormalisation group psrg with which we study the scaling properties of isolated polymer chains we model a chain by a self avoiding walk constrained to a lattice for rescaling factors b s 6 we calculate recursion relations analytically on the square lattice with several different choices for the psrg weight function we also calculate implicit cell to cell transformations in which a cell of size b is rescaled to a cell of size b the results of these psrgs improve both as b increases and as b b 1 in addition we construct a true infinitesimal psrg transformation which appears to become exact as the dimensionality d approaches 1 we obtain the closed form expression for the correlation length exponent u d l d in d the flory formula deviates from this already at first order in d 1 we also develop a constant fugacity monte carlo method which enables us to simu late in an unbiased way within the grand canonical ensemble chains of up to lo3 bonds with this method we extend the psrg to larger cells b s 150 on the square lattice our numerical method provides high statistical accuracy for all cell sizes however in the range of b we study the asymptotic behaviour of our results appears to depend on the choice of weight function one weight function provides smooth behaviour as a function of b and with it we extrapolate to find u 0 756 0 004 further work is required to resolve the apparent anomalies in the results based on the other weight functions

monte carlo test of a hyperscaling relation for the two dimensional self avoiding walk the authors simulated self avoiding walks on the square lattice with fixed endpoints by means of a dynamic monte carlo algorithm from these data they obtain an evaluation of the effective coordination number mu and the critical exponents alpha and v they can therefore test the hyperscaling relation 2 alpha dv with a careful estimate of systematic and statistical errors

polymer conformations through wiggling a new monte carlo method is proposed which allows for the efficient generation of equilibrium conformations of polymer chains in two and three dimensions the method treats each site monomer as a potential pivot around which a new conformation may be generated by rotating a portion of the chain the method does not suffer from the severe attrition associated with the simple sampling of self avoiding walks and may be extended to treat the interacting polymer chain the authors find in two dimensions that nu 0 748 or 0 005 exact 0 750 and in three dimensions nu 0 595 or 0 005 series expansion and renormalisation group predict nu approximately 0 588 the end end distances calculated for shorter chains are in good agreement with the exact values from enumeration techniques

critical crossover phenomena in disordered ising systems the author has investigated the critical behaviour of site disordered ising systems over a large range of dilution 0 6 or p or 1 0 investing about 1015 single spin flips with conventional local dynamics critical temperatures have been determined with high precision using the cumulant method the finite size simulations lead to concentration dependent exponents which seem to violate universality the author shows that the concentration dependence is induced by a crossover phenomenon which governs a large interval of the critical region the author finds that the scaling functions of systems with different disorder converge asymptotically to universal behaviour consistent with the fixed point of weak disorder

on the mean radius of gyration of a polymer chain calculates the intrachain bead to bead square distance of a real polymer chain close to the critical dimensionality d 4 from this the authors obtain the mean square radius of gyration s2 of the polymer as a function of the molecular weight n of the chain and the excluded volume parameter mu a proportionality relationship between s2 and the mean square end to end distance r2 of the coil previously suggested by enumerations of self avoiding walks on lattice is shown to be true an estimate of the universal ratio s2 r2 is given

a computational approach to soliton solutions of the kadomtsev petviashvili equation in this paper we present a computational approach to develop soliton solutions of the nonlinear kadomtsev petviashvili equation our approach rests mainly on the adomian decomposition method to include few components of the decomposition series the proposed framework is presented in a general way so that it can be used in nonlinear evolution equations of the same type numerical examples are tested to illustrate the proposed scheme

on the probabilistic meaning of copula based extensions of fuzzy measures applications to target based utilities and multi state reliability systems abstract aggregations functions that are obtainable as copula based extensions of fuzzy measures may emerge in several applied fields we concentrate attention on the probabilistic interpretation of such objects starting from this issue we point out the related meaning in the context of multi attribute target based utilities and multi state reliability systems analogies and relations between the two fields of decisions under uncertainty and systems reliability have been already remarked in the literature here we prove in particular that aggregation functions specifically emerging in the setting of multi attribute target based utilities and in the setting of multi state systems do exactly share the same analytic structure we will show that this identification emerges naturally when the multi state systems are formed with binary components from a technical viewpoint the comparison between two different representations for the considered aggregations and the specific role of the mobius transform have a basic relevance in the proofs of our results and in the development of related discussions

