International Journal of Modern Physics C

We describe a new application of an existing perfect sampling technique of Corcoran and Tweedie to estimate the self energy of an interacting Fermion model via Monte Carlo summation. Simulations suggest that the algorithm in this context converges extremely rapidly and results compare favorably to true values obtained by brute force computations for low dimensional toy problems. A variant of the perfect sampling scheme which improves the accuracy of the Monte Carlo sum for small samples is also given.

We investigate using molecular dynamics, the tensile failure of single-crystal and nanocrystalline Lennard-Jones solids under uniaxial strain. Stresses are relaxed by plasticity and tensile failure, which are induced via stacking faults, twin planes, void nucleation and growth, and their interactions. Stacking faults and twin planes as well as multiple nanovoids are nucleated at grain boundaries in a nanocrystalline solid. Void formation is characterized by under-coordinated atoms with coordination number ≤ 7, and the critical void size is comparable to a vacancy. For a single crystal, the number of stacking faults and twin planes decreases during failure mostly due to the absorption by nanovoids. In contrast, it increases with strain monotonically for a nanocrystalline solid, where abundant grain boundaries help the nucleation and deter the propagation and absorption of the stacking faults and twin planes, inducing effective dislocation pile-ups at grain boundaries even in the presence of nanovoids.

Stability and accuracy of the numerical schemes obtained from the lattice Boltzmann equation (LBE) used for numerical solutions of two-dimensional advection-diffusion equations are presented. Three kinds of velocity models are used to determine the moving velocity of particles on a squre lattice. A system of explicit finite difference equations are derived from the LBE based on the Bhatnagar, Gross and Krook (BGK) model for individual velocity model. In order to approximate the advecting velocity field, a linear equilibrium distribution function is used for each of the moving directions. The stability regions of the schemes in the special case of the relaxation parameter ω in the LBE being set to ω=1 are found by analytically solving the eigenvalue problems of the amplification matrices corresponding to each scheme. As for the cases of general relaxation parameters, the eigenvalue problems are solved numerically. A benchmark problem is solved in order to investigate the relationship between the accuracy of the numerical schemes and the order of the Peclet number. The numerical experiments result in indicating that for the scheme based on a 9-velocity model we can find the parameters depending on the order of the given Peclet number, which generate accurate solutions in the stability region.

The model of laminated wave turbulence presented recently unites both types of turbulent wave systems — statistical wave turbulence (introduced by Kolmogorov and brought to the present form by numerous works of Zakharov and his scientific school since nineteen sixties) and discrete wave turbulence (developed in the works of Kartashova in nineteen nineties). The main new feature described by this model is the following: discrete effects do appear not only in the long-wave part of the spectral domain (corresponding to small wave numbers) but all through the spectra thus putting forth a novel problem — construction of fast algorithms for computations in integers of order 10¹² and more. In this paper we present a generic algorithm for polynomial dispersion functions and illustrate it by application to gravitational water waves and oceanic planetary waves.

We study the behavior of the numbers in 412 light curves of cataclysmic variables, x-ray binary systems, galaxies, pulsars, supernovae remnants and other x-ray sources present in the public data collected by the instrument All Sky Monitor on board of the satellite Rossi x-ray timing explorer. The temporal light curves were analyzed applying Newcomb-Benford Law. The first digit of the x-ray light curves coming from astrophysical systems obeys the Newcomb-Benford Law as an intrinsic behavior. The nonextensive statistical mechanics behavior of astrophysical sources seem to be the cause for these sources to obey the Newcomb-Benford law. Some x-ray binary systems, however, do not follow this behavior. These systems obey either a gaussian or a bimodal distribution.

Generalizing the motion representation we introduced for number-conserving rules, we give a systematic way to construct a generalized motion representation valid for non-conservative rules using the expression of the current, which appears in the discrete version of the continuity equation, completed by the discrete analogue of the source term. This new representation is general, but not unique, and can be used to represent, in a more visual way, any one-dimensional cellular automaton rule. A few illustrative examples are presented.

