Biomedical study researchers using animals to model disease and treatment need fast, deep, noninvasive, and inexpensive multi-channel imaging methods. Traditional fluorescence microscopy meets those criteria to an extent. Specifically, two-photon and confocal microscopy, the two most commonly used methods, are limited in penetration depth, cost, resolution, and field of view. In addition, two-photon microscopy has limited ability in multi-channel imaging. Light sheet microscopy, a fast developing 3D fluorescence imaging method, offers attractive advantages over traditional two-photon and confocal microscopy. Light sheet microscopy is much more applicable for in vivo 3D time-lapsed imaging, owing to its selective illumination of tissue layer, superior speed, low light exposure, high penetration depth, and low levels of photobleaching. However, standard light sheet microscopy using Gaussian beam excitation has two main disadvantages: 1) the field of view (FOV) of light sheet microscopy is limited by the depth of focus of the Gaussian beam. 2) Light-sheet images can be degraded by scattering, which limits the penetration of the excitation beam and blurs emission images in deep tissue layers. While two-sided sheet illumination, which doubles the field of view by illuminating the sample from opposite sides, offers a potential solution, the technique adds complexity and cost to the imaging system. We investigate a new technique to address these limitations: Bessel light sheet microscopy in combination with incoherent nonlinear Structured Illumination Microscopy (SIM). Results demonstrate that, at visible wavelengths, Bessel excitation penetrates up to 250 microns deep in the scattering media with single-side illumination. Bessel light sheet microscope achieves confocal level resolution at a lateral resolution of 0.3 micron and an axial resolution of 1 micron. Incoherent nonlinear SIM further reduces the diffused background in Bessel light sheet images, resulting in confocal quality images in thick tissue. The technique was applied to live transgenic zebra fish tg(kdrl:GFP), and the sub-cellular structure of fish vasculature genetically labeled with GFP was captured in 3D. The superior speed of the microscope enables us to acquire signal from 200 layers of a thick sample in 4 minutes. The compact microscope uses exclusively off-the-shelf components and offers a low-cost imaging solution for studying small animal models or tissue samples.

Orientador: Marcos Roberto da Rocha Gesualdi. / Dissertação (mestrado) - Universidade Federal do ABC. Programa de Pós Graduação em Física, 2010.

O objetivo principal deste trabalho é a obtenção dos modos e as freqüências naturais de vigas de variação linear e em forma de cunha, com condições de contorno clássicas e não-clássicas, descritas pelo modelo estrutural de Euler-Bernoulli. A forma dos modos foi determinado com o uso das funções cilíndricas. No caso forçado se considera uma força harmônica e se resolve o problema pelo método espectral, utuilizando o software simbólico Maple V5. Realiza-se uma análise comparativa dos resultados obtidos com os resultados existentes na literatura para vigas uniformes.

The need for non-contact micromanipulation methods is apparent for a number of different applications. Optical tweezers, a technique which uses highly focused laser beams to trap and move microscopic objects, has become an important tool for many applications owing to its incredible precision and dexterity. Optical trapping is, however, limited in several ways. It often struggles with particles larger than 10 micrometers, agglomerates and large numbers of particles. Complimentary technologies such as acoustic trapping, aim to overcome some of these limitations. This technique, also termed as Sonotweezers, uses ultrasonic fields to manipulate particles and can manipulate large particles with ease and manipulate large numbers of polydisperse particles and agglomerations, although they currently lack the dexterity of optical tweezers. Combining these two trapping modalities overcomes the some of the limitations of both of them and opens up a new range of useful applications. Three main types of hybrid optical and acoustic traps have been devised and are presented here. The first is an acoustic Bessel beam trap which is used to arrange a large number of polydisperse particles into concentric rings whereupon the smaller particles can then be further manipulated using a single beam optical tweezer. A rudimentary optical sorting system, which pushes particles in a flow laterally using an optical trap, has been combined with an acoustic levitator, which moves all particles away from the edges of the microfluidic channel reducing on sticking and other negative effects. A novel optically transparent ultrasonic device has been developed for easier integration into optical traps without the need for modication. This transparent trap has also been used in combination with a multibeam interference optical sorter to improve the separation between 5 and 10 micron particles.

