# Kinetics of the $A+B \\to 0$ reaction with mass-dependent fragmentation

Source: [Kinetics of the $A+B \\to 0$ reaction with mass-dependent fragmentation](<https://www.sota2.com/research/paper/68fa20ac7a2b558e293328d8>)

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

Data updated: 2025-10-23T22:44:39.259Z

Authors: Sungchul Kwon, Yup Kim

Published: 2006-12-18T08:19:37.000Z

## Abstract

We investigate the kinetics of uniformly driven $A+B \\to 0$ reaction with mass-dependent fragmentation in one dimension. In this model, the fragmented mass $m$ of a site with mass $n\_i$ is given as $m=n^{\\lambda}\_i$, and it is driven to the one direction. When opposite species masses occupy the same site, mass reaction takes place instantaneously. Since the fragmented mass $m$ of $\\lambda\<1$ is less than mass $n\_i$ of a site, the exponent $\\lambda$ controls the attractive interaction between particles at the same site. The $\\lambda=0$ case corresponds to hard-core (HC) particle system. With equal initial densities of both species, we numerically confirm that the scaling behaviors of density and lengths except the domain length $\\ell$ are the same as that of the uniformly driven HC particle system. The scaling behavior of $\\ell$ is $\\ell \\sim t^{2/3}$. The kinetics of the reaction is independent of $\\lambda$ as long as $\\lambda\<1$. The $\\lambda$-independent kinetics results from the $\\lambda$-independent collective motions of single species domains.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0612443>)

[PDF](<https://arxiv.org/pdf/cond-mat/0612443.pdf>)