Noise and topology in driven systems - An application to interface dynamics

Stewart Barnes, Jean Pierre Eckmann, Thierry Giamarchi, Vivien Lecomte

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Motivated by a stochastic differential equation describing the dynamics of interfaces, we study the bifurcation behaviour of a more general class of such equations. These equations are characterized by a two-dimensional phase space (describing the position of the interface and an internal degree of freedom). The noise accounts for thermal fluctuations of such systems. The models considered show a saddle-node bifurcation and have furthermore homoclinic orbits, i.e. orbits leaving an unstable fixed point and returning to it. Such systems display intermittent behaviour. The presence of noise combined with the topology of the phase space leads to unexpected behaviour as a function of the bifurcation parameter, i.e. of the driving force of the system. We explain this behaviour using saddle-point methods and considering global topological aspects of the problem. This then explains the non-monotonic force-velocity dependence of certain driven interfaces.

Original languageEnglish (US)
Pages (from-to)1427-1441
Number of pages15
JournalNonlinearity
Volume25
Issue number5
DOIs
StatePublished - May 2012

Fingerprint

Interface Dynamics
Orbits
topology
Topology
Phase Space
Differential equations
Bifurcation
orbits
Saddle Point Method
Saddle-node Bifurcation
Homoclinic Orbit
saddles
display devices
Driving Force
saddle points
Stochastic Equations
differential equations
degrees of freedom
Orbit
Unstable

ASJC Scopus subject areas

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

Cite this

Noise and topology in driven systems - An application to interface dynamics. / Barnes, Stewart; Eckmann, Jean Pierre; Giamarchi, Thierry; Lecomte, Vivien.

In: Nonlinearity, Vol. 25, No. 5, 05.2012, p. 1427-1441.

Research output: Contribution to journalArticle

Barnes, Stewart ; Eckmann, Jean Pierre ; Giamarchi, Thierry ; Lecomte, Vivien. / Noise and topology in driven systems - An application to interface dynamics. In: Nonlinearity. 2012 ; Vol. 25, No. 5. pp. 1427-1441.
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