International Journal of Modern Physics C

The kinetics of domain growth of fluid mixtures quenched from a disordered to a lamellar phase has been studied in three dimensions. We use a numerical approach based on the lattice Boltzmann method (LBM). A novel implementation for LBM which "fuses" the collision and streaming steps is used in order to reduce memory and bandwidth requirements. We find that extended defects between stacks of lamellae with different orientation dominate the late time dynamics.

The rural-urban migration phenomenon is analyzed by using an agent-based computational model. Agents are placed on lattices which dimensions varying from d =2 up to d =7. The localization of the agents in the lattice defines that their social neighborhood (rural or urban) is not related to their spatial distribution. The effect of the dimension of lattice is studied by analyzing the variation of the main parameters that characterizes the migratory process. The dynamics displays strong effects even for around one million of sites, in higher dimensions (d =6, 7).

We investigate the critical features of coupling parameters in the synchronization of the ensemble of identical neural networks with small-world connectivity. An exponential decay form is observed in the extreme case of global coupling among subsystems and full connection in each networks: there exists a maximum and a minimum of the critical coupling intensity for synchronization in this spatially extended system. For partial coupling, we present the primary result about the critical coupling fraction for various linked degree of subnetworks.

We develop a two-dimensional cellular automaton (CA) as a simple model for agents moving from origins to destinations. Each agent moves towards an empty neighbor site corresponding to the minimal distance to its destination. The stochasticity or noise (p) is introduced in the model dynamics, through the uncertainty in estimating the distance from the destination. The friction parameter "μ" is also introduced to control the probability that movement of all involved agents to the same site (conflict) is denied at each time step. This model displays two states; namely the freely moving and the jamming state. If μ is large and p is low, the system is in the jamming state even if the density is low. However, if μ is large and p is high, a freely moving state takes place whenever the density is low. The cluster size and the travel time distributions in the two states are studied in detail. We find that only very small clusters are present in the freely moving state, while the jamming state displays a bimodal distribution. At low densities, agents can take a very long time to reach their destinations if μ is large and p is low (jamming state); but long travel times are suppressed if p becomes large (freely moving state).

The multi-species ecological system with cyclic dominance and vacant sites is studied. The theme is the forming problem of species' defensive alliances in the corresponding systems. György Szabó and Gustavo Arial Sznaider have discussed the forming problem of species' defensive alliance in Phys. Rev. E69, 031911 (2004). Now, this problem is discussed in depth. The following conclusions are obtained: Firstly, the necessary and sufficient condition of forming defensive alliances is that the number of species is even. Secondly, in the condition where the number of species is an even number, for any density of vacant sites, there is three forms of defensive alliance as follow:

• Deadlock — the habitats of specie's individuals in each alliance interweave together.

• Relative preponderance — the different of the number of species' individuals between the two defensive alliances keeps steadily.

• Absolute preponderance — the different of the number of species' individuals between the two defensive alliances enlarges continuously.

This paper discusses the relations between the number of species and the forming of the defensive alliances, and shows the corresponding three statistical distributions of discrete density of vacant sites when there are four species.

We simulate the progression of the HIV-1 infection in untreated host organisms. The phenotype features of the virus are represented by the replication rate, the probability of activating the transcription, the mutation rate and the capacity to stimulate an immune response (the so-called immunogenicity).

It is very difficult to study in-vivo or in-vitro how these characteristics of the virus influence the evolution of the disease. Therefore we resorted to simulations based on a computer model validated in previous studies.

We observe, by means of computer experiments, that the virus continuously evolves under the selective pressure of an immune response whose effectiveness downgrades along with the disease progression. The results of the simulations show that immunogenicity is the most important factor in determining the rate of disease progression but, by itself, it is not sufficient to drive the disease to a conclusion in all cases.

