TY - JOUR A1 - Becker, Fabian A1 - Djurdjevac Conrad, Natasa A1 - Eser, Raphael A. A1 - Helfmann, Luzie A1 - Schütt, Brigitta A1 - Schütte, Christof A1 - Zonker, Johannes T1 - The Furnace and the Goat—A spatio-temporal model of the fuelwood requirement for iron metallurgy on Elba Island, 4th century BCE to 2nd century CE JF - PLOS ONE Y1 - 2020 UR - https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0241133 U6 - https://doi.org/10.1371/journal.pone.0241133 VL - 15 SP - 1 EP - 37 PB - Public Library of Science ER - TY - JOUR A1 - Götschel, Sebastian A1 - Schiela, Anton A1 - Weiser, Martin T1 - Kaskade 7 - a Flexible Finite Element Toolbox JF - Computers and Mathematics with Applications N2 - Kaskade 7 is a finite element toolbox for the solution of stationary or transient systems of partial differential equations, aimed at supporting application-oriented research in numerical analysis and scientific computing. The library is written in C++ and is based on the \textsc{Dune} interface. The code is independent of spatial dimension and works with different grid managers. An important feature is the mix-and-match approach to discretizing systems of PDEs with different ansatz and test spaces for all variables. We describe the mathematical concepts behind the library as well as its structure, illustrating its use at several examples on the way. Y1 - 2021 U6 - https://doi.org/10.1016/j.camwa.2020.02.011 VL - 81 SP - 444 EP - 458 ER - TY - JOUR A1 - Jäger, Klaus A1 - Tillmann, Peter A1 - Becker, Christiane T1 - Detailed illumination model for bifacial solar cells JF - Opt. Express Y1 - 2020 U6 - https://doi.org/10.1364/OE.383570 VL - 28 SP - 4751 ER - TY - JOUR A1 - Feis, Joshua A1 - Beutel, Dominik A1 - Köpfler, Julian A1 - Santiago, Xavier Garcia A1 - Rockstuhl, Carsten A1 - Wegener, Martin A1 - Fernandez-Corbaton, Ivan T1 - Helicity-Preserving Optical Cavity Modes for Enhanced Sensing of Chiral Molecules JF - Phys. Rev. Lett. Y1 - 2020 U6 - https://doi.org/10.1103/PhysRevLett.124.033201 VL - 124 SP - 033201 ER - TY - JOUR A1 - Werdehausen, Daniel A1 - Burger, Sven A1 - Staude, Isabelle A1 - Pertsch, Thomas A1 - Decker, Manuel T1 - Flat optics in high numerical aperture broadband imaging systems JF - J. Opt. Y1 - 2020 U6 - https://doi.org/10.1088/2040-8986/ab8ea2 VL - 22 SP - 065607 ER - TY - JOUR A1 - Farchmin, Nando A1 - Hammerschmidt, Martin A1 - Schneider, Philipp-Immanuel A1 - Wurm, Matthias A1 - Bodermann, Bernd A1 - Bär, Markus A1 - Heidenreich, Sebastian T1 - Efficient Bayesian inversion for shape reconstruction of lithography masks JF - J. Micro/Nanolith. MEMS MOEMS Y1 - 2020 U6 - https://doi.org/10.1117/1.JMM.19.2.024001 VL - 19 SP - 024001 ER - TY - JOUR A1 - Binkowski, Felix A1 - Betz, Fridtjof A1 - Colom, Rémi A1 - Hammerschmidt, Martin A1 - Zschiedrich, Lin A1 - Burger, Sven T1 - Quasinormal mode expansion of optical far-field quantities JF - Phys. Rev. B Y1 - 2020 U6 - https://doi.org/10.1103/PhysRevB.102.035432 VL - 102 SP - 035432 ER - TY - JOUR A1 - Musiał, Anna A1 - Żołnacz, Kinga A1 - Srocka, Nicole A1 - Kravets, Oleh A1 - Große, Jan A1 - Olszewski, Jacek A1 - Poturaj, Krzysztof A1 - Wojcik, Grzegorz A1 - Mergo, Paweł A1 - Kamil, Dybka A1 - Dyrkacz, Mariusz A1 - Dlubek, Michal A1 - Lauritsen, Kristian A1 - Bülter, Andreas A1 - Schneider, Philipp-Immanuel A1 - Zschiedrich, Lin A1 - Burger, Sven A1 - Rodt, Sven A1 - Urbanczyk, Wacław A1 - Sek, Grzegorz A1 - Reitzenstein, Stephan T1 - Plug&play fibre-coupled 73 kHz single-photon source operating in the telecom O-band JF - Adv. Quantum Technol. Y1 - 2020 U6 - https://doi.org/10.1002/qute.202000018 VL - 3 SP - 2000018 ER - TY - JOUR A1 - Colom, Rémi A1 - Stout, Brian A1 - Bonod, Nicolas T1 - Modal Expansion of the Impulse Response Function for Predicting the Time Dynamics of Open Optical Cavities JF - arXiv Y1 - 2020 ER - TY - BOOK A1 - Reuter, Bernhard T1 - Generalisierte Markov-Modellierung N2 - Markov State Models (MSM) sind der Goldstandard zur Modellierung biomolekularer Dynamik, da sie die Identifizierung und Analyse metastabiler Zustände ermöglichen. Die robuste Perron-Cluster-Cluster-Analyse (PCCA+) ist ein verbreiteter Spectral-Clustering-Algorithmus, der für das Clustering hochdimensionaler MSM verwendet wird. Da die PCCA+ auf reversible Prozesse beschränkt ist, wird sie zur Generalisierten PCCA+ (G-PCCA) verallgemeinert, die geeignet ist, nichtreversible Prozesse aufzuklären. Bernhard Reuter untersucht hier mittels G-PCCA die nichtthermischen Auswirkungen von Mikrowellen auf die Proteindynamik. Dazu führt er molekulardynamische Nichtgleichgewichtssimulationen des Amyloid-β-(1–40)-Peptids durch und modelliert diese. Y1 - 2020 SN - 978-3-658-29711-4 U6 - https://doi.org/10.1007/978-3-658-29712-1 PB - Springer Spektrum, Wiesbaden ER - TY - THES A1 - Wulkow, Hanna T1 - Regularization of Elliptic Partial Differential Equations using Neural Networks N2 - This thesis presents a method for interpolating data using a neural network. The data is sparse and perturbed and is used as training data for a small neural network. For severely perturbed data, the network does not manage to find a smooth interpolation. But as the data resembles the solution to the one-dimensional and time-independent heat equation, the weak form of this PDE and subsequently its functional can be written down. If the functional is minimized, a solution to the weak form of the heat equation is found. The functional is now added to the traditional loss function of a neural network, the mean squared error between the network prediction and the given data, in order to smooth out fluctuations and interpolate between distanced grid points. This way, the network minimizes both the mean squared error and the functional, resulting in a smoother curve that can be used to predict u(x) for any grid point x. KW - elliptic partial differential equations KW - neural networks Y1 - 2020 ER -