Fractional generalization of Fick's law: a microscopic approach

Journal Article · Mon Jan 01 04:00:00 EST 2007 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.99.230603· OSTI ID:932091

Calvo, Ivan ^[1]; Sanchez, Raul ^[2]; Carreras, Benjamin A ^[2]; van Milligen, B. Ph. ^[3]

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1. CIEMAT, Madrid
2. ORNL
3. Asociacion EURATOM-CIEMAT

In the study of transport in inhomogeneous systems it is common to construct transport equations invoking the inhomogeneous Fick law. The validity of this approach requires that at least two ingredients be present in the system. First, finite characteristic length and time scales associated to the dominant transport process must exist. Secondly, the transport mechanism must satisfy a microscopic symmetry: global reversibility. Global reversibility is often satisfied in nature. However, many complex systems exhibit a lack of finite characteristic scales. In this Letter we show how to construct a generalization of the inhomogeneous Fick law that does not require the existence of characteristic scales while still satisfying global reversibility.

• Research Organization: Oak Ridge National Laboratory (ORNL)
• Sponsoring Organization: ORNL LDRD Director's R&D
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 932091
• Journal Information: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 23 Vol. 99; ISSN 0031-9007; ISSN PRLTAO
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
99 GENERAL AND MISCELLANEOUS
CALCULATION METHODS
FICK LAWS
Fick's law
TRANSPORT
fractional closure
inhomogeneous diffusion
turbulence