fuzzy reliability assessment of systems with multiple dependent competing degradation processes components are often subject to multiple competing degradation processes for multicomponent systems the degradation dependence within one component or and among components need to be considered physics based models and multistate models are often used for component degradation processes particularly when statistical data are limited in this paper we treat dependence between degradation processes within a piecewise deterministic markov process pdmp modeling framework epistemic subjective uncertainty can arise due to the incomplete or imprecise knowledge about the degradation processes and the governing parameters to take this into account we describe the parameters of the pdmp model as fuzzy numbers then we extend the finite volume method to quantify the fuzzy reliability of the system the proposed method is tested on one subsystem of the residual heat removal system of a nuclear power plant and a comparison is offered with a monte carlo simulation solution the results show that our method can be most efficient

dimensions of the branches of a uniform brush polymer excluded volume effects increase the dimensions of the various branches of a uniform brush polymer to different extents the authors use monte carlo methods and perturbation calculations to study the mean square end to end branch lengths of a uniform brush with two branch points as a function of the number n of monomers in a branch and the functionalities f1 and f2 of the branch points the mean square end to end length rn2 of a branch scales like bn2v and they investigate how the amplitude b varies for the different types of branch as f1 and f2 vary the amplitude ratios are expected to be lattice independent and they find good agreement between their numerical estimates of these ratios from perturbation and monte carlo calculations they have extended the perturbation calculations to make predictions for the corresponding amplitude ratios for the mean square radii of gyration of the various branches

the decomposition method applied to systems of partial differential equations and to the reaction diffusion brusselator model in this work systems of linear and nonlinear partial differential equations and the reaction diffusion brusselator model are handled by applying the decomposition method the advantage of this work is twofold firstly the decomposition method reduces the computational work secondly in comparison with existing techniques the decomposition method is an improvement with regard to its accuracy and rapid convergence the decomposition method has the advantage of being more concise for analytical and numerical purposes

critical exponent for the loop erased self avoiding walk by monte carlo methods a monte carlo simulation was performed for loop erased self avoiding walks lesaw to ascertain the exponentv for the z2 and z3 lattices the estimated values were 2v 1 600 0 006 in two dimensions and 2v 1 232 0 008 in three dimensions leading to the conjecturev 4 5 for the two dimensional lesaw these results add to existing evidence that the loop erased self avoiding walks are not in the same universality class as self avoiding walks

nonergodicity of local length conserving monte carlo algorithms for the self avoiding walk it is proved that every dynamic monte carlo algorithm for the self avoiding walk based on a finite repertoire of local n conserving elementary moves is nonergodic heren is the number of bonds in the walk indeed for largen each ergodic class forms an exponentially small fraction of the whole space this invalidates at least in principle the use of the verdier stockmayer algorithm and its generalizations for high precision monte carlo studies of the self avoiding walk

critical properties of the three dimensional self avoiding walk accurate monte carlo data are used to determine the critical exponent nu 0 590 or 0 001 or inverse fractal dimension of the three dimensional self avoiding walk the leading correction to scaling term is non analytic and is near 0 5

the dimensions of knotted polygons the authors study the dimensions mean square radius of gyration and mean span of self avoiding polygons on the simple cubic lattice with fixed knot type the approach used is a monte carlo algorithm which is a combination of the bfacf algorithm and the pivot algorithm so that the polygons are studied in the grand canonical ensemble but the autocorrelation time is not too large they show that although the dimensions of polygons are sensitive to knot type the critical exponent v and the leading amplitude are independent of the knot type of the polygon the knot type influences the confluent correction to the scaling term and hence the rate of approach to the limiting behaviour

