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  <doc>
    <id>1034</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-11-15</completedDate>
    <publishedDate>2007-11-15</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimality Conditions for Convex State Constrained Optimal Control Problems with Discontinuous States</title>
    <abstract language="eng">We discuss first order optimality conditions for state constrained optimal control problems. Our concern is the treatment of problems, where the solution of the state equation is not known to be continuous, as in the case of boundary control in three space dimensions or optimal control with parabolic partial differential equations. We show existence of measure valued Lagrangian multipliers, which have just enough additional regularity to be applicable to all possibly discontinuous solutions of the state equation.</abstract>
    <identifier type="serial">07-35</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1063</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10342</identifier>
    <author>Anton Schiela</author>
    <submitter>unknown unknown</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>07-35</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>state constraints</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimality conditions</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="49K20">Problems involving partial differential equations</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1034/fopaper.pdf</file>
  </doc>
  <doc>
    <id>1053</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-01-14</completedDate>
    <publishedDate>2008-01-14</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A priori Tabulation of Turbulent Flame Speeds via a Combination of a Stochastic Mixing Model and Flamelet Generated Manifolds</title>
    <abstract language="eng">In this paper we propose a technique for a priori turbulent flame speed tabulation (TFST) for a given parameter space in standard combustion-regime diagrams. It can be used as a subgrid-scale (SGS) model in Large Eddy Simulation (LES). In a first step, stationary laminar flamelets are computed and stored over the progress variable following the ideas of flamelet generated manifolds (FGM). In a second step, the incompressible one-dimensional Navier-Stokes equations supplemented by the equation for the progress variable are solved on a grid that resolves all turbulent scales. Additionally, turbulent transport is implemented via the linear eddy model (LEM). The turbulent flame structures are solved until a statistically stationary mean value of the turbulent flame speed has been reached. The results are stored in a table that could be used by large scale premixed combustion models, e.g. front tracking schemes. Results are compared to an algebraic model and to direct numerical simulations (DNS).</abstract>
    <identifier type="serial">08-02</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1082</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10532</identifier>
    <author>Heiko Schmidt</author>
    <submitter>unknown unknown</submitter>
    <author>Michael Oevermann</author>
    <author>Rob J.M. Bastiaans</author>
    <author>Alan R. Kerstein</author>
    <series>
      <title>ZIB-Report</title>
      <number>08-02</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Verbrennung</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Flammenstrukturen</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>stochastisches Turbulenzmodell</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>FGM</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>turbulente Brenngeschwindigkeiten</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>turbulent premixed combustion</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>flame structures</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>linear eddy model</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>flamelet generated manifolds</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>turbulent flame speeds</value>
    </subject>
    <collection role="ddc" number="620">Ingenieurwissenschaften und zugeordnete Tätigkeiten</collection>
    <collection role="ccs" number="J.2">PHYSICAL SCIENCES AND ENGINEERING</collection>
    <collection role="pacs" number="02.50.Ey">Stochastic processes</collection>
    <collection role="pacs" number="47.70.Pq">Flames; combustion</collection>
    <collection role="msc" number="65L80">Methods for differential-algebraic equations</collection>
    <collection role="msc" number="65M06">Finite difference methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1053/HSchmidt_ZR_01_2008.pdf</file>
  </doc>
  <doc>
    <id>1054</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-01-14</completedDate>
    <publishedDate>2008-01-14</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Asymptotic Scale Analysis of Precipitating Clouds</title>
    <abstract language="eng">Asymptotic analyses of the three dimensional compressible flow equations coupled with transport equations for the mixing ratios of water vapour, cloud water and rain water are described. We obtain reduced systems of equations for two particular regimes of length and time scales: Models for the long time evolution of deep convective columns and for the short time evolution of shallow convective layers. The asymptotic deep convective column model is anelastic, yet the vertical motion is pressure free, i.e., it evolves freely in interaction with buoyancy while the horizontal divergence adjusts to fullfil the anelastic constraint. The perturbation pressure guaranteeing compliance with the horizontal divergence constraint obeys a Poisson-type equation. Surprisingly, the vertical velocity plays an important role in the horizontal dynamics through the Coriolis term. The vertical acceleration in a saturated column is directly determined by the buoyancy induced by potential temperature differences relative to the background stratification. This potential temperature deviation is a conserved quantity. Evaporation is the only important microphysical process in the undersaturated regime. The evaporation rate depends on the saturation deficit and the amount of rain water present and