Nonlinear non-Gaussian state-space models arise in numerous applications in statistics and signal processing. In this context, one of the most successful and popular approximation techniques is the sequential Monte-Carlo (SMC) algorithm, also known as the particle filter. Nevertheless, this method tends to be inefficient when applied to high-dimensional problems. In this chapter, we present, an...

Despite the ever increasing availability of computational resources, fully resolved simulations of magnetohydrodynamic (MHD) turbulence are not going to be feasible for quite some time. For this reason, large eddy simulations (LES) have been introduced that only resolve large scales. In LES a low-pass filter is applied to the evolution equations, which introduces additional unknown terms. These...

The estimation of time-varying aerosol size distributions on the basis of differential mobility particle sizer measurements is a dynamical inverse problem with a non-linear/non-Gaussian state space model. A sequential Monte Carlo approach for determining approximations for the state estimates is proposed. The vapour pressure, which is difficult to measure accurately, is here taken as an unknown...

Large Eddy Simulation (LES) has become an increasingly attractive option for turbulence modeling due to the rise in computing power and the improvement in sub-grid scale (SGS) parameterizations. This study tests the improvements in simulations of wall-bounded flows over heterogeneous surfaces attained by the implementation of three improvements in the eddy-viscosity SGS closure: the dynamic mod...

The combination of a high-order unstructured spectral difference (SD) spatial discretization scheme with sub-grid scale (SGS) modeling for large-eddy simulation is investigated with particular focus on the consistent implementation of a structural mixed model based on the scale similarity hypothesis. The difficult task of deriving a consistent formulation for the discrete filter within the SD e...

We report direct numerical simulation (DNS) and large-eddy simulation (LES) of statistically stationary buoyancy-driven turbulent mixing of an active scalar. We use an adaptation of the fringe-region technique, which continually supplies the flow with unmixed fluids at two opposite faces of a triply periodic domain in the presence of gravity, effectively maintaining an unstably stratified, but ...

A "realistic" interpolation or extrapolation of bathymetry, i.e., one that honors both the statistical character and the deterministic constraints of the data, is referred to as a "conditional simulation." The first step in generating a conditional simulation is derivation of a statistical model for bathymetry. We typically employ the anisotropic von Kármán model (Goff and Jordan, 1988), which ...

We develop a simulation-based method for the online updating of Gaussian process regression and classification models. Our method exploits sequential Monte Carlo to produce a thrifty sequential design algorithm, in terms of computational speed, compared to the established MCMC alternative. The latter is less ideal for sequential design since it must be restarted and iterated to convergence with...