International Journal of Modern Physics C

The Piecewise Parabolic Method (PPM) hydrodynamics code and other codes based on the PPM technique have been used extensively for the simulation of astrophysical phenomena. A new version of the PPM hydrodynamics code under development at the Laboratory for Computational Science and Engineering (LCSE) at the University of Minnesota is described. This new code incorporates a version of dynamic local adaptive mesh refinement (AMR) targeted specifically at improving the treatment of shocks and contact discontinuities. This AMR technique is not intended to increase grid resolution in entire regions of the problem for which standard techniques of nonuniform grids and simple grid motion are adequate. Because the AMR is targeted at surfaces within a flow that can develop complex shapes, a cell-by-cell approach to the grid refinement is adopted in order to minimize the number of refined grid cells, with the hope of controlling the computational cost. As a result of this approach, the number of refined cells needed across a given shock or captured contact discontinuity is modest (< 10). Because the PPM method is very complex, ordinarily its wide difference stencil demands that a relatively large number of extra grid cells need to be added to each end of a grid strip, even when adapting to a thin feature of the flow. To avoid the work associated in handling these extra cells, only to conveniently produce valid data in the thin strip of actual interest, we have used intermediate results of the coarse grid calculation in order to eliminate the need for all but two of these extra cells at each end of the refined grid strip. The benefits of this approach will be described through sample results in 2D, and the method for handling the boundaries of the refined grid strips efficiently will be discussed. The data structures in this method are being carefully designed to permit efficient implementation of the algorithm on clusters of shared memory machines, with automatic dynamic balancing of computational loads over the cluster members.

Cellular automata (CA) have been used in pseudorandom number generation for over a decade. Recent studies show that controllable CA (CCA) can generate better random sequences than conventional one-dimensional (1D) CA and compete with two-dimensional (2D) CA. Yet the structural complexity of CCA is higher than that of 1D programmable cellular automata (PCA). It would be good if CCA can attain a good randomness quality with the least structural complexity. In this paper, we evolve PCA/CCA to their lowest complexity level using genetic algorithms (GAs). Meanwhile, the randomness quality and output efficiency of PCA/CCA are also evolved. The evolution process involves two algorithms — a multi-objective genetic algorithm (MOGA) and an algorithm for incremental evolution. A set of PCA/CCA are evolved and compared in randomness, complexity, and efficiency. The results show that without any spacing, the CCA could generate good random number sequences that could pass DIEHARD. To obtain the same randomness quality, the structural complexity of the CCA is not higher than that of 1D CA. Furthermore, the methodology developed could be used to evolve other CA or serve as a yardstick to compare different types of CA.

The question: whether quantum coherent states can sustain decoherence, heating and dissipation over time scales comparable to the dynamical timescales of brain neurons, has been actively discussed in the last years. A positive answer on this question is crucial, in particular, for consideration of brain neurons as quantum computers. This discussion was mainly based on theoretical arguments. In the present paper nonlinear statistical properties of the Ventral Tegmental Area (VTA) of genetically depressive limbic brain are studied in vivo on the Flinders Sensitive Line of rats (FSL). VTA plays a key role in the generation of pleasure and in the development of psychological drug addiction. We found that the FSL VTA (dopaminergic) neuron signals exhibit multifractal properties for interspike frequencies on the scales where healthy VTA dopaminergic neurons exhibit bursting activity. For high moments the observed multifractal (generalized dimensions) spectrum coincides with the generalized dimensions spectrum calculated for a spectral measure of a quantum system (so-called kicked Harper model, actively used as a model of quantum chaos). This observation can be considered as a first experimental (in vivo) indication in the favor of the quantum (at least partially) nature of brain neurons activity.

An empirical many-body potential energy function has been developed to investigate the structural features and energetics of Zn_kCd_l (k+l=3, 4) microclusters. The most stable structures were found to be triangular for the three-atom clusters and tetrahedral for the four-atom clusters. The present results are in good agreement with available literature values.

