TY - JOUR A1 - Weber, Marcus T1 - Adaptive Spectral Clustering in Molecular Simulation. In: Studies in Classification, Data Analysis, and Knowledge Organization JF - XIV: Classification and Data Mining, A. Giusti, G. Ritter, M. Vichi (Eds.), Springer Series Y1 - 2013 SP - 147 EP - 157 ER - TY - JOUR A1 - Fackeldey, Konstantin A1 - Röblitz, Susanna A1 - Scharkoi, O. A1 - Weber, Marcus T1 - Soft Versus Hard Metastable Conformations in Molecular Simulations JF - Particle Methods II, Fundamentals and Applications, Barcelona, Spain 26-28 Oct. 2011, E. Onate and D.R.J. Owen (eds.) Y1 - 2011 SP - 899 EP - 909 ER - TY - JOUR A1 - Shan, Min A1 - Bujotzek, Alexander A1 - Abendroth, Frank A1 - Seitz, Oliver A1 - Weber, Marcus A1 - Haag, Rainer T1 - Conformational Analysis of Bivalent Estrogen Receptor-Ligands: From Intramolecular to Intermolecular Binding JF - ChemBioChem, 12(17) Y1 - 2011 U6 - https://doi.org/10.1002/cbic.201100529 SP - 2587 EP - 2598 ER - TY - JOUR A1 - Günther, Andreas A1 - Lamecker, Hans A1 - Weiser, Martin T1 - Flexible Shape Matching with Finite Element Based LDDMM JF - International Journal of Computer Vision N2 - We consider Large Deformation Diffeomorphic Metric Mapping of general $m$-currents. After stating an optimization algorithm in the function space of admissable morph generating velocity fields, two innovative aspects in this framework are presented and numerically investigated: First, we spatially discretize the velocity field with conforming adaptive finite elements and discuss advantages of this new approach. Second, we directly compute the temporal evolution of discrete $m$-current attributes. Y1 - 2013 U6 - https://doi.org/10.1007/s11263-012-0599-3 VL - 105 IS - 2 SP - 128 EP - 143 ER - TY - GEN A1 - Günther, Andreas A1 - Lamecker, Hans A1 - Weiser, Martin ED - Pennec, X. ED - Joshi, S. ED - Nielsen, M. T1 - Direct LDDMM of Discrete Currents with Adaptive Finite Elements T2 - Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy - Geometrical and Statistical Methods for Modelling Biological Shape Variability N2 - We consider Large Deformation Diffeomorphic Metric Mapping of general $m$-currents. After stating an optimization algorithm in the function space of admissable morph generating velocity fields, two innovative aspects in this framework are presented and numerically investigated: First, we spatially discretize the velocity field with conforming adaptive finite elements and discuss advantages of this new approach. Second, we directly compute the temporal evolution of discrete $m$-current attributes. Y1 - 2011 SP - 1 EP - 14 ER - TY - GEN A1 - Schiela, Anton A1 - Weiser, Martin ED - Diehl, M. ED - Glineur, F. ED - Jarlebring, E. ED - Michiels, W. T1 - Barrier methods for a control problem from hyperthermia treatment planning T2 - Recent Advances in Optimization and its Applications in Engineering (Proceedings of 14th Belgian-French-German Conference on Optimization 2009) N2 - We consider an optimal control problem from hyperthermia treatment planning and its barrier regularization. We derive basic results, which lay the groundwork for the computation of optimal solutions via an interior point path-following method. Further, we report on a numerical implementation of such a method and its performance at an example problem. Y1 - 2010 SP - 419 EP - 428 PB - Springer ER - TY - JOUR A1 - Weiser, Martin A1 - Röllig, Mathias A1 - Arndt, Ralf A1 - Erdmann, Bodo T1 - Development and test of a numerical model for pulse thermography in civil engineering JF - Heat and Mass Transfer N2 - Pulse thermography of concrete structures is used in civil engineering for detecting voids, honeycombing and delamination. The physical situation is readily modeled by Fourier's law. Despite the simplicity of the PDE structure, quantitatively realistic numerical 3D simulation faces two major obstacles. First, the short heating pulse induces a thin boundary layer at the heated surface which encapsulates all information and therefore has to be resolved faithfully. Even with adaptive mesh refinement techniques, obtaining useful accuracies requires an unsatisfactorily fine discretization. Second, bulk material parameters and boundary conditions are barely known exactly. We address