uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Numerical Solution Methods in Stochastic Chemical Kinetics
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis , 2008. , 68 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 564
Keyword [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: diva2:172728
Public defence
2008-11-28, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2008-11-07 Created: 2008-11-07 Last updated: 2011-10-26Bibliographically approved
List of papers
1. Computing the moments of high dimensional solutions of the master equation
Open this publication in new window or tab >>Computing the moments of high dimensional solutions of the master equation
2006 (English)In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 180, 498-515 p.Article in journal (Refereed) Published
National Category
Computational Mathematics
Identifiers
urn:nbn:se:uu:diva-84013 (URN)10.1016/j.amc.2005.12.032 (DOI)000242276500008 ()
Available from: 2006-11-11 Created: 2006-11-11 Last updated: 2011-11-29Bibliographically approved
2. Spectral approximation of solutions to the chemical master equation
Open this publication in new window or tab >>Spectral approximation of solutions to the chemical master equation
2009 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, Vol. 229, 208-221 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Science
Identifiers
urn:nbn:se:uu:diva-97687 (URN)10.1016/j.cam.2008.10.029 (DOI)000266511500022 ()
Available from: 2008-11-07 Created: 2008-11-07 Last updated: 2011-11-30Bibliographically approved
3. Galerkin spectral method applied to the chemical master equation
Open this publication in new window or tab >>Galerkin spectral method applied to the chemical master equation
2009 (English)In: Communications in Computational Physics, ISSN 1815-2406, Vol. 5, 871-896 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Science
Identifiers
urn:nbn:se:uu:diva-97688 (URN)000265386400002 ()
Available from: 2008-09-29 Created: 2008-11-07 Last updated: 2012-11-26Bibliographically approved
4. Simulation of stochastic reaction-diffusion processes on unstructured meshes
Open this publication in new window or tab >>Simulation of stochastic reaction-diffusion processes on unstructured meshes
2009 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 31, 1774-1797 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Science
Identifiers
urn:nbn:se:uu:diva-97689 (URN)10.1137/080721388 (DOI)000267746200008 ()
Available from: 2008-11-07 Created: 2008-11-07 Last updated: 2011-11-30Bibliographically approved
5. Parallel in time simulation of multiscale stochastic chemical kinetics
Open this publication in new window or tab >>Parallel in time simulation of multiscale stochastic chemical kinetics
2009 (English)In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 8, 46-68 p.Article in journal (Refereed) Published
National Category
Computational Mathematics Computer Science
Identifiers
urn:nbn:se:uu:diva-97690 (URN)10.1137/080733723 (DOI)000271722900003 ()
Available from: 2008-11-07 Created: 2008-11-07 Last updated: 2011-11-30Bibliographically approved

Open Access in DiVA

fulltext(2001 kB)1223 downloads
File information
File name FULLTEXT01.pdfFile size 2001 kBChecksum SHA-1
6818e85f299903080f3d0f8829e64aec9d1034441dfe53dd662002609dcb022a0a475b93
Type fulltextMimetype application/pdf
Buy this publication >>

Search in DiVA

By author/editor
Engblom, Stefan
By organisation
Division of Scientific ComputingNumerical Analysis
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 1223 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 2270 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf