A finite element/volume method model of the depth-averaged horizontally 2D shallow water equations

Analysis of surface water flows is of central importance in understanding and predicting a wide range of water engineering issues. Dynamics of surface water is reasonably well described using the shallow water equations (SWEs) with the hydrostatic pressure assumption. The SWEs are nonlinear hyperbolic partial differential equations that are in general required to be solved numerically. Application of a simple and efficient numerical model is desirable for solving the SWEs in practical problems. This study develops a new numerical model of the depth-averaged horizontally 2D SWEs referred to as 2D finite element/volume method (2D FEVM) model. The continuity equation is solved with the conforming, standard Galerkin FEM scheme and momentum equations with an upwind, cell-centered finite volume method scheme, utilizing the water surface elevation and the line discharges as unknowns aligned in a staggered manner. The 2D FEVM model relies on neither Riemann solvers nor high-resolution algorithms in order to serve as a simple numerical model. Water at a rest state is exactly preserved in the model. A fully explicit temporal integration is achieved in the model using an efficient approximate matrix inversion method. A series of test problems, containing three benchmark problems and three experiments of transcritical flows, are carried out to assess accuracy and versatility of the model

In vivo 3D MRI staining of mouse brain after subcutaneous application of MnCl2

Follow-up T-1-weighted 3D gradient-echo MRI (2.35 T) of murine brain in vivo (N = 5) at 120 mum isotropic resolution revealed spatially distinct signal increases 6-48 hr after subcutaneous application of MnCl2 (20 mg/kg). The effects result from a shortening of the water proton T-1 relaxation time due to the presence of unchelated paramagnetic Mn2+ ions, which access the brain by systemic circulation and crossing of the blood-brain barrier (BBB). A pronounced Mn2+-induced signal enhancement was first seen in structures without a BBB, such as the choroid plexus, pituitary gland, and pineal gland. Within 24 hr after administration, Mn2+ contrast highlighted the olfactory bulb, inferior colliculi, cerebellum, and the CA3 subfield of the hippocampus. The affinity of Mn2+ to various brain systems suggests the neuronal uptake of Mn2+ ions from the extracellular space and subsequent axonal transport. Thus, at least part of the Mn2+ contrast reflects a functional brain response of behaving animals, for example, in the olfactory system. In vivo MRI staining of the brain by systemic administration of MnCl2 may contribute to phenotyping mutant mice with morphologic and functional alterations of the central nervous system. (C) 2002 Wiley-Liss, Inc