TY - THES A1 - Frech, Ralf T1 - Das Konzept der Flussdichte und sein Bezug zur Bohmschen Mechanik Y1 - 2014 ER - TY - THES A1 - Makarenko, Oleksandra T1 - Square Root Approximation und statistische Umgewichtungstechnik für das Faltungsverhalten von Polymerbürsten Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65283 ER - TY - JOUR A1 - Berg, Mascha A1 - Plöntzke, Julia A1 - Leonhard-Marek, Sabine A1 - Müller, Kerstin-Elisabeth A1 - Röblitz, Susanna T1 - A dynamic model to simulate potassium balance in dairy cows JF - Journal of Dairy Science N2 - High-performing dairy cows require a particular composition of nutritional ingredients, adapted to their individual requirements and depending on their production status. The optimal dimensioning of minerals in the diet, one being potassium, is indispensable for the prevention of imbalances. Potassium balance in cows is the result of potassium intake, distribution in the organism, and excretion, and it is closely related to glucose and electrolyte metabolism. In this paper, we present a dynamical model for potassium balance in lactating and nonlactating dairy cows based on ordinary differential equations. Parameter values were obtained from clinical trial data and from the literature. To verify the consistency of the model, we present simulation outcomes for 3 different scenarios: potassium balance in (1) nonlactating cows with varying feed intake, (2) nonlactating cows with varying potassium fraction in the diet, and (3) lactating cows with varying milk production levels. The results give insights into the short- and long-term potassium metabolism, providing an important step toward the understanding of the potassium network, the design of prophylactic feed additives, and possible treatment strategies. Y1 - 2017 U6 - https://doi.org/10.3168/jds.2016-12443 VL - 100 IS - 12 SP - 9799 EP - 9814 ER - TY - JOUR A1 - Gul, Raheem A1 - Schütte, Christof A1 - Bernhard, Stefan T1 - Mathematical modeling and sensitivity analysis of arterial anastomosis in arm arteries JF - Applied Mathematical Modelling Y1 - 2016 U6 - https://doi.org/10.1016/j.apm.2016.03.041 ER - TY - CHAP A1 - Schmidt, Frank ED - Piprek, Joachim T1 - Photonics T2 - Handbook of Optoelectronic Device Modeling and Simulation Y1 - 2017 SN - 9781498749381 PB - CRC Press ER - TY - CHAP A1 - Gregersen, Niels A1 - de Lasson, Jakob Rosenkrantz A1 - Frandsen, Lars Hagedorn A1 - Kim, Oleksiy S. A1 - Breinbjerg, Olav A1 - Wang, Fengwen A1 - Sigmund, Ole A1 - Ivinskaya, Aliaksandra A1 - Lavrinenko, Andrei A1 - Gutsche, Philipp A1 - Burger, Sven A1 - Häyrynen, Teppo A1 - Merk, Jesper T1 - Comparison of five numerical methods for computing quality factors and resonance wavelengths in photonic crystal membrane cavities T2 - CLEO/Europe-EQEC Y1 - 2017 U6 - https://doi.org/10.1109/CLEOE-EQEC.2017.8087750 ER - TY - JOUR A1 - Ehrig, Rainald A1 - Heller, Markus O. T1 - On intrinsic equivalences of the finite helical axis, the instantaneous helical axis, and the SARA approach. A mathematical perspective. JF - Journal of Biomechanics Y1 - 2019 U6 - https://doi.org/10.1016/j.jbiomech.2018.12.034 VL - 84 SP - 4 EP - 10 ER - TY - GEN A1 - Fackeldey, Konstantin A1 - Koltai, Péter A1 - Névir, Peter A1 - Rust, Henning A1 - Schild, Axel A1 - Weber, Marcus T1 - From Metastable to Coherent Sets - time-discretization schemes N2 - 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. T3 - ZIB-Report - 17-74 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66074 SN - 1438-0064 ER - TY - JOUR A1 - Schnauber, Peter A1 - Schall, Johannes A1 - Bounouar, Samir A1 - Höhne, Theresa A1 - Park, Suk-In A1 - Ryu, Geun-Hwan A1 - Heindel, Tobias A1 - Burger, Sven A1 - Song, Jin-Dong A1 - Rodt, Sven A1 - Reitzenstein, Stephan T1 - Deterministic integration of quantum dots into on-chip multi-mode interference beamsplitters using in-situ electron beam lithography JF - Nano Lett. Y1 - 2018 U6 - https://doi.org/10.1021/acs.nanolett.7b05218 VL - 18 SP - 2336 ER - TY - JOUR A1 - Jäger, Klaus A1 - Köppel, Grit A1 - Hammerschmidt, Martin A1 - Burger, Sven A1 - Becker, Christiane T1 - On accurate simulations