arXiv subjects

Vladimir Privman

Publications and source records attributed to Vladimir Privman.

131 records · Page 8Linked to original sources

arXiv1992

Discrete to Continuous-Time Crossover due to Anisotropy in Diffusion-Limited Two-Particle Annihilation Reactions

Diffusion-limited reaction A+A->inert with anisotropic hopping on the d=1 lattice, is solved exactly for a simultaneous updating, discrete time-step dynamics. Diffusion-dominated processes slow down as the anisotropy increases. For large times or large anisotropy, one can invoke the appropriate continuum limits. In these limits the effects of the anisotropy on variation of particle density can be absorbed in time rescaling. However, in other regimes, when the discreteness of the time steps is nonnegligible, the anisotropy effects are nontrivial, although they are always quite small numerically.

cond-mat↗

arXiv1992

Random Sequential Adsorption on a Line: Mean-Field Theory of Diffusional Relaxation

We develop a new fast-diffusion approximation for the kinetics of deposition of extended objects on a linear substrate, accompanied by diffusional relaxation. This new approximation plays the role of the mean-field theory for such processes and is valid over a significantly larger range than an earlier variant, which was based on a mapping to chemical reactions. In particular, continuum-limit off-lattice deposition is described naturally within our approximation. The criteria for the applicability of the mean-field theory are derived. While deposition of dimers, and marginally, trimers, is affected by fluctuations, we find that the k-mer deposition kinetics is asymptotically mean-field like for all k=4,5,..., where the limit k->infinity, when properly defined, describes deposition-diffusion kinetics in the continuum.

cond-mat↗

arXiv1992

Model of Cluster Growth and Phase Separation: Exact Results in One Dimension

We present exact results for a lattice model of cluster growth in 1D. The growth mechanism involves interface hopping and pairwise annihilation supplemented by spontaneous creation of the stable-phase, +1, regions by overturning the unstable-phase, -1, spins with probability p. For cluster coarsening at phase coexistence, p=0, the conventional structure-factor scaling applies. In this limit our model falls in the class of diffusion-limited reactions A+A->inert. The +1 cluster size grows diffusively, ~t**(1/2), and the two-point correlation function obeys scaling. However, for p>0, i.e., for the dynamics of formation of stable phase from unstable phase, we find that structure-factor scaling breaks down; the length scale associated with the size of the growing +1 clusters reflects only the short-distance properties of the two-point correlations.

cond-mat↗

arXiv1992

Exact Results for a Three-Body Reaction-Diffusion System

A system of particles hopping on a line, singly or as merged pairs, and annihilating in groups of three on encounters, is solved exactly for certain symmetrical initial conditions. The functional form of the density is nearly identical to that found in two-body annihilation, and both systems show non-mean-field, ~1/t**(1/2) instead of ~1/t, decrease of particle density for large times.

cond-mat↗

arXiv1992

Fluctuating Interfaces, Surface Tension, and Capillary Waves: An Introduction

We present an introduction to modern theories of interfacial fluctuations and the associated interfacial parameters: surface tension and surface stiffness, as well as their interpretation within the capillary wave model. Transfer matrix spectrum properties due to fluctuation of an interface in a long-cylinder geometry are reviewed. The roughening transition and properties of rigid interfaces below the roughening temperature in 3d lattice models are surveyed with emphasis on differences in fluctuations and transfer matrix spectral properties of rigid vs. rough interfaces.

cond-mat↗