Finite-size effects on active chaotic advection

Takashi Nishikawa, Zoltán Toroczkai, Celso Grebogi, T. Tél

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

A small (but finite-size) spherical particle adverted by fluid flows obeys equations of motion that are inherently dissipative, due to the Stokes drag. The dynamics of the adverted particle can be chaotic even with a flow field that is simply time periodic. Similar to the case of ideal tracers, whose dynamics is Hamiltonian, chemical or biological activity involving such particles can be analyzed using the theory of chaotic dynamics. Using the example of an autocatalytic reaction, A +B → 2B, we show that the balance between dissipation in the particle dynamics ana. production due to reaction leads to a steady state distribution of the reagent. We also show that, in the case of coalescence reaction, B+B → B, the decay of the particle density obeys a universal scaling law as approximately t -1 and that the particle distribution becomes restricted to a subset with fractal dimension D 2, where D 2 is the correlation dimension of the chaotic attractor in the particle dynamics.

Original languageEnglish
Article number026216
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume65
Issue number2
DOIs
Publication statusPublished - Feb 2002

Fingerprint

Chaotic Advection
Finite Size Effects
advection
flow equations
Correlation Dimension
activity (biology)
Steady-state Distribution
Coalescence
scaling laws
Chaotic Attractor
coalescing
Chaotic Dynamics
set theory
drag
Scaling Laws
fluid flow
tracers
reagents
Drag
Stokes

ASJC Scopus subject areas

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

Cite this

Finite-size effects on active chaotic advection. / Nishikawa, Takashi; Toroczkai, Zoltán; Grebogi, Celso; Tél, T.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 65, No. 2, 026216, 02.2002.

Research output: Contribution to journalArticle

Nishikawa, Takashi ; Toroczkai, Zoltán ; Grebogi, Celso ; Tél, T. / Finite-size effects on active chaotic advection. In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2002 ; Vol. 65, No. 2.
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