simple diagonal locally finite lie algebras the ground field f is an algebraically closed field of zero characteristic and bbb n is the set of natural numbers let l be a locally finite dimensional or em locally finite for brevity lie algebra assume for simplicity that l has countable dimension then one can choose finite dimensional subalgebras l i i in bbb n of l in such a way that l i subset l i 1 for all i and l bigcup i in bbb n l i the set l i mid i in bbb n is called a em local system of l assume that l is simple then all l i can be chosen to be perfect that is l i l i l i we shall call such local systems em perfect let s i s i 1 oplus ldots oplus s i n i be a levi subalgebra of l i where s i 1 ldots s i n i are simple components of s i and let v i k be the standard s i k module since l i is perfect for every k there exists a unique irreducible l i module cal v i k such that the restriction cal v i k downarrow s i k is isomorphic to v i k an embedding l i to l i 1 is called em diagonal if for each l any non trivial composition factor of the restriction cal v i 1 l downarrow l i is isomorphic to cal v i k or its dual cal v i k for some k we prove that a simple locally finite lie algebra l can be embedded into a locally finite associative algebra if and only if there exists a perfect local system l i i in bbb n of l such that all embeddings l i to l i 1 are diagonal note that this result can be considered as a version of ado s theorem for simple locally finite lie algebras let v be a vector space an element x in frak gl v is called em finitary if dim xv infty the finitary transformations of v form an ideal frak fgl v of frak gl v and any subalgebra of frak fgl v is called a em finitary lie algebra we classify all finitary simple lie algebras of countable dimension it turns out that there are only three frak sl infty f frak so infty f and frak sp infty f the author has classified all finitary simple lie algebras and will describe this in a subsequent paper the analogous problem in group theory has been recently solved by j i hall he classified simple locally finite groups of finitary linear transformations 1991 mathematics subject classification 17b35 17b65

self averaging in the statistical mechanics of some lattice models we discuss self averaging of thermodynamic properties in some random lattice models in particular we investigate when self averaging in an almost sure sense of the free energy implies self averaging of the energy and heat capacity and we discuss the connection between self averaging in the almost sure sense and self averaging in an l p sense under quite general conditions we show that the average of the finite size heat capacity converges to the second derivative of the limiting quenched average free energy we consider the application of these ideas to the problem of adsorption of a random copolymer at a surface and to some related systems

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

critical behavior of a three dimensional random bond ising model using finite time scaling with extensive monte carlo renormalization group method we have investigated the critical behavior of a three dimensional random bond ising model for a series of the disorder strength by a finite time scaling combining with monte carlo renormalization group method in the presence of a linearly varying temperature the method enables us to estimate a lot of critical exponents of both static and dynamic nature independently as well as the critical temperatures the static exponents obtained agree well with most existing results verify both the hyperscaling and the rushbrooke scaling laws and their combined scaling law which in turn validate their asymptotic nature and corroborate the universality of the relevant random fixed point with respect to the forms of disorder the dynamic critical exponent z is estimated to 2 114 51 which is compatible with those obtained from experiments and renormalization group analyses the exponents at low and high disorder strengths do not satisfy all scaling laws and are argued to be crossover exponents that reflect crossover from the random fixed point to the pure and the percolation fixed point they also indicate that the exponents that were previously suggested to be a distinct universality class for strong disorder strength in the literature may be just crossover our results demonstrate the effectiveness of the finite time scaling method

the thermodynamic limit for long range random systems long range spin systems with random interactions are considered a simple argument is presented showing that the thermodynamic limit of the free energy exists and depends neither on the specific random configuration nor on the sample shape provided there is no external field the argument is valid for both classical and quantum spin systems and can be applied to a spins randomly distributed on a lattice and interacting via dipolar interactions and b spin systems with potentials of the formj x 1 x 2 x 1 x 2 d where thej x 1 x 2 are independent random variables with mean zero d is the dimension and 1 2 the key to the proof is a multidimensional subadditive ergodic theorem as a corollary we show that for random ferromagnets the correlation length is a nonrandom quantity

a monte carlo study of polymer adsorption random copolymers and random surfaces we consider a model of random copolymer adsorption in which an n edge self avoiding walk in three dimensions interacts with a plane defining a half space to which the walk is confined each vertex of the walk is randomly labelled a with probability p or b with probability 1 p and only vertices labelled a are attracted to the surface plane the system is quenched i e the labelling is fixed and then the thermodynamic properties are computed we use monte carlo methods to investigate the behaviour of this system we observe self averaging of the energy as n increases and investigate the location of the adsorption transition for various values of p in addition we compare the behaviour of this system with that of a homopolymer adsorbing at a randomly heterogeneous surface consisting of two types of sites only one of which interacts with the monomers of the polymer

localization of a random copolymer at an interface an untethered self avoiding walk model we consider two related n step self avoiding walk models of a copolymer at an interface between two bulk phases in one case the walk is confined to start in the interface while in the other this condition is relaxed we prove that both models have the same limiting free energy in the n limit and hence that their phase diagrams are identical we also show that the limits n and certain energy parameters going to plus or minus infinity can be interchanged these latter results are interesting from the viewpoint of numerical studies