By driving to extinction species that are less or poorly adapted, the Darwinian evolutionary theory is intrinsically an optimization theory. We investigate two optimization algorithms with such evolutionary characteristics: the Bak–Sneppen and the Extremal Optimization. By comparing their mean fitness in the steady state regime, we conclude that the Bak–Sneppen dynamics is more efficient than the Extremal Optimization if the parameter τ is in the interval [0, 0.86]. The determination of the spatial correlation and the probability distribution of the avalanches show that the Extremal Optimization dynamics does not lead the system into a critical self-organized state. Through a discrete form of the Bak–Sneppen model we argue that biodiversity is an essential prerequisite to preserve the self-organized criticality.

Using an inverse of the standard linear congruential random number generator, large randomly occupied lattices can be visited by a random walker without having to determine the occupation status of every lattice site in advance. In seven dimensions, at the percolation threshold with L⁷ sites and L≤420, we confirm the expected time-dependence of the end-to-end distance (including the corrections to the asymptotic behavior).

The two-dimensional form of the Taylor series expansion- and least square-based lattice Boltzmann method (TLLBM) was recently presented by Shu et al.⁸ TLLBM is based on the standard lattice Boltzmann method (LBM), Taylor series expansion and the least square optimization. The final formulation is an algebraic form and essentially has no limitation on the mesh structure and lattice model. In this paper, TLLBM is extended to the three-dimensional case. The resultant form keeps the same features as the two-dimensional one. The present form is validated by its application to simulate the three-dimensional lid-driven cavity flow at Re=100, 400 and 1000. Very good agreement was achieved between the present results and those of Navier–Stokes solvers.

In this work we have considered the Taylor series expansion of the dynamic scaling relation of the magnetization with respect to small initial magnetization values in order to study the dynamic scaling behavior of two- and three-dimensional Ising models. We have used the literature values of the critical exponents and of the new dynamic exponent x₀ to observe the dynamic finite-size scaling behavior of the time evolution of the magnetization during early stages of the Monte Carlo simulation. For the three-dimensional Ising model we have also presented that this method opens the possibility of calculating z and x₀ separately. Our results show good agreement with the literature values. Measurements done on lattices with different sizes seem to give very good scaling.

Self-organized patterns in an immiscible fluid mixture of dissimilar particles driven from a source at the bottom are examined as a function of hydrostatic pressure bias by a Monte Carlo computer simulation. As the upward pressure bias competes with sedimentation due to gravity, a multi-phase system emerges: a dissociating solid phase from the source is separated from a migrating gas phase towards the top by an interface of mixed (bi-continuous) phase. Scaling of solid-to-gas phase with the altitude is nonuniversal and depends on both the range of the height/depth and the magnitude of the pressure bias. Onset of phase separation and layering is pronounced at low bias range.

The Sato–Crutchfield equations are analytically and numerically studied. The Sato–Crutchfield formulation corresponds to losing memory. Then the Sato–Crutchfield formulation is applied for some different types of games including hawk–dove, prisoner's dilemma and the battle of the sexes games. The Sato–Crutchfield formulation is found not to affect the evolutionarily stable strategy of the ordinary games. But choosing a strategy becomes purely random, independent of the previous experiences, initial conditions, and the rules of the game itself. The Sato–Crutchfield formulation for the prisoner's dilemma game can be considered as a theoretical explanation for the existence of cooperation in a population of defectors.

Models are presented suitable for a description of speciation processes arising due to reproductive isolation depending on genetic distance. The main attention is paid to the model of a one-dimensional closed population, which describes the evolution of littoral benthic organisms. In order to correspond the modeling results to the results obtained in the course of experimental phylogenetic studies, all individual-based models described here involve neutrally evolving and maternally inherited DNA sequence. Sub-samples of the resulting sequences were used for a posteriori phylogenetic inferences which then were compared to the "true" evolutionary histories.

We propose a hybrid algorithm, which combines the features of the energy landscape paving (ELP) and Monte Carlo Minimization (MCM) methods. We have tested its performance in studying the low-energy conformations of the heptapeptide deltorphin.