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  <doc>
    <id>687</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2002-04-11</completedDate>
    <publishedDate>2002-04-11</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">From Molecular Dynamics to Conformational Dynamics in Drug Design</title>
    <abstract language="eng">Computational drug design studies molecular recognition in the {\em virtual lab}. The arising Hamiltonian dynamics is known to be chaotic and ill-conditioned already after picoseconds, whereas times are $msec$ up to $min$. Classical molecular dynamics with long term trajectory computation gives, at best, information about time and statistical ensemble averages. The present paper surveys a recent new modeling approach called {\em conformational dynamics}, which is due to the author and Ch. Schütte. This approach achieves information about the dy time scales by telescoping a short term deterministic model with a statistical model. Examples of small biomolecules are included.</abstract>
    <identifier type="serial">02-20</identifier>
    <identifier type="opus3-id">688</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-6878</identifier>
    <enrichment key="SourceTitle">Appeared in: M. Kirkilionis, S. Krömker, R. Rannacher, F. Toni (eds.) Trends in Nonlinear Analysis. Springer 2003, pp. 269-288</enrichment>
    <author>Peter Deuflhard</author>
    <series>
      <title>ZIB-Report</title>
      <number>02-20</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>molecular dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>conformational dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>drug design</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Hamiltonian dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>almost invariant sets</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transition operator</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov chain</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Perro</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="62P10">Applications to biology and medical sciences</collection>
    <collection role="msc" number="65C05">Monte Carlo methods</collection>
    <collection role="msc" number="65F15">Eigenvalues, eigenvectors</collection>
    <collection role="msc" number="65L05">Initial value problems</collection>
    <collection role="msc" number="65L08">Improperly posed problems</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/687/ZR-02-20.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/687/ZR-02-20.pdf</file>
  </doc>
  <doc>
    <id>424</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1999-10-18</completedDate>
    <publishedDate>1999-10-18</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Transfer Operator Approach to Conformational Dynamics in Biomolecular Systems</title>
    <abstract language="eng">The article surveys the development of novel mathematical concepts and algorithmic approaches based thereon in view of their possible applicability to biomolecular design. Both a first deterministic approach, based on the Frobenius-Perron operator corresponding to the flow of the Hamiltonian dynamics, and later stochastic approaches, based on a spatial Markov operator or on Langevin dynamics, can be subsumed under the unified mathematical roof of the transfer operator approach to effective dynamics of molecular systems. The key idea of constructing specific transfer operators especially taylored for the purpose of conformational dynamics appears as the red line throughout the paper. Different steps of the algorithm are exemplified by a trinucleotide molecular system as a small representative of possible RNA drug molecules.</abstract>
    <identifier type="serial">SC-99-36</identifier>
    <identifier type="opus3-id">425</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-4247</identifier>
    <enrichment key="SourceTitle">Appeared in: Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems. B. Fiedler (ed.) Springer 2001, pp. 191-223</enrichment>
    <author>Christof Schütte</author>
    <author>Wilhelm Huisinga</author>
    <author>Peter Deuflhard</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-99-36</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Transfer operator</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov process</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov chain</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>molecular dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>biomolecular conformations</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>canonical ensemble</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transition prohability</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Ha</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="47B15">Hermitian and normal operators (spectral measures, functional calculus, etc.)</collection>
    <collection role="msc" number="60J25">Continuous-time Markov processes on general state spaces</collection>
    <collection role="msc" number="60J60">Diffusion processes [See also 58J65]</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="deuflhard">Deuflhard, Peter</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/424/SC-99-36.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/424/SC-99-36.pdf</file>
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