Mean Field Theory of Polynuclear Surface Growth

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.

revtex, 7 pages, 4 figs

References in corpus (2)

• Exact results for nucleation-and-growth in one dimension
• Absence of non-trivial asymptotic scaling in the Kashchiev model of polynuclear growth

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