Search results for "Bessel function"
showing 10 items of 61 documents
On first exit times and their means for Brownian bridges
2017
For a Brownian bridge from $0$ to $y$ we prove that the mean of the first exit time from interval $(-h,h), \,\, h>0,$ behaves as $O(h^2)$ when $h \downarrow 0.$ Similar behavior is seen to hold also for the 3-dimensional Bessel bridge. For Brownian bridge and 3-dimensional Bessel bridge this mean of the first exit time has a puzzling representation in terms of the Kolmogorov distribution. The result regarding the Brownian bridge is applied to prove in detail an estimate needed by Walsh to determine the convergence of the binomial tree scheme for European options.
On 1-Laplacian Elliptic Equations Modeling Magnetic Resonance Image Rician Denoising
2015
Modeling magnitude Magnetic Resonance Images (MRI) rician denoising in a Bayesian or generalized Tikhonov framework using Total Variation (TV) leads naturally to the consideration of nonlinear elliptic equations. These involve the so called $1$-Laplacian operator and special care is needed to properly formulate the problem. The rician statistics of the data are introduced through a singular equation with a reaction term defined in terms of modified first order Bessel functions. An existence theory is provided here together with other qualitative properties of the solutions. Remarkably, each positive global minimum of the associated functional is one of such solutions. Moreover, we directly …
Single-shot ultrafast laser processing of high-aspect-ratio nanochannels using elliptical Bessel beams
2017
Ultrafast lasers have revolutionized material processing, opening a wealth of new applications in many areas of science. A recent technology that allows the cleaving of transparent materials via non-ablative processes is based on focusing and translating a high-intensity laser beam within a material to induce a well-defined internal stress plane. This then enables material separation without debris generation. Here, we use a non-diffracting beam engineered to have a transverse elliptical spatial profile to generate high aspect ratio elliptical channels in glass of dimension 350 nm x 710 nm, and subsequent cleaved surface uniformity at the sub-micron level.
Stationary heat flux profile in turbulent helium II in a semi-infinite cylindrical channel
2012
In this paper we determine a set of solutions for a system of partial dif- ferential equations describing stationary heat flux in a semi-infinite cylindrical channel filled with turbulent superfluid helium. This study uses a continuous model for liquid helium II, derived from Extended Thermodynamics, in which the heat flux q is a fundamental variable. The influence of the vortex line den- sity on the radial distribution of the heat flux is especially discussed.
The exact distribution of a weighted Convolution of two Gamma distributions
2006
Si considera una rappresentazione della funzione di densit`a di probabilit`a di una Convoluzione ponderata di distribuzioni Gamma, in cui una funzione ipergeometrica confluente descrive come le differenze tra i parametri di scala delle componenti determinino allontanamenti da una densit`a Gamma. Si considera il caso specifico di una convoluzione di due variabili gamma per mostrare, come al vantaggio interpretativo si aggiunga la possibilit`a di derivare in forma esplicita e computazionalmente semplice, espressioni della funzione di ripartizione e dei momenti. Si mostra la relazione tra tale distribuzione ed il sistema delle distribuzioni di Bessel, e si generalizza inoltre al caso di convol…
High speed cleaving of crystals with ultrafast Bessel beams
2017
International audience; We develop a novel concept for ultra-high speed cleaving of crystalline materials with femtosecond lasers. Using Bessel beams in single shot, fracture planes can be induced nearly all along the Bessel zone in sapphire. For the first time, we show that only for a pulse duration below 650 fs, a single fracture can be induced in sapphire, while above this duration, cracks appear in all crystallographic orientations. We determine the influential parameters which are polarization direction, crystallographic axes and scanning direction. This is applied to cleave sapphire with a spacing as high as 25 μm between laser impacts.
Micron-precision in cleaving glass using ultrafast bessel beams with engineered transverse beam shapes
2017
International audience; Ultrafast lasers in association to beam shaping have shown to be excellent candidates for transparent material processing. Non-diffractive solutions such as Bessel beams allows for precise energy deposition since they are robust to undesired non-linear effects and as they do not distort along the propagation. This offers important opportunities in laser-assisted cleaving, i.e. mechanical medium separation after single-pass laser illumination. Here we break the Bessel beam cylindrical symmetry using a novel anisotropic and non-diffractive solutions to investigate both lateral intensity contributions on material response and induced processing effect for non-cylindrica…
Mutual inductance for an explicitly finite number of turns
2011
Published version of an article published in Progress In Electromagnetics Research B, 28, 273-287. Also available from the publisher at http://www.jpier.org/pierb/pier.php?paper=10110103 Non coaxial mutual inductance calculations, based on a Bessel function formulation, are presented for coils modelled by an explicitly finite number of circular turns. The mutual inductance of two such turns can be expressed as an integral of a product of three Bessel functions and an exponential factor, and it is shown that the exponential factors can be analytically summed as a simple geometric progression, or other related sums. This allows the mutual inductance of two thin solenoids to be expressed as an…
Stealth dicing with Bessel beams and beyond
2016
In the context of laser cutting of transparent materials, we investigate glass cleaving with Bessel beams and report that a modification of the beam with 3 main lobes drastically enhances cleavability and reduces defects.
Bounds for Bessel functions
1989
We establish lower and upper bounds for the Bessel functionJ v (x) and the modified Bessel functionI v(x) of the first kind. Our chief tool is the differential equation satisfied by these functions.