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 behavior of an even offspringed branching and annihilating random walk cellular automaton with spatial disorder a stochastic cellular automaton exhibiting a parity conserving class transition has been investigated in the presence of quenched spatial disorder by large scale simulations numerical evidence has been found that weak disorder causes irrelevant perturbation for the universal behavior of the transition and the absorbing phase of this model this opens up the possibility for experimental observation of the critical behavior of a nonequilibrium phase transition to absorbing state for very strong disorder the model breaks up into blocks with exponential size distribution and continuously changing critical exponents are observed for strong disorder the randomly distributed diffusion walls introduce another transition within the inactive phase of the model in which residual particles survive the extinction the critical dynamical behavior of this transition has been explored

power law and multiscaling properties of the chinese stock market abstract we investigate the cumulative probability density function pdf and the multiscaling properties of the returns in the chinese stock market by using returns data adjusted for thin trading we find that the distribution has power law tails at shorter microscopic timescales or lags however the distribution follows an exponential law for longer timescales furthermore we investigate the long range correlation and multifractality of the returns in the chinese stock market by the dfa and mfdfa methods we find that all the scaling exponents are between 0 5 and 1 by dfa method which exhibits the long range power law correlations in the chinese stock market moreover we find by mfdfa method that the generalized hurst exponents h q are not constants which shows the multifractality in the chinese stock market we also find that the correlation of shenzhen stock market is stronger than that of shanghai stock market

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

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

relationship between the fractal dimension and the power law index for a time series a numerical investigation abstract a time series showing self affine over all time scales follows a power law spectrum when such a time series x j j 1 2 n is transformed into the discrete fourier transformation i e x j n 2 k 0 c k cos 2 jkn k where c k and k are the amplitude and phase for wavenumber k respectively the power spectrum density for wavenumber k is given by p k c 2 k n k the relationship between the power law index and the fractal dimension d for a time series following a power law spectrum is investigated by using a numerical experiment it should be noted that the time series with the same power law index shows various behaviors in a time domain depending on distribution of k and gives different values of the fractal dimension accordingly in short the phase distribution strongly affects the irregularity represented in terms of the fractal dimension in addition the relationships between and d are also examined both for the differenced and for the integrated time series

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 averaging distribution of pseudocritical temperatures and finite size scaling in critical disordered systems we evaluate by monte carlo simulations various singular thermodynamic quantities x for ensembles of quenched random ising and ashkin teller models the measurements are taken at t c and we study how the distributions p x and in particular their relative squared width r x over the ensemble depend on the system size l the ashkin teller model was studied in the regime where bond randomness is irrelevant and we found weak self averaging r x ensuremath sim l ensuremath alpha ensuremath nu ensuremath rightarrow 0 where ensuremath alpha l0 and ensuremath nu are the exponents of the pure model fixed point governing the transition for the site dilute ising model on a cubic lattice known to be governed by a random fixed point we find that r x tends to a constant as predicted by aharony and harris we tested whether this constant is universal however this constant is different for canonical and grand canonical disorder we identify the pseudocritical temperature of each sample i t c i l as the temperature at which the susceptibility reaches its maximal value ensuremath chi mathrm max the distribution of these sample dependent t c i l was investigated we found that its variance scales as ensuremath delta t c l 2 ensuremath sim l ensuremath 2 ensuremath nu our previously proposed finite size scaling ansatz for disordered systems was tested and found to hold we did observe deviations from a single function which imply that sample dependent scaling functions are needed these deviations are however relatively small and hence to obtain a fixed statistical error it may be more computationally efficient to measure ensuremath chi mathrm max than the commonly used ensuremath chi t c ensuremath infty

