Nishikawa T, Toroczkai Z, Grebogi C
Department of Mathematics, Arizona State University, Tempe, Arizona 85287, USA.
Phys Rev Lett. 2001 Jul 16;87(3):038301. doi: 10.1103/PhysRevLett.87.038301. Epub 2001 Jun 29.
We investigate the reaction kinetics of small spherical particles with inertia, obeying coalescence type of reaction, B+B-->B, and being advected by hydrodynamical flows with time-periodic forcing. In contrast to passive tracers, the particle dynamics is governed by the strongly nonlinear Maxey-Riley equations, which typically create chaos in the spatial component of the particle dynamics, appearing as filamental structures in the distribution of the reactants. Defining a stochastic description supported on the natural measure of the attractor, we show that, in the limit of slow reaction, the reaction kinetics assumes a universal behavior exhibiting a t(-1) decay in the amount of reagents, which become distributed on a subset of dimension D2, where D2 is the correlation dimension of the chaotic flow.