both issues by a semi-analytic reformulation of the heat transport problem and by parameter identification. Numerical results are compared with measurements of test specimens. Y1 - 2010 VL - 46 IS - 11-12 SP - 1419 EP - 1428 ER - TY - JOUR A1 - Blome, Mark A1 - Maurer, HR A1 - Greenhalgh, S. T1 - Geoelectric experimental design — Efficient acquisition and exploitation of complete pole-bipole data sets JF - GEOPHYSICS Y1 - 2011 U6 - https://doi.org/10.1190/1.3511350 VL - 76 IS - 1 SP - F15 EP - F26 ER - TY - JOUR A1 - Plattner, A. A1 - Maurer, H. A1 - Vorloeper, J. A1 - Blome, Mark T1 - 3-D electrical resistivity tomography using adaptive wavelet parameter grids JF - Geophysical Journal International Y1 - 2012 VL - 189 SP - 317 EP - 330 ER - TY - JOUR A1 - Ranneberg, Maximilian A1 - Weiser, Martin A1 - Weihrauch, Mirko A1 - Budach, Volker A1 - Gellermann, Johanna A1 - Wust, Peter T1 - Regularized Antenna Profile Adaptation in Online Hyperthermia Treatment JF - Medical Physics Y1 - 2010 U6 - https://doi.org/10.1118/1.3488896 VL - 37 SP - 5382 EP - 5394 ER - TY - JOUR A1 - Jäger, Klaus A1 - Barth, Carlo A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Burger, Sven A1 - Schmidt, Frank A1 - Becker, Christiane T1 - Simulations of sinusoidal nanotextures for coupling light into c-Si thin-film solar cells JF - Opt. Express Y1 - 2016 U6 - https://doi.org/10.1364/OE.24.00A569 VL - 24 SP - A569 ER - TY - JOUR A1 - Ledentsov, Jr., Nikolay A1 - Shchukin, Vitaly A1 - Kropp, Jörg-R. A1 - Burger, Sven A1 - Schmidt, Frank A1 - Ledentsov, Jr., Nikolay T1 - Direct visualization of the in-plane leakage of high-order transverse modes in vertical-cavity surface-emitting lasers mediated by oxide-aperture engineering JF - Proc. SPIE Y1 - 2016 U6 - https://doi.org/10.1117/12.2208909 VL - 9766 SP - 976608 ER - TY - GEN A1 - Fackeldey, Konstantin T1 - Challenges in Atomistic-to-Continuum Coupling T2 - ZIB Report N2 - This paper is concerned with the design, analysis, and implementation of concurrent coupling approaches where different (atomic and continuous) models are used simultaneously within a single simulation process. Thereby, several problems or pitfalls can happen, for example, the reflection of molecular movements at the “boundary” between the atomic and continuum regions which leads to an unphysical increase in energy in the atomic model. We investigate the problems with the aim of giving an introduction into this field and preventing errors for scientists starting their research towards multiscale methods. Y1 - 2010 U6 - https://doi.org/10.1155/2015/834517 VL - 2010 ET - 10-12 ER - TY - JOUR A1 - Durmaz, Vedat T1 - Markov model-based polymer assembly from force field-parameterized building blocks JF - Journal of Computer-Aided Molecular Design N2 - A conventional by hand construction and parameterization of a polymer model for the purpose of molecular simulations can quickly become very workintensive and time-consuming. Using the example of polyglycerol, I present a polymer decompostion strategy yielding a set of five monomeric residues that are convenient for an instantaneous assembly and subsequent force field simulation of a polyglycerol polymer model. Force field parameters have been developed in accordance with the classical Amber force field. Partial charges of each unit were fitted to the electrostatic potential using quantumchemical methods and slightly modified in order to guarantee a neutral total polymer charge. In contrast to similarly constructed models of amino acid and nucleotide sequences, the glycerol building blocks may yield an arbitrary degree of bifurcations depending on the underlying probabilistic model. The iterative development of the overall structure as well as the relation of linear to branching units is controlled by a simple Markov model which is presented with few algorithmic details. The resulting polymer is highly suitable for classical explicit water molecular dynamics simulations on the atomistic level after a structural relaxation step. Moreover, the decomposition strategy presented here can easily be adopted to many other (co)polymers. Y1 - 2015 U6 - https://doi.org/10.1007/s10822-014-9817-0 VL - 29 SP - 225 EP - 232 ER - TY - JOUR A1 - Heye, Katharina A1 - Becker, Dennis A1 - Lütke-Eversloh, Christian A1 - Durmaz, Vedat A1 - Ternes, Thomas A1 - Oetken, Matthias A1 - Oehlmann, Jörg T1 - Effects of carbamazepine and two of its metabolites on the non-biting midge Chironomus riparius in a sediment full life cycle toxicity test JF - Water Research N2 - The antiepileptic drug carbamazepine (CBZ) and its main metabolites carbamazepine-10,11-epoxide (EP-CBZ) and 10,11-dihydro-10,11-dihydroxy-carbamazepine (DiOH-CBZ) were chosen as test substances to assess chronic toxicity on the non-biting midge Chironomus riparius. All three substances were tested in a 40-day sediment full life cycle test (according to OECD 233) in which mortality, emergence, fertility, and clutch size were evaluated. In addition, these parameters were integrated into the population growth rate to reveal population relevant effects. With an LC50 of 0.203 mg/kg (time-weighted mean), the metabolite EP-CBZ was significantly more toxic than the parent substance CBZ (LC50: 1.11 mg/kg). Especially mortality, emergence, and fertility showed to be sensitive parameters under the exposure to CBZ and EP-CBZ. By using classical molecular dynamics (MD) simulations, the binding of CBZ to the ecdysone receptor was investigated as one possible mode of action but showed to be unlikely. The second metabolite DiOH-CBZ did not show any effects within the tested concentration rage (0.171 – 1.22 mg/kg). Even though CBZ was less toxic compared to EP-CBZ, CBZ is found in the environment at much higher concentrations and causes therefore a higher potential risk for sediment dwelling organisms compared to its metabolites. Nevertheless, the current study illustrates the importance of including commonly found metabolites into the risk assessment of parent substances. Y1 - 2016 VL - 98 SP - 19 EP - 27 ER - TY - JOUR A1 - Lubkoll, Lars A1 - Schiela, Anton A1 - Weiser, Martin T1 - An affine covariant composite step method for optimization with PDEs as equality constraints JF - Optimization Methods and Software N2 - We propose a composite step method, designed for equality constrained optimization with partial differential equations. Focus is laid on the construction of a globalization scheme, which is based on cubic regularization of the objective and an affine covariant damped Newton method for feasibility. We show finite termination of the inner loop and fast local convergence of the algorithm. We discuss preconditioning strategies for the iterative solution of the arising linear systems with projected conjugate gradient. Numerical results are shown for optimal control problems subject to a nonlinear heat equation and subject to nonlinear elastic equations arising from an implant design problem in craniofacial surgery. Y1 - 2017 U6 - https://doi.org/10.1080/10556788.2016.1241783 VL - 32 IS - 5 SP - 1132 EP - 1161 ER - TY - JOUR A1 - Bienefeld, Kaspar A1 - Zautke, Fred A1 - Gupta, Pooja T1 - A novel method for undisturbed long-term observation of the honey bee (Apis mellifera) behaviour – illustrated by the hygienic behaviour towards Varroa infestation JF - Journal of Apicultural Research Y1 - 2016 VL - 54(5) SP - 541 EP - 547 ER - TY - JOUR A1 - Spötter, Andreas A1 - Gupta, Pooja A1 - Mayer, Manfred A1 - Reinsch, Norbert A1 - Bienefeld, Kaspar T1 - Genome-wide association study of a Varroa-specific defense behavior in honeybees (Apis mellifera) JF - Journal of Heredity Y1 - 2016 VL - 107 IS - 3 SP - 220 EP - 227 ER - TY - GEN A1 - Götschel, Sebastian A1 - Maierhofer, Christiane A1 - Müller, Jan P. A1 - Rothbart, Nick A1 - Weiser, Martin T1 - Quantitative Defect Reconstruction in Active Thermography for Fiber-Reinforced Composites N2 - Carbon-fiber reinforced composites are becoming more and more important in the production of light-weight structures, e.g., in the automotive and aerospace industry. Thermography is often used for non-destructive testing of these products, especially to detect delaminations between different layers of the composite. In this presentation, we aim at methods for defect reconstruction from thermographic measurements of such carbon-fiber reinforced composites. The reconstruction results shall not only allow to locate defects, but also give a quantitative characterization of