# Kinetic Regimes and Cross-Over Times in Many-Particle Reacting Systems

Source: [Kinetic Regimes and Cross-Over Times in Many-Particle Reacting Systems](<https://www.sota2.com/research/paper/68fa248e2c2a3760193a5c1f>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T09:18:10.151Z

Authors: Ben O'Shaughnessy, Dimitrios Vavylonis (2) \_\_INSTITUTION\_2\_\_ Dept. Chemical Engineering, Columbia University, (2) Dept. Physics, Columbia University)

Published: 1998-05-27T23:36:33.000Z

## Abstract

We study kinetics of single species reactions ("A+A -\> 0") for general local reactivity Q and dynamical exponent z (rms displacement x\_t ~ t^{1/z}.) For small molecules z=2, whilst z=4,8 for certain polymer systems. For dimensions d above the critical value d\_c=z, kinetics are always mean field (MF). Below d\_c, the density n\_t initially follows MF decay, n\_0 - n\_t ~ n\_0^2 Q t. A 2-body diffusion-controlled regime follows for strongly reactive systems (Q\>Qstar ~ n\_0^{(z-d)/d}) with n\_0 - n\_t ~ n\_0^2 x\_t^d. For Q\<Qstar, MF kinetics persist, with n\_t ~ 1/Qt. In all cases n\_t ~ 1/x\_t^d at the longest times. Our analysis avoids decoupling approximations by instead postulating weak physically motivated bounds on correlation functions.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9805356>)

[PDF](<https://arxiv.org/pdf/cond-mat/9805356.pdf>)