# Finite-size effects on active chaotic advection.

@article{Nishikawa2002FinitesizeEO, title={Finite-size effects on active chaotic advection.}, author={Takashi Nishikawa and Zolt{\'a}n Toroczkai and Celso Grebogi and Tam{\'a}s T{\'e}l}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2002}, volume={65 2 Pt 2}, pages={ 026216 } }

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+Bright…

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## References

SHOWING 1-2 OF 2 REFERENCES

### Petrovskii,Numerical Study of Plankton-Fish Dynamics in a Spatially Structured and No Environment

- 2001

### Spatiotemporal Models of Population and Comm nity Dynamics~Chapman

- 1998