Intermittency, stochastic growth and phase transition in a simple deterministic partial differential equation with a singular term

M. Vicsek, T. Vicsek

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We show by numerical integration that the discretized version of simple deterministic partial differential equations with singular terms proposed by Zhang (1992) exhibit rich spatio-temporal behaviour representing a mixture of stochastic and deterministic regimes. Varying the relative weight B of the singular term we have been able to detect transitions in the global behaviour of the solutions by determining their total width w(t). In particular, we have found intermittent solutions as well as a power-law dependence of W=w(t to infinity ) on B.

Original languageEnglish
Article number001
JournalJournal of Physics A: Mathematical and General
Volume28
Issue number11
DOIs
Publication statusPublished - 1995

Fingerprint

Intermittency
intermittency
partial differential equations
Partial differential equations
Phase Transition
Partial differential equation
Phase transitions
Term
numerical integration
infinity
Numerical integration
Power Law
Infinity

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

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abstract = "We show by numerical integration that the discretized version of simple deterministic partial differential equations with singular terms proposed by Zhang (1992) exhibit rich spatio-temporal behaviour representing a mixture of stochastic and deterministic regimes. Varying the relative weight B of the singular term we have been able to detect transitions in the global behaviour of the solutions by determining their total width w(t). In particular, we have found intermittent solutions as well as a power-law dependence of W=w(t to infinity ) on B.",
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