the defect properties. We discuss the simulation of the measurement process using finite element methods, as well as the experimental validation on flat bottom holes. Especially in pulse thermography, thin boundary layers with steep temperature gradients occurring at the heated surface need to be resolved. Here we use the combination of a 1D analytical solution combined with numerical solution of the remaining defect equation. We use the simulations to identify material parameters from the measurements. Finally, fast heuristics for reconstructing defect geometries are applied to the acquired data, and compared for their accuracy and utility in detecting different defects like back surface defects or delaminations. T3 - ZIB-Report - 16-13 KW - thermography KW - inverse problems KW - parameter identification KW - geometry identification KW - nondestructive testing Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-58374 UR - https://www.wcndt2016.com/portals/wcndt/bb/Th4C4.pdf SN - 1438-0064 ER - TY - GEN A1 - Götschel, Sebastian A1 - Höhne, Christian A1 - Kolkoori, Sanjeevareddy A1 - Mitzscherling, Steffen A1 - Prager, Jens A1 - Weiser, Martin T1 - Ray Tracing Boundary Value Problems: Simulation and SAFT Reconstruction for Ultrasonic Testing N2 - The application of advanced imaging techniques for the ultrasonic inspection of inhomogeneous anisotropic materials like austenitic and dissimilar welds requires information about acoustic wave propagation through the material, in particular travel times between two points in the material. Forward ray tracing is a popular approach to determine traveling paths and arrival times but is ill suited for inverse problems since a large number of rays have to be computed in order to arrive at prescribed end points. In this contribution we discuss boundary value problems for acoustic rays, where the ray path between two given points is determined by solving the eikonal equation. The implementation of such a two point boundary value ray tracer for sound field simulations through an austenitic weld is described and its efficiency as well as the obtained results are compared to those of a forward ray tracer. The results are validated by comparison with experimental results and commercially available UT simulation tools. As an application, we discuss an implementation of the method for SAFT (Synthetic Aperture Focusing Technique) reconstruction. The ray tracer calculates the required travel time through the anisotropic columnar grain structure of the austenitic weld. There, the formulation of ray tracing as a boundary value problem allows a straightforward derivation of the ray path from a given transducer position to any pixel in the reconstruction area and reduces the computational cost considerably. T3 - ZIB-Report - 16-14 KW - ray tracing KW - ODE boundary value problems KW - ultrasonics KW - nondestructive testing Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-58386 UR - https://www.wcndt2016.com/portals/wcndt/bb/Fr1H4.pdf SN - 1438-0064 ER - TY - JOUR A1 - Pomplun, Jan A1 - Burger, Sven A1 - Zschiedrich, Lin A1 - Gutsche, Philipp A1 - Schmidt, Frank T1 - Method for fast computation of angular light scattering spectra from 2D periodic arrays JF - Proc. SPIE Y1 - 2016 U6 - https://doi.org/10.1117/12.2219666 VL - 9778 SP - 977839 ER - TY - GEN A1 - Koltai, Peter A1 - Ciccotti, Giovanni A1 - Schütte, Christof T1 - On metastability and Markov state models for non-stationary molecular dynamics BT - 2016 Editor's Choice of The Journal of Chemical Physics T2 - The Journal of Chemical Physics N2 - We utilize the theory of coherent sets to build Markov state models for non- equilibrium molecular dynamical systems. Unlike for systems in equilibrium, “meta- stable” sets in the non-equilibrium case may move as time evolves. We formalize this concept by relying on the theory of coherent sets, based on this we derive finite-time non-stationary Markov state models, and illustrate the concept and its main differences to equilibrium Markov state modeling on simple, one-dimensional examples. T3 - ZIB-Report - 16-11 KW - coherent set, KW - Markov state model KW - non-equilibrium molecular dynamics KW - metastability Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57869 