We performed numerical simulations on a one-dimensional diatomic gas to investigate the possible long time scale in Hamiltonian systems with internal degrees of freedom. In the limit of the large system size, the time scale for energy sharing between the translational motion and the vibrational...

We consider a stochastic model of N evolving particles studied by Brunet and Derrida. This model can be seen as a directed polymer in random medium with N sites in the transverse direction. Cook and Derrida use heuristic arguments to obtain a formula for the ground state energy of the polymer....

The coarsening of an array of vortex ripples prepared in an unstable state is discussed within the framework of a simple mass transfer model first introduced by K. H. Andersen et al. (see Ref. 1). Two scenarios for the selection of the final pattern are identified. When the initial state is...

This paper studies a reaction–diffusion–chemotaxis model for bacterial aggregation patterns on the surface of thin agar plates. It is based on the non-linear degenerate cross diffusion model proposed by Kawasaki et al. (1997) [5] and it includes a suitable nutrient chemotactic term...

We consider a monoparametric family of reaction–diffusion equations endowed with both a nonlinear diffusion term and a nonlinear reaction one that possess exact time-dependent particular solutions of the Tsallis’ maximum entropy (MaxEnt) form. The evolution of these solutions is governed by...

Probabilistic methods are presented to solve one-dimensional nonlinear reaction–diffusion equations. Computational particles are used to approximate the spatial derivative of the solution. The random walk principle is used to model the diffusion term. We investigate the effect of replacing...

To bridge the structure gap, electrochemical reactions can be studied in flow cells with nm-sized catalyst particles deposited or fabricated on the cell walls. The understanding of the role of mass transport in such cells is now limited. To clarify the likely effects in this field, we analyze...

The tanh technique is used to solve exactly a set of nonlinear coupled equations small describing a problem arising in geochemistry. Next a coupled problem originating from the field of (deterministic) random walk theory with reaction kinetics is investigated but now solved approximately. The...

A stochastic model for replicators in catalyzed RNA-like polymers is presented and numerically solved. The model consists of a system of reaction–diffusion equations describing the evolution of a population formed by RNA-like molecules with catalytic capabilities in a prebiotic process. The...

We consider a model introduced recently [Nature 424(2003)900], for describing competition between two languages, which in typical situations predicts the extinction of one of them. We generalize it by introducing a spatial dependence in terms of a reaction–diffusion equation. We show that in...