Optimal Paths in Random Conductor Networks

Abstract

In this master thesis, the spanning path through a random conductor network with aquenched threshold distribuion has been studied. An argument is made using a hierar-chial model, that for bonds having a piecewise linear character with slopes α before thethreshold and β after, with α, β ∈ [0, ∞), it is the ratio r = α/β which is important forwhere the spanning path forms. It is shown that in the limit of r → ∞, the spanningpath follows the optimal path through the network, as in the case of a perfect plastic.Numerical results which support the argument are also given. The fracture path inbrittle fracture has also been studied in a hierarchy of optimal paths, without leadingto any conclusions.