S. L. Moss

We present a theory of long-wavelength acoustic phonons localized at the apex of a variable-angle semi-infinite wedge made up of an isotropic cubic elastic medium. Stress-free boundary conditions are incorporated into the calculation by assuming position-dependent elastic constants. The equations of motion are solved numerically by first performing a linear mapping of the wedge into a right-angle wedge, and then expanding each displacement component in a double series of Laguerre functions. When the Cauchy relation is satisfied and when the interior angle of the wedge is between 125\ifmmode^\circ\else\textdegree\fi{} and 180\ifmmode^\circ\else\textdegree\fi{}, the speed of the lowest-frequency edge mode, which is of ${\ensuremath{\Gamma}}_{1}$ symmetry, is very nearly equal to the speed of Rayleigh surface waves. For wedge angles less than 100\ifmmode^\circ\else\textdegree\fi{}, the speed of the lowest-frequency edge mode, which is now of ${\ensuremath{\Gamma}}_{2}$ symmetry, decreases rapidly with angle and appears to vanish in the limit as the angle approaches 0\ifmmode^\circ\else\textdegree\fi{}. For these acute angles, additional edge modes of ${\ensuremath{\Gamma}}_{2}$ symmetry appear with speeds below the Rayleigh value.

An exact result is obtained for the dispersion relation for magnons localized at the apex of a semi-infinite, right-angle wedge of a simple-cubic, Heisenberg ferromagnet, with nearest- and next-nearest-neighbor exchange interactions, formed by the intersection of two (100) surfaces. The modes studied are wavelike in the direction parallel to the edge of the wedge, and they are characterized by a one-dimensional wave vector $q$. Their amplitudes decay exponentially with increasing distance into the wedge from its apex. The finite difference equation of motion for the magnon creation operators is solved by expanding the latter in a double series of Gottlieb functions. The dispersion relation for these edge localized modes is obtained for all values of $q$ in the one-dimensional first Brillouin zone of the wedge. In the long-wavelength limit it agrees with the result obtained recently in this limit by Sharon and Maradudin.

A linear array consisting of twenty-four 1 Hz geophones at 10 m spacing was used to measure the passive surface waves at the UTexas1 site. This paper describes analysis of this dataset using three different methods: ESPAC (extended spatial autocorrelation), f-k (frequency-wavenumber), and ReMi (refraction microtremor). Dispersion curves were developed using each method and the median trends as well as the uncertainty about the medians are compared. The dispersion curves were then individually inverted to estimate shear wave velocity profiles. The inversion results are compared, and a bounded best-estimate shear wave velocity profile is presented. For the site conditions, specific recording equipment, and array geometry the ESPAC method was the most consistent between recordings, and able to resolve the lowest frequency Rayleigh waves. The shear wave velocity of all three methods were in close agreement in the upper 20 m above a stiff layer, but were increasing disparate as depth increased. All three methods resolved a velocity inversion, a stiff layer, at roughly 20 m to 55 m depth overlying softer material. As is expected with surface wave methods, and particularly with passive methods that are measuring ambient noise along single linear array, the uncertainty in the dispersion curves increased with decreasing frequency, and the uncertainty in the shear wave velocity profiles increased with increasing depth.

This is an introduction to a new concept of quantum gravity that seamlessly merges General Relativity to the Standard Model. Based upon a novel patent-pending magnetic confinement method that was designed to emulate how our sun confines and rotates charged particles about a singularity; this confinement method uses a collective of off-centered confinement coils that are directed to curve rotating charged particles about a singularity in a way that allows charged particles to relatively accelerate from geodesic deviation. With this confinement method, the subtle Relative Accelerated Energy (RAE) from deviating charged particles has the capability to be focused and exponentially increased relative to the mass-energy of a closed system; which allows for a simple pathway to understand how black holes operate at their singularities. While in the pursuit of proving that this novel method of confinement mimics how our sun operates; I was also able to develop a logical explanation of how our sun reverses its magnetic poles and cycles using the core principles of Michael Faraday. If this concept of quantum gravity is correct, there is a simple explanation for the additional observed gravitational force about the galaxies that are said to obtain dark matter. In short, this theory of quantum gravity has the potential to fully discredit the existence of theorized dark matter with a simple experiment.