statistical complexity measure of pseudorandom bit generators abstract pseudorandom number generators prng are extensively used in monte carlo simulations gambling machines and cryptography as substitutes of ideal random number generators rng each application imposes different statistical requirements to prngs as l ecuyer clearly states the main goal for monte carlo methods is to reproduce the statistical properties on which these methods are based whereas for gambling machines and cryptology observing the sequence of output values for some time should provide no practical advantage for predicting the forthcoming numbers better than by just guessing at random in accordance with different applications several statistical test suites have been developed to analyze the sequences generated by prngs in a recent paper a new statistical complexity measure phys lett a 311 2003 126 has been defined here we propose this measure as a randomness quantifier of a prngs the test is applied to three very well known and widely tested prngs available in the literature all of them are based on mathematical algorithms another prngs based on lorenz 3d chaotic dynamical system is also analyzed prngs based on chaos may be considered as a model for physical noise sources and important new results are recently reported all the design steps of this prng are described and each stage increase the prng randomness using different strategies it is shown that the mpr statistical complexity measure is capable to quantify this randomness improvement the prng based on the chaotic 3d lorenz dynamical system is also evaluated using traditional digital signal processing tools for comparison

age representation of levy walks partial density waves relaxation and first passage time statistics l vy walks lws define a fundamental class of finite velocity stochastic processes that can be introduced as a special case of continuous time random walks alternatively there is a hyperbolic representation of them in terms of partial probability density waves using the latter framework we explore the impact of aging on lws which can be viewed as a specific initial preparation of the particle ensemble with respect to an age distribution we show that the hyperbolic age formulation is suitable for a simple integral representation in terms of linear volterra equations for any initial preparation on this basis relaxation properties i e the convergence towards equilibrium of a generic thermodynamic function dependent on the spatial particle distribution and first passage time statistics in bounded domains are studied by connecting the latter problem with solute release kinetics we find that even normal diffusive lws where the long term mean square displacement increases linearly with time may display anomalous relaxation properties such as stretched exponential decay we then discuss the impact of aging on the first passage time statistics of lws by developing the corresponding volterra integral representation as a further natural generalization the concept of lws with wearing is introduced to account for mobility losses

to what class of fractals does the alexander orbach conjecture apply discussion de la decouverte numerique recente d alexander et orbach selon laquelle pour un agregat infini naissant en percolation le rapport d f d w dimension fractale de l agregat dimension fractale d une marche aleatoire dans l agregat est approximativement independant de d pour d 1

structure and perimeters of percolation clusters site percolation clusters are simulated at the percolation threshold on the square lattice an algorithm for walks around each cluster is used to obtain information on its fractal geometry the fractal dimensionality of the external perimeter is found to depend on the size of adsorbent particles used to measure it if the vacant perimeter sites have only nearest neighbour connectivity then the perimeter has dimension de 1 37 or 0 03 instead of that of the hull dh 1 75 the authors also measured the mass of internal dangling sites surrounded by the backbone s blobs singly and doubly connected sites the number of blobs and the average linear distance between entry into the exit from a blob

size dependent diffusion coefficient in a myopic random walk on a strip abstract we consider a random walk in discrete time n 0 1 2 on a square lattice of finite width in the y direction i e j m j z m 1 2 3 n a myopic walker at j 1 or j n jumps with probability 1 3 to any of the available nearest neighbor sites at the end of a time step this couples the motions in the x and y directions and leads to several interesting features including a coefficient of diffusion in the x direction that depends on the transverse size n of the strip explicit solutions for x2n and the lateral variance y2n are given for small values of n a closed form expression is obtained for the discrete laplace transform of x2n for general n the asymptotic behaviors of x2n and y2n are found the corrections falling off exponentially with increasing n the results obtained are generalized to a myopic random walk in d dimensions and it is shown that the diffusion coefficient has an explicit geometry dependence involving the surface to volume ratio this coefficient can therefore serve as a probe of the geometry of the structure on which diffusion takes place

