User:AsmundErvik
Hi all,
I'm a Norwegian scientist working on numerical physics, in particular multiphase flows and fluid mechanics. I try to contribute to physics articles that are lacking content, as well as battling pseudoscience wherever I see it.
- Åsmund.
Temporary Storage[edit]
Articles that I'm working on are stored here until deemed fit for the public content.
General Equivalent Points[edit]
- REDIRECT general equivalent positions
The method of general equivalent points (sometimes called general equivalent positions) is a method used in solid state physics and crystallography when considering the point group of the crystal lattice. The purpose of the method is to easily determine the number of elements in the point group, an otherwise nontrivial task.
The Method[edit]
Consider the unit cell of a crystal lattice. In the unit cell, the principal axis, i.e. the axis with the highest symmetry, is determined. Then the unit cell is drawn as a projection onto the plane perpendicular to this axis. Next, a general point is drawn on the projection. As the name suggests, this point should not be located at a symmetry axis or mirror plane of any kind, but be as general as possible.[1]
When this first general point has been established, one tries to find all general equivalent points, or GEPs for short. These are the points that are equivalent with the first general point under the symmetry operations available.[1] In order to do this, the simplest idea is to use all the symmetry operations available to permute the point to all its possible positions on the projection. This is a tedious operation, however, as this number can be large. A much easier approach is to
Weighted Essentially Non-Oscillatory schemes[edit]
Weighted Essentially Non-Oscillatory schemes, or WENO schemes, is a class of numerical discretization schemes used in solving hyperbolic partial differential equations. These PDEs often have solutions that contain shocks, which causes ordinary finite difference methods to fail. This is a consequence of Godunov's theorem. WENO schemes have been developed to solve these problems, and can give very accurate solutions containing various types of shocks. Perhaps the most common WENO method is the WENO-5 method, which is fifth-order accurate in space.