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Title:

Optimal elliptic regularity at the crossing of a material interface and a Neumann boundary edge

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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.

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. Minimize

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Berlin : WIAS ; Hannover : Technische Informationsbibliothek u. Universitätsbibliothek

Year of Publication:

2010

Subjects:

31.00

31.00 Minimize

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Title:

Analyticity for some operator functions from statistical quantum mechanics

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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 coeffi...

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. Minimize

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Berlin : WIAS ; Göttingen : Niedersächsische Staats- und Universitätsbibliothek ; Hannover : Technische Informationsbibliothek u. Universitätsbibliothek

Year of Publication:

2008

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31.00

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Title:

Eigensolutions of the Wigner-Eisenbud problem for a cylindrical nanowire within finite volume method

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We present a finite volume method for computing a representative range of eigenvalues and eigenvectors of the Schrödinger operator on a three dimensional cylindrically symmetric bounded domain with mixed boundary conditions. More specifically, we deal with a semiconductor nanowire which consists of a dominant host material and contains heterostr...

We present a finite volume method for computing a representative range of eigenvalues and eigenvectors of the Schrödinger operator on a three dimensional cylindrically symmetric bounded domain with mixed boundary conditions. More specifically, we deal with a semiconductor nanowire which consists of a dominant host material and contains heterostructure features such as double-barriers or quantum dots. The three dimensional Schrödinger operator is reduced to a family of two dimensional Schrödinger operators distinguished by a centrifugal potential. Ultimately, we numerically treat them by means of a finite volume method. We consider a uniform, boundary conforming Delaunay mesh, which additionally conforms to the material interfaces. The 1/r singularity is eliminated by approximating r at the vertexes of the Voronoi boxes. We study how the anisotropy of the effective mass tensor acts on the uniform approximation of the first K eigenvalues and eigenvectors and their sequential arrangement. There exists an optimal uniform Delaunay discretization with matching anisotropy. This anisotropic discretization yields best accuracy also in the presence of a mildly varying scattering potential, shown exemplarily for a nanowire resonant tunneling diode. For potentials with 1/r singularity one retrieves the theoretically established first order convergence, while the second order convergence is recovered only on uniform grids with an anisotropy correction. Minimize

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Berlin : WIAS ; Hannover : Technische Informationsbibliothek u. Universitätsbibliothek ; Göttingen : Niedersächsische Staats- und Universitätsbibliothek

Year of Publication:

2012

Subjects:

31.00

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DDC:

510 Mathematics *(computed)*

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Title:

Direct computation of elliptic singularities across anisotropic, multi-material edges

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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 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. Minimize

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Berlin : WIAS ; Göttingen : Niedersächsische Staats- und Universitätsbibliothek ; Hannover : Technische Informationsbibliothek u. Universitätsbibliothek

Year of Publication:

2009

Subjects:

31.00

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Title:

Modeling and Simulation of Strained Quantum Wells in Semiconductor Lasers

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-09-19

Source:

http://www.wias-berlin.de/publications/preprints/582/wias_preprints_582.pdf

http://www.wias-berlin.de/publications/preprints/582/wias_preprints_582.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Modeling and Simulation of Strained Quantum Wells in Semiconductor Lasers

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-09-19

Source:

http://www.wias-berlin.de/publications/preprints/582/wias_preprints_582.ps

http://www.wias-berlin.de/publications/preprints/582/wias_preprints_582.ps Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Classical Solutions of Quasilinear Parabolic Systems on Two Dimensional Domains

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Using a classical theorem of Sobolevskii on equations of parabolic type in a Banach space and recently obtained results on elliptic operators with discontinuous coefficients including mixed boundary conditions we prove that quasilinear parabolic systems in diagonal form admit a local, classical solution in the space of p--integrable functions, f...