determines the (downward) vertical velocity and the distribution of water vapour. To connect the deep convective column solutions to top and bottom boundary conditions, a different flow regime needs to be accounted for. Within shallow layers whose depth is comparable to the column diameters, adjustment to physical boundary conditions can take place. This is the second regime considered in this report. The shallow convective layer regime is shown to be asymptotically described by Boussinesq-type equations. These equations are closed by evolution equations which show that, in the saturated regime, the distributions of potential temperature and cloud water are determined by a condensation rate that is directly proportional to the vertical velocity. In the undersaturated regime, the potential temperature distribution is determined by the amount of rain present, since the water vapour in this case is shown to be a conserved quantity. In both regimes the distribution of rain water depends on the rain water flux.</abstract>
    <identifier type="serial">08-03</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1083</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10548</identifier>
    <author>Gunter Carqué</author>
    <submitter>unknown unknown</submitter>
    <author>Antony Z. Owinoh</author>
    <author>Rupert Klein</author>
    <author>Andrew J. Majda</author>
    <series>
      <title>ZIB-Report</title>
      <number>08-03</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>atmospheric moist convection</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>deep convection</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>shallow convection</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>precipitating clouds</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>asymptotic analysis</value>
    </subject>
    <collection role="ddc" number="550">Geowissenschaften</collection>
    <collection role="pacs" number="92.60.-e">Properties and dynamics of the atmosphere; meteorology (see also 92.40.Zg Hydrometeorology, hydroclimatology)</collection>
    <collection role="pacs" number="92.60.Nv">Cloud physics and chemistry</collection>
    <collection role="msc" number="76M45">Asymptotic methods, singular perturbations</collection>
    <collection role="msc" number="76U05">Rotating fluids</collection>
    <collection role="msc" number="86A10">Meteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1054/ZIB_report_submission.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1054/ZIB_report_submission.ps</file>
  </doc>
  <doc>
    <id>1056</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-01-29</completedDate>
    <publishedDate>2008-01-29</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Linear-Eddy Modeling of Autoignition under Thermal Stratification</title>
    <abstract language="eng">The influence of thermal stratification on autoignition at constant volume and high pressure is investigated under turbulent conditions using the one-dimensional Linear-Eddy Model (LEM) and detailed hydrogen/air chemistry. Results are presented for the influence of initial temperature inhomogeneities on the heat release rate and the relative importance of diffusion and chemical reactions. The predicted heat release rates are compared with heat release rates of Chen et al. and Hawkes et al. obtained by two-dimensional Direct Numerical Simulations (DNS). Using the definition of Chen et al. for the displacement speed of the H2 mass fraction tracked at the location of maximum heat release, and a comparison of budget terms, different combustion modes including ignition front propagation and deflagration waves are identified and the results are compared to the DNS data. The LEM approach shows qualitatively and quantitatively reasonable agreement with the DNS data over the whole range of investigated temperature fluctuations. The results presented in this work suggest that LEM is a potential candidate as a sub-model for CFD calculations of HCCI engines.</abstract>
    <identifier type="serial">08-05</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1085</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10562</identifier>
    <author>Michael Oevermann</author>
    <submitter>unknown unknown</submitter>
    <author>Heiko Schmidt</author>
    <author>Alan R. Kerstein</author>
    <series>
      <title>ZIB-Report</title>
      <number>08-05</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>HCCI</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Selbstzündung</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Turbulenz</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Linear-Eddy Modell</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>HCCI</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>autoignition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>thermal explosion</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>turbulence</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Linear-Eddy Model</value>
    </subject>
    <collection role="ddc" number="620">Ingenieurwissenschaften und zugeordnete Tätigkeiten</collection>
    <collection role="msc" number="76F25">Turbulent transport, mixing</collection>
    <collection role="msc" number="80A25">Combustion</collection>
    <collection role="msc" number="80A32">Chemically reacting flows [see also 92C45, 92E20]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1056/ZR_08_05.pdf</file>
  </doc>
  <doc>
    <id>1059</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2008-02-12</completedDate>
    <publishedDate>2008-02-12</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Extended Mathematical Framework for Barrier Methods in Function Space</title>
    <abstract language="eng">An extended mathematical framework for barrier methods for state constrained optimal control compared to [Schiela, ZIB-Report 07-07] is considered. This allows to apply the results derived there to more general classes of optimal control problems, in particular to boundary control and finite dimensional control.</abstract>
    <identifier type="serial">08-07</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1088</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-10593</identifier>
