Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-03T08:33:35.104Z Has data issue: false hasContentIssue false
  • English
  • Français

Phase Transitions, Patterns and Statistical Mechanics of Front Propagation in a Dynamic Random Impurity Model for Strip, Unusual Trees and Other Geometries

Published online by Cambridge University Press:  10 February 2011

N. Vandewalle  and
M. Ausloos
N. Vandewalle
Affiliation:
SUPRAS, Institut de Physique B5, Université de Liège, B-4000 Liège, Belgium
M. Ausloos
Affiliation:
SUPRAS, Institut de Physique B5, Université de Liège, B-4000 Liège, Belgium
Get access

Abstract

A dynamic random impurity model is studied lor describing the evolution of an advancing interface through a multiphase random medium containing mobile impurities. A short range repulsion between the Iront and the impurities leads to an aggregation process along the front, and to the trapping of aggregates behind the front. The patterns of trapped impurities are found to be self-organized. Some theoretical treatment is performed through a transfer matrix technique in various geometries: trees with loops instead of branches, chains of squares and triangles joined by vertices. Arguments are given for applications of such concepts, techniques and models in various cases: chemistry, biology, trafic, sociology, economy,…

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 463: Symposia EE – Statistical Mechanics in Physics and Biology , 1996 , 287
Copyright
Copyright © Materials Research Society 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Cross, M.C. and Hohenbcrg, R.C., Rev. Mod. Phys. 65, 851 (1993)Google Scholar
2. Kim, C.-J., Lai, S.H., and McGinn, P.J., Materials Lett. 1 9, 185 (1994)Google Scholar
3. Hanley, T. O'D. and Vo Van, T., J. Crysl. Growth 1 9, 147 (1973)Google Scholar
4. Körber, C, Quart. Rev. Biophys. 2 1, 229 (1988)Google Scholar
5. Uhlmann, D.R., Chalmers, B. and Jackson, K.A., J. Appl. Phys. 35, 2986 (1964)Google Scholar
6. Vandewalle, N. and Ausloos, M., J. Phys. A 29, 309 (1996)Google Scholar
7. Julien, R. and Botet, R., J. Phys. A 1 8, 2279 (1985)Google Scholar
8. Vandewalle, N., Ph.D. thesis (University of Liège, Belgium, 1996), unpublishedGoogle Scholar
9. Vandewalle, N. and Ausloos, M., Phys. Rev. Lett. 7 7, 510 (1996)Google Scholar
10. Bunde, A., Herrmann, H.J., Margolina, A. and Stanley, H.E., Phys. Rev. Lett. 55, 653 (1985)Google Scholar
11. Stauffer, D. and Aharony, A., Introduction to Percolation Theory, (Taylor & Francis, London, 1994) 2nd printingGoogle Scholar
12. Vandewalle, N. and Ausloos, M., Phys. Rev. E 54, 3499 (1996)Google Scholar
13. Vandewalle, N. and Ausloos, M., Physica A 200, 1 (1996)Google Scholar