Two loop integrals and QCD scattering

We present the techniques for the calculation of one- and two-loop integrals contributing to the virtual corrections to 2→2 scattering of massless particles. First, tensor integrals are related to scalar integrals with extra powers of propagators and higher dimension using the Schwinger representation. Integration By Parts and Lorentz Invariance recurrence relations reduce the number of independent scalar integrals to a set of master integrals for which their expansion in є = 2 — D/2 is calculated using a combination of Feynman parameters, the Negative Dimension Integration Method, the Differential Equations Method, and Mellin-Barnes integral representations. The two-loop matrix-elements for light-quark scattering are calculated in Conventional Dimensional Regularisation by direct evaluation of the Feynman diagrams. The ultraviolet divergences are removed by renormalising with the MS scheme. Finally, the infrared singular behavior is shown to be in agreement with the one anticipated by the application of Catani's formalism for the infrared divergences of generic QCD two-loop amplitudes

A relative moment tensor inversion technique applied to seismicity induced by mining

Three hybrid moment tensor inversion methods were developed for seismic sources originating from a small source region. These techniques attempt to compensate for various types of systematic error (or noise) that influence seismograms recorded in the underground environment in order to achieve an accurate and robust measure of the seismic moment tensor. The term 'hybrid' was used to distinguish between the relative method proposed by Dahm (1995) and the methods developed in this thesis. The hybrid methods were essentially weighting schemes designed to enhance the accuracy of the computed moment tensors by decreasing the influence of any low quality observations, to damp (or amplify) any signals that have been overestimated (or underestimated) due to local site effects, and to correct for raypath focussing or defocussing that results from inhomogeneities in the rockmass. The weighting or correction applied to a particular observation was derived from the residuals determined when observed data were compared with corresponding theoretical data (for a particular geophone site, sensor orientation and wave phase) and were calculated using a cluster of events rather than a single event. The first and second weighting schemes were indirectly related to the mean and the median of the residuals where the residuals were defined as the ratio of the theoretical to observed data. In the third scheme, the residuals were defined as the difference between the observed and theoretical data and the weights were based on the distance of a data point (measured in standard deviations) from the mean residual. In each of the weighting schemes, the correction was applied iteratively until the standard error of the least-squares solution (normalised to the scalar seismic moment) was a minimum. The schemes were non-linear because new weights were calculated for each iteration. A number of stability tests using synthetic data were carried out to quantify the source resolving capabilities of the hybrid methods under various extreme conditions. The synthetic events were pure double-couple sources having identical fault-plane orientations, and differing only in rake. This similarity in the mechanisms was chosen because the waveforms of tightly grouped events recorded underground often show high degrees of similarity. For each test, the results computed using the three hybrid methods were compared with one another and with those computed using the single event, absolute method and two relative methods (with and without a reference mechanism). In the noise-free situation, it was found that the relative method without reference mechanism showed the highest resolution of mechanisms, provided that the coverage of the focal sphere was not too sparse (> 3 stations). The hybrid method using a median correction was found to be the most robust of all the methods tested in the most extreme case of poor coverage (2 stations) of the focal sphere. When increasing levels of pseudo-random noise were applied to the data, the absolute moment tensor inversion method, the hybrid method using a median correction, and the hybrid method using a weighted mean correction all showed similar robustness and stability in extreme configurations concerning network coverage of the focal sphere and noise level. When increasing levels of systematic noise were added to the data, the hybrid methods using a median correction and weighted mean correction were found to exhibit similar robustness and stability in extreme configurations concerning network coverage of the focal sphere and systematic noise. In all situations investigated, these two hybrid methods outperformed the relative and absolute methods. The hybrid moment tensor inversion methods using a median and weighted mean correction were applied to a cluster of 14 events, having remarkably similar waveforms, recorded at Oryx Gold Mine. For comparative purposes, the absolute method was also applied. The inputs to the inversion methods consisted of the spectral plateaus of both P- and S-waves at frequencies below the comer frequency of the time-integrated displacement traces. The polarities of dominant motion were used as an additional constraint and were determined from cross-correlation of observed with synthetic P- or S-waves. The solutions computed using the hybrid moment tensor inversion using a median correction displayed a distinct improvement after the iterative residual correction procedure was applied. The radiation patterns and faultplane solutions showed a high degree of similarity, and are probably more accurate reflections of reality than those computed using the absolute moment tensor inversion methods. These observations are very encouraging and point towards the method's potential for use as a standard processing tool for mine seismicity. The implications of this work are a better understanding of the focal mechanisms of seismic events induced by mining activities, ultimately leading to improved safety underground