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

low temperature properties of directed walks with random self interactions we consider a simple model for a chain with random self interactions each monomer on the chain carries a charge which is a random variable and the configurations of the chain are directed walks we show that at zero temperature the end to end distance r and the energy e of chains with total charge q approximately nx scale as r approximately nnu x and e approximately ntheta x the exponents thus depend on the total charge through the parameter x these exponents are measured numerically and compared to the predictions of some simple arguments at a finite temperature r is extensive and appears to be independent of x

a monte carlo study of adsorption of random copolymers on random surfaces we study the adsorption problem of a random copolymer on a random surface in which a self avoiding walk in three dimensions interacts with a plane defining a half space to which the walk is confined each vertex of the walk is randomly labelled a with probability pp or b with probability 1 pp and only vertices labelled a are attracted to the surface plane each lattice site on the plane is also labelled either a with probability ps or b with probability 1 ps and only lattice sites labelled a interact with the walk we study two variations of this model in the first case the a vertices of the walk interact only with the a sites on the surface in the second case the constraint of selective binding is removed that is any contact between the walk and the surface that involves an a labelling either from the surface or from the walk is counted as a visit to the surface the system is quenched in both cases i e the labellings of the walk and of the surface are fixed as thermodynamic properties are computed we present monte carlo simulation results which provide evidence for second order transitions in both cases we observe that in both cases the adsorption location depends on both ps and pp the dilution of the interactive sites on the surface and the walk we compare critical properties for the two cases and find that the adsorption location varies for different models while the crossover exponent is independent of the details of the models

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

surrogate time series before we apply nonlinear techniques e g those inspired by chaos theory to dynamical phenomena occurring in nature it is necessary to first ask if the use of such advanced techniques is justified by the data while many processes in nature seem very unlikely a priori to be linear the possible nonlinear nature might not be evident in specific aspects of their dynamics the method of surrogate data has become a very popular tool to address such a question however while it was meant to provide a statistically rigorous foolproof framework some limitations and caveats have shown up in its practical use in this paper recent efforts to understand the caveats avoid the pitfalls and to overcome some of the limitations are reviewed and augmented by new material in particular we will discuss specific as well as more general approaches to constrained randomisation providing a full range of examples new algorithms will be introduced for unevenly sampled and multivariate data and for surrogate spike trains the main limitation which lies in the interpretability of the test results will be illustrated through instructive case studies we will also discuss some implementational aspects of the realisation of these methods in the tisean software package

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 statistical mechanics of random copolymers random copolymers are polymers with two or more types of monomer where the monomer sequence is determined by some random process once determined the sequence is fixed so random copolymers are an example of a system with quenched randomness we review the statistical mechanics of random copolymers focusing on self avoiding walk models where there are two types of monomers a and b which are randomly distributed along the polymer chain theoretical approximate and numerical results are reviewed for models of the random copolymer adsorption localization and collapse phase transitions we concentrate on what is known about the existence of phase transitions the morita approximation and results about self averaging we also discuss in less detail the replica trick and numerical methods including monte carlo methods exact enumeration and transfer matrix methods important open problems are identified throughout and highlighted in the conclusions

approach to an irregular time series on the basis of the fractal theory we present a technique to measure the fractal dimension of the set of points t f t forming the graph of a function f defined on the unit interval first we apply it to a fractional brownian function 1 which has a property of self similarity for all scales and we can get the stable and precise fractal dimension this technique is also applied to the observational data of natural phenomena it does not show self similarity all over the scale but has a different self similarity across the characteristic time scale the present method gives us a stable characteristic time scale as well as the fractal dimension

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

finitary lie algebras abstract an algebra is called finitary if it consists of finite rank transformations of a vector space we classify finitary simple and finitary irreducible lie algebras over an algebraically closed field of characteristic 2 3

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

probability distribution of persistent spins in an ising chain we study the probability distribution q n t of n t the fraction of spins unflipped up to time t in an ising chain with ferromagnetic interactions the distribution shows a peak at n nmax and in general is non gaussian and asymmetric in nature however for n nmax it shows a gaussian decay data collapse can be obtained when q n t l versus n nmax l is plotted with 0 45 and 0 6 interestingly nmax t shows different behaviour compared to n t p t the persistence probability which follows the well known behaviour p t t a quantitative estimate of the asymmetry and non gaussian nature of q n t is made by calculating its skewness and kurtosis

self averaging in finite random copolymers we investigate how martingale techniques can be used to derive information on the extent of self averaging of the free energy for some lattice models of finite random copolymers

