uu.seUppsala University Publications

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Numerical Solution Methods in Stochastic Chemical KineticsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2008 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala: Acta Universitatis Upsaliensis , 2008. , p. 68
##### Series

Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 564
##### Keywords [en]

stochastic models, chemical master equation, mesoscopic kinetics, Markov property, jump process, moment closure problem, spectral-Galerkin method, high dimensional problem, hybrid methods, time-parallel, homogenization
##### National Category

Computational Mathematics
##### Research subject

Scientific Computing with specialization in Numerical Analysis
##### Identifiers

URN: urn:nbn:se:uu:diva-9342ISBN: 978-91-554-7322-8 (print)OAI: oai:DiVA.org:uu-9342DiVA, id: diva2:172728
##### Public defence

2008-11-28, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 13:15 (English)
##### Opponent

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##### Supervisors

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt485",{id:"formSmash:j_idt485",widgetVar:"widget_formSmash_j_idt485",multiple:true}); Available from: 2008-11-07 Created: 2008-11-07 Last updated: 2011-10-26Bibliographically approved
##### List of papers

This study is concerned with the numerical solution of certain stochastic models of chemical reactions. Such descriptions have been shown to be useful tools when studying biochemical processes inside living cells where classical deterministic rate equations fail to reproduce actual behavior. The main contribution of this thesis lies in its theoretical and practical investigation of different methods for obtaining numerical solutions to such descriptions.

In a preliminary study, a simple but often quite effective approach to the moment closure problem is examined. A more advanced program is then developed for obtaining a consistent representation of the high dimensional probability density of the solution. The proposed method gains efficiency by utilizing a rapidly converging representation of certain functions defined over the semi-infinite integer lattice.

Another contribution of this study, where the focus instead is on the spatially distributed case, is a suggestion for how to obtain a consistent stochastic reaction-diffusion model over an unstructured grid. Here it is also shown how to efficiently collect samples from the resulting model by making use of a hybrid method.

In a final study, a time-parallel stochastic simulation algorithm is suggested and analyzed. Efficiency is here achieved by moving parts of the solution phase into the deterministic regime given that a parallel architecture is available.

Necessary background material is developed in three chapters in this summary. An introductory chapter on an accessible level motivates the purpose of considering stochastic models in applied physics. In a second chapter the actual stochastic models considered are developed in a multi-faceted way. Finally, the current state-of-the-art in numerical solution methods is summarized and commented upon.

1. Computing the moments of high dimensional solutions of the master equation$(function(){PrimeFaces.cw("OverlayPanel","overlay111921",{id:"formSmash:j_idt539:0:j_idt543",widgetVar:"overlay111921",target:"formSmash:j_idt539:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Spectral approximation of solutions to the chemical master equation$(function(){PrimeFaces.cw("OverlayPanel","overlay172724",{id:"formSmash:j_idt539:1:j_idt543",widgetVar:"overlay172724",target:"formSmash:j_idt539:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. Galerkin spectral method applied to the chemical master equation$(function(){PrimeFaces.cw("OverlayPanel","overlay172725",{id:"formSmash:j_idt539:2:j_idt543",widgetVar:"overlay172725",target:"formSmash:j_idt539:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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5. Parallel in time simulation of multiscale stochastic chemical kinetics$(function(){PrimeFaces.cw("OverlayPanel","overlay172727",{id:"formSmash:j_idt539:4:j_idt543",widgetVar:"overlay172727",target:"formSmash:j_idt539:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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