Capacitances and singularities of the unit triangle, square, tetrahedron and cube

The boundary element method has been used to obtain the electrical capacitances of the unit equilateral triangle, square, regular tetrahedron and cube. For each of these objects, a series of values of the number N of segments has been used and then empirical formulae have been used to extrapolate N...

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Bibliographic Details
Published in:Compel 2004-06, Vol.23 (2), p.572-578
Main Author: Read, F.H.
Format: Article
Language:English
Subjects:
Analysis
Approximation
Boundaryelements methods
Capacitance
Charged particles
Density
Electrical engineering
Geometry
Materials science
Physical properties of materials
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Summary:The boundary element method has been used to obtain the electrical capacitances of the unit equilateral triangle, square, regular tetrahedron and cube. For each of these objects, a series of values of the number N of segments has been used and then empirical formulae have been used to extrapolate N to infinity. The singularities of the charge densities at the edges and corners of these objects can be characterised by power laws, the relevant exponents of which have also been determined.
ISSN:0332-1649
2054-5606
DOI:10.1108/03321640410510758