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Beyond fick's equations, an overview

  • Jean Philibert
Published/Copyright: June 11, 2013
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International Journal of Materials Research
From the journal International Journal of Materials Research Volume 100 Issue 6

Abstract

Fick's equations do not allow modelling of a large number of diffusion phenomena. Several extensions are described and some applications outside the field of physical metallurgy are briefly described. Departure from Brownian motion appears to be very common, so that anomalous diffusion would actually appear as normal.

Keywords: Brownian motion; Levy flights; Anomalous diffusion; Ecology and epidemics; Richardson equations
* Correspondence address, Prof. Jean Philibert 24 rue Sainte Radegonde F-78100 Saint-Germain-en-Laye, France Tel.: +33 1 39 73 29 37 E-mail:

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Received: 2009-2-11
Accepted: 2009-4-8
Published Online: 2013-06-11
Published in Print: 2009-06-01

© 2009, Carl Hanser Verlag, München

Articles in the same Issue

  1. Contents
  2. Contents
  3. Feature
  4. Beyond fick's equations, an overview
  5. Review
  6. The high-temperature creep properties of materials processed using severe plastic deformation
  7. Nanostructuring of metallic materials by spd processing for advanced properties
  8. Basic
  9. Some factors affecting the creep behaviour of metallic materials processed by equal-channel angular pressing
  10. The elastic–plastic transition in nanograined polycrystals
  11. Synchrotron X-ray line-profile analysis experiments for the in-situ microstructural characterisation of SPD nanometals during tensile deformation
  12. Tensile and fatigue properties of sub-microcrystalline ultra-low carbon steel produced by hpt-straining
  13. Precipitation Effects in Ultra-Fine-Grained Mg–RE Alloys
  14. EBSD investigation of the grain boundary distributions in ultrafine-grained Cu and Cu–Zr polycrystals prepared by equal-channel angular pressing
  15. Acoustic emission study of the deformation behaviour of magnesium sheets
  16. Mechanical properties of pure titanium and Ti-6Al-4V alloys with a new tailored nano/meso hybrid microstructure
  17. In-situ SEM/EBSD observation of abnormal grain growth in electrodeposited nanocrystalline nickel
  18. High-temperature creep properties of Fe–Al alloys modified by Zr
  19. ALCHEMI study of chromium doped iron-aluminides
  20. Intermetallic compounds at the interface between Sn–Cu(–Ni) solders and Cu substrate
  21. The effect of the microstructure on elastic properties of a polycrystalline stoichiometric NiAl
  22. Ab-initio simulation of the tensile strength of silicon nanofilms
  23. New properties of halogen plasma-treated Cu films
  24. Applied
  25. High-speed deformation of titanium during dynamic channel-angular pressing
  26. Microstructural evolution of equal-channel angular pressed interstitial-free steel
  27. Effect of equal channel angular pressing on microstructure, texture, and high-cycle fatigue performance of wrought magnesium alloys
  28. The characteristics of superplastic flow in a magnesium alloy processed by ECAP
  29. Deformation behaviour of ultrafine-grained 7075 aluminium alloy
  30. The optimization of ECAP conditions to achieve high strain-rate superplasticity in a Zr- and Sc-modified aa 7075 aluminum alloy
  31. Multilayer composite al99.99/almg3 sheets prepared by accumulative roll bonding
  32. Preparation of ultrafine-grained twin-roll cast AlMg3 sheets by accumulative roll bonding
  33. Recovery and recrystallization behavior of aluminum processed by extrusion-preceded equal channel angular pressing
  34. Low sliding-wear resistance of ultrafine-grained Al alloys and steel having undergone severe plastic deformation
  35. Study of the recrystallization of AW-5049 and AW-5754 twin-roll cast alloys by EBSD
  36. XRD profile analysis of ECAP Cu and Cu + Zr samples
  37. Stability of microstructure in silver processed by severe plastic deformation
  38. Acoustic emission study of the mechanical anisotropy of the extruded AZ31 alloy
  39. Effects of shot peening on internal friction in cp aluminum and aluminum alloy 6008
  40. Effects of grain growth on microhardness and coercivity in electrodeposited nanocrystalline nickel
  41. Strain release from pre-deformed Ni53.6Mn27.1Ga19.3 shape memory alloy during thermal cycling
  42. Simulation of the growth kinetics of FeB and Fe2B phases on the AISI M2 borided steel: Effect of the paste thickness
  43. High-pressure torsion deformation of a magnesium-based nanocomposite
  44. Fracture behavior of Mg–Li matrix composites
  45. Notifications
  46. The 80th Birthday of Dr.-Ing. Wolfgang Eychmüller
  47. Personal
https://doi.org/10.3139/146.110130
Keywords for this article
Brownian motion; Levy flights; Anomalous diffusion; Ecology and epidemics; Richardson equations

