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A Theory for Growing Interfaces in Laplacian Fields: A Many-Body Formulation and Statistical Analysis

Published online by Cambridge University Press:  03 September 2012

Raphael Blumenfeld
Raphael Blumenfeld*
Affiliation:
Center for Nonlinear studies and Theoretical Division, MS B25 Los Alamos National Laboratory, Los Alanmos, NM 87545, USA
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Abstract

I formulate a theory for the growth of an interface in a Laplacian field. The problem is mapped to a many-body system and the process is shown to be Hamiltonian. The corresponding set of dynamical equations is analysed and surface effects are introduced as a term in the Hamiltonian that gives rise to a repulsion between the quasi-particles and the interface. The theory accommodates anisotropic surface effects. The underlying Hamiltonian allows a statistical-mechanical analysis of the limit distribution of the quasi-particles. Noise can be naturally incorporated in this formalism. Finally the distribution of the particles is translated into the statistics of the interface, which leads to predictions on the morphology. The main thrust of this approach is in finding a statistical mechanical approach to this nonequilibrium process.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 367: Symposium P – Fractal Aspects of Materials , 1994 , 53
Copyright
Copyright © Materials Research Society 1995

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References

1. Piteronero, L., Erzan, A. and Evertsz, C., Phys. Rev. Lett. 61 (1988) 861, Physica A151 (1988) 207; T. C. Halsey, Phys. Rev. Lett. 72 (1994) 1228.Google Scholar
2. Galin, L. A., Dokl. Akad. Nauk USSR 47 (1945) 246; P. Ya. Polubarinova-Kochina, Dokl. Akad. Nauk USSR 47 (1945) 254; Prikl. Math. Mech. 9 (1945) 79.Google Scholar
3. Shraiman, B. and Bensimon, D., Phys. Rev. A 30 (1984) 2840.Google Scholar
4. Richardson, S., J. Fluid Mech. 56 (1972) 609; M. B. Mineev, Physica D 43 (1990) 288.Google Scholar
5. Blumenfeld, R. and Ball, R. C., Phys. Rev. E, submitted.Google Scholar
6. Blumenfeld, R., in Nonlinear Evolution Equations and Dynamical Systems, ed. Makhankov, V.G. (World Scientific, 1995).Google Scholar
7. Blumenfeld, R., in Fluctuations and Order: The New Synthesis, ed. Milonas, M.M. (Springer-Verlag, 1994).Google Scholar
8. Blumenfeld, R., Phys. Rev. E, To be published.Google Scholar
9. Mullins, W. W. and Sekerka, R. F., J. Appl. Phys. 34 (1963) 323.Google Scholar
10. Howison, S. D., J. Fluid Mech. 167 (1986) 439.Google Scholar
11. Halsey, T. C., Phys. Rev. Lett. 59 (1987) 2067.Google Scholar
12. Ball, R. C. and Blumenfeld, R., Phys. Rev. A 44 (1991) R828.Google Scholar