a monte carlo method for series expansions the authors describe a simple and general algorithm to calculate series expansions in enumeration problems to large orders approximately by a monte carlo method it can be used to generate unbiased samples in cluster studies e g linear or branched polymers random surfaces etc in any dimension they calculate the number of site animals of size n on the square lattice for n or 50 and their average size to better than 1 accuracy

exact enumeration of self avoiding walks on critical percolation clusters in 2 7 dimensions we study self avoiding walks on critical percolation clusters by means of a recently developed exact enumeration method which can handle walks of several thousand steps we had previously presented results for the two and three dimensional cases here we take a wider perspective and vary the system s dimensions up to d 7 beyond the supposed upper critical dimension of these results may serve to check analytical predictions and help understand how the medium s fractal structure impacts on the walks scaling behavior

self avoiding walks in quenched random environments the self avoiding walk in a quenched random environment is studied using realspace and field theoretic renormalization and flory arguments these methods indicate that the system is described for d de by a strong disorder fixed point corresponding to a glass state in which the polymer is confined to the lowest energy path this fixed point is characterized by scaling laws for the size of the walk l n with n the number of steps and the fluctuations in the free energy af l the bound 1 co pore and suggests that this inequality holds for d 2 and 3 although pure cannot be excluded particularly for d 2 for d d c there is a transition between strong and weak disorder phases at which pure the strong disorder fixed point for saws on percolation clusters is discussed the analogy with directed walks is emphasized

self avoiding walks in four dimensions logarithmic corrections we present simulation results for long n or 4000 self avoiding walks in four dimensions we find definite indications of logarithmic corrections but the data are poorly described by the asymptotically leading terms detailed comparisons are presented with renormalization group flow equations derived by direct renormalization and with the results of a field theoretic calculation

biased and greedy random walks on two dimensional lattices with quenched randomness the greedy ant within a disordered environment the main characteristics of biased greedy random walks bgrws on two dimensional lattices with real valued quenched disorder on the lattice edges are studied here the disorder allows for negative edge weights in previous studies considering the negative weight percolation nwp problem this was shown to change the universality class of the existing static percolation transition in the presented study four different types of bgrws and an algorithm based on the ant colony optimization heuristic were considered regarding the bgrws the precise configurations of the lattice walks constructed during the numerical simulations were influenced by two parameters a disorder parameter ensuremath rho that controls the amount of negative edge weights on the lattice and a bias strength b that governs the drift of the walkers along a certain lattice direction the random walks are greedy in the sense that the local optimal choice of the walker is to preferentially traverse edges with a negative weight associated with a net gain of energy for the walker here the pivotal observable is the probability that after termination a lattice walk exhibits a total negative weight which is here considered as percolating the behavior of this observable as function of ensuremath rho for different bias strengths b is put under scrutiny upon tuning ensuremath rho the probability to find such a feasible lattice walk increases from zero to 1 this is the key feature of the percolation transition in the nwp model here we address the question how well the transition point ensuremath rho mathrm c resulting from numerically exact and static simulations in terms of the nwp model can be resolved using simple dynamic algorithms that have only local information available one of the basic questions in the physics of glassy systems

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

chain polymers near an adsorbing surface we present improved estimates of critical exponents for 3d polymers near a plane adsorbing surface the improvements were possible by simulating rather long chains up to n 2000 by means of a new algorithm apart from minor but significant adjustments in the location of the tricritical point and in the various gamma exponents our main result is that the crossover exponent for critical adsorption is compatible with phi 1 2 this is much lower than previous estimates and suggests that this exponent might be superuniversal

