Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems.

@article{Venturi2014ConvolutionlessNE,
title={Convolutionless Nakajima-Zwanzig equations for stochastic analysis in nonlinear dynamical systems.},
author={Daniele Venturi and George Em Karniadakis},
journal={Proceedings. Mathematical, physical, and engineering sciences},
year={2014},
volume={470 2166},
pages={20130754}
}

Determining the statistical properties of stochastic nonlinear systems is of major interest across many disciplines. Currently, there are no general efficient methods to deal with this challenging problem that involves high dimensionality, low regularity and random frequencies. We propose a framework for stochastic analysis in nonlinear dynamical systems based on goal-oriented probability density function (PDF) methods. The key idea stems from techniques of irreversible statistical mechanics… CONTINUE READING

On proper orthogonal decomposition of randomly perturbed fields with applications to flow past a cylinder and natural convection over a horizontal plate

D. Venturi

J. Fluid Mech.,

2006

1 Excerpt

Applications of Dirac’s delta function in statistics