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  <doc>
    <id>406</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>habilitation</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1999-06-14</completedDate>
    <publishedDate>1999-06-14</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Conformational Dynamics: Modelling, Theory, Algorithm, and Application to Biomolecules</title>
    <abstract language="eng">The function of many important biomolecules comes from their dynamic properties and their ability to switch between different {\em conformations}. In a conformation, the large scale geometric structure of the molecule is understood to be conserved, whereas on smaller scales the system may well rotate, oscillate or fluctuate. In a recent article [J. Comp. Phys., 151,1 (1999)], the present author and coworkers demonstrated that (a) conformations can be understood as almost invariant sets of some Markov chain being defined via the Hamiltonian system governing the molecular dynamics and that (b) these sets can efficiently be computed via eigenvectors of the corresponding Markov operator. The persent manuscript reviews the mathematical modelling steps behind the novel concept, includes a rigorous analytical justification of this approach and especially of the numerical details of the algorithm, and illustrates its performance when applied to realistic molecular systems.</abstract>
    <identifier type="serial">SC-99-18</identifier>
    <identifier type="opus3-id">407</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-4063</identifier>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-99-18</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>biochemical conformation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>almost invariant set</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov chain</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Hamiltonian system</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov operator</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>quasi-compact operator</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Perron root</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Perron-</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="34E10">Perturbations, asymptotics</collection>
    <collection role="msc" number="46B09">Probabilistic methods in Banach space theory [See also 60Bxx]</collection>
    <collection role="msc" number="60J27">Continuous-time Markov processes on discrete state spaces</collection>
    <collection role="msc" number="65C05">Monte Carlo methods</collection>
    <collection role="msc" number="82C05">Classical dynamic and nonequilibrium statistical mechanics (general)</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="collections" number="">Habilitationen</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/406/SC-99-18.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/406/SC-99-18.pdf</file>
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