International Journal of Modern Physics C

Site and bond percolation thresholds are calculated for the face centered cubic, body centered cubic and diamond lattices in four, five and six dimensions. The results are used to study the behavior of percolation thresholds as a functions of dimension. It is shown that the predictions from a recently proposed invariant for percolation thresholds are not satisfactory for these lattices.

There are 880 magic squares of size 4 by 4, and 275 305 224 of size 5 by 5. It seems very difficult if not impossible to count exactly the number of higher order magic squares. We propose a method to estimate these numbers by Monte Carlo simulating magic squares at finite temperature. One is led to perform low temperature simulations of a system with many ground states that are separated by energy barriers. The Parallel Tempering Monte Carlo method turns out to be of great help here. Our estimate for the number of 6 by 6 magic squares is (0.17745± 0.00016)×10²⁰.

We address the following: Are there several optimal strategies for a hunter-gatherer society in a given environment, in which the society has an evolving level of technology and/or skills? We use the Genetic Algorithm, with point mutations, to facilitate the search for these strategies. We find that, in a generous environment, several optimal strategies are possible; there is no unique optimal strategy. We are now in a position, with the Genetic Algorithm, to assess different approaches to resource exploitation and the role of contingency.

In this paper we consider a microscopic model of a simple ecosystem. The basic ingredients of this model are individuals, and both the phenotypic and genotypic levels are taken in account. The model is based on a long range cellular automaton (CA); introducing simple interactions between the individuals, we get some of the complex collective behaviors observed in a real ecosystem. Since our fitness function is smooth, the model does not exhibit the error threshold transition; on the other hand the size of total population is not kept constant, and the mutational meltdown transition is present. We study the effects of competition between genetically similar individuals and how it can lead to species formation. This speciation transition does not depend on the mutation rate. We present also an analytical approximation of the model.

We have developed a distributed algorithm for the simulation of systems that evolve continuously, but which are also subject to discrete events that affect their evolution. As an example we consider the description through the BUU equations of the time evolution of a highly excited nuclear system, and show that this algorithm attains almost optimal speedups.

The sensitivity on shape and boundaries at the Curie point of the universal critical ratio L^dM²/χ for the Ising model is confirmed by a comparison of square and rectangular lattices. Tests with three different algorithms give the same results for the universal critical ratio on various lattice types and always the same dependence on the system's aspect ratio.

The ground state symmetry of an electrorheological fluid is studied numerically using a finite element method. The free energies of body-centered cubic, body-centered tetragonal, simple hexagonal, hexagonal close-packed, simple cubic, simple hexagonal, and honeycomb structures are calculated for systems containing homogeneous particles with the dielectric constant greater or smaller than that of the base fluid. In accordance with other studies, the body-centered tetragonal symmetry was found to be the most favored lattice symmetry. The ground state of an ER system containing two types of particles, i.e., particles with the dielectric constant greater and smaller than that of the base fluid, was found to consist of separated particle columns each of which has only one type of particles. These separated particle columns preferred body-centered tetragonal symmetry. However, simple hexagonal and honeycomb symmetries were found to be energetically quite close to a body-centered tetragonal symmetry. In addition, simple hexagonal and honeycomb symmetries do not need phase separation between different types of particles and are thus more likely to form. Dynamical effects were studied using a point dipole model. Within the time-span studied the system seemed to form a polycrystalline structure.

Using a recently proposed directed random walk test, we systematically investigate the popular random number generator RANLUX developed by Lüscher and implemented by James. We confirm the good quality of this generator with the recommended luxury level. At a smaller luxury level (for instance equal to 1) resonances are observed in the random walk test. We also find that the lagged Fibonacci and Subtract-with-Carry recipes exhibit similar failures in the random walk test. A revised analysis of the corresponding dynamical systems leads to the observation of resonances in the eigenvalues of Jacobi matrix.

For square and simple cubic Ising models at T=T_c, we look at the tails of the magnetization distribution for untypically large magnetizations. No indications for a stretched exponential or power law behavior are found.

We propose a simple model describing the dynamics of a system of two populations — more numerous natives and less numerous immigrants. The immigrants' birth rate is higher than that of the natives. Several modifications of this model taking into account changes of the birth rates due to external factors and/or possibility of contacts between the populations, are also introduced. The model is studied within two approaches — by solving a set of differential equations and through a Monte Carlo simulations. We show that the question of which population will eventually dominate depends on such factors as the probability of producing offsprings of mixed origin, assimilation of the immigrants, the ratio of the birth rates, initial numbers of the populations and the average age of an individual. In all, but two extreme cases, both populations will survive.

The fractions of samples spanning a lattice at its percolation threshold are found by computer simulation of random site-percolation in two- and three-dimensional hypercubic lattices using different boundary conditions. As a byproduct we find p_c=0.311605(5) in the cubic lattice.

This work presents a dynamical version of the LCAO method which includes extension variables, such as temperature and pressure. As an illustrative example, the method is applied to the temperature response of small silicon clusters. A comparison is made with molecular dynamics calculations using standard interatomic potentials.

The universal law for percolation thresholds proposed by Galam and Mauger (GM) is found to apply also to dynamical situations. This law depends solely on two variables, the space dimension d and a coordinance number q. For regular lattices, q reduces to the usual coordination number while for anisotropic lattices it is an effective coordination number. For dynamical percolation we conjecture that the law is still valid if we use the number q₂ of second nearest neighbors instead of q. This conjecture is checked for the dynamic epidemic model which considers the percolation phenomenon in a mobile disordered system. The agreement is good.