Search results
Results from the WOW.Com Content Network
A polytrope with index n = 3 is a good model for the cores of white dwarfs of higher masses, according to the equation of state of relativistic degenerate matter. [7] A polytrope with index n = 3 is usually also used to model main-sequence stars like the Sun, at least in the radiation zone, corresponding to the Eddington standard model of ...
A solution to the Lane–Emden equation using a polytropic fluid is known as a polytrope. See also. Adiabatic process; Compressor; Internal combustion engine;
A polygon is a 2-dimensional polytope. Polygons can be characterised according to various criteria. Some examples are: open (excluding its boundary), bounding circuit only (ignoring its interior), closed (including both its boundary and its interior), and self-intersecting with varying densities of different regions.
where is a dimensionless radius and is related to the density, and thus the pressure, by = for central density .The index is the polytropic index that appears in the polytropic equation of state, = + where and are the pressure and density, respectively, and is a constant of proportionality.
Many examples of bounded convex polytopes can be found in the article "polyhedron".In the 2-dimensional case the full-dimensional examples are a half-plane, a strip between two parallel lines, an angle shape (the intersection of two non-parallel half-planes), a shape defined by a convex polygonal chain with two rays attached to its ends, and a convex polygon.
In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry.In particular, all its elements or j-faces (for all 0 ≤ j ≤ n, where n is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are themselves regular polytopes of dimension j≤ n.
The polytopes of rank 2 (2-polytopes) are called polygons.Regular polygons are equilateral and cyclic.A p-gonal regular polygon is represented by Schläfli symbol {p}.. Many sources only consider convex polygons, but star polygons, like the pentagram, when considered, can also be regular.
This equation of state is also a general case of the older Polytrope relation [6] which also has a constant power relation. In some circumstances, particularly in connection with ab initio calculations, the expression of the energy as a function of the volume will be preferred, [ 7 ] which can be obtained by integrating the above equation ...