Title: A Unified Approach for Solving Stochastic Problems in Engineering

Speaker: Mircea Grigoriu, Cornell University

Date/Time: Monday, May 14, 2007, 1:00 pm – 2:00 pm – New Time.

Location: CSRI Building, Room 90 (Sandia NM)

Brief Abstract: A method is presented for solving a broad range of linear/nonlinear random vibration problems and calculating effective properties of random heterogeneous materials. The method is based on Ito's formula for semimartingales and properties of semimartingales. The semimartingales considered in this presentation satisfy stochastic differential equations driven by Gaussian, Poisson, and Levy white noise processes, defined as formal time derivatives of Brownian motion, compound Poisson, and Levy motion processes. The method is applied to (1) calculate moments, characteristic functions, and other output statistics for the state of linear and nonlinear dynamic systems subjected to Gaussian and non-Gaussian noise and (2) determine effective properties for material specimens with conductivity varying randomly in space.