Supersymmetry, the Cosmological Constant and a Theory of Quantum Gravity in Our Universe

There are many theories of quantum gravity, depending on asymptotic boundary conditions, and the amount of supersymmetry. The cosmological constant is one of the fundamental parameters that characterize different theories. If it is positive, supersymmetry must be broken. A heuristic calculation shows that a cosmological constant of the observed size predicts superpartners in the TeV range. This mechanism for SUSY breaking also puts important constraints on low energy particle physics models. This essay was submitted to the Gravity Research Foundation Competition and is based on a longer article, which will be submitted in the near future

Richardson Extrapolation for Linearly Degenerate Discontinuities

In this paper we investigate the use of Richardson extrapolation to estimate the convergence rates for numerical solutions to advection problems involving discontinuities. We use modified equation analysis to describe the expectation of the approach. In general, the results do not agree with a-priori estimates of the convergence rates. However, we identify one particular use case where Richardson extrapolation does yield the proper result. We then demonstrate this result using a number of numerical examples.Comment: 19 pages, 4 figur

On damping mechanisms in beams

A partial differential equation model of a cantilevered beam with a tip mass at its free end is used to study damping in a composite. Four separate damping mechanisms consisting of air damping, strain rate damping, spatial hysteresis and time hysteresis are considered experimentally. Dynamic tests were performed to produce time histories. The time history data is then used along with an approximate model to form a sequence of least squares problems. The solution of the least squares problem yields the estimated damping coefficients. The resulting experimentally determined analytical model is compared with the time histories via numerical simulation of the dynamic response. The procedure suggested here is compared with a standard modal damping ratio model commonly used in experimental modal analysis

Letter from J. D. Banks to Mims Williams

Letter from J. D. Banks to Mims Williams, regarding the contested will of William Douglass.https://scholarsjunction.msstate.edu/mss-williams-papers/1007/thumbnail.jp

Letter to Virginia Williams from J. D. Banks

Letter to Virginia Williams from J. D. Banks in Kirbyville, Texas, regarding the contested will of William Douglass.https://scholarsjunction.msstate.edu/mss-williams-papers/1015/thumbnail.jp

Letter to Virginia Williams

Letter to Virginia Williams from J. D. Banks, regarding the contested will of William Douglass.https://scholarsjunction.msstate.edu/mss-williams-papers/1048/thumbnail.jp