Dresden 2006 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 46: Poster
DY 46.64: Poster
Donnerstag, 30. März 2006, 16:00–18:00, P1
Fractional calculus applied to the ion dynamics in porous matter — •Dean Korošak1, Bruno Cvikl1,2, Renata Jecl1, Janja Kramer1, and Anita Prapotnik Brdnik1 — 1University of Maribor, Faculty of Civil Engineering, Chair for Applied Physics, Smetanova 17, 2000 Maribor Slovenia — 2J. Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
We present the application of fractional calculus in the analysis of the measured dielectric response of the clay-water system which exhibits anomalus features in its low frequency part.
The conductivity spectra for samples with higher water content are shown to collapse to a single master curve when appropriately rescaled. The frequency dependence of the conductivity is shown to follow the power-law with the exponent n=0,67 before reaching the frequency-independent part. It is argued that the observed conductivity dispersion is a consequence of the anomalously diffusing ions in the clay-water system. It is however a non-trivial task to determine the correct underlying diffusion process since different dynamic processes yield the same mean square time dependence as for instance do fractional Brownian motion and fractal time process. The fractional Langevin equation is used to describe the stochastic dynamics of the single ion connecting the power-law exponent of the observed conductivity dispersion to the order of the fractional derivative in the fractional Langevin equation.
[1] R. Hilfer, Phys. Rev. B vol 44, 1991, pp. 60-75.
[2] E. Lutz, Phys. Rev. E vol 64, 2001, 051106.