    <enrichment key="SourceTitle">Appeared in: Domain Decomposition Methods in Science and Engineering XVIII Bercovier, M.; Gander, M.J.; Kornhuber, R.; Widlund, O. (Eds.) 2009. Lecture Notes in Computational Science and Engineering 70, pp 201-208</enrichment>
    <author>Anton Schiela</author>
    <submitter>unknown unknown</submitter>
    <series>
      <title>ZIB-Report</title>
      <number>08-07</number>
    </series>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1059/ZR_08_07.pdf</file>
  </doc>
  <doc>
    <id>955</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-05-22</completedDate>
    <publishedDate>2007-05-22</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Transparent boundary conditons for time-dependent problems</title>
    <abstract language="eng">A new approach to derive transparent boundary conditions (TBCs) for wave, Schrödinger, heat and drift-diffusion equations is presented. It relies on the pole condition and distinguishes between physical reasonable and unreasonable solutions by the location of the singularities of the spatial Laplace transform of the exterior solution. To obtain a numerical algorithm, a Möbius transform is applied to map the Laplace transform onto the unit disc. In the transformed coordinate the solution is expanded into a power series. Finally, equations for the coefficients of the power series are derived. These are coupled to the equation in the interior, and yield transparent boundary conditions. Numerical results are presented in the last section, showing that the error introduced by the new approximate TBCs decays exponentially in the number of coefficients.</abstract>
    <identifier type="serial">07-12</identifier>
    <identifier type="opus3-id">955</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9558</identifier>
    <enrichment key="SourceTitle">Appeared in: SIAM J. Sci. Comput., Vol. 30 (5) , 2358-2385 (2008)</enrichment>
    <author>Daniel Ruprecht</author>
    <author>Achim Schädle</author>
    <author>Frank Schmidt</author>
    <author>Lin Zschiedrich</author>
    <series>
      <title>ZIB-Report</title>
      <number>07-12</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>transparent boundary condition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>non-reflecting boundary condition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>pole condition</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>wave equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Schrödinger equation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>drift diffusion equation</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="30E10">Approximation in the complex domain</collection>
    <collection role="msc" number="65M20">Method of lines</collection>
    <collection role="msc" number="65M60">Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="institutes" number="compnano">Computational Nano Optics</collection>
    <collection role="persons" number="zschiedrich">Zschiedrich, Lin Werner</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/955/ZR-07-12.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/955/ZR-07-12.ps</file>
  </doc>
  <doc>
    <id>960</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2007-07-23</completedDate>
    <publishedDate>2007-07-23</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics</title>
    <abstract language="eng">Wigner transformation provides a one-to-one correspondence between functions on position space (wave functions) and functions on phase space (Wigner functions). Weighted integrals of Wigner functions yield quadratic quantities of wave functions like position and momentum densities or expectation values. For molecular quantum systems, suitably modified classical transport of Wigner functions provides an asymptotic approximation of the dynamics in the high energy regime. The article addresses the computation of Wigner functions by Monte Carlo quadrature. An ad aption of the Metropolis algorithm for the approximation of signed measures with disconnected support is systematically tested in combination with a surface hopping algorithm for non-adiabatic quantum dynamics. The numerical experiments give expectation values and level populations with an error of two to three percent, which agrees with the theoretically expected accuracy.</abstract>
    <identifier type="serial">07-17</identifier>
    <identifier type="opus3-id">960</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-9604</identifier>
    <enrichment key="SourceTitle">A rev. vers. appeared in: Journal of Computational Physics 228 (2009) pp. 1947-1962. doi:10.1016/j.jcp.2008.11.016</enrichment>
    <author>Susanna Kube</author>
    <author>Caroline Lasser</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>07-17</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Metropolis Monte Carlo</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>approximation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>quadrature</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>oscillating functions</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="62D05">Sampling theory, sample surveys</collection>
    <collection role="msc" number="65D30">Numerical integration</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="institutes" number="compsys">Computational Systems Biology</collection>
    <collection role="persons" number="susanna.roeblitz">Röblitz, Susanna</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/960/ZR_07_17.pdf</file>
  </doc>
  <doc>
    <id>8267</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>2021-06-28</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics</title>
    <abstract language="eng">Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance to the calcium channels determines the release probability and thereby the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact ﬁrst- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the ﬁltered signal’s second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to eﬃciently compare diﬀerent spatial coarse graining approaches for a speciﬁc model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a ﬁltered stochastic signal.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-82674</identifier>
