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1
Elad, Altman Henri. "Integration by parts formulae for the laws of Bessel bridges, and Bessel stochastic PDEs." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS441.
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Dans cette thèse, nous obtenons des formules d’intégration par parties pour les lois de ponts de Bessel de dimension δ > 0, étendant ainsi les formules précédemment obtenues par Zambotti dans le cas δ ≥ 3. Ceci nous permet d’identifier la structure de certaines EDP stochastiques (EDPS) ayant la loi d’un pont de Bessel de dimension δ ∈ (0, 3) pour mesure invariante, et qui étendent de manière naturelle les EDPS considérées précédemment par Zambotti dans le cas δ ≥ 3. Nous nommons ces équations EDPS de Bessel, et les écrivons à l’aide de temps locaux renormalisés. Dans les cas particuliers δ = 1, 2, en utilisant la théorie des formes de Dirichlet, nous construisons une solution d’une version faible de ces EDPS. Nous prouvons également plusieurs résultats partiels qui suggèrent que les EDPS de Bessel de paramètre δ < 3 possèdent certaines propriétés importantes: propriété de Feller forte, existence de temps locaux. Enfin, nous considérons différents modèles de pinning critiques dynamiques, discret et continu, et prouvons un résultat de tension. Nous conjecturons que ces modèles ont une même limite en loi décrite par l’EDPS de Bessel associée à δ = 1<br>In this thesis, we derive integration by parts formulae (IbPF) for the laws of Bessel bridges of dimension δ > 0, thus extending previous formulae obtained by Zambotti in the case δ ≥ 3. This allows us to identify the structure of some stochastic PDEs (SPDEs) having the law of a Bessel bridge of dimension δ < 3 as invariant measure, and which extend in a natural way the family of SPDEs previously considered by Zambotti for δ ≥ 3. We call these equations Bessel SPDEs, and write them using renormalized local times. In the particular cases δ = 1, 2, using Dirichlet forms, we construct a solution to a weak version of these SPDEs. We also provide several partial results suggesting that the SPDEs associated with δ < 3 should have several important properties: strong Feller property, existence of local times. Finally, we consider dynamical critical wetting models, in the discrete and in the continuum, and prove a tightness result. We conjecture that these models have a common limit in law which should be described by the Bessel SPDE associated with δ = 1
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Maahs, Ilse [Verfasser], and Hans Rudolf [Akademischer Betreuer] Lerche. "Curved boundary crossing of bessel processes." Freiburg : Universität, 2016. http://d-nb.info/1119717701/34.
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Dallaire, Michael. "Faisceaux Bessel spatiotemporels : théorie et expérimentation." Thesis, Université Laval, 2013. http://www.theses.ulaval.ca/2013/29894/29894.pdf.
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Les travaux présentés dans cette thèse portent en premier lieu sur l’établissement d’un modèle théorique décrivant une nouvelle famille de faisceaux invariants reposant sur une distribution correspondant à la fonction de Bessel dans le plan spatiotemporel, d’où leur nom de faisceaux Bessel spatiotemporels (BST). Le modèle analytique décrivant ces faisceaux n’a pas de bornes physiques, ce qui se traduit par une impossibilité de les générer expérimentalement. Il est cependant possible dans les faits de limiter l’étendue spatiale et temporelle de ceux-ci en utilisant par exemple une enveloppe gaussienne, dont la taille est variable. La limitation physique par enveloppe gaussienne altère la nature invariante des faisceaux BST en introduisant une dépendance spatiale qui affecte de manière plus ou moins prononcée leur invariance, selon que la taille de l’enveloppe est petite ou large relativement à la structure interne du faisceau. Un modèle théorique présente par la suite les caractéristiques physiques des faisceaux BST limités par une enveloppe gaussienne, appelés faisceaux Bessel-Gauss spatiotemporels (BGST). Une méthode expérimentale de génération des faisceaux BGST centrés à 800 nm est également présentée. Les méthodes de caractérisation reposent quant à elles sur l’analyse du profil spatial, temporel et du spectre résolu spatialement (SRS). Le SRS permet d’obtenir la distribution des longueurs d’onde en fonction de la position transversale du faisceau, et permet une reconstruction partielle de la structure spatiotemporelle des faisceaux BGST via une transformée de Fourier. Les méthodes d’analyse développées ont permis de comparer les faisceaux générés expérimentalement avec les modèles théoriques pour en faire ressortir une très bonne correspondance.
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Noshirvani, Allahabadi Golchehr, and Allahabadi Golchehr Noshirvani. "Bessel Light Sheet Structured Illumination Microscopy." Diss., The University of Arizona, 2016. http://hdl.handle.net/10150/621810.
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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.
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Dallaire, Michaël. "Faisceaux Bessel spatiotemporels : théorie et expérimentation." Doctoral thesis, Université Laval, 2013. http://hdl.handle.net/20.500.11794/24630.
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Les travaux présentés dans cette thèse portent en premier lieu sur l’établissement d’un modèle théorique décrivant une nouvelle famille de faisceaux invariants reposant sur une distribution correspondant à la fonction de Bessel dans le plan spatiotemporel, d’où leur nom de faisceaux Bessel spatiotemporels (BST). Le modèle analytique décrivant ces faisceaux n’a pas de bornes physiques, ce qui se traduit par une impossibilité de les générer expérimentalement. Il est cependant possible dans les faits de limiter l’étendue spatiale et temporelle de ceux-ci en utilisant par exemple une enveloppe gaussienne, dont la taille est variable. La limitation physique par enveloppe gaussienne altère la nature invariante des faisceaux BST en introduisant une dépendance spatiale qui affecte de manière plus ou moins prononcée leur invariance, selon que la taille de l’enveloppe est petite ou large relativement à la structure interne du faisceau. Un modèle théorique présente par la suite les caractéristiques physiques des faisceaux BST limités par une enveloppe gaussienne, appelés faisceaux Bessel-Gauss spatiotemporels (BGST). Une méthode expérimentale de génération des faisceaux BGST centrés à 800 nm est également présentée. Les méthodes de caractérisation reposent quant à elles sur l’analyse du profil spatial, temporel et du spectre résolu spatialement (SRS). Le SRS permet d’obtenir la distribution des longueurs d’onde en fonction de la position transversale du faisceau, et permet une reconstruction partielle de la structure spatiotemporelle des faisceaux BGST via une transformée de Fourier. Les méthodes d’analyse développées ont permis de comparer les faisceaux générés expérimentalement avec les modèles théoriques pour en faire ressortir une très bonne correspondance.
