In 1920, Rudolf Bach proposed an action based on the square of the Weyl tensor or CabcdCabcd where the Weyl tensor is an invariant under a scaling of the metric. A variation of the metric leads to the field equation known as the Bach equation. In this dissertation, the same action is analyzed, but as a conformal gauge theory. It is shown that this action is a result of a particular gauging of this group. By treating it as a gauge theory, it is natural to vary all of the gauge fields independently, rather than performing the usual fourth-order metric variation only. We show that solutions of the resulting vacuum field equations are all solutions to the vacuum Einstein equation, up to a conformal factor—a result consistent with local scale freedom. We also show how solutions for the gauge fields imply there is no gravitational self energy.

Ph.D., Faculty of Science, University of Witwatersrand, 2011 / Operators in N = 4 super Yang-Mills theory with an R-charge of O(N2) are dual to backgrounds which are asymtotically AdS5 S5. In this thesis we develop e cient techniques that allow the computation of correlation functions in these backgrounds. We nd that (i) contractions between elds in the string words and elds in the operator creating the background are the eld theory accounting of the new geometry, (ii) correlation functions of probes in these backgrounds are given by the free eld theory contractions but with rescaled propagators and (iii) in these backgrounds there are no open string excitations with their special end point interactions; we have only closed string excitations. Furthermore, these correlation functions are not well approximated by the planar limit. The non-planar diagrams, which in the bulk spacetime correspond to string loop corrections, are enhanced by huge combinatorial factors. We show how these loop corrections can be resummed. As a typical example of our results, in the half-BPS background of M maximal giant gravitons we nd the usual 1=N expansion is replaced by a 1=(M +N) expansion. Further, we nd that there is a simple exact relationship between amplitudes computed in the trivial background and amplitudes computed in the background of M maximal giant gravitons. We also nd strong evidence for the BMN-type sectors suggested in arXiv:0801.4457. The problem of computing the anomalous dimensions of (nearly) half-BPS operators with a large R-charge is reduced to the problem of diagonalizing a Cuntz oscillator chain. Due to the large dimension of the operators we consider, non-planar corrections must be summed to correctly construct the Cuntz oscillator dynamics. These non-planar corrections do not represent quantum corrections in the dual gravitational theory, but rather, they account for the backreaction from the heavy operator whose dimension we study. Non-planar corrections accounting for quantum corrections seem to spoil integrability, in general. It is interesting to ask if non-planar corrections that account for the backreaction also spoil integrability. We nd a limit in which our Cuntz chain continues to admit extra conserved charges suggesting that integrability might survive.

A non-supersymmetric Yi-deformed AdS/CFT correspondence has recently been conjectured by Frolov. A detailed description of both sides of this proposed gauge/string duality is presented. The analogy that exists between single trace gauge theory operators in the SU(3) sector and i-deformed SU(3) integrable spin chains is also discussed. Frolov, Roiban and Tseytlin’s leading order comparison between the ideformed spin chain coherent state action and i-deformed string worldsheet action in the semiclassical limit is reviewed. A particular Lax pair representation for the first order semiclassical i-deformed spin chain/string action is then constructed.

With over 10,000 acres burned in wildland fires in 2014 in Mississippi, accurate fire hazard prediction is of great importance. Soil moisture, fuel moisture, and fire hazard are inextricably linked. Remote estimation of soil moisture in the Southeastern United States for fire hazard modeling is hampered by the use of models engineered for other physiographic regions and the prevalence of deep, fast-draining sands underneath heavy vegetation. United States Geologic Service hydrographs were investigated and compared to nearby soil moisture and precipitation readings in an attempt to identify the links between stream gauge readings and watershed soil moisture. Stream gauge peaks corresponded within a three day window of soil moisture peaks 73.3% of the time, with 43.8% of peaks occurring simultaneously, thus verifying the indicative nature of local hydrographs. With further study, this easily accessed proxy variable could enhance currently used soil moisture models and drought indices.

No description available.

No description available.

No description available.

This thesis researched why light gauge steel framing members are not used more in single-family residential construction. A survey was designed to extract information from licensed contractors in Utah on uses of light gauge steel framing members in residential homes. The purpose of the research was to discover what Utah builder's perception was concerning light gauge steel framing. Also, the researcher tried to learn a little about the contractors to see if there was a correlation between contractors that used light gauge steel and those that did not. Names of licensed general building contractors and residential contractors and their contact information were acquired from the State of Utah's Department of Professional Licensing. A random sample of the licensed contractors was selected. They were contacted by mail and telephone and invited to participate in a survey. The researcher discovered that light gauge steel was used in a very limited amount. The respondents seemed build using traditional methods, namely lumber. They were unfimiliar with light gauge steel and its properties, as well as the benefits and disadvantages of light gauge steel.

Biological tissues routinely experience large strains and undergo large deformations during normal physiologic activity. Biological tissue deformation is well beyond the range of standard strain gauges, and hence must often be captured using expensive and non-portable options such as optical marker tracking methods that may rely upon significant post-processing. This study develops portable gauges that operate in real time and are compatible with the large strains seen by biological materials. The new gauges are based on a relatively new technique for quantifying large strain in real-time (up to 40 %) by use of a piezoresistive nano-composite strain gauge. The nano-composite strain gauges (NCSGs) are manufactured by suspending nickel nanostrands within a biocompatible silicone matrix. The conductive nickel filaments come into progressively stronger electrical contact with each other as the NCSG is strained, thus reducing the electrical resistance that is then measured using a four-probe method. This thesis summarizes progress in the understanding, design and application of NCSGs for biomechanical applications. The advanced understanding arises from a nano-junction-level finite element analysis of gap evolution that models how the geometry varies with strain in the critical regions between nickel particles. Future work will incorporate this new analysis into global models of the overall piezoresistive phenomenon. The improvements in design focused on the manufacturing route to obtain a reliable thin and flexible gauge, along with a modified connection and data extraction system to reduce drift issues that were present in all previous tests. Furthermore, a pottable data logging system was developed for mobile applications. Finally, a method of analyzing the resultant data was formulated, based upon cross-correlation techniques, in order to distinguish between characteristic wave-forms for distinct physical activities. All of these improvements were successfully demonstrated via a gait-tracking system applied to the insole of standard running shoes.

To compensate the strong Troposheric impairments caused in the Ka frequency band, it is necessary to use Fade Mitigation Techniques. To develop and validate such techniques, time series of rain attenuation are needed. Nevertheless, these data are difficult to obtain. An alternative to using real rain attenuation time series is to develop a model of rain rate time series synthesizer. Nevertheless, real rain rate time series are needed to develop and validate this model. The aim of this internship is to provide real rain rate data useful for the development, parameterization and validation of this new model. In the first part of this report, different rain rate computation methods will be presented. Then, real data from a rain gauge located at Onera premises in Toulouse will be processed according to the presented methods and to a novel one. Results will be statistically analysed and finally a study of both the error of the methods and the uncertainty of the experimental devices and tools will be carried out. / <p>Validerat; 20120514 (anonymous)</p>