Nonlocal maps

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

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 - Jan 1 1984
Externally publishedYes

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preserving
fission
fusion
high resolution
interactions

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Condensed Matter Physics

Cite this

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

Nonlocal maps. / Berry, M. V.; Indekeu, J. O.; Tabor, Michael; Balazs, N. L.

In: Physica D: Nonlinear Phenomena, Vol. 11, No. 1-2, 01.01.1984, p. 1-24.

Research output: Contribution to journalArticle

Berry, MV, Indekeu, JO, Tabor, M & Balazs, NL 1984, 'Nonlocal maps', Physica D: Nonlinear Phenomena, vol. 11, no. 1-2, pp. 1-24. https://doi.org/10.1016/0167-2789(84)90434-2
Berry, M. V. ; Indekeu, J. O. ; Tabor, Michael ; Balazs, N. L. / Nonlocal maps. In: Physica D: Nonlinear Phenomena. 1984 ; Vol. 11, No. 1-2. pp. 1-24.
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