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Fay, TH, and PH Kloppers. "The Gibbs’ phenomenon for Fourier–Bessel series." International Journal of Mathematical Education in Science and Technology, 2003. http://encore.tut.ac.za/iii/cpro/DigitalItemViewPage.external?sp=1001984.
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Summary
The paper investigates the Gibbs’ phenomenon at a jump discontinuity for
Fourier–Bessel series expansions. The unexpected thing is that the Gibbs’
constant for Fourier–Bessel series appears to be the same as that for Fourier
series expansions. In order to compute the coefficients for Fourier–Bessel
functionsefficiently, several integral formulasare derived and the Struve
functions and their asymptotic expansions discussed, all of which significantly
ease the computations. Three numerical examples are investigated. Findings
suggest further investigations suitable for undergraduate research projects or
small student group investigations.
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Omoefe, Idisi David, and Andrew Forbes. "Creation and detection of Vector Bessel Beams." Thesis, University of Fort Hare, 2016. http://hdl.handle.net/10353/1785.
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Bessel beams are optical fields which falls into the category of non-diffracting beams. Vector Bessel beams are vector beams possessing cylindrical symmetry. Cylindrically symmetric beams tend to have a tight focal point during propagation. The tight focal beam nature of vector Bessel beams makes them a good potential in various facets of science such as biological optical trapping, wireless communications, remote sensing, microscopy etc. In this research work, vector Bessel beams were generated using the phase of an Axicon that was encoded into a spatial light modulator. Firstly, scalar Bessel beams which possess linear polarization were generated and converted to circularly polarized vector beams by the use of a q-plate. The orbital angular momentum (OAM) modes that are embedded in the vortex beams were detected using modal decomposition technique. This was implemented for both the scalar and vector case using a quarter wave plate. The measure of the degree of non-separability of the vector Bessel beams using tomographic quantum tools was also implemented where the density matrix was reconstructed. The concurrence and fidelity which explore the measure of vectorness of both scalar and vector Bessel beams were calculated from the density matrix. The obtained results show that the spatial modes and polarization are coupled in the vector case as expected.
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Qi, Zhi. "Theory of Bessel Functions of High Rank." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1428530485.
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Ouadghiri, Idrissi Ismail. "Nonlinear instabilities and filamentation of Bessel beams." Thesis, Bourgogne Franche-Comté, 2018. http://www.theses.fr/2018UBFCD071/document.
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Un faisceau de Bessel est un champ électromagnétique résistant à la diffraction. il peut se propager en préservant son profile transversal d'intensité même en régime de filamentation. Ceci est très avantageux pour les applications laser de haute puissance, en particulier parce qu’ils permettent de générer des canaux de plasma homogènes dans les diélectriques. Cependant, à haute intensité, les impulsions laser ultracourtes subissent, dans certaines conditions expérimentales (faible focalisation), des instabilités non linéaires entraînant la modulation d’intensité du lobe central au cours de la propagation, ce qui peut être néfaste pour ces applications comme l’usinage des matériaux transparents. L’objectif de cette thèse est de contrôler la génération de canaux de plasma par impulsions de Bessel via le contrôle du profil spatial de ces impulsions. Nous avons dans une première partie, développé une méthode expérimentale pour manipuler le profil d’intensité axiale en régime linéaire. La seconde partie concerne l’étude et le contrôle des instabilités non linéaires induites par l’effet Kerr. Nous avons développé un modèle théorique du mélange à quatre ondes dans les faisceaux de Bessel et avons démontré une nouvelle approche pour manipuler ces instabilités par une mise en forme appropriée de l’intensité axiale des faisceaux de Bessel. Nous avons ensuite étudié la validité des modèles de filamentation basés l’équation non linéaire de Schrödinger et le modèle de Drude. Les résultats expérimentaux de la filamentation des faisceaux de Bessel dans le verre ont montré un comportement invariant par propagation, contrairement aux modèles numériques. Nous avons testé et amendé les modèles de dynamiques de plasma et de propagation. Nos simulations sont comparées à des résultats expérimentaux. Nous montrons que les corrections que nous avons pu apporter par rapport à l’état de l’art sont insuffisantes et rendent nécessaire une autre forme de modèle<br>Bessel beams are solutions of Helmholtz equation. They can propagate while conserving their transverse intensity profile in space even in filamentation regime. This feature is very advantageous in high power laser applications such as plasma waveguide generation and laser ablation because they can generate homogeneous plasma channels in dielectrics. However, for moderate to low focusing conditions, Bessel pulses can sustain nonlinear instabilities, which consist in the modulation of the central core intensity along the propagation. Such a feature can prevent efficient energy deposition which hampers the applicability of Bessel pulses. The aim of this thesis is to investigate the possibility to control laser-generated plasma channels using spatially-reshaped Bessel pulses. In a first part, we have developed an experimental method based on a spatial light modulator to modify the evolution of the on-axis intensity of Bessel beams in the linear propagation regime. To study and control Kerr-induced instabilities, we developed, in a second part, a novel model based on four wave mixing interactions in Bessel beams. We have then demonstrated a novel approach to control these instabilities via on-axis intensity shaping. Bessel filamentation models in transparent media were then studied. Most models used in literature are based on nonlinear Schrödinger equation for light propagation and Drude model for laser-matter coupling. Experimental results on Bessel filamentation in glass showed propagation-invariant features in contrast with numerical simulations. Several corrections to this model were discussed. Our results show that such models are insufficient to explain our experimental results and thus the need to develop a more suitable one
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Fortin, Pierre-Yves. "Figure d'interférence par faisceaux Bessel, étude et applications." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/mq33637.pdf.
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Müller, Angelina [Verfasser], and Ulrike [Akademischer Betreuer] Wallrabe. "Micro-optical components for depth-controlled Bessel beams." Freiburg : Universität, 2019. http://d-nb.info/1188196006/34.
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Caron, Christian Frédéric Roger Caron. "Harmonic generation in gases using Bessel-Gauss beams." Thesis, Durham University, 1998. http://etheses.dur.ac.uk/4668/.
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The generation and propagation of harmonics in an atomic gas are described for the case of an incident Bessel-Gauss beam. Theoretical expressions are derived for the far-field amplitude of the harmonic field by solving the propagation equation using an elaborate integral formalism. We establish simple rules which determine the optimum Bessel-Gauss beam with respect to phase-matching as a function of the medium properties, such as the dispersion and the gas density. Target depletion due to photoionization and refractive index variations originating from both free electrons and dressed linear atomic susceptibilities are taken into account. The intensity-dependent complex atomic dipole moment is calculated using nonpertur- bative methods. Numerical propagation calculations for hydrogen, xenon and argon are presented. For hydrogen we consider the third harmonic of a 355-nm, 15-ps pump beam up to 3 X 10(^13) W/cm(^2) intensity, similarly for xenon, but at lower intensities. For argon we consider the 17th and 19th harmonic of a 810-nm, 30-fs pump beam around 10(^14) W/cm(^2) intensity. We compare conversion efficiencies and both spatial and temporal far-field profiles for an optimized Bessel-Gauss beam with respect to a Gaussian beam of same power and/or peak focal intensity. For the case of hydrogen, we investigate the effect of an ac-Stark-shift induced atomic resonance. We find all results in good agreement with our theoretical predictions. We conclude from our studies that Bessel-Gauss beams can perform better in terms of conversion efficiency than a comparable Gaussian beam. We find this to originate essentially from the more flexible phase-matching conditions for Bessel-Gauss beams. Bessel-Gauss beams also allow for spatial separation of the harmonic and the incident field in the far-field region, owing to the conical shape of their spatial far-field profile. Both features make Bessel-Gauss beams an attractive alternative to Gaussian beams in a limited but substantial number of experimental conditions.
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Hornik, Kurt, and Bettina Grün. "Amos-type bounds for modified Bessel function ratios." Elsevier, 2013. http://dx.doi.org/10.1016/j.jmaa.2013.05.070.
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Dion, Jean-François. "Conception et réalisation d'un résonateur Bessel auto-filtrant." Master's thesis, Université Laval, 2015. http://hdl.handle.net/20.500.11794/26011.
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Le faisceau Bessel, solution exacte de l’équation d’onde, possède une zone où il garde pratiquement la même forme et les mêmes dimensions ; dans cette zone, il ne diffracte pas. Cette propriété intéressante a amené, depuis les années 80, plusieurs groupes de recherche à concevoir des cavités laser produisant ce type de faisceau non-diffractant. Une des difficultés de cette tâche réside dans la sélection des modes transverses du résonateur. Dans la plupart des cas, le problème est résolu en bloquant les modes supérieurs avec un iris, ce qui limite souvent le faisceau en propagation et en puissance. Ce projet de résonateur Bessel propose une nouvelle manière de sélectionner les modes en utilisant un miroir coupleur de petite taille, laquelle est adaptée aux dimensions du lobe central du faisceau Bessel J0. Le faisceau Bessel est généré à l’intérieur de la cavité grâce à un miroir conique, ou axicon, conçu et caractérisé dans nos laboratoires tout comme le coupleur. Une fois la cavité montée et alignée, nous avons mesuré les différentes distributions en champ proche, en champ lointain et à l’intérieur de la cavité. Les simulations numériques faites à l’aide de la méthode de Prony, pour le calcul de la proportion des principaux modes transverses présents dans le résonateur, nous ont permis d’observer de grandes similitudes avec les distributions mesurées. Il s’avère que le mode principal, comme le révèlent les simulations du champ lointain, n’est pas tout à fait un faisceau Bessel J0, quoique très ressemblant. Le calcul de l’énergie encerclée du mode dominant en champ lointain est presque identique à celui de l’énergie encerclée sur les distributions obtenues expérimentalement, le bruit en moins, ce qui semble confirmer l’unicité du mode transverse issu de la cavité.
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Dib, Hacen. "Fonctions de Bessel sur une algèbre de Jordan." Université Louis Pasteur (Strasbourg) (1971-2008), 1988. http://www.theses.fr/1988STR13150.
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Grecco, Ryan Francis. "Microwave Bessel-Beam Propagation through Spatially Inhomogeneous Media." ScholarWorks @ UVM, 2017. http://scholarworks.uvm.edu/graddis/726.
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Long range wireless power transmission (WPT) is a critical technology for the development of remote power systems for air and space vehicles as well as for point-to-point transmission on Earth. This can be achieved using either a laser for transmission in the infrared to optical frequency domain or by using microwaves. The objective of this research is to study the application of microwave power transmission (MPT) through the use of a so-called Bessel-beam whose unique propagation properties include a self-healing ability as well as non-diffractive properties. These two unique properties lead to an increase in the efficiency of microwave power transmission. In this research the propagation of a microwave Bessel-beam through a spatially inhomogeneous medium will be simulated in MATLAB using a plane wave spectrum representation of the electromagnetic beam field. The spatially inhomogeneous medium of interest here is the Earth's atmosphere whose electromagnetic properties (dielectric permittivity and electric conductivity) vary with altitude up through the ionosphere. The purpose of this research is to determine how efficiently a microwave Bessel beam can propagate in point-to-point transmission through the Earth's atmosphere as well as between satellites in Earth orbit.
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Norfolk, Andrew W. G. "Bessel beams : a novel approach to periodic structures." Thesis, Imperial College London, 2010. http://hdl.handle.net/10044/1/6035.
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Bessel and Bessel-like beams in Kerr-like nonlinear materials are numerically investigated. This is conducted with a view to exploiting the behaviour of such profiles for the direct laser writing of periodic structures in highly nonlinear glasses. A highly efficient numerical model is developed for the propagation of radially symmetric profiles based on the quasi-discrete Hankel transform (QDHT), making use of a reconstruction relation to allow the field to be sampled at arbitrary positions that do not coincide with the numerical grid. This Hankel-based Adaptive Radial Propagator (HARP) is shown to be up to 1000 times faster than standard FFT-based methods. The critical self-focusing of the Gaussian beam is reproduced to confirm the accuracy of HARP. Following this the critical self-focusing behaviour of a Bessel-Gauss beam is investigated. It is observed that, for certain parameters, increasing the beam power may prevent blowup in the Bessel-Gauss beam. Below the threshold for self-focusing the Bessel-Gauss beam exhibits periodic modulation in the direction of propagation. The existing equation describing this behaviour is shown to be inaccurate and a modification is proposed based on a power dependent beat-length. This modified beat-length equation is demonstrated to be accurate in both the paraxial and quasi-nonparaxial regime. As the beam decays, the intensity modulation appears negatively chirped. It is demonstrated that this chirp may be controlled through careful shaping of the window. It is also shown that a small Gaussian seed beam may be used to control the positions of the maxima. It is demonstrated that a set of nonlinear Bessel functions exist that exhibit a similar quasi-stationary behaviour in a nonlinear medium to the linear Bessel beam in a linear medium. Furthermore it is shown for the first time that higher-order, Bessel-like, stationary solutions exist for beams with azimuthal phase, and boundary conditions for these functions are derived.
