Localization-delocalization transition of a reaction-diffusion front near a semipermeable wall

The A+B --> C reaction-diffusion process is studied in a system where the reagents are separated by a semipermeable wall. We use reaction-diffusion equations to describe the process and to derive a scaling description for the long-time behavior of the reaction front. Furthermore, we show that a critical localization-delocalization transition takes place as a control parameter which depends on the initial densities and on the diffusion constants is varied. The transition is between a reaction front of finite width that is localized at the wall and a front which is detached and moves away from the wall. At the critical point, the reaction front remains at the wall but its width diverges with time [as t^(1/6) in mean-field approximation].Comment: 7 pages, PS fil

Reaction-diffusion fronts with inhomogeneous initial conditions

Properties of reaction zones resulting from A+B -> C type reaction-diffusion processes are investigated by analytical and numerical methods. The reagents A and B are separated initially and, in addition, there is an initial macroscopic inhomogeneity in the distribution of the B species. For simple two-dimensional geometries, exact analytical results are presented for the time-evolution of the geometric shape of the front. We also show using cellular automata simulations that the fluctuations can be neglected both in the shape and in the width of the front.Comment: 11 pages, 3 figures, submitted to J. Phys.

Critical behavior and Griffiths effects in the disordered contact process

We study the nonequilibrium phase transition in the one-dimensional contact process with quenched spatial disorder by means of large-scale Monte-Carlo simulations for times up to $10^9$ and system sizes up to $10^7$ sites. In agreement with recent predictions of an infinite-randomness fixed point, our simulations demonstrate activated (exponential) dynamical scaling at the critical point. The critical behavior turns out to be universal, even for weak disorder. However, the approach to this asymptotic behavior is extremely slow, with crossover times of the order of $10^4$ or larger. In the Griffiths region between the clean and the dirty critical points, we find power-law dynamical behavior with continuously varying exponents. We discuss the generality of our findings and relate them to a broader theory of rare region effects at phase transitions with quenched disorder.Comment: 10 pages, 8 eps figures, final version as publishe

Formation of Liesegang patterns: A spinodal decomposition scenario

Spinodal decomposition in the presence of a moving particle source is proposed as a mechanism for the formation of Liesegang bands. This mechanism yields a sequence of band positions x_n that obeys the spacing law x_n~Q(1+p)^n. The dependence of the parameters p and Q on the initial concentration of the reagents is determined and we find that the functional form of p is in agreement with the experimentally observed Matalon-Packter law.Comment: RevTex, 4 pages, 4 eps figure

Computing Aggregate Properties of Preimages for 2D Cellular Automata

Computing properties of the set of precursors of a given configuration is a common problem underlying many important questions about cellular automata. Unfortunately, such computations quickly become intractable in dimension greater than one. This paper presents an algorithm --- incremental aggregation --- that can compute aggregate properties of the set of precursors exponentially faster than na{\"i}ve approaches. The incremental aggregation algorithm is demonstrated on two problems from the two-dimensional binary Game of Life cellular automaton: precursor count distributions and higher-order mean field theory coefficients. In both cases, incremental aggregation allows us to obtain new results that were previously beyond reach

Liesegang patterns: Effect of dissociation of the invading electrolyte

The effect of dissociation of the invading electrolyte on the formation of Liesegang bands is investigated. We find, using organic compounds with known dissociation constants, that the spacing coefficient, 1+p, that characterizes the position of the n-th band as x_n ~ (1+p)^n, decreases with increasing dissociation constant, K_d. Theoretical arguments are developed to explain these experimental findings and to calculate explicitly the K_d dependence of 1+p.Comment: RevTex, 8 pages, 3 eps figure

Collective traffic-like movement of ants on a trail: dynamical phases and phase transitions

The traffic-like collective movement of ants on a trail can be described by a stochastic cellular automaton model. We have earlier investigated its unusual flow-density relation by using various mean field approximations and computer simulations. In this paper, we study the model following an alternative approach based on the analogy with the zero range process, which is one of the few known exactly solvable stochastic dynamical models. We show that our theory can quantitatively account for the unusual non-monotonic dependence of the average speed of the ants on their density for finite lattices with periodic boundary conditions. Moreover, we argue that the model exhibits a continuous phase transition at the critial density only in a limiting case. Furthermore, we investigate the phase diagram of the model by replacing the periodic boundary conditions by open boundary conditions.Comment: 8 pages, 6 figure

Signs of low frequency dispersions in disordered binary dielectric mixtures (50-50)

Dielectric relaxation in disordered dielectric mixtures are presented by emphasizing the interfacial polarization. The obtained results coincide with and cause confusion with those of the low frequency dispersion behavior. The considered systems are composed of two phases on two-dimensional square and triangular topological networks. We use the finite element method to calculate the effective dielectric permittivities of randomly generated structures. The dielectric relaxation phenomena together with the dielectric permittivity values at constant frequencies are investigated, and significant differences of the square and triangular topologies are observed. The frequency dependent properties of some of the generated structures are examined. We conclude that the topological disorder may lead to the normal or anomalous low frequency dispersion if the electrical properties of the phases are chosen properly, such that for ``slightly'' {\em reciprocal mixture}--when $\sigma_1\gg\sigma_2$, and $\epsilon_1<\epsilon_2$--normal, and while for ``extreme'' {\em reciprocal mixture}--when $\sigma_1\gg\sigma_2$, and $\epsilon_1\ll\epsilon_2$--anomalous low frequency dispersions are obtained. Finally, comparison with experimental data indicates that one can obtain valuable information from simulations when the material properties of the constituents are not available and of importance.Comment: 13 pages, 7 figure

Band Formation during Gaseous Diffusion in Aerogels

We study experimentally how gaseous HCl and NH_3 diffuse from opposite sides of and react in silica aerogel rods with porosity of 92 % and average pore size of about 50 nm. The reaction leads to solid NH_4Cl, which is deposited in thin sheet-like structures. We present a numerical study of the phenomenon. Due to the difference in boundary conditions between this system and those usually studied, we find the sheet-like structures in the aerogel to differ significantly from older studies. The influence of random nucleation centers and inhomogeneities in the aerogel is studied numerically.Comment: 7 pages RevTex and 8 figures. Figs. 4-8 in Postscript, Figs. 1-3 on request from author

Finite difference lattice Boltzmann model with flux limiters for liquid-vapor systems

In this paper we apply a finite difference lattice Boltzmann model to study the phase separation in a two-dimensional liquid-vapor system. Spurious numerical effects in macroscopic equations are discussed and an appropriate numerical scheme involving flux limiter techniques is proposed to minimize them and guarantee a better numerical stability at very low viscosity. The phase separation kinetics is investigated and we find evidence of two different growth regimes depending on the value of the fluid viscosity as well as on the liquid-vapor ratio.Comment: 10 pages, 10 figures, to be published in Phys. Rev.