Analytical Study of Light Propagation in Highly Nonlinear Media

The present dissertation is devoted to the construction of exact and approximate analytical solutions of the problem of light propagation in highly nonlinear media. It is demonstrated that for many experimental conditions, the problem can be studied under the geometrical optics approximation with a sufficient accuracy. Based on the renormalization group symmetry analysis, exact analytical solutions of the eikonal equations with a higher order refractive index are constructed. A new analytical approach to the construction of approximate solutions is suggested. Based on it, approximate solutions for various boundary conditions, nonlinear refractive indices and dimensions are constructed. Exact analytical expressions for the nonlinear self-focusing positions are deduced. On the basis of the obtained solutions a general rule for the single filament intensity is derived; it is demonstrated that the scaling law (the functional dependence of the self-focusing position on the peak beam intensity) is defined by a form of the nonlinear refractive index but not the beam shape at the boundary. Comparisons of the obtained solutions with results of experiments and numerical simulations are discussed.

Theoretical study of magnetism, structure and chemical order in transition-metal alloy clusters

Research on transition-metal nanoalloy clusters composed of a few atoms is fascinating by their unusual properties due to the interplay among the structure, chemical order and magnetism. Such nanoalloy clusters, can be used to construct nanometer devices for technological applications by manipulating their remarkable magnetic, chemical and optical properties. Determining the nanoscopic features exhibited by the magnetic alloy clusters signifies the need for a systematic global and local exploration of their potential-energy surface in order to identify all the relevant energetically low-lying magnetic isomers. In this thesis the sampling of the potential-energy surface has been performed by employing the state-of-the-art spin-polarized density-functional theory in combination with graph theory and the basin-hopping global optimization techniques. This combination is vital for a quantitative analysis of the quantum mechanical energetics. The first approach, i.e., spin-polarized density-functional theory together with the graph theory method, is applied to study the Fe$_m$Rh$_n$ and Co$_m$Pd$_n$ clusters having $N = m+n \leq 8$ atoms. We carried out a thorough and systematic sampling of the potential-energy surface by taking into account all possible initial cluster topologies, all different distributions of the two kinds of atoms within the cluster, the entire concentration range between the pure limits, and different initial magnetic configurations such as ferro- and anti-ferromagnetic coupling. The remarkable magnetic properties shown by FeRh and CoPd nanoclusters are attributed to the extremely reduced coordination number together with the charge transfer from 3$d$ to 4$d$ elements. The second approach, i.e., spin-polarized density-functional theory together with the basin-hopping method is applied to study the small Fe$_6$, Fe$_3$Rh$_3$ and Rh$_6$ and the larger Fe$_{13}$, Fe$_6$Rh$_7$ and Rh$_{13}$ clusters as illustrative benchmark systems. This method is able to identify the true ground-state structures of Fe$_6$ and Fe$_3$Rh$_3$ which were not obtained by using the first approach. However, both approaches predict a similar cluster for the ground-state of Rh$_6$. Moreover, the computational time taken by this approach is found to be significantly lower than the first approach. The ground-state structure of Fe$_{13}$ cluster is found to be an icosahedral structure, whereas Rh$_{13}$ and Fe$_6$Rh$_7$ isomers relax into cage-like and layered-like structures, respectively. All the clusters display a remarkable variety of structural and magnetic behaviors. It is observed that the isomers having similar shape with small distortion with respect to each other can exhibit quite different magnetic moments. This has been interpreted as a probable artifact of spin-rotational symmetry breaking introduced by the spin-polarized GGA. The possibility of combining the spin-polarized density-functional theory with some other global optimization techniques such as minima-hopping method could be the next step in this direction. This combination is expected to be an ideal sampling approach having the advantage of avoiding efficiently the search over irrelevant regions of the potential energy surface.

Meshing highly regular structures: The case of super carbon nanotubes of arbitrary order

Mesh generation is an important step inmany numerical methods.We present the “HierarchicalGraphMeshing” (HGM)method as a novel approach to mesh generation, based on algebraic graph theory.The HGM method can be used to systematically construct configurations exhibiting multiple hierarchies and complex symmetry characteristics. The hierarchical description of structures provided by the HGM method can be exploited to increase the efficiency of multiscale and multigrid methods. In this paper, the HGMmethod is employed for the systematic construction of super carbon nanotubes of arbitrary order, which present a pertinent example of structurally and geometrically complex, yet highly regular, structures. The HGMalgorithm is computationally efficient and exhibits good scaling characteristics. In particular, it scales linearly for super carbon nanotube structures and is working much faster than geometry-based methods employing neighborhood search algorithms. Its modular character makes it conducive to automatization. For the generation of a mesh, the information about the geometry of the structure in a given configuration is added in a way that relates geometric symmetries to structural symmetries. The intrinsically hierarchic description of the resulting mesh greatly reduces the effort of determining mesh hierarchies for multigrid and multiscale applications and helps to exploit symmetry-related methods in the mechanical analysis of complex structures.

