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- ItemTransient radiation from a circular string of dipoles excited at superluminal velocity(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Arkhipov, Rostislav M.; Arkhipov, Mikhail V.; Babushkin, Ihar; Tolmachev, Yurii A.This paper discusses the features of transient radiation from periodic one-dimensional resonant medium excited by ultrashort pulse. The case of circular geometry is considered for the harmonic distribution of the density of the particles along the circle. It is shown that a new frequency component arises in the spectrum of the scattered radiation in addition to the resonance frequency of medium. The new frequency appears both in the case of linear and nonlinear interaction, its value depends on the velocity of excitation pulse propagation and on the period of spatial modulation. In addition, the case when excitation moves at superluminal velocity and Cherenkov radiation arises is also studied.
- ItemEfficient coupling of inhomogeneous current spreading and dynamic electro-optical models for broad-area edge-emitting semiconductor devices(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Radziunas, Mindaugas; Zeghuzi, Anissa; Fuhrmann, Jürgen; Koprucki, Thomas; Wünsche, Hans-Jürgen; Wenzel, Hans; Bandelow, UweWe extend a 2 (space) + 1 (time)-dimensional traveling wave model for broad-area edgeemitting semiconductor lasers by a model for inhomogeneous current spreading from the contact to the active zone of the laser. To speedup the performance of the device simulations, we suggest and discuss several approximations of the inhomogeneous current density in the active zone.
- ItemChirped photonic crystal for spatially filtered optical feedback to a broad-area laser(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Brée, Carsten; Gailevicius, Darius; Purlys, Vytautas; Werner, Guillermo Garre; Staliunas, Kestutis; Rathsfeld, Andreas; Schmidt, Gunther; Radziunas, MindaugasWe derive and analyze an efficient model for reinjection of spatially filtered optical feedback from an external resonator to a broad area, edge emitting semiconductor laser diode. Spatial filtering is achieved by a chirped photonic crystal, with variable periodicity along the optical axis and negligible resonant backscattering. The optimal chirp is obtained from a genetic algorithm, which yields solutions that are robust against perturbations. Extensive numerical simulations of the composite system with our optoelectronic solver indicate that spatially filtered reinjection enhances lower-order transversal optical modes in the laser diode and, consequently, improves the spatial beam quality.
- ItemA review of variational multiscale methods for the simulation of turbulent incompressible flows(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Ahmed, Naveed; Rebollo, Tomás Chacón; John, Volker; Rubino, SamueleVarious realizations of variational multiscale (VMS) methods for simulating turbulent incompressible flows have been proposed in the past fifteen years. All of these realizations obey the basic principles of VMS methods: They are based on the variational formulation of the incompressible Navier-Stokes equations and the scale separation is defined by projections. However, apart from these common basic features, the various VMS methods look quite different. In this review, the derivation of the different VMS methods is presented in some detail and their relation among each other and also to other discretizations is discussed. Another emphasis consists in giving an overview about known results from the numerical analysis of the VMS methods. A few results are presented in detail to highlight the used mathematical tools. Furthermore, the literature presenting numerical studies with the VMS methods is surveyed and the obtained results are summarized.
- ItemPoint contacts and boundary triples(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Lotoreichik, Vladimir; Neidhardt, Hagen; Popov, Igor Yu.We suggest an abstract approach for point contact problems in the framework of boundary triples. Using this approach we obtain the perturbation series for a simple eigenvalue in the discrete spectrum of the model self-adjoint extension with weak point coupling.
- ItemOn the structure of the quasiconvex hull in planar elasticity(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Heinz, SebastianLet K and L be compact sets of real 2x2 matrices with positive determinant. Suppose that both sets are frame invariant, meaning invariant under the left action of the special orthogonal group. Then we give an algebraic characterization for K and L to be incompatible for homogeneous gradient Young measures. This result permits a simplified characterization of the quasiconvex hull and the rank-one convex hull in planar elasticity.
- ItemTopology optimization subject to additive manufacturing constraints(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Ebeling-Rump, Moritz; Hömberg, Dietmar; Lasarzik, Robert; Petzold, ThomasIn Topology Optimization the goal is to find the ideal material distribution in a domain subject to external forces. The structure is optimal if it has the highest possible stiffness. A volume constraint ensures filigree structures, which are regulated via a Ginzburg-Landau term. During 3D Printing overhangs lead to instabilities, which have only been tackled unsatisfactorily. The novel idea is to incorporate an Additive Manufacturing Constraint into the phase field method. A rigorous analysis proves the existence of a solution and leads to first order necessary optimality conditions. With an Allen-Cahn interface propagation the optimization problem is solved iteratively. At a low computational cost the Additive Manufacturing Constraint brings about support structures, which can be fine tuned according to engineering demands. Stability during 3D Printing is assured, which solves a common Additive Manufacturing problem.
- ItemGradient bounds and rigidity results for singular, degenerate, anisotropic partial differential equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Cozzi, Matteo; Farina, Alberto; Valdinoci, EnricoWe consider the Wulff-type energy functional where B is positive, monotone and convex, and H is positive homogeneous of degree 1. The critical points of this functional satisfy a possibly singular or degenerate, quasilinear equation in an anisotropic medium. We prove that the gradient of the solution is bounded at any point by the potential F(u) and we deduce several rigidity and symmetry properties.
- ItemImage analysis and statistical inference in neuroimaging with R(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Tabelow, Karsten; Clayden, Jon D.; Lafaye de Micheaux, Pierre; Polzehl, Jörg; Schmid, Volker J.; Whitcher, BrandonR is a language and environment for statistical computing and graphics. It can be considered an alternative implementation of the S language developed in the 1970s and 1980s for data analysis and graphics (Becker and Chambers, 1984; Becker et al., 1988). The R language is part of the GNU project and offers versions that compile and run on almost every major operating system currently available. We highlight several R packages built specifically for the analysis of neuroimaging data in the context of functional MRI, diffusion tensor imaging, and dynamic contrast-enhanced MRI. We review their methodology and give an overview of their capabilities for neuroimaging. In addition we summarize some of the current activities in the area of neuroimaging software development in R.
- ItemRelating phase field and sharp interface approaches to structural topology optimization(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Blank, Luise; Farshbaf-Shaker, M. Hassan; Garcke, Harald; Styles, VanessaA phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. We also discuss how to deal with triple junctions where e.g. two materials and the void meet. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement.