Showing papers in "International Journal of Modern Physics C in 1996"
TL;DR: In this article, it was shown that multiplicative random processes in (not necessarily equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the elementary variables.
Abstract: Multiplicative random processes in (not necessarily equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the elementary variables. In terms of the original variables this gives a power-law distribution. This mechanism implies certain relations between the constraints of the system, the power of the distribution and the dispersion law of the fluctuations. These predictions are validated by Monte Carlo simulations and experimental data. We speculate that stochastic multiplicative dynamics might be the natural origin for the emergence of criticality and scale hierarchies without fine-tuning.
259 citations
TL;DR: The results suggest that evolved generators are at least as good as previously described CAs, with notable advantages arising from the existence of a "tunable" algorithm for obtaining random number generators.
Abstract: Random numbers are needed in a variety of applications, yet finding good random number generators is a difficult task. In this paper non-uniform cellular automata (CA) are studied, presenting the cellular programming algorithm for co-evolving such CAs to perform computations. The algorithm is applied to the evolution of random number generators; our results suggest that evolved generators are at least as good as previously described CAs, with notable advantages arising from the existence of a "tunable" algorithm for obtaining random number generators.
92 citations
TL;DR: In this paper, an efficient Monte Carlo algorithm for simulating hardly-relaxing systems is proposed, and the results show that reasonable values of the critical temperature and critical exponents can be obtained within Monte Carlo steps much shorter than the observation time a conventional simulation usually requires.
Abstract: An efficient Monte Carlo algorithm for simulating hardly-relaxing systems is proposed. By using this algorithm the three-dimensional ± J Ising spin glass model is studied. The result shows that reasonable values of the critical temperature and of the critical exponents can be obtained within Monte Carlo steps much shorter than the observation time a conventional simulation usually requires.
89 citations
TL;DR: In this paper, the authors studied the stationary regime of a previously introduced dynamical microscopic model of the stock market and found that the wealth distribution among investors spontaneously converges to a power law.
Abstract: Power laws are found in a wide range of different systems: From sand piles to word occurrence frequencies and to the size distribution of cities. The natural emergence of these power laws in so many different systems, which has been called self-organized criticality, seems rather mysterious and awaits a rigorous explanation. In this letter we study the stationary regime of a previously introduced dynamical microscopic model of the stock market. We find that the wealth distribution among investors spontaneously converges to a power law. We are able to explain this phenomenon by simple general considerations. We suggest that similar considerations may explain self-organized criticality in many other systems. They also explain the Levy distribution.
84 citations
TL;DR: In this article, the authors extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom, and show that these systems fulfill nonlinear time evolution equations similar to the ones encountered in Spontaneous Symmetry Breaking (SSB) dynamics and evolve spontaneously towards "fixed trajectories" indexed by the average value of their degree of freedom.
Abstract: We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for certain parameter ranges, the new systems fulfill nonlinear time evolution equations similar to the ones encountered in Spontaneous Symmetry Breaking (SSB) dynamics and evolve spontaneously towards "fixed trajectories" indexed by the average value of their degrees of freedom (which corresponds to the SSB order parameter). The "fixed trajectories" dynamics evolves on the edge between explosion and collapse/extinction. The systems present power laws with exponents which in a wide range (α −2 there is no "thermodynamic limit" and the fluctuations are dominated by a few, largest degrees of freedom which leads to macroscopic fluctuations, chaos, and bursts/intermittency.
76 citations
TL;DR: In this paper, an extension into three dimensions of an existing two-dimensional technique for simulating brittle solid fracture is described, where the fracture occurs on a simulated solid created by "gluing" together space-filling polyhedral elements with compliant interelement joints.
Abstract: This paper describes an extension into three dimensions of an existing two-dimensional technique for simulating brittle solid fracture. The fracture occurs on a simulated solid created by "gluing" together space-filling polyhedral elements with compliant interelement joints. Such a material can be shown to have well-defined elastic properties. However, the "glue" can only support a specified tensile stress and breaks when that stress is exceeded. In this manner, a crack can propagate across the simulated material. A comparison with experiment shows that the simulation can accurately reproduce the size distributions for all fragments with linear dimensions greater than three element sizes.
47 citations
TL;DR: This work has reached real-time for the whole German Autobahn network on a 16-CPU SGI Power Challenger and a 12-CPU SUN workstation-cluster.
Abstract: This work is part of our ongoing effort to design and implement a traffic simulation application capable of handling realistic problem sizes in multiple real-time. Our traffic simulation model includes multi-lane vehicular traffic and individual route-plans. On a 16-CPU SGI Power Challenger and a 12-CPU SUN workstation-cluster we have reached real-time for the whole German Autobahn network.
44 citations
TL;DR: In this article, a hybrid eight-algebraic-order two-step method with phase-lag of order ten was developed for computing elastic scattering phase shifts of the one-dimensional Schrodinger equation.