a fuzzy set based approach for modeling dependence among human errors the assessment of dependence among human errors is an important aspect of human reliability analysis when dependence between two tasks exists the probability of the operators failure on one task is higher if they have failed on the preceding task compared to when they have succeeded in current practice the task of assessing dependence among successive operator actions relies to a great extent to expert judgment often with lack of traceability and repeatability to overcome these limitations this work presents a systematic framework for the elicitation of expert knowledge on the factors influencing the dependence between two successive tasks the framework is based on a fuzzy expert system in which a set of transparent fuzzy logic rules is used to represent the relationship between the input factors and the conditional human error probability the proposed modeling approach is applied to two tasks required in response to an accident scenario at a nuclear power plant given the methodological scope of the work the fuzzy expert system is tested directly on a working model of dependence whereas no actual exercise of expert judgment elicitation is carried out

monte carlo simulation of 3d self avoiding walks presents simulation results for 3d self avoiding walks of moderate length n or 2000 using a recently introduced recursive sampling method it is shown that this method is indeed maximally efficient for determining the connectivity constant mu combining the data with previous results from exact enumerations and from simulations of very long walks using the pivot algorithm the author obtains very precise estimates of mu and of the critical exponents gamma and nu he also points out significant deviations from uniformity in a very popular random number generator which was considered safe until now

risk assessment system of natural hazards a new approach based on fuzzy probability this paper presents a system for assessing the risk of natural disasters particularly under highly uncertain conditions i e where neither the statistical data nor the physical knowledge required for a purely probabilistic risk analysis are sufficient the theoretical foundation of this study is based on employing fuzzy set theory to complement the probability theory with an additional dimension of uncertainty this would allow for expressing the likelihood of natural hazards by fuzzy probability the fuzzy probability is characterized in terms of possibility probability distributions for which a new approach has been developed the new approach has been compared with an alternative approach moreover uncertainties about the correlation of the parameters of hazard intensity damage and loss i e vulnerability relations have been considered by means of fuzzy relations the composition of fuzzy probability of hazard and fuzzy vulnerability relation yields the fuzzy probability of damage or loss the system has been applied for assessing the earthquake risk in istanbul metropolitan area

on the probability distribution of the end to end vector of a polymer chain the author calculates the fourth and sixth moments of the probability distribution of the end to end vector of a polymer chain close to the critical dimensionality 4 the results support that the excluded volume interactions do not change the gaussian structure of the probability for large distances depending on the value of the excluded volume parameter u an expansion or a shrinkage to this probability occurs even for the dimensionality 4

a lattice model of uniform star polymers the authors present monte carlo and exact enumeration results for three and four arm stars on a variety of lattices they estimate the exponents for the number of stars and the mean square end to end length of a branch and compare these results with scaling and renormalisation group predictions

confidence interval estimation using standardized time series observations of a stationary stochastic process can be transformed into a standardized time series this paper presents a lemma giving the asymptotic properties of this standardized series under quite general conditions in particular the conditions are satisfied by stationary discrete event simulations confidence intervals can be constructed using this lemma for illustration we develop two easily computed interval estimators for the process mean when independent replications of the series are available such as in computer simulation experiments these interval estimators may be combined with the classical confidence interval estimator these interval estimators also tend to compensate for simulation initialization bias if the sign of the bias is known in an empirical study using three elementary simulated processes the interval estimators presented here compare favorably with the classical interval estimator in a recent paper goldsman and schruben goldsman d l schruben 1982 asymptotic properties of some confidence interval estimators tech rep 544 school of o r i e cornell university ithaca ny show that the asymptotic properties of the confidence intervals presented in this paper strictly dominate those of classical confidence intervals

end to end distance of linear polymers in two dimensions a reassessment recent exact enumeration studies of the two dimensional self avoiding walk have produced evidence in support of non analytic scaling corrections newly extended series for the triangular and square lattices to n 19 and 25 respectively are examined in the light of recent monte carlo results suggesting the absence of corrections of this type using a modified approach to series analysis it is concluded that the end to end distance can best be understood in terms of analytic corrections alone in view of the lack of theoretical support there is little reason to introduce additional kinds of correction in attempting to explain the data

