International Journal of Modern Physics C

A model for the monomer–monomer surface reaction of the type A + B → AB, with diffusion of A and B monomers on a surface and reaction only on active sites randomly distributed on the surface, has been proposed and studied. For a critical point where both adsorption probabilities are the same, a seemingly reactive steady state transforms itself into a poisoned state. In this transient state, the production of AB molecules, in relation to the density of active sites, is considered and an inert-reactive irreversible phase transition is observed. The critical values of the density of active sites, where the irreversible phase transition occurs, is obtained in the limit L → ∞ by means of a finite-size scaling analysis. The critical exponents that dominate the correlation length of clusters, as well as the production of AB molecules at criticality, are determined.

We propose and solve a Hamiltonian model for multidimensional epistatic interactions between beneficial mutations. The model gives rise to either a phase transition between two equilibrium states, without any coexistence, or exhibits a state where hybrid species coexist, with gradual passage from one wild type to another. The transition takes place as a function of the tolerance of the environment, which we defined as the amount of noise in the system.

In this paper, an exponentially fitted and trigonometrically fitted predictor–corrector class of methods is developed. These methods represent a totally new area of application for the explicit advanced step-point or EAS methods developed by Psihoyios and Cash. Numerical examples show that the newly developed procedure is much more efficient than well-known methods for the numerical solution of initial value problems with oscillating solutions.

We analyze the amino acid sequences of the proteins of different structural classes using the method of power spectrum density. It was found that the protein hydrophobicity sequences of different structural classes show different significant periodicity, which relates closely to the order of the α-helices and β-strands in their polypeptide chains.

We present a new extension of Conway's game of life for two players, which we call "p2life". P2life allows one of two types of token, black or white, to inhabit a cell and adds competitive elements into the birth and survival rules of the original game. We solve the mean-field equation for p2life and determine, using simulation, that the asymptotic density of p2life approaches 0.0362.

A novel algorithm for performing parallel, distributed computer simulations on the Internet using Internet protocol (IP) control messages is introduced. The algorithm employs carefully constructed Internet control message protocol (ICMP) packets that enable the required computations to be completed as part of the standard IP communication protocol. After providing a detailed description of the algorithm, experimental applications in the areas of stochastic neural networks and deterministic cellular automata are discussed. As an example of the algorithm's potential power, a simulation of a deterministic cellular automaton involving 10⁵ Internet-connected devices was performed.

The direct reduction method and computerized symbolic computation are extended to the Brusselator reaction–diffusion model, which describes a biochemical system and consists of two coupled nonlinear partial differential equations. New similarity reductions are obtained, which could be of biochemical interest. The resulting nonlinear ordinary differential equation in one dynamical variable cannot be transformed into any of the six standard forms which have solutions in terms of the Painlevé transcendents. Thus, the Brusselator model is not integrable according to the Painlevé conjecture.

The calculation of the Shannon entropy of Hartree–Fock electron density is reported for the K–Xe atoms in the fourth and fifth rows of the periodic table in the ground state. In local plasma approximation, the Shannon entropy calculated is used directly to estimate mean excitation energies. To our knowledge, the mean excitation energies of K–Xe atoms are presented here for the first time.

With the aid of symbolic computation, an extended Jacobian elliptic function expansion method is further extended to the complex nonlinear Schrödinger⁺ equation. As a result, 24 families of the envelope doubly-periodic solutions with Jacobian elliptic functions are obtained. When the modulus m → 1 or zero, the corresponding six envelope solitary wave solutions and six envelope singly-periodic (trigonometric function) solutions are also found. This powerful method can also be applied to other equations, such as the nonlinear Schrödinger equation and Zakharov equation.

The model of Bonabeau explains the emergence of social hierarchies from the memory of fights in an initially egalitarian society. Introducing a feedback from the social inequality into the probability to win a fight, we find a sharp transition between an egalitarian society at low population density and a hierarchical society at high population density.

We introduce into the Penna Model of biological aging a mechanism to maximize the ability of a sperm to compete with those of other males. Such a selfish mechanism increases the rate of success of male reproduction, but may decrease the survival probability of the female population, depending on its mode of action. We also find a dynamic phase transition induced by the existence of an absorbing state, where no selfish males survive.