Autocatalytic reactions of phase distributed active particles

We investigate the effect of asynchronism of autocatalytic reactions taking place in open hydrodynamical flows, by assigning a phase to each particle in the system to differentiate the timing of the reaction, while the reaction rate (periodicity) is kept unchanged. The chaotic saddle in the flow dynamics acts as a catalyst and enhances the reaction in the same fashion as in the case of a synchronous reaction that was studied previously, proving that the same type of nonlinear reaction kinetics is valid in the phase-distributed situation. More importantly, we show that, in a certain range of a parameter, the phenomenon of phase selection can occur, when a group of particles with a particular phase is favored over the others, thus occupying a larger fraction of the available space, or eventually leading to the extinction of the unfavored phases. We discuss the biological relevance of this latter phenomenon. (c) 2002 American Institute of Physics.

Noise-induced enhancement of chemical reactions in nonlinear flows

Motivated by the problem of ozone production in atmospheres of urban areas, we consider chemical reactions of the general type: A+B-->2C, in idealized two-dimensional nonlinear flows that can generate Lagrangian chaos. Our aims differ from those in the existing work in that we address the role of transient chaos versus sustained chaos and, more importantly, we investigate the influence of noise. We find that noise can significantly enhance the chemical reaction in a resonancelike manner where the product of the reaction becomes maximum at some optimal noise level. We also argue that chaos may not be a necessary condition for the observed resonances. A physical theory is formulated to understand the resonant behavior. (c) 2002 American Institute of Physics.

Diffusivity dependence of ozone depletion over the midnorthern latitudes

The mixing and reaction properties of advected chemicals (and passive scalars) are determined by the fractal dimension D of the interface between the chemicals. We show that the scaling of the amount m of reacted chemicals with diffusivity kappa is m(0)-m(kappa) proportional, proportional to kappa(1-D/2) in the two-dimensional case. This relation is valid in a range of times and diffusivities where the diffusive length scales of the chemicals are within the range of scales where the chemical interface has a well-defined fractal dimension. We apply the relation to the problems of chlorine deactivation and ozone depletion over the midnorthern latitudes. We determine numerically the fractal dimension of an interface advected by stratospheric winds. This allows us, first, to explain the diffusivity dependence of chlorine deactivation and ozone depletion that was previously observed in numerical simulations (Tan et al., J. Geophys. Res., [Atmos.] 103, 1585 (1998)) and, second, to extrapolate the results of such simulations down to realistically low diffusivities.

Chemical or biological activity in open chaotic flows

We investigate the evolution of particle ensembles in open chaotic hydrodynamical flows. Active processes of the type A+B-->2B and A+B-->2C are considered in the limit of weak diffusion. As an illustrative advection dynamics we consider a model of the von Kármán vortex street, a time-periodic two-dimensional flow of a viscous fluid around a cylinder. We show that a fractal unstable manifold acts as a catalyst for the process, and the products cover fattened-up copies of this manifold. This may account for the observed filamental intensification of activity in environmental flows. The reaction equations valid in the wake are derived either in the form of dissipative maps or differential equations depending on the regime under consideration. They contain terms that are not present in the traditional reaction equations of the same active process: the decay of the products is slower while the productivity is much faster than in homogeneous flows. Both effects appear as a consequence of underlying fractal structures. In the long time limit, the system locks itself in a dynamic equilibrium state synchronized to the flow for both types of reactions. For particles of finite size an emptying transition might also occur leading to no products left in the wake.