computational study of the percolation phenomena in inhomogeneous two and three dimensional systems in this paper the results of computer investigation of the percolation processes in inhomogeneous lattices are discussed the inhomogeneity is simulated by a random distribution of obstacles differing in size and number the influence of obstacles on the parameters critical concentration average number of sites in finite clusters percolation probability critical exponents and fractal and spectral dimensions of a percolation cluster characterizing the percolation in the system is analysed it is demonstrated that all these parameters essentially depend on the linear size and relative area of the obstacles

sparre andersen theorem with spatiotemporal correlations the sparre andersen theorem is a remarkable result in one dimensional random walk theory concerning the universality of the ubiquitous first passage time distribution it states that the probability distribution n of the number of steps needed for a walker starting at the origin to land on the positive semiaxes does not depend on the details of the distribution for the jumps of the walker provided this distribution is symmetric and continuous where in particular n n 3 2 for large number of steps n on the other hand there are many physical situations in which the time spent by the walker in doing one step depends on the length of the step and the interest concentrates on the time needed for a return not on the number of steps here we modify the sparre andersen proof to deal with such cases in rather general situations in which the time variable correlates with the step variable as an example we present a natural process in 2d that shows that deviations from normal scaling are present for the first passage time distribution on a semiplane

a note on coniglio s lemma it is proved that coniglio s 1981 1982 lemma holds for any pair of points in any graph in the low density series expansion of the cut edge weighted pair connectedness

higher genus modular graph functions string invariants and their exact asymptotics the concept and the construction of modular graph functions are generalized from genus one to higher genus surfaces the integrand of the four graviton superstring amplitude at genus two provides a generating function for a special class of such functions a general method is developed for analyzing the behavior of modular graph functions under non separating degenerations in terms of a natural real parameter t for arbitrary genus the arakelov green function and the kawazumi zhang invariant degenerate to a laurent polynomial in t of degree 1 1 in the limit t to infty for genus two each coefficient of the low energy expansion of the string amplitude degenerates to a laurent polynomial of degree w w in t where w 2 is the degree of homogeneity in the kinematic invariants these results are exact to all orders in t up to exponentially suppressed corrections the non separating degeneration of a general class of modular graph functions at arbitrary genus is sketched and similarly results in a laurent polynomial in t of bounded degree the coefficients in the laurent polynomial are generalized modular graph functions for a punctured riemann surface of lower genus

fractal landscapes in physics and biology the purpose of this talk is to describe some recent progress in three aspects of statistical physics that overlap biology the first of these represents a discovery about the real world for which we presently have no theoretical understanding 1 the second concerns the solution of a rich model of many body physics which should apply to a wide range of biological situations but presently applies primarily to mathematical ecology 2 the third concerns what on the one hand might be a mere numerical coincidence or on the other hand might represent evidence that diffusion limited aggregation describes the physical mechanism underlying the growth of nerve cells at least the quasi two dimensional nerve cells that grow in the retina 3

vectorized and parallel simulations of the kardar parisi zhang equation in 3 1 dimensions the kardar parisi zhang kpz equation describing kinetic roughening is solved numerically for 3 1 dimensional systems in the strong coupling phase by massive use of supercomputing tools we calculate for the first time the exponent beta 0 181 or 0 007 with an accuracy comparable with that of lattice growth model simulations a possible source of errors in parallel monte carlo calculations is pointed out

topological properties of percolation clusters percolation properties including the total cluster mass s the shell mass b and the linear geometrical size r are studied as a function of the topological chemical distance parameter l all critical exponents are shown to be related to an apparently new exponent nu defined by r approximately lv critical exponents are calculated exactly for percolation clusters on the cayley tree a model for 6d percolation for which s approximately l2 b approximately l and r2 approximately l for diffusion on such clusters one finds that l3 approximately t numerical estimates of the exponents are obtained for other dimensions a conjecture which relates nu to beta and nu is discussed

