Two-scale mathematics and fractional calculus for thermodynamics

By Ji-Huan He, Feiyu Ji. Thermal Science, 2019

234 citations recorded by the source corpus.

A three dimensional problem can be approximated by either a two-dimensional or one-dimensional case, but some information will be lost. To reveal the lost information due to the lower dimensional approach, two-scale mathematics is needed. Generally one scale is established by usage where traditional calculus works, and the other scale is for revealing the lost information where the continuum assumption might be forbidden, and fractional calculus or fractal calculus has to be used. The two-scale transform can approximately convert the fractional calculus into its traditional partner, making the two-scale thermodynamics much promising.

Subfields: Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9becacd1bc75237b9ff7d8a56228e687c6ea1af8

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In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle (2020, background): “T tα = (61) The explanation of the two scale transform was given in [4, 5].”
The simplest approach to nonlinear oscillators (2019, unknown): “From the SelectedWorks of Ji-Huan He 2019 results-in-physics.pdf Ji-Huan He Available at: https://works.bepress.com/ji_huan_he/105/ Contents lists available at ScienceDirect Results in Physics journal homepage: www.elsevier.com/locate/rinp Microarticle The simplest approach to nonlinear oscillators…”