Ballistic annihilation kinetics for a multi-velocity one-dimensional ideal gas

Ballistic annihilation kinetics for a multi-velocity one-dimensional ideal gas is studied in the framework of an exact analytic approach. For an initial symmetric three-velocity distribution, the problem can be solved exactly and it is shown that different regimes exist depending on the initial fraction of particles at rest. Extension to the case of a n-velocity distribution is discussed.Comment: 19 pages, latex, uses Revtex macro

Transfer matrix spectrum of two-dimensional layered Ising models

A class of layered Ising models interpolating between the homogeneous Ising model and the McCoy-Wu model (1973) is studied. Critical exponents and the transfer matrix spectrum at the critical point are calculated numerically using finite-size scaling techniques and analytically by using an analogy with an electron gas in a crystal with impurities. The transfer matrix spectrum is compared with those of some strongly anisotropic critical systems

Multiparticle lattice gas automata for reaction diffusion systems

Lattice gas automata are a powerful tool to model reaction-diffusion processes. However, the evolution rules limit the number of particles that can be present at each lattice site. This restriction is often a strong limitation to modelling several reaction-diffusion phenomena and, also, lead to very noisy numerical simulations. We propose and study new algorithms which allow for an arbitrary number of particle, while keeping the benefits of the cellular automata approach (close to a microscopic level of description, deal correctly with all degrees of freedom, and is numerically exact)

New Analytic Approach to Multivelocity Annihilation in the Kinetic Theory of Reactions

A new, exact, analytic approach to multivelocity, one-species, ballistic annihilation in one dimension is proposed. For an arbitrary one-particle initial velocity distribution, the problem can be solved rigorously in terms of the two-particle conditional probability, which obeys a closed nonlinear integro-differential equation. We present a method for solving this equation for an arbitrary discrete velocity distribution. This method is applied to the three-velocity case. The outcome of numerical simulations compares well with our exact results