Effective Rates in Dilute Reaction-Advection Systems for the Annihilation Process A+A→∅ View Full Text


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Article Info

DATE

2013-11

AUTHORS

G. Krstulovic, M. Cencini, J. Bec

ABSTRACT

A dilute system of reacting particles transported by fluid flows is considered. The particles react as A+A→∅ with a given rate when they are within a finite radius of interaction. The system is described in terms of the joint n-point number spatial density that it is shown to obey a hierarchy of transport equations. An analytic solution is obtained in the dilute or, which is equivalent, the long-time limit by using a Lagrangian approach where statistical averages are performed along non-reacting trajectories. In this limit, it is shown that the moments of the number of particles have an exponential decay rather than the algebraic prediction of standard mean-field approaches. The effective reaction rate is then related to Lagrangian pair statistics by a large-deviation principle. A phenomenological model is introduced to study the qualitative behavior of the effective rate as a function of the interaction length, the degree of chaoticity of the dynamics and the compressibility of the carrier flow. Exact computations, obtained via a Feynman–Kac approach, in a smooth, compressible, random delta-correlated-in-time Gaussian velocity field support the proposed heuristic approach. More... »

PAGES

530-550

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10955-013-0823-8

DOI

http://dx.doi.org/10.1007/s10955-013-0823-8

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1033918458


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