current algebra on the torus we derive the n point one loop correlation functions for the currents of an arbitrary affine kac moody algebra the one loop amplitudes which are elliptic functions defined on the torus riemann surface are specified by group invariant tensors and certain constant tau dependent functions we compute the elliptic functions via a generating function and explicitly construct the invariant tensor functions recursively in terms of young tableaux the lowest tensors are related to the character formula of the representation of the affine algebra these general current algebra loop amplitudes provide a building block for open twistor string theory among other applications

cumulant renormalisation group and its application to the incipient infinite cluster in percolation the authors introduce the cumulant method into the context of position space renormalisation group the advantage of this method over previous procedures is that one need not systematically evaluate all 2n states of each kadanoff cell where n is the number of elements sites or bonds in the cell they illustrate this method by calculating for bond percolation with an eight bond cell the critical exponents characterizing the following quantities i the mean number of backbone bonds ii the mean number of bonds in the minimum and maximum paths along the backbone iii the mean number of singly connected red bonds and iv the mean number of bonds in all the self avoiding walks connecting the two extreme points they derive previously obtained results of the conductivity and resistivity

fragmentation of percolation cluster perimeters we introduce a model for the fragmentation of porous random solids under the action of an external agent in our model the solid is represented by a bond percolation cluster on the square lattice and bonds are removed only at the external perimeter or hull of the cluster this model is shown to be related to the self avoiding walk on the manhattan lattice and to the disconnection events at a diffusion front these correspondences are used to predict the leading and the first correction to scaling exponents for several quantities defined for hull fragmentation our numerical results support these predictions in addition the algorithm used to construct the perimeters reveals itself to be a very efficient tool for detecting subtle correlations in the pseudo random number generator used we present a quantitative test of two generators which supports recent results reported in more systematic studies

backbone and elastic backbone of percolation clusters obtained by the new method of burning we introduce a method of obtaining information about percolation clusters in which the clusters are burned in different ways this method yields the backbone and the elastic backbone their number of loops shortest path and other quantities it works in any dimension and can be applied also to other clusters we obtain accurate estimates for the backbone exponents in two and three dimensions

bit level correlations in some pseudorandom number generators we present results of extensive bit level tests on some pseudorandom number generators which are commonly used in physics applications the generators have first been tested with an extended version of the d tuple test second we have developed a cluster test where a physical analogy of the binary numbers with the two dimensional ising model has been utilized we demonstrate that this new test is rather powerful in finding periodic correlations on bit level results of both test methods are presented for each bit of the output of the generators some generators exhibit clear bit level correlations but we find no evidence of discernible correlations for generators which have recently produced systematic errors in monte carlo simulations

spreading of percolation in three and four dimensions the authors present monte carlo simulations of the spreading of bond percolation on three and four dimensional simple hyper cubic lattices the algorithm is the same as that applied previously in two dimensions with the spreading proceeding from a hyperplane they find the spreading dimension to be d 1 82 or 0 02 three dimensional and d 1 88 or 0 03 four dimensional also they obtain values of the percolation probability and of the static exponents with errors at least comparable to the best values from the literature

random walk on the prime numbers the one dimensional random walk rw where steps up and down are performed according to the occurrence of special primes is defined some quantities characterizing rw are investigated the mean fluctuation function f l displays perfect power law dependence f l l1 2 indicating that the defined rw is not correlated the number of returns of this special rw to the origin is investigated it turns out that this single very special realization of rw is a typical one in the sense that the usual characteristics used to measure rw take values close to the ones averaged over all random walks this fact suggests that random numbers of good quality could be obtained by means of rw on prime numbers the fractal structure on the subset of primes is also found

