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- ItemMode competition in broad-ridge-waveguide lasers(Bristol : IOP Publ., 2020) Koester, J.-P.; Putz, A.; Wenzel, H.; Wünsche, H.-J.; Radziunas, M.; Stephan, H.; Wilkens, M.; Zeghuzi, A.; Knigge, A.The lateral brightness achievable with high-power GaAs-based laser diodes having long and broad waveguides is commonly regarded to be limited by the onset of higher-order lateral modes. For the study of the lateral-mode competition two complementary simulation tools are applied, representing different classes of approximations. The first tool bases on a completely incoherent superposition of mode intensities and disregards longitudinal effects like spatial hole burning, whereas the second tool relies on a simplified carrier transport and current flow. Both tools yield agreeing power-current characteristics that fit the data measured for 5-23 µm wide ridges. Also, a similarly good qualitative conformance of the near and far fields is found. However, the threshold of individual modes, the partition of power between them at a given current, and details of the near and far fields show differences. These differences are the consequence of a high sensitivity of the mode competition to details of the models and of the device structure. Nevertheless, it can be concluded concordantly that the brightness rises with increasing ridge width irrespective of the onset of more and more lateral modes. The lateral brightness W mm-1at 10 MW cm-2 power density on the front facet of the investigated laser with widest ridge (23 µm) is comparable with best values known from much wider broad-area lasers. In addition, we show that one of the simulation tools is able to predict beam steering and coherent beam coupling without introducing any phenomenological coupling coefficient or asymmetries. © 2020 The Author(s). Published by IOP Publishing Ltd.
- ItemAnalysis and simulations for a phase-field fracture model at finite strains based on modified invariants(Berlin : Wiley-VCH, 2020) Thomas, Marita; Bilgen, Carola; Weinberg, KerstinPhase-field models have already been proven to predict complex fracture patterns for brittle fracture at small strains. In this paper we discuss a model for phase-field fracture at finite deformations in more detail. Among the identification of crack location and projection of crack growth the numerical stability is one of the main challenges in solid mechanics. Here we present a phase-field model at finite strains, which takes into account the anisotropy of damage by applying an anisotropic split of the modified invariants of the right Cauchy-Green strain tensor. We introduce a suitable weak notion of solution that also allows for a spatial and temporal discretization of the model. In this framework we study the existence of solutions and we show that the time-discrete solutions converge in a weak sense to a solution of the time-continuous formulation of the model. Numerical examples in two and three space dimensions illustrate the range of validity of the analytical results.
- ItemExperimental proof of Joule heating-induced switched-back regions in OLEDs(London : Nature Publishing Group, 2020) Kirch, Anton; Fische, Axel; Liero, Matthias; Fuhrmann, Jürgen; Glitzky, Annegret; Reineke, SebastianOrganic light-emitting diodes (OLEDs) have become a major pixel technology in the display sector, with products spanning the entire range of current panel sizes. The ability to freely scale the active area to large and random surfaces paired with flexible substrates provides additional application scenarios for OLEDs in the general lighting, automotive, and signage sectors. These applications require higher brightness and, thus, current density operation compared to the specifications needed for general displays. As extended transparent electrodes pose a significant ohmic resistance, OLEDs suffering from Joule self-heating exhibit spatial inhomogeneities in electrical potential, current density, and hence luminance. In this article, we provide experimental proof of the theoretical prediction that OLEDs will display regions of decreasing luminance with increasing driving current. With a two-dimensional OLED model, we can conclude that these regions are switched back locally in voltage as well as current due to insufficient lateral thermal coupling. Experimentally, we demonstrate this effect in lab-scale devices and derive that it becomes more severe with increasing pixel size, which implies its significance for large-area, high-brightness use cases of OLEDs. Equally, these non-linear switching effects cannot be ignored with respect to the long-term operation and stability of OLEDs; in particular, they might be important for the understanding of sudden-death scenarios. © 2020, The Author(s).
- ItemDensity of convex intersections and applications(London : Royal Society, 2017) Hintermüller, M.; Rautenberg, C.N.; Rösel, S.In this paper, we address density properties of intersections of convex sets in several function spaces. Using the concept of Γ-convergence, it is shown in a general framework, how these density issues naturally arise from the regularization, discretization or dualization of constrained optimization problems and from perturbed variational inequalities. A variety of density results (and counterexamples) for pointwise constraints in Sobolev spaces are presented and the corresponding regularity requirements on the upper bound are identified. The results are further discussed in the context of finite-element discretizations of sets associated with convex constraints. Finally, two applications are provided, which include elasto-plasticity and image restoration problems.
- ItemRobust homoclinic orbits in planar systems with Preisach hysteresis operator(Bristol : IOP Publ., 2016) Pimenov, Alexander; Rachinskii, DmitriiWe construct examples of robust homoclinic orbits for systems of ordinary differential equations coupled with the Preisach hysteresis operator. Existence of such orbits is demonstrated for the first time. We discuss a generic mechanism that creates robust homoclinic orbits and a method for finding them. An example of a homoclinic orbit in a population dynamics model with hysteretic response of the prey to variations of the predator is studied numerically.