SN - 1438-0064 VL - 174103 ET - 145 ER - TY - JOUR A1 - Gutsche, Philipp A1 - Poulikakos, Lisa A1 - Hammerschmidt, Martin A1 - Burger, Sven A1 - Schmidt, Frank T1 - Time-harmonic optical chirality in inhomogeneous space JF - Proc. SPIE Y1 - 2016 U6 - https://doi.org/10.1117/12.2209551 VL - 9756 SP - 97560X ER - TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Weber, Marcus A1 - Schütte, Christof T1 - Finding dominant structures of nonreversible Markov processes JF - Multiscale Modeling and Simulation Y1 - 2016 U6 - https://doi.org/10.1137/15M1032272 VL - 14 IS - 4 SP - 1319 EP - 1340 ER - TY - JOUR A1 - Hammerschmidt, Martin A1 - Barth, Carlo A1 - Pomplun, Jan A1 - Burger, Sven A1 - Becker, Christiane A1 - Schmidt, Frank T1 - Reconstruction of photonic crystal geometries using a reduced basis method for nonlinear outputs JF - Proc. SPIE N2 - Maxwell solvers based on the hp-adaptive finite element method allow for accurate geometrical modeling and high numerical accuracy. These features are indispensable for the optimization of optical properties or reconstruction of parameters through inverse processes. High computational complexity prohibits the evaluation of the solution for many parameters. We present a reduced basis method (RBM) for the time-harmonic electromagnetic scattering problem allowing to compute solutions for a parameter configuration orders of magnitude faster. The RBM allows to evaluate linear and nonlinear outputs of interest like Fourier transform or the enhancement of the electromagnetic field in milliseconds. We apply the RBM to compute light-scattering off two dimensional photonic crystal structures made of silicon and reconstruct geometrical parameters. Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-58187 VL - 9756 SP - 97561R ER - TY - JOUR A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Pomplun, Jan A1 - Burger, Sven A1 - Schmidt, Frank T1 - Model order reduction for the time-harmonic Maxwell equation applied to complex nanostructures JF - Proc. SPIE N2 - Fields such as optical metrology and computational lithography require fast and efficient methods for solving the time-harmonic Maxwell's equation. Highly accurate geometrical modelling and numerical accuracy at low computational costs are a prerequisite for any simulation study of complex nano-structured photonic devices. We present a reduced basis method (RBM) for the time-harmonic electromagnetic scattering problem based on the hp-adaptive finite element solver JCMsuite capable of handling geometric and non-geometric parameter dependencies allowing for online evaluations in milliseconds. We apply the RBM to compute light-scattering at optical wavelengths of periodic arrays of fin field-effect transistors (FinFETs) where geometrical properties such as the width and height of the fin and gate can vary in a large range. Y1 - 2016 U6 - https://doi.org/10.1117/12.2212367 VL - 9742 SP - 97420M ER - TY - GEN A1 - Gutsche, Philipp A1 - Läuter, Matthias A1 - Schmidt, Frank T1 - Parameter-dependent Parallel Block Sparse Arnoldi and Döhler Algorithms on Distributed Systems N2 - We summarize the basics and first results of the analyses within our ZIB Bridge Project and give an outlook on further studies broadening the usage of hardware acceleration within the Finite Element Method (FEM) based solution of Maxwell’s equations. T3 - ZIB-Report - 16-15 KW - Generalized Eigenvalue Problem KW - Many Integrated Core Coprocessor (MIC) KW - Finite Element Method Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-58202 SN - 1438-0064 ER - TY - JOUR A1 - Hammerschmidt, Martin A1 - Herrmann, Sven A1 - Pomplun, Jan A1 - Burger, Sven A1 - Schmidt, Frank T1 - Reduced basis method for electromagnetic scattering problem: a case study for FinFETs JF - Optical and Quantum Electronics N2 - Optical 3D simulations in many-query and real-time contexts require new solution strategies. We study an adaptive, error controlled reduced basis method for solving parametrized time-harmonic optical scattering problems. Application fields are, among others, design and optimization problems of nano-optical devices as well as inverse problems for parameter reconstructions occurring e. g. in optical metrology. The reduced