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  <doc>
    <id>6486</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>2017-09-08</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A multi scale perturbation expansion approach for Markov state modeling of non-stationary molecular dynamics</title>
    <abstract language="eng">We investigate metastable dynamical systems subject to non-stationary forcing as they appear in molecular dynamics for systems driven by external fields. We show, that if the strength of the forcing is inversely proportional to the length of the slow metastable time scales of the unforced system, then the effective behavior of the forced system on slow time scales can be described by a low-dimensional reduced master equation. Our construction is explicit and uses the multiscale perturbation expansion method called two-timing, or method of multiple scales. The reduced master equation—a Markov state model—can be assembled by constructing two equilibrium Markov state models; one for the unforced system, and one for a slightly perturbed one.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-64868</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2018-08-15</enrichment>
    <enrichment key="SubmissionStatus">accepted for publication</enrichment>
    <author>Péter Koltai</author>
    <submitter>Paulina Bressel</submitter>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-49</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov state model</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>non-equilibrium molecular dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>two timescale master equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>non-stationary forcing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>metastability</value>
    </subject>
    <collection role="msc" number="34E13">Multiple scale methods</collection>
    <collection role="msc" number="60J20">Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]</collection>
    <collection role="msc" number="60J60">Diffusion processes [See also 58J65]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="projects" number="no-project">no-project</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6486/ZIB-Report_17-49.pdf</file>
  </doc>
</export-example>
