Spin-1/2 chains demonstrate some of the striking effects of interactions and quantum fluctuations in one-dimensional systems. The XXZ model has been used to study the unusual properties of anisotropic spin chains in an external magnetic field. The zero temperature phase diagram for this model exhibits a critical or quasi-long-range-ordered phase which is a realization of a Luttinger liquid. While many static properties of spin-1/2 chains have been explained by combinations of analytical techniques such as bosonization and Bethe ansatz, the standard approach fails in the calculation of some time-dependent correlation functions. I present a study of the longitudinal dynamical structure factor for the XXZ model in the critical regime. I show that an approximation for the line shape of the dynamical structure factor in the limit of small momentum transfer can be obtained by going beyond the Luttinger model and treating irrelevant operators associated with band curvature effects. This approach is able to describe the width of the on-shell peak and the high-frequency tail at finite magnetic field. Integrability is shown to affect the low-energy effective model at zero field, with consequences for the line shape. The power-law singularities at the thresholds of the particle-hole continuum are investigated using an analogy with the X-ray edge problem. Using methods of Bethe ansatz and conformal field theory, I compute the exact exponents for the edge singularities of the dynamical structure factor. The same methods are used to study the long-time asymptotic behavior of the spin self-correlation function, which is shown to be dominated by a high-energy excitation.

Thesis (Ph. D.)--Florida State University, 2006. / Advisor: Philip Bowers, Florida State University, College of Arts and Sciences, Dept. of Mathematics. Title and description from dissertation home page (viewed Sept. 15, 2006). Document formatted into pages; contains ix, 98 pages. Includes bibliographical references.

Thesis (Ph. D. in Mathematics)--Vanderbilt University, Aug. 2006. / Title from title screen. Includes bibliographical references.

Made available in DSpace on 2014-06-11T19:32:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-03-29Bitstream added on 2014-06-13T21:03:30Z : No. of bitstreams: 1 osoriomayor_c_dr_ift.pdf: 2657448 bytes, checksum: 8caa54bb4cbd339dbb5bc2222636af8e (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Na presença de uma constante cosmológica, interpretada como uma entidade puramente geométrica, a ausência de matéria é representada pelo espaço de de Sitter. Como consequência, a relatividade especial de Poincaré não é mais válida e deve ser substituída por uma relatividade especial baseada no grupo de de Sitter, o que produz modificações em todas as áreas da física. Nesta tese, vamos estudar os fundamentos da relatividade especial de de Sitter, bem como algumas implicações para o problema da energia escura, para a propagação de raios gama de altíssimas energias e para o espalhamento Compton. Como um subproduto desses estudos, desenvolvemos um novo método de se obter equações de campo com invariância conforme, o qual faz uso dos invariantes de Casimir do grupo de de Sitter. Usando esse novo método, fazemos um estudo crítico das equações que descrevem um campo fundamental de spin-2 / The presence of a cosmological constant, interpreted as a purely geometric entity, absence of matter ir represented by a de Sitter spacetime. As a consequence, ordinary Poincaré specil relativity is no longer valid and must be replaced by a special relativity based on the de Sitter group, which produces concomitant changes in all areas of physics. In this thesis, we are going to explore the implications for the dark energy problem, for the propagation of ultra high-energy gamma rays, and for the Compton scattering formula. As a byoproduct of these studies, we developed a new method for obtaining conformal invariant fiels equations, which makes use of the Casimir operators of the de Sitter group. Using this new method, we make a critical review of the fiels equations describing a fundamental spin-2 field

O principal objetivo deste trabalho é estudar a quantização covariante da corda bosônica e da supercorda RNS, explorando as simetrias envolvidas, ou seja, as simetrias BRST e conforme no caso da corda bosônica e as generalizações correspondentes para a corda fermiônica. Em particular, discutimos alguns aspectos perturbativos da teoria bosônica e a construção de operadores de vértice da corda fermiônica. / The main goal of this work is to study the covariant quantization of the bosonic and RNS string theories by exploiting the involved symmetries, namely, the BRST and conformal invariance for the bosonic string and the corresponding supersymmetric generalizations for the fermionic case. In particular, we discuss some perturbative aspects of the bosonic theory and the construction of vertex operators for the fermionic string.

