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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of thermal analysis and calorimetry 57 (1999), S. 717-736 
    ISSN: 1572-8943
    Keywords: chalcogenides ; dielectric relaxation ; excitations ; fragility ; glassformer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract In this paper we introduce two key notions related to understanding the ‘glassy state’ problem. One is the notion of the ‘excitation profile’ for an amorphous system, and the other is the notion of the ‘simple glassformer’. The attributes of the latter may be used, in quite different ways, to calculate and characterize the former. The excitation profile itself directly reflects the combined phonon/configuron density of states, which in turn determines the liquid fragility. In effect, we are examining the equivalent, for liquids, of the low temperature Einstein-Debye regime for solids though, in the liquid heat capacity case, there is no equivalent of the Dulong/Pettit classical limit for solids. To quantify these notions we apply simple calorimetric methods in a novel manner. First we use DTA techniques to define some glass-forming systems that are molecularly simpler than any described before, including cases which are 80 mol% CS2, or 100% S2Cl2. We then use the same data to obtain the fragility of these simple systems by a new approach, the 'reduced glass transition width' method. This method will be justified using data on a wider variety of well characterized glassformers, for which the unambiguous F1/2 fragility measures are available. We also describe a new DTA method for obtaining F1/2 fragilities in a single scan. We draw surprising conclusions about the fragility of the simplest molecular glassformers, the mixed LJ glasses, which have been much studied by molecular dynamics computer simulation. These ideas are then applied to a different kind of simple glass — one whose thermodynamics is dominated by breaking and making of covalent bonds — for which case the excitation profile can be straight-forwardly modeled. Comparisons with the profile obtained from computer studies of the molecularly simple glasses are made, and the differences in profiles implied for strong vs. fragile systems are discussed. The origin of fragility in the relation between the vibrational and configurational densities of states is discussed, and the conditions under which high fragility can convert to a first order liquid-liquid transition, is outlined.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 15 (1992), S. 613-623 
    ISSN: 0271-2091
    Keywords: Large sparse non-symmetric linear system ; Multilevel iteration ; Generalized minimal residual method ; Parallel computing ; Distributed memory ; Computational fluid dynamics ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Linearization of the non-linear systems arising from fully implicit schemes in computational fluid dynamics often result in a large sparse non-symmetric linear system. Practical experience shows that these linear systems are ill-conditioned if a higher than first-order spatial discretization scheme is used. To solve these linear systems, an efficient multilevel iterative method, the α-GMRES method, is proposed which incorporates a diagonal preconditioning with a damping factor α so that a balanced fast convergence of the inner GMRES iteration and the outer damping loop can be achieved. With this simple and efficient preconditioning and damping of the matrix, the resulting method can be effectively parallelized. The parallelization maintains the effectiveness of the original scheme due to the algorithm equivalence of the sequential and the parallel versions.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 21 (1995), S. 723-733 
    ISSN: 0271-2091
    Keywords: global method ; GDQ and GIQ ; polynomial approximation ; weighting coefficients ; boundary layer solutions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Based on the work of generalized differential quadrature (GDQ), a global method of generalized integral quadrature (GIQ) is developed in this paper for approximating an integral of a function over a part of the closed domain. GIQ approximates the integral of a function over the part of the whole closed domain by a linear combination of all the functional values in the whole domain with higher order of accuracy. The weighting coefficients of GIQ can be easily determined from those of GDQ. Applications of GDQ and GIQ to solve boundary layer equations demonstrated that accurate numerical results can be obtained using just a few grid points.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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