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

Łukasz Stępień () and Zbigniew A. Łagodowski
Additional contact information
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

Energies, 2023, vol. 16, issue 20, 1-19

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.

Keywords: Ornstein–Uhlenbeck process; heat transfer; thermal conductivity; interacting particle systems (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/1996-1073/16/20/7117/pdf (application/pdf)
https://www.mdpi.com/1996-1073/16/20/7117/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jeners:v:16:y:2023:i:20:p:7117-:d:1261215

Access Statistics for this article

Energies is currently edited by Ms. Agatha Cao

More articles in Energies from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().