$Two-scale mathematics and fractional calculus for thermodynamics$

Two-scale mathematics and fractional calculus for thermodynamics

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...

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Main Authors:	He Ji-Huan, Ji Fei-Yu
Format:	Article
Language:	English
Published:	VINCA Institute of Nuclear Sciences 2019-01-01
Series:	Thermal Science
Subjects:	continuum mechanics fractal space fractal derivative fractional derivative scale-dependent law two-scale thermodynamics
Online Access:	http://www.doiserbia.nb.rs/img/doi/0354-9836/2019/0354-98361904131H.pdf

id	doaj-2bbd3e9c496046beb351be5145bf1b7c
record_format	Article
spelling	doaj-2bbd3e9c496046beb351be5145bf1b7c2021-01-02T09:37:51ZengVINCA Institute of Nuclear SciencesThermal Science0354-98362019-01-012342131213310.2298/TSCI1904131H0354-98361904131HTwo-scale mathematics and fractional calculus for thermodynamicsHe Ji-Huan0Ji Fei-Yu1School of Science, Xi'an University of Architecture and Technology, Xi’an, China + National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, Suzhou, ChinaNational Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, Suzhou, ChinaA 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.http://www.doiserbia.nb.rs/img/doi/0354-9836/2019/0354-98361904131H.pdfcontinuum mechanicsfractal spacefractal derivativefractional derivativescale-dependent lawtwo-scale thermodynamics
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	He Ji-Huan Ji Fei-Yu
spellingShingle	He Ji-Huan Ji Fei-Yu Two-scale mathematics and fractional calculus for thermodynamics Thermal Science continuum mechanics fractal space fractal derivative fractional derivative scale-dependent law two-scale thermodynamics
author_facet	He Ji-Huan Ji Fei-Yu
author_sort	He Ji-Huan
title	Two-scale mathematics and fractional calculus for thermodynamics
title_short	Two-scale mathematics and fractional calculus for thermodynamics
title_full	Two-scale mathematics and fractional calculus for thermodynamics
title_fullStr	Two-scale mathematics and fractional calculus for thermodynamics
title_full_unstemmed	Two-scale mathematics and fractional calculus for thermodynamics
title_sort	two-scale mathematics and fractional calculus for thermodynamics
publisher	VINCA Institute of Nuclear Sciences
series	Thermal Science
issn	0354-9836
publishDate	2019-01-01
description	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.
topic	continuum mechanics fractal space fractal derivative fractional derivative scale-dependent law two-scale thermodynamics
url	http://www.doiserbia.nb.rs/img/doi/0354-9836/2019/0354-98361904131H.pdf
work_keys_str_mv	AT hejihuan twoscalemathematicsandfractionalcalculusforthermodynamics AT jifeiyu twoscalemathematicsandfractionalcalculusforthermodynamics
_version_	1724355879342440448

Two-scale mathematics and fractional calculus for thermodynamics

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