periodic orbits of the ensemble of sinai arnold cat maps and pseudorandom number generation we propose methods for constructing high quality pseudorandom number generators rngs based on an ensemble of hyperbolic automorphisms of the unit two dimensional torus sinai arnold map or cat map while keeping a part of the information hidden the single cat map provides the random properties expected from a good rng and is hence an appropriate building block for an rng although unnecessary correlations are always present in practice we show that introducing hidden variables and introducing rotation in the rng output accompanied with the proper initialization dramatically suppress these correlations we analyze the mechanisms of the single cat map correlations analytically and show how to diminish them we generalize the percival vivaldi theory in the case of the ensemble of maps find the period of the proposed rng analytically and also analyze its properties we present efficient practical realizations for the rngs and check our predictions numerically we also test our rngs using the known stringent batteries of statistical tests and find that the statistical properties of our best generators are not worse than those of other best modern generators

numerical simulation of randomly forced turbulent flows several authors have proposed studying randomly forced turbulent flows e g e a novikov soviet physics jetp 20 5 1290 1965 more recently theoretical investigations e g renormalization group have focused on white noise forced navier stokes equations v yakhot and s a orszag j sci comput 1 1 3 1986 the present article aims to provide an appropriate numerical method for the simulation of randomly forced turbulent systems the spatial discretization is based on the classical fourier spectral method the time integration is performed by a second order runge kutta scheme the consistency of an extension of this scheme to treat additive noise stochastic differential equations is proved the random number generator is based on lagged fibonacci series results are presented for two randomly forced problems the burgers and the incompressible navier stokes equations with a white noise in time forcing term characterized by a power law correlation function in spectral space a variety of statistics are computed for both problems including the structure functions the third order structure functions are compared with their exact expressions in the inertial subrange the influence of the dissipation mechanism viscous or hyperviscous on the inertial subrange is discussed in particular probability density functions of velocity increments are computed for the navier stokes simulation finally for both burgers and navier stokes problems our results support the view that random sweeping is the dominant effect of the large scale motion on the small scales

tests of randomness by the gambler s ruin algorithm abstract in the gambler s ruin algorithm on the cyclic group z n 0 1 n 1 we consider arrival time at 0 starting from a fixed point x 0 and use several versions of arrival time algorithm to test pseudorandom number generators this kind of test based on the exact probability density for a random walk on a finite group is done for the first time the test results show hidden defects in some generators such as combined multiple recursive generators and mersenne twister generators

hurst s rescaled range statistical analysis for pseudorandom number generators used in physical simulations the rescaled range statistical analysis r s is proposed as a method to detect correlations in pseudorandom number generators used in monte carlo simulations in an extensive test it is demonstrated that the r s analysis provides a very sensitive method to reveal hidden long run and short run correlations several widely used and also some recently proposed pseudorandom number generators are subjected to this test in many generators correlations are detected and quantified

chaos induced true randomness abstract we investigate functions of type x n p z n where p t is a periodic function and z are real parameters we show that these functions produce truly random sequences we prove that a class of autonomous dynamical systems containing nonlinear terms described by periodic functions of the variables can generate random dynamics we generalize these results to dynamical systems with nonlinearities in the form of noninvertible functions several examples are studied in detail we discuss how the complexity of the dynamics depends on the kind of nonlinearity we present real physical systems that can produce random time series we report the results of real experiments using nonlinear circuits with noninvertible i v characteristics in particular we show that a josephson junction coupled to a chaotic circuit can generate unpredictable dynamics

are random walks random abstract random walks have been created using the pseudo random generators in different computer language compilers basic pascal fortran c using a pentium processor all the obtained paths have apparently a random behavior for short walks 214 steps from long random walks 233 steps different periods have been found the shortest being 218 for pascal and the longest 231 for fortran and c while basic had a 224 steps period the basic pascal and fortran long walks had even 2 or 4 symmetries the c walk systematically roams away from the origin using deviations from the mean distance rule for random walks d2 n a more severe criterion is found e g random walks generated by a pascal compiler fulfills this criterion to n 000

noisy integer maps abstract the combined effects of discretization and noise in iterated maps are studied with simulations and a transfer matrix technique the resulting changes in a typical map s invariant distribution are illustrated

