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Accuracy aspects of the reaction-diffusion master equation on unstructured meshes
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing.
2011 (English)Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

The reaction-diffusion master equation (RDME) is a stochastic model for spatially heterogeneous chemical systems. Stochastic models have proved to be useful for problems from molecular biology since copy numbers of participating chemical species often are small, which gives a stochastic behaviour. The RDME is a discrete space model, in contrast to spatially continuous models based on Brownian motion. In this thesis two accuracy issues of the RDME on unstructured meshes are studied. The first concerns the rates of diffusion events. Errors due to previously used rates are evaluated, and a second order accurate finite volume method, not previously used in this context, is implemented. The new discretisation improves the accuracy considerably, but unfortunately it puts constraints on the mesh, limiting its current usability. The second issue concerns the rates of bimolecular reactions. Using the macroscopic reaction coefficients these rates become too low when the spatial resolution is high. Recently, two methods to overcome this problem by calculating mesoscopic reaction rates for Cartesian meshes have been proposed. The methods are compared and evaluated, and are found to work remarkably well. Their possible extension to unstructured meshes is discussed.

Place, publisher, year, edition, pages
2011.
Series
UPTEC F, ISSN 1401-5757 ; 11014
Keywords [en]
master equation, Gillespie algorithm, unstructured mesh, diffusion, maximum principle
National Category
Natural Sciences
Identifiers
URN: urn:nbn:se:uu:diva-145978OAI: oai:DiVA.org:uu-145978DiVA, id: diva2:397279
Educational program
Master Programme in Engineering Physics
Uppsok
Technology
Supervisors
Examiners
Available from: 2011-02-14 Created: 2011-02-14 Last updated: 2014-01-10Bibliographically approved

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CiteExportLink to record
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