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Dib, Hacen. "Fonctions de Bessel sur une algèbre de Jordan." Grenoble 2 : ANRT, 1988. http://catalogue.bnf.fr/ark:/12148/cb37613169j.
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Bhattarai, Dipesh. "Application of Bessel beams in the human eye." Thesis, Queensland University of Technology, 2019. https://eprints.qut.edu.au/129455/9/Dipesh_Bhattarai_Thesis.pdf.
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Bessel light beams have spread-resistant and self-reconstruction properties. These beams were compared with conventional light beams for ophthalmic applications. The Bessel beams increased the strength of reflections used to determine ocular lens parameters, improved fixation stability, and decreased light loss during imaging of the retina. These findings indicate that Bessel beams have application in clinical ophthalmic instruments.
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Chellali, Mustapha. "Congruences, nombres de Bernoulli et polynômes de Bessel." Université Joseph Fourier (Grenoble ; 1971-2015), 1989. http://www.theses.fr/1989GRE10091.
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En premiere partie, on donne des congruences entre nombres de bernoulli-hcowitz dans le cas supersingulier. En deuxieme partie, on montre que la suite des nombres de bernoulli verifie des formules de recurrence qui servent a tester si un nombre premier est irregulier. En troisieme partie, on etudie les zeros des polynomes de bessel generalises, en particulier on encadre un zero reel, apres developpement asymptotique, et on donne des estimations uniformes des valeurs de ces polynomes
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Polat, Zeynep Sonay. "Studies On The Generalized And Reverse Generalized Bessel Polynomials." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12604961/index.pdf.
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The special functions and, particularly, the classical orthogonal polynomials encountered in many branches of applied mathematics and mathematical physics satisfy a second order differential equation, which is known as the equation of the hypergeometric type. The variable coefficients in this equation of the hypergeometric type are of special structures. Depending on the coefficients the classical orthogonal polynomials associated with the names Jacobi, Laguerre and Hermite can be derived as solutions of this equation.
In this thesis, these well known classical polynomials as well as another class of polynomials, which receive less attention in the literature called Bessel polynomials have been studied.
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Tovmasyan, Nariné. "Optimisation de la sensibilité d'un interféromètre à faisceaux Bessel." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/MQ57892.pdf.
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Rogel-Salazar, Jesus. "Aspects of Bose-Einstein condensation and Bessel beam resonators." Thesis, Imperial College London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.397329.
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Rodrigues, Fabio Grangeiro 1980. "Sobre cálculo fracionário e soluções da equação de Bessel." [s.n.], 2015. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306992.
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Orientador: Edmundo Capelas de Oliveira<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-26T23:00:41Z (GMT). No. of bitstreams: 1
Rodrigues_FabioGrangeiro_D.pdf: 1185818 bytes, checksum: 96f82c6ff4622e4ecdd3ccae79803dae (MD5)
Previous issue date: 2015<br>Resumo: Neste trabalho é apresentado um modo de se obter soluções de um caso particular da equação hipergeométrica confluente, a equação de Bessel de ordem p, utilizando-se da teoria do cálculo de ordem arbitrária, também conhecido popularmente por cálculo fracionário. Em particular, discutimos alguns equívocos identificados na literatura e levantamos questionamentos sobre algumas interpretações a respeito dos operadores formulados segundo Riemann-Liouville quando aplicados a certos tipos de funções. Para tanto, apresentamos inicialmente os operadores de integração e diferenciação fracionárias segundo as formulações mais clássicas (Riemann-Liouville, Caputo e Grünwald-Letnikov) e, em seguida, apresentamos o operador de integrodiferenciação fracionária que é a tentativa de unificar as operações de integração e diferenciação sob um único operador. Ao longo do texto indicamos as principais propriedades destes operadores e citamos algumas das suas aplicações comumente encontrados na Matemática, Física e Engenharias<br>Abstract: In this thesis we discuss the solvability of the Bessel's differential equation of order p, which is a particular case of the confluent hypergeometric equation, from the perspective of the theory of calculus of arbitrary order, also commonly known as fractional calculus. In particular, we expose some misconceptions encountered in the literature and we raise some questions about interpretations of the Riemann-Liouville operators when acting on certain types of functions. In order to do so, we present the main fractional operators (Riemann-Liouville, Caputo and Grünwald-Letnikov) as well as the fractional integrodifferential operator, which is an unified view of both integration and differentiation under a single operator. We also show the main properties of these operators and mention some of its applications in Mathematics, Physics and Engeneering<br>Doutorado<br>Matematica Aplicada<br>Doutor em Matemática Aplicada
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Favreau, Luc. "Combinatoire des tableaux oscillants et des polynomes de Bessel." Bordeaux 1, 1991. http://www.theses.fr/1991BOR10527.
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Nous nous interessons, dans ce travail, a la classe des tableaux oscillants generalisant les tableaux de young standards (ces derniers ayant ete abondamment etudies, par exemple dans le cadre des representations du groupe symetrique). Nous proposons une correspondance entre tableaux oscillants et generateurs de l'algebre de brauer possedant des proprietes analogues a celle de robinson-schensted pour le groupe symetrique. Nous en deduisons des formules d'enumeration pour ces tableaux suivant plusieurs parametres: longueur, forme finale et hauteur de la bande dans laquelle ils evoluent. Pour terminer, nous realisons une theorie combinatoire complete des polynomes de bessel (equation differentielle, recurrence a trois termes, serie generatrice et orthogonalite) a la base de laquelle se trouve une famille particuliere de tableaux oscillants reliee aux involutions
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Castillo, René Erlin. "Generalized Non-Autonomous Kato Classes and Nonlinear Bessel Potentials." Ohio University / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1121964346.
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Bélanger, Brigitte. "Auto-imagerie en coordonnées cylindriques à l'aide de faisceaux Bessel." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/mq25490.pdf.
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Ben, Ghanem Riadh. "Fonctions de Bessel et formules de quadrature de type gaussien." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ32584.pdf.
