Continuum approach to discreteness

P. G. Kevrekidis, I. G. Kevrekidis, A. R. Bishop, E. S. Titi

Research output: Contribution to journalArticle

63 Scopus citations

Abstract

We study analytically and numerically continuum models derived on the basis of Padé approximations and their effectiveness in modeling spatially discrete systems. We not only analyze features of the temporal dynamics that can be captured through these continuum approaches (e.g., shape oscillations, radiation effects, and trapping) but also point out ones that cannot be captured (such as Peierls-Nabarro barriers and Bloch oscillations). We analyze the role of such methods in providing an effective "homogenization" of spatially discrete, as well as of heterogeneous continuum equations. Finally, we develop numerical methods for solving such equations and use them to establish the range of validity of these continuum approximations, as well as to compare them with other semicontinuum approximations.

Original languageEnglish (US)
Article number046613
Pages (from-to)046613/1-046613/13
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume65
Issue number4
DOIs
StatePublished - Apr 1 2002

All Science Journal Classification (ASJC) codes

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

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    Kevrekidis, P. G., Kevrekidis, I. G., Bishop, A. R., & Titi, E. S. (2002). Continuum approach to discreteness. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 65(4), 046613/1-046613/13. [046613]. https://doi.org/10.1103/PhysRevE.65.046613