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

adsorption of a random heteropolymer at a potential well revisited location of transition point and design of sequences the adsorption of an ideal heteropolymer loop at a potential point well is investigated within the framework of standard random matrix theory on the basis of a semi analytical semi numerical approach a histogram of transition points for the ensemble of quenched heteropolymer structures with bimodal symmetric distribution of types of chain links is constructed it is shown that the sequences having transition points in the tail of the histogram display correlations between nearest neighbour monomers

monofractal and multifractal analysis of simulated heat release fluctuations in a spark ignition heat engine abstract we study data from cycle by cycle variations in heat release for a simulated spark ignited engine our analyses are based on nonlinear scaling properties of heat release fluctuations obtained from a turbulent combustion model we apply monofractal and multifractal methods to characterize the fluctuations for several fuel air ratio values from lean mixtures to stoichiometric situations the monofractal approach reveals that for lean and stoichiometric conditions the fluctuations are characterized by the presence of weak anticorrelations whereas for intermediate mixtures we observe complex dynamics characterized by a crossover in the scaling exponents for short scales the variations display positive correlations while for large scales the fluctuations are close to white noise moreover a broad multifractal spectrum is observed for intermediate fuel ratio values while for low and high the fluctuations lead to a narrow spectrum finally we explore the origin of correlations by using the surrogate data method to compare the findings of multifractality and scaling exponents between original simulated and randomized data

thermodynamics of a brownian bridge polymer model in a random environment we consider a directed random walk making either 0 or 1 moves and a brownian bridge independent of the walk conditioned to arrive at point b at time t the hamiltonian is defined as the sum of the square of the increments of the bridge between the moments of jump of the random walk and is interpreted as an energy function over the bridge configuration the random walk acts as the random environment this system provides a soluble model inspired by a closely related but distinct model of proteins the thermodynamic limit of the quenched specific free energy is shown to exist and to be self averaging i e it is equal to a trivial explicitly computed random variable an estimate of the asymptotic behaviour of the ground state energy is also obtained

configurational statistics of a disordered polymer chain a problem of the configurational properties of a long flexible polymer chain with a quenched disorder is considered the chain is assumed to be randomly constructed from monomers of two different kinds with different constants for the two body interaction near the theta point i e when the average interaction of monomers is small the spatial correlation of the repulsive and attractive monomers of different kinds leads to an increase of effects of the disorder on large scales there is also the competing effect of the repulsive three body interaction which tends to screen the effects of disorder on large scales for both effects the upper critical dimension is dc 3 a solution of the renormalisation group equation indicates that there always exists a critical scale at which the relative dispersion of sizes of polymers with different random sequences of monomers becomes of the order of unity the magnitude of this critical scale depends strongly on the relation between the constant which characterises the dispersion of the two body interaction b0 and the constant of the repulsive three body interaction v0 if b0 3 32v0 at each physically attainable scale the effects of screening are prevalent and the dispersion of sizes of polymers with different sequences of monomers is small near the theta point if the reverse inequality holds the dispersion of sizes becomes of the order of unity near the theta point

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

multiscale entropy analysis of complex physiologic time series there has been considerable interest in quantifying the complexity of physiologic time series such as heart rate however traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long range correlations this paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics we introduce a method to calculate multiscale entropy mse for complex time series we find that mse robustly separates healthy and pathologic groups and consistently yields higher values for simulated long range correlated noise compared to uncorrelated noise

criticality in the randomness induced second order phase transition of the triangular ising antiferromagnet with nearest and next nearest neighbor interactions abstract using a wang landau entropic sampling scheme we investigate the effects of quenched bond randomness on a particular case of a triangular ising model with nearest j n n and next nearest neighbor j n n n antiferromagnetic interactions we consider the case r j n n n j n n 1 for which the pure model is known to have a columnar ground state where rows of nearest neighbor spins up and down alternate and undergo a weak first order phase transition from the ordered to the paramagnetic state with the introduction of quenched bond randomness we observe the effects signaling the expected conversion of the first order phase transition to a second order phase transition and using the lee kosterlitz method we quantitatively verify this conversion the emerging under random bonds continuous transition shows a strongly saturating specific heat behavior corresponding to a negative exponent and belongs to a new distinctive universality class with 1 135 11 1 744 9 and 0 124 8 thus our results for the critical exponents support an extensive but weak universality and the emerged continuous transition has the same magnetic critical exponent but a different thermal critical exponent as a wide variety of two dimensional 2d systems without and with quenched disorder

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

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

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

a survey of one dimensional random polymers in the last decade there has been an enormous progress in the mathematical understanding of one dimensional polymer measures which are path measures that suppress self intersections we are currently in the situation that many interesting questions have either been answered or that essential new ideas are needed in this survey paper we discuss the most relevant results open questions and heuristics

long time tails in the parabolic anderson model with bounded potential we consider the parabolic anderson problem t u u u on 0 z d with random i i d potential z z zd and the initial condition u 0 1 our main assumption is that esssup 0 0 depending on the thickness of the distribution prob 0 close to its essential supremum we identify both the asymptotics of the moments of u t 0 and the almost sure asymptotics of u t 0 as t in terms of variational problems as a by product we establish lifshitz tails for the random schrodinger operator at the bottom of its spectrum in our class of distributions the lifshitz exponent ranges from d 2 to the power law is typically accompanied by lower order corrections

