Efficient simulation of threshold behavior

Abstract

The paper discusses a new method for the propagation of risk levels. This discretization takes place by considering the phase space of the state and its subdivision into boxes. In each time step, the method computes the probability of the state being in one box. We start with a variety of technical and physical problems by showing how discrete modeling under uncertainties is technically meaningful and often even problem inherent. Then we select the technical problem of contaminant spread in water grids, to which we apply the method of risk-level propagation in depth. Extensions of the method such as modeling of contaminant mixing at junctions in the discretized phase space and the applicability of conservation laws arise naturally along these lines and are discussed in the context of the general theory.