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  • 1
    Electronic Resource
    Electronic Resource
    Application of Onsager's reciprocity relations to interface motion during phase transformations (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 1133-1140 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A number of theories have been developed for the kinetics of steady-state interface motion during a phase transformation. One requirement of such theories is that they satisfy Onsager's reciprocity relations for coupled irreversible processes. We show how to apply Onsager's relations to a phase transformation at a moving planar interface in a two-component system. The appropriate pairs of thermodynamic forces and conjugate fluxes are determined and used to test two proposed theories for interface motion during solidification of binary alloys. It is shown that the continuous growth model "with solute drag'' of Aziz and Kaplan is inconsistent with Onsager's relations, but the continuous growth model "without solute drag'' is consistent with Onsager's relations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.456168
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  • 2
    Electronic Resource
    Electronic Resource
    Restricted applicability of Onsager's reciprocity relations to models of interface motion (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 8031-8037 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Onsager's reciprocity relations have been applied to the motion of a planar interface in a phase transformation in a two-component system, in order to provide a test of kinetic models of alloy solidification. Although applicable to such models in general, Onsager's relations yield no information for a subclass of models in which the thermodynamic driving forces are linearly dependent to first order, as is the case for several models of alloy solidification including the continuous growth model (CGM) of Aziz and Kaplan. As a consequence, experimental tests will likely be required to distinguish between these models. If the CGM is generalized to include diffusion in the growing phase, Onsager's relations are applicable under some circumstances.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.465628
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  • 3
    Electronic Resource
    Electronic Resource
    Surface strains in epitaxial systems (1995)
    Woodbury, NY : American Institute of Physics (AIP)
    Applied Physics Letters 66 (1995), S. 1924-1926 
    Details
    ISSN: 1077-3118
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The stress state of heteroepitaxial film systems is examined using a boundary integral method together with boundary conditions that allow deflections at the substrate/film interface. It is found that for geometries that deviate from planar structures significant variations in surface strain and film energy arise. These calculations explain recent important experimental results for Ge growth on Si, including observations for Ge islands on Si that show the surface lattice constant can exceed the bulk Ge value, and observations that the preferred region for growth on terraced films is not necessarily at the steps. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.113278
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  • 4
    Electronic Resource
    Electronic Resource
    Galerkin boundary integral method for evaluating surface derivatives (1998)
    Springer
    Computational mechanics 22 (1998), S. 187-193 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A Galerkin boundary integral procedure for evaluating the complete derivative, e.g., potential gradient or stress tensor, is presented. The expressions for these boundary derivatives involve hypersingular kernels, and the advantage of the Galerkin approach is that the integrals exist when a continuous surface interpolation is employed. As a consequence, nodal derivative values, at smooth surface points or at corners, can be obtained directly. This method is applied to the problem of electromigration-driven void dynamics in thin film aluminum interconnects. In this application, the tangential component of the electric field on the boundary is required to compute the flux of atoms at the void surface.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660050352
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  • 5
    Electronic Resource
    Electronic Resource
    Evaluation of the anisotropic Green's function in three dimensional elasticity (1996)
    Springer
    Computational mechanics 17 (1996), S. 255-261 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A perturbation expansion technique for approximating the three dimensional anisotropic elastic Green's function is presented. The method employs the usual series for the matrix (I−A)-1 to obtain an expansion in which the zeroth order term is an isotropic fundamental solution. The higher order contributions are expressed as contour integrals of matrix products, and can be directly evaluated with a symbolic manipulation program. A convergence condition is established for cubic crystals, and it is shown that convergence is enhanced by employing Voigt averaged isotropic constants to define the expansion point. Example calculations demonstrate that, for moderately anisotropic materials, employing the first few terms in the series provides an accurate solution and a fast computational algorithm. However, for strongly anisotropic solids, this approach will most likely not be competitive with the Wilson-Cruse interpolation algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00364828
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  • 6
    Electronic Resource
    Electronic Resource
    Evaluation of the anisotropic Green’s function in three dimensional elasticity (1996)
    Springer
    Computational mechanics 17 (1996), S. 255-261 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract  A perturbation expansion technique for approximating the three dimensional anisotropic elastic Green’s function is presented. The method employs the usual series for the matrix to obtain an expansion in which the zeroth order term is an isotropic fundamental solution. The higher order contributions are expressed as contour integrals of matrix products, and can be directly evaluated with a symbolic manipulation program. A convergence condition is established for cubic crystals, and it is shown that convergence is enhanced by employing Voigt averaged isotropic constants to define the expansion point. Example calculations demonstrate that, for moderately anisotropic materials, employing the first few terms in the series provides an accurate solution and a fast computational algorithm. However, for strongly anisotropic solids, this approach will most likely not be competitive with the Wilson-Cruse interpolation algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660050108
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  • 7
    Electronic Resource
    Electronic Resource
    Symmetric Galerkin boundary integral fracture analysis for plane orthotropic elasticity (1997)
    Springer
    Computational mechanics 20 (1997), S. 26-33 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper discusses the formulation and implementation of the symmetric Galerkin boundary integral method for two dimensional linear elastic orthotropic fracture analysis. For the usual case of a traction-free crack, the symmetry of the coefficient matrix can be effectively exploited to significantly reduce the computational work required to construct the linear system. In addition, computation time is reduced by employing efficient analytic integration formulas for the analysis of the orthotropic singular and hypersingular integrals. Preliminary test calculations indicate that the method is both accurate and efficient.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660050212
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  • 8
    Electronic Resource
    Electronic Resource
    A Hermite interpolation algorithm for hypersingular boundary integrals (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 2357-2367 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a conforming C1 boundary integral algorithm based on Hermite interpolation. This work is motivated by the requirement that the surface function multiplying a hypersingular kernel be differentiable at the collocation nodes. The unknown surface derivatives utilized by the Hermite approximation are determined, consistent with other boundary values, by writing a tangential hypersingular equation. Hypersingular equations are primarily invoked for solving crack problems, and the focus herein is on developing a suitable approximation for this geometry. Test calculations for the Laplace equation in two dimensions indicate that the algorithm is a promising technique for three-dimensional problems.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620361404
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  • 9
    Electronic Resource
    Electronic Resource
    Structure of amphotericin B aggregates based on calculations of optical spectra (1983)
    New York : Wiley-Blackwell
    Biopolymers 22 (1983), S. 911-918 
    Details
    ISSN: 0006-3525
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The Degenerate ground state approximation was used to calculate the optical absorption and CD spectra for helical polymer models of amphotericin B aggregates in aqueous solution. Comparisons with experimental spectra indicate that a two-molecule/unit cell helical polymer model is a possible structure for aggregates of amphotericin B.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/bip.360220312
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  • 10
    Electronic Resource
    Electronic Resource
    A faster Galerkin boundary integral algorithm (1998)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 14 (1998), S. 1109-1117 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The symmetry present in Green's functions is exploited to significantly reduce the matrix assembly time for a Galerkin boundary integral analysis. A relatively simple modification of the standard Galerkin implementation for computing the non-singular integrals yields a 20-30 per cent decrease in computation time. This faster Galerkin method is developed for both singular and hypersingular equations, and applied to symmetric-Galerkin implementations in two dimensions for the Laplace equation and for orthotropic elasticity. In three dimensions, the modified algorithm has been implemented for the singular equation for the Laplace and elastodynamics equations. Comparison timing results for standard and modified algorithms are presented. Copyright © 1998 John Wiley & Sons, Ltd.
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
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