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Efficient sampling in event-driven algorithms for reaction-diffusion processes
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för beräkningsvetenskap. Uppsala universitet, Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Numerisk analys.
2013 (engelsk)Inngår i: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 13, s. 958-984Artikkel i tidsskrift (Fagfellevurdert) Published
sted, utgiver, år, opplag, sider
2013. Vol. 13, s. 958-984
HSV kategori
Identifikatorer
URN: urn:nbn:se:uu:diva-181793DOI: 10.4208/cicp.271011.230312aISI: 000322065200002OAI: oai:DiVA.org:uu-181793DiVA, id: diva2:557752
Prosjekter
eSSENCETilgjengelig fra: 2012-09-21 Laget: 2012-09-28 Sist oppdatert: 2017-12-07bibliografisk kontrollert
Inngår i avhandling
1. Stochastic Simulation of Reaction-Diffusion Processes
Åpne denne publikasjonen i ny fane eller vindu >>Stochastic Simulation of Reaction-Diffusion Processes
2013 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

Numerical simulation methods have become an important tool in the study of chemical reaction networks in living cells. Many systems can, with high accuracy, be modeled by deterministic ordinary differential equations, but other systems require a more detailed level of modeling. Stochastic models at either the mesoscopic level or the microscopic level can be used for cases when molecules are present in low copy numbers.

In this thesis we develop efficient and flexible algorithms for simulating systems at the microscopic level. We propose an improvement to the Green's function reaction dynamics algorithm, an efficient microscale method. Furthermore, we describe how to simulate interactions with complex internal structures such as membranes and dynamic fibers.

The mesoscopic level is related to the microscopic level through the reaction rates at the respective scale. We derive that relation in both two dimensions and three dimensions and show that the mesoscopic model breaks down if the discretization of space becomes too fine. For a simple model problem we can show exactly when this breakdown occurs.

We show how to couple the microscopic scale with the mesoscopic scale in a hybrid method. Using the fact that some systems only display microscale behaviour in parts of the system, we can gain computational time by restricting the fine-grained microscopic simulations to only a part of the system.

Finally, we have developed a mesoscopic method that couples simulations in three dimensions with simulations on general embedded lines. The accuracy of the method has been verified by comparing the results with purely microscopic simulations as well as with theoretical predictions.

sted, utgiver, år, opplag, sider
Uppsala: Acta Universitatis Upsaliensis, 2013. s. 46
Serie
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1042
Emneord
stochastic simulation, microscale, mesoscale, Smoluchowski's equation, hybrid methods
HSV kategori
Forskningsprogram
Beräkningsvetenskap med inriktning mot numerisk analys
Identifikatorer
urn:nbn:se:uu:diva-198522 (URN)978-91-554-8667-9 (ISBN)
Disputas
2013-06-05, Room 2446, Polacksbacken, Lägerhyddsvägen 2D, Uppsala, 10:15 (engelsk)
Opponent
Veileder
Prosjekter
eSSENCE
Tilgjengelig fra: 2013-05-14 Laget: 2013-04-18 Sist oppdatert: 2013-08-30bibliografisk kontrollert

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