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  <doc>
    <id>6099</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-11-18</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The spatiotemporal master equation: approximation of reaction-diffusion dynamics via Markov state modeling</title>
    <abstract language="eng">Accurate modeling and numerical simulation of reaction kinetics is a topic of steady interest. We consider the spatiotemporal chemical master equation (ST-CME) as a model for stochastic reaction-diffusion systems that exhibit properties of metastability. The space of motion is decomposed into metastable compartments and diffusive motion is approximated by jumps between these compartments. Treating these jumps as first-order reactions, simulation of the resulting stochastic system is possible by the Gillespie method. We present the theory of Markov state models (MSM) as a theoretical foundation of this intuitive approach. By means of Markov state modeling, both the number and shape of compartments  and the transition rates between them can be determined. We consider the ST-CME for two reaction-diffusion systems and compare it to more detailed models. Moreover, a rigorous formal justification of the ST-CME by  Galerkin projection methods is presented.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-60999</identifier>
    <enrichment key="SourceTitle">AIP - Journal of Chemical Physics 145 (2016)</enrichment>
    <author>Stefanie Winkelmann</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-60</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>reaction-diffusion</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stochastic chemical kinetics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>chemical master equation</value>
    </subject>
    <collection role="ccs" number="">Stochastic processes (NEW)</collection>
    <collection role="msc" number="60J27">Continuous-time Markov processes on discrete state spaces</collection>
    <collection role="msc" number="82C22">Interacting particle systems [See also 60K35]</collection>
    <collection role="msc" number="82C31">Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="SFB1114-C3">SFB1114-C3</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6099/ZIB-report_SpatiotemporalCME.pdf</file>
  </doc>
</export-example>
