Determination of the fractal dimension of equipotential surfaces in a region confined by rough conductors

We consider a region bounded by two conductors held to a constant voltage bias, one of them with an irregular rough shape and the other being a flat one. The irregular profile can be either a curve with a formation rule or the result of a deposition process. The rough shape of the profile influences...

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Bibliographic Details
Published in:Physica A 2004-10, Vol.342 (1), p.388-394
Main Authors: de O. Dias Filho, H., de Castilho, C.M.C., Miranda, J.G.V., Andrade, R.F.S.
Format: Article
Language:English
Subjects:
Fractal Dimension
Laplace's equation
Surfaces
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Summary:We consider a region bounded by two conductors held to a constant voltage bias, one of them with an irregular rough shape and the other being a flat one. The irregular profile can be either a curve with a formation rule or the result of a deposition process. The rough shape of the profile influences the equipotential lines, which we have characterized by numerically evaluating their roughness exponent α and fractal dimension D f . For a fixed finite size system, the less corrugated lines, far away from the rough profile, have higher α. For a line corresponding to a fixed value of the potential, the roughness exponent decreases with the size of the profile, suggesting that a single constant value characterizes all lines for an infinite system.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2004.04.099