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  • 1
    Electronic Resource
    Electronic Resource
    A generalized non-muffin-tin theory of band structureThis work was supported by the U.S. Army Research Office. (1984)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 26 (1984), S. 87-104 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: A generalized non-muffin-tin band structure method is presented in the context of multiple scattering off of the Wigner-Seitz cell. This technique has the following desirable features: it is formally exact and rapidly convergent; it preserves the separation between the nondiagonal scattering matrix for the cell and the usual structure constants of KKR in the secular determinant; it produces an accurate representation of the wave function throughout the sphere bounding the Wigner-Seitz cell and hence is suitable for self-consistent field calculations and applications that require a detailed knowledge of the unperturbed crystal potential and wave functions. Various aspects of the application of this theory to the empty lattice and sodium are presented, and its limitations discussed. Some future lines of research are briefly reviewed.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560260813
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Statistical microdynamics of extended systems in natural function spaces (1993)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 48 (1993), S. 363-375 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: An approximate numerical method of solving the Generalized Master Equation for a many-body problem is presented, with examples of its application. This method involves the construction from the full Hamiltonian (of the system plus the “bath”) of a set of unitary Langevin equations that combine deterministic microcanonical, stochastic canonical (heat bath), and stochastic nonthermal dynamics in a single time-integration scheme. If implemented in a representation that captures the essential physics and repeatedly run from a given initial condition, this method evaluates stochastic representatives from the actual fiber bundle of system worldlines that flow from the initial condition and, hence, numerically evaluates the path integral. © 1993 John Wiley & Sons, Inc.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560480837
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  • 3
    Electronic Resource
    Electronic Resource
    A generalized non-muffin-tin theory of band structure (1985)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 27 (1985), S. 803-804 
    Details
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/qua.560270614
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  • 4
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    Petrov-Galerkin methods for natural convection in directional solidification of binary alloys (1987)
    In:  Other Sources
    Details
    Publication Date: 2011-08-19
    Description: A Petrov-Galerkin finite element method is presented for calculation of the steady, axisymmetric thermosolutal convection and interface morphology in a model for vertical Bridgman crystal growth of nondilute binary alloys. The Petrov-Galerkin method is based on the formulation for biquadratic elements developed by Heinrich and Zienkiewicz and is introduced into the calculation of the velocity, temperature and concentration fields. The algebraic system is solved simultaneously for the field variables and interface shape by Newton's method. The results of the Petrov-Galerkin method are compared critically with those of Galerkin's method using the same finite element grids. Significant improvements in accuracy are found with the Petrov-Galerkin method only when the mesh is refined and when the formulation of the residual equations is modified to account for the mixed boundary conditions that arise at the solidification interface. Calculations for alloys with stable and unstable solute gradients show the occurrence of classical flow transitions and morphological instabilities in the solidification system.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: International Journal for Numerical Methods in Fluids (ISSN 0271-2091); 7; 761-791
    Format: text
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    NASA TECHNICAL REPORTS
  • 5
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    Third-order resonance effects and the nonlinear stability of drop oscillations (1987)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: The three-dimensional nonlinear oscillations of an isolated, inviscid drop with surface tension are studied by a multiple timescale analysis and pre-averaging applied to the variational principle for the appropriate Lagrangian. Amplitude equations are derived which describe the generic cubic resonance caused by the spatial degeneracy of the eigenfrequencies of the linear normal modes. This resonant coupling leads to the instability of the finite amplitude axisymmetric oscillations to small nonaxisymmetric perturbations, as is demonstrated here for the three- and four-lobed normal modes. Solutions to the interaction equations that describe finite amplitude, nonaxisymmetric traveling-wave solutions are also obtained and their stability is investigated. A nongeneric cubic resonance between the two-lobed and four-lobed oscillatory modes leads to quasi-periodic motions.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Fluid Mechanics (ISSN 0022-1120); 183; 95-121
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    NASA TECHNICAL REPORTS
  • 6
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    Dynamic centering of liquid shells (1987)
    In:  Other Sources
    Details
    Publication Date: 2019-07-12
    Description: The moderate-amplitude axisymmetric oscillations of an inviscid liquid shell surrounding an incompressible gas bubble are calculated by a multiple-time-scale expansion for initial deformations composed of two-lobed perturbations of the shell and a displacement of the bubble from the center of mass of the liquid. Two types of small-amplitude motion are identified and lead to very different nonlinear dynamic interactions, as described by the results valid up to second order in the amplitude of the initial deformation. In the 'bubble mode', the oscillations of the captive bubble and the liquid shell are exactly in phase and the bubble vibrates about its initial eccentric location. The bubble moves toward the center of the drop when the shell is perturbed into a 'sloshing mode' of oscillation where both interfaces move out of phase. These results explain the centering of liquid shells observed in several experiments.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physics of Fluids (ISSN 0031-9171); 30; 27-35
    Format: text
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    NASA TECHNICAL REPORTS
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