When an intense femtosecond laser pulse propagates in a gas, it undergoes filamentation, a spectacular process where the pulse spatial, spectral and temporal characteristics change considerably. A thin short-lived plasma column is formed in the wake of the propagating pulse. My PhD work has been dedicated to the further understanding of the filamentation process. In a first part, I compare the properties of a usual filament with those of a filament formed by a femtosecond laser pulse with a Bessel beam profile. Using a laser pulse of same intensity and duration, I show that a Bessel beam can form a longer and more uniform plasma column in air, but that the plasma density is significantly lower. In a second part, I show that it is possible to increase considerably the lifetime of the plasma column, using a dual femtosecond/nanosecond laser pulse technique. To obtain an increased lifetime over a significant segment of a plasma column, I rely on the properties of Bessel beams in the nonlinear regime developed in the first chapter. In a third part, I study the dynamics of free electrons that are produced in the filamentation process. To do this, I have developed a specially designed current probe. Experiments reveal a very rich behaviour. The longitudinal displacements of electrons in the plasma column depend sensitively on the nature of the gas and its pressure as well as on the laser polarization of the laser. I propose a model to explain this behaviour. The direction of electron flow results from the competition between pure laser forces and a Coulomb wake field force. In the last chapter, I study filamentation in a Helium gas. This required improving the laser characteristics in order to reach the necessary power for filamentation. Improved characteristics have been achieved by implementing a planar compression stage which shortened the laser pulse from 50 fs to 10 fs without appreciable energy loss. The first experimental evidence for filamentation in He is presented at the end of the thesis. Agreement is found with a numerical simulation.

In the thesis, we propose a newly-developed method called the method of Connected Local Fields (CLF) to analyze opto-electromagnetic passive devices. The method of CLF somewhat resembles a hybrid between the finite difference and pseudo-spectral methods. For opto-electromagnetic passive devices, our primary concern is their steady state behavior, or narrow-band characteristics, so we use a frequency-domain method, in which the system is governed by the Helmholtz equation. The essence of CLF is to use the intrinsic general solution of the Helmholtz equation to expand the local fields on the compact stencil. The original equation can then be transformed into the discretized form called LFE-9 (in 2-D case), and the intrinsic reconstruction formulae describing each overlapping local region can be obtained. Further, we present rigorous analysis of the numerical dispersion equation of LFE-9, by means of first-order approximation, and acquire the closed-form formula of the relative numerical dispersion error. We are thereby able to grasp the tangible influences brought both by the sampling density as well as the propagation direction of plane wave on dispersion error. In our dispersion analysis, we find that the LFE-9 formulation achieves the sixth-order accuracy: the theoretical highest order for discretizing elliptic partial differential equations on a compact nine-point stencil. Additionally, the relative dispersion error of LFE-9 is less than 1%, given that sampling density greater than 2.1 points per wavelength. At this point, the sampling density is nearing that of the Nyquist-Shannon sampling limit, and therefore computational efforts can be significantly reduced.

In the thesis, the error and stability analysis is made for the 2D Helmholtz equation by the method of fundamental solutions (MFS) using both Bessel and Neumann functions. The bounds of errors in bounded simply-connected domains are derived, while the bounds of condition number are derived only for disk domains. The MFS using Bessel functions is more efficient than the MFS using Neumann functions. Interestingly, for the MFS using Bessel functions, the radius R of the source points is not necessarily larger than the maximal radius r_max of the solution domain. This is against the traditional condition: r_max < R for MFS. Numerical experiments are carried out to support the analysis and conclusions made.

Cette thèse est composée de cinq chapitres qui correspondent à cinq articles. Le premier article étudie d'un point de vue théorique les modèles à volatilités locale et stochastique, et leur relation, d'ailleurs illustrée d'exemples. Enfin, l'impact de taux stochastiques sur ces deux modélisations est analysé ainsi que l'effet de taux stochastiques sur le lien entre volatilités locale et stochastique. Les articles 2 et 3 étudient des modèles de type Constant Elasticity of Variance pour valoriser des produits hybrides crédit et action. L'article 4 se propose de prendre en compte l'effet de frais de gestion et de performance sur la valorisation d'options sur hedge funds et ainsi sont fournies des formules quasi-fermées de pricing d'options vanilles sur hedge funds. Enfin, le chapitre 5 avec examine à un niveau conceptuel illustré d'exemples provenant de propriétés fines du mouvement Brownien et des grossissements de filtration, la question des risques qui sont ou ne sont pas pricés dans une économie.

We extend our results on the degree of ill-posedness for linear integration opera- tors A with weights mapping in the Hilbert space L^2(0,1), which were published in the journal 'Inverse Problems' in 2005 ([5]). Now we can prove that the degree one also holds for a family of exponential weight functions. In this context, we empha- size that for integration operators with outer weights the use of the operator AA^* is more appropriate for the analysis of eigenvalue problems and the corresponding asymptotics of singular values than the former use of A^*A.

O objetivo principal deste trabalho é a obtenção dos modos e as freqüências naturais de vigas de variação linear e em forma de cunha, com condições de contorno clássicas e não-clássicas, descritas pelo modelo estrutural de Euler-Bernoulli. A forma dos modos foi determinado com o uso das funções cilíndricas. No caso forçado se considera uma força harmônica e se resolve o problema pelo método espectral, utuilizando o software simbólico Maple V5. Realiza-se uma análise comparativa dos resultados obtidos com os resultados existentes na literatura para vigas uniformes.