Obtivemos os teoremas de baixa energia no espalhamento Compton em terceira e quarta ordem na freqüência da fóton incidente. Em seguida calculamos a secção de choque polarizada em terceira ordem e a não polarizada até quarta ordem, em termos de amplitudes parciais não cobertos pelos teoremas de baixa energia o que permitirá a determinação experimental dessas amplitudes parciais / We have obtained the low energy theorems in Compton scatering to third and fourth order in the frequency of that incident photon. Next we calculated the polarized cross section to third order and the unpolarized to fourth order in terms of partial amplitudes not covered by the low energy theorems, what will permit the experimental determination of these partial amplitudes

Obtivemos os teoremas de baixa energia no espalhamento Compton em terceira e quarta ordem na freqüência da fóton incidente. Em seguida calculamos a secção de choque polarizada em terceira ordem e a não polarizada até quarta ordem, em termos de amplitudes parciais não cobertos pelos teoremas de baixa energia o que permitirá a determinação experimental dessas amplitudes parciais / We have obtained the low energy theorems in Compton scatering to third and fourth order in the frequency of that incident photon. Next we calculated the polarized cross section to third order and the unpolarized to fourth order in terms of partial amplitudes not covered by the low energy theorems, what will permit the experimental determination of these partial amplitudes

In this dissertation we describe a coordinate scaling technique for the numerical approximation of solutions to certain problems posed on unbounded domains in two and three dimensions. This technique amounts to introducing variable coefficients into the problem, which results in defining a solution coinciding with the solution to the original problem inside a bounded domain of interest and rapidly decaying outside of it. The decay of the solution to the modified problem allows us to truncate the problem to a bounded domain and subsequently solve the finite element approximation problem on a finite domain. The particular problems that we consider are exterior problems for the Laplace equation and the time-harmonic acoustic and elastic wave scattering problems. We introduce a real scaling change of variables for the Laplace equation and experimentally compare its performance to the performance of the existing alternative approaches for the numerical approximation of this problem. Proceeding from the real scaling transformation, we introduce a version of the perfectly matched layer (PML) absorbing boundary as a complex coordinate shift and apply it to the exterior Helmholtz (acoustic scattering) equation. We outline the analysis of the continuous PML problem, discuss the implementation of a numerical method for its approximation and present computational results illustrating its efficiency. We then discuss in detail the analysis of the elastic wave PML problem and its numerical discretiazation. We show that the continuous problem is well-posed for sufficiently large truncation domain, and the discrete problem is well-posed on the truncated domain for a sufficiently small PML damping parameter. We discuss ways of avoiding the latter restriction. Finally, we consider a new non-spherical scaling for the Laplace and Helmholtz equation. We present computational results with such scalings and conduct numerical experiments coupling real scaling with PML as means to increase the efficiency of the PML techniques, even if the damping parameters are small.