compactly supported orthogonal and biorthogonal sqrt 5 refinement wavelets with 4 fold symmetry recently radic5 refinement hierarchical sampling has been studied and radic5 refinement has been used for surface subdivision compared with other refinements such as the dyadic or quincunx refinement radic5 refinement has a special property that the nodes in a refined lattice form groups of five nodes with these five nodes having different x and y coordinates this special property has been shown to be very useful to represent adaptively and render complex and procedural geometry when radic5 refinement is used for multiresolution data processing radic5 refinement filter banks and wavelets are required while the construction of 2 d nonseparable bi orthogonal wavelets with the dyadic or quincunx refinement has been studied by many researchers the construction of bi orthogonal wavelets with radic5 refinement has not been investigated the main goal of this paper is to construct compactly supported orthogonal and biorthogonal wavelets with radic5 refinement in this paper we obtain block structures of orthogonal and biorthogonal radic5 refinement fir filter banks with 4 fold rotational symmetry we construct compactly supported orthogonal and biorthogonal wavelets based on these block structures

exact enumeration study of self avoiding walks on two dimensional percolation clusters quenched disorder averages for the number and size of the self avoiding walks on two dimensional percolation clusters very near pc are calculated by exact enumeration of all walks which start at the seed site from which clusters have been generated by monte carlo simulation the authors results are in good agreement with previous work which generated the walks by monte carlo simulation rather than by enumeration on the incipient infinite cluster

on a self organized critical forest fire model the author studies a forest fire model introduced in a paper by drossel and schwabl 1992 by means of simulations with high statistics and very close to the critical point in this way he can correct some statements made in that paper in particular he finds that the critical exponents are not the classical ones proposed by drossel and schwabl in spite of scaling laws with anomalous exponents the typical states of the system are not critical in the sense of being marginally stable locally

recursive sampling of random walks self avoiding walks in disordered media the author presents a new algorithm for simulating random walks which is simple versatile and efficient it uses recursive function calls and can be used to obtain unbiased samples with any given length distribution this makes it particularly useful in disordered geometries where the effective connectivity constant is not known a priori when applying it to self avoiding random walks on two dimensional media with quenched randomness he finds evidence for at least two new renormalization group fixed points

graph animals subgraph sampling and motif search in large networks we generalize a sampling algorithm for lattice animals connected clusters on a regular lattice to a monte carlo algorithm for graph animals i e connected subgraphs in arbitrary networks as with the algorithm in n kashtan et al bioinformatics 20 1746 2004 it provides a weighted sample but the computation of the weights is much faster linear in the size of subgraphs instead of superexponential this allows subgraphs with up to ten or more nodes to be sampled with very high statistics from arbitrarily large networks using this together with a heuristic algorithm for rapidly classifying isomorphic graphs we present results for two protein interaction networks obtained using the tandem affinity purification tap method one of escherichia coli with 230 nodes and 695 links and one for yeast saccharomyces cerevisiae with roughly ten times more nodes and links we find in both cases that most connected subgraphs are strong motifs z scores 10 or antimotifs z scores 10 when the null model is the ensemble of networks with fixed degree sequence strong differences appear between the two networks with dominant motifs in e coli being nearly bipartite graphs and having many pairs of nodes that connect to the same neighbors while dominant motifs in yeast tend towards completeness or contain large cliques we also explore a number of methods that do not rely on measurements of z scores or comparisons with null models for instance we discuss the influence of specific complexes like the 26s proteasome in yeast where a small number of complexes dominate the k cores with large k and have a decisive effect on the strongest motifs with 6 8 nodes we also present zipf plots of counts versus rank they show broad distributions that are not power laws in contrast to the case when disconnected subgraphs are included

the extension of self avoiding random walk series in two dimensions the authors have extended the enumeration of square lattice and triangular lattice self avoiding walks and their end to end distance by two terms they have also calculated 17 terms in the series for the resistance of saws with bridges on the square lattice analysis of the new data allows the connective constants to be more accurately estimated and affirms the values gamma 43 32 and v 3 4 and 1 gamma for the exponent of the resistance series

directed polymers in a random medium abstract the problem of a polymer in a random medium can be formulated as follows consider a regular lattice with on each bond ij a random energy ij the energy e w of a self avoiding walk w on this lattice is the sum of the energies of all the bonds visited by the walk then the problem is to compute the partition function z w exp e w t several recent results will be presented 1 the mean field version of this problem can be solved exactly and one observes a low temperature phase similar to the spin glass phase 2 for finite dimensional lattices one can derive bounds on the transition temperature in high enough dimension 3 for hierarchical lattices the problem can be reduced to finding stable laws when one combines random variables in a non linear way for example z z 1 z 2 z 3 z 4

