Mean-field theory of polynuclear surface growth
نویسنده
چکیده
We study statistical properties of a continuum model of polynuclear surface growth on an infinite substrate. We develop a self-consistent mean-field theory which is solved to deduce the growth velocity and the extremal behaviour of the coverage. Numerical simulations show that this theory gives an improved approximation for the coverage compared to the previous linear recursion relations approach. Furthermore, these two approximations provide useful upper and lower bounds for a number of characteristics including the coverage, growth velocity and the width exponent.
منابع مشابه
Limiting distributions for a polynuclear growth model with external sources
The purpose of this paper is to investigate the limiting distribution functions for a polynuclear growth model with two external sources, which was considered by Prähofer and Spohn in [13]. Depending on the strength of the sources, the limiting distribution functions are either the Tracy-Widom functions of random matrix theory, or a new explicit function which has the special property that its ...
متن کاملAnalytic Approximations for the Velocity of Field-Driven Ising Interfaces
We present analytic approximations for the field, temperature, and orientation dependences of the interface velocity in a two-dimensional kinetic Ising model in a nonzero field. The model, which has nonconserved order parameter, is useful for ferromagnets, ferroelectrics, and other systems undergoing order-disorder phase transformations driven by a bulk free-energy difference. The Solid-on-Soli...
متن کاملMean field theory for skewed height profiles in nonlinear growth processes
We propose a mean field theory for interfaces growing according to the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. The mean field equations are formulated in terms of densities at different heights, taking surface tension and the influence of the nonlinear term in the KPZ equation into account. Although spatial correlations are neglected, the mean field equations still reflect the spa...
متن کاملEffectiveness of an Educational Intervention Based on the Theory of Planned Behavior on Fertility Intention of Single-Child Women: A Field Trial Study
Aims Fertility is an important factor for population growth and its proportion. Regarding the overall decrease in the total fertility rate in Iran and reaching below the replacement rate, this study aimed at determining the effect of the education based on the Theory of Planned Behavior (TPB) on women’s fertility intention. Methods & Materials This interventional study was conducted on 100 pre...
متن کاملStochastic Surface Growth
Growth phenomena constitute an important field in nonequilibrium statistical mechanics. On the one hand, they are ubiquitous in nature, on the other hand, their theoretical understanding poses a challenging problem for the methods of theoretical physics. Typically, growth processes lead to statistically scale invariant structures. For nonlocal growth, selfsimilar clusters are generated in the f...
متن کامل