Spinning Down a Black Hole With Scalar Fields

We study the evolution of a Kerr black hole emitting scalar radiation via the Hawking process. We show that the rate at which mass and angular momentum are lost by the black hole leads to a final evolutionary state with nonzero angular momentum, namely $a/M \approx 0.555$.Comment: 4 pages (including 3 postscript figures), Revtex, uses epsf.tex, twocolumn.sty and header.sty (included). Submitted to Physical Review Letter

Evaporation of a Kerr black hole by emission of scalar and higher spin particles

We study the evolution of an evaporating rotating black hole, described by the Kerr metric, which is emitting either solely massless scalar particles or a mixture of massless scalar and nonzero spin particles. Allowing the hole to radiate scalar particles increases the mass loss rate and decreases the angular momentum loss rate relative to a black hole which is radiating nonzero spin particles. The presence of scalar radiation can cause the evaporating hole to asymptotically approach a state which is described by a nonzero value of $a_* \equiv a / M$. This is contrary to the conventional view of black hole evaporation, wherein all black holes spin down more rapidly than they lose mass. A hole emitting solely scalar radiation will approach a final asymptotic state described by $a_* \simeq 0.555$. A black hole that is emitting scalar particles and a canonical set of nonzero spin particles (3 species of neutrinos, a single photon species, and a single graviton species) will asymptotically approach a nonzero value of $a_*$ only if there are at least 32 massless scalar fields. We also calculate the lifetime of a primordial black hole that formed with a value of the rotation parameter $a_{*}$, the minimum initial mass of a primordial black hole that is seen today with a rotation parameter $a_{*}$, and the entropy of a black hole that is emitting scalar or higher spin particles.Comment: 22 pages, 13 figures, RevTeX format; added clearer descriptions for variables, added journal referenc

Solutions of Higher Dimensional Gauss-Bonnet FRW Cosmology

We examine the effect on cosmological evolution of adding a Gauss-Bonnet term to the standard Einstein-Hilbert action for a (1 + 3)+ d dimensional Friedman-Robertson-Walker (FRW) metric. By assuming that the additional dimensions compactify as a power law as the usual 3 spatial dimensions expand, we solve the resulting dynamical equations and find that the solution may be of either de Sitter or Kasner form depending upon whether the Gauss-Bonnet term or the Einstein term dominates.Comment: 10 pages, references added/corrected, accepted for publication in General Relativity and Gravitatio

Adaptive Basketball Shooter - Final Project Report

The Friday Club is a joint venture between the Cal Poly Kinesiology Department and the San Luis Obispo Special Olympics that offers people with varying degrees of disability the opportunity to meet weekly and learn various sports and games. At Friday Club, athletes in wheelchairs with limited arm strength use devices built by Cal Poly mechanical engineering students in order to participate in various sports. Many devices are designed to attach to the Universal Play Frame (UPF), a wheel-chair attachment. The purpose of this project was to design and build a UPF device that will launch a basketball, so that an athlete can participate in a game of “Horse.” The project was worked on over the course of the 2013-2014 school year. To begin, the team developed a list of objectives for the device to meet and researched existing solutions for various facets of our design. The next step was to generate concepts of our device, and using Pugh matrices, proof of concept testing, and debate to narrow down to a single concept. Next, this concept was transformed into a fully-fledged design backed by engineering analysis. After design approval, all necessary parts and materials were ordered and a prototype was built over a 10 week period. The final prototype was tested with the Friday Club and displayed at the Senior Project Expo on May 31, 2014. The final device that our team designed is a slingshot that launches the ball by releasing stretched elastic bands. Our design attaches to the UPF at two points, and can be aimed to shoot a basket from anywhere between 5 and 15 feet away. The athlete has the ability to control the direction, power, and release of each shot. The device can be set up in under five minutes by a single person and takes only 30 seconds to reset between shots. Of all customer requirements that the device was to meet, it only failed to meet one of them. The first was that it should be able to shoot a three-pointer. Unfortunately, our device either did not have strong enough elastic, or did not have enough space to pull back the ball and carriage sufficiently. Therefore, our device can shoot a basket from a maximum of only 15 feet away, or a free throw. Other future recommendations are to strengthen some parts that take high impacts and to reduce the weight of some unnecessarily bulky parts. Our budget for this project was $1,500 but over the course of this project our team spent a little over$1,750. After analyzing our spending, we found that over $300 was spent because of manufacturing mistakes and mid-construction design changes. If we were to build another device with the exact same design as our final prototype, and with no mistakes, the device would cost about$1,400. In this report, our team’s entire design process is cataloged in detail. Also enclosed are detailed part drawings for each manufactured part of our final device, as well as a safety and operation manual

Besov Space, Schatten Classes And Commutators Of Riesz Transforms Associated With The Neumann Laplacian

This article provides a deeper study of the Riesz transform commutators associated with the Neumann Laplacian operator $\Delta_N$ on $\mathbb R^n$. Along the line of singular value estimates for Riesz transform commutators established by Janson--Wolff and Rochberg--Semmes, we establish a full range of Schatten-$p$ class characterization for these commutators

Superior multifunctional activity of nanoporous carbons with widely tuneable porosity: enhanced storage capacities for carbon-dioxide, hydrogen, water and electric charge

Nanoporous carbons (NPCs) with engineered specific pore sizes and sufficiently high porosities (both specific surface area and pore volume) are necessary for storing energy in the form of electric charges and molecules. Herein, NPCs, derived from biomass pine‐cones, coffee‐grounds, graphene‐oxide and metal‐organic frameworks, with systematically increased pore width (50 Wh kg−1 at high power density, 1000 W kg−1) are achieved to form the highest reported values among the range of carbons in the literature. The noteworthy energy storage performance of the NPCs for all five cases (CO2, H2, H2O, and capacitance in aqueous and organic electrolytes) is highlighted by direct comparison to numerous existing porous solids. A further analysis on the specific pore type governed physisorption capacities is presented