of thin-film solar cells with a thick glass superstrate JF - Opt. Express Y1 - 2018 U6 - https://doi.org/10.1364/OE.26.000A99 VL - 26 SP - A99 ER - TY - JOUR A1 - Cockayne, Jon A1 - Oates, Chris A1 - Sullivan, T. J. A1 - Girolami, Mark T1 - Bayesian Probabilistic Numerical Methods JF - SIAM Review N2 - Over forty years ago average-case error was proposed in the applied mathematics literature as an alternative criterion with which to assess numerical methods. In contrast to worst-case error, this criterion relies on the construction of a probability measure over candidate numerical tasks, and numerical methods are assessed based on their average performance over those tasks with respect to the measure. This paper goes further and establishes Bayesian probabilistic numerical methods as solutions to certain inverse problems based upon the numerical task within the Bayesian framework. This allows us to establish general conditions under which Bayesian probabilistic numerical methods are well defined, encompassing both the non-linear and non-Gaussian context. For general computation, a numerical approximation scheme is proposed and its asymptotic convergence established. The theoretical development is extended to pipelines of computation, wherein probabilistic numerical methods are composed to solve more challenging numerical tasks. The contribution highlights an important research frontier at the interface of numerical analysis and uncertainty quantification, and a challenging industrial application is presented. Y1 - 2019 U6 - https://doi.org/10.1137/17M1139357 VL - 61 IS - 4 SP - 756 EP - 789 ER - TY - GEN A1 - Bittracher, Andreas A1 - Banisch, Ralf A1 - Schütte, Christof T1 - Data-driven Computation of Molecular Reaction Coordinates N2 - The identification of meaningful reaction coordinates plays a key role in the study of complex molecular systems whose essential dynamics is characterized by rare or slow transition events. In a recent publication, the authors identified a condition under which such reaction coordinates exist - the existence of a so-called transition manifold - and proposed a numerical method for their point-wise computation that relies on short bursts of MD simulations. This article represents an extension of the method towards practical applicability in computational chemistry. It describes an alternative computational scheme that instead relies on more commonly available types of simulation data, such as single long molecular trajectories, or the push-forward of arbitrary canonically-distributed point clouds. It is based on a Galerkin approximation of the transition manifold reaction coordinates, that can be tuned to individual requirements by the choice of the Galerkin ansatz functions. Moreover, we propose a ready-to-implement variant of the new scheme, that computes data-fitted, mesh-free ansatz functions directly from the available simulation data. The efficacy of the new method is demonstrated on a realistic peptide system. T3 - ZIB-Report - 17-77 KW - reaction coordinate KW - coarse graining KW - transition manifold KW - transfer operator KW - Galerkin method KW - meshfree basis KW - data-driven Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66179 SN - 1438-0064 ER - TY - GEN A1 - Lie, Han Cheng A1 - Sullivan, T. J. A1 - Teckentrup, Aretha T1 - Random forward models and log-likelihoods in Bayesian inverse problems T2 - SIAM/ASA Journal on Uncertainty Quantification N2 - We consider the use of randomised forward models and log-likelihoods within the Bayesian approach to inverse problems. Such random approximations to the exact forward model or log-likelihood arise naturally when a computationally expensive model is approximated using a cheaper stochastic surrogate, as in Gaussian process emulation (kriging), or in the field of probabilistic numerical methods. We show that the Hellinger distance between the exact and approximate Bayesian posteriors is bounded by moments of the difference between the true and approximate log-likelihoods. Example applications of these stability results are given for randomised misfit models in