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On the stochastic modelling of surface reactions through reflected chemical Langevin equations

Pineda, M; Stamatakis, M; (2018) On the stochastic modelling of surface reactions through reflected chemical Langevin equations. Computers & Chemical Engineering , 117 pp. 145-158. 10.1016/j.compchemeng.2018.05.003. Green open access

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Abstract

Modelling of small-scale heterogeneous catalytic systems with master equations captures the impact of molecular noise, but can be computationally expensive. On the other hand, the chemical Fokker-Planck approximation offers an excellent alternative from an efficiency perspective. The Langevin equation can generate stochastic realisations of the Fokker-Planck equation; yet, these realisations may violate the conditions 0 <= θ <= 1 (where θ is surface coverage). In this work, we adopt Skorokhod’s formulations to impose reflective boundaries that remedy this issue. We demonstrate the approach on a simple system involving a single species and describing adsorption, desorption, reaction and diffusion processes on a lattice. We compare different numerical schemes for the solution of the resulting reflected Langevin equation and calculate rates of convergence. Our benchmarks should guide the choice of appropriate numerical methods for the accurate and efficient simulation of chemical systems in the catalysis field.

Type: Article
Title: On the stochastic modelling of surface reactions through reflected chemical Langevin equations
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.compchemeng.2018.05.003
Publisher version: https://doi.org/10.1016/j.compchemeng.2018.05.003
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Molecular noise, Chemical master equation, Fokker–Planck equation, Langevin equation, Reflective boundary, Gillespie algorithm
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Chemical Engineering
URI: https://discovery.ucl.ac.uk/id/eprint/10048047
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