cascades and self organized criticality we generalize the model of self organized critical systems to cases where due to some internal degrees of freedom the local conservation law is violated this can be realized by taking a transfer ratio different from the critical one in a sand pile model global violation or allowing fluctuations around the critical ratio local violation in the first case the deviation from the critical ratior is a critical parameter and the characteristic avalanche size diverges as r in the second case the global conservation assures criticality however our numerical results indicate that the model is in a new universality class

exact series studies of self avoiding walks on two dimensional critical percolation clusters the author presents results of exact series studies of self avoiding walks on percolation clusters on the square lattice performed very close to the percolation threshold and estimates the critical exponents nu and gamma defined by the disorder averages of the mean square radius of gyration or the end to end distance and the number of self avoiding walks respectively the self avoiding walk configurations are enumerated exactly up to 35 steps the result for nu indicates a large increase compared with the self avoiding walks on fully occupied lattice the result for gamma however indicates a behaviour similar to that on a fully occupied lattice the result for nu is completely different from that of lee nakanishi and kim 1989

the efficient determination of the percolation threshold by a frontier generating walk in a gradient the frontier in gradient percolation is generated directly by a type of self avoiding random walk the existence of the gradient permits one to generate an infinite walk on a computer of finite memory from this walk the percolation threshold pc for a two dimensional lattice can be determined with apparently maximum efficiency for a naive monte carlo calculation or n 12 for a square lattice the value pc 0 592745 or 0 000002 is found for a simulation of n 2 6 1011 total steps occupied and blocked perimeter sites the power of the method is verified on the kagome site percolation case

join and cut algorithm for self avoiding walks with variable length and free endpoints we introduce a new monte carlo algorithm for generating self avoiding walks of variable length and free endpoints the algorithm works in the unorthodox ensemble consisting of all pairs of saws such that the total number of stepsntot in the two walks is fixed the elementary moves of the algorithm are fixed n e g pivot moves on the individual walks and a novel join and cut move that concatenates the two walks and then cuts them at a random location we analyze the dynamic critical behavior of the new algorithm using a combination of rigorous heuristic and numerical methods in two dimensions the autocorrelation time in cpu units grows as n 1 5 and the behavior improves in higher dimensions this algorithm allows high precision estimation of the critical exponent

self avoiding walks on self similar structures finite versus infinite ramification self avoiding walks saws generated by exact enumeration techniques are studied on the sierpinski carpet d 2 and on the sierpinski sponge d 3 also called sierpinski square lattices a detailed comparison of the results for saws on these infinitely ramified fractals to saws on finitely ramified sierpinski gaskets sierpinski triangular lattices on regular lattices and on the incipient percolation cluster is done providing insight into the behaviour of saws on ordered and disordered structures the saws on sierpinski square lattices are found to display a kind of intermediate behaviour sharing aspects of both saws on ordered and on fractal structures as a consequence a des cloizeaux relation does not seem to hold for this structure as opposed to its validity for saws on regular lattices on sierpinski triangular lattices and on the incipient percolation cluster

dynamics of linear polymers in random media we study phenomenological scaling theories of the polymer dynamics in random media employing the existing scaling theories of polymer chains and the percolation statistics we investigate both the rouse and the zimm model for brownian dynamics and estimate the diffusion constant of the center of mass of the chain in such disordered media for internal dynamics of the chain we estimate the dynamic exponents we propose similar scaling theory for the reptation dynamics of the chain in the framework of flory theory for the disordered medium the modifications in the case of correlated disorders are also discussed

