International Journal of Modern Physics C

In this paper, we study Klein tunneling in random media. To this purpose, we simulate the propagation of a relativistic Gaussian wave packet through a disordered medium with randomly distributed potential barriers (impurities). The simulations, based on a relativistic quantum lattice Boltzmann (QLB) method, permit to compute the transmission coefficient across the sample, thereby providing an estimate for the conductivity (or permeability) as a function of impurity concentration and strength of the potentials. It is found that the conductivity loss due to impurities is significantly higher for wave packets of massive particles, as compared to massless ones. A general expression for the loss of conductivity as a function of the impurity percentage is presented and successfully compared with the Kozeny–Carman law for disordered media in classical fluid-dynamics.

Since cultural interactions between a pair of social agents involve changes in both individuals, we present simulations of a new model based on Axelrod's homogenization mechanism that includes hybridization or mixture of the agents' features. In this new hybridization model, once a cultural feature of a pair of agents has been chosen for the interaction, the average of the values for this feature is reassigned as the new value for both agents after interaction. Moreover, a parameter representing social tolerance is implemented in order to quantify whether agents are similar enough to engage in interaction, as well as to determine whether they belong to the same cluster of similar agents after the system has reached the frozen state. The transitions from a homogeneous state to a fragmented one decrease in abruptness as tolerance is increased. Additionally, the entropy associated to the system presents a maximum within the transition, the width of which increases as tolerance does. Moreover, a plateau was found inside the transition for a low-tolerance system of agents with only two cultural features.

The epidemic spreading on spatial-driven network is studied with the spatial susceptible-infected-susceptible (SIS) model. The network is constructed by random addition of nodes on the plan. The probability for a previous node to be connected to the new one is inversely proportional to their spatial distance to the power α. The spreading rate between two nodes is inversely proportional to their spatial distance. The effective spreading time increases with the increasing of α. The proportional coefficient is found to have a α-dependent threshold with a maximum situated in the interval 1.5 < α < 2.

Explosive percolation proposed by Achlioptas et al. has attracted much attention recently. To understand how the product rule delays the phase transition, in this paper, we will concentrate our efforts on the influence of product rule in the transition from Erdős–Rényi (ER) percolation to Achlioptas explosive percolation. In our model, only a fraction of the adding edges will obey the product rule. With the probability p, the edge is selected under the Achlioptas's product rule; with 1 - p the edge is added between two randomly chosen nodes, that is, the ER rule. When the product rule plays a dominant role in the evolution, p > 0.5, the percolation transition delays more abruptly and instantaneously. The location of the critical points is independent of the network size and satisfies , where and are the critical points of ER percolation and Achlioptas one. We present the largest gap Δs_max and the critical region Δ as a function of p and N. The giant component s in terms of the edge density t above t_c is also analyzed. We find that all the critical values have a linear relationship against p.

A new computational procedure is offered to provide simple, accurate and flexible methods for using modern computers to give numerical evaluations of the various Bessel functions. The trapezoidal rule, applied to suitable integral representations, may become the method of choice for evaluation of the many special functions of mathematical physics.

Excitable cellular automata with dynamical excitation interval exhibit a wide range of space-time dynamics based on an interplay between propagating excitation patterns which modify excitability of the automaton cells. Such interactions leads to formation of standing domains of excitation, stationary waves and localized excitations. We analyzed morphological and generative diversities of the functions studied and characterized the functions with highest values of the diversities. Amongst other intriguing discoveries we found that upper boundary of excitation interval more significantly affects morphological diversity of configurations generated than lower boundary of the interval does and there is no match between functions which produce configurations of excitation with highest morphological diversity and configurations of interval boundaries with highest morphological diversity. Potential directions of future studies of excitable media with dynamically changing excitability may focus on relations of the automaton model with living excitable media, e.g. neural tissue and muscles, novel materials with memristive properties and networks of conductive polymers.

Similarity of opinions and memory about recent interactions are two main factors determining likelihood of social contacts. Here, we explore the Axelrod model with an extended conservativeness which incorporates not only similarity between individuals but also a preference to the last source of accepted information. The additional preference given to the last source of information increases the initial decay of the number of ideas in the system, changes the character of the phase transition between homogeneous and heterogeneous final states and could increase the number of stable regions (clusters) in the final state.

A prescribed pressure is the most common flow boundary condition used in flow simulations. In the Direct Simulation Monte Carlo (DSMC) method, boundary pressure is controlled by the number flux of the simulating molecules entering the domain. In the conventional DSMC algorithm, this number flux is calculated iteratively using sampled values of velocity and number density by means of an expression derived from the Maxwell distribution function. It is known that this procedure does not work well for low speed flows which are of interest in most micro-flow applications and the statistical scatter of the DSMC results is generally stated to be the main reason. However, the Maxwell distribution used in the pressure boundary treatment is valid for equilibrium conditions, and therefore, current implementations of the DSMC pressure boundary treatment are limited to boundaries with sufficiently small rarefaction effects. This is not the case for some practical problems in which highly rarefied flows through the boundaries lead to considerable nonequilibrium effects. In this study, an expression for the species number flux is derived using the Chapman–Enskog velocity distribution to improve the pressure boundary condition. The resulting algorithm is then used for modeling a micro-channel binary gas mixture flow with prescribed pressure boundary conditions.