Network Algorithms and Critical Manifolds in Disordered Systems

Random manifolds in the form of critical paths or surfaces, are observed in a wide variety of processes in materials physics. Spectacular examples are critical manifolds on which failure occurs, for example strain localisation and fracture of materials under stress and electric current localisation in dielectric failure. In these cases localisation of the applied load on a low dimensional manifold acts as a precursor to the failure instability. Failure is an irreversible process, however critical manifolds also emerge in reversible nonlinear processes such as the onset of voltage in an ideal superconductor and the onset of current in a varistor. We shall show that it is possible to study these latter cases in great detail using network optimization algorithms.