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

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

pulling polymers adsorbed on a striped surface we consider the adsorption of a linear homopolymer on a striped surface where the monomers have different energies of interaction with each of the two kinds of stripe in addition the polymer is subject to a force that tends to desorb the polymer and the force can be applied at different angles we consider both a partially directed walk model and a self avoiding walk model we solve the problem for the partially directed walk problem essentially completely and give phase diagrams in the force temperature plane for various values of the direction in which the force is applied the phase diagrams show re entrance phenomena and for some force directions degenerate ground states we also present a low temperature treatment that helps to interpret the results from the combinatorial solution for the self avoiding walk model we present monte carlo results and show that the phase diagrams for the partially directed walk and self avoiding walk are qualitatively similar and at low temperatures are in quantitative agreement

on the universality class of the 3d ising model with long range correlated disorder abstract we analyze a controversial topic about the universality class of the three dimensional ising model with long range correlated disorder whereas both theoretical and numerical studies agree on the validity of the extended harris criterion a weinrib b i halperin phys rev b 27 1983 413 and indicate the existence of a new universality class numerical values of the critical exponents found so far differ considerably to resolve this discrepancy we perform extensive monte carlo simulations of a 3d ising model with non magnetic impurities being arranged in a form of lines along randomly chosen axes of a lattice the swendsen wang algorithm is used alongside with a histogram reweighting technique and finite size scaling analysis to evaluate the values of critical exponents governing magnetic phase transition our estimates for these exponents differ from both previous numerical simulations and are in favor of a non trivial dependency of the critical exponents on the peculiarities of long range correlation decay

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

long range anticorrelations and non gaussian behavior of the heartbeat we find that the successive increments in the cardiac beat to beat interals of healthy subjects display scale invariant long range anticorrelations up to 10 4 heart beats furthermore we find that the histogram for the heartbeat intervals increments is well described by a l evy stable distribution for a group of subjects with severe heart disease we find that the distribution is unchanged but the long range correlations vanish therefore the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat

interacting self avoiding walks and polygons in three dimensions self interacting walks and polygons on the simple cubic lattice undergo a collapse transition at the point we consider self avoiding walks and polygons with an additional interaction between pairs of vertices which are unit distance apart but not joined by an edge of the walk or polygon we prove that these walks and polygons have the same limiting free energy if the interactions between nearest neighbour vertices are repulsive the attractive interaction regime is investigated using monte carlo methods and we find evidence that the limiting free energies are also equal here in particular this means that these models have the same point in the asymptotic limit the dimensions and shapes of walks and polygons are also examined as a function of the interaction strength

finitary simple lie algebras abstract an algebra is called finitary if it consists of finite rank transformations of a vector space we classify finitary simple lie algebras over a field of characteristic 0 we also describe finitary irreducible lie algebras

a self avoiding walk model of random copolymer adsorption there is an error in the proof of lemma 3 4 which can be remedied by using 3 22 and 3 13 directly the proof of lemma 3 2 can also be simplified please see pdf for details

are crude oil markets multifractal evidence from mf dfa and mf ssa perspectives abstract in this article we investigated the multifractality and its underlying formation mechanisms in international crude oil markets namely brent and wti which are the most important oil pricing benchmarks globally we attempt to find the answers to the following questions 1 are those different markets multifractal 2 what are the dynamical causes for multifractality in those markets if any to answer these questions we applied both multifractal detrended fluctuation analysis mf dfa and multifractal singular spectrum analysis mf ssa based on the partition function two widely used multifractality detecting methods we found that both markets exhibit multifractal properties by means of these methods furthermore in order to identify the underlying formation mechanisms of multifractal features we destroyed the underlying nonlinear temporal correlation by shuffling the original time series thus we identified that the causes of the multifractality are influenced mainly by a nonlinear temporal correlation mechanism instead of a non gaussian distribution at last by tracking the evolution of left and right half multifractal spectra we found that the dynamics of the large price fluctuations is significantly different from that of the small ones our main contribution is that we not only provided empirical evidence of the existence of multifractality in the markets but also the sources of multifractality and plausible explanations to current literature furthermore we investigated the different dynamical price behaviors influenced by large and small price fluctuations