    <identifier type="doi">10.1016/j.mbs.2021.108760</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="SourceTitle">Mathematical Biosciences 343:108760</enrichment>
    <author>Ariane Ernst</author>
    <submitter>Ariane Ernst</submitter>
    <author>Christof Schütte</author>
    <author>Stephan Sigrist</author>
    <author>Stefanie Winkelmann</author>
    <series>
      <title>ZIB-Report</title>
      <number>21-15</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>linear reaction networks</value>
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    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cross-correlation</value>
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    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>neurotransmission</value>
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    <collection role="msc" number="60-XX">PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX)</collection>
    <collection role="msc" number="92-XX">BIOLOGY AND OTHER NATURAL SCIENCES</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
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  <doc>
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    <publishedYear/>
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    <publishedDate>2021-07-07</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design</title>
    <abstract language="eng">Initiated by mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands in normal versus diseased (inflamed) environments, we previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. Uniquely, this design recognised that GPCRs function differently under pathological versus healthy conditions. &#13;
We now present a novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels associated with parameters of inflamed tissue (pH, radicals). By means of molecular dynamics simulations, we also assessed qualitative changes of the reaction rates due to additional disulfide bridges inside the GPCR binding pocket and used these rates for stochastic simulations of the corresponding reaction jump process. &#13;
The modelling results were validated with in vitro experiments measuring calcium currents and G-protein activation. &#13;
We found markedly reduced G-protein dissociation and calcium channel inhibition induced by NFEPP at normal pH, and enhanced constitutive G-protein activation but lower probability of ligand binding with increasing radical concentrations. &#13;
These results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-82797</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <author>Sourav Ray</author>
    <submitter>Stefanie Winkelmann</submitter>
    <author>Arne Thies</author>
    <author>Vikram Sunkara</author>
    <author>Hanna Wulkow</author>
    <author>Özgür Celik</author>
    <author>Fatih Yergöz</author>
    <author>Christof Schütte</author>
    <author>Christoph Stein</author>
    <author>Marcus Weber</author>
    <author>Stefanie Winkelmann</author>
    <series>
      <title>ZIB-Report</title>
      <number>21-19</number>
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    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
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    <collection role="persons" number="sunkara">Sunkara, Vikram</collection>
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  <doc>
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    <publishedDate>2022-11-12</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles</title>
    <abstract language="eng">Our theoretical study concerns an urea-urease-based pH oscillator confined to giant lipid vesicles. Under suitable conditions, differential transport of urea and hydrogen ion across the unilamellar vesicle membrane periodically resets the pH clock that switches the system from acid to basic, resulting in self-sustained oscillations. We analyse the structure of the limit cycle, which controls the dynamics for giant vesicles and dominates the strongly stochastic oscillations in small vesicles of submicrometer size. To this end, we derive reduced models, amenable to analytic treatments, and show that the accuracy of predictions, including the period of oscillations, is highly sensitive to the choice of the reduction scheme. In particular, we suggest an accurate two-variable model and show its equivalence to a three-variable model that admits an interpretation in terms of a chemical reaction network. The accurate description of a single pH oscillator appears crucial for rationalizing experiments and understanding communication of vesicles and synchronization of rhythms.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="doi">10.12752/8817</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-88179</identifier>
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    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Arthur Straube</author>
    <submitter>Arthur Straube</submitter>
    <author>Stefanie Winkelmann</author>
    <author>Felix Höfling</author>
    <series>
      <title>ZIB-Report</title>
      <number>22-21</number>
    </series>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="vas">Distributed Algorithms and Supercomputing</collection>
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    <collection role="persons" number="winkelmann">Winkelmann, Stefanie</collection>
    <collection role="persons" number="hoefling">Höfling, Felix</collection>
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  <doc>
    <id>8676</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2022-05-11</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Understanding the Romanization Spreading on Historical Interregional Networks in Northern Tunisia</title>
    <abstract language="eng">Spreading processes are important drivers of change in social systems. To understand the mechanisms of spreading it is fundamental to have information about the underlying contact network and the dynamical parameters of the process.&#13;
