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- 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.
- ItemDeath and rebirth of neural activity in sparse inhibitory networks([London] : IOP, 2017) Angulo-Garcia, David; Luccioli, Stefano; Olmi, Simona; Torcini, AlessandroInhibition is a key aspect of neural dynamics playing a fundamental role for the emergence of neural rhythms and the implementation of various information coding strategies. Inhibitory populations are present in several brain structures, and the comprehension of their dynamics is strategical for the understanding of neural processing. In this paper, we clarify the mechanisms underlying a general phenomenon present in pulse-coupled heterogeneous inhibitory networks: inhibition can induce not only suppression of neural activity, as expected, but can also promote neural re-activation. In particular, for globally coupled systems, the number of firing neurons monotonically reduces upon increasing the strength of inhibition (neuronal death). However, the random pruning of connections is able to reverse the action of inhibition, i.e. in a random sparse network a sufficiently strong synaptic strength can surprisingly promote, rather than depress, the activity of neurons (neuronal rebirth). Thus, the number of firing neurons reaches a minimum value at some intermediate synaptic strength. We show that this minimum signals a transition from a regime dominated by neurons with a higher firing activity to a phase where all neurons are effectively sub-threshold and their irregular firing is driven by current fluctuations. We explain the origin of the transition by deriving a mean field formulation of the problem able to provide the fraction of active neurons as well as the first two moments of their firing statistics. The introduction of a synaptic time scale does not modify the main aspects of the reported phenomenon. However, for sufficiently slow synapses the transition becomes dramatic, and the system passes from a perfectly regular evolution to irregular bursting dynamics. In this latter regime the model provides predictions consistent with experimental findings for a specific class of neurons, namely the medium spiny neurons in the striatum.
- ItemConvective Nozaki-Bekki holes in a long cavity OCT laser(Washington, DC : Soc., 2019) Slepneva, Svetlana; O'Shaughnessy, Ben; Vladimirov, Andrei G.; Rica, Sergio; Viktorov, Evgeny A.; Huyet, GuillaumeWe show, both experimentally and theoretically, that the loss of coherence of a long cavity optical coherence tomography (OCT) laser can be described as a transition from laminar to turbulent flows. We demonstrate that in this strongly dissipative system, the transition happens either via an absolute or a convective instability depending on the laser parameters. In the latter case, the transition occurs via formation of localised structures in the laminar regime, which trigger the formation of growing and drifting puffs of turbulence. Experimentally, we demonstrate that these turbulent bursts are seeded by appearance of Nozaki-Bekki holes, characterised by the zero field amplitude and π phase jumps. Our experimental results are supported with numerical simulations based on the delay differential equations model.
- ItemAnisotropic solid-liquid interface kinetics in silicon: An atomistically informed phase-field model(Bristol : IOP Publ., 2017) Bergmann, S.; Albe, K.; Flege, E.; Barragan-Yani, D.A.; Wagner, B.We present an atomistically informed parametrization of a phase-field model for describing the anisotropic mobility of liquid–solid interfaces in silicon. The model is derived from a consistent set of atomistic data and thus allows to directly link molecular dynamics and phase field simulations. Expressions for the free energy density, the interfacial energy and the temperature and orientation dependent interface mobility are systematically fitted to data from molecular dynamics simulations based on the Stillinger–Weber interatomic potential. The temperature-dependent interface velocity follows a Vogel–Fulcher type behavior and allows to properly account for the dynamics in the undercooled melt.
- ItemThe Turing bifurcation in network systems : collective patterns and single differentiated nodes(Berlin: Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Wolfrum, MatthiasWe study the emergence of patterns in a diffusively coupled network that undergoes a Turing instability. Our main focus is the emergence of stable solutions with a single differentiated node in systems with large and possibly irregular network topology. Based on a mean-field approach, we study the bifurcations of such solutions for varying system parameters and varying degree of the differentiated node. Such solutions appear typically before the onset of Turing instability and provide the basis for the complex scenario of multistability and hysteresis that can be observed in such systems. Moreover, we discuss the appearance of stable collective patterns and present a codimension-two bifurcation that organizes the interplay between collective patterns and patterns with single differentiated nodes
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