Fourier and Gegenbauer expansions for a fundamental solution of the Laplacian in the hyperboloid model of hyperbolic geometry

Due to the isotropy $d$-dimensional hyperbolic space, there exist a spherically symmetric fundamental solution for its corresponding Laplace-Beltrami operator. On the $R$-radius hyperboloid model of $d$-dimensional hyperbolic geometry with $R>0$ and $d\ge 2$, we compute azimuthal Fourier expansions for a fundamental solution of Laplace's equation. For $d\ge 2$, we compute a Gegenbauer polynomial expansion in geodesic polar coordinates for a fundamental solution of Laplace's equation on this negative-constant sectional curvature Riemannian manifold. In three-dimensions, an addition theorem for the azimuthal Fourier coefficients of a fundamental solution for Laplace's equation is obtained through comparison with its corresponding Gegenbauer expansion.Comment: arXiv admin note: substantial text overlap with arXiv:1201.440

Developments in determining the gravitational potential using toroidal functions

have shown how the integration/summation expression for the Green's function in cylindrical coordinates can be written as an azimuthal Fourier series expansion, with toroidal functions as expansion coefficients. In this paper, we show how this compact representation can be extended to other rotationally invariant coordinate systems which are known to admit separable solutions for Laplace's equation

Non-Linear Evolution of the r-Modes in Neutron Stars

The evolution of a neutron-star r-mode driven unstable by gravitational radiation (GR) is studied here using numerical solutions of the full non-linear fluid equations. The amplitude of the mode grows to order unity before strong shocks develop which quickly damp the mode. In this simulation the star loses about 40% of its initial angular momentum and 50% of its rotational kinetic energy before the mode is damped. The non-linear evolution causes the fluid to develop strong differential rotation which is concentrated near the surface and especially near the poles of the star.Comment: 4 pages, 7 eps figures, revtex; revised, typos correcte

Bond strength of orthodontic direct-bonding cement-bracket systems as studied in vitro

Tensile bond strength and failure location were evaluated in vitro for three types of direct bonding cements (unfilled, low filled, and highly filled) with three types of brackets (polycarbonate, stainless steel, and ceramic) using natural teeth and plastic as substrates. An unfilled acrylic cement gave the highest values of bond strength for both the plastic and ceramic brackets, whereas a highly-filled diacrylate cement gave the highest bond strength for the metal brackets. Bond failures occurred at the bracket-cement interface with the stainless steel brackets with each cement, whereas failure locations occurred at the bracket-cement interface, within the cement, and within the bracket for the plastic and ceramic brackets. There were no significant differences in bond strength nor failure location between tooth and plastic substrates.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24092/1/0000348.pd

Developments in determining the gravitational potential using toroidal functions

Cohl & Tohline (1999) have shown how the integration/summation expression for the Green\u27s function in cylindrical coordinates can be written as an azimuthal Fourier series expansion, with toroidal functions as expansion coefficients. In this paper, we show how this compact representation can be extended to other rotationally invariant coordinate systems which are known to admit separable solutions for Laplace\u27s equation