1,736,338 research outputs found
Nonparaxial accelerating Bessel-like beams
Get PDFA new class of nonparaxial accelerating optical waves is introduced. These are beams with a Bessel-like profile that are capable of shifting laterally along fairly arbitrary trajectories as the wave propagates in free space. The concept expands on our previous proposal of paraxial accelerating Bessel-like beams to include beams with subwavelength lobes and/or large trajectory angles. Such waves are produced when the phase at the input plane is engineered so that the interfering ray cones are made to focus along the prespecified path. When the angle of these cones is fixed, the beams possess a diffraction-free Bessel profile on planes that stay normal to their trajectory, which can be considered as a generalized definition of diffractionless propagation in the nonparaxial regime. The analytical procedure leading to these results is based on a ray optics interpretation of Rayleigh-Sommerfeld diffraction and is presented in detail. The evolution of the proposed waves is demonstrated through a series of numerical examples and a variety of trajectories
Bounds and algorithms for the K-Bessel function of imaginary order
Get PDFUsing the paths of steepest descent, we prove precise bounds with numerical implied constants for the modified Bessel function of imaginary order and its first two derivatives with respect to the order. We also prove precise asymptotic bounds on more general (mixed) derivatives without working out numerical implied constants. Moreover, we present an absolutely and rapidly convergent series for the computation of and its derivatives, as well as a formula based on Fourier interpolation for computing with many values of . Finally, we have implemented a subset of these features in a software library for fast and rigorous computation of
Bessel-Bessel laser bullets doing the twist
No full textBessel beams carry orbital angular momentum (OAM). Opening up of the Hilbert space of OAM for information coding makes Bessel beams potential candidates for utility in data transfer and optical communication. A laser bullet is the ultra-short and tightly-focused analogue of a non-diffracting and non-dispersing laser Bessel beam. Here, we show fully analytically that a Bessel-Bessel laser bullet possesses orbital angular momentum. Analytic investigation of the energy, linear momentum, energy flux, and angular momentum, associated with the fields of a Bessel-Bessel bullet, in an under-dense plasma, is conducted. The expressions reported here will play a crucial role in preparing the laser bullets for practical applications, such as data transfer in optical communication, x- and gamma-ray generation from colliding bullets with counter-propagating electron bunches, particle trapping, tweezing and laser acceleration
Author Keynote: Dr. Bessel van der Kolk
No full textCWU Libraries and the Institute of Museum and Library Services are pleased to virtually bring Dr. Bessel van der Kolk to CWU and the Ellensburg community as part of our Community Resilience in Times of Changes series. Renowned trauma expert Dr. van der Kolk\u27s seminal work, The Body Keeps the Score; Brain, Mind, and Body in the Healing of Trauma, has been hailed as An authoritative guide to the effects of trauma, and pathways to recovery. (Rachel Yehuda, Ph.D.) Dr. van der Kolk has spent his career studying how people adapt to traumatic events. He is the president of the Trauma Research Foundationhttps://digitalcommons.cwu.edu/libraryevents/1243/thumbnail.jp
Abhandlungen von Friedrich Wilhelm Bessel : in drei Bänden
No full textBd. 1 Bewegungen der Körper im Sonnensystem, Sphärische AstronomieBd. 2 Theorie der Instrumente, Stellarastronomie, MathematikBd. 3 Geodäsie, Physik, Verschiedenes, Literaturhrsg. von Rudolf Engelman
A equação de kepler por Bessel e Fourier
Get PDFTCC (graduação) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas, Curso de Matemática.Três nomes muito importantes da história da humanidade aparecem no título deste trabalho. Kepler, Bessel e Fourier foram homens que contribuíram muito na história humana. Graças a Fourier, por exemplo, exames de ressonância magnética são possíveis, e graças a estes minha mãe está viva atualmente. Nesta monografia foram estudadas as biografias de Kepler, Fourier e Bessel bem como alguns de seus trabalhos. Deduziu-se a fórmula da elipse em coordenadas polares para dar base à demonstração das leis de Kepler do movimento planetário. Sobre estas foram feitos comentários e estudos de algumas aplicações. A equação de Kepler, importante em mecânica celeste, é uma equação cuja solução já foi encontrada por mais de cem métodos distintos
FOURIER-BESSEL LIPSCHITZ FUNCTIONS IN THE SPACE LP
Get PDFIn this paper, we obtain an analog of Youniss Theorem 5.2 in [5] forthe generalized Fourier-Bessel transform on the real line for functions satisfying the Fourier-Bessel Lipschitz condition in the space L
Bessel-Gauss Coherently Combined Beams
No full textThe application of a conical wavefront in the near field of the tiled aperture coherent beam combination (CBC) produces a “star-like” Bessel-Gauss irradiance pattern i.e. BG-CBC, in the far field. The properties of such a structured optical field were numerically investigated. In contrast to that for the classical CBC, the power diffracted beyond the first few BG-CBC rings is nearly homogenously distributed. Additionally, shaping the segmented conical wavefront can result in a significantly increased caustic length
Discrete damage traces from filamentation of Gauss-Bessel pulses
Get PDFFilamentation of Bessel-Gauss pulses propagating in borosilicate glass is found to produce damage lines extending over hundreds of micrometers and consisting of discrete, equidistant damage spots. These discrete damage traces are explained by self-regeneration of Gauss-Bessel beams during propagation and are potentially applicable in laser microfabrication of transparent materials
An Application to Transient Current Signal based Induction Motor Fault Diagnosis of Fourier-Bessel Expansion and Simplified Fuzzy ARTMAP
Get PDFThe start-up transient signals have been widely used for fault diagnosis of induction motor because they can reveal early defects in the development process, which are not easily detected with the signals in the steady state operation. However, transient signals are non-linear and contain multi components which need a suitable technique to process and identify the fault pattern. In this paper, the fault diagnosis problem of induction motor is conducted by a data driven framework where the Fourier-Bessel (FB) expansion is used as a tool to decompose transient current signal into series of single components. For each component, the statistical features in the time and the frequency domains are extracted to represent the characteristics of motor condition. The high dimensionality of the feature set is solved by generalized discriminant analysis (GDA) implementation to decrease the computational complexity of classification. In the meantime, with the aid of GDA, the separation of the feature clusters is increased, which enables the more classification accuracy to be achieved. Finally, the reduced dimensional features are used for classifier to perform the fault diagnosis results. The classifier used in this framework is the simplified fuzzy ARTMAP (SFAM) which belongs to a special class of neural networks (NNs) and provides a lower training time in comparison to other traditional NNs. The proposed framework is validated with transient current signals from an induction motor under different conditions including bowed rotor, broken rotor bar, eccentricity, faulty bearing, mass unbalance and phase unbalance. Additionally, this paper provides the comparative performance of (i) SFAM and support vector machine (SVM), (ii) SVM in the framework and SVM combined with wavelet transform in previous studies, (iii) the use of FB decomposition and Hilbert transform decomposition. The results show that the proposed diagnosis framework is capable of significantly improving the classification accuracy
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