	However, in many real-wold examples, this information is not known and needs to be inferred from data. State-of-the-art spreading inference methods have mostly been applied to modern social systems, as they rely on availability of very detailed data. In this paper we study the inference challenges for historical spreading processes, for which only very fragmented information is available. To cope with this problem, we extend existing network models by formulating a model on a mesoscale with temporal spreading rate. Furthermore, we formulate the respective parameter inference problem for the extended model. We apply our approach to the romanization process of Northern Tunisia, a scarce dataset, and study properties of the inferred time-evolving interregional networks. As a result, we show that (1) optimal solutions consist of very different network structures and spreading rate functions; and that (2) these diverse solutions produce very similar spreading patterns. Finally, we discuss how inferred dominant interregional connections are related to available archaeological traces. Historical networks resulting from our approach can help understanding complex processes of cultural change in ancient times.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-86764</identifier>
    <author>Margarita Kostré</author>
    <submitter>Margarita Kostre</submitter>
    <author>Vikram Sunkara</author>
    <author>Christof Schütte</author>
    <author>Nataša Djurdjevac Conrad</author>
    <series>
      <title>ZIB-Report</title>
      <number>22-10</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>mesoscale spreading process, network inference, time-evolving network, romanization spreading, scarce data</value>
    </subject>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="schuette">Schütte, Christof</collection>
    <collection role="persons" number="natasa.conrad">Conrad, Natasa</collection>
    <collection role="persons" number="sunkara">Sunkara, Vikram</collection>
    <collection role="persons" number="kostre">Kostre, Margarita</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="projects" number="MathPlusEF5-2">MathPlusEF5-2</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/8676/ZIBReportKostre.pdf</file>
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  <doc>
    <id>5960</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-06-03</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Using sparse kernels to design computer experiments with tunable precision</title>
    <abstract language="eng">Statistical methods to design computer experiments usually rely on a Gaussian process (GP) surrogate model, and typically aim at selecting design points (combinations of algorithmic and model parameters) that minimize the average prediction variance, or maximize the prediction accuracy for the hyperparameters of the GP surrogate.&#13;
In many applications, experiments have a tunable precision, in the sense that one software parameter controls the tradeoff between accuracy and computing time (e.g., mesh size in FEM simulations or number of Monte-Carlo samples).&#13;
We formulate the problem of allocating a budget of computing time over a finite set of candidate points for the goals mentioned above. This is a continuous optimization problem, which is moreover convex whenever the tradeoff function accuracy vs. computing time is concave.&#13;
On the other hand, using non-concave weight functions can help to identify sparse designs. In addition, using sparse kernel approximations drastically reduce the cost per iteration of the multiplicative weights updates that can be used to solve this problem.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-59605</identifier>
    <enrichment key="SourceTitle">Appeared in: Ana Colubi, Angela Blanco and Cristian Gatu (eds.) 22nd Intern. Conf. on Computational Statistics - COMSTAT 2016, Oviedo, Spain, 23-26 August 2016, Proceedings ISBN 978-90-73592-36-0. Pp. 397-408</enrichment>
    <author>Guillaume Sagnol</author>
    <submitter>Guillaume Sagnol</submitter>
    <author>Hans-Christian Hege</author>
    <author>Martin Weiser</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-33</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Optimal design of computer experiments</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Sparse kernels</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Gaussian Process</value>
    </subject>
    <collection role="msc" number="62K05">Optimal designs</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="vis">Visual Data Analysis</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="compmed">Computational Medicine</collection>
    <collection role="institutes" number="visalgo">Visual Data Analysis in Science and Engineering</collection>
    <collection role="institutes" number="traffic">Mathematics of Transportation and Logistics</collection>
    <collection role="persons" number="hege">Hege, Hans-Christian</collection>
    <collection role="persons" number="sagnol">Sagnol, Guillaume</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="projects" number="ZIB-HPC-DoE">ZIB-HPC-DoE</collection>
    <collection role="institutes" number="VDcC">Visual and Data-centric Computing</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5960/optdes_kriging_compstat_v2_zib.pdf</file>
  </doc>
  <doc>
    <id>6035</id>
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    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
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    <pageNumber/>
    <edition/>
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    <completedDate>--</completedDate>
    <publishedDate>2016-05-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes</title>
    <abstract language="eng">In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to the time scale of interest, i.e., of the whole process. In this setting, the detection of a global cyclic behavior of the process becomes difficult because transitions between individual states may appear almost reversible on the small time scale of the simulation. We address this difficulty using a mixed-integer programming model that allows us to compute a cycle of clusters with maximum net flow, i.e., large forward and small backward probability. For a synthetic genetic regulatory network consisting of a ring-oscillator with three genes, we show that this approach can detect the most productive overall cycle, outperforming classical spectral analysis methods. Our method applies to general non-equilibrium steady state systems such as catalytic reactions, for which the objective value computes the effectiveness of the catalyst.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-60353</identifier>
