E cient and robust multigrid solvers for anisotropic problems typically use either semi-coarsened grids or implicit smoothers line relaxation in 2D and plane relaxation in 3D. However, both of these may be di cult to implement in codes using multiblock structured grids where there may be no natural de nition of a global `line' or `plane'. These multi-block structured grids are often used in uid...

The aim of this study is the evaluation of the e ect of microencapsulation of nanoparticles in composite microparticles on the reduction of burst release. Microparticles (simple and composite) and nanoparticles were prepared by using water-in-oil-in-water (W/O1/W2 double-emulsion solvent di usion/evaporation method), using di erent drug/polymer ratios. For preparation of the composite micropart...

Subgrid-scale models for large-eddy simulation that are based on exact series expansions for ltered products are considered. In particular, if the rst two terms are retained, the result is a di usive subgrid term with a tensor di usivity. This tensor is proportional to the rate-of-strain tensor of the large-scale velocity eld. This leads to negative di usion in the stretching directions. Implic...

In this paper we introduce and study a least squares nite element approximation for singu larly perturbed convection di usion equations of second order By introducing the ux di usive plus convective as a new unknow the problem is written in a mixed form as a rst order system Further the ux is augmented by adding the lower order terms with a small parameter The new rst order system is approximat...

We use a rapidly rotating tank lled with water to study the random walks of tracer particles in two di erent ows: one with coherent structures (vortices and jets), and one without (weakly turbulent). Most random walks, such as those taken by dye molecules di using by Brownian motion, obey the Central Limit Theorem; their motion can be characterized by a di usion constant. The random walks in ou...

We present a corrected operator splitting COS method for solving nonlinear parabolic equations of convection di usion type The main feature of this method is the ability to correctly resolve nonlinear shock fronts for large time steps as opposed to standard operator splitting OS which fails to do so COS is based on solving a conservation law for modeling convection a heat type equation for mode...

Up owing salty groundwater, evaporating completely at the ground surface, leads to the buildup of a saline boundary layer, usually with solid salt on the surface. The di usion layer below the surface, if stable, may grow to a nite thickness at equilibrium between the up owing salt and downward di usion. Because of the di erent densities of the uids (low fresh water density in the deeper undergr...

We study variational formulas for maximizers for domain functionals F (x0; u (x0)), x0 2 , and R F (x; u (x)) dx over all Lipschitz domains satisfying the constraint R g (x) dx = 1. Here u is the solution of a di usion equation in . Functional variations are computed using domain variations which preserve the constraint exactly. We show that any maximizer solves a moving boundary problem for th...

Synopsis We compute the higher-order statistics of the 3D spin displacement probability distributions measured with mean apparent propagator (MAP) MRI and quantify microstructural tissue parameters such as the mean kurtosis (MK), axial kurtosis (K ), radial kurtosis (K ) and kurtosis fractional anisotropy (FA ). This extension of the family of MAP tissue parameters provides a direct link betwee...

This paper develops a Multivariate Weighted Nonlinear Least Square estimator for a jumpdi usion interest rate model (hereafter MWNLS-JD), which also admits a closed form solution to bond price under an equilibrium martingale pricing theorem. The instantaneous interest rate is modeled as a mixture of a continuous square-root di usion and a discrete Poisson jump process, with the jump sizes unifo...