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 behavior of the pure and random bond two dimensional triangular ising ferromagnet we investigate the effects of quenched bond randomness on the critical properties of the two dimensional ferromagnetic ising model embedded in a triangular lattice the system is studied in both the pure and disordered versions by the same efficient two stage wang landau method in the first part of our study we present the finite size scaling behavior of the pure model for which we calculate the critical amplitude of the specific heat s logarithmic expansion for the disordered system the numerical data and the relevant detailed finite size scaling analysis along the lines of the two well known scenarios logarithmic corrections versus weak universality strongly support the field theoretically predicted scenario of logarithmic corrections a particular interest is paid to the sample to sample fluctuations of the random model and their scaling behavior that are used as a successful alternative approach to criticality

a numerical study of self averaging in adsorption of random copolymers and random surfaces numerical studies involving random copolymers and random surfaces assume self averaging of thermodynamic and metric properties of the systems to calculate different properties for the problem of adsorption of a random copolymer rigorous proofs regarding self averaging of some properties such as free energy in the thermodynamic limit n exist this says little about the extent of self averaging for finite size systems used in numerical studies for the problem of adsorption of a homopolymer on a random surface no analytical proofs regarding self averaging exist in this work assumptions of self averaging of thermodynamic and metric properties of a self avoiding walk model of random copolymer adsorption are tested via multiple markov chain monte carlo method numerical evidence is provided in support of self averaging of energy heat capacity and the z component of the self avoiding walk in different temperature intervals self averaging in energy of a homopolymer interacting with a random surface is also examined

quenched bond dilution in two dimensional potts models we report a numerical study of the bond diluted two dimensional potts model using transfer matrix calculations for different numbers of states per spin we show that the critical exponents at the random fixed point are the same as in self dual random bond cases in addition we determine the multifractal spectrum associated with the scaling dimensions of the moments of the spin spin correlation function in the cylinder geometry we show that the behaviour is fully compatible with the one observed in the random bond case confirming the general picture according to which a unique fixed point describes the critical properties of different classes of disorder dilution self dual binary random bond self dual continuous random bond

locally simple subalgebras of diagonal lie algebras abstract we describe up to isomorphism all locally simple subalgebras of any diagonal locally simple lie algebra

critical behavior of the 3d ising model on a poissonian random lattice abstract the single cluster monte carlo algorithm and the reweighting technique are used to simulate the 3d ferromagnetic ising model on 3d voronoi delauney lattices it is assumed that the coupling factor j varies with the distance r between the first neighbors as j r e a r with a 0 the critical exponents and are calculated and according to the present estimates for the critical exponents we argue that this random system belongs to the same universality class of the pure 3d ferromagnetic ising model

non self averaging in autocorrelations for potts models on quenched random gravity graphs we investigate the non self averaging properties of the dynamics of ising 4 state potts and 10 state potts models in single cluster monte carlo simulations on quenched ensembles of planar trivalent 3 random graphs which we use as an example of relevant quenched connectivity disorder we employ a novel application of scaling techniques to the cumulative probability distribution of the autocorrelation times for both the energy and magnetization in order to discern non self averaging although the specific results discussed here are for quenched random graphs the method has quite general applicability

locally semisimple and maximal subalgebras of the finitary lie algebras gl sl so and sp abstract we describe all locally semisimple subalgebras and all maximal subalgebras of the finitary lie algebras gl sl so and sp for simple finite dimensional lie algebras these classes of subalgebras have been described in the classical works of a malcev and e dynkin

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

self averaging in models of random copolymer collapse we give a set of conditions under which a system is thermodynamically self averaging and show that several lattice models of interacting copolymers satisfy these conditions we prove this result for a general potential which is linear in the numbers of various types of contacts and show that this includes two potentials which have previously been used in models of random interacting linear copolymers

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

localization transition for a polymer near an interface consider the directed process i s i where the second component is simple random walk on mathbb z s 0 0 define a transformed path measure by weighting each n step path with a factor exp lambda sum 1 leq i leq n omega i h sign s i here omega i i geq 1 is an i i d sequence of random variables taking values pm 1 with probability 1 2 acting as a random medium while lambda in 0 infty and h in 0 1 are parameters the weight factor has a tendency to pull the path towards the horizontal because it favors the combinations s i 0 omega i 1 and s i 0 omega i 1 the transformed path measure describes a heteropolymer consisting of hydrophylic and hydrophobic monomers near an oil water interface we study the free energy of this model as n to infty and show that there is a critical curve lambda to h c lambda where a phase transition occurs between localized and delocalized behavior in the vertical direction we derive several properties of this curve in particular its behavior for lambda downarrow 0 to obtain this behavior we prove that as lambda h downarrow 0 the free energy scales to its brownian motion analogue

a model of continuous polymers with random charges we study a model of polymers with random charges the possible shapes of the polymer are represented by the sample paths of a brownian motion and the cumulative charge distribution along a polymer is modeled by a realization of a brownian bridge charges interact through a general positive definite two body potential we study the infinite volume free energy density for a fixed realization of the brownian motion this is not self averaging but shows on the contrary a sample dependence through the local time of the brownian motion we obtain an explicit series representation for the free energy density this has a finite radius of convergence but the free energy is nevertheless analytic in the inverse temperature in the physical domain

