Mean Field Theory of Polynuclear Surface Growth,
E. Ben-Naim, A.R. Bishop, I. Daruke, and P.L. Krapivsky
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.
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