Daniele Venturi (Brown University) "Convolutionless Nakajima-Zwanzig probability-density-function equations for stochastic analysis in large scale simulations"
Tuesday, December 3, 2013, 4:00pm to 5:00pm | Room 1-375
Determining the statistical properties of stochastic nonlinear systems is a problem of major interest in many areas of science and engineering. Even with recent theoretical and computational advancements, no broadly applicable technique has yet been developed for dealing with the challenging problems of high dimensionality, low regularity and random frequencies. In this talk we present a new framework for stochastic analysis in large scale simulations based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics, and it relies on deriving evolution equations for the PDF of quantities of interest, e.g., functionals of the solution to systems of stochastic ordinary and partial differential equations. Such quantities could be low-dimensional objects in infinite dimensional phase spaces. We develop the goal-oriented PDF method in the context of the time-convolutionless Nakajima-Zwanzig-Mori formalism. We address the question of approximation of reduced-order density equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Numerical examples are presented for stochastic resonance, stochastic advection-reaction and Burgers equations.
Short bio: Daniele Venturi received the B.S. and Sc.M. degrees in Mechanical Engineering at the University of Bologna in 2002. Then he joined the Department of Energy, Nuclear and Environmental Engineering at the University of Bologna where he received the Ph.D. degree in thermo-fluid dynamics in 2006. Since 2010 he has been appointed as research assistant professor at the Division of Applied Mathematics of Brown University. His research interests embrace a wide range of topics. In particular, he has been working on theoretical and computational fluid dynamics, stochastic low-dimensional modeling and simulation of complex systems, probability density function methods and nonlinear functional analysis.