Mean Field Theory of Polynuclear Surface Growth

TL;DR

This paper develops a mean-field theoretical approach to analyze polynuclear surface growth, providing improved predictions for growth velocity and coverage, with bounds established through simulations.

Contribution

It introduces a self-consistent mean-field theory for polynuclear surface growth, offering more accurate estimates and bounds compared to previous methods.

Findings

Mean-field theory accurately predicts growth velocity.

Numerical simulations validate the improved coverage approximation.

Bounds for coverage, velocity, and roughness are established.

Abstract

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 behavior of the coverage. Numerical simulations show that this theory gives an improved approximation for the coverage compare 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 roughness exponent.