Neste trabalho apresentamos alguns resultados da invariância conforme e da teoria de escala para sistemas finitos. Estudamos, usando tais técnicas, dois modelos estatísticos (modelos 1 e 2). Para cada modelo obtivemos a anomalia conforme e as dimensões dos operadores energia e magnetização bem como seus respectivos descendentes / In this work we show some results of conformal invariance theory and finite-size scaling. We study by using these theories two statistical mechanics models (models 1 and 2). To each model we obtained the conformal anomaly, the dimensions of energy and magnetization operators as well their respective descendents

In September 2016, work was initiated on the subprojects which comprise the Conformal C-Band/Multiband Antenna project: SARD #1: Broadband Conformal C-Band Missile Wraparound Antennas; SARD #2: Beam Switching Array Antennas; SARD #3: Multiband Conformal Antennas for Aircraft Applications; SARD #4: High Altitude Coronal Efforts on Antenna Performance; and SARD #5: Small, Medium Gain Multiband Receive Antennas. A brief status of each of them will be discussed and detail the technology areas being developed by each.

This research has been conducted in order to develop a short-range ensemble numerical weather prediction system over southern Africa using the Conformal-Cubic Atmospheric Model (CCAM). An ensemble prediction system (EPS) combines several individual weather model setups into an average forecast system where each member contributes to the final weather forecast. Four different EPSs were configured and rainfall forecasts simulated for seven days ahead for the summer months of January and February, 2009 and 2010, for high (15 km) and low (50 km) resolution over the southern African domain. Statistical analysis was performed on the forecasts so as to determine which EPS was the most skilful at simulating rainfall. Measurements that were used to determine the skill of the EPSs were: reliability diagrams, relative operating characteristics, the Brier skill score and the root mean square error. The results show that the largest ensemble is consistently the most skilful for all forecasts for both the high and the low resolution cases. The higher resolution forecasts were also seen to be more skilful than the forecasts made at the low resolution. These findings conclude that the largest ensemble at high resolution is the best system to predict rainfall over southern Africa using the CCAM. / Dissertation (MSc)--University of Pretoria, 2014. / gm2014 / Geography, Geoinformatics and Meteorology / unrestricted

Open file dissertation.pdf to read abstract / Dissertation (MSc)--University of Pretoria, 2007. / Geography, Geoinformatics and Meteorology / Unrestricted

The study aims to generate a simulated, ultra high-resolution climatology over the southwestern Cape of South Africa, and in particular the Stellenbosch wine producing region, by the dynamical downscaling of observed synoptic-scale circulation. A variable-resolution global model, the conformal-cubic atmospheric model (CCAM), and a multiple-nudging strategy are applied in order to reach this goal. CCAM is employed in stretched-grid mode as a regional climate model (RCM) to simulate climate for the period 1976-2005 at four different spatial resolutions. Nudging from coarse-resoltion (2.5° in latitude and longitude), the model was first applied at a 60 km resolution over southern Africa in order to obtain a simulation of the synoptic-scale circulation over the region. Two higher resolution simulations, at 8 km and 1 km resolution, were obtained consecutively over the western and southwestern Cape, nudging from the 60 km and 8 km simulations, respectively. Finally, a 200 m simulation was performed over the Stellenbosch region. Because of the high computational requirements of high-resolution runs, each progressively higher resolution simulation is performed over a progressively smaller area of interest over which the spatial resolution is high. The simulations verify well against observed datasets, and generally capture the important climatic features over the area of interest. The 60 km CCAM simulation gives a good representation of the synoptic scale weather over southern Africa, with realistic seasonal circulation patterns and rainfall percentages as well as intra-annual rainfall totals over various regions. The mesoscale climate over the Western Cape of South Africa is captured by the 8 km simulation, especially with respect to seasonal variations in temperature and rainfall percentages - although the actual rainfall over the southwestern tip of the Western Cape is severely underestimated. The ultra high-resolution simulated diurnal cycle of temperature, relative humidity and screen level wind speed compared well against observations for the month of February. The CCAM climate simulations might not be accurate enough for some of the very sensitive studies of the wine industry, but it can have great value for the demarcation of areas which are climatically suited for viticulture and some more general viticultural studies. Ultra high-resolution climate parameter maps are presented for 1976-2005. / Dissertation (MSc)--University of Pretoria, 2009. / Geography, Geoinformatics and Meteorology / Unrestricted