Paper Titles

First Principles Suggestions of Targeted Diffusion Experiments on SiO₂
p.127

Comparative Ab Initio Study of Point Defect Energies and Atom Migration Profiles in the L1₂-Ordered Intermetallic Compounds Ni₃Al, Ni₃Ga, Pt₃Ga, Pt₃In
p.133

Experimental Errors in Studying the Defect Mobility in Nonstoichiometric Metal Oxides
p.139

Determination of the Stress Distribution at the Interface Metal-Oxide: Numerical and Theoretical Considerations
p.145

Kinetic Constraints in Diffusion
p.151

Random Walk Model of the Mechanical Relaxation
p.157

Zinc Self-Diffusion in ZnO
p.163

Diffusion of Confined Polymer Chains
p.169

On Vacancy Concentrations in Dilute FCC Alloys
p.175

HomeDefect and Diffusion ForumDefect and Diffusion Forum Vols. 237-240Kinetic Constraints in Diffusion

Kinetic Constraints in Diffusion

Article Preview

Abstract:

In the presence of strong external fields and steep gradients the flux formulae are not linear. The relation between the flux and the diffusion coefficient must be modified. The different flux-limited theories are presented. The flux formulae for solid systems far from equilibrium are derived and different forms of phenomenological flux limiters are discussed. It is shown that in order to accurately compute diffusion flow that is generated by strong force fields and/or discontinuities, the flux-limited diffusion must be considered. The flux limiters improve the spatial accuracy and allow to avoid baseless oscillations in the solutions.

You might also be interested in these eBooks

Diffusion in Materials - DIMAT2004

Info:

Periodical:

Defect and Diffusion Forum (Volumes 237-240)

Pages:

151-156

DOI:

https://doi.org/10.4028/www.scientific.net/DDF.237-240.151

Citation:

Cite this paper

Online since:

April 2005

Authors:

Marek Danielewski, M. Wakihara

Keywords:

Boundary Condition, Diffusion, Flux Limiters, Kinetic Constraints

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

© 2005 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] C. D. Levermore, J. Quant. Spect. Rad. Transfer. 31, 149 (1984).

[2] G. M. Kremer and I. Müller, J. Math. Phys. 33, 2265 (1992).

[3] A. M. Anile, S. Pennisi and M. Sammartino, J. Math. Phys. 32, 544 (1991).

[4] M. Zakari and D. Jou, J. Non-Equilib. Thermodyn. 20, 342 (1995).

[5] E. M. Epperlein, G. J. Rickard and A. R. Bell, Phys. Rev. Lett. 61, 2453 (1988).

[6] G. J. Rickard, A. R. Bell and E. M. Epperlein, Phys. Rev. Lett. 62, 2687 (1989).

[7] A. M. Anile and S. Pennisi, Phys. Rev. B 46, 13186 (1992).

[8] M. Waldman and E. A. Mason, Chem. Phys. 58, 121 (1981).

[9] F. J. Uribe and E. A. Mason, Chem. Phys. 133, 335 (1989).

[10] S. A. Hope, G. Féat and P. T. Landsberg, J. Phys. A 14, 2377 (1981).

[11] J. González and D. Jou, Phys. Lett. A 168, 375 (1992).

[12] M. Zakari, Physica A 240, 676 (1997).

[13] J. W. Cahn and J. E. Hilliard, J. Chem. Phys. 28, 258 (1958).

[14] A. L. Greer, Appl. Surface Sci. 86, 329 (1995).

[15] D. Jou, J. Casas-Vázquez and G. Lebon, Rep. Prog. Phys. 51, 1105 (1988).

[16] P. Rosenau, Phys. Rev. A 46, R7371 (1992).

[17] G. L. Olson, L. H. Auer and M. L. Hall, Los Alamos LA-UR-99-471.

[18] . E. Morel, J. Quantitative Spectr. & Radiative Transfer, 65, 769 (2000).

[19] G. A. Moses and J. Yuan, Univ. of Wisconsin UWFDM-1213 (2003).

[20] M. Zakari, J-E. Llebot and D. Jou, Phys. Lett. A 173, 421 (1993).

[21] M. Zakari and D. Jou, Physica A 253, 205 (1998).

[22] E. Scalas, R. Gorenflo, F. Mainardi and M. Raberto, J. of Quantitative Finance [Preprint in http: /xxx. lanl. gov/abs/cond-mat/0210166, v2 11 Oct 2002].

[23] T. Hillen and H. G. Othmer, SIAM J. Appl. Math, 61, 751 (2000).

[24] R. Ghez, Diffusion Phenomena, Kluwer Academic/Plenum Publishers (New York 2001).