# Domain Growth in the Active Model B: Critical and Off-critical Composition

Source: [Domain Growth in the Active Model B: Critical and Off-critical Composition](<https://www.sota2.com/research/paper/68fa3f3c1e209131ce8ebe0f>)

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

Data updated: 2025-10-25T02:17:25.818Z

Authors: Sudipta Pattanayak, Shradha Mishra, Sanjay Puri

Published: 2021-05-27T13:46:49.000Z

## Abstract

We study the ordering kinetics of an assembly of {\\it active Brownian particles} (ABPs) on a two-dimensional substrate. We use a coarse-grained equation for the composition order parameter $\\psi ({\\bf r},t)$, where ${\\bf r}$ and $t$ denote space and time, respectively. The model is similar to the {\\it Cahn-Hilliard equation} or {\\it Model B} (MB) for a conserved order parameter with an additional activity term of strength $\\lambda$. This model has been introduced by Wittkowski et al., Nature Comm. {\\bf 5}, 4351 (2014), and is termed {\\it Active Model B} (AMB). We study domain growth kinetics and dynamical scaling of the correlation function for the AMB with critical and off-critical compositions. The quantity $P = \\mbox{sign}(\\lambda \\times \\psi\_0)$ governs the asymptotic growth kinetics for the off-critical AMB, where $\\psi\_0$ denotes the average order parameter. For negative $P$, the domain growth law is the usual Lifshitz-Slyozov growth law with $L(t,\\lambda) \\sim t^{1/3}$. For positive $P$, the growth law shows a crossover to a novel growth law $L(t,\\lambda) \\sim t^{1/4}$. Further, the correlation function shows good dynamical scaling for the off-critical AMB but the scaling function has a dependency on $\\psi\_0$ and $\\lambda$. We also study the effects of both additive and multiplicative noise on the AMB.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2105.13143>)

[PDF](<https://arxiv.org/pdf/2105.13143.pdf>)