    <identifier type="doi">10.1137/16M1091162</identifier>
    <author>Jakob Witzig</author>
    <submitter>Jakob Witzig</submitter>
    <author>Isabel Beckenbach</author>
    <author>Leon Eifler</author>
    <author>Konstantin Fackeldey</author>
    <author>Ambros Gleixner</author>
    <author>Andreas Grever</author>
    <author>Marcus Weber</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-39</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Non-reversible Markov Processes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>NESS</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Mixed-Integer Programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Markov State Models</value>
    </subject>
    <collection role="msc" number="60-XX">PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX)</collection>
    <collection role="msc" number="62-XX">STATISTICS</collection>
    <collection role="msc" number="82-XX">STATISTICAL MECHANICS, STRUCTURE OF MATTER</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="compmol">Computational Molecular Design</collection>
    <collection role="institutes" number="mip">Mathematical Optimization Methods</collection>
    <collection role="persons" number="fackeldey">Fackeldey, Konstantin</collection>
    <collection role="persons" number="weber">Weber, Marcus</collection>
    <collection role="persons" number="beckenbach">Beckenbach, Isabel</collection>
    <collection role="projects" number="MIP-ZIBOPT">MIP-ZIBOPT</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="SparseApproxiTN">SparseApproxiTN</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6035/ZR-16-39-revised2.pdf</file>
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    <publishedYear/>
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    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
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    <completedDate>--</completedDate>
    <publishedDate>2017-04-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Reliable approximation of long relaxation timescales in molecular dynamics</title>
    <abstract language="eng">Many interesting rare events in molecular systems like ligand association, protein folding or con- formational changes happen on timescales that often are not accessible by direct numerical simulation. Therefore rare event approximation approaches like interface sampling, Markov state model building or advanced reaction coordinate based free energy estimation have attracted huge attention recently. In this article we analyze the reliability of such approaches: How precise is an estimate of long relaxation timescales of molecular systems resulting from various forms of rare event approximation methods? Our results give a theoretical answer to this question by relating it with the transfer operator approach to molecular dynamics. By doing so they also allow for understanding deep connections between the different approaches.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-63718</identifier>
    <identifier type="doi">10.3390/e19070367</identifier>
    <author>Wei Zhang</author>
    <submitter>Erlinda Körnig</submitter>
    <author>Christof Schütte</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-19</number>
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    <collection role="msc" number="37A60">Dynamical systems in statistical mechanics [See also 82Cxx]</collection>
    <collection role="msc" number="60J35">Transition functions, generators and resolvents [See also 47D03, 47D07]</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="SFB-1114-B3">SFB-1114-B3</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6371/ZIB-Report_17-19.pdf</file>
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  <doc>
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    <language>eng</language>
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    <edition/>
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    <publishedDate>2017-10-06</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Variational characterization of free energy: Theory and algorithms</title>
    <abstract language="eng">The article surveys and extends variational formulations of the thermodynamic free&#13;
energy and discusses their information-theoretic content from the perspective of mathematical statistics. We revisit the well-known Jarzynski equality for  nonequilibrium free energy sampling within the framework of importance sampling and Girsanov change-of-measure transformations. The implications of the different variational formulations for designing efficient stochastic optimization and nonequilibrium simulation algorithms for computing free energies are discussed and illustrated.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-65045</identifier>
    <author>Carsten Hartmann</author>
    <submitter>Paulina Bressel</submitter>
    <author>Lorenz Richter</author>
    <author>Christof Schütte</author>
    <author>Wei Zhang</author>
    <series>
      <title>ZIB-Report</title>
      <number>17-52</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Importance sampling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Donsker-Varadhan principle</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>thermodynamic free energy</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>nonequilibrium molecular dynamics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stochastic approximation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>cross-entropy method</value>
    </subject>
    <collection role="msc" number="37A60">Dynamical systems in statistical mechanics [See also 82Cxx]</collection>
    <collection role="msc" number="60J60">Diffusion processes [See also 58J65]</collection>
    <collection role="msc" number="82C05">Classical dynamic and nonequilibrium statistical mechanics (general)</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>
    <collection role="persons" number="zhang">Zhang, Wei</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/6504/ZIB-Report_17-52.pdf</file>
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