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Dusablon, Laurent. "Faisceaux Bessel-Gauss spatiotemporels : interférométrie spectrale par transformée de Fourier." Master's thesis, Université Laval, 2015. http://hdl.handle.net/20.500.11794/26525.
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Xu, Dongli, Weibin Zhou, and Leilei Peng. "Cellular resolution multiplexed FLIM tomography with dual-color Bessel beam." OPTICAL SOC AMER, 2017. http://hdl.handle.net/10150/623268.
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Fourier multiplexed FLIM (FmFLIM) tomography enables multiplexed 3D lifetime imaging of whole embryos. In our previous FmFLIM system, the spatial resolution was limited to 25 mu m because of the trade-off between the spatial resolution and the imaging depth. In order to achieve cellular resolution imaging of thick specimens, we built a tomography system with dual-color Bessel beam. In combination with FmFLIM, the Bessel FmFLIM tomography system can perform parallel 3D lifetime imaging on multiple excitation-emission channels at a cellular resolution of 2.8 mu m. The image capability of the Bessel FmFLIM tomography system was demonstrated by 3D lifetime imaging of dual-labeled transgenic zebrafish embryos. (C) 2017 Optical Society of America
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Hassan, Mostafa. "Ultrafast imaging of Bessel beam generated nano-plasmas within dielectrics." Electronic Thesis or Diss., Bourgogne Franche-Comté, 2022. http://indexation.univ-fcomte.fr/nuxeo/site/esupversions/9cc27edd-c3bb-4525-a1f5-e5e8f55c54c1.
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Les lasers femtoseconde ultra-intense sont largement utilisés pour le traitement des matériaux à l'échelle micro et nanométrique. Dans ce contexte, il est nécessaire de contrôler l'interaction laser-matière. Les faisceaux non diffractants, tels que les faisceaux de Bessel, offrent des avantages substantiels en ce qui concerne la stabilité de la propagation non linéaire dans les diélectriques. Ils ont permis la génération de nano-vides de rapport d'aspect extrêmement élevé. Cependant, les modèles conventionnels décrivant l'interaction Bessel-diélectrique ne parviennent pas à expliquer les observations expérimentales. Par conséquent, cette thèse vise à développer un ensemble de techniques pour retrouver les paramètres des plasmas générés par laser. La première partie développe une approche pour façonner la polarisation du faisceau de Bessel le long de sa propagation grâce à des lames demi-onde variant dans l'espace. La deuxième partie de ce travail est dédiée à l'imagerie de l'interaction entre le plasma généré par le début de l'impulsion et la majeure partie de l'impulsion. Nous avons confirmé une génération de nano-plasma avec une densité dépassant la densité critique, et un diamètre de typiquement 200 nm. La troisième partie de ce travail se concentre sur l'imagerie du plasma en utilisant une approche pompe-sonde. Ce nouveau concept est basé sur la mise en forme de la sonde comme un faisceau de Bessel d'ordre supérieur. Les paramètres du plasma sont extraits d'un ensemble de mesures de réflectivité en amplitude et en phase pour différents ordres et angles de l'impulsion de la sonde<br>Ultra-intense femtosecond lasers are widely used for nano and micro-material processing. Explaining the laser-matter interaction is needed to control the processing. In this context, non-diffracting beams, such as Bessel beams, provided substantial advantages regarding the stability of the non-linear propagation within dielectrics. They allowed the generation of extremely high aspect ratio nanovoids. However, conventional models describing Bessel-dielectric interaction fail to explain experimental observations. Therefore, this thesis aims to develop a set of techniques to retrieve the parameters of laser-generated plasmas. The first part develops an approach to shape the polarization of the Bessel beam along its propagation based on spatially-varying waveplates. The second part of this work is dedicated to the imaging of the interaction between the plasma generated by the onset of the pulse and the trailing part inside sapphire. We confirmed a generation of nano-plasma with a density exceeding the critical density, and a diameter of typically 200 nm. Then, the third part of this work focuses on imaging the plasma using a pump-probe approach. This new concept is based on shaping the probe as a higher-order Bessel beam. The plasma parameters are extracted from a set of measurements of reflectivity in amplitude and phase for different orders and angles of the probe pulse
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Adeyemi, Oluwafemi Ibukunoluwa. "The design of GaAs HEMT and HBT Bessel-type transimpedance amplifiers." Thesis, Texas A&M University, 2006. http://hdl.handle.net/1969.1/4663.
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The need of the everyday user to transfer large amounts of data is driving the need for larger data transfer capacity. Optical communication networks can satisfy this need. To be economically viable, optical transceivers must be integrated onto chips at low cost, using relatively cheap semiconductor processes. The optical preamplifier (transimpedance amplifier) receives optical information and converts it to a useful electrical form. It must operate at high speed, contribute little distortion to the input signal, and add little electrical noise to the incoming signal. This thesis investigates the design techniques in the literature, and proposes new architectures. Two high performance preamplifiers are designed, one using GaAs HEMTs, and the other using GaAs HBTs, each with different circuit techniques. The HEMT preamplifier has a transimpedance gain of 1.4 kâ¦, the highest in the literature for 10 Gb/s operation, along with a low input referred noise current of about 15 pA/Hz1/2 at a bandwidth of 6.3 GHz. The HBT preamplifier also has a transimpedance gain of 1.5 kâ¦, with a low input referred noise current of about 7 pA/Hz1/2. Both have clear, open eye-diagrams with a 10 Gb/s bit stream input, and are suitable for integration on a chip. The HEMT preamplifier was implemented as a common-gate, common-source amplifier cascade with a darlington output driver for a 50 ⦠load. The HBT preamplifier was implemented as common-emitter darlington amplifier with shunt peaking, and a simple emitter degenerated output driver for a 50 ⦠load. Both implementations exceeded the bandwidth, transimpedance gain and noise performance typically expected of the transistor technologies used. It is shown that the transimpedance limit can be circumvented by the use of novel architectures and shunt peaking.
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DeFranco, Mario A. (Mario Anthony). "The unramified principal series of p-adic groups : the Bessel function." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/90183.
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 99-101).<br>Let G be a connected reductive group with a split maximal torus defined over a nonarchimedean local field. I evaluate a matrix coefficient of the unramified principal series of G known as the "Bessel function" at torus elements of dominant coweight. I show that the Bessel function shares many properties with the Macdonald spherical function of G, in particular the properties described in Casselman's 1980 evaluation of that function. The analogy I demonstrate between the Bessel and Macdonald spherical functions extends to an analogy between the spherical Whittaker function, evaluated by Casselman and Shalika in 1980, and a previously unstudied matrix coefficient.<br>by Mario A. DeFranco.<br>Ph. D.
