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Main Authors: Mickens, Ronald, Washington, Talitha
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2503.21299
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author Mickens, Ronald
Washington, Talitha
author_facet Mickens, Ronald
Washington, Talitha
contents We show that it is possible to construct microscopic-level discrete equations from macroscopic modeling PDEs for heat conduction in one space dimension. The significance of this result is that, in general, one starts from microscopic theories and then take their continuum limits to obtain the corresponding macroscopic PDEs, whereas here it is demonstrated that the reverse procedure is also possible. While our focus is on heat conduction, we discuss the applicability of our methodology to other physical systems.
format Preprint
id arxiv_https___arxiv_org_abs_2503_21299
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Microscopic limits of PDEs modeling macroscopic heat conduction
Mickens, Ronald
Washington, Talitha
Analysis of PDEs
35B09, 35G16, 35K05, 65M06, 80A10,
We show that it is possible to construct microscopic-level discrete equations from macroscopic modeling PDEs for heat conduction in one space dimension. The significance of this result is that, in general, one starts from microscopic theories and then take their continuum limits to obtain the corresponding macroscopic PDEs, whereas here it is demonstrated that the reverse procedure is also possible. While our focus is on heat conduction, we discuss the applicability of our methodology to other physical systems.
title Microscopic limits of PDEs modeling macroscopic heat conduction
topic Analysis of PDEs
35B09, 35G16, 35K05, 65M06, 80A10,
url https://arxiv.org/abs/2503.21299