large data applications and the probabilistic solution of ordinary differential equations. T3 - ZIB-Report - 18-03 KW - Bayesian inverse problem KW - random likelihood KW - surrogate model KW - posterior consistency KW - probabilistic numerics KW - uncertainty quantification KW - randomised misfit Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66324 SN - 1438-0064 VL - 6 IS - 4 SP - 1600 EP - 1629 ER - TY - CHAP A1 - Abebe, Muluneh G. A1 - Gomard, Guillaume A1 - Zschiedrich, Lin A1 - Rockstuhl, Carsten A1 - Paetzold, Ulrich W. A1 - Abass, Aimi T1 - Thermodynamics of Photon Recycling in Four Terminal Perovskite/si Tandem Solar Cells T2 - Optical Nanostructures and Advanced Materials for Photovoltaics Y1 - 2017 U6 - https://doi.org/10.1364/PV.2017.PM4A.2 SP - PM4A.2 ER - TY - THES A1 - Djurdjevac Conrad, Natasa T1 - Methods for analyzing complex networks using random walker Y1 - 2012 ER - TY - JOUR A1 - Banisch, Ralf A1 - Djurdjevac Conrad, Natasa T1 - Cycle-flow-based module detection in directed recurrence networks JF - EPL (Europhysics Letters) Y1 - 2014 U6 - https://doi.org/10.1209/0295-5075/108/68008 VL - 108 IS - 6 ER - TY - JOUR A1 - Lorenz, Philipp A1 - Wolf, Frederik A1 - Braun, Jonas A1 - Djurdjevac Conrad, Natasa A1 - Hövel, Philipp T1 - Capturing the Dynamics of Hashtag-Communities JF - International Workshop on Complex Networks and their Applications Y1 - 2017 U6 - https://doi.org/10.1007/978-3-319-72150-7_33 SP - 401 EP - 413 ER - TY - JOUR A1 - Villatoro, Jose A1 - Zühlke, Martin A1 - Riebe, Daniel A1 - Riedel, Jens A1 - Beitz, Toralf A1 - Löhmannsröben, Hans-Gerd T1 - IR-MALDI ion mobility spectrometry JF - Analytical and Bioanalytical Chemistry Y1 - 2016 U6 - https://doi.org/10.1007/s00216-016-9739-x VL - 408 IS - 23 SP - 6259 EP - 6268 ER - TY - JOUR A1 - Igde, Sinaida A1 - Röblitz, Susanna A1 - Müller, Anne A1 - Kolbe, Katharina A1 - Boden, Sophia A1 - Fessele, Claudia A1 - Lindhorst, Thisbe A1 - Weber, Marcus A1 - Hartmann, Laura T1 - Linear Precision Glycomacromolecules with Varying Interligand Spacing and Linker Functionalities Binding to Concanavalin A and the Bacterial Lectin FimH JF - Marcomolecular Bioscience Y1 - 2017 U6 - https://doi.org/10.1002/mabi.201700198 VL - 17 IS - 12 SP - 1700198 ER - TY - GEN A1 - Volkwein, Stefan A1 - Weiser, Martin T1 - Affine Invariant Convergence Analysis for Inexact Augmented Lagrangian-SQP Methods N2 - An affine invariant convergence analysis for inexact augmented Lagrangian-SQP methods is presented. The theory is used for the construction of an accuracy matching between iteration errors and truncation errors, which arise from the inexact linear system solves. The theoretical investigations are illustrated numerically by an optimal control problem for the Burgers equation. T3 - ZIB-Report - 00-56 KW - nonlinear programming KW - multiplier methods KW - affine invariant norms KW - Burgers' equation Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6243 ER - TY - GEN A1 - Erdmann, Bodo A1 - Kober, Cornelia A1 - Lang, Jens A1 - Sader, Robert A1 - Zeilhofer, Hans-Florian A1 - Deuflhard, Peter T1 - Efficient and Reliable Finite Element Methods for Simulation of the Human Mandible N2 - By computed tomography data (CT), the individual geometry of the mandible is quite well reproduced, also the separation between cortical and trabecular bone. Using anatomical knowledge about the architecture and the functional potential of the masticatory muscles, realistic situations were approximated. The solution of the underlying partial differential equations describing linear elastic material behaviour is provided by an adaptive finite element method. Estimations of the discretization error, local grid refinement, and multilevel techniques guarantee the reliability and efficiency of the method. T3 - ZIB-Report - 01-14 KW - mandible KW - sensitivity analysis KW - finite element method KW - adaptive grid refinement Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6403 ER - TY - GEN A1 - Weiser, Martin T1 - Linear convergence of an interior point method for linear control constrained optimal control problems N2 - The paper provides a detailed analysis of a short step interior point algorithm applied to linear control constrained optimal control problems. Using an affine invariant local norm and an inexact Newton corrector, the well-known convergence results from finite dimensional linear programming can be extended to the infinite dimensional setting of optimal control. The present work complements a recent paper of Weiser and Deuflhard, where convergence rates have not been derived. The choice of free parameters, i.e. the corrector accuracy and the number of corrector steps, is discussed. T3 - ZIB-Report - 02-13 KW - linear optimal control KW - infinite dimensional KW - interior point methods KW - inexact Newton methods Y1 - 2002 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-6809 ER - TY - GEN A1 - Hinze, Michael A1 - Schiela, Anton T1 - Discretization of Interior Point Methods for State Constrained Elliptic Optimal Control Problems: Optimal Error Estimates and Parameter Adjustment N2 - An adjustment scheme for the relaxation parameter of interior point approaches to the numerical solution of pointwise state constrained elliptic optimal control problems is introduced. The method is based on error estimates of an associated finite element discretization of the relaxed problems and optimally selects the relaxation parameter in dependence on the mesh size of discretization. The finite element analysis for the relaxed problems is carried out and a numerical example is presented which confirms our analytical findings. T3 - ZIB-Report - 07-40 KW - Elliptic optimal control problem KW - error estimates KW - interior point method KW - pointwise state constraints Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10414 SN - 1438-0064 ER - TY - GEN A1 - Schiela, Anton T1 - An Interior Point Method in Function Space for the Efficient Solution of State Constrained Optimal Control Problems N2 - We propose and analyse an interior point path-following method in function space for state constrained optimal control. Our emphasis is on proving convergence in function space and on constructing a practical path-following algorithm. In particular, the introduction of a pointwise damping step leads to a very efficient method, as verified by numerical experiments. T3 - ZIB-Report - 07-44 KW - interior point methods in function space KW - optimal control KW - state constraints Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10471 SN - 1438-0064 ER - TY - GEN A1 - Weiser, Martin T1 - Pointwise Nonlinear Scaling for Reaction-Diffusion-Equations N2 - Parabolic reaction-diffusion systems may develop sharp moving reaction fronts which pose a challenge even for adaptive finite element methods. We propose a method to transform the equation into an equivalent form that usually exhibits solutions which are easier to discretize, giving higher accuracy for a given number of degrees of freedom. The transformation is realized as an efficiently computable pointwise nonlinear scaling that is optimized for prototypical planar travelling wave solutions of the underlying reaction-diffusion equation. The gain in either performance or accuracy is demonstrated on different numerical examples. T3 - ZIB-Report - 07-45 KW - reaction-diffusion equations KW - travelling waves KW - nonlinear scaling KW - discretization error Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10493 SN - 1438-0064 ER - TY - THES A1 - Farshbaf-Shaker, Mohammad-Hassan T1 - Ein neues Verfahren zur Lösung des Streuproblems der Maxwell-Gleichungen Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9914 ER - TY - THES A1 - Gerber, Susanne T1 - Perfusionsmodellierung in menschlichen Tumoren N2 - Im Rahmen dieser Arbeit wurde ein individuell anpassungsfähiges Modell entwickelt und implementiert, das die Perfusion in menschlichen soliden Tumoren beschreibt und für verschiedene Zeitpunkte w¨ahrend regionaler Hyperthermie ein lokal abhängiges Temperaturprofil berechnet. Da vor jeder Simulation alle wichtigen Parameter anhand von Ultraschall-, MRT- oder Angiogrammbildern individuell bestimmt werden können, wird eine patientenspezifische