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Numerical Analysis and Computation Commons™

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2011

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Articles 31 - 39 of 39

Full-Text Articles in Numerical Analysis and Computation

Quantum Mechanical Model Of The Hydrogen Atom, Andres Ortiz^, Snehanshu Saha* Mar 2011

Quantum Mechanical Model Of The Hydrogen Atom, Andres Ortiz^, Snehanshu Saha*

COURI Symposium Abstracts, Spring 2011

The quantum mechanical wave function of an object under a certain potential is determined by the Schrödinger equation. It is known that the latter equation can be solved analytically only for a finite number of distinct potentials, being a Coulomb potential one of them. For an electron in a hydrogen atom, we analytically find the angular parts of its wave function by the usual method. Under the appropriate change of variable, the radial part of the equation is turned into a Legendre differential equation whose solutions are Legendre polynomials. Using finite difference method and shooting method taking into account physically …

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Complete Characterizations Of Local Weak Sharp Minima With Applications To Semi-Infinite Optimization And Complementarity, Boris S. Mordukhovich, Naihua Xiu, Jinchuan Zhou Mar 2011

Complete Characterizations Of Local Weak Sharp Minima With Applications To Semi-Infinite Optimization And Complementarity, Boris S. Mordukhovich, Naihua Xiu, Jinchuan Zhou

Mathematics Research Reports

In this paper we identify a favorable class of nonsmooth functions for which local weak sharp minima can be completely characterized in terms of normal cones and subdifferentials, or tangent cones and subderivatives, or their mixture in finite-dimensional spaces. The results obtained not only significantly extend previous ones in the literature, but also allow us to provide new types of criteria for local weak sharpness. Applications of the developed theory are given to semi-infinite programming and to semi-infinite complementarity problems.

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Waves In Microstructured Solids: A Unified Viewpoint Of Modelling, Arkadi Berezovski, Juri Engelbrecht, Mihhail Berezovski Mar 2011

Waves In Microstructured Solids: A Unified Viewpoint Of Modelling, Arkadi Berezovski, Juri Engelbrecht, Mihhail Berezovski

Publications

The basic ideas for describing the dispersive wave motion in microstructured solids are discussed in the one-dimensional setting because then the differences between various microstructure models are clearly visible. An overview of models demonstrates a variety of approaches, but the consistent structure of the theory is best considered from the unified viewpoint of internal variables. It is shown that the unification of microstructure models can be achieved using the concept of dual internal variables.

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On The Stability Of A Microstructure Model, Mihhail Berezovski, Arkadi Berezovski Feb 2011

On The Stability Of A Microstructure Model, Mihhail Berezovski, Arkadi Berezovski

Publications

The asymptotic stability of solutions of the Mindlin-type microstructure model for solids is analyzed in the paper. It is shown that short waves are asymptotically stable even in the case of a weakly non-convex free energy dependence on microdeformation.

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Modeling Diverse Physics Of Nanoparticle Self-Assembly In Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner Jan 2011

Modeling Diverse Physics Of Nanoparticle Self-Assembly In Pulsed Laser-Irradiated Metallic Films, Mikhail Khenner

Mathematics Faculty Publications

Presents physics behind dewetting of thin liquid films and mathematical/computational modeling tools (Educational/Research presentation for senior physics majors).

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Stability Of A Strongly Anisotropic Thin Epitaxial Film In A Wetting Interaction With Elastic Substrate, Mikhail Khenner, Wondimu T. Tekalign, Margo S. Levine Jan 2011

Stability Of A Strongly Anisotropic Thin Epitaxial Film In A Wetting Interaction With Elastic Substrate, Mikhail Khenner, Wondimu T. Tekalign, Margo S. Levine

Mathematics Faculty Publications

The linear dispersion relation for longwave surface perturbations, as derived by Levine et al. Phys. Rev. B 75, 205312 (2007) is extended to include a smooth surface energy anisotropy function with a variable anisotropy strength (from weak to strong, such that sharp corners and slightly curved facets occur on the corresponding Wulff shape). Through detailed parametric studies it is shown that a combination of a wetting interaction and strong anisotropy, and even a wetting interaction alone results in complicated linear stability characteristics of strained and unstrained films.

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Stability Of A Strongly Anisotropic Thin Epitaxial Film In A Wetting Interaction With Elastic Substrate, Mikhail Khenner, Wondimu Tekalign, Margo Levine Jan 2011

Stability Of A Strongly Anisotropic Thin Epitaxial Film In A Wetting Interaction With Elastic Substrate, Mikhail Khenner, Wondimu Tekalign, Margo Levine

Mathematics Faculty Publications

The linear dispersion relation for longwave surface perturbations, as derived by Levine et al. Phys. Rev. B 75, 205312 (2007) is extended to include a smooth surface energy anisotropy function with a variable anisotropy strength (from weak to strong, such that sharp corners and slightly curved facets occur on the corresponding Wulff shape). Through detailed parametric studies it is shown that a combination of a wetting interaction and strong anisotropy, and even a wetting interaction alone results in complicated linear stability characteristics of strained and unstrained films.

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Dispersive Wave Equations For Solids With Microstructure, A. Berezovski, Juri Engelbrecht, Mihhail Berezovski Jan 2011

Dispersive Wave Equations For Solids With Microstructure, A. Berezovski, Juri Engelbrecht, Mihhail Berezovski

Publications

The dispersive wave motion in solids with microstructure is considered in the one-dimensional setting in order to understand better the mechanism of dispersion. It is shown that the variety of dispersive wave propagation models derived by homogenization, continualisation, and generalization of continuum mechanics can be unified in the framework of dual internal variables theory.

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Acceleration Techniques By Post-Processing Of Numerical Solutions Of The Hammerstein Equation, Khomsan Neamprem, Hideaki Kaneko Jan 2011

Acceleration Techniques By Post-Processing Of Numerical Solutions Of The Hammerstein Equation, Khomsan Neamprem, Hideaki Kaneko

Mathematics & Statistics Faculty Publications

No abstract provided.

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