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

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  • 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
  • Matteo Nicoli (1,*); Chaouqi Misbah (2); Paolo Politi (3) (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
  • Matteo Nicoli (1,*); Chaouqi Misbah (2); Paolo Politi (3) (literal)
Pagina inizio
  • 063302 (literal)
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  • http://pre.aps.org/abstract/PRE/v87/i6/e063302 (literal)
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  • 87 (literal)
Rivista
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  • 10 (literal)
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  • 6 (literal)
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  • ISI Web of Science (WOS) (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • (1) Physique de la Matière Condensée, École Polytechnique, CNRS, Palaiseau, F-91128, France (2) Univ. Grenoble 1 / CNRS, LIPhy UMR 5588, Grenoble, F-38041, France (3) Istituto dei Sistemi Complessi, Consiglio Nazionale Delle Ricerche, via Madonna Del Piano 10, I-50019 Sesto Fiorentino, Italy *Present address: Center for Interdisciplinary Research on Complex Systems, Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA. (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)?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(?), the phase diffusion coefficient, as a function of the wavelength ? 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. (literal)
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