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We describe the construction and implementation of a stochastic Navier–Stokes solver. The solver combines a spectral stochastic uncertainty representation scheme with a finite difference projection method for flow simulation. The uncertainty quantification scheme is adapted from the spectral stochastic finite element method (SSFEM), which is based on(More)
We present an equation-free computational approach to the study of the coarse-grained dynamics of finite assemblies of nonidentical coupled oscillators at and near full synchronization. We use coarse-grained observables which account for the (rapidly developing) correlations between phase angles and natural frequencies. Exploiting short bursts of(More)
Microsystems have become an integral part of our lives and can be found in homeland security, medical science, aerospace applications and beyond. Many critical microsys-tem applications are in harsh environments, in which long-term reliability needs to be guaranteed and repair is not feasible. For example, gyroscope microsystems on satellites need to(More)
We study a one-dimensional elliptic problem with highly oscillatory random diffusion coefficient. We derive a homogenized solution and a so-called Gaussian corrector. We also prove a " pointwise " large deviation principle (LDP) for the full solution and approximate this LDP with a more tractable form. Applications to uncertainty quan-tification are(More)
This paper gives an overview of the use of Polynomial Chaos expansions to represent stochastic processes in numerical simulations. Several methods are presented to perform arithmetic on, as well as to evaluate polynomial and non-polynomial functions of variables respresented with Polynomial Chaos expansions. These methods include Taylor series, a newly(More)