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Codes which calculate exactly electromagnetic scattering by an aggregate of spheres and spheres within spheres for complex materials. Works in parallel as well. 2015 py_gmm G. Pellegrini [20] Python + Fortran A Python + Fortran 90 implementation of the Generalized Multiparticle Mie method, especially suited for plasmonics and near field ...
Here F N is the Newtonian force, m is the object's (gravitational) mass, a is its acceleration, μ (x) is an as-yet unspecified function (called the interpolating function), and a 0 is a new fundamental constant which marks the transition between the Newtonian and deep-MOND regimes. Agreement with Newtonian mechanics requires
where F is the gravitational force acting between two objects, m 1 and m 2 are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant. The first test of Newton's law of gravitation between masses in the laboratory was the Cavendish experiment conducted by the British scientist Henry ...
In the spherical-coordinates example above, there are no cross-terms; the only nonzero metric tensor components are g rr = 1, g θθ = r 2 and g φφ = r 2 sin 2 θ. In his special theory of relativity, Albert Einstein showed that the distance ds between two spatial points is not constant, but depends on the motion of the observer.
the vector r is the position of one body relative to the other; r, v, and in the case of an elliptic orbit, the semi-major axis a, are defined accordingly (hence r is the distance) μ = Gm 1 + Gm 2 = μ 1 + μ 2, where m 1 and m 2 are the masses of the two bodies. Then: for circular orbits, rv 2 = r 3 ω 2 = 4π 2 r 3 /T 2 = μ
For two pairwise interacting point particles, the gravitational potential energy is the work that an outside agent must do in order to quasi-statically bring the masses together (which is therefore, exactly opposite the work done by the gravitational field on the masses): = = where is the displacement vector of the mass, is gravitational force acting on it and denotes scalar product.
There are many useful features of the effective potential, such as . To find the radius of a circular orbit, simply minimize the effective potential with respect to , or equivalently set the net force to zero and then solve for : = After solving for , plug this back into to find the maximum value of the effective potential .
Here, 1 / 2 σ μν and F μν stand for the Lorentz group generators in the Dirac space, and the electromagnetic tensor respectively, while A μ is the electromagnetic four-potential. An example for such a particle [9] is the spin 1 / 2 companion to spin 3 / 2 in the D (½,1) ⊕ D (1,½) representation space of the ...