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Ratsibi, Humbelani Edzani. "Laser drilling of metals and glass using zero-order bessel beams." University of the Western Cape, 2013. http://hdl.handle.net/11394/5428.
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>Magister Scientiae - MSc<br>This dissertation consists of two main sections. The first section focuses on generating zero order Bessel beams using axicons. An axicon with an opening angle y = 5⁰ was illuminated with a Gaussian beam of width ω₀ = 1.67 mm from a cw fiber laser with central wavelength λ = 1064 nm to generate zero order Bessel beams with a central spot radius r₀ = 8.3 ± 0.3 μm and propagation distance ½zmax = 20.1 ± 0.5 mm. The central spot size of a Bessel beam changes slightly along the propagation distance. The central spot radius r₀ can be varied by changing the opening angle of the axicon, y, and the wavelength of the beam. The second section focuses on applications of the generated Bessel beams in laser microdrilling. A Ti:Sapphire pulsed femtosecond laser (λ = 775 nm, ω₀ = 2.5 mm, repetition rate kHz, pulse energy mJ, and pulse duration fs) was used to generate the Bessel beams for drilling stainless steel thin sheets of thickness 50 μm and 100 μm and microscopic glass slides 1 mm thick. The central spot radius was r₀ = 15.9 ± 0.3 μm and ½zmax = 65.0 ± 0.5 mm. The effect of the Bessel beam shape on the quality of the holes was analysed and the results were discussed. It was observed that Bessel beams drill holes of better quality on transparent microscopic glass slides than on stainless steel sheet. The holes drilled on stainless steel sheets deviated from being circular on both the top and bottom surface for both thicknesses. However the holes maintained the same shape on both sides of each sample, indicating that the walls are close to being parallel. The holes drilled on the glass slides were circular and their diameters could be measured. The measured diameter (15.4±0.3 μm) of the hole is smaller than the diameter of the central spot (28.2 ± 0.1 μm) of the Bessel beam. Increasing the pulse energy increased the diameter of the drilled hole to a value close to the measured diameter of the central spot.
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Takata, Tomohiro. "Certain multiple orthogonal polynomials and a discretization of the Bessel equation." 京都大学 (Kyoto University), 2006. http://hdl.handle.net/2433/144354.
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Kyoto University (京都大学)<br>0048<br>新制・課程博士<br>博士(理学)<br>甲第11975号<br>理博第2955号<br>新制||理||1442(附属図書館)<br>23788<br>UT51-2006-C655<br>京都大学大学院理学研究科数学・数理解析専攻<br>(主査)教授 上野 健爾, 教授 井川 満, 教授 河野 明<br>学位規則第4条第1項該当
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Charpin, Pierre-Jean. "Modélisation de l'interaction laser-plasma dans les faisceaux de Bessel femtoseconde." Electronic Thesis or Diss., Bourgogne Franche-Comté, 2024. http://indexation.univ-fcomte.fr/nuxeo/site/esupversions/fe2dc0aa-3386-4ecd-a96f-7f70a3113aa7.
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Les impulsions femtoseconde mises en forme de faisceaux de Bessel permettent de créer des nano-plasmas denses dans les diélectriques, menant à la formation de nano-vides à très haut rapport de forme pour des applications dans le domaine de la microélectronique. La modélisation de l'interaction laser-plasma est de prime importance pour comprendre l'évolution spatio-temporelle de la création de plasma et du dépôt d'énergie par l'impulsion laser femtoseconde. Ceci permettra de développer une interaction laser-matière extrêmement efficace dans d'autres géométries et matériaux. La thèse a pour objectif d'adapter des modèles d'ionisation et d'interaction laser plasma, de développer des outils d'analyse d'expériences, pour converger vers un modèle prédictif<br>Femtosecond pulses shaped as Bessel beams create dense nano-plasma in dielectrics, leading to the formation of very high aspect ratio nano-voids for microelectronics applications. The modeling of laser-plasma interaction is very important to understand the spatio-temporal evolution of plasma creation and energy deposition by the femtosecond laser pulse. This will allow the development of highly efficient laser-matter interaction in other geometries and materials. The thesis aims to adapt ionization and plasma laser interaction models, to develop tools for the analysis of experiments, in order to converge towards a predictive model. Translated with www.DeepL.com/Translator (free version)
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Queiroz, Pedro Afonso Teodoro Faria. "Aplicação da equação de Bessel fracionária na descrição da topografia da córnea." Master's thesis, Universidade de Aveiro, 2016. http://hdl.handle.net/10773/21196.
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Mestrado em Matemática e Aplicações<br>A visão é o sentido mais crucial que possuímos, uma vez que nos permite
perceber o mundo de forma muito precisa. Com o avanço da tecnologia
médica, o tratamento de diversas doenças oftalmológicas torna-se mais
adequado e bem sucedido. Isso não seria possível sem os devidos modelos
matemáticos da biomecânica do olho e seus constituintes. Uma das partes
mais importantes do olho humano é a córnea, porque é responsável por cerca
de dois terços do poder da refração. A descrição matemática da topografia da
córnea é muito importante do ponto de vista dos oftalmologistas porque muitos
dos distúrbios têm como origem algumas distorções na geometria da córnea.
Pretende-se com este trabalho mostrar a aplicação da equação diferencial
fracionária modificada de Bessel para o problema de descrição da topografia
da córnea. A solução do problema é dada em termos de séries de potência.
Esta solução tem um comportamento interessante no infinito que é uma
generalização dos resultados clássicos para função de Bessel modificada de
ordem 0.<br>Vision is the most crucial sense that we possess, once that enables us to
observe the world in very precise way. With the advancement of medical
technology, the treatment of various eye diseases becomes more appropriate
and successful. This would not have been possible without the appropriate
mathematical models of the biomechanics of the eye and its constituents. One
of the most important parts of the human eye is the cornea, because it is
responsible for about two-thirds of the power of refraction. The mathematical
description of the corneal topography is very important from the point of view of
the ophthalmologists because many disorders are caused by some distortions
in the corneal geometry. The aim of this work is the application of a fractional
modified differential equation to the problem of the corneal topography
description. The solution of the problem is given in terms of power series. This
solution has an interesting behaviour at infinity which is a generalization of the
classics results for the modified Bessel function of order 0.