Conditions for Viewpoint Dependent Face Recognition

Poggio and Vetter (1992) showed that learning one view of a bilaterally symmetric object could be sufficient for its recognition, if this view allows the computation of a symmetric, "virtual," view. Faces are roughly bilaterally symmetric objects. Learning a side-view--which always has a symmetric view--should allow for better generalization performances than learning the frontal view. Two psychophysical experiments tested these predictions. Stimuli were views of shaded 3D models of laser-scanned faces. The first experiment tested whether a particular view of a face was canonical. The second experiment tested which single views of a face give rise to best generalization performances. The results were compatible with the symmetry hypothesis: Learning a side view allowed better generalization performances than learning the frontal view.

Experimental design on the simplex

Optimum experimental designs depend on the design criterion, the model and the design region. The talk will consider the design of experiments for regression models in which there is a single response with the explanatory variables lying in a simplex. One example is experiments on various compositions of glass such as those considered by Martin, Bursnall, and Stillman (2001). Because of the highly symmetric nature of the simplex, the class of models that are of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather different from those of standard regression analysis. The optimum designs are also rather different, inheriting a high degree of symmetry from the models. In the talk I will hope to discuss a variety of modes for such experiments. Then I will discuss constrained mixture experiments, when not all the simplex is available for experimentation. Other important aspects include mixture experiments with extra non-mixture factors and the blocking of mixture experiments. Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007). If time and my research allows, I would hope to finish with a few comments on design when the responses, rather than the explanatory variables, lie in a simplex. References Atkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum Experimental Designs, with SAS. Oxford: Oxford University Press. Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results on optimal and efficient designs for constrained mixture experiments. In A. C. Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000, pp. 225–239. Dordrecht: Kluwer. Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal Statistical Society, Ser. B 20, 344–360. 1

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Exam 2001

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Impacto de la auto - percepción de imagen corporal en sujetos con VIH y lipoatrofia facial.

La lipoatrofia facial es uno de los efectos secundarios que con más frecuencia se presenta y afecta la calidad de vida del paciente con VIH que recibe tratamiento antiretroviral. Metodología: Estudio observacional de corte transversal que involucró 126 sujetos, a quienes se aplicó una encuesta semi-estructurada para determinar cómo percibe el paciente que la lipoatrofia facial lo afecta en áreas afectiva, social, laboral y ocupacional; evaluar la percepción de la imagen corporal; caracterizar sociodemográficamente; determinar la prevalencia de lipoatrofia facial y establecer si hay diferencias de percepción de la imagen corporal según la caracterización sociodemográfica. Resultados: La Prevalencia de lipoatrofia facial fue del 57.1%. El grado de satisfacción en cuanto a apariencia física tuvo un promedio de 5.01±2.69. El 88.7% y 80.3% de los pacientes evaluados sintieron tristeza y frustración con su apariencia respectivamente. El 53.5% y el 42.9% informaron menos oportunidades laborales y educativas. La orientación sexual reportada con mayor frecuencia fue homosexualidad. No hubo diferencias estadísticamente significativas entre el grado de satisfacción de apariencia con aspectos sociodemográficos excepto en pacientes que recibieron apoyo psicológico. Conclusión: Primer estudio en el país que evalúa el impacto de la lipoatrofia facial en pacientes con VIH y tratamiento antiretroviral. Aunque la presencia de lipoatrofia facial sobre la cotidianidad no es estadísticamente significativa, si resulta trascendental pues existen porcentajes importantes de emociones y alteraciones psicológicas que afectan directamente a estos sujetos en las áreas afectiva, social, laboral y ocupacional. Se hace necesaria la realización de más estudios que permitan obtener mayor de evidencia.

Efectividad del tratamiento con neurofeedback en trastornos del estado del ánimo, ansiedad y fibromialgia: una revisión de literatura

El neurofeedback es una técnica no invasiva en la que se pretende corregir, mediante condicionamiento operante, ondas cerebrales que se encuentren alteradas en el electroencefalograma. Desde 1967, se han conducido numerosas investigaciones relacionadas con los efectos de la técnica en el tratamiento de alteraciones psicológicas. Sin embargo, a la fecha no existen revisiones sistemáticas que reúnan los temas que serán aquí tratados. El aporte de este trabajo es la revisión de 56 artículos, publicados entre los años 1995 y 2013 y la evaluación metodológica de 29 estudios incluidos en la revisión. La búsqueda fue acotada a la efectividad del neurofeedback en el tratamiento de depresión, ansiedad, trastorno obsesivo compulsivo (TOC), ira y fibromialgia. Los hallazgos demuestran que el neurofeedback ha tenido resultados positivos en el tratamiento de estos trastornos, sin embargo, es una técnica que aún está en desarrollo, con unas bases teóricas no muy bien establecidas y cuyos resultados necesitan de diseños metodológicamente más sólidos que ratifiquen su validez.

