Electrical properties of the unit square plate

Abstract

Numerical values of electrostatic properties of the cube are well investigated whereas numerical ones of the square plate are not. In this paper, we update the numerical values of electrostatic properties of the unit square plate, such as the capacitance, and the edge and corner singularity exponents. For the capacitance, we use the refined Brownian dynamics algorithm with "walk-on-planes"(WOP) method (a kind of first -passage algorithm) and for the edge singularity and corner exponents, the sphere last -passage algorithm.