Phase diffusion and phase propagation: interesting connections

Alan C Newell, Yves Pomeau

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We explore parallels between Whitham theory (nonlinear geometrical optics) applied to gradient systems, such as high Prandtl number pattern forming convection layers, and Hamiltonian systems, such as superfluids at zero temperature and thin elastic shells. In particular, we discuss certain universal features such as the canonical nature of the averaged equations and the relation between the conditions for the onset of vortices, the Eckhaus and Landau criteria respectively. We also show that there is an analogue to the zig-zag instability experienced by gradient systems for Hamiltonian systems and discuss how the asymptotic states may relate. We discuss a new approach for obtaining weak and singular solutions (concave and convex disclinations in phase gradient systems and their composites, phase grain boundaries) which takes advantage of a geometrical property of the phase surface, namely that it has zero Gaussian curvature almost everywhere. We exploit similar ideas in the Hamiltonian context.

Original languageEnglish (US)
Pages (from-to)216-232
Number of pages17
JournalPhysica D: Nonlinear Phenomena
Volume87
Issue number1-4
DOIs
StatePublished - Oct 15 1995
Externally publishedYes

Fingerprint

gradients
propagation
elastic shells
nonlinear optics
geometrical optics
Prandtl number
convection
grain boundaries
curvature
vortices
analogs
composite materials
temperature

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

Phase diffusion and phase propagation : interesting connections. / Newell, Alan C; Pomeau, Yves.

In: Physica D: Nonlinear Phenomena, Vol. 87, No. 1-4, 15.10.1995, p. 216-232.

Research output: Contribution to journalArticle

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