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Notaros, Jelena. "Fresnel-focusing and bessel-beam integrated optical phased arrays for optical trapping applications." Thesis, Massachusetts Institute of Technology, 2017. http://hdl.handle.net/1721.1/112046.
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Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2017.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 107-112).<br>Optical trapping and tweezing - the manipulation of particles using optical forces - enables direct interaction with biological samples and non-invasive monitoring of their properties. As such, optical trapping has become a common tool in biology with applications ranging from better understanding of DNA mechanics to non-invasive manipulation of red blood cells in vivo. While optical trapping using bulk optics is a well established technique, recent work has turned towards chip-based optical trapping using integrated devices. However, many of these integrated systems are fundamentally limited to passive demonstrations within microns of the chip surface. Integrated optical phased arrays, which manipulate and dynamically steer light, provide one possible approach to scaling and arbitrary tweezing of optical traps. However, current on-chip optical phased array demonstrations have focused on systems which form and steer beams or project arbitrary radiation patterns in the far field. In this thesis, Fresnel-lens-inspired focusing integrated optical phased arrays are demonstrated for the first time and proposed as a method for chip-based optical trapping. These systems focus radiated light to tightly-confined spots in the near field above the chip to enable applications in wide-angle trapping at millimeter scales. Furthermore, integrated optical phased arrays are proposed and demonstrated for the first time as a method for generating quasi-Bessel beams in a fully-integrated, compact-form-factor system. Through generation of quasi-Bessel beams with elongated properties, these devices have potential for applications in multi-particle, multi-plane optical trapping. To enable these phased array systems, a suite of integrated nanophotonic architectures and devices for waveguiding, coupling, routing, phase control, and radiation are developed, simulated, fabricated, and tested and a CMOS-compatible foundry platform is leveraged for natural scaling to active demonstrations.<br>by Jelena Notaros.<br>S.M.
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Grosjean, Thierry. "Concept et étude d'un microscope optique en champ proche à pointe virtuelle pouvant travailler en zone de non couplage." Besançon, 2003. http://www.theses.fr/2003BESA2030.
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Manz, Thomas. "Stimulierte Stokes- und Anti-Stokes-Raman-Streuung mit Bessel-Bündeln in Aceton und Wasserstoff." [S.l. : s.n.], 2005. http://deposit.ddb.de/cgi-bin/dokserv?idn=975789325.
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Vieira, Tárcio de Almeida. "Axicons fotorrefrativos : estudo de Efeitos Foto-Induzidos por feixe de Bessel em cristais fotorrefrativos." reponame:Repositório Institucional da UFABC, 2010.
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Orr, Andrew McLean White. "Computational techniques for evaluating extremely low frequency electromagnetic fields produced by a horizontal electric dipole in seawater." Thesis, King's College London (University of London), 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.326222.
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Béraud, Jean-François. "Étude topologique des cartes, équations fonctionnelles et énumérations." Université de Marne-la-Vallée, 1998. http://www.theses.fr/1998MARN0038.
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Ce travail est divise en trois parties : apres avoir introduit les notions de cartes pointees topologiques et combinatoires, on presente differentes operations topologiques sur les cartes pointees. Les principales operations traitees sont l'operation topologique de suppression du brin pointe tout d'abord, et ensuite les operations plus complexes d'ouverture du sommet pointe et d'extraction du schema de carte. La deuxieme partie presente en premier lieu les equations que l'on peut obtenir a partir des operations topologiques presentees dans la premiere partie. On montre ensuite diverses enumerations obtenues a partir de ces equations fonctionnelles. En particulier, on enumere les cartes pointees sur la bouteille de klein, puis un certain nombre de familles de cartes pointees considerees independamment du type : orientables, localement orientables, arbres, et enfin hypercartes. Les resultats enumeratifs concernant les cartes independamment du type sont obtenus sous la forme de fractions continues. Ensuite, on applique des methodes simples issues de la combinatoire algebrique pour obtenir des formules d'enumeration pour des familles de cartes independamment du type. On prouve que les series obtenues par cette methode sont solutions des equations topologiques precedentes. Enfin, on observe des liens entre une fonction de bessel modifiee et certaines series generatrices de cartes. Cela nous permet d'obtenir de nouvelles equations differentielles dont les series generatrices des cartes en question (arbres pointes planaires, sur le tore, cartes planaires pointees) sont solutions. La derniere partie presente une librairie maple permettant d'effectuer des calculs liees aux series generatrices de cartes. Cette librairie regroupe la plupart des resultats connus pour les cartes pointees, les divers parametrages utilises dans la litterature, et integre egalement des outils d'investigations. Ces fonctionnalites sont decrites avec des exemples d'utilisation
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Siriwardena, Pathiranage Lochana Pabakara. "STOCHASTIC MODELS IN POPULATION DYNAMICS." OpenSIUC, 2014. https://opensiuc.lib.siu.edu/dissertations/908.
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This dissertation discusses the construction of some stochastic models for population dynamics with a variety of birth and death rate functions. A general model is constructed considering a fundamental growth rate function of the population while allowing random births and deaths in the population. Four stochastic discrete delay models and two non-delay models using the infinitesimal mean and variance given by birth and death rate functions have been produced and analyzed. In these constructions drift terms are in the form of logistic growth or logistic growth with delay. Logistic growth models are well known to biologists and economists. For each model, the existence and uniqueness of the global solution, non-negativeness of the solution is discussed, and for some models, boundedness of the path is also given. Persistence of the population and the boundary behavior have also been discussed through the hitting times. Here, a new method to analyze the hitting times for a specific class of stochastic delay models is presented. This work is related to and also extends the work of Edward Allen, Linda Allen and Bernt Oksendal in population dynamics.
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MAINSEL, FRANCIOSO ANNE-MARIE. "La maladie exostosante ou maladie de bessel-hagen : a propos d'une serie hospitaliere de 7 cas." Saint-Etienne, 1990. http://www.theses.fr/1990STET6202.
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Meinert, Tobias [Verfasser], Alexander [Akademischer Betreuer] Rohrbach, and Ulrich [Akademischer Betreuer] Kubitscheck. "Optimierungsstrategien zur computerholographischen Beleuchtung und zur Abbildung streuender Objekte in der Lichtscheibenmikroskopie mit Bessel-Strahlen." Freiburg : Universität, 2018. http://d-nb.info/1151817910/34.
