Mean Field Theory of Polynuclear Surface Growth

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 im...

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Bibliographic Details
Published in:arXiv.org 1997-11
Main Authors: Ben-Naim, E, Bishop, A R, Daruka, I, Krapivsky, P L
Format: Article
Language:English
Subjects:
Computer simulation
Continuum modeling
Lower bounds
Mathematical models
Mean field theory
Substrates
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.9711249