2022, Hirsch, Christian, Jahnel, Benedikt, Muirhead, Stephen

We prove the sharpness of the percolation phase transition for a class of Cox percolation models, i.e., models of continuum percolation in a random environment. The key requirements are that the environment has a finite range of dependence and satisfies a local boundedness condition, however the FKG inequality need not hold. The proof combines the OSSS inequality with a coarse-graining construction.

2008, Beyer, Matthias, Lucas, D., Kussin, J., Schütz, P.

[no abstract available]

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.

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.

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

[no abstract available]

2012, Bennewitz, Roland

[no abstract available]

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.

2008, Benson, Dave, Iyengar, Srikanth B., Krause, Henning

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context. Others include new proofs of the tensor product theorem and of the classification of thick subcategories of the finitely generated modules which avoid the use of cyclic shifted subgroups. Along the way we establish similar classifications for differential graded modules over graded polynomial rings, and over graded exterior algebras.

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.