Reactions in Flows with Nonhyperbolic Dynamics

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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
Issue number3
Publication statusPublished - Sept 2004


  • open chaotic flows
  • advection
  • scattering
  • fields


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