Continuous description of lattice discreteness effects in front propagation

Marcel G. Clerc, Ricardo G. Elías, René G. Rojas

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

Models describing microscopic or mesoscopic phenomena in physics are inherently discrete, where the lattice spacing between fundamental components, such as in the case of atomic sites, is a fundamental physical parameter. The effect of spatial discreteness over front propagation phenomenon in an overdamped one-dimensional periodic lattice is studied. We show here that the study of front propagation leads in a discrete description to different conclusions that in the case of its, respectively, continuous description, and also that the results of the discrete model, can be inferred by effective continuous equations with a supplementary spatially periodic term that we have denominated Peierls-Nabarro drift, which describes the bifurcation diagram of the front speed, the appearance of particle-type solutions and their snaking bifurcation diagram. Numerical simulations of the discrete equation show quite good agreement with the phenomenological description. This journal is

Original languageEnglish
Pages (from-to)412-424
Number of pages13
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume369
Issue number1935
DOIs
StatePublished - 28 Jan 2011
Externally publishedYes

Keywords

  • Front propagation
  • Fronts interaction
  • Nonlinear waves

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