Libration-induced mean flow in a spherical shell

Libration-induced mean flow in a spherical shell

Convection patterns in a spherical fluid shell.

Symmetry-breaking bifurcations have been studied for convection in a nonrotating spherical shell whose outer radius is twice the inner radius, under the influence of an externally applied central force field with a radial dependence proportional to 1/r(5). This work is motivated by the GeoFlow experiment, which is performed under microgravity condition at the International Space Station where t...

Conducting Spherical Shell with a Circular Orifice

A conducting spherical shell with a circular orifice of half angle θ0 is at electric potential V0. Show that the difference between the charge densities on the inner and outer surfaces is independent of position, and estimate the ratio of the electric charge on the inner surface to that on the outer. Correct results can be inferred from “elementary” arguments based on superposition, and more “e...

Casimir Energy of a Spherical Shell

The Casimir energy for a conducting spherical shell of radius a is computed using a direct mode summation approach. An essential ingredient is the implementation of a recently proposed method based on Cauchy's theorem for an evaluation of the eigenfrequencies of the system. It is shown, however, that this earlier calculation uses an improper set of modes to describe the waves exterior to the sp...

Expanding Spherical Shell of Charge

in Gaussian units and in spherical coordinates where a(t) is the radius of the shell, Q is the total surface charge, and H(x, x0) = ∫ x −∞ δ(x ′ − x0) dx′ is the Heaviside step function. However, magnetic charges do not exist, so we cannot have a radial magnetic field of the form (1). That is, the magnetic field is zero, B = 0 everywhere, no matter what is the time dependence a(t) of the radius...