Titel: Die Darstellung der Rheumatoiden Arthritis im Frühstadium mittels Streulichtanalyse der proximalen Interphalangealgelenke Zielstellung: In dieser Studie wird eine neues laser-basiertes bildgebendes Verfahren zur Darstellung entzündlich-rheumatischer Veränderungen der Fingergelenke evaluiert und mit den etablierten Verfahren Röntgen, Sonographie und Magnetresonanztomographie verglichen. Methoden: Die proximalen Interphalangealgelenke (PIP) von 102 Patienten mit Verdacht auf Rheumatoide Arthritis (RA) und 40 Kontrollpatienten wurden mit der Laser-Streulicht-Analyse untersucht und die daraus resultierende mathematische Funktion des Streulichtverteilungsbildes mittels fünf verschiedener Kennwerte berechnet. Als Referenz wurden 1136 PIP klinisch untersucht, 800 Röntgenaufnahmen angefertigt, 688 Sonographien und 208 magnetresonanztomographische Bilder erstellt, die zur Klassifizierung der Entzündungsakuität dienten. Ergebnisse: Die Ergebnisse zeigten, dass die untersuchten Kennwerte Breite, Asymmetrie, Steilheit links, Steilheit rechts und Intensität keine Korrelation mit dem Entzündungsgrad des Gelenks mit früher Rheumatoider Arthritis gaben. Schlussfolgerung: Zum jetzigen Stand der Entwicklung erbringt die laser-basierte Streulichtanalyse in der Diagnosefindung der RA keinen Fortschritt, da gesunde Gelenke von floride entzündeten nicht differenziert werden können. Die Ergebnisse legen nahe, dass die Ursache hierfür in einer zu hohen Sensitivität und mangelnder Reproduzierbarkeit bei der Fingerpositionierung in der Apparatur des Gerätes zu suchen ist. / Title: Imaging of early rheumatoid arthritis with scattering light analysis of the proximal interphalangeal joints Objective: In this study a novel laser-based imaging technique for early rheumatoid arthritis of the finger joints is evaluated and compared to radiography, ultrasound and magnetic-resonance-tomography. Methods: The proximal interphalangeal joints (PIP) of 102 patients with early rheumatoid arthritis (RA) and 40 patients of a control group were measured with laser scattering light analysis and five values describing the resulting image were calculated. The clinical examination of 1136 PIP, 800 x-rays, 688 ultrasound-pictures and 208 magnetic resonance pictures were taken as reference to assess the acuity of inflammation. Results: No correlation was seen for the values to calculate the scattering light image curve (width, asymmetry, left and right skewness and intensity) and the severity of finger joint inflammation. Conclusion: At present the new laser-based imaging technique is not superior to the usual imaging methods for diagnosis of RA This is probably due to a too high sensitivity and a lack of reproducibility for finger positioning in the measuring unit.

Low-temperature weak-localization (WL) and antilocalization (AL) magnetotransport measurements are sensitive to electron interference, and thus can be used as a probe of quantum states. The spin-dependent interactions between controllable surface magnetism and itinerant electrons in a non-magnetic host provide insight for spin-based technologies, magnetic data storage and quantum information processing. This dissertation studies two different host systems, an In$_{0.53}$Ga$_{0.47}$As quantum well at a distance from the surface of a heterostructure, and an accumulation layer on an InAs surface. Both the systems are two-dimensional electron systems (2DESs), and possess prominent Rashba spin-orbit interaction caused by structural inversion asymmetry, which meets the prerequisites for AL. The surface local moments influence the surrounding electrons in two ways, increasing their spin-orbit scattering, and inducing magnetic spin-flip scattering, which carries information about magnetic interactions. The two effects modify the AL signals in opposing directions: the spin-flip scattering of electrons shrinks the signal, and requires a close proximity to the species, whereas the increase of spin-orbit scattering broadens and increases the signal. Accordingly, we only observe an increase in spin-orbit scattering in the study of the interactions between ferromagnetic Co$_{0.6}$Fe$_{0.4}$ nanopillars and the relatively distant InGaAs quantum well. With these CoFe nanopillars, a decrease in spin decoherence time is observed, attributed to the spatially varying magnetic field from the local moments. A good agreement between the data and a theoretical calculation suggests that the CoFe nanopillars also generate an appreciable average magnetic field normal to the surface, of value $\sim$ 35 G. We also performed a series of comparative AL measurements to experimentally investigate the interactions and spin-exchange between InAs surface accumulation electrons and local magnetic moments of rare earth ions Sm$^{3+}$, Gd$^{3+}$, Ho$^{3+}$, of transition metal ions Ni$^{2+}$, Co$^{2+}$, and Fe$^{3+}$, and of Ni$^{2+}$-, Co$^{2+}$-, and Fe$^{3+}$-phthalocyanines deposited on the surface. The deposited species generate magnetic scattering with magnitude dependent on their electron configurations and effective moments. Particularly for Fe$^{3+}$, the significant spin-flip scattering due to the outermost 3d shell and the fairly high magnetic moments modifies the AL signal into a WL signal. Experiments indicate a temperature-independent magnetic spin-flip scattering for most of the species except for Ho$^{3+}$ and Co$^{2+}$. Ho$^{3+}$ yields electron spin-flip rates proportional to the square root of temperature, resulting from transitions between closely spaced energy levels of spin-orbit multiplets. In the case of Co$^{2+}$, either a spin crossover or a spin-glass system forms, and hence spin-flip rates transit between two saturation regions as temperature varies. Concerning the spin-orbit scattering rate, we observe an increase for all the species, and the increase is correlated with the effective electric fields produced by the species. In both 2DESs, the inelastic time is inversely proportional to temperature, consistent with phase decoherence via the Nyquist mechanism. Our method provides a controlled way to probe the quantum spin interactions of 2DESs, either in a quantum well, or on the surface of InAs. / Ph. D.