self avoiding walks in wedges the authors consider the number of self avoiding walks confined to a subset zd f of the d dimensional hypercubic lattice zd such that the coordinates x1 x2 xd of each vertex in the walk satisfy x1 or 0 and 0 or xk or fk x1 for k 2 3 d they show that if fk x to infinity as x to infinity the connective constant of walks in zd f is identical to the convective constant of walks in zd they also explore conditions on fk which lead to a smaller connective constant for walks in zd f and in particular consider walks between two parallel d 1 dimensional hyperplanes finally they contrast some of these results with recent work by grimmett on percolation on subsets of the square lattice

excluded volume effects in the end to end distance of two generation dendritic polymers ttt and hh combs excluded volume effects in the end to end distances of two generation dendritic polymers with various numbers of branches and branch lengths are determined by calculating the expansion factors of the branches to the order e 4 d the general solution correctly recovers known results of materials with fewer junctions and generations such as star brush and block co polymers this general solution also predicts the behaviors of three junction ttt and hh polymers containing equal length branches pivot monte carlo simulations on the last two classes of polymers compare well with the first order e renormalization group results

new monte carlo method for the self avoiding walk we introduce a new monte carlo algorithm for the self avoiding walk saw and show that it is particularly efficient in the critical region long chains we also introduce new and more efficient statistical techniques we employ these methods to extract numerical estimates for the critical parameters of the saw on the square lattice we find 2 63820 0 00004 0 00030 1 352 0 006 0 025 v 0 7590 0 0062 0 0042 where the first error bar represents systematic error due to corrections to scaling subjective 95 confidence limits and the second bar represents statistical error classical 95 confidence limits these results are based on saws of average length 166 using 340 hours cpu time on a cdc cyber 170 730 we compare our results to previous work and indicate some directions for future research

a fuzzy measure approach to systems reliability modeling our objective here is to study the role that fuzzy measures can play in systems reliability modeling we first introduce some basic ideas from fuzzy measure theory and then introduce some specialized ideas about fuzzy measures cardinality index and attitudinal character which will later be useful in comparing systems reliability basic ideas of reliability modeling and the role of the system structure function are discussed the system s signatures associated with a structure function are introduced and we show their relationship to expected time to system failure we show how we can model a systems structure function using a fuzzy measure s a description of the role of a measures cardinality index and attitudinal character in providing tools for comparing systems reliability is provided we describe how to obtain a structure model of a complex system using aggregation operators and the measure representation of individual components

the self avoiding walk on the honeycomb lattice the author analyses the chain generating function for the self avoiding walk problem on the honeycomb lattice she uses the exact critical point value of nienhuis and finds exponent values of gamma approximately 1 344 and delta 1 approximately 0 93 for the dominant and first confluent exponents the former value is in agreement with nienhuis exact result second and third confluent exponents delta 2 approximately 1 2 and delta 3 approximately 1 5 are also identified these exponents being consistent with monte carlo results and nienhuis exact irrelevant eigenvalue respectively

fuzzy universal generating functions for multi state system reliability assessment the paper considers a multi state system mss where performance rates or and corresponding state probabilities are presented as fuzzy values in many real world msss it is difficult to estimate precise values of performance rates and their probabilities because of two main reasons the first reason is inaccuracy and insufficiency of data the second one is based on the fact that msss are often used as the approximation for continuous state systems in order to simplify computational burden to overcome these deficiencies performance rates levels or and corresponding probabilities are considered as fuzzy values in this paper the fuzzy universal generating function fugf is developed to extend the universal generating function with crisp sets the composition operators are extended for fugfs and introduced in more general forms based on this a special technique for reliability assessment of such msss is developed illustrative examples are presented to demonstrate the technique

