CHARACTERIZATION OF CHLORIDE IONS DIFFUSION IN CONCRETE USING FRACTIONAL BROWNIAN MOTION RUN WITH POWER LAW CLOCK

Shengjie Yan, Yingjie Liang and Wei Xu
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Shengjie Yan: College of Mechanics and Materials, Hohai University, Nanjing, P. R. China
Yingjie Liang: College of Mechanics and Materials, Hohai University, Nanjing, P. R. China†Institute of Physics & Astronomy, University of Potsdam, Potsdam-Golm, Germany
Wei Xu: ��College of Science, Qingdao University of Technology, Qingdao, Shandong, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 09, 1-9

Abstract: In this paper, we propose a revised fractional Brownian motion run with a nonlinear clock (fBm-nlc) model and utilize it to illustrate the microscopic mechanism analysis of the fractal derivative diffusion model with variable coefficient (VC-FDM). The power-law mean squared displacement (MSD) links the fBm-nlc model and the VC-FDM via the two-parameter power law clock and the Hurst exponent is 0.5. The MSD is verified by using the experimental points of the chloride ions diffusion in concrete. When compared to the linear Brownian motion, the results show that the power law MSD of the fBm-nlc is much better in fitting the experimental points of chloride ions in concrete. The fBm-nlc clearly interprets the VC-FDM and provides a microscopic strategy in characterizing different types of non-Fickian diffusion processes with more different nonlinear functions.

Keywords: Mean Squared Displacement; Anomalous Diffusion; Fractal Derivative; Fractional Brownian Motion; Nonlinear Clock (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22501778

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