Discrete exterior calculus (DEC) for the surface Navier-Stokes equation

We consider a numerical approach for the incompressible surface Navier-Stokes equation. The approach is based on the covariant form and uses discrete exterior calculus (DEC) in space and a semi-implicit discretization in time. The discretization is described in detail and related to finite difference schemes on staggered grids in flat space for which we demonstrate second order convergence. We compare computational results with a vorticity-stream function approach for surfaces with genus 0 and demonstrate the interplay between topology, geometry and flow properties. Our discretization also allows to handle harmonic vector fields, which we demonstrate on a torus.Comment: 21 pages, 9 figure

Diagnosis of inflammatory demyelination in biopsy specimens: a practical approach

Multiple sclerosis is the most frequent demyelinating disease in adults. It is characterized by demyelination, inflammation, gliosis and a variable loss of axons. Clinically and histologically, it shares features with other demyelinating and/or inflammatory CNS diseases. Diagnosis of an inflammatory demyelinating disease can be challenging, especially in small biopsy specimens. Here, we summarize the histological hallmarks and most important neuropathological differential diagnoses of early MS, and provide practical guidelines for the diagnosis of inflammatory demyelinating diseases