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.

2018, Brée, Carsten, Gailevicius, Darius, Purlys, Vytautas, Werner, Guillermo Garre, Staliunas, Kestutis, Rathsfeld, Andreas, Schmidt, Gunther, Radziunas, Mindaugas

We 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.

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.

2012, Heinz, Sebastian

Let 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.

2017, Radziunas, Mindaugas, Zeghuzi, Anissa, Fuhrmann, Jürgen, Koprucki, Thomas, Wünsche, Hans-Jürgen, Wenzel, Hans, Bandelow, Uwe

We 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.

2012, Bennewitz, Roland

[no abstract available]

2020, Stonyakin, Fedor, Dvinskikh, Darina, Dvurechensky, Pavel, Kroshnin, Alexey, Kuznetsova, Olesya, Agafonov, Artem, Gasnikov, Alexander, Tyurin, Alexander, Uribe, Cesar A., Pasechnyuk, Dmitry, Artamonov, Sergei

We consider optimization methods for convex minimization problems under inexact information on the objective function. We introduce inexact model of the objective, which as a particular cases includes inexact oracle [19] and relative smoothness condition [43]. We analyze gradient method which uses this inexact model and obtain convergence rates for convex and strongly convex problems. To show potential applications of our general framework we consider three particular problems. The first one is clustering by electorial model introduced in [49]. The second one is approximating optimal transport distance, for which we propose a Proximal Sinkhorn algorithm. The third one is devoted to approximating optimal transport barycenter and we propose a Proximal Iterative Bregman Projections algorithm. We also illustrate the practical performance of our algorithms by numerical experiments.

2012, Wolfgang Buscher, Wolfgang Buscher, Ehlbeck, Jörg, Piechotta, Christian

[no abstract available]

2015, Ahmed, Naveed, Rebollo, Tomás Chacón, John, Volker, Rubino, Samuele

Various 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.

2020, Geiersbach, Caroline, Wollner, Winnifried

We analyze a convex stochastic optimization problem where the state is assumed to belong to the Bochner space of essentially bounded random variables with images in a reflexive and separable Banach space. For this problem, we obtain optimality conditions that are, with an appropriate model, necessary and sufficient. Additionally, the Lagrange multipliers associated with optimality conditions are integrable vector-valued functions and not only measures. A model problem is given demonstrating the application to PDE-constrained optimization under uncertainty.