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A Stochastic Model of Anomalously Fast Transport of Heat Energy in Crystalline Bodies

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  • Łukasz Stępień

    (Department of Mathematics, Lublin University of Technology, Nadbystrzycka 38, 20-618 Lublin, Poland)

  • Zbigniew A. Łagodowski

    (Department of Mathematics, Lublin University of Technology, Nadbystrzycka 38, 20-618 Lublin, Poland)

Abstract

In this work, a new method for constructing the infinite-dimensional Ornstein–Uhlenbeck stochastic process is introduced. The constructed process is used to perturb the harmonic system in order to model anomalously fast heat transport in one-dimensional nanomaterials. The introduced method made it possible to obtain a transition probability function that allows for a different approach to the analysis of equations with such a disturbance. This creates the opportunity to relax assumptions about temporal correlations for such a process, which may lead to a qualitatively different model of energy transport through vibrations of the crystal lattice and, as a result, to obtain the superdiffusion equation on a macroscopic scale with an order of the fractional Laplacian different from the value of 3/4 obtained so far in stochastic models. Simulations confirming these predictions are presented and discussed.

Suggested Citation

  • Łukasz Stępień & Zbigniew A. Łagodowski, 2023. "A Stochastic Model of Anomalously Fast Transport of Heat Energy in Crystalline Bodies," Energies, MDPI, vol. 16(20), pages 1-19, October.
    • Handle: RePEc:gam:jeners:v:16:y:2023:i:20:p:7117-:d:1261215
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    1. repec:dau:papers:123456789/334 is not listed on IDEAS
    2. Bernardin, Cédric, 2007. "Hydrodynamics for a system of harmonic oscillators perturbed by a conservative noise," Stochastic Processes and their Applications, Elsevier, vol. 117(4), pages 487-513, April.
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