New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle

New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle

Any physical laws are scale-dependent, the same phenomenon might lead to debating theories if observed using different scales. The two-scale thermodynamics observes the same phenomenon using two different scales, one scale is generally used in the conventional continuum mechanics, and the other scal...

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Bibliographic Details
Published in:Thermal science 2020, Vol.24 (2 Part A), p.659-681
Main Authors: He, Ji-Huan, Ain, Qura-Tul
Format: Article
Language:eng
Subjects:
Calculus
Calculus of variations
Computational fluid dynamics
Continuum mechanics
Dark energy
Fluid mechanics
Fractal models
Fractal transforms
Fractals
Thermodynamics
Variational principles
Online Access:Get full text
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Summary:Any physical laws are scale-dependent, the same phenomenon might lead to debating theories if observed using different scales. The two-scale thermodynamics observes the same phenomenon using two different scales, one scale is generally used in the conventional continuum mechanics, and the other scale can reveal the hidden truth beyond the continuum assumption, and fractal calculus has to be adopted to establish governing equations. Here basic properties of fractal calculus are elucidated, and the relationship between the fractal calculus and traditional calculus is revealed using the two-scale transform, fractal variational principles are discussed for 1-D fluid mechanics. Additionally planet distribution in the fractal solar system, dark energy in the fractal space, and a fractal ageing model are also discussed. nema
ISSN:0354-9836
2334-7163