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Singular Interfacial Hydrodynamics and the Dielectric Breakdown Model

Published online by Cambridge University Press:  03 September 2012

H.G.E. Hentschel
H.G.E. Hentschel*
Affiliation:
Emory University, Department of Physics, Rollins Research Center, Atlanta, GA 30322
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Abstract

The equations of motion for the interfacial dynamics in the dielectric breakdown model are derived. They form a set of coupled hydrodynamic equations for the interfacial curvature and growth probability in which the conserved densities are transported by a nonlocal velocity. From these equations the dynamical manner in which singularities in these conserved densities evolve can be studied both analytically and numerically. Shock-like behaviour associated with velocity attractor and repellor points on the evolving interface lead to bifurcations in the velocity field and finally to fractal structures in the curvature and growth probability in the absence of surface tension. In the presence of surface tension spatiotemporal chaos is observed.

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Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 367: Symposium P – Fractal Aspects of Materials , 1994, 33
Copyright
Copyright © Materials Research Society 1995

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