Abstract: A new hybrid eighth-algebraic-order two-step method with phase-lag of order ten is developed for computing elastic scattering phase shifts of the one-dimensional Schrodinger equation. Based on this new method and on the method developed recently by Simos we obtain a new variable-step procedure for the numerical integration of the Schrodinger equation. Numerical results obtained for the integration of the phase shift problem for the well known case of the Lenard–Jones potential show that this new method is better than other finite difference methods.
34 citations
TL;DR: This work has tested many commonly-used random number generators with high precision Monte Carlo simulations of the 2-d Ising model using the Metropolis, Swendsen-Wang, and Wolff algorithms, and recommendations for random number generator for high-performance computers, particularly for lattice Monte Carlo simulation.
Abstract: Large-scale Monte Carlo simulations require high-quality random number generators to ensure correct results. The contrapositive of this statement is also true — the quality of random number generators can be tested by using them in large-scale Monte Carlo simulations. We have tested many commonly-used random number generators with high precision Monte Carlo simulations of the 2-d Ising model using the Metropolis, Swendsen-Wang, and Wolff algorithms. This work is being extended to the testing of random number generators for parallel computers. The results of these tests are presented, along with recommendations for random number generators for high-performance computers, particularly for lattice Monte Carlo simulations.
34 citations
TL;DR: In this article, a two-step method is developed for computing eigenvalues and resonances of the radial Schrodinger equation, which is better than other similar methods, such as the one presented in this paper.
Abstract: A two-step method is developed for computing eigenvalues and resonances of the radial Schrodinger equation. Numerical results obtained for the integration of the eigenvalue and the resonance problem for several potentials show that this new method is better than other similar methods.
32 citations
TL;DR: In this paper, the authors determined the exponent for the normal conductivity at the threshold of three-dimensional site and bond percolation using 20 months of CPU time on a special purpose computer "Percola".
Abstract: Using 20 months of CPU time on our special purpose computer "Percola" we determined the exponent for the normal conductivity at the threshold of three-dimensional site and bond percolation. The extrapolation analysis taking into account the first correction to scaling gives a value of t/ν = 2.26±0.04 and a correction exponent ω around 1.4.
TL;DR: In this article, the authors studied the low-velocity impact of two solid discs of equal size using a cell model of brittle solids and obtained the velocity and the mass distribution of the debris.
Abstract: We study the phenomena associated with the low-velocity impact of two solid discs of equal size using a cell model of brittle solids. The fragment ejection exhibits a jet-like structure the direction of which depends on the impact parameter. We obtain the velocity and the mass distribution of the debris. Varying the radius and the initial velocity of the colliding particles, the velocity components of the fragments show anomalous scaling. The mass distribution follows a power law in the region of intermediate masses.
TL;DR: In this paper, a set of expressions for evaluating energies and forces between particles interacting logarithmically in a finite two-dimensional system with periodic boundary conditions is presented, which can be used for fast and accurate, dynamical or Monte Carlo, simulations of interacting line charges or interactions between point and line charges.
Abstract: We present a set of expressions for evaluating energies and forces between particles interacting logarithmically in a finite two-dimensional system with periodic boundary conditions. The formalism can be used for fast and accurate, dynamical or Monte Carlo, simulations of interacting line charges or interactions between point and line charges. The expressions are shown to converge to usual computer accuracy (~10–16) by adding only few terms in a single sum of standard trigonometric functions.
TL;DR: A new general numerical method to compute many Green's functions for complex non-singular matrices within one iteration process and can be integrated within any Krylov subspace solver is presented.
Abstract: The availability of efficient Krylov subspace solvers plays a vital role in the solution of a variety of numerical problems in computational science. Here we consider lattice field theory. We present a new general numerical method to compute many Green's functions for complex non-singular matrices within one iteration process. Our procedure applies to matrices of structure A = D − m, with m proportional to the unit matrix, and can be integrated within any Krylov subspace solver. We can compute the derivatives x(n) of the solution vector x with respect to the parameter m and construct the Taylor expansion of x around m. We demonstrate the advantages of our method using a minimal residual solver. Here the procedure requires one intermediate vector for each Green's function to compute. As real-life example, we determine a mass trajectory of the Wilson fermion matrix for lattice QCD. Here we find that we can obtain Green's functions at all masses ≥ m at the price of one inversion at mass m.
TL;DR: In this paper, the authors present a status report on the ongoing analysis of the 3D Ising model with nearest-neighbor interactions using the Monte Carlo Renormalization Group (MCRG) and finite size scaling (FSS) methods on 643, 1283, and 2563 simple cubic lattices.
