Zero gravity liquid transfer screen

A liquid transfer device for use in a zero gravity environment, for transferring liquid from one container to another is described. The device includes a spiral shaped screen type member which is carried in the container for collecting the randomly dispersed liquid and transferring such to an exit port

Fourier, Gegenbauer and Jacobi Expansions for a Power-Law Fundamental Solution of the Polyharmonic Equation and Polyspherical Addition Theorems

We develop complex Jacobi, Gegenbauer and Chebyshev polynomial expansions for the kernels associated with power-law fundamental solutions of the polyharmonic equation on d-dimensional Euclidean space. From these series representations we derive Fourier expansions in certain rotationally-invariant coordinate systems and Gegenbauer polynomial expansions in Vilenkin's polyspherical coordinates. We compare both of these expansions to generate addition theorems for the azimuthal Fourier coefficients

Fourier expansions for a logarithmic fundamental solution of the polyharmonic equation

In even-dimensional Euclidean space for integer powers of the Laplacian greater than or equal to the dimension divided by two, a fundamental solution for the polyharmonic equation has logarithmic behavior. We give two approaches for developing a Fourier expansion of this logarithmic fundamental solution. The first approach is algebraic and relies upon the construction of two-parameter polynomials. We describe some of the properties of these polynomials, and use them to derive the Fourier expansion for a logarithmic fundamental solution of the polyharmonic equation. The second approach depends on the computation of parameter derivatives of Fourier series for a power-law fundamental solution of the polyharmonic equation. The resulting Fourier series is given in terms of sums over associated Legendre functions of the first kind. We conclude by comparing the two approaches and giving the azimuthal Fourier series for a logarithmic fundamental solution of the polyharmonic equation in rotationally-invariant coordinate systems

Floating baffle to improve efficiency of liquid transfer from tanks

When liquid tank is full, baffle is held up against a stop on top of shaft to prevent restriction of flow from outlet. As tank is being emptied, baffle, floating on top of liquid surface, descends with liquid level toward outlet until it reaches its bottom stop. Baffle prevents gas pull-through until practically all liquid is emptied from tank

Opposite Antipodal Fundamental Solution of Laplace's Equation in Hyperspherical Geometry

Due to the isotropy of $d$-dimensional hyperspherical space, one expects there to exist a spherically symmetric opposite antipodal fundamental solution for its corresponding Laplace-Beltrami operator. The $R$-radius hypersphere ${\mathbf S}_R^d$ with $R>0$, represents a Riemannian manifold with positive-constant sectional curvature. We obtain a spherically symmetric opposite antipodal fundamental solution of Laplace's equation on this manifold in terms of its geodesic radius. We give several matching expressions for this fundamental solution including a definite integral over reciprocal powers of the trigonometric sine, finite summation expressions over trigonometric functions, Gauss hypergeometric functions, and in terms of the Ferrers function of the second with degree and order given by $d/2-1$ and $1-d/2$ respectively, with real argument $x\in(-1,1)$.Comment: essentially corrected versio