Estimating Dirichlet's integral and electrical conductance for systems which are not self-adjoint
نویسندگان
چکیده
In simple electrical flow problems the Dirichlet integral of the potential function gives the electrical conductance. Moreover the Dirichlet integral of an arbitrary function satisfying the boundary condition gives an upper bound for the conductance. This last property (Dirichlet's principle) does not hold if the boundary value problem is not self-adjoint. This paper develops new algorithms for estimating the conductance The proof of these algorithms replaces the Dirichlet principle with the elliptic maximum principle. There is an analogous discrete problem for conductance of electrical networks of the non-reciprocal type. The conductance problem both for continuous bodies and discrete networks can be treated by a single postulational theory. HUNT LIBRARY CARNEGIE-MELLON UNIVERSITY Estimating Dirichlets Integral and Electrical Conductance For Systems Which Are Not Self-Adjoint* R. J. Duffin
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