On the applicability of Fick's law to diffusion in inhomogeneous systems

European Journal of Physics

Volumn 26, Issue 5, 2005, Pages 913-925

  Van Milligen, B Ph ^a   Bons, P D ^b   Carreras, B A ^c   Snchez R ^d  

^a CIEMAT   (Spain)

^b UNIVERSITY OF TÜBINGEN   (Germany)

^c OAK RIDGE NATIONAL LABORATORY   (United States)

^d UNIVERSIDAD CARLOS III DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

CYLINDERS (CONTAINERS); FLUXES; GEOMAGNETISM; MAGNETIC FIELD EFFECTS; MAGNETIC FLUX; MATHEMATICAL MODELS; MIRRORS; SURFACE TREATMENT;

FICK'S LAW; PARTICLE DYNAMICS; PARTICLE FLUX; PARTICLE MOTION;

DIFFUSION;

EID: 23844486722     PISSN: 01430807     EISSN: 01430807     Source Type: Journal    
DOI: 10.1088/0143-0807/26/5/023     Document Type: Article

References (19)

1. Fick A 1855 Über diffusion Ann. Phys., Lpz. 23 59
2. Feller W 1971 An Introduction to Probability Theory and Its Applications vol 2 (New York: Wiley)
3. Risken H 1984 The Fokker-Planck Equation (Berlin: Springer)
4. Landsberg P T 1984 D grad ν or grad (Dν)? J. Appl. Phys. 56 1119
5. Collins R and Takemori T 1989 A sum rule for unbiased Brownian motion, and generalizations of Fick's law for space-dependent diffusivity J. Phys.: Condens. Matter 1 3801
6. Collins R, Carson S R and Matthew J A D 1997 Diffusion equation for one-dimensional unbiased hopping Am. J. Phys. 65 230
7. Montroll E W and West B J 1987 Fluctuation Phenomena ed E W Montroll and J L Lebowitz (Amsterdam: North-Holland)
8. Einstein A 1905 Über die von der molekulartheoretischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen Ann. Phys., Lpz. 17 549
9. Montroll E W and Weiss G 1965 Random walks on lattices. II J. Math. Phys. 6 167
10. Kenkre V M, Montroll E W and Shlesinger M F 1973 Generalized master equations for continuous-time random walks J. Stat. Phys. 9 45
11. Klafter J and Silbey R 1980 Derivation of the continuous-time random walk equation Phys. Rev. Lett. 44 55
12. van Milligen B Ph, Sánchez R and Carreras B A 2004 Probabilistic finite-size transport models for fusion: anomalous transport and scaling laws Phys. Plasmas 11 2272
13. Sánchez R, Carreras B A and van Milligen B Ph 2005 Fluid limit of nonintegrable continuous-time random walks in terms of fractional differential equations Phys. Rev. E 71 011111
14. Barenblatt G I 1996 Scaling, Self-similarity, and Intermediate Asymptotics (Cambridge: Cambridge University Press)
15. Zaslavsky G M 2002 Chaos, fractional kinetics, and anomalous transport Phys. Rep. 371 461
16. Metzler R and Klafter J 2000 The random walk's guide to anomalous diffusion: a fractional dynamics approach Phys. Rep. 339 1
17. van Milligen B Ph, Carreras B A and Sánchez R 2004 Uphill transport and the probabilistic transport model Phys. Plasmas 11 3787
18. Scalas E, Gorenflo R and Mainardi F 2004 Uncoupled continuous-time random walks: solution and limiting behavior of the master equation Phys. Rev. E 69 011107
19. Sánchez R, van Milligen B Ph and Carreras B A 2005 Probabilistic transport models for plasma transport in the presence of critical thresholds: beyond the diffusive paradigm Phys. Plasmas 12 056105