universal properties of a run and tumble particle in arbitrary dimension we consider an active run and tumble particle rtp in d dimensions starting from the origin and evolving over a time interval 0 t we examine three different models for the dynamics of the rtp the standard rtp model with instantaneous tumblings a variant with instantaneous runs and a general model in which both the tumblings and the runs are noninstantaneous for each of these models we use the sparre andersen theorem for discrete time random walks to compute exactly the probability that the x component does not change sign up to time t showing that it does not depend on d as a consequence of this result we compute exactly other x component properties namely the distribution of the time of the maximum and the record statistics showing that they are universal i e they do not depend on d moreover we show that these universal results hold also if the speed v of the particle after each tumbling is random drawn from a generic probability distribution our findings are confirmed by numerical simulations some of these results have been announced in a recent letter phys rev lett 124 090603 2020 10 1103 physrevlett 124 090603

pseudo random coins show more heads than tails tossing a coin is the most elementary monte carlo experiment in a computer the coin is replaced by a pseudo random number generator it can be shown analytically and by exact enumerations that popular random number generators are not capable of imitating a fair coin pseudo random coins show more heads than tails this bias explains the empirically observed failure of some random number generators in random walk experiments it can be traced down to the special role of the value zero in the algebra of finite fields

possibly exact fractal dimensions from conformal invariance based on an equivalence between the q state potts model and conformally invariant field theories the author speculates that all fractal dimensionalities of two dimensional percolation are given by the formula d 100 x2 48 where x is an integer the same formula should also apply to self avoiding walks and lattice animals this approach is extended to cluster weighted percolation his conjecture seems to agree with previous exact and numerical results except for the backbone exponent and possibly for lattice animals

diffusion on percolation clusters at criticality the concept of fractal dimensionality is used to study the problem of diffusion on percolation clusters the authors find from monte carlo simulations that the fractal dimensionality of a random walk on a critical percolation cluster in three dimensional space is d 3 3 or 0 1 where the size of the cluster is restricted to be larger than the span of the walk and is d 3 9 or 0 1 for a walk on clusters not subject to this restriction for two dimensional space they find d approximately d approximately 2 7 or p0 1 the exponent d and d is related to the scaling of the average length r of n steps via rd varies as n the fracton dimensionality which is related to the density of states was found to be 1 26 or 0 1 these results are in good agreement with the predictions of alexander and orbach 1982

universal survival probability for a d dimensional run and tumble particle we consider an active run and tumble particle rtp in d dimensions and compute exactly the probability s t that the x component of the position of the rtp does not change sign up to time t when the tumblings occur at a constant rate we show that s t is independent of d for any finite time t and not just for large t as a consequence of the celebrated sparre andersen theorem for discrete time random walks in one dimension moreover we show that this universal result holds for a much wider class of rtp models in which the speed v of the particle after each tumbling is random drawn from an arbitrary probability distribution we further demonstrate as a consequence the universality of the record statistics in the rtp problem

a fractal model for band structures just above percolation threshold a two dimensional regular fractal model is proposed to imitate the geometric texture of percolating networks just above percolation threshold the system is self similar fractal on length scales smaller than the connectedness length but becomes homogeneous non fractal square lattice on larger length scales the scaling of vibrational density of states and band structures are studied by using exact renormalisation group methods it is shown that an infinite number of narrow bands appear to have self similar structures of typical cantor sets at low frequency

physical tests for random numbers in simulations we propose three physical tests to measure correlations in random numbers used in monte carlo simulations the first test uses autocorrelation times of certain physical quantities when the ising model is simulated with the wolff algorithm the second test is based on random walks and the third on blocks of ital n successive numbers we apply the tests to show that recent errors in high precision ising simulations using generalized feedback shift register algorithms are due to short range correlations in random number sequences

