International Journal of Modern Physics C

The reaction–diffusion systems represent various problems in the real world. For the Abrahams–Tsuneto reaction–diffusion system arising in superconductivity, we perform computerized symbolic computation and find its new exact analytic solutions, which are solitonic. We see the possibility that by way of the shock waves, the self–consistent superconducting interaction drives the Ginzburg–Landau order parameter, which might be observable.

The coupled Korteweg-de Vries (KdV) equations are important in many fields, such as nonlinear optics, fluid dynamics, supersymmetry and so on. In this paper, we modify the recently proposed variable-coefficient balancing-act algorithm, and thus obtain some exact analytic solutions for the nonintegrable Hirota–Satsuma system of coupled KdV equations, which in fluid dynamics describe interactions of two long waves with different dispersion relations.

Positons are a new concept in nonlinear sciences. In this paper, we report some positonic, exact analytic solutions for a variable-coefficient Korteweg-de Vries (KdV) equation arising from fluid dynamics and plasma physics.

We present an efficient way to evaluate the Ühling–Uhlenbeck (UU) collision term in the case of semi-classical dynamics. We focus on finite fermionic systems such as small metal clusters, which we recently pointed out the importance of the UU collision term for the electronic dynamics. We show, how far the hybrid method, which lies between the full and the parallel ensemble methods, allows an efficient and accurate treatment of a Boltzmann–like collision term. We finally give a guideline to define the best parameter of the hybrid ensemble method for a given cluster size.

In this paper we describe procedures for the construction of efficient methods for the numerical solution of second order initial value problems (IVPs) with oscillating solutions. Based on the described procedures we develop two simple and efficient multistep methods for the solution of the above problems. The first method is exponentially-fitted and trigonometrically-fitted and the second has a minimal phase-lag. Both methods are symmetric. Numerical results obtained for several well known problems show the efficiency of the new methods when they are compared with known methods in the literature.

We use a simple model for biological aging to study the mortality of the population, obtaining a good agreement with the Gompertz law. We also simulate the same model on a square lattice, considering different strategies of parental care. The results are in agreement with those obtained earlier with the more complicated Penna model for biological aging. Finally, we present the sexual version of this simple model.

Time series corresponding to nominal exchange rates between the US dollar and Argentina, Brazil and European Economic Community currencies; different financial indexes as the Industrial Dow Jones, the British Footsie, the German DAX Composite, the Australian Share Price and the Nikkei Cash and also different Argentine local tax revenues, are analyzed looking for the appearance of simple patterns and the possible definition of forecast evaluators. In every case, the statistical fractal dimensions are obtained from the behavior of the corresponding variance of increments at a given lag. The detrended fluctuation analysis of the data in terms of the corresponding exponent in the resulting power law is carried out. Finally, the frequency power spectra of all the time series considered are computed and compared

The acoustic wave equation is solved numerically for two and three-dimensional systems at the limit between near and far field propagation. Our results show that for large sound velocities, corresponding to wavelengths larger than the system, near field properties are dominant. When the near field conditions are no longer satisfied, standing waves close to the sound emitters and interference patterns between the near field and far field solutions appear. Our procedure is applied to sound sources, which broadcast coherent and continuous waves as well as to sources emitting bursts of incoherent and uncorrelated waves. Both cases can be used to simulate the spreading of low frequency seismic waves observed close to volcanoes and hydrocarbon reservoirs.

The Sznajd sociophysics model is generalized on the triangular lattice with pure antiferromagnetic opinion and also with both ferromagnetic and antiferromagnetic opinions. The slogan of the trade union "united we stand, divided we fall" can be realized via the propagation of ferromagnetic opinion of adjacent people in the union, but the propagation of antiferromagnetic opinion can be observed among the third countries between two big super powers or among the family members of conflicting parents. Fixed points are found in both models. The distributions of relaxation time of the mixed model are dispersed and become closer to log–normal as the initial concentration of down spins approaches 0.5, whereas for pure antiferromagnetic spins, they are collapsed into one master curve, which is roughly log–normal. We do not see the phase transition in the model.

In this paper we discuss the application of reinforcement learning algorithms to the problem of autonomous robot navigation. We show that the autonomous navigation using the standard delayed reinforcement learning algorithms is an ill posed problem and we present a more efficient algorithm for which the convergence speed is greatly improved. The proposed algorithm (Deep-Sarsa) is based on a combination between the Depth-First Search (a graph searching algorithm) and Sarsa (a delayed reinforcement learning algorithm).

In the present paper, we will study the general telegraph coupled map lattice and finite amplitude instability will be discussed. The persistence in telegraph reaction diffusion equation (TRD) will be studied in two dimensional systems and we show the critical size effect where phenomena persist only if the domain is large enough. Some applications are introduced and we made a simulation on the small world network, which is more realistic than the ordinary lattices in many cases.

The Sznajd model for the opinion formation is generalized to small-world networks. This generalization destroyed the stalemate fixed point. Then a simple definition of leaders is included. No fixed points are observed. This model displays some interesting aspects in sociology. The model is investigated using time series analysis.