Dielectric breakdown model (DBM) is a macroscopic
mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
combining the
diffusion-limited aggregation
Diffusion-limited aggregation (DLA) is the process whereby particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such particles. This theory, proposed by T.A. Witten Jr. and L.M. Sander in 1981, is a ...
model with
electric field. It was developed by Niemeyer, Pietronero, and Weismann in 1984.
It describes the patterns of
dielectric breakdown
Electrical breakdown or dielectric breakdown is a process that occurs when an electrical insulating material, subjected to a high enough voltage, suddenly becomes an electrical conductor and electric current flows through it. All insulating mate ...
of solids, liquids, and even gases, explaining the formation of the branching,
self-similar
__NOTOC__
In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically s ...
Lichtenberg figure
A Lichtenberg figure (German ''Lichtenberg-Figuren''), or Lichtenberg dust figure, is a branching electric discharge that sometimes appears on the surface or in the interior of insulating materials. Lichtenberg figures are often associated w ...
s.
See also
*
Eden growth model
The Eden growth model describes the growth of specific types of clusters such as bacterial colonies and deposition of materials. These clusters grow by random accumulation of material on their boundary. These are also an example of a surface fra ...
*
Lichtenberg
Lichtenberg () is the eleventh borough of Berlin, Germany. In Berlin's 2001 administrative reform it absorbed the former borough of Hohenschönhausen.
Overview
The district contains the Tierpark Berlin in Friedrichsfelde, the larger of Berlin' ...
figure
*
Diffusion-limited aggregation
Diffusion-limited aggregation (DLA) is the process whereby particles undergoing a random walk due to Brownian motion cluster together to form aggregates of such particles. This theory, proposed by T.A. Witten Jr. and L.M. Sander in 1981, is a ...
References
External links
Dielectric Breakdown Model
Electricity
Mathematical modeling
Electrical breakdown
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