We derive the continuum equation for a discrete model for ion sputtering. We follow an approach based on the master equation, and discuss how it can be truncated to a Fokker-Planck equation and mapped to a discrete Langevin equation. By taking the continuum limit, we arrive at the Kuramoto-Sivashinsky equation with a stochastic noise term.
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Brown Univ, Dept Phys, Providence, RI 02912 USABrown Univ, Dept Phys, Providence, RI 02912 USA
Obeid, D.
Kosterlitz, J. M.
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Brown Univ, Dept Phys, Providence, RI 02912 USA
Korea Inst Adv Study, Sch Computat Sci, Seoul 130722, South KoreaBrown Univ, Dept Phys, Providence, RI 02912 USA