percolation thresholds and fractal dimensions for square and cubic lattices with long range correlated defects we study long range power law correlated disorder on square and cubic lattices in particular we present high precision results for the percolation thresholds and the fractal dimension of the largest clusters as a function of the correlation strength the correlations are generated using a discrete version of the fourier filtering method we consider two different metrics to set the length scales over which the correlations decay showing that the percolation thresholds are highly sensitive to such system details by contrast we verify that the fractal dimension d f is a universal quantity and unaffected by the choice of metric we also show that for weak correlations its value coincides with that for the uncorrelated system in two dimensions we observe a clear increase of the fractal dimension with increasing correlation strength approaching d f 2 the onset of this change does not seem to be determined by the extended harris criterion

integrated approach to the assessment of long range correlation in time series data to assess whether a given time series can be modeled by a stochastic process possessing long range correlation one usually applies one of two types of analysis methods the spectral method and the random walk analysis the first objective of this work is to show that each one of these methods used alone can be susceptible to producing false results we thus advocate an integrated approach which requires the use of both methods in a consistent fashion we provide the theoretical foundation of this approach and illustrate the main ideas using examples the second objective relates to the observation of long range anticorrelation hurst exponent hl1 2 in real world time series data the very peculiar nature of such processes is emphasized in light of the stringent condition under which such processes can occur using examples we discuss the possible factors that could contribute to the false claim of long range anticorrelations and demonstrate the particular importance of the integrated approach in this case

multifractal detrended fluctuation analysis of nonstationary time series abstract we develop a method for the multifractal characterization of nonstationary time series which is based on a generalization of the detrended fluctuation analysis dfa we relate our multifractal dfa method to the standard partition function based multifractal formalism and prove that both approaches are equivalent for stationary signals with compact support by analyzing several examples we show that the new method can reliably determine the multifractal scaling behavior of time series by comparing the multifractal dfa results for original series with those for shuffled series we can distinguish multifractality due to long range correlations from multifractality due to a broad probability density function we also compare our results with the wavelet transform modulus maxima method and show that the results are equivalent

extent of self averaging in the statistical mechanics of finite random copolymers we investigate the extent of thermodynamic self averaging in a coloured self avoiding walk model of finite random copolymer adsorption we derive a bound on the extent of self averaging as a function of the length of the self avoiding walk

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

monte carlo study of the triangular blume capel model under bond randomness the effects of bond randomness on the universality aspects of a two dimensional d 2 blume capel model embedded in the triangular lattice are discussed the system is studied numerically in both its first and second order phase transition regimes by a comprehensive finite size scaling analysis for a particularly suitable value of the disorder strength we find that our data for the second order phase transition emerging under random bonds from the second order regime of the pure model are compatible with the universality class of the two dimensional 2d random ising model furthermore we find evidence that the second order transition emerging under bond randomness from the first order regime of the pure model belongs again to the same universality class although the first finding reinforces the scenario of strong universality in the 2d ising model with quenched disorder the second is in difference from the critical behavior emerging under randomness in the cases of the ex first order transitions of the potts model finally our results verify previous renormalization group calculations on the blume capel model with disorder in the crystal field coupling

self avoiding walks interacting with a surface discusses two models of polymer adsorption in one model a self avoiding walk on a d dimensional lattice interacts with a d 1 dimensional hyperplane in the other model this walk must also lie in or on one side of this hyperplane both models exhibit non analytic behaviour corresponding to a phase transition but these phase transitions do not occur at the same point the authors give numerical estimates of the locations of these transitions

self averaging in random self interacting polygons we prove that a lattice polygon model of a self interacting random ring copolymer is thermodynamically self averaging the proof is quite general and applies to any two body potential linear in the numbers of contacts of different types

spin models on random lattices under certain conditions phase transitions in systems with quenched disorder are expected to exhibit a dierent behaviour than in the corresponding pure system here we discuss a series of monte carlo studies of a special type of such disordered systems namely spin models dened on quenched random lattices exhibiting geometrical disorder in the connectivity of the lattice sites in two dimensions we present results for the q state potts model on random tri valent 3 planar graphs which appear quite naturally in the dynamically triangulated random surface dtrs approach to quantum gravity as well as on poissonian random lattices of voronoi delaunay type both cases q64 and 4 are discussed which in the pure model without disorder give rise to second and rst order phase transitions respectively in three dimensions results for the ising model on poissonian random lattices are briey described we conclude with a comparison of the two types of connectivity disorder with the more standard case of bond disorder and a discussion of the distinguishing dierences c 2000 elsevier science b v all rights reserved