basis method pre- sented here relies on a finite element modeling of the scattering problem with parametrization of materials, geometries and sources. Y1 - 2016 U6 - https://doi.org/10.1007/s11082-016-0530-1 VL - 48 SP - 250 ER - TY - THES A1 - Nielsen, Adam T1 - Computation Schemes for Transfer Operators Y1 - 2016 ER - TY - THES A1 - Sikorski, Alexander T1 - PCCA+ and Its Application to Spatial Time Series Clustering Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-58769 ER - TY - GEN A1 - Bojarovski, Stefan A1 - Hege, Hans-Christian A1 - Lie, Han Cheng A1 - Weber, Marcus T1 - Topological analysis and visualization of scalar functions characterizing conformational transitions of molecules on multiple time-scales T2 - Shape Up 2015 - Exercises in Materials Geometry and Topology, 14-18 Sept. 2015, Berlin, Germany N2 - Molecular processes such as protein folding or ligand-receptor-binding can be understood by analyzing the free energy landscape. Those processes are often metastable, i.e. the molecular systems remain in basins around local minima of the free energy landscape, and in rare cases undergo gauche transitions between metastable states by passing saddle-points of this landscape. By discretizing the configuration space, this can be modeled as a discrete Markov process. One way to compute the transition rates between conformations of a molecular system is by utilizing Transition Path Theory and the concept of committor functions. A fundamental problem from the computational point of view is that many time-scales are involved, ranging from 10^(-14) sec for the fastest motion to 10^(-6) sec or more for conformation changes that cause biological effects. The goal of our work is to provide a better understanding of such transitions in configuration space on various time-scales by analyzing characteristic scalar functions topologically and geometrically. We are developing suitable visualization and interaction techniques to support our analysis. For example, we are analyzing a transition rate indicator function by computing and visualizing its Reeb graph together with the sets of molecular states corresponding to maxima of the transition rate indicator function. A particular challenge is the high dimensionality of the domain which does not allow for a straightforward visualization of the function. The computational topology approach to the analysis of the transition rate indicator functions for a molecular system allows to explore different time scales of the system by utilizing coarser or finer topological partitioning of the function. A specific goal is the development of tools for analyzing the hierarchy of these partitionings. This approach tackles the analysis of a complex and sparse dataset from a different angle than the well-known spectral analysis of Markov State Models. Y1 - 2015 ER - TY - BOOK A1 - Weiser, Martin T1 - Inside Finite Elements N2 - All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered as far as it gives insight into the construction of algorithms.Throughout the exercises a complete FE-solver for scalar 2D problems will be implemented in Matlab/Octave. Y1 - 2016 PB - De Gruyter ER - TY - JOUR A1 - Krebek, von, Larissa K. S. A1 - Achazi, Andreas J. A1 - Solleder, Marthe A1 - Weber, Marcus A1 - Paulus, Beate A1 - Schalley, Christoph A. T1 - Allosteric and Chelate Cooperativity in Divalent Crown Ether–Ammonium Complexes with Strong Binding Enhancements JF - Chem. Eur. J. Y1 - 2016 U6 - https://doi.org/10.1002/chem.201603098 N1 - Has been announced under the title: Cooperativity in Multivalent Binding: A Detailed Experimental and Theoretical Thermochemical Study of Divalent Crown Ether-Ammonium Complexes VL - 22 IS - 43 SP - 15475 EP - 15484 ER - TY - THES A1 - Fackeldey, Konstantin T1 - Crossing the Scales in Structural Mechanics and Molecular Research Y1 - 2015 ER - TY - JOUR A1 - Owhadi, Houman A1 - Scovel, Clint A1 - Sullivan, T. J. T1 - On the Brittleness of Bayesian Inference JF - SIAM Review N2 - With the advent of high-performance computing, Bayesian methods are becoming increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods can impact the making of sometimes critical decisions in increasingly complicated contexts, the sensitivity of