International Journal of Modern Physics C

In nature many animal groups, such as fish schools or bird flocks, clearly display structural order and appear to move as a single coherent entity. In order to understand the complex behavior of these systems, many models have been proposed and tested so far. This paper deals with an extension of the Vicsek model, by including a second zone of repulsion, where each agent attempts to maintain a minimum distance from the others. The consideration of this zone in our study seems to play an important role during the travel of agents in the two-dimensional (2D) flocking models. Our numerical investigations show that depending on the basic ingredients such as repulsion radius (R₁), effect of density of agents (ρ) and noise (η), our nonequilibrium system can undergo a kinetic phase transition from no transport to finite net transport. For different values of ρ, kinetic phase diagrams in the plane (η ,R₁) are found. Implications of these findings are discussed.

In this paper, the behavior of a genetic algorithm is modeled to enhance its applicability as a modeling tool of biological systems. A new description model for selection mechanism is introduced which operates on a portion of individuals of population. The extinction and recolonization mechanism is modeled, and solving the dynamics analytically shows that the genetic drift in the population with extinction/recolonization is doubled. The mathematical analysis of the interaction between selection and extinction/recolonization processes is carried out to assess the dynamics of motion of the macroscopic statistical properties of population. Computer simulations confirm that the theoretical predictions of described models are in good approximations. A mathematical model of GA dynamics was also examined, which describes the anti-predator vigilance in an animal group with respect to a known analytical solution of the problem, and showed a good agreement between them to find the evolutionarily stable strategies.

A numerical technique is described that can efficiently compute solutions of interface problems. These are problems with data, such as the coefficients of differential equations, discontinuous or even singular across one or more interfaces. A prime example of these problems are optical waveguides, and as such the scheme is applied to Maxwell's equations as they are formulated to describe light confinement in Bragg fibers. It is based on standard finite differences appropriately modified to take into account all possible discontinuities across the waveguide's interfaces due to the change of the refractive index. Second- and fourth-order schemes are described with additional adaptations to handle matrix eigenvalue problems, demanding geometries and defects.

In this short paper, we study the measure directional entropy of a ℤ²-action generated by an invertible one-dimensional linear cellular automaton and the shift map acting on the compact metric space . We obtain an upper bound of the measure directional entropy of the ℤ²-action with respect to arbitrary Bernoulli measures without making use of the natural extension previously used in the paper [M. Courbage and B. Kaminski, Studia Math. 153(3), 285–295 (2002)].

Standard order–disorder phase transition in the Ising model is described in terms of rates of processes of spin flips. This formulation allows to extend numerous results on phase transition for sciences other than physics of magnetism. We apply it to the problem of norm breaking. Two strategies: to cooperate or to defect, form an analogy to two spin orientations. An example is a crowd at an exit, where to defect means to push others, and to cooperate is to move slowly together.

The lattice Boltzmann method (LBM) has been applied to electrohydrodynamics (EHD) in recent years. In this paper, Shan–Chen (SC) single-component multiphase LBM is developed to study large-density-ratio EHD problems. The deformation/motion of a droplet suspended in a viscous liquid under an applied external electric field is studied with three different electric field models. The three models are leaky dielectric model, perfect dielectric model and constant surface charge model. They are used to investigate the effects of the electric field, electric properties of liquids and electric charges. The leaky dielectric model and the perfect dielectric model are validated by the comparison of LBM results with theoretical analysis and available numerical data. It shows that the SC LBM coupled with these electric field models is able to predict the droplet deformation under an external electric field. When net charges are present on the droplet surface and an electric field is applied, both droplet deformation and motion are reasonably predicted. The current numerical method may be an effective approach to analyze more complex EHD problems.

Traffic jam has become a big problem in the development of economy. How to effectively improve the road capacity is becoming the key problem in the research of traffic flow. As the core part of the next generation intelligent transportation systems, the feedback strategy has attracted much attention. In recent years, researchers have proposed many effective strategies. In this paper, a strategy called speed of last vehicle feedback strategy is introduced, and simulated in a two-route scenario with one exit. Result shows that compared with other strategies, this strategy has certain advantages on average flux — a criteria describing traffic capacity of traffic systems. More importantly, the implementation of this strategy is very simple.

A weighted mechanism in neural networks is studied. This paper focuses on the neuron's behaviors in an area of brain. Our model could regenerate the power-law behaviors and finite size effects of neural avalanche. The probability density functions (PDFs) for the neural avalanche size differing at different times (lattice size) have fat tails with a q-Gaussian shape and the same parameter value of q in the thermodynamical limit. Above two kinds of behaviors show that our neural model can well present self-organized critical behavior. The robustness of PDFs shows the stability of self-organized criticality. Meanwhile, the avalanche scaling relation of the waiting time has been found.