Articles in the same Issue

  1. Contents
  2. Contents
  3. Feature
  4. Beyond fick's equations, an overview
  5. Review
  6. The high-temperature creep properties of materials processed using severe plastic deformation
  7. Nanostructuring of metallic materials by spd processing for advanced properties
  8. Basic
  9. Some factors affecting the creep behaviour of metallic materials processed by equal-channel angular pressing
  10. The elastic–plastic transition in nanograined polycrystals
  11. Synchrotron X-ray line-profile analysis experiments for the in-situ microstructural characterisation of SPD nanometals during tensile deformation
  12. Tensile and fatigue properties of sub-microcrystalline ultra-low carbon steel produced by hpt-straining
  13. Precipitation Effects in Ultra-Fine-Grained Mg–RE Alloys
  14. EBSD investigation of the grain boundary distributions in ultrafine-grained Cu and Cu–Zr polycrystals prepared by equal-channel angular pressing
  15. Acoustic emission study of the deformation behaviour of magnesium sheets
  16. Mechanical properties of pure titanium and Ti-6Al-4V alloys with a new tailored nano/meso hybrid microstructure
  17. In-situ SEM/EBSD observation of abnormal grain growth in electrodeposited nanocrystalline nickel
  18. High-temperature creep properties of Fe–Al alloys modified by Zr
  19. ALCHEMI study of chromium doped iron-aluminides
  20. Intermetallic compounds at the interface between Sn–Cu(–Ni) solders and Cu substrate
  21. The effect of the microstructure on elastic properties of a polycrystalline stoichiometric NiAl
  22. Ab-initio simulation of the tensile strength of silicon nanofilms
  23. New properties of halogen plasma-treated Cu films
  24. Applied
  25. High-speed deformation of titanium during dynamic channel-angular pressing
  26. Microstructural evolution of equal-channel angular pressed interstitial-free steel
  27. Effect of equal channel angular pressing on microstructure, texture, and high-cycle fatigue performance of wrought magnesium alloys
  28. The characteristics of superplastic flow in a magnesium alloy processed by ECAP
  29. Deformation behaviour of ultrafine-grained 7075 aluminium alloy
  30. The optimization of ECAP conditions to achieve high strain-rate superplasticity in a Zr- and Sc-modified aa 7075 aluminum alloy
  31. Multilayer composite al99.99/almg3 sheets prepared by accumulative roll bonding
  32. Preparation of ultrafine-grained twin-roll cast AlMg3 sheets by accumulative roll bonding
  33. Recovery and recrystallization behavior of aluminum processed by extrusion-preceded equal channel angular pressing
  34. Low sliding-wear resistance of ultrafine-grained Al alloys and steel having undergone severe plastic deformation
  35. Study of the recrystallization of AW-5049 and AW-5754 twin-roll cast alloys by EBSD
  36. XRD profile analysis of ECAP Cu and Cu + Zr samples
  37. Stability of microstructure in silver processed by severe plastic deformation
  38. Acoustic emission study of the mechanical anisotropy of the extruded AZ31 alloy
  39. Effects of shot peening on internal friction in cp aluminum and aluminum alloy 6008
  40. Effects of grain growth on microhardness and coercivity in electrodeposited nanocrystalline nickel
  41. Strain release from pre-deformed Ni53.6Mn27.1Ga19.3 shape memory alloy during thermal cycling
  42. Simulation of the growth kinetics of FeB and Fe2B phases on the AISI M2 borided steel: Effect of the paste thickness
  43. High-pressure torsion deformation of a magnesium-based nanocomposite
  44. Fracture behavior of Mg–Li matrix composites
  45. Notifications
  46. The 80th Birthday of Dr.-Ing. Wolfgang Eychmüller
  47. Personal
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