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search.filters.applied.f.access: openAccess × Author: Kaiser, Hans-Christoph × Author: Rehberg, Joachim × Start date: 2000 × DDC: 510 × Has files: Yes × Type: Text × Version: publishedVersion ×

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Now showing 1 - 7 of 7
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    Optimal elliptic Sobolev regularity near three-dimensional, multi-material Neumann vertices
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Haller-Dintelmann, Robert; Höppner, Wolfgang; Kaiser, Hans-Christoph; Rehberg, Joachim; Ziegler, Günter M.
    We study relative stability properties of different clusters of closely packed one- and two-dimensional localized peaks of the Swift-Hohenberg equation. We demonstrate the existence of a 'spatial Maxwell' point where clusters are almost equally stable, irrespective of the number of pes involved. Above (below) the Maxwell point, clusters become more (less) stable with the increase of the number of peaks
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    Direct computation of elliptic singularities across anisotropic, multi-material edges
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Haller-Dintelmann, Robert; Kaiser, Hans-Christoph; Rehberg, Joachim
    We characterise the singularities of elliptic div-grad operators at points or edges where several materials meet on a Dirichlet or Neumann part of the boundary of a two- or three-dimensional domain. Special emphasis is put on anisotropic coefficient matrices. The singularities can be computed as roots of a characteristic transcendental equation. We establish uniform bounds for the singular values for several classes of three- and fourmaterial edges. These bounds can be used to prove optimal regularity results for elliptic div-grad operators on three-dimensional, heterogeneous, polyhedral domains with mixed boundary conditions. We demonstrate this for the benchmark Lshape problem.
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    Optimal Sobolev regularity for linear second-order divergence elliptic operators occurring in real-world problems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Disser, Karoline; Kaiser, Hans-Christoph; Rehberg, Joachim
    On bounded three-dimensional domains, we consider divergence-type operators including mixed homogeneous Dirichlet and Neumann boundary conditions and discontinuous coefficient functions. We develop a geometric framework in which it is possible to prove that the operator provides an isomorphism of suitable function spaces. In particular, in these spaces, the gradient of solutions turns out to be integrable with exponent larger than the space dimension three. Relevant examples from real-world applications are provided in great detail.
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    Analyticity for some operator functions from statistical quantum mechanics : dedicated to Günter Albinus
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Hoke, Kurt; Kaiser, Hans-Christoph; Rehberg, Joachim; Albinus, Günter
    For rather general thermodynamic equilibrium distribution functions the density of a statistical ensemble of quantum mechanical particles depends analytically on the potential in the Schrödinger operator describing the quantum system. A key to the proof is that the resolvent to a power less than one of an elliptic operator with non-smooth coefficients, and mixed Dirichlet/Neumann boundary conditions on a bounded up to three-dimensional Lipschitz domain factorizes over the space of essentially bounded functions.
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    Modeling and simulation of strained quantum wells in semiconductorlasers
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2000) Bandelow, Uwe; Kaiser, Hans-Christoph; Koprucki, Thomas; Rehberg, Joachim
    A model allowing for efficiently obtaining band structure information on semiconductor Quantum Well structures will be demonstrated which is based on matrix-valued kp-Schrödinger operators. Effects such as confinement, band mixing, spin-orbit interaction and strain can be treated consistently. The impact of prominent Coulomb effects can be calculated by including the Hartree interaction via the Poisson equation and the bandgap renormalization via exchange-correlation potentials, resulting in generalized (matrix-valued) Schrödinger-Poisson systems. Band structure information enters via densities and the optical response function into comprehensive simulations of Multi Quantum Well lasers. These device simulations yield valuable information on device characteristics, including effects of carrier transport, waveguiding and heating and can be used for optimization.
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    Optimal elliptic regularity at the crossing of a material interface and a Neumann boundary edge
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Kaiser, Hans-Christoph; Rehberg, Joachim
    We investigate optimal elliptic regularity of anisotropic div-grad operators in three dimensions at the crossing of a material interface and an edge of the spatial domain on the Neumann boundary part within the scale of Sobolev spaces.
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    Monotonicity properties of the quantum mechanical particle density
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Kaiser, Hans-Christoph; Neidhardt, Hagen; Rehberg, Joachim
    An elementary proof of the anti-monotonicity of the quantum mechanical particle density with respect to the potential in the Hamiltonian is given for a large class of admissible thermodynamic equilibrium distribution functions. In particular the zero temperature case is included.