Aussage ¨uber das intratumorale Antwortverhalten bereits vor der eigentlichen Behandlung möglich. In Abh¨angigkeit von der Qualität der zur Verfügung stehenden anatomischen Daten über das zu simulierende Gebiet kann das Modell beliebig verfeinert oder bei Mangel an detaillierten Informationen auch mit Minimaldaten und reduzierter räumlicher Genauigkeit benutzt werden. Die für eine Simulation benötigten 2- oder 3- dimensionalen Geometrien können leicht mit der am ZIB entwickelten Software Amira erstellt und zur Berechnung in KARDOS, einem ebenfalls am ZIB implementierten Löser für nichtlineare partielle Differentialgleichungen, eingelesen werden. Mit Hilfe dieses Modells wird eine einfache, aber realistische und aussagekräftige Simulation für die Therapieplanung einer klinischen Hyperthermieanwendung ermöglicht, die innerhalb kurzer Zeit vorbereitet und durchgeführt werden kann. Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9923 ER - TY - GEN A1 - Weber, Marcus T1 - Conformation-based transition state theory N2 - For the treatment of equilibrated molecular systems in a heat bath we propose a transition state theory that is based on conformation dynamics. In general, a set-based discretization of a Markov operator ${\cal P}^\tau$ does not preserve the Markov property. In this article, we propose a discretization method which is based on a Galerkin approach. This discretization method preserves the Markov property of the operator and can be interpreted as a decomposition of the state space into (fuzzy) sets. The conformation-based transition state theory presented here can be seen as a first step in conformation dynamics towards the computation of essential dynamical properties of molecular systems without time-consuming molecular dynamics simulations. T3 - ZIB-Report - 07-18 KW - dynamical systems KW - transition state theory KW - rare events Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9612 ER - TY - THES A1 - Riemer, Alexander T1 - Accuracy, Stability, Convergence of Rigorous Thermodynamic Sampling Methods Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10052 ER - TY - GEN A1 - Schenk, Olaf A1 - Wächter, Andreas A1 - Weiser, Martin T1 - Inertia Revealing Preconditioning For Large-Scale Nonconvex Constrained Optimization N2 - Fast nonlinear programming methods following the all-at-once approach usually employ Newton's method for solving linearized Karush-Kuhn-Tucker (KKT) systems. In nonconvex problems, the Newton direction is only guaranteed to be a descent direction if the Hessian of the Lagrange function is positive definite on the nullspace of the active constraints, otherwise some modifications to Newton's method are necessary. This condition can be verified using the signs of the KKT's eigenvalues (inertia), which are usually available from direct solvers for the arising linear saddle point problems. Iterative solvers are mandatory for very large-scale problems, but in general do not provide the inertia. Here we present a preconditioner based on a multilevel incomplete $LBL^T$ factorization, from which an approximation of the inertia can be obtained. The suitability of the heuristics for application in optimization methods is verified on an interior point method applied to the CUTE and COPS test problems, on large-scale 3D PDE-constrained optimal control problems, as well as 3D PDE-constrained optimization in biomedical cancer hyperthermia treatment planning. The efficiency of the preconditioner is demonstrated on convex and nonconvex problems with $150^3$ state variables and $150^2$ control variables, both subject to bound constraints. T3 - ZIB-Report - 07-32 KW - nonconvex constrained optimization KW - interior-point method KW - inertia KW - multilevel incomplete factorization Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10314 SN - 1438-0064 ER - TY - GEN A1 - Antoine, Xavier A1 - Arnold, Anton A1 - Besse, Christophe A1 - Ehrhardt, Matthias A1 - Schädle, Achim T1 - A Review of Transparent and Artificial Boundary Conditions Techniques for Linear and Nonlinear Schrödinger Equations N2 - In this review article we discuss