Examinando por Materia "Bessel functions"

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    Spatial epidemic patterns recognition using computer algebra
    (SPRINGER, 2007-01-01) Hincapié, D.; Ospina, J.; Hincapié, D.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
    An exploration in Symbolic Computational bio-surveillance is showed. The main obtained results are that the geometry of the habitat determines the critical parameters via the zeroes of the Bessel functions and the explicit forms of the static and non-static spatial epidemic patterns. © Springer-Verlag Berlin Heidelberg 2007.
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    Symbolic solution for generalized quantum cylindrical wells using computer algebra
    (2008-01-01) Pulgarin, E.Y.V.; Pulgarin, E.Y.V.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
    This paper present how to solve the problem of cylindrical quantum wells with potential energy different from zero and with singularity of the energy on the axis of the cylinder. The solution to the problem was obtained using methods of computer algebra. The results depend of Bessel and Kummer functions. This paper present energy levels and wave functions in some of the cases with an exactly form and in other cases with an approximated form, this form depended on the possibility of integrating the special functions and calculating the zeros of these functions. Here we can see the power of the method in the applications concerning complex problems of quantum mechanics, and the possibility of being able to apply this method in order to solve other problems in science and also in engineering.
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    The scattering of SH waves by a finite crack with a superposition based diffraction technique
    (Universidad EAFIT, 2014) Valencia Gómez, Camilo Andrés; Gómez Cataño, Juan David
    The problem of diffraction of cylindrical and plane SH waves by a finite crack is revisited -- We construct an approximate solution by the addition of independent diffracted terms -- We start with the derivation of the fundamental case of a semi-infinite crack obtained as a degenerate case of generalized wedge -- This building block is then used to compute the diffraction of the main incident waves -- The interaction between the opposite edges of the crack is then considered one term at a time until a desired tolerance is reached -- We propose a recipe to determine the number of required interactions as a function of frequency -- The solution derived with the superposition technique can be applied at low and high frequencies
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    Using Maple and special functions to study the propagation of coherent light beams inside the Earth-ionosphere waveguide with turbulent media
    (SPIE-INT SOC OPTICAL ENGINEERING, 2012-05-07) Montoya Isaza, Sebastian; Ospina Giraldo, Juan Fernando; Montoya Isaza, Sebastian; Ospina Giraldo, Juan Fernando; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
    Some special functions of the Mathematical Physics are a very helpful resource in problems involving the propagation of coherent light beams, which will suffer dispersion in a turbulent media such as the Earth's ionosphere waveguide. Unfortunately, these tools are difficult to use because it involves very complex mathematical developments. For this reason it is interesting to find a friendly method to make the implementation of these special functions possible. Using Maple I will be able to overcome the mathematical difficulty of solving these equations and get to the understanding of these phenomena. Specifically I will consider the excitation of the Earth's ionosphere as a cavity or a waveguide by satellite borne current sources in the form of satellite-based antennas when the medium inside the waveguide is turbulent. As a result, three kinds of coherent light beams will be derived: Bessel beams, for relatively low turbulence, Whittaker beams, for moderate turbulence, and Heun beams, for strong or fully developed turbulence. These beams are represented by the corresponding electric fields but the associated magnetic fields can be derived as well. It is verified that Maple is a very powerful tool in the study of the propagation of an input field through axially symmetric systems using the methods of the Mathematical Physics. It is expected that Maple will have important applications for more general models concerning propagation trough turbulent environments. © 2012 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).