Abstract: We present a status report on the ongoing analysis of the 3D Ising model with nearest-neighbor interactions using the Monte Carlo Renormalization Group (MCRG) and finite size scaling (FSS) methods on 643, 1283, and 2563 simple cubic lattices. Our MCRG estimates are and ν = 0.625(1). The FSS results for Kc are consistent with those from MCRG but the value of ν is not. Our best estimate η = 0.025(6) covers the spread in the MCRG and FSS values. A surprise of our calculation is the estimate ω ≈ 0.7 for the correction-to-scaling exponent. We also present results for the renormalized coupling gR along the MCRG flow and argue that the data support the validity of hyperscaling for the 3D Ising model.
TL;DR: In this paper, the authors report large systematic errors in Monte Carlo simulations of the tricritical Blume-Capel model using single spin Metropolis updating, manifest as a 20% asymmetry in the magnetization distribution.
Abstract: We report large systematic errors in Monte Carlo simulations of the tricritical Blume–Capel model using single spin Metropolis updating. The error, manifest as a 20% asymmetry in the magnetization distribution, is traced to the interplay between strong triplet correlations in the shift register random number generator and the large tricritical clusters. The effect of these correlations is visible only when the system volume is a multiple of the random number generator lag parameter. No such effects are observed in related models.
TL;DR: In this article, the stock market model of Levy, Persky, Solomon is simulated for much larger numbers of investors and the resulting prices of large markets oscillate smoothly in a semi-regular fashion.
Abstract: The stock market model of Levy, Persky, Solomon is simulated for much larger numbers of investors. While small markets can lead to realistically looking prices, the resulting prices of large markets oscillate smoothly in a semi-regular fashion.
TL;DR: The sand pile model is shown to be able to simulate, by specific configurations, logic gates and registers and, therefore any computer program, and to give its interpretation in terms of a set of several one-dimensional interacting avalanches.
Abstract: We show that the sand pile model is able to simulate, by specific configurations, logic gates and registers and, therefore any computer program. Further, we give its interpretation in terms of a set of several one-dimensional interacting avalanches.
TL;DR: It appears feasible to investigate the thermodynamics of a full gravitating n-body problem with O(16.000) particles using the new method on a QH4 system, and the interprocessor communication costs of the standard and hyper-systolic approaches are compared for various granularities.
Abstract: We investigate the performance gains from hyper-systolic implementations of n2-loop problems on the massively parallel computer Quadrics, exploiting its three-dimensional interprocessor connectivity. For illustration we study the communication aspects of an exact molecular dynamics simulation of n particles with Coulomb (or gravitational) interactions. We compare the interprocessor communication costs of the standard-systolic and the hyper-systolic approaches for various granularities. We predict gain factors as large as three on the Q4 and eight on the QH4 and measure actual performances on these machine configurations. We conclude that it appears feasible to investigate the thermodynamics of a full gravitating n-body problem with O(16.000) particles using the new method on a QH4 system.
TL;DR: In this paper, the authors investigated the electromagnetic influence of the surrounding idle region on static fluxons in window Josephson junctions and derived approximate expressions for the case of small and large idle regions.
Abstract: We investigate the electromagnetic influence of the surrounding idle (no tunneling) region on static fluxons in window Josephson junctions. We calculated the fluxon width as a function of the size of the idle region for three different window (active tunneling area) geometries, namely elongated truncated rhombus, rectangular and bow-tie and derived approximate expressions for the case of small and large idle regions. The window geometry affects both the fluxon width and the fluxon stability. One can define an effective λJ which depends on the junction width, the idle region width and the inductance ratio and has important consequences on the static and dynamic properties of window Josephson junctions. We also show the effect of the idle region on the maximum tunneling current as a function of the external magnetic field.
TL;DR: In this paper, the two-dimensional simulations of Majumdar, Bray, Cornell, and Sire were generalized to three to five dimensions and confirmed with their epsilon expansion.
Abstract: The two-dimensional simulations of Majumdar, Bray, Cornell, and Sire are confirmed and generalized to three to five dimensions. They agree with their epsilon expansion.
TL;DR: In this article, a physically motivated ansatz based on locally defined drag forces is proposed to deal efficiently with large numbers of particles in incompressible fluids, where the interactions between particles and fluid are taken into account by a physically-motivated ansatz.
Abstract: We present a numerical method to deal efficiently with large numbers of particles in incompressible fluids. The interactions between particles and fluid are taken into account by a physically motivated ansatz based on locally defined drag forces. We demonstrate the validity of our approach by performing numerical simulations of sedimenting non-Brownian spheres in two spatial dimensions and compare our results with experiments. Our method reproduces qualitatively important aspects of the experimental findings, in particular the strong anisotropy of the hydrodynamic bulk self-diffusivities.
TL;DR: In this paper, the authors show how repeated simulations can be used so that drivers can explore different paths, and how macroscopic quantities such as locations of jams or network throughput change as a result of this.