Studies of final state photon radiation at LEP

We consider two aspects of calculations involving the production of final state photons at LEP. The first addresses photons produced in association with hadrons. We motivate a measurement of the quark to photon fragmentation function and show how it can be used to account for isolated and non-isolated production rates. The second concerns the rare Z-decay to photons. We expose a subtle relationship between its various contributions. Following its investigation, we offer an improved method of calculation for weak processes at one loop

Investigation of nanoscale thermal radiation : theory and experiments

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.Includes bibliographical references (p. 134-145).The ability to control the radiative properties of objects is of prime importance in diverse areas like solar and thermophotovoltaic energy conversion, narrowband thermal emitters, and camouflage in military applications. Thermal radiation at the nanometer scale is significantly different from classical or macroscopic radiative energy transport - wave effects, such as interference and diffraction, and near-field effects play a significant role. By modeling thermal radiation as governed by Maxwell's equations and relating the source of thermal radiation to temperature induced fluctuations of electric currents, it becomes possible to capture the nanaoscale effects that differrentiate it from classical blackbody radiation. This work is focused on two aspects of nanoscale thermal radiation - the ability to tailor the emissive properties using 1D photonic crystals and the enhancement of radiative heat transfer due to electromagnetic surface waves. Theoretical investigation of thermal radiation in ID photonic crystals led to the proposal of new type of selective emitters using 1D metallo-dielectric photonic crystals that rival the more intricate 2D and 3D counterparts.(cont.) In addition to far-field spectral control, near-field enhancement due to surface phonon polaritons is shown to be useful for enhancing the power density of thermophotovoltaic energy conversion. The difficulties of experimental investigation of near-field phenomena between macroscopic parallel surfaces led to the theoretical investigation of near-field effects between two spheres and experimental investigation between a sphere and a flat plate. A new technique for measuring the radiative transfer between a sphere and a substrate using a bi-material atomic force microscope cantilever as the sensor was developed. By measuring "heat transfer-distance" curves, just as one measures "force-distance" curves in atomic force microscopy, the experimental results are shown to be in agreement with a theory.by Arvind Narayanaswamy.Ph.D

Modeling EMI Resulting from a Signal Via Transition Through Power/Ground Layers

Signal transitioning through layers on vias are very common in multi-layer printed circuit board (PCB) design. For a signal via transitioning through the internal power and ground planes, the return current must switch from one reference plane to another reference plane. The discontinuity of the return current at the via excites the power and ground planes, and results in noise on the power bus that can lead to signal integrity, as well as EMI problems. Numerical methods, such as the finite-difference time-domain (FDTD), Moment of Methods (MoM), and partial element equivalent circuit (PEEC) method, were employed herein to study this problem. The modeled results are supported by measurements. In addition, a common EMI mitigation approach of adding a decoupling capacitor was investigated with the FDTD method

Acoustical characterization and parameter optimization of polymeric noise control materials

The sound transmission loss (STL) characteristics of polymer-based materials are considered. Analytical models that predict, characterize and optimize the STL of polymeric materials, with respect to physical parameters that affect performance, are developed for single layer panel configuration and adapted for layered panel construction with homogenous core. An optimum set of material parameters is selected and translated into practical applications for validation. Sound attenuating thermoplastic materials designed to be used as barrier systems in the automotive and consumer industries have certain acoustical characteristics that vary in function of the stiffness and density of the selected material. The validity and applicability of existing theory is explored, and since STL is influenced by factors such as the surface mass density of the panel\u27s material, a method is modified to improve STL performance and optimize load-bearing attributes. An experimentally derived function is applied to the model for better correlation. In-phase and out-ofphase motion of top and bottom layers are considered. It was found that the layered construction of the coinjection type would exhibit fused planes at the interface and move in-phase. The model for the single layer case is adapted to the layered case where it would behave as a single panel. Primary physical parameters that affect STL are identified and manipulated. Theoretical analysis is linked to the resin\u27s matrix attribute. High STL material with representative characteristics is evaluated versus standard resins. It was found that high STL could be achieved by altering materials\u27 matrix and by integrating design solution in the low frequency range. A suggested numerical approach is described for STL evaluation of simple and complex geometries. In practice, validation on actual vehicle systems proved the adequacy of the acoustical characterization process

Radiation from the inset dielectric guide: Applications to antenna arrays and transitions

SIGLEAvailable from British Library Document Supply Centre- DSC:DX96923 / BLDSC - British Library Document Supply CentreGBUnited Kingdo