Coarsening dynamics in one dimension: The phase diffusion equation and its numerical implementation (Articolo in rivista)

Type
Label
  • Coarsening dynamics in one dimension: The phase diffusion equation and its numerical implementation (Articolo in rivista) (literal)
Anno
  • 2013-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1103/PhysRevE.87.063302 (literal)
Alternative label
  • M.Nicoli, P.Politi, C.Misbah (2013)
    Coarsening dynamics in one dimension: The phase diffusion equation and its numerical implementation
    in Physical review. E, Statistical, nonlinear, and soft matter physics (Print)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • M.Nicoli, P.Politi, C.Misbah (literal)
Pagina inizio
  • 063302-1 (literal)
Pagina fine
  • 063302-10 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://pre.aps.org/abstract/PRE/v87/i6/e063302 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 87 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#pagineTotali
  • 10 (literal)
Note
  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • - Ecole Polytech, CNRS, F-91128 Palaiseau, France - Univ Grenoble 1, CNRS, LIPhy UMR 5588, F-38041 Grenoble, France - CNR, Ist Sistemi Complessi, I-50019 Sesto Fiorentino, Italy (literal)
Titolo
  • Coarsening dynamics in one dimension: The phase diffusion equation and its numerical implementation (literal)
Abstract
  • 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. (literal)
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