cluster structure near the percolation threshold derives exact relations that allow one to describe unambiguously and quantitatively the structure of clusters near the percolation threshold pc in particular the author proves the relations p dpij dp lambda ij where p is the bond density pij is the pair connectedness function and lambda ij is the average number of cutting bonds between i and j from this relation it follows that the average number of cutting bonds between two points separated by a distance of the order of the connectedness length xi diverges as mod p pc mod 1 the remaining multiply connected bonds in the percolating backbone which lump together in blobs diverge with a dimensionality dependent exponent he also shows that in the cell renormalisation group of reynolds et al 1978 1980 the thermal eigenvalue is simply related to the average number of cutting bonds in the spanning cluster he discusses a percolation model in which the blobs can be controlled by varying a parameter and study the influence on the critical exponents

distributions and moments of structural properties for percolation clusters we study numerically and by scaling methods the distributions and moments of several structural properties of percolation clusters in two and three dimensions the clusters are generated at criticality and properties such as the distribution of the mass as a function of linear size or chemical distance are studied our results suggest that the hierarchy of moments can be represented by a single gap exponent using a scaling approach we obtain analytical forms for the different distribution functions which agree very well with the numerical data

diffusion on random systems above below and at their percolation threshold in two and three dimensions a detailed monte carlo study is presented for classical diffusion random walks on random l l triangular and l l l simple cubic lattices with l up to 4096 and 256 respectively the speed of a cyber 205 vector computer is found to be about one order of magnitude larger than that of a usual cdc cyber 76 computer to reach the asymptotic scaling regime walks with up to 10 million steps were simulated with about 10 jl steps in total for l 256 at the percolation threshold we review and extend the dynamical scaling description for the distance traveled as function of time the diffusivity above the threshold and the cluster radius below earlier discrepancies between scaling theory and computer experiment are shown to be due to insufficient monte carlo data the conductivity exponent is found to be 2 0 0 2 in three and 1 28 0 02 in two dimensions our data in three dimensions follow well the finite size scaling theory below the threshold the approach of the distance traveled to its asymptotic value is consistent with theoretical speculations and an exponent 2 5 independent of dimensionality the correction to scaling exponent at pc seems to be larger in two than in three dimensions

on the spreading dimension of percolation and directed percolation clusters the authors study the number an of sites that are accessible after n steps at most on clusters at the percolation threshold on a cayley tree an is of order n2 if the origin belongs to a larger cluster whereas its average over all clusters is of order n this suggests that the intrinsic spreading dimension d defined by an approximately nd is equal to two for fractal percolation clusters in space dimensions d or 6 and depends on d for d 6 for directed percolation clusters they argue that d is related to usual critical exponents by d beta gamma nu sub monte carlo data that support this relation are presented in two dimensions analogous results are derived for lattice animals d 2 on the cayley tree and d 1 nu sub for directed animals in any dimensions

order propagation near the percolation threshold a new monte carlo method for studying bond percolation clusters is developed and used to identify new critical quantities associated with the percolation threshold the bonds in each cluster are partitioned into three distinct connectivity classes red singly connected backbone bonds blue multiply connected backbone bonds and yellow non backbone bonds often called dangling ends among the new cluster properties studied are the mean number of red bonds a critical quantity diverging at p c with exponent y r approximately 1 and the length of the shortest connected path through the cluster which is critical with exponent y min 1 35 0 02 for all cluster properties studies the authors also compute averages over only the largest clusters the corresponding critical exponents are found to be significantly different from those obtained by averaging over clusters of all sizes

stationary states in two dimensional systems driven by bivariate levy noises systems driven by ensuremath alpha stable noises could be very different from their gaussian counterparts stationary states in single well potentials can be multimodal moreover a potential well needs to be steep enough in order to produce stationary states here it is demonstrated that two dimensional 2d systems driven by bivariate ensuremath alpha stable noises are even more surprising than their 1d analogs in 2d systems intriguing properties of stationary states originate not only due to heavy tails of noise pulses which are distributed according to ensuremath alpha stable densities but also because of properties of spectral measures consequently 2d systems are described by a whole family of langevin and fractional diffusion equations solutions of these equations bear some common properties but also can be very different it is demonstrated that also for 2d systems potential wells need to be steep enough in order to produce bounded states moreover stationary states can have local minima at the origin the shape of stationary states reflects symmetries of the underlying noise i e its spectral measure finally marginal densities in power law potentials also have power law asymptotics