We model formation and evolution of transverse dune fields. In the model, only the cross section of the dune is simulated. The only physical variable of relevance is the dune height, from which the dune width and velocity are determined, as well as phenomenological rules for interaction between two dunes of different heights. We find that dune fields with no sand on the ground between dunes are unstable, i.e., small dunes leave the higher ones behind. We then introduce a saturation length to simulate transverse dunes on a sand bed and show that this leads to stable dune fields with regular spacing and dune heights. Finally, we show that our model can be used to simulate coastal dune fields if a constant sand influx is considered, where the dune height increases with the distance from the beach, reaching a constant value.

The sand-pile models exhibit a great diversity of behavioral patterns. The average height as a function on time points out the variety of the sand-pile's criticality. We define the classes of universality for the sand-piles in terms of the spectrum of the average height. The definition, in particular, distinguishes two classes with Manna's and Bak et al. sand-piles as the typical representatives. The one-parametric family of the models investigated in this paper develops a crossover between the classes and introduces the infinite quantity of other sand-pile's classes. The parameter is the number of grains that any unstable cell transfers to its neighbors. The sand-piles admit a certain normalization generating unified laws. The spectral approach increases the precision of the universalities from our size distribution analysis. The latter describes the sand-piles' typical distribution, sets the correspondence between the sand-piles with small and large parameter values, but fails to determine their diversity.

We study numerically a prototype equation which arises generically as an envelope equation for a weakly inverted bifurcation associated to traveling waves: The complex quintic Ginzburg–Landau equation. We show six different stable localized structures including stationary pulses, moving pulses, stationary holes and moving holes, starting from localized initial conditions with periodic and Neumann boundary conditions.

We present some simulations results of population growth and evolution, using the standard asexual Penna model, with individuals characterized by a string of bits representing a genome containing some possible mutations. After about 20 000 simulation steps, when only a few genetic families are still present from among rich variety of families at the beginning of the simulation game, strong peaks in mutation distribution functions are observed. This known effect is due to evolution rules with hereditary mechanism. The birth and death balance in the simulation game also leads to elimination of families specified by different genomes. The number of families G(t) versus time t follow the power law, G∝tⁿ. Our results show the power coefficient exponent n is changing with time. Starting from about -1, smoothly achieves about -2 after hundreds of steps, and finally has semi-smooth transition to 0, when only one family exists in the environment. This is in contrast with constant n about -1 as found, for example, in Ref. 1. We suspect that this discrepancy may be due to two different time scales in simulations — initial stages follow the n ≈ -1 law, yet for large number of simulation steps we get n ≈ -2, provided the random initial population was sufficiently big to allow for still reliable statistical analysis. The n ≈ -1 evolution stage seems to be associated with the Verhulst mechanism of population elimination due to the limited environmental capacity — when the standard evolution rules were modified, we observed a plateau (n =0) in the power law in short time scale, again followed by n ≈ -2 law for longer times. The modified model uses birth rate controlled by the current population instead of the standard Verhulst death factor.

A Lattice Boltzmann model for simulating micro flows has been proposed by us recently (Europhysics Letters, 67(4), 600–606 (2004)). In this paper, we will present a further theoretical and numerical validation of the model. In this regards, a theoretical analysis of the diffuse-scattering boundary condition for a simple flow is carried out and the result is consistent with the conventional slip velocity boundary condition. Numerical validation is highlighted by simulating the two-dimensional isothermal pressure-driven micro-channel flows and the thin-film gas bearing lubrication problems, and comparing the simulation results with available experimental data and analytical predictions.

We present an iterative Monte Carlo algorithm for which the temperature variable is attracted by a critical point. The algorithm combines techniques of single histogram reweighting and linear filtering. The ferromagnetic 2D Ising model is studied numerically as an illustration. In that case, the iterations reach a stationary regime with an invariant probability distribution function of temperature which peaked near the pseudocritical temperature of the specific heat. The sequence of generated temperatures is analyzed in terms of stochastic autoregressive model. The error of histogram reweighting can be better understood within the suggested model. The presented model yields a simple relation, connecting the variance of pseudocritical temperature and the parameter of linear filtering.