Renormalization group theory and variational calculations for propagating fronts

Lin Yuan Chen, Nigel Goldenfeld, Y. Oono

Research output: Contribution to journalArticlepeer-review

Abstract

We study the propagation of uniformly translating fronts into a linearly unstable state, both analytically and numerically. We introduce a perturbative renormalization group approach to compute the change in the propagation speed when the fronts are perturbed by structural modification of their governing equations. This approach is successful when the fronts are structurally stable, and allows us to select uniquely the (numerical) experimentally observable propagation speed. For convenience and completeness, the structural stability argument is also briefly described. We point out that the solvability condition widely used in studying dynamics of nonequilibrium systems is equivalent to the assumption of physical renormalizability. We also implement a variational principle, due to Hadeler and Rothe [J. Math. Biol. 2, 251 (1975)], which provides a very good upper bound and, in some cases, even exact results on the propagation speeds, and which identifies the transition from "linear marginal stability" to "nonlinear marginal stability" as parameters in the governing equation are varied.

Original languageEnglish (US)
Pages (from-to)4502-4511
Number of pages10
JournalPhysical Review E
Volume49
Issue number5
DOIs
StatePublished - 1994

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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