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Continuous Time Random Walk (CTRW) put to work

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  • Harvey Scher

    (Weizmann Institute of Science)

Abstract

A personal history of the first applications of CTRW to the physics of transport and diffusion in disordered media is presented. The sequence of steps leading to the introduction of novel ψ(t), the probability density of particle-transfer times, without moments is briefly outlined. The key concept that emerged from those early applications is anomalous or non-Fickian transport. The latter involved spatial moments of the particle propagator with completely different time behavior, e.g., the mean ∝ t β , 0 ∕σ = constant. With these results many puzzling experimental data were explained. The data ranged from electronic dynamics of amorphous films to chemical migration and interaction in the subsurface of the Earth. These were not anticipated results but a consequence of the CTRW with these special ψ(t).

Suggested Citation

  • Harvey Scher, 2017. "Continuous Time Random Walk (CTRW) put to work," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(12), pages 1-5, December.
    • Handle: RePEc:spr:eurphb:v:90:y:2017:i:12:d:10.1140_epjb_e2017-80416-9
    DOI: 10.1140/epjb/e2017-80416-9
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    Cited by:

    1. Szarek, Dawid & Maraj-Zygmąt, Katarzyna & Sikora, Grzegorz & Krapf, Diego & Wyłomańska, Agnieszka, 2022. "Statistical test for anomalous diffusion based on empirical anomaly measure for Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    2. Zachary R. Fox & Eli Barkai & Diego Krapf, 2021. "Aging power spectrum of membrane protein transport and other subordinated random walks," Nature Communications, Nature, vol. 12(1), pages 1-9, December.

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