### Abstract

A small (but finite-size) spherical particle advected by fluid flows obeys equations of motion that are inherently dissipative, due to the Stokes drag. The dynamics of the advected 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 and production due to reaction leads to a steady state distribution Or the reagent. We also,chow 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 language | English |
---|---|

Article number | 026216 |

Number of pages | 11 |

Journal | Physical Review. E, Statistical, Nonlinear and Soft Matter Physics |

Volume | 65 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2002 |

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### Keywords

- plankton dynamics
- open flows
- particles
- coexistence
- attractors
- diffusion
- motion
- fields
- model

### Cite this

*Physical Review. E, Statistical, Nonlinear and Soft Matter Physics*,

*65*(2), [026216]. https://doi.org/10.1103/Phys.RevE.65.026216

**Finite-size Effects on Active Chaotic Advection.** / Nishikawa, T ; Toroczkai, Z ; Grebogi, C ; Tel, T .

Research output: Contribution to journal › Article

*Physical Review. E, Statistical, Nonlinear and Soft Matter Physics*, vol. 65, no. 2, 026216. https://doi.org/10.1103/Phys.RevE.65.026216

}

TY - JOUR

T1 - Finite-size Effects on Active Chaotic Advection

AU - Nishikawa, T

AU - Toroczkai, Z

AU - Grebogi, C

AU - Tel, T

PY - 2002/2

Y1 - 2002/2

N2 - A small (but finite-size) spherical particle advected by fluid flows obeys equations of motion that are inherently dissipative, due to the Stokes drag. The dynamics of the advected 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 and production due to reaction leads to a steady state distribution Or the reagent. We also,chow 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.

AB - A small (but finite-size) spherical particle advected by fluid flows obeys equations of motion that are inherently dissipative, due to the Stokes drag. The dynamics of the advected 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 and production due to reaction leads to a steady state distribution Or the reagent. We also,chow 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.

KW - plankton dynamics

KW - open flows

KW - particles

KW - coexistence

KW - attractors

KW - diffusion

KW - motion

KW - fields

KW - model

U2 - 10.1103/Phys.RevE.65.026216

DO - 10.1103/Phys.RevE.65.026216

M3 - Article

VL - 65

JO - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

JF - Physical Review. E, Statistical, Nonlinear and Soft Matter Physics

SN - 1539-3755

IS - 2

M1 - 026216

ER -