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Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Année : 2013

Coarsening dynamics in one dimension: The phase diffusion equation and its numerical implementation

Matteo Nicoli
  • Fonction : Auteur
Paolo Politi
  • Fonction : Auteur

Résumé

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)≈tn, 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(λ), the phase diffusion coefficient, as a function of the wavelength λ of the base steady state u0(x). D carries all information about coarsening dynamics and, through the relation |D(L)|≃L2/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.

Dates et versions

hal-00881097 , version 1 (07-11-2013)

Identifiants

Citer

Matteo Nicoli, Chaouqi Misbah, Paolo Politi. Coarsening dynamics in one dimension: The phase diffusion equation and its numerical implementation. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2013, 87, pp.63302. ⟨10.1103/PHYSREVE.87.063302⟩. ⟨hal-00881097⟩
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