different techniques to solve numerically the time-dependent Schrödinger equation on unbounded domains. We present in detail the most recent approaches and describe briefly alternative ideas pointing out the relations between these works. We conclude with several numerical examples from different application areas to compare the presented techniques. We mainly focus on the one-dimensional problem but also touch upon the situation in two space dimensions and the cubic nonlinear case. T3 - ZIB-Report - 07-34 KW - Schrödinger equation KW - transparent boundary condition KW - discrete convolution KW - unbounded domain Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10332 SN - 1438-0064 ER - TY - GEN A1 - Schiela, Anton T1 - Optimality Conditions for Convex State Constrained Optimal Control Problems with Discontinuous States N2 - 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. T3 - ZIB-Report - 07-35 KW - optimal control KW - state constraints KW - optimality conditions Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10342 SN - 1438-0064 ER - TY - GEN A1 - Schmidt, Heiko A1 - Oevermann, Michael A1 - Bastiaans, Rob J.M. A1 - Kerstein, Alan R. T1 - A priori Tabulation of Turbulent Flame Speeds via a Combination of a Stochastic Mixing Model and Flamelet Generated Manifolds N2 - 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). T3 - ZIB-Report - 08-02 KW - Verbrennung KW - Flammenstrukturen KW - stochastisches Turbulenzmodell KW - FGM KW - turbulente Brenngeschwindigkeiten KW - turbulent premixed combustion KW - flame structures KW - linear eddy model KW - flamelet generated manifolds KW - turbulent flame speeds Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10532 SN - 1438-0064 ER - TY - GEN A1 - Carqué, Gunter A1 - Owinoh, Antony Z. A1 - Klein, Rupert A1 - Majda, Andrew J. T1 - Asymptotic Scale Analysis of Precipitating Clouds N2 - 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. T3 - ZIB-Report - 08-03 KW - atmospheric moist convection KW - deep convection KW - shallow convection KW - precipitating clouds KW - asymptotic analysis Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10548 SN - 1438-0064 ER - TY - GEN A1 - Oevermann, Michael A1 - Schmidt, Heiko A1 - Kerstein, Alan R. T1 - Linear-Eddy Modeling of Autoignition under Thermal Stratification N2 - 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. T3 - ZIB-Report - 08-05 KW - HCCI KW - Selbstzündung KW - Turbulenz KW - Linear-Eddy Modell KW - HCCI KW - autoignition KW - thermal explosion KW - turbulence KW - Linear-Eddy Model Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10562 SN - 1438-0064 ER - TY - GEN A1 - Schiela, Anton T1 - An Extended Mathematical Framework for Barrier Methods in Function Space N2 - 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. T3 - ZIB-Report - 08-07 Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10593 SN - 1438-0064 ER - TY - GEN A1 - Ruprecht, Daniel A1 - Schädle, Achim A1 - Schmidt, Frank A1 - Zschiedrich, Lin T1 - Transparent boundary conditons for time-dependent problems N2 - 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. T3 - ZIB-Report - 07-12 KW - transparent boundary condition KW - non-reflecting boundary condition KW - pole condition KW - wave equation KW - Schrödinger equation KW - drift diffusion equation Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9558 ER - TY - GEN A1 - Kube, Susanna A1 - Lasser, Caroline A1 - Weber, Marcus T1 - Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics N2 - 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. T3 - ZIB-Report - 07-17 KW - Metropolis Monte Carlo KW - approximation KW - quadrature KW - oscillating functions Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9604 ER - TY - JOUR A1 - Garcia Santiago, Xavier A1 - Hammerschmidt, Martin A1 - Sachs, Johannes A1 - Burger, Sven A1 - Kwon, Hyunah A1 - Knöller, Marvin A1 - Arens, Tilo A1 - Fischer, Peer A1 - Fernandez-Corbaton, Ivan A1 - Rockstuhl, Carsten T1 - Toward maximally electromagnetically chiral scatterers at optical frequencies JF - ACS Photonics Y1 - 2022 U6 - https://doi.org/10.1021/acsphotonics.1c01887 