English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A dilute system of reacting particles transported by fluid flows isconsidered. The particles react as $A + A \to \varnothing$ with a given ratewhen they are within a finite radius of interaction. The system is described interms of the joint n-point number spatial density that it is shown to obey ahierarchy of transport equations. An analytic solution is obtained in eitherthe dilute or the long-time limit by using a Lagrangian approach wherestatistical averages are performed along non- reacting trajectories. In thislimit, it is shown that the moments of the number of particles have anexponential decay rather than the algebraic prediction of standard mean-fieldapproaches. The effective reaction rate is then related to Lagrangian pairstatistics by a large-deviation principle. A phenomenological model isintroduced to study the qualitative behavior of the effective rate as afunction of the interaction length, the degree of chaoticity of the dynamicsand the compressibility of the carrier flow. Exact computations, obtained via aFeynman-Kac approach, in a smooth, compressible, randomdelta-correlated-in-time Gaussian velocity field support the proposed heuristicapproach.

Effective rates in dilute reaction-advection systems for the annihilation process $A + A \to \varnothing$