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Transport Equation for Subdiffusion of Mixed Origin

  • ORDER, DISORDER, AND PHASE TRANSITION IN CONDENSED SYSTEM
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Abstract

The transport equation is proposed for the model, which is a combination of the random barrier model and the multiple trapping model. Negative correlations due to barriers are simulated by adding the source and sink terms to the equation. For processes preserving the probability, the proposed equation is equivalent to the equation that has been derived earlier. However, for processes with probability flows through boundaries, the results are basically different. In particular, this transport equation gives different values of the first passage time for stationary and nonstationary subdiffusion. In the case of stationary subdiffusion, it reproduces the result of the model of fractional Brownian motion, while for nonstationary subdiffusion, it reproduces the result of continuous time random walk model. The thermodynamic consistency of the equation is demonstrated for diffusion in a harmonic potential.

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Authors and Affiliations

  1. Chuyko Institute of Surface Chemistry, National Academy of Science of Ukraine, 03164, Kiev, Ukraine

    V. P. Shkilev

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  1. V. P. Shkilev
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Correspondence to V. P. Shkilev.

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Translated by N. Wadhwa

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Shkilev, V.P. Transport Equation for Subdiffusion of Mixed Origin. J. Exp. Theor. Phys. 133, 88–97 (2021). https://doi.org/10.1134/S1063776121070098

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  • DOI: https://doi.org/10.1134/S1063776121070098

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