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Augello, Elisa. "Precise Near-Field Focusing exploiting Bessel Beam Launchers for Wireless Power Transfer at millimeter waves." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2022. http://amslaurea.unibo.it/25774/.
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Wireless Power Transfer has become a promising technology to overcome the limits of wired solutions. Within this framework, the objective of this thesis is to study a WPT link at millimeter waves involving a particular type of antenna working in the radiative near-field, known as Bessel Beam (BB) Launcher. This antenna has been chosen for its peculiarity of generating a Bessel Beam which is by nature non-diffractive, showing good focusing and self-healing capabilities. In particular, a Bull-Eye Leaky Wave Antenna is designed and analysed, fed by a loop antenna and resonating at approximately 30 GHz. The structure excites a Hybrid-TE mode showing zeroth-order Bessel function over the z-component of the magnetic field. The same antenna is designed with two different dimensions, showing good wireless power transport properties. The link budgets obtained for different configurations are reported. With the aim of exploiting BB Launchers in wearable applications, a further analysis on the receiving part is conducted. For WPT wearable or implantable devices a reduced dimension of the receiver system must be considered. Therefore, an electrically large loop antenna in planar technology is modified, inserting phase shifters in order to increase the intensity of the magnetic field in its interrogation zone. This is fundamental when a BB Launcher is involved as transmitter. The loop antenna, in reception, shows a further miniaturization level since it is built such that its interrogation zone corresponds to the main beam dimension of transmitting BB Launcher. The link budget is evaluated with the new receiver showing comparable results with respect to previous configurations, showing an efficient WPT link for near-field focusing. Finally, a matching network and a full-wave rectifying circuit are attached to two of the different receiving systems considered. Further analysis will be carried out about the robustness of the square loop over biological tissues.
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Marzec, Jolanta. "On Bessel models for GSp₄ and Fourier coefficients of Siegel modular forms of degree 2." Thesis, University of Bristol, 2016. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.702462.
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In this work, we make a detailed study of the Fourier coefficients of cuspidal Siegel modular forms of degree 2. We derive a very general relation between the Fourier coefficients that extends previous work in this direction by Andrianov, Kowalski-Saha-Tsimerman and others. The basis for our relation is the dependence between values of global Bessel periods and averages of Fourier coefficients. Consequently our relation applies also to Bessel periods of more general automorphic forms on GSp4(A). We use our relation to prove that cuspidal Siegel modular forms associated to P-CAP representations (Saito-Kurokawa lifts with level) satisfy the so-called Maass relations. This is the first result of this kind for Siegel modular forms with respect to general congruence subgroups. Another important corollary of our work is the existence of non-zero Fourier coefficients of the simplest form possible (often fundamental or primitive) for a wide family of cuspidal Siegel modular forms of degree 2. Finally, using classical methods, we are able to prove that paramodular newforms of square-free level have infinitely many non-zero fundamental Fourier coefficients. This result extends previous work by Saha in the full-level case, and is especially interesting because of the paramodular conjecture connecting paramodular newforms of weight 2 and rational abelian surfaces.
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F, SARRI. "Optical microstructuring of alkali metal nanoparticle coatings on porous silica substrates induced by Bessel beam." Doctoral thesis, Università di Siena, 2019. http://hdl.handle.net/11365/1075534.
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The ability to control atomic adsorption/desorption processes by light as well as nanoparticle growth
on proper substrates is nowadays recognized as a promising technique in nanotechnology. This
subject is a part of a rising area of research devoted to the development of micro and nanophotonic
devices, sensors, metamaterials. The experimental work in this thesis aims at obtaining ordered
microstructures exploiting atomic desorption phenomena such as LIAD (Light Induced Atomic
Desorption). The suitable substrates consist in nanoporous silica matrices sealed inside cells and
exposed to alkaline atom vapor. A Gaussian beam generated by a laser, transformed in Bessel beam
by a conical shape lens, has been used as desorption light: in such way, the nanoparticles are created
on the pores and they are arranged following the Bessel beam profile, obtaining then the order
microscopic structure. More efficiently a coating of alkali metal nanoparticles has been grown on the
porous substrate due to LIAD induced by a Hg lamp and then the atomic desorption induced by a
Bessel beam has been responsible for the redistribution of the generated nanoparticles in the
micrometric concentric ring structure following the beam profile. The experiments have been
performed using different alkaline atom vapors, moreover porous silica samples with different pore
size and lasers with different wavelengths have been used.
During the work, the experimental setup and procedure have been optimized, evaluating the best
conditions for obtaining a well defined structure, in particular as regards the power emitted by the
desorbing lasers and the lighting time intervals for the porous silica samples. Through adjustments to
these parameters multiple, overlapping or side-by-side, illuminations, without incurring erasing
phenomena, have been possible thus creating complex structures.
The structures thus obtained, whether simple or complex, act as micrometric masks made out of
nanoparticles, and they are persistent and reversible. These masks can be detected by illuminating
them with laser light and observing the ring-shaped pattern produced by diffraction.
The generated structures have been systematically analyzed verifying the effective formation of the
nanoparticles by detection of their absorption spectra, observing the microstructures under a
microscope and recording them with a CCD camera. By an image analysis software, the concentric ring
pattern, corresponding to a 2D quasi-Bessel function, has been studied, evaluating the spacing ring
distance from its Fourier transform using the FFT algorithm; in this way, the relationship between the
characteristics of the Bessel beam, the wavelength of the radiation and the physical characteristics of
the conical lens have been verified. Also, images of the ring-shaped pattern obtained by diffraction
have also been registered, in order to estimate the contrast with the background and its persistence
on the sample.
The experimental results on this thesis suggest a new technique for the laser structuring of alkali metal
nanoparticles in ordered patterns on micrometric scale resolution promising for many applications in
all-optical photonic devices.
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Kalliterakis, Adonios. "Comportement à l'inifini des fonctions de Bessel associées aux représentations des algèbres de Jordan euclidiennes." Nancy 1, 1996. http://www.theses.fr/1996NAN10309.
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On étudie le comportement asymptotique de la fonction de Bessel généralisée (au sens de J. Faraut et G. Travaglini) d'une algèbre de Jordan euclidienne simple associée à une représentation régulière. On établit, par la méthode de la phase stationnaire, le développement asymptotique de cette fonction le long d'un rayon appartenant au cône symétrique fermé de l'algèbre, et on obtient une estimation uniforme précise.