the fractal dimension of cluster perimeters generated by a kinetic walk the fractal dimension dg of cluster perimeters generated by a recently proposed butterfly growth walk is considered in the long range limit of the walk on a percolation cluster dg appears to be equal to the fractal dimension of the singly connected bonds dg 1 nu the new relation for chemical dimension dl is proposed dl df df dg in the short range limit the butterfly walk on a euclidean lattice appears to be in the same universality class as a random walk the dynamic aspect of the growth walk is discussed and the continuously tunable spectral dimension is obtained both short and long range limits of this diffusion process are different from a random diffusion on percolation

modelling porous structures by repeated sierpinski carpets abstract porous materials such as sedimentary rocks often show a fractal character at certain length scales deterministic fractal generators iterated upto several stages and then repeated periodically provide a realistic model for such systems on the fractal diffusion is anomalous and obeys the law r 2 t 2 d w where r 2 is the mean square distance covered in time t and d w 2 is the random walk dimension the question is how is the macroscopic diffusivity related to the characteristics of the small scale fractal structure which is hidden in the large scale homogeneous material in particular do structures with same d w necessarily lead to the same diffusion coefficient at the same iteration stage the present paper tries to shed some light on these questions

diffusion coefficient for random walks on strips with spatially inhomogeneous boundaries the authors determine the diffusion constant k for unbiased discrete time random walks on infinitely long planar strips of finite width with regularly spaced stepped edges that model albeit in a simple and regular manner some of the features of the corrugated surfaces of diffusion channels in porous media they derive a formal expression for k and use it to compute k exactly for a range of values of the strip width and the step width the latter serving as a measure of the roughness of the boundaries they also consider the role of specific boundary conditions at the edges by determining k for both myopic and blind random walkers in each case the results shed some light on the effects of spatially inhomogeneous transverse boundaries on the coefficient of diffusion in the longitudinal direction

simulation of a directed random walk model the effect of pseudo random number correlations abstract we investigate the mechanism that leads to systematic deviations in cluster monte carlo simulations when correlated pseudo random numbers are used we present a simple model which enables an analysis of the effects due to correlations in several types of pseudo random number sequences this model provides qualitative understanding of the bias mechanism in a class of cluster monte carlo algorithms

application of fractal concepts to polymer statistics and to anomalous transport in randomly porous media we consider the application of fractal concepts to polymer statistics and to anomalous transport in randomly porous media it is found that answers to interesting physics questions can be expressed in terms of several new fractal dimensions in addition to the fractal dimensiond f 1 d the fractal dimension of the backbone arises in connection with electric current flow 2 d red the fractal dimension of the singly connected bonds in the backbone arises in connection with its equivalence to the thermal scaling power 3 d e the fractal dimension of the of the elastic backbone 4 d u the fractal dimension of the unscreened perimeter arises in connection with the viscosity singularity at the gelation threshold 5 d min the fractal dimension of the minimum path or chemical distance between two sites arises in co nnection with the aharony stauffer conjecture 6 dw the fractal dimension of a random walk 7 d g the fractal dimension of growth sites that arise as a random walk creates a cluster relations among these fractal dimensions are discussed some of which can be proved and others of which are conjectures whose validity has been established only in certain limiting cases

aggregation by attractive particle cluster interaction a quasideterministic irreversible growth model is studied where aggregates are generated by attractive cluster particle forces proportional ro r alpha it is shown that fractal dimensions and growth site probability measures of the resulting fractal structures strongly depend on the parameter alpha comparison with experimental results indicates that this model represents a further step towards realistic simulations of growth processes