International Journal of Modern Physics C

Cellular programming is a coevolutionary algorithm by which parallel cellular systems evolve to solve computational tasks. The evolving system is a massively parallel, locally interconnected grid of cells, where each cell operates according to a local interaction rule. If this rule is identical for all cells, the system is referred to as uniform, otherwise, it is non-uniform. This paper describes an experiment that addresses the following question: Employing a local coevolutionary process to solve a hard problem, known as density classification, can an optimal uniform solution be found? Since our approach involves the evolution of non-uniform CAs, where cellular rules are initially assigned at random, such convergence to uniformity cannot be a priori expected to easily emerge. The question is of both theoretical and practical interest. As for the latter, one major advantage of local evolutionary processes is their amenability to parallel implementation, using commercially available parallel machines or specialized hardware. Our experiment shows that when such local evolution is applied to the density problem, the optimal solution can be found.

Saturated capacities in traffic systems evoke increasing interest in simulations of complex networks serving as laboratory environment for developing management strategies. Especially for urban areas questions concerning overall traffic control have to be considered with regard to their impacts on the whole network. Modeling traffic flow dynamics using cellular automata allows us to run large network traffic simulations with only comparatively low computational efforts. We present a traffic simulation tool for urban road networks which is based on the Nagel–Schreckenberg Model. Arbitrary kinds of roads and crossings are modeled as combinations of only a few basic elements. Furthermore parking capacities are considered as well as circulations of public transports. The vehicles are driven corresponding to route plans or at random depending on the available data. The application of this network simulation covers investigations on the field of traffic planning as well as online simulations based on real-time traffic data as basis for dynamic traffic management systems.

We present exact and stochastic diagonalization results for a BCS-reduced Hubbard model. The kinetic Hamiltonian is the same as in the single band Hubbard model with additional next nearest neighbor hopping. The interaction of this model is designed to inhibit superconductivity in the d_x²-y² channel. The ground state of this model is studied by exact and stochastic diagonalization technique. We present a review of the technical details of the application of the stochastic diagonalization algorithm on this problem. To verify our results obtained with the stochastic diagonalization, they are compared with the exact diagonalization results. In order to show the convergence of the stochastic diagonalization we give a detailed analysis of the behavior of physical properties with increasing number of states. Finally we study superconductivity in this BCS-reduced Hubbard model. As an indicator of superconductivity we use the occurrence of Off Diagonal Long Range Order. We study the scaling behavior of this model for various attractive interactions and in addition the dependence of the superconducting correlation functions from the filling of the system.

A general numerical method is presented to locate the partition function zeros in the complex β plane for large lattice sizes. We apply this method to the 2D Ising model and results are reported for square lattice sizes up to L = 64. We also propose an alternative method to evaluate corrections to scaling which relies only on the leading zeros. This method is illustrated with our data.

In this work we present some results from computer simulations of dynamical aspects of drop formation in a leaky faucet. Our results, which agree very well with the experiments, suggest that only a few elements, at the microscopic level, would be necessary to describe the most important features of this system. We were able to set all parameters of the model in terms of real ones. This is an additional advantage with respect to previous theoretical works.

The three-dimensional 3-state Potts model has been investigated by examining the average cluster size distributions. Cluster distributions give evidence for the weak first-order nature of the transition for lattice sizes as small as 16³, where the energy histogram method fails to exhibit the true nature of the transition.

We describe a simple ansatz to approximate the low temperature behavior of proteins and peptides by a mean-field-like model which is analytically solvable. For a small peptide some thermodynamic quantities are calculated and compared with numerical results of an all-atoms simulation. Our approach can be used to determine the weights for a multicanonical simulation of the molecule under consideration.

In this work we revisit the Hopfield–Tank algorithm for the traveling salesman problem (J. J. Hopfield and D. W. Tank, Biol. Cybern. 52, 141 (1985)) and report encouraging results, with a different dynamics, that makes the algorithm more efficient, finding better solutions in much less computational time.

In this article we consider the optimization of np-complete problems with a genetic algorithm. For "real word" problems we regard it to be sufficient to get close to the optimal solution without any guarantee of ever hitting it. Our algorithm was tested on two problem classes: the traveling salesman problem and the product ordering problem; the first is a standard problem, the latter a problem we were confronted with in a practical application. For all investigated problem instances we found very good solutions (<0.2% above optimum) in each run and even the global optimum in some runs on a Pentium/100 MHz-PC. For one instance of the TSP problem we could verify that the time spent to find the optimum follows a logarithmic normal distribution.

We take further the study of a learning-generalization process in a hidden-layer network for a given three-bit feature distinction by application of the replica method. When doing so, we are led to an Ising model with both external and random fields which cause considerable difficulties. Several approximations for this system are discussed

We report on implementation and performance of the program IMD, designed for short range molecular dynamics simulations on massively parallel computers. After a short explanation of the cell-based algorithm, its extension to parallel computers as well as two variants of the communication scheme are discussed. We provide performance numbers for simulations of different sizes and compare them with values found in the literature. Finally we describe two applications, namely a very large scale simulation with more than 1.23×10⁹ atoms, to our knowledge the largest published MD simulation up to this day and a simulation of a crack propagating in a two-dimensional quasicrystal.

Even for 693760 * 693760 square lattices, we found fast convergence into fixed points when each spin ± 1 was flipped if and only if more than half of its four neighbors point into the opposite direction. A percolation threshold was found near an initial concentration of 0.5007 and may belong to the universality class of random percolation.

We implement the numerical method of summing Green function diagrams on the Matsubara frequency axis for the fluctuation exchange (FLEX) approximation. Our method has previously been applied to the attractive Hubbard model for low density. Here we apply our numerical algorithm to the Hubbard model close to half filling (ρ =0.40), and for T/t = 0.03, in order to study the dynamics of one- and two-particle Green functions. For the values of the chosen parameters we see the formation of three branches which we associate with the two-peak structure in the imaginary part of the self-energy. From the imaginary part of the self-energy we conclude that our system is a Fermi liquid (for the temperature investigated here), since Im Σ(k, ω) ≈ w² around the chemical potential. We have compared our fully self-consistent FLEX solutions with a lower order approximation where the internal Green functions are approximated by free Green functions. These two approches, i.e., the fully self-consistent and the non-self-consistent ones give different results for the parameters considered here. However, they have similar global results for small densities.

In this work we employ an algebraic computational method to solve the integrals which arise in the study of diatomic molecules. Using the Slater-type orbitals (STO), we obtain analytical solutions for the one-center and two-center hybrid and Coulomb integrals. The exchange integrals are considered, as much as possible, in a similar manner. These results are used to calculate the electronic properties of the ground state of the LiH molecule, by means of a variational calculation using a basis of molecular orbitals. The behavior of the Slater exponents of the atomic orbitals are studied as functions of internuclear distance. We show that the STO undergo a lengthening of their shape when the nuclear separation increases.

We find that when two or more spanning clusters exist at the percolation threshold, the mass of each scales with the same fractal dimension D=1.89 in two dimensions and D=2.53 in three dimensions. We also determine the ratios of the masses of the spanning clusters. In two dimensions, this is done for different lattices of different shapes. In the case of two spanning clusters, the ratio of the larger spanning cluster to the smaller lies around 1.4 for two dimensions, almost independent of lattice structure and shape.