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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Autor*in:	He Ji-Huan [verfasserIn] Ain Qura-Tul [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	two-scale fractal dimension two scale mathematics fractal space fractal variational theory local property

Übergeordnetes Werk:	In: Thermal Science - VINCA Institute of Nuclear Sciences, 2006, 24(2020), 2 Part A, Seite 659-681
Übergeordnetes Werk:	volume:24 ; year:2020 ; number:2 Part A ; pages:659-681

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.2298/TSCI200127065H

Katalog-ID:	DOAJ055720056

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callnumber-first	T - Technology
author	He Ji-Huan
spellingShingle	He Ji-Huan misc TJ1-1570 misc two-scale fractal dimension misc two scale mathematics misc fractal space misc fractal variational theory misc local property misc Mechanical engineering and machinery New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle
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topic_title	TJ1-1570 New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle two-scale fractal dimension two scale mathematics fractal space fractal variational theory local property
topic	misc TJ1-1570 misc two-scale fractal dimension misc two scale mathematics misc fractal space misc fractal variational theory misc local property misc Mechanical engineering and machinery
topic_unstemmed	misc TJ1-1570 misc two-scale fractal dimension misc two scale mathematics misc fractal space misc fractal variational theory misc local property misc Mechanical engineering and machinery
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title	New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle
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title_sort	new promises and future challenges of fractal calculus: from two-scale thermodynamics to fractal variational principle
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title_auth	New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle
abstract	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.
abstractGer	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.
abstract_unstemmed	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.
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container_issue	2 Part A
title_short	New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle
url	https://doi.org/10.2298/TSCI200127065H https://doaj.org/article/b59804114331402d8687a6cac3c2ef09 http://www.doiserbia.nb.rs/img/doi/0354-9836/2020/0354-98362000065H.pdf https://doaj.org/toc/0354-9836
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New promises and future challenges of fractal calculus: From two-scale thermodynamics to fractal variational principle

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