- ItemCompact high order finite difference schemes for linear Schrödinger problems on non-uniform meshes(Berlin: Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Radziunas, Mindaugas; Čiegis, Raimondas; Mirinavičius, AleksasIn the present paper a general technique is developed for construction of compact high-order finite difference schemes to approximate Schrödinger problems on nonuniform meshes. Conservation of the finite difference schemes is investigated. Discrete transparent boundary conditions are constructed for the given high-order finite difference scheme. The same technique is applied to construct compact high-order approximations of the Robin and Szeftel type boundary conditions. Results of computational experiments are presented
- ItemScattering of time harmonic electromagnetic plane waves by perfectly conducting diffraction gratings(Berlin: Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Hu, Guanghui; Rathsfeld, AndreasConsider scattering of time-harmonic lectromagnetic plane waves by a doubly periodic surface in R^3. The medium above the surface is supposed to be homogeneous and isotropic with a constant dielectric coefficient, while below is a perfectly conducting material. This paper is concerned with the existence of quasiperiodic solutions for any frequency of incidence. Based on an equivalent variational formulation established by the mortar technique of Nitsche, we verify the existence of solutions for a broad class of incident waves including plane waves, under the assumption that the grating profile is a Lipschitz biperiodic surface. Our solvability result covers the resonance case where a Rayleigh frequency is allowed. Non-uniqueness examples are also presented in the resonance case and the TE or TM polarization case for classical gratings.
- ItemOperation mechanism of high performance organic permeable base transistors with an insulated and perforated base electrode(Melville, NY : American Inst. of Physics, 2016) Kaschura, Felix; Fischer, Axel; Klinger, Markus P.; Doan, Duy Hai; Koprucki, Thomas; Glitzky, Annegret; Kasemann, Daniel; Widmer, Johannes; Leo, KarlThe organic permeable base transistor is a vertical transistor architecture that enables high performance while maintaining a simple low-resolution fabrication. It has been argued that the charge transport through the nano-sized openings of the central base electrode limits the performance. Here, we demonstrate by using 3D drift-diffusion simulations that this is not the case in the relevant operation range. At low current densities, the applied base potential controls the number of charges that can pass through an opening and the opening is the current limiting factor. However, at higher current densities, charges accumulate within the openings and in front of the base insulation, allowing for an efficient lateral transport of charges towards the next opening. The on-state in the current-voltage characteristics reaches the maximum possible current given by space charge limited current transport through the intrinsic semiconductor layers. Thus, even a small effective area of the openings can drive huge current densities, and further device optimization has to focus on reducing the intrinsic layer thickness to a minimum.
- ItemInfluence of cell shape, inhomogeneities and diffusion barriers in cell polarization models(Philadelphia, Pa. : IOP Publ., 2015) Giese, Wolfgang; Eigel, Martin; Westerheide, Sebastian; Engwer, Christian; Klipp, EddaIn silico experiments bear the potential for further understanding of biological transport processes by allowing a systematic modification of any spatial property and providing immediate simulation results. Cell polarization and spatial reorganization of membrane proteins are fundamental for cell division, chemotaxis and morphogenesis. We chose the yeast Saccharomyces cerevisiae as an exemplary model system which entails the shuttling of small Rho GTPases such as Cdc42 and Rho, between an active membrane-bound form and an inactive cytosolic form. We used partial differential equations to describe the membrane-cytosol shuttling of proteins. In this study, a consistent extension of a class of 1D reaction-diffusion systems into higher space dimensions is suggested. The membrane is modeled as a thin layer to allow for lateral diffusion and the cytosol is modeled as an enclosed volume. Two well-known polarization mechanisms were considered. One shows the classical Turing-instability patterns, the other exhibits wave-pinning dynamics. For both models, we investigated how cell shape and diffusion barriers like septin structures or bud scars influence the formation of signaling molecule clusters and subsequent polarization. An extensive set of in silico experiments with different modeling hypotheses illustrated the dependence of cell polarization models on local membrane curvature, cell size and inhomogeneities on the membrane and in the cytosol. In particular, the results of our computer simulations suggested that for both mechanisms, local diffusion barriers on the membrane facilitate Rho GTPase aggregation, while diffusion barriers in the cytosol and cell protrusions limit spontaneous molecule aggregations of active Rho GTPase locally.
- ItemMaximally dissipative solutions for incompressible fluid dynamics(Cham (ZG) : Springer International Publishing AG, 2021) Lasarzik, RobertWe introduce the new concept of maximally dissipative solutions for a general class of isothermal GENERIC systems. Under certain assumptions, we show that maximally dissipative solutions are well-posed as long as the bigger class of dissipative solutions is non-empty. Applying this result to the Navier–Stokes and Euler equations, we infer global well-posedness of maximally dissipative solutions for these systems. The concept of maximally dissipative solutions coincides with the concept of weak solutions as long as the weak solutions inherits enough regularity to be unique.