exponential convergence to equilibrium for a class of random walk models we prove exponential convergence to equilibrium l 2 geometric ergodicity for a random walk with inward drift on a sub cayley rooted tree this randomwalk model generalizes a monte carlo algorithm for the self avoiding walk proposed by berretti and sokal if the number of vertices of leveln in the tree grows asc n n n 1 we prove that the autocorrelation time satisfies n 2 n 1

internal structure of polymer chains abstract the asymptotic behaviour of isolated long chain polymers in good solvents is modelled well by the self avoiding walk on a regular crystal lattice in this paper we investigate the typical scaling length and the probability distribution function for the position of the end point and an interior point for self avoiding walks on a simple cubic lattice we find that for n step walks the typical internal scaling length r n n associated with the position of the n th step has a similar functional form to the external scaling length r n the associated exponent is found to be the same for both scaling lengths within the confidence limits of our simulations the internal probability distribution function p n n r is shown to be skew gaussian and furthermore has a similar form to the external distribution function p n n r r r n n a exp r r n n where a 2 42 0 08 and 2 50 0 09

lattice models of branched polymers uniform combs in two dimensions the authors establish rigorously the relationship between the growth constant of uniform trees with two branch points and that of self avoiding walks for combs they estimate the corresponding exponent and study the mean square lengths of the internal and external branches

efficient simulation of the random cluster model the simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down a number of cluster algorithms usually based on the fortuin kasteleyn representation of the potts model and suitable generalizations for continuous spin models have been used to increase simulation efficiency the first algorithm making use of this representation suggested by sweeny in 1983 has not found widespread adoption due to problems in its implementation however it has been recently shown that it is indeed more efficient in reducing critical slowing down than the more well known algorithm due to swendsen and wang here we present an efficient implementation of sweeny s approach for the random cluster model using recent algorithmic advances in dynamic connectivity algorithms

convergence and extrapolation in finite size scaling renormalization abstract finite size renormalization technique is studied by examining a test model which is exactly solvable and the problem of lattice animals and self avoiding walks bulk estimates of the leading irrelevant rg eigenvalue are found and compared with independent estimates from finite size data we introduce an extrapolation technique which is applicable to non monotonic sequences of exponent approximants

numerical doubly periodic solution of the kdv equation with the initial condition via the decomposition method in this paper a scheme is extended to study numerical doubly periodic solutions of the kortweg de vries kdv equation with initial conditions using the adomian decomposition method as a result we obtain the numerical doubly periodic solutions of the kdv equation with initial conditions the numerical doubly periodic solution is compared with the exact doubly periodic solution moreover we analyze the absolute error and relative error between them and also give the contour and density plots of the numerical doubly periodic solutions with two different moduli m 15 78

the diffusion of self avoiding random walk in high dimensions we use the brydges spencer lace expansion to prove that the mean square displacement of at step strictly self avoiding random walk in thed dimensional square lattice is asymptotically of the formdt ast approaches infinity ifd is sufficiently large the diffusion constantd is greater than one

numerical solutions of coupled burgers equations with time and space fractional derivatives in this paper by introducing the fractional derivative in the sense of caputo the adomian decomposition method is directly extended to study the coupled burgers equations with time and space fractional derivatives as a result the realistic numerical solutions are obtained in a form of rapidly convergent series with easily computable components the figures show the effectiveness and good accuracy of the proposed method

nonuniform star polymers in two dimensions we present simulation results for nonuniform 2d star polymers using a recursive implementation of the enrichment method we show that the choice of parameters in this method is not trivial and that a good choice can lead to extremely efficient code we find that the exponents gamma f governing the increase of the f star partition function with n are compatible with the prediction gamma funiform f 1 by duplantier 1986

two dimensional polymers universality and correction to scaling improved monte carlo methods have been used to study the asymptotic behaviour of self avoiding walks on two dimensional lattices the mean square end to end distance rn2 and radius of gyration sn2 are both found to scale as n2v with exponent values very close to the expected v 3 4 and an amplitude ratio that is universal small n deviations of rn2 from the asymptotic results indicate a correction to scaling exponent delta 1 a value that differs from previous estimates

the pivot algorithm a highly efficient monte carlo method for the self avoiding walk the pivot algorithm is a dynamic monte carlo algorithm first invented by lal which generates self avoiding walks saws in a canonical fixed n ensemble with free endpoints heren is the number of steps in the walk we find that the pivot algorithm is extraordinarily efficient one effectively independent sample can be produced in a computer time of ordern this paper is a comprehensive study of the pivot algorithm including a heuristic and numerical analysis of the acceptance fraction and autocorrelation time an exact analysis of the pivot algorithm for ordinary random walk a discussion of data structures and computational complexity a rigorous proof of ergodicity and numerical results on self avoiding walks in two and three dimensions our estimates for critical exponents are 0 7496 0 0007 ind 2 and 0 592 0 003 ind 3 95 confidence limits based on saws of lengths 200 n 10000 and 200 n 3000 respectively

on the correction to scaling exponent of linear polymers in two dimensions the authors present new results which indicate that the leading correction to scaling exponent in the mean squared end to end distance in two dimensions is the analytic term a potential source of the various correction to scaling terms reported in the literature is pointed out

on three dimensional self avoiding walks long self avoiding walks of up to 2400 steps have been generated on the sc and bcc lattices using an improved monte carlo technique analysis of the asymptotic length dependence of the end to end distance and radius of gyration of the walks leads to values in the range 0 591 0 593 for the critical exponent nu the simple power law dependence on length provides an excellent fit to the data over walk lengths between 120 and 2400 with fluctuations around the asymptotic results averaging to a mere 0 13 systematic deviations from asymptotic behaviour in short self avoiding walks have also been examined using monte carlo generated walks ranging in length from 12 to 60 the results do not support the existence of the non analytic correction predicted by the renormalisation group in the light of this unexpected result available series expansions for walks on the fcc lattice have been re examined and previous claims to have observed non analytic behaviour questioned equal if not better convergence of the extrapolated series can be obtained without resorting to non analytic correction terms finally an analysis has been made of the radius of gyration series to which several new terms have been added

random linking of lattice polygons we study the linking probability of polygons on the simple cubic lattice in particular we consider two polygons each having n edges confined to a cube of side l and ask for the linking probability as a function of n and l we also consider other situations in which the polygons are restricted to be not too far apart but not necessarily confined to a cube we prove several rigorous results and use monte carlo methods to address some questions which we are unable to answer rigorously an interesting feature is that the linking probability is a function of l nv where v is the exponent characterizing the radius of gyration of a polygon

on two dimensional self avoiding random walks following nienhuis 1982 exact evaluation of the connective constant of the honeycomb lattice self avoiding walk model and the exact exponent values he has conjectured the author has re examined the available data on all three regular two dimensional lattices in the case of the triangular lattice the author has additionally corrected and extended the extant series the author finds support for nienhuis value gamma 111 32 for all three lattices and further finds that alpha 1 2 for all three lattices as given by nienhuis result nu 3 4 and the hyperscaling relation d nu 2 alpha the author is unable to find any consistent evidence of a correction to scaling exponent delta 1 1 cannot be ruled out

numerical solutions for fractional kdv burgers equation by adomian decomposition method abstract based on the symbolic computation system maple adomian decomposition method developed for differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional kdv burgers equation the fractional derivatives are described in the caputo sense according to my knowledge this paper represents the first available numerical solutions of the nonlinear fractional kdv burgers equation with time and space fractional derivatives finally the solutions of our model equation are calculated in the form of convergent series with easily computable components

free energy of self interacting uniform stars we consider uniform star polymers on a variety of lattices with an additional contact interaction between pairs of vertices which are unit distance apart and are not joined by an edge of the star we present some rigorous results and other evidence which indicate that these systems have the same limiting free energy as self interacting self avoiding walks we discuss the extension of these results to other homeomorphism types and to systems with an additional surface interaction term