This research program will develop new methods for the study of material microscale geometric and physical randomness. The effort will focus on the areas of effective response of graph- representable materials, and on neighborhoods (which allows for both nearest and distant neighbor interaction) will be used, leading to Markov field models that will be used to predict effective response laws and the onset of instabilities. Emphasis in the second area is on the development of a stochastic method and solutions for determining plastic flow and stress fields in a granular medium whose yield condition is a random field of space coordinates. This will lead to a procedure for the stochastic generalization of the method of characteristics, which will allow for the study of slip-line fields and wave propagation in realistic models of granular media.*** //