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

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

upper critical dimension of the negative weight percolation problem by means of numerical simulations we investigate the geometric properties of loops on hypercubic lattice graphs in dimensions d 2 through 7 where edge weights are drawn from a distribution that allows for positive and negative weights we are interested in the appearance of system spanning loops of total negative weight the resulting negative weight percolation nwp problem is fundamentally different from conventional percolation as we have seen in previous studies of this model for the two dimensional case here we characterize the transition for hypercubic systems where the aim of the present study is to get a grip on the upper critical dimension d u of the nwp problem for the numerical simulations we employ a mapping of the nwp model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms we characterize the loops via observables similar to those in percolation theory and perform finite size scaling analyses e g three dimensional hypercubic systems with side length up to l 56 sites in order to estimate the critical properties of the nwp phenomenon we find our numerical results consistent with an upper critical dimension d u 6 for the nwp problem

where two fractals meet the scaling of a self avoiding walk on a percolation cluster the scaling properties of self avoiding walks on a d dimensional diluted lattice at the percolation threshold are analyzed by a field theoretical renormalization group approach to this end we reconsider the model of y meir and a b harris phys rev lett 63 2819 1989 and argue that via renormalization its multifractal properties are directly accessible while the former first order perturbation did not agree with the results of other methods our analytic result gives an accurate description of the available mc and exact enumeration data in a wide range of dimensions 2 ensuremath leqslant d ensuremath leqslant 6

damage spreading and critical exponents for model a ising dynamics using damage spreading and heat bath dynamics we study the ising model in 2 and 3 dimensions with non conservative dynamics our algorithm differs in some important points from previous ones which makes it rather efficient we give estimates for the exponent z which seem to be the most precise published so far 2 172 0 006 for d 2 2 032 0 004 for d 3 we also give precise estimates of the exponent introduced by janssen et al z phys b 73 1989 539 and of analogous but in principle independent exponents we find surprisingly that some of the latter agree with and give an explanation for this

the size and number of rings on the square lattice the authors have calculated the number of self avoiding polygons on the square lattice to 56 steps and the caliper size to 54 steps analysis of the generating function permits estimates of the connective constant mu 2 638 1585 or 10 6 and the critical exponents alpha 0 500 06 or 0 000 06 and v 0 753 or 0 007 the singularity structure of the polygon generating function is found to be consistent with a correction to the scaling exponent delta 1 5 as predicted by nienhuis 1982 1984 the confluent part however maps into the additive analytic term due to the value of the exponent alpha

vibroacoustics of the piano soundboard reduced models mobility synthesis and acoustical radiation regime abstract in string musical instruments the sound is radiated by the soundboard subject to the strings excitation this vibration of this rather complex structure is described here with models which need only a small number of parameters predictions of the models are compared with the results of experiments that have been presented in ege et al vibroacoustics of the piano soundboard non linearity and modal properties in the low and mid frequency ranges journal of sound and vibration 332 5 2013 1288 1305 the apparent modal density of the soundboard of an upright piano in playing condition as seen from various points of the structure exhibits two well separated regimes below and above a frequency f lim that is determined by the wood characteristics and by the distance between ribs above f lim most modes appear to be localised presumably due to the irregularity of the spacing and height of the ribs the low frequency regime is predicted by a model which consists of coupled sub structures the two ribbed areas split by the main bridge and in most cases one or two so called cut off corners in order to assess the dynamical properties of each of the subplates considered here as homogeneous plates we propose a derivation of the low frequency modal density of an orthotropic homogeneous plate which accounts for the boundary conditions on an arbitrary geometry above f lim the soundboard as seen from a given excitation point is modelled as a set of three structural wave guides namely the three inter rib spacings surrounding the excitation point based on these low and high frequency models computations of the point mobility and of the apparent modal densities seen at several excitation points match published measurements the dispersion curve of the wave guide model displays an acoustical radiation scheme which differs significantly from that of a thin homogeneous plate it appears that piano dimensioning is such that the subsonic regime of acoustical radiation extends over a much wider frequency range than it would be for a homogeneous plate with the same low frequency vibration one problem in piano manufacturing is examined in relationship with the possible radiation schemes induced by the models