Search results for "Bessel functions"
showing 5 items of 5 documents
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.
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…
Impact of a temporal sinusoidal phase modulation on the optical spectrum
2018
International audience; We discuss the effects of imparting a temporal sinusoidal phase modulation to a continuous wave on the frequency spectrum. While a practical analytical solution to this problem already exists, we present here a physical interpretation based on interference processes. This simple model will help the students better understand the origin of the oscillatory structure that can be observed in the resulting spectrum and that is characteristic of Bessel functions of the first kind. We illustrate our approach with an example from the field of optics.
Further monotonicity and convexity properties of the zeros of cylinder functions
1992
AbstractLet cvk be the kth positive zero of the cylinder function Cv(x,α)=Jv(x) cos α−Yv sin α, 0⩽α<π, where Jv(x) and Yv(x) are the Bessel functions of the first and the second kind, respectively. We prove that the function v(d2cvkddv2+δ)cvk increases with v⩾0 for suitable values of δ and k−απ⩾ 0.7070… . From this result under the same conditions we deduce, among other things, that cvk+12δv2 is convex as a function of v⩾0. Moreover, we show some monotonicity properties of the function c2vkv. Our results improve known results.
Products of Bessel functions and associated polynomials
2013
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.