0000000000061860
AUTHOR
Vladimir Privman
showing 7 related works from this author
Locally Frozen Defects in Random Sequential Adsorption with Diffusional Relaxation
1993
Random sequential adsorption with diffusional relaxation, of two by two square objects on the two-dimensional square lattice is studied by Monte Carlo computer simulation. Asymptotically for large lattice sizes, diffusional relaxation allows the deposition process to reach full coverage. The coverage approaches the full occupation value, 1, as a power-law with convergence exponent near 1/2. For a periodic lattice of finite (even) size $L$, the final state is a frozen random rectangular grid of domain walls connecting single-site defects. The domain sizes saturate at L**0.8. Prior to saturation, i.e., asymptotically for infinite lattice, the domain growth is power-law with growth exponent ne…
Continuum limit in random sequential adsorption.
1991
We develop analytical estimates of the late-stage (long-time) asymptotic behavior of the coverage in the D-dimensional lattice models of irreversible deposition of hypercube-shaped particles. Our results elucidate the crossover from the exponential time dependence for the lattice case to the power-law behavior with a multiplicative logarithmic factor, in the continuum deposition. Numerical Monte Carlo results are reported for the two-dimensional (2D) deposition, both lattice and continuum. Combined with the exact 1D results, they are used to test the general theoretical expectations for the late-stage deposition kinetics. New accurate estimates of the jamming coverages in 2D rule out some e…
Irreversible Multilayer Adsorption
1993
Random sequential adsorption (RSA) models have been studied due to their relevance to deposition processes on surfaces. The depositing particles are represented by hard-core extended objects; they are not allowed to overlap. Numerical Monte Carlo studies and analytical considerations are reported for 1D and 2D models of multilayer adsorption processes. Deposition without screening is investigated, in certain models the density may actually increase away from the substrate. Analytical studies of the late stage coverage behavior show the crossover from exponential time dependence for the lattice case to the power law behavior in the continuum deposition. 2D lattice and continuum simulations r…
Finite-size tests of hyperscaling.
1985
The possible form of hyperscaling violations in finite-size scaling theory is discussed. The implications for recent tests in Monte Carlo simulations of the d = 3 Ising model are examined, and new results for the d = 5 Ising model are presented.
Diffusional Relaxation in Dimer Deposition
1992
In deposition of dimers on a 1D lattice substrate, we find by analytical arguments, supported by numerical Monte Carlo simulations, that the effect of added diffusional relaxation is to allow the full, saturation coverage, 100%, for large times. This limiting coverage is approached according to the ~ 1/√t power law preceded, for fast diffusion, by the mean-field crossover regime with the intermediate ~ 1/t behavior.
Collective Effects in Random Sequential Adsorption of Diffusing Hard Squares
1992
We study by Monte Carlo computer simulations random sequential adsorption (RSA) with diffusional relaxation, of lattice hard squares in two dimensions. While for RSA without diffusion the coverage approaches its maximum jamming value (large-time fractional coverage) exponentially, added diffusion allows the deposition process to proceed to the full coverage. The approach to the full coverage is consistent with the t**(-1/2) power law reminiscent of the equilibrium cluster coarsening in models with nonconserved order-parameter dynamics.
RANDOM SEQUENTIAL ADSORPTION ON A LINEAR LATTICE: EFFECT OF DIFFUSIONAL RELAXATION
1992
In this paper, the authors offer phenomenological arguments, supported by numerical Monte Carlo data, suggesting that the asymptotic large-time behavior of the coverage in the 1D lattice deposition of k-mers with k {gt} 3, accompanied by k-mer diffusion, is governed by the same mean-field dynamics as the lattice chemical reaction kA {yields} inert. The latter reaction is considered to occur with partial probability. The coverage in the deposition process approaches full saturation for any nonzero diffusion rate, and the void fraction decreases according to the power-law t{sup {minus}1/(k{minus}1)}.