2002/04/26 by Klaus Kassner, Chaouqi Misbah · 1 citation
Physics and Astronomy · #cond-mat
paper · pdf · doi:10.1103/physreve.66.026102
LaTeX source, 12 pages, 4 figures, accepted for Physical Review E
arxiv created 2002/04/26 · arxiv updated 2009/11/30
We derive amplitude equations for interface dynamics in pattern forming systems with long-range interactions. The basic condition for the applicability of the method developed here is that the bulk equations are linear and solvable by integral transforms. We arrive at the interface equation via long-wave asymptotics. As an example, we treat the Grinfeld instability, and we also give a result for the Saffman-Taylor instability. It turns out that the long-range interaction survives the long-wave limit and shows up in the final equation as a nonlocal and nonlinear term, a feature that to our knowledge is not shared by any other known long-wave equation. The form of this particular equation will then allow us to draw conclusions regarding the universal dynamics of systems in which nonlocal effects persist at the level of the amplitude description.