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Exploring the impact of a moving sink in a reaction–diffusion system: exact dynamics for two simple potentials

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Abstract

This paper presents a novel method for solving diffusion–reaction systems exactly in the time domain for linear and flat potential energies with a moving sink. Such systems are commonly modelled by the Smoluchowski equation with a sink term, which is a function of space and time and responsible for reaction phenomena. Obtaining a time-domain solution for such equations analytically is challenging and typically limited to specific cases, necessitating the use of Laplace domain or numerical methods. Our proposed method employs a simple transformation, allowing the solution for a particular potential energy to be derived from known solutions of another potential. Importantly, our approach can be applied to both static and dynamic sinks, including moving linear or nonlinear time-dependent sinks. Overall, this new methodology provides a powerful tool for analysing and understanding reaction–diffusion systems in various contexts.

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Acknowledgements

One of the authors (CS) would like to thank the institute for providing a Half-Time Research Assistantship fellowship.

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Authors and Affiliations

  1. School of Chemical Sciences, Indian Institute of Technology Mandi, Kamand,  175 005, India

    Chinmoy Samanta & Aniruddha Chakraborty

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  1. Chinmoy Samanta
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  2. Aniruddha Chakraborty
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Correspondence to Chinmoy Samanta.

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Samanta, C., Chakraborty, A. Exploring the impact of a moving sink in a reaction–diffusion system: exact dynamics for two simple potentials. Pramana - J Phys 97, 204 (2023). https://doi.org/10.1007/s12043-023-02684-0

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  • DOI: https://doi.org/10.1007/s12043-023-02684-0

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