Reactions in Flows with Nonhyperbolic Dynamics

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We study the reaction dynamics of active particles that are advected passively by 2D incompressible open flows, whose motion is nonhyperbolic. This nonhyperbolicity is associated with the presence of persistent vortices near the wake, wherein fluid is trapped. We show that the fractal equilibrium distribution of the reactants is described by an effective dimension d(eff), which is a finite resolution approximation to the fractal dimension. Furthermore, d(eff) depends on the resolution epsilon and on the reaction rate 1/tau. As tau is increased, the equilibrium distribution goes through a series of transitions where the effective dimension increases abruptly. These transitions are determined by the complex structure of Cantori surrounding the Kolmogorov-Arnold-Moser (KAM) islands.

Original languageEnglish
Article number036216
Number of pages9
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume70
Issue number3
DOIs
Publication statusPublished - Sep 2004

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Effective Dimension
Equilibrium Distribution
Active Particles
fractals
Reaction Rate
Wake
Complex Structure
Fractal Dimension
Vortex
Fractal
Fluid
wakes
Series
Motion
reaction kinetics
Approximation
vortices
fluids
approximation

Keywords

  • open chaotic flows
  • advection
  • scattering
  • fields

Cite this

Reactions in Flows with Nonhyperbolic Dynamics. / de Moura, A P S ; Grebogi, C .

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 70, No. 3, 036216, 09.2004.

Research output: Contribution to journalArticle

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AB - We study the reaction dynamics of active particles that are advected passively by 2D incompressible open flows, whose motion is nonhyperbolic. This nonhyperbolicity is associated with the presence of persistent vortices near the wake, wherein fluid is trapped. We show that the fractal equilibrium distribution of the reactants is described by an effective dimension d(eff), which is a finite resolution approximation to the fractal dimension. Furthermore, d(eff) depends on the resolution epsilon and on the reaction rate 1/tau. As tau is increased, the equilibrium distribution goes through a series of transitions where the effective dimension increases abruptly. These transitions are determined by the complex structure of Cantori surrounding the Kolmogorov-Arnold-Moser (KAM) islands.

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