稀释反应-平流系统中湮灭过程$A + A \to \varnothing$的有效速率
Effective rates in dilute reaction-advection systems for the annihilation process $A + A \to \varnothing$
摘要：
考虑了由流体流动输送的反应颗粒的稀体系。当粒子在有限的相互作用半径内时，它们以给定的速率作为$A + A \to \varnothing$反应。该系统中描述的联合n点的数量的空间密度，它是服从一个层次的传输方程。通过使用拉格朗日方法，其中沿非反应轨迹执行统计平均，在稀或长时间限制中获得解析解。在这个限制，它表明，粒子数的时刻有一个指数衰减，而不是代数预测的标准平均场方法。有效的反应速率，然后相关的拉格朗日对统计的大偏差原则。引入一个唯象模型来研究有效速率作为相互作用长度、动力学的混沌程度和载流子流的可压缩性的函数的定性行为。精确的计算，通过费曼-卡茨的方法，在一个光滑的，可压缩的，随机增量相关的时间高斯速度场支持所提出的启发式方法。
英文摘要：
A dilute system of reacting particles transported by fluid flows is considered. The particles react as $A + A \to \varnothing$ 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 either the dilute or 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
