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The action of GL(n) extends naturally to a free transitive action of the affine group Aff(n) on FA, so that FA is an Aff(n)-torsor, and the choice of a reference frame identifies FA → A with the principal bundle Aff(n) → Aff(n)/GL(n). On FA there is a collection of n + 1 functions defined by
If the principal bundle P is the frame bundle, or (more generally) if it has a solder form, then the connection is an example of an affine connection, and the curvature is not the only invariant, since the additional structure of the solder form θ, which is an equivariant R n-valued 1-form on P, should be taken into account.
The Levi-Civita connection is named after Tullio Levi-Civita, although originally "discovered" by Elwin Bruno Christoffel.Levi-Civita, [1] along with Gregorio Ricci-Curbastro, used Christoffel's symbols [2] to define the notion of parallel transport and explore the relationship of parallel transport with the curvature, thus developing the modern notion of holonomy.
Here, the electric quadrupole interaction is due to the 14 N-nucleus, the hyperfine nuclear spin-spin splitting is from the magnetic coupling between nitrogen, 14 N (I N = 1), and hydrogen, 1 H (I H = 1 ⁄ 2), and a hydrogen spin-rotation interaction due to the 1 H-nucleus. These contributing interactions to the hyperfine structure in the ...
Affine gauge theory is classical gauge theory where gauge fields are affine connections on the tangent bundle over a smooth manifold.For instance, these are gauge theory of dislocations in continuous media when =, the generalization of metric-affine gravitation theory when is a world manifold and, in particular, gauge theory of the fifth force.
Concentrated solar power can achieve the high temperatures necessary to split water. Hydrosol-2 is a 100-kilowatt pilot plant at the Plataforma Solar de Almería in Spain which uses sunlight to obtain the required 800 to 1,200 °C (1,070 to 1,470 K; 1,470 to 2,190 °F) to split water. Hydrosol II has been in operation since 2008.
In atomic physics, the Landé interval rule [1] states that, due to weak angular momentum coupling (either spin-orbit or spin-spin coupling), the energy splitting between successive sub-levels are proportional to the total angular momentum quantum number (J or F) of the sub-level with the larger of their total angular momentum value (J or F).
The Advection Upstream Splitting Method (AUSM) is a numerical method used to solve the advection equation in computational fluid dynamics. It is particularly useful for simulating compressible flows with shocks and discontinuities. The AUSM is developed as a numerical inviscid flux function for solving a general system of conservation equations.