VL - 9 SP - 1954 ER - TY - GEN A1 - Ernst, Ariane A1 - Schütte, Christof A1 - Sigrist, Stephan A1 - Winkelmann, Stefanie T1 - Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics N2 - 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. T3 - ZIB-Report - 21-15 KW - linear reaction networks KW - cross-correlation KW - neurotransmission Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82674 SN - 1438-0064 ER - TY - JOUR A1 - Thies, Arne A1 - Sunkara, Vikram A1 - Ray, Sourav A1 - Wulkow, Hanna A1 - Celik, M. Özgür A1 - Yergöz, Fatih A1 - Schütte, Christof A1 - Stein, Christoph A1 - Weber, Marcus A1 - Winkelmann, Stefanie T1 - Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design JF - Scientific Reports N2 - We previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. The design process of NFEPP was based on mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands, recognizing that GPCRs function differently under pathological versus healthy conditions. We now present an additional and novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels and their dependence on parameters of inflamed and healthy tissue (pH, radicals). The model is validated against in vitro experimental data for the ligands NFEPP and fentanyl at different pH values and radical concentrations. We observe markedly reduced binding affinity and calcium channel inhibition for NFEPP at normal pH compared to lower pH, in contrast to the effect of fentanyl. For increasing radical concentrations, we find enhanced constitutive G-protein activation but reduced ligand binding affinity. Assessing the different effects, the 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. Y1 - 2023 U6 - https://doi.org/10.1038/s41598-023-27699-w VL - 13 IS - 607 ER - TY - GEN A1 - Ray, Sourav A1 - Thies, Arne A1 - Sunkara, Vikram A1 - Wulkow, Hanna A1 - Celik, Özgür A1 - Yergöz, Fatih A1 - Schütte, Christof A1 - Stein, Christoph A1 - Weber, Marcus A1 - Winkelmann, Stefanie T1 - Modelling altered signalling of G-protein coupled receptors in inflamed environment to advance drug design N2 - 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. 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. The modelling results were validated with in vitro experiments measuring calcium currents and G-protein activation. 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. 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. T3 - ZIB-Report - 21-19 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-82797 SN - 1438-0064 ER - TY - THES A1 - Pakhomov, Anton T1 - Efficient modeling and optimization of surface second-harmonic generation from nanophotonic components Y1 - 2021 U6 - https://doi.org/10.22032/dbt.49369 ER - TY - JOUR A1 - Djurdjevac, Ana T1 - Linear Parabolic Problems in Random Moving Domains N2 - We consider linear parabolic equations on a random non-cylindrical domain. Utilizing the domain mapping method, we write the problem as a partial differential equation with random coefficients on a cylindrical deterministic domain. Exploiting the deterministic results concerning equations on non-cylindrical domains, we state the necessary assumptions about the velocity filed and in addition, about the flow transformation that this field generates. In this paper we consider both cases, the uniformly bounded with respect to the sample and log-normal type transformation. In addition, we give an explicit example of a log-normal type transformation and prove that it does not satisfy the uniformly bounded condition. We define a general framework for considering linear parabolic problems on random non-cylindrical domains. As the first example, we consider the heat equation on a random tube domain and prove its well-posedness. Moreover, as the other example we consider the parabolic Stokes equation which illustrates the case when it is not enough just to study the plain-back transformation of the function, but instead to consider for example the Piola type transformation, in order to keep the divergence free property. Y1 - 2021 U6 - https://doi.org/https://doi.org/10.1137/19M1284889 VL - 9 IS - 2 SP - 848 EP - 879 ER - TY - JOUR A1 - Djurdjevac, Ana A1 - Gräser, Carsten A1 - Herbert, Philip J. T1 - Non-stationary incompressible linear fluid equations in a moving domain JF - arXiv N2 - This article considers non-stationary incompressible linear fluid equations in a moving domain. We demonstrate the existence and uniqueness of an appropriate weak formulation of the problem by making use of the theory of time-dependent Bochner spaces. It is not possible to directly apply established evolving Hilbert space theory due to the incompressibility constraint. After we have established the well-posedness, we derive and analyse a time discretisation of the system. Y1 - 2021 ER - TY - JOUR A1 - Colom, Remi A1 - Mikheeva, Elena A1 - Achouri, Karim A1 - Zuniga-Perez, Jesus A1 - Bonod, Nicolas A1 - Martin, Olivier J. F. A1 - Burger, Sven A1 - Genevet, Patrice T1 - Crossing of the branch cut: the topological origin of a universal 2π-phase retardation in non-Hermitian metasurfaces JF - Laser Photonics Rev. Y1 - 2023 U6 - https://doi.org/10.1002/lpor.202200976 VL - 17 SP - 2200976 ER - TY - JOUR A1 - Montefusco, Alberto A1 - Schütte, Christof A1 - Winkelmann, Stefanie T1 - A route to the hydrodynamic limit of a reaction-diffusion master equation using gradient structures JF - SIAM Journal on Applied Mathematics N2 - The reaction-diffusion master equation (RDME) is a lattice-based stochastic model for spatially resolved cellular processes. It is often interpreted as an approximation to spatially continuous reaction-diffusion models, which, in the limit of an infinitely large population, may be described by means of reaction-diffusion partial differential equations. Analyzing and understanding the relation between different mathematical models for reaction-diffusion dynamics is a research topic of steady interest. In this work, we explore a route to the hydrodynamic limit of the RDME which uses gradient structures. Specifically, we elaborate on a method introduced in [J. Maas and A. Mielke, J. Stat. Phys., 181 (2020), pp. 2257–2303] in the context of well-mixed reaction networks by showing that, once it is complemented with an appropriate limit procedure, it can be applied to spatially extended systems with diffusion. Under the assumption of detailed balance, we write down a gradient structure for the RDME and use the method in order to produce a gradient structure for its hydrodynamic limit, namely, for the corresponding RDPDE. Y1 - 2023 U6 - https://doi.org/10.1137/22M1488831 VL - 83 IS - 2 SP - 837 EP - 861 ER - TY - JOUR A1 - Dellnitz, Michael A1 - Hüllermeier, Eyke A1 - Lücke, Marvin A1 - Ober-Blöbaum, Sina A1 - Offen, Christian A1 - Peitz, Sebastian A1 - Pfannschmidt, Karlson T1 - Efficient Time-Stepping for Numerical Integration Using Reinforcement Learning JF - SIAM Journal on Scientific Computing Y1 - 2023 U6 - https://doi.org/10.1137/21M1412682 VL - 45 IS - 2 SP - A579 EP - A595 ER - TY - GEN A1 - Pflüger, Mika A1 - Kline, R Joseph A1 - Fernández Herrero, Analía A1 - Hammerschmidt, Martin A1 - Soltwisch, Victor A1 - Krumrey, Michael T1 - Extracting dimensional parameters of gratings produced with self-aligned multiple patterning using grazing-incidence small-angle x-ray scattering [Source Code] Y1 - 2020 U6 - https://doi.org/10.24433/CO.0953516.v2 ER - TY - JOUR A1 - Gao, Timm A1 - Rickert, Lucas A1 - Urban, Felix A1 - Große, Jan A1 - Srocka, Nicole A1 - Rodt, Sven A1 - Musial, Anna A1 - Zolnacz, Kinga A1 - Mergo, Pawel A1 - Dybka, Kamil A1 - Urbanczyk, Waclaw A1 - Sek, Grzegorz A1 - Burger, Sven A1 - Reitzenstein, Stephan A1 - Heindel, Tobias T1 - A quantum key distribution testbed using a plug&play telecom-wavelength single-photon source JF - Appl. Phys. Rev. Y1 - 2022 U6 - https://doi.org/10.1063/5.0070966 VL - 9 SP - 011412 ER - TY - JOUR A1 - Torun, Cem Güney A1 - Schneider, Philipp-Immanuel A1 - Hammerschmidt, Martin A1 - Burger, Sven A1 - Munns, Joseph H.D. A1 - Schröder, Tim T1 - Optimized diamond inverted nanocones for enhanced color center to fiber coupling JF - Appl. Phys. Lett. Y1 - 2021 U6 - https://doi.org/10.1063/5.0050338 VL - 118 SP - 234002 ER -