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  • 1
    Electronic Resource
    Electronic Resource
    Painlevé test and exact similarity solutions of a class of nonlinear diffusion equations (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2456-2463 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For (1+1)-dimensional diffusion equations where the diffusion coefficient is an arbitrary power of the dependent variable, a Painlevé test is performed on both the partial differential equation and the similarity reductions. The invariance of the Painlevé property under a large class of similarity reductions is shown. For the reductions with the Painlevé property, the explicit similarity solutions are given. It is demonstrated how results of a Painlevé analysis can be used to obtain further exact similarity solutions, even in cases without the Painlevé property.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529615
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Fractional relaxation and the time-temperature superposition principle (1994)
    Springer
    Rheologica acta 33 (1994), S. 337-343 
    Details
    ISSN: 1435-1528
    Keywords: Rheological models ; viscoelasticity ; fractional differentiation ; non-Debye relaxation ; thermo-rheological simplicity ; projection operator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Relaxation processes in complex systems like polymers or other viscoelastic materials can be described by equations containing fractional differential or integral operators. In order to give a physical motivation for fractional order equations, the fractional relaxation is discussed in the framework of statistical mechanics. We show that fractional relaxation represents a special type of a non-Markovian process. Assuming a separation condition and the validity of the thermo-rheological principle, stating that a change of the temperature only influences the time scale but not the rheological functional form, it is shown that a fractional operator equation for the underlying relaxation process results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00366960
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Retardation experiments in glass-forming liquids and their description in terms of the conformon model (1996)
    Weinheim : Wiley-Blackwell
    Acta Polymerica 47 (1996), S. 150-160 
    Details
    ISSN: 0323-7648
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Relaxation in glass-forming liquids as measured by dielectric, by light- and by neutron-scattering experiments can be described with the aid of the conformon model. Conformons behave like bosons which display a photon statistics. Conformons are excited and can also be annihilated. They show a universal reduced energy density distribution, revealing their thermodynamic roots. Each relaxation mode is assumed to be directly connected with a distinct conformon. The coupling is described by an empirical power law. The actual relaxation time distribution is then obtained by scaling each relaxation mode with the same kinetic factor. The relaxation behavior of liquids is therefore self-similar, characterized by individual factors such as the relaxation power, the coupling parameter and the temperature of pressure dependence of the kinetic factor (“shift factor”).
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/actp.1996.010470403
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    Paper (German National Licenses)
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