Proceso de negociación del tratado sobre el comercio de armas: tensiones y dinámicas de poder

El interés del presente estudio de caso es analizar la articulación de las dinámicas de poder y estrategias de negociación detrás de un proceso tan complejo como el de la creación del Tratado sobre el Comercio de Armas.El estudio examina la evolución de las tensiones principales entre los Estados participantes frente al Tratado y resalta las lógicas de poder al interior de las negociaciónes, así como los factores externos que influyeron para solucionar o agravar dichas tensiones. Con el apoyo de diferentes conceptos teóricos de negociación, se observa en específico el rol de las coaliciones como una importante estrategia utilizada por Estados pequeños para contrarrestar de alguna forma la asimetría de poder en un escenario donde los grandes exportadores e importadores de armas en la negociación tienen mayor peso.

The curvature of the conical intersection seam: an approximate second-order analysis

We present a method for analyzing the curvature (second derivatives) of the conical intersection hyperline at an optimized critical point. Our method uses the projected Hessians of the degenerate states after elimination of the two branching space coordinates, and is equivalent to a frequency calculation on a single Born-Oppenheimer potential-energy surface. Based on the projected Hessians, we develop an equation for the energy as a function of a set of curvilinear coordinates where the degeneracy is preserved to second order (i.e., the conical intersection hyperline). The curvature of the potential-energy surface in these coordinates is the curvature of the conical intersection hyperline itself, and thus determines whether one has a minimum or saddle point on the hyperline. The equation used to classify optimized conical intersection points depends in a simple way on the first- and second-order degeneracy splittings calculated at these points. As an example, for fulvene, we show that the two optimized conical intersection points of C2v symmetry are saddle points on the intersection hyperline. Accordingly, there are further intersection points of lower energy, and one of C2 symmetry - presented here for the first time - is found to be the global minimum in the intersection space

Síntesi, caracterització i avaluació com a catalitzadors de nous complexos quirals de platí

The oxidative addition proved to be a useful method to prepare platinum (II) hydridotiolate by reaction of tetrakis(triphenylphosphine)platinum(0) with aminothiolate and phosphinothiolate ligands like cysteamine, cysteine ethyl and methyl Esther, 2-(diphenylphosphino)ethanetiol and 2-(diphenylphosphino)propanetiol. The complexes are square-planar and the aminothiolate or phosphinothiolate ligands are chelated to platinum (II). The hydrido ligand is trans to the sulfur and the other coordination position is occuped by a triphenylphosphine ligand. The complexes are mononuclear and they show low symmetry. The only symmetry element, the plan is broke if the ligand is branched, obtaining asymmetric complexes C1. If the ligand has electronic or esteric impediments the reaction doesn't run and the starting products are recovered. This was observed with N,N-dimethylcysteamine and penicylamine methyl esther ligands. In the special case of orthoaminotiophenol the hydridotiolate was obtained but the ligand was not chelated. The aminothiolate complexes don't show solution equilibrium. Otherwise, the complexe with 2-(diphenylphosphino)ethanetiol show an isomerisation equilibrium which forms cis isomer as a minor component. The complexe with 2-(diphenylphosphino)-propanetiol shows a conformational equilibrium between chair and twist forms. The complexes have been tested as catalyst precursors in hydroformylation and hydrosilylation reactions. The hydroformylation reaction runs only in presence of SnCl2 as cocatalyst. Catalytic activity depends on the presence of triphenylphosphine and, with less magnitude, CO and H2 pressure. We also studied the enantioselectivity using a chiral complexe. In the hydrosililation reaction, catalysts run with good results (<90%) using triethylsilane as silicon hydride. Dehydrogenative addition product has been also found in this reaction.

View-based approaches to spatial representation in human vision

In an immersive virtual environment, observers fail to notice the expansion of a room around them and consequently make gross errors when comparing the size of objects. This result is difficult to explain if the visual system continuously generates a 3-D model of the scene based on known baseline information from interocular separation or proprioception as the observer walks. An alternative is that observers use view-based methods to guide their actions and to represent the spatial layout of the scene. In this case, they may have an expectation of the images they will receive but be insensitive to the rate at which images arrive as they walk. We describe the way in which the eye movement strategy of animals simplifies motion processing if their goal is to move towards a desired image and discuss dorsal and ventral stream processing of moving images in that context. Although many questions about view-based approaches to scene representation remain unanswered, the solutions are likely to be highly relevant to understanding biological 3-D vision.