Reductive renormalization of the phase-field crystal equation

Y. Oono, Y. Shiwa

Research output: Contribution to journalArticlepeer-review


It has been known for some time that singular perturbation and reductive perturbation can be unified from the renormalization-group theoretical point of view: Reductive extraction of space-time global behavior is the essence of singular perturbation methods. Reductive renormalization was proposed to make this unification practically accessible; actually, this reductive perturbation is far simpler than most reduction methods, such as the rather standard scaling expansion. However, a rather cryptic exposition of the method seems to have been the cause of some trouble. Here, an explicit demonstration of the consistency of the reductive renormalization-group procedure is given for partial differentiation equations (of a certain type, including time-evolution semigroup type equations). Then, the procedure is applied to the reduction of a phase-field crystal equation to illustrate the streamlined reduction method. We conjecture that if the original system is structurally stable, the reductive renormalization-group result and that of the original equation are diffeomorphic.

Original languageEnglish (US)
Article number061138
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number6
StatePublished - Dec 28 2012

ASJC Scopus subject areas

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


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