This research relates to a numerical integrator with post-stabilization of several constraints for an autonomous dynamical system. A generally analytical approach shows that the total energy correction is not valid in most cases, while post-stabilization of each independent energy is. As a typical test example, we consider a non-integrable Hamiltonian system of three degrees of freedom, which can be split into two independent pieces, one 1D harmonic oscillator and another 2D non-integrable system, by using a transformation of variables. Phase portraits on Poincaré sections about the 2D system manifest that our analysis is reasonable. In addition, a problem how to compute Lyapunov exponents in constrained systems is proposed. As a suggestion, it is best to stabilize all constraints involving each energy integral and its corresponding variation in order to avoid spurious Lyapunov exponents. Because an appropriately larger time step is acceptable in this sense, it is not expensive to use the fast Lyapunov indicators to describe the global dynamics of phase space for the 3D system, where regions of chaos and order are clearly identified.

A model of dynamics of three interacting species is presented. Two of the species are prey and one is predator, which feeds on both prey, however with some preference to one type. Prey compete for space (breeding) although they always have access to food. Predators in order to survive and reproduce must catch prey, otherwise they die of hunger. The dynamics of the model is found via differential equations in the mean-field like approach and through computer simulations for agent-based method. We show that the coexistence of the three species is possible in the mean-field model, provided the preference of the predators is small, whereas from simulation it follows that the stochastic fluctuations drive, generally, one of the prey populations into extinction. We have found a different type of behavior for small and large systems and a rather unexpected dependence of the coexistence chance of the preference parameter in bigger lattices.

We present a stochastic approach to modeling the dynamics of coexistence of prey and predator populations. It is assumed that the space of coexistence is explicitly subdivided in a grid of cells. Each cell can be occupied by only one individual of each species or can be empty. The system evolves in time according to a probabilistic cellular automaton composed by a set of local rules which describe interactions between species individuals and mimic the process of birth, death and predation. By performing computational simulations, we found that, depending on the values of the parameters of the model, the following states can be reached: a prey absorbing state and active states of two types. In one of them both species coexist in a stationary regime with population densities constant in time. The other kind of active state is characterized by local coupled time oscillations of prey and predator populations. We focus on the self-organized structures arising from spatio-temporal dynamics of the coexistence. We identify distinct spatial patterns of prey and predators and verify that they are intimally connected to the time coexistence behavior of the species.

Quantitative evaluation of the changes in skin topographic structures are of great importance in the dermocosmetic field to assess subjects response to medical or cosmetic treatments. Although many devices and methods are known to measure these changes, they are not suitable for a routine approach and most of them are invasive. Moreover, it has always been difficult to give a measure of the skin health status as well as of the human aging process by simply analyzing the skin surface appearance. This work describes how a portable capacitive device could be utilized to achieve measurements of skin ageing in vivo and routinely. The capacitive images give a high resolution representation of the skin micro-relief, both in terms of skin surface tissue and wrinkles. In a previous work we dealt with the former; here we have addressed the latter. The algorithm we have developed allowed us to extract two original features from wrinkles: the first is based on photometric properties while the second has been achieved through the multiresolution analysis of the wavelet transform. Accurate experiments accomplished on 87 subjects show how the features we conceived are related to skin ageing.

A new method, based on the original theory of conservation of sum of kinetic and potential energy defined for prices is proposed and applied on the Dow Jones Industrials Average (DJIA). The general trends averaged over months or years gave a roughly conserved total energy, with three different potential energies, i.e., positive definite quadratic, negative definite quadratic and linear potential energy for exponential rises (and falls), sinusoidal oscillations and parabolic trajectories, respectively. Corresponding expressions for force (impact) are also given.

In this paper, the individual is represented by a Bit-String based on the Penna model. The infection information is also denoted by a Bit-String including 0 and 1. The degree of getting an infection is rested with the matching degree between the Bit-String of the individual and the Bit-String of infection information. Thus, we define the Hamming Distance with age. The infection rules among individuals is described by Cellular Automata on the lattice with L * L. We discuss the existence and extinction for a certain infection on the process of evolution.