their posterior conclusions with respect to the underlying models and prior beliefs is a pressing question to which there currently exist positive and negative answers. We report new results suggesting that, although Bayesian methods are robust when the number of possible outcomes is finite or when only a finite number of marginals of the data-generating distribution are unknown, they could be generically brittle when applied to continuous systems (and their discretizations) with finite information on the data-generating distribution. If closeness is defined in terms of the total variation (TV) metric or the matching of a finite system of generalized moments, then (1) two practitioners who use arbitrarily close models and observe the same (possibly arbitrarily large amount of) data may reach opposite conclusions; and (2) any given prior and model can be slightly perturbed to achieve any desired posterior conclusion. The mechanism causing brittleness/robustness suggests that learning and robustness are antagonistic requirements, which raises the possibility of a missing stability condition when using Bayesian inference in a continuous world under finite information. Y1 - 2015 U6 - https://doi.org/10.1137/130938633 VL - 57 IS - 4 SP - 566 EP - 582 ER - TY - BOOK A1 - Sullivan, T. J. T1 - Introduction to Uncertainty Quantification Y1 - 2015 SN - 978-3-319-23394-9 U6 - https://doi.org/10.1007/978-3-319-23395-6 VL - 63 PB - Springer ER - TY - CHAP A1 - Bienefeld, Kaspar A1 - Spötter, Andreas A1 - Reinsch, Norbert A1 - Mayer, Manfred A1 - Gupta, Pooja T1 - A new approach for honeybee breeding - genomic selection T2 - 44th Apimondia International Apicultural congress, 2015. Daejeon, South Korea Y1 - 2015 ER - TY - THES A1 - Gupta, Pooja T1 - Integrating high-density marker information into the genetic evaluation of the honey bee Y1 - 2013 ER - TY - GEN A1 - Gupta, Pooja A1 - Röblitz, Susanna A1 - Krause, Carola A1 - Knaus, Petra A1 - Schütte, Christof T1 - Mathematical modeling of the Smad and Non-Smad BMP signaling pathways in context of cell density T2 - Computational Models in biology and medicine, 2013, Dresden, Germany Y1 - 2013 ER - TY - CHAP A1 - Gupta, Pooja A1 - Krause, Carola A1 - Rikeit, Paul A1 - Röblitz, Susanna A1 - Knaus, Petra A1 - Schütte, Christof T1 - Modeling of the BMP mediated co-regulation of the Smad and Non-Smad pathways in the context of cell density T2 - 10th International BMP conference, 2014, Berlin, Germany Y1 - 2014 ER - TY - THES A1 - Brust, Lisa T1 - Moleküldynamik-Simulation via eines Faltungsansatzes im Potential Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65198 ER - TY - THES A1 - Röhl, Susanne T1 - Computing the minimal rebinding effect for nonreversible processes Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65203 ER - TY - THES A1 - Röhm, Jonas T1 - Non-Negative Matrix Factorization for Raman Data Spectral Analysis Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65217 ER - TY - THES A1 - Grever, Andreas T1 - Estimating Missing Entries of a Partial Mean First Passage Time Matrix Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65228 ER - TY - THES A1 - Solleder, Marthe T1 - Molecular Dynamics Simulations : What is the Effect of a Spin Probe on the Drug Loading of a Nanocarrier Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-65239 ER - TY - THES A1 - Schöpke, Jessica T1 - Korrelation für lineare und nichtlineare Zusammenhänge Y1 - 2015 ER - TY - THES A1 - Tumescheit, Charlotte T1 - Using Birkhoff-von Neumann und Sinkhorn Algorithm to Find Dominating Cycles Y1 - 2014 ER - 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 - TY - JOUR A1 - Ahiboz, Doguscan A1 - Andresen, Elina A1 - Manley, Phillip A1 - Resch-Genger, Ute A1 - Würth, Christian A1 - Becker, Christiane T1 - Metasurface-Enhanced Photon Upconversion upon 1550 nm Excitation JF - Adv. Opt. Mater. Y1 - 2021 U6 - https://doi.org/10.1002/adom.202101285 VL - 9 SP - 2101285 ER - TY - JOUR A1 - Martens, Kevin A1 - Funck, Timon A1 - Santiago, Eva Y. A1 - Govorov, Alexander O. A1 - Burger, Sven A1 - Liedl, Tim T1 - Onset of Chirality in Plasmonic Meta-Molecules and Dielectric Coupling JF - ACS Nano Y1 - 2022 U6 - https://doi.org/10.1021/acsnano.2c04729 VL - 16 SP - 16143 ER -