Using a classical theorem of Sobolevskii on equations of parabolic type in a Banach space and recently obtained results on elliptic operators with discontinuous coefficients including mixed boundary conditions we prove that quasilinear parabolic systems in diagonal form admit a local, classical solution in the space of p--integrable functions, for some p > 1, over a bounded two dimensional space domain. As applications we have in mind systems of reaction diffusion equations, e.g. van Roosbroeck's system. The treatment of such equations in a space of integrable functions enables us to define the normal component of the flow across any part of the Dirichlet boundary by Gauss' theorem. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-17

Source:

http://www.ma.utexas.edu/mp_arc/e/02-399.ps

http://www.ma.utexas.edu/mp_arc/e/02-399.ps Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Modeling and Simulation of Strained Quantum Wells in Semiconductor Lasers

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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 calcu...

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. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-17

Source:

http://www.wias-berlin.de/publications/preprints/582/document.ps

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text

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en

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Title:

About A One-Dimensional Stationary Schrödinger-Poisson System With Kohn-Sham Potential

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The stationary Schrödinger-Poisson system with a self-consistent effective Kohn-Sham potential is a system of PDEs for the electrostatic potential and the envelopes of wave functions defining the quantum mechanical carrier densities in a semiconductor nanostructure. We regard both Poisson's and Schrödinger's equation with mixed boundary conditio...

The stationary Schrödinger-Poisson system with a self-consistent effective Kohn-Sham potential is a system of PDEs for the electrostatic potential and the envelopes of wave functions defining the quantum mechanical carrier densities in a semiconductor nanostructure. We regard both Poisson's and Schrödinger's equation with mixed boundary conditions and discontinuous coefficients. Without an exchange correlation potential the Schrödinger-Poisson system is a nonlinear Poisson equation in the dual of a Sobolev space which is determined by the boundary conditions imposed on the electrostatic potential. The nonlinear Poisson operator involved is strongly monotone and boundedly Lipschitz continuous, hence the operator equation has a unique solution. The proof rests upon the following property: the quantum mechanical carrier density operator depending on the potential of the defining Schrödinger operator is antimonotone and boundedly Lipschitz continuous. The solution of the Schrödinger-Poisson system. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-01-21

Source:

http://www.wias-berlin.de/WIAS_publ_preprints_nr368.PS

http://www.wias-berlin.de/WIAS_publ_preprints_nr368.PS Minimize

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text

Language:

en

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Title:

On Stationary Schrödinger-Poisson Equations Modelling An Electron Gas With Reduced Dimension

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. We regard the Schrodinger--Poisson system arising from the modelling of an electron gas with reduced dimension in a bounded up to three-- dimensional domain and establish the method of steepest descent. The electrostatic potentials of the iteration scheme will converge uniformly on the spatial domain. To get this result we investigate the Schr...

. We regard the Schrodinger--Poisson system arising from the modelling of an electron gas with reduced dimension in a bounded up to three-- dimensional domain and establish the method of steepest descent. The electrostatic potentials of the iteration scheme will converge uniformly on the spatial domain. To get this result we investigate the Schrodinger operator, the Fermi level and the quantum mechanical electron density operator for square integrable electrostatic potentials. On bounded sets of potentials the Fermi level is continuous and bounded, and the electron density operator is monotone and Lipschitz continuous. --- As a tool we develop a Riesz--Dunford functional calculus for semibounded self--adjoint operators using paths of integration which enclose a real half axis. Institut fur Angewandte Analysis und Stochastik Mohrenstraße 39 D--10117 Berlin Germany Fax: + 49 30 2004975 E--mail: preprint@iaas-berlin.d400.de 1991 Mathematics Subject Classification. 35J05/10/20/60/65, 35P15. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-12

Source:

http://www.wias-berlin.de/WIAS_publ_preprints_nr66.PS

http://www.wias-berlin.de/WIAS_publ_preprints_nr66.PS Minimize

Document Type:

text

Language:

en

Subjects:

2 HANS--CHRISTOPH KAISER AND JOACHIM REHBERG On Stationary Schrodinger--Poisson Equations Modelling

2 HANS--CHRISTOPH KAISER AND JOACHIM REHBERG On Stationary Schrodinger--Poisson Equations Modelling Minimize

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