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    <id>7223</id>
    <completedYear/>
    <publishedYear>2019</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>012101</pageFirst>
    <pageLast>012101</pageLast>
    <pageNumber>11</pageNumber>
    <edition/>
    <issue/>
    <volume>29</volume>
    <type>article</type>
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    <title language="eng">From metastable to coherent sets - Time-discretization schemes</title>
    <abstract language="eng">In this article, we show that these well-established spectral algorithms (like PCCA+, Perron Cluster Cluster Analysis) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-time-discretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.</abstract>
    <parentTitle language="eng">Chaos: An Interdisciplinary Journal of Nonlinear Science</parentTitle>
    <identifier type="doi">10.1063/1.5058128</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2019-01-28</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-66074</enrichment>
    <author>Konstantin Fackeldey</author>
    <submitter>Marcus Weber</submitter>
    <author>Peter Koltai</author>
    <author>Peter Nevir</author>
    <author>Henning Rust</author>
    <author>Axel Schild</author>
    <author>Marcus Weber</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
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  <doc>
    <id>6607</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
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    <publishedDate>2017-12-08</publishedDate>
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    <title language="eng">From Metastable to Coherent Sets - time-discretization schemes</title>
    <abstract language="eng">Given a time-dependent stochastic process with trajectories x(t) in a space $\Omega$, there may be sets such that the corresponding trajectories only very rarely cross the boundaries of these sets. We can analyze such a process in terms of metastability or coherence. Metastable sets M are defined in space $M\subset\Omega$, coherent sets $M(t)\subset\Omega$ are defined in space and time. Hence, if we extend the space by the time-variable t, coherent sets are metastable sets in  $\Omega\times[0,\infty]$. This relation can be exploited, because there already exist spectral algorithms for the identification of metastable sets. In this article we show that these well-established spectral algorithms (like PCCA+) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-timediscretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-66074</identifier>
    <author>Konstantin Fackeldey</author>
    <submitter>Paulina Bressel</submitter>
    <author>Péter Koltai</author>
    <author>Peter Névir</author>
    <author>Henning Rust</author>
    <author>Axel Schild</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-74</number>
    </series>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="projects" number="SFB1114-A5">SFB1114-A5</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6607/ZIB-Report_17-74.pdf</file>
  </doc>
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