stable branching rules for classical symmetric pairs we approach the problem of obtaining branching rules from the point of view of dual reductive pairs specifically we obtain a stable branching rule for each of 10 classical families of symmetric pairs in each case the branching multiplicities are expressed in terms of littlewood richardson coefficients some of the formulas are classical and include for example littlewood s restriction rule as a special case

statistical mechanics of directed models of polymers in the square lattice directed square lattice models of polymers and vesicles have received considerable attention in the recent mathematical and physical sciences literature these are idealized geometric directed lattice models introduced to study phase behaviour in polymers and include dyck paths partially directed paths directed trees and directed vesicles models directed models are closely related to models studied in the combinatorics literature and are often exactly solvable they are also simplified versions of a number of statistical mechanics models including the self avoiding walk lattice animals and lattice vesicles the exchange of approaches and ideas between statistical mechanics and combinatorics have considerably advanced the description and understanding of directed lattice models and this will be explored in this review the combinatorial nature of directed lattice path models makes a study using generating function approaches most natural in contrast the statistical mechanics approach would introduce partition functions and free energies and then investigate these using the general framework of critical phenomena generating function and statistical mechanics approaches are closely related for example questions regarding the limiting free energy may be approached by considering the radius of convergence of a generating function and the scaling properties of thermodynamic quantities are related to the asymptotic properties of the generating function in this review the methods for obtaining generating functions and determining free energies in directed lattice path models of linear polymers is presented these methods include decomposition methods leading to functional recursions as well as the temperley method that is implemented by creating a combinatorial object one slice at a time a constant term formulation of the generating function will also be reviewed the thermodynamic features and critical behaviour in models of directed paths may be informative about the underlying properties that determine phase diagrams for wider classes of models including physical models of polymers of particular interest are adsorption and collapse transitions in models of polymers and copolymers the properties of thermodynamic quantities in those models are described by tricritical scaling this is reviewed for directed path models and the generating function approaches can be used to apply tricritical scaling to models of adsorbing inflating and collapsing directed lattice paths critical exponents for a variety of models can be obtained in this manner and with it a better understanding and a classification of the models

evidence of intermittent cascades from discrete hierarchical dissipation in turbulence abstract we present the results of a search of log periodic corrections to scaling in the moments of the square of velocity increments taken as proxies of the energy dissipation rate in experiments at high reynolds number 2500 of three dimensional fully developed turbulence a simple dynamical representation of the richardson kolmogorov cartoon of a cascade shows that standard averaging techniques erase by their very construction the possible existence of log periodic corrections to scaling associated with a discrete hierarchy to remedy this drawback we introduce a novel canonical averaging that we test extensively on synthetic examples constructed to mimic the interplay between a weak log periodic component and rather strong multiplicative and phase noises tests are also presented on 1 f5 3 random phase noise on the multifractal random walk model and on lattice and non lattice multifractal models our extensive tests confirm the remarkable observation of statistically significant log periodic corrections to scaling with a preferred scaling ratio for length scales compatible with the value 2 a strong confirmation of this result is provided by the identification of up to five harmonics of the fundamental log periodic undulations associated with up to five levels of the underlying hierarchical dynamical structure a natural interpretation of our results is that the richardson kolmogorov mental picture of a cascade becomes a realistic description if one allows for intermittent births and deaths of discrete cascades at varying scales

nonequilibrium relaxation study on spin glass model ferromagnetic fm transition point and universality class of the j ising model on cubic lattice are studied by computer simulation using the nonequilibrium relaxation ner method at fm bond density p between multicritical one pmc and 1 static exponents take universal values which are different from those of p 1 or p pmc and they are consistent with the values of the random fixed point and of the simulations and experiments for diluted ising systems the dynamical exponent however seems to depend on p and not to be universal although it may be due to finite time correction the estimation of pmc on square lattice is also refined to be 0 8894 9 which is consistent with the nishimori and nemoto s conjecture 0 889972

self averaging in many body quantum systems out of equilibrium time dependence of distributions in a disordered system a quantity is self averaging when the ratio between its variance for disorder realizations and the square of its mean decreases as the system size increases here we consider a chaotic disordered many body quantum system and search for a relationship between self averaging behavior and the properties of the distributions over disorder realizations of various quantities and at different timescales an exponential distribution as found for the survival probability at long times explains its lack of self averaging since the mean and the dispersion are equal gaussian distributions however are obtained for both self averaging and non self averaging quantities our studies show also that one can make conclusions about the self averaging behavior of one quantity based on the distribution of another related quantity this strategy allows for semianalytical results and thus circumvents the limitations of numerical scaling analysis which are restricted to few system sizes