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...

EURegulation 2009/72/EC concerning common rules for internalmarket in electricity calls upon80% of EU electricity consumers to be equippedwith smartmetering systems by 2020, provided that a positive economic assessment of all long-term costs and benefits to themarket and the individual consumer is guaranteed. Understanding the impact that smart metering systems may have on the electricity stake...

We establish L convergence of a viscous splitting method for nonlinear possibly strongly degenerate convection-di usion problems. Since we allow the equations to be strongly degenerate, solutions can be discontinuous and they are not, in general, uniquely determined by their data. We thus consider entropy weak solutions realized by the vanishing viscosity method. This notion is broad enough to ...

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...

We present a study of the local discontinuous Galerkin method for transient convection-di usion problems in one dimension. We show that p degree piecewise polynomial discontinuous nite element solutions of convection-dominated problems are O( xp+2) superconvergent at Radau points. For di usion-dominated problems, the solution's derivative is O( xp+2) superconvergent at the roots of the derivati...

GIS managers traditionally consider three perspectives of the nature of GIS when introducing GIS into an organization. When the GIS is developed to address focused and well de® ned problems of the organization, these perspectives adequately describe the changing identities of GIS in the study of its di€ usion. However when the GIS is developed to address strategic, but vaguely de® ned problems,...

This paper deals with development and analysis of a fully discrete nite element method for a nonlinear di erential system for describing an air water system in groundwater hydrol ogy The nonlinear system is written in a fractional ow formulation i e in terms of a saturation and a global pressure The saturation equation is approximated by a nite element method while the pressure equation is trea...

The di culty encountered when solving singularly perturbed differential equations is that errors introduced in layers pollute the solution in smooth regions. Since a priori control of the errors in layers is di cult, special methods must be designed to reduce or eliminate polluting errors. Successful methods add dissipation to a computational scheme to enlarge layers to the mesh spacing. We foc...