Dresden 2020 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 13: Glasses and Glass Transition (joint session DY/CPP)

DY 13.4: Talk

Monday, March 16, 2020, 16:00–16:15, ZEU 118

Interpreting the Types of Derivatives in Fractional Relaxation Models — •Tillmann Kleiner and Rudolf Hilfer — Institute for Computational Physics, University of Stuttgart, Germany

The excess wing of α-relaxation peaks and the phenomenon of nearly constant loss that have been observed in dielectric spectra of glass forming materials [1] are predicted by susceptibility functions that involve stretching exponents derived from fractional dynamics [2,3]. The relaxation motions predicted by such models can be described by initial value problems involving fractional derivatives with a type parameter. Special choices for the type parameter yield Liouville-Caputo and Riemann-Liouville derivatives.

Using a translation invariant fractional derivative the fractional initial value problems are reformulated as linear response equations. The influence of the type parameter is then described by additional fractional derivative expressions. The reformulation brings the advantage that the mathematical external force term coincides with the physical external force term which is not guaranteed for all types in the initial value problem formulation. Further, predictions for realistic spectroscopy and relaxation experiments are now described in a unified way and physical predictions depend continuously and more transparently on the parameters of the model.

[1] F. Kremer and A. Loidl, The Scaling of Relaxation Processes, Springer, (2018)

[2] R. Hilfer, Analysis 36, 49-64 (2016)

[3] R. Hilfer, J. Stat. Mech. (2019) 104007