期刊
PHYSICAL REVIEW E
卷 87, 期 6, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.87.063302
关键词
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资金
- Italian Ministry of Research [PRIN 2007JHLPEZ]
- MICINN (Spain) [FIS2009-12964-C05-01]
- CNES (Centre National d'Etudes Spatiales)
- Italian CNR
Many nonlinear partial differential equations (PDEs) display a coarsening dynamics, i.e., an emerging pattern whose typical length scale L increases with time. The so-called coarsening exponent n characterizes the time dependence of the scale of the pattern, L(t) approximate to t(n), and coarsening dynamics can be described by a diffusion equation for the phase of the pattern. By means of a multiscale analysis we are able to find the analytical expression of such diffusion equations. Here, we propose a recipe to implement numerically the determination of D(lambda), the phase diffusion coefficient, as a function of the wavelength lambda of the base steady state u(0)(x). D carries all information about coarsening dynamics and, through the relation vertical bar D(L)vertical bar similar or equal to L-2/t, it allows us to determine the coarsening exponent. The main conceptual message is that the coarsening exponent is determined without solving a time-dependent equation, but only by inspecting the periodic steady-state solutions. This provides a much faster strategy than a orward time-dependent calculation. We discuss our method for several different PDEs, both conserved and not conserved.
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