International Journal of Modern Physics C

In this paper, we show how computerized symbolic computations can be used to find an auto-Bäcklund transformation and a family of exact analytical solutions to the variant Boussinesq model for water waves. Sample explicit solutions are presented, which are respectively solitonic and rational.

We present a simple model of selection and mutation of cell populations in the immune system. This is based on generic assumptions and in this respect it resembles a model for evolution in simple ecosystems. In this case the selection acts by means of the affinity function representing the ability of a certain class of lymphocytes to recognize a foreign antigen. Carrying out some analytical and numerical studies we determine the critical values for the parameters ruling the selection and mutation.

Boundary conditions in a recently-proposed finite volume lattice Boltzmann method are discussed. Numerical simulations for simple shear flow indicate that the extrapolation and the half-covolume techniques for the boundary conditions are workable in conjunction with the finite volume lattice Boltzmann method for arbitrary meshes.

We have determined families of two-dimensional deterministic totalistic cellular automaton rules whose stationary density of active sites exhibits a period two in time. Each family of deterministic rules is characterized by an "average probabilistic totalistic rule" exhibiting the same periodic behavior.

Lattice models describing the spatial spread of rabies among foxes are studied. In these models, the fox population is divided into three-species: susceptible (S), infected or incubating (I), and infectious or rabid (R). They are based on the fact that susceptible and incubating foxes are territorial while rabid foxes have lost their sense of direction and move erratically. Two different models are investigated: a one-dimensional coupled-map lattice model, and a two-dimensional automata network model. Both models take into account the short-range character of the infection process and the diffusive motion of rabid foxes. Numerical simulations show how the spatial distribution of rabies, and the speed of propagation of the epizootic front depend upon the carrying capacity of the environment and diffusion of rabid foxes out of their territory.

A detailed description and validation of a recently developed integration scheme is here reported for one- and two-dimensional reaction–diffusion models. As paradigmatic examples of this class of partial differential equations the complex Ginzburg–Landau and the Fitzhugh–Nagumo equations have been analyzed. The novel algorithm has precision and stability comparable to those of pseudo-spectral codes, but is more convenient to be employed for systems with large linear extention L. As for finite-difference methods, the implementation of the present scheme requires only information about the local enviroment and this allows us to treat systems with very complicated boundary conditions.

The overlap lattice-Dirac operator contains the sign function ∊(H). Recent practical implementations replace ∊(H) by a ratio of polynomials, H P_n(H²)/Q_n(H²), and require storage of 2n+2 large vectors. Here I show that one can use only four large vectors at the cost of executing the core conjugate algorithm twice. The slow-down might be less than by a factor of 2, depending on the architecture of the computer one uses.

The scaling law of Edwards et al., for cluster fragmentation of critical percolation clusters is not confirmed by analogous Monte Carlo simulations at the Curie point of the two-dimensional Ising model.

A high-performance general program is presented to deal with the multi-parameter optimization problems in physics. Considering the requirements of physical application, some small but significant modifications were made on the conventional simulated annealing algorithm. A parallel realization was suggested to further improve the performance of the program. Mathematical and physical examples were taken to test the feasibility and the efficiency of the program. The source code is available from the authors free of charge.

A simple stochastic cellular automaton model is proposed for ripples and dunes formation. Saltation and avalanches are the unique ingredients of the model. The dynamics of ripple formation is found to be logarithmic in time while the ripple merging as well as the dune growth is faster and occurs by bursts. The ripple state turns out to be metastable.

The kinetics of NO decomposition on transition metals is studied through Monte Carlo simulation, including the effects of adsorbate-adsorbate interactions and of surface energetic heterogeneity. For a homogeneous surface, it is found that previous quasi-chemical approximation calculations are reasonably in agreement with Monte Carlo results except for strong repulsive interactions. In this last case, quasi-chemical predictions largely overestimate the decomposition rate. It is found that energetic heterogeneity introduces interesting behaviors which depend on the energetic topography considered.

We use computerized symbolic computation to study the similarity reductions of a generalized Kadomtsev–Petviashvili (KP) equation, with its space- and time-dependent coefficients arising in plasma physics and fluid mechanics. We obtain a couple of reductions involving those coefficient functions, one of which is to the fourth Painlevé equation, while the other is to one of the second Painlevé equation, the first Painlevé equation or a Weierstrass elliptic function equation. Our results agree with the Painlevé Conjecture. The cylindrical KP equation is presented as an example, which describes nonlinear cylindrical water waves in shallow water with a weak azimuthal dependence.

We document and analyze the empirical facts concerning one of the clearest evidence of speculation in financial trading as observed in the postage collection stamp market. We unravel some of the mechanisms of speculative behavior which emphasize the role of fancy and collective behavior. In our conclusion, we propose a classification of speculative markets based on two parameters, namely the amplitude of the price peak and a second parameter that measures its "sharpness". This study is offered to anchor modeling efforts to realistic market constraints and observations.

In this work we investigate the use of a speaker adaptation technique, for speech recognition, based on neural network spectral mapping. Different multilayer perceptron neural network architectures are analyzed in order to optimize the spectral difference reduction in acoustic data of two speakers. Experiments are carried out in a telecontrol environment, used to provide voice commands to a mobile robot, based on DTW pattern matching.

We present a progress report on the Cluster Processor, a special-purpose computer system for the Wolff simulation of the three-dimensional Ising model, including an analysis of simulation results obtained thus far. These results allow, within narrow error margins, a determination of the parameters describing the phase transition of the simple-cubic Ising model and its universality class. For an improved determination of the correction-to-scaling exponent, we include Monte Carlo data for systems with nearest-neighbor and third-neighbor interactions in the analysis.

We propose a model with heterogeneous interacting traders which can explain some of the stylized facts of stock market returns. A generalized version of the Random Field Ising Model (RFIM) is introduced to describe trading behavior. Imitation effects, which induce agents to trade, can generate avalanches in trading volume and large gaps in demand and supply. A trade friction is introduced which, by responding to price movements, creates a feedback mechanism on future trading and generates volatility clustering.

Computer studies of evolution in migrating population are presented. The model is based on the Penna model. Migration for better living conditions does influence population dynamics in different locations. Examples of different scenarios of preferences to live in bigger or smaller populations (or environmental capacity, or living space available) are discussed. In the limiting case of low migration intensity, each location evolves independently according to its local rules and conditions, as expected. With increasing migration, the population distribution between locations changes, including the critical behavior of extinction of population for some locations for a specific set of the rules. Then, the deserted location may become populated again if the migration is still increasing as result of a pressure to move. The present version is devoted to the migration controlled exclusively by environmental factors, yet the model is primarily designed to describe both inherited mutations on environmental factors and can be used to study the effect of different races mixing, or recovery of environmental capacity of the fields when chasing 2 flocks of geese in a cyclic manner across 3 fields.