Abstract: Traffic simulations are made more realistic by giving individual drivers intentions, i.e., an idea of where they want to go. One possible implementation of this idea is to give each driver an exact pre-computed path, that is, a sequence of roads this driver wants to follow. This paper shows, in a realistic road network, how repeated simulations can be used so that drivers can explore different paths, and how macroscopic quantities such as locations of jams or network throughput change as a result of this.
TL;DR: In this paper, the results of the recent numerical simulations on vector spin glasses are presented, along with numerical evidence of the novel chiral-glass state, accompanied with broken spin-reflection symmetry with preserving spin-rotation symmetry.
Abstract: The results of the recent numerical simulations on vector spin glasses are presented. Numerical evidence of the novel chiral-glass state, accompanied with broken spin-reflection symmetry with preserving spin-rotation symmetry, is presented. Implication to experiments on spin-glass transitions is discussed.
TL;DR: In this paper, a large number of random bond configurations are probed in the framework of quenched averages, motivated by the relationship between hierarchical lattice models whose partition function zeros fall on Julia sets and chaotic renormalization group flows in such models with frustration.
Abstract: We study the pattern of zeros emerging from exact partition function evaluations of Ising spin glasses on conventional finite lattices of varying sizes. A large number of random bond configurations are probed in the framework of quenched averages. This study is motivated by the relationship between hierarchical lattice models whose partition function zeros fall on Julia sets and chaotic renormalization group flows in such models with frustration, and by the possible connection of the latter with spin glass behavior. In any finite volume, the simultaneous distribution of the zeros of all partition functions can be viewed as part of the more general problem of finding the location of all the zeros of a certain class of random polynomials with positive integer coefficients. Some aspects of this problem have been studied in various areas of mathematics, and we show in particular how polynomial mappings which are used in graph theory to classify graphs, may help in characterizing the distribution of zeros. We finally discuss the possible limiting set of these zeros as the volume is sent to infinity.
TL;DR: From presumed world-record simulations and from the Ito algorithm applied to smaller 3D lattices, the dynamical critical exponent z near 2.05 in three dimensions and J/kBTc = 0.11391 in five is obtained.
Abstract: From presumed world-record simulations up to 48003 and 1125 and from the Ito algorithm applied to smaller 3D lattices we obtain the dynamical critical exponent z near 2.05 in three dimensions and J/kBTc = 0.11391 in five.
TL;DR: This investigation reveals an intricate interplay between temporal and spatial factors, with the presence of different rules in the grid giving rise to complex dynamics.
Abstract: We study the effects of random faults on the behavior of one-dimensional, non-uniform cellular automata (CA), where the local update rule need not be identical for all grid sites. The CA systems examined were obtained via an approach known as cellular programming, which involves the evolution of non-uniform CAs to perform non-trivial computational tasks. Using the "system replicas" methodology, involving a comparison between a perfect, non-perturbed version of the CA and a faulty one, we find that our evolved systems exhibit graceful degradation in performance, able to tolerate a certain level of faults. We then "zoom" into the fault-tolerant zone, where "good" computational behavior is exhibited, introducing measures to fine-tune our understanding of the faulty CAs' operation. We study the error level as a function of time and space, as well as the recuperation time needed to recover from faults. Our investigation reveals an intricate interplay between temporal and spatial factors, with the presence of different rules in the grid giving rise to complex dynamics. Studies along this line may have applications to future computing systems that will contain thousands or even millions of computing elements, rendering crucial the issue of resilience.
TL;DR: In this paper, the probability of getting more than one spanning cluster at PC for site percolation in dimensions of two to five was studied. The probability increases from 0.003 in two dimensions to 0.16 in five.
Abstract: We study the probability of getting more than one spanning cluster at pc for site percolation in dimensions of two to five. The probability increases from ~0.003 in two dimensions to ~0.16 in five. This shows that although there can be only one infinite cluster of finite density, there can be several spanning clusters at the same time.
TL;DR: In the framework of the bit-string model of biological ageing, it is shown that the survival chance of a small population in an environment of limited carrying capacity grows exponentially with the size of the habitat.
Abstract: In the framework of the bit-string model of biological ageing we show that the survival chance of a small population in an environment of limited carrying capacity grows exponentially with the size of the habitat. Extinction is usually preceded by a gradual decline of the genetic condition of the population. With death due to senescence coming earlier, the typical population size shrinks, and at some stage the population dies out due to the fluctuations.
TL;DR: It is observed that the survival state selects an adequate distribution of the minimum reproduction age autonomously and the minimum reproduce age is made variable.
Abstract: The reproduction risk is introduced into the Penna model of reproducing systems. And the minimum reproduction age is made variable. It is observed that the survival state selects an adequate distribution of the minimum reproduction age autonomously.