Apresentamos os resultados do estudo das não-linearidades ópticas de origem eletrônica de duas moléculas da classe dos oligômeros de anilina: o dímero e o tetrâmero. Foram medidas quatro concentrações de tetrâmero, puras e também dopadas em 33 e 100%; uma de dímero pura e outra dopada em 100%. As soluções foram preparadas usando dimetil-sulfóxido (DMSO) como solvente e a dopagem foi realizada com ácido clorídrico. As amostras foram caracterizadas por medidas de absorção linear e fluorescência antes das medidas não-lineares. Obtivemos os valores da primeira hiperpolarizabilidade (?) para todas as amostras, o índice de refração não-linear (n2) do tetrâmero dopado e não dopado, e a absorção não-linear em função da intensidade e da concentração do tetrâmero. As medidas foram realizadas através das técnicas de Varredura-Z, absorção não-linear e espalhamento Hiper-Rayleigh. Os resultados foram interpretados em termos da comparação entre diferentes estados de dopagem e da variação da seção de choque do estado fundamental para o primeiro excitado. / We report on the study of electronic optical non linearities in two aniline oligomers: dimer and the tetramer. Four tetramer concentrations were measured, pure and also 33 and 100% doped; one of dimer non doped another 100% doped. The solutions were prepared using dimethyl sulfoxide (DMSO) as solvent and the doping was performed with hydrochloric acid. The samples were characterized by measurements of linear absorption and fluorescence. We obtained the values of the first hyperpolarizability (?) for all samples, the non linear index of refraction (n2) for non doped and doped tetramer, and the non linear absorption in function of intensity and concentration of the tetramer. The measurements were accomplished through the techniques of Z-Scan, non linear absorption and Hyper-Rayleigh Scattering. The results were interpreted in terms of the comparison among different doping states and of the variation of cross-section for the transition from ground to the first excited states.

Apresentamos os resultados do estudo das não-linearidades ópticas de origem eletrônica de duas moléculas da classe dos oligômeros de anilina: o dímero e o tetrâmero. Foram medidas quatro concentrações de tetrâmero, puras e também dopadas em 33 e 100%; uma de dímero pura e outra dopada em 100%. As soluções foram preparadas usando dimetil-sulfóxido (DMSO) como solvente e a dopagem foi realizada com ácido clorídrico. As amostras foram caracterizadas por medidas de absorção linear e fluorescência antes das medidas não-lineares. Obtivemos os valores da primeira hiperpolarizabilidade (?) para todas as amostras, o índice de refração não-linear (n2) do tetrâmero dopado e não dopado, e a absorção não-linear em função da intensidade e da concentração do tetrâmero. As medidas foram realizadas através das técnicas de Varredura-Z, absorção não-linear e espalhamento Hiper-Rayleigh. Os resultados foram interpretados em termos da comparação entre diferentes estados de dopagem e da variação da seção de choque do estado fundamental para o primeiro excitado. / We report on the study of electronic optical non linearities in two aniline oligomers: dimer and the tetramer. Four tetramer concentrations were measured, pure and also 33 and 100% doped; one of dimer non doped another 100% doped. The solutions were prepared using dimethyl sulfoxide (DMSO) as solvent and the doping was performed with hydrochloric acid. The samples were characterized by measurements of linear absorption and fluorescence. We obtained the values of the first hyperpolarizability (?) for all samples, the non linear index of refraction (n2) for non doped and doped tetramer, and the non linear absorption in function of intensity and concentration of the tetramer. The measurements were accomplished through the techniques of Z-Scan, non linear absorption and Hyper-Rayleigh Scattering. The results were interpreted in terms of the comparison among different doping states and of the variation of cross-section for the transition from ground to the first excited states.