Nonlocal maps

M. V. Berry, J. O. Indekeu, M. Tabor, N. L. Balazs

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

A new kind of area-preserving map of the phase plane is introduced to represent the dynamics of interacting particles on a line. Unlike the familiar point map, the map is nonlocal in the sense that the evolution of a point in the phase plane depends not only on its position but also on the positions of other points, weighted by an evolving phase-plane density. In the case where this density is uniform and confined within a closed boundary B in the phase plane, the evolution of B is followed for a great variety of interaction potentials. Numerical experiments and analytical arguments show that a simple B develops great complexity. The resulting morphologies, incorporating fission and fusion of particle densities, are illustrated by high resolution graphics.

Original languageEnglish (US)
Pages (from-to)1-24
Number of pages24
JournalPhysica D: Nonlinear Phenomena
Volume11
Issue number1-2
DOIs
StatePublished - May 1984

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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    Berry, M. V., Indekeu, J. O., Tabor, M., & Balazs, N. L. (1984). Nonlocal maps. Physica D: Nonlinear Phenomena, 11(1-2), 1-24. https://doi.org/10.1016/0167-2789(84)90434-2