Calculating the near Field of a Line of Sources Using Mellin Transforms
نویسنده
چکیده
In slender-body theories, one often has to find asymptotic approximations for certain integrals, representing distributions of sources along a line segment. Here, such approximations are obtained by a systematic method that uses Mellin transforms. Results are given near the line (using cylindrical polar coordinates) and near the ends of the line segment (using spherical polar coordinates).
منابع مشابه
GENERAL SOLUTION OF ELASTICITY PROBLEMS IN TWO DIMENSIONAL POLAR COORDINATES USING MELLIN TRANSFORM
Abstract In this work, the Mellin transform method was used to obtain solutions for the stress field components in two dimensional (2D) elasticity problems in terms of plane polar coordinates. the Mellin transformation was applied to the biharmonic stress compatibility equation expressed in terms of the Airy stress potential function, and the boundary value problem transformed to an algebraic ...
متن کاملCalculating of Dose Distribution in Tongue Brachytherapy by Different Radioisotopes using Monte Carlo Simulation and Comparing by Experimental Data
Introduction: Among different kinds of oral cavity cancers, the frequency of tongue cancer occurrence is more significant. Brachytherapy is the most common method to cure tongue cancers. Long sources are used in different techniques of tongue brachytherapy. The objective of this study is to asses the dose distribution around long sources, comparing different radioisotopes as brachytherapy sourc...
متن کاملQuasi-Static Deformation of a Uniform Thermoelastic Half –Space Due to Seismic Sources and Heat Source
This paper investigates the quasi-static plane deformation of an isotropic thermoelastic half-space due to buried seismic sources and heat source. Governing equations of thermo-elasticity are solved to obtain solutions for seismic sources in a thermoelastic half-space. The general solutions are acquired with the aid of Laplace and Fourier transforms and with the use of boundary conditions. The ...
متن کاملDimensional Regularization and Mellin Summation in High-Temperature Calculations
The infinite sums often encountered in thermal Feynman diagrams are commonly computed using the function coth, or one with similar properties, to generate poles in the complex plane whose residues correspond to the terms in the sum [1]. This transforms the summation into a contour integration and conveniently splits the zero-temperature and thermal contributions. The method ceases to be ideal w...
متن کاملSpecial functions and the Mellin transforms of Laguerre and Hermite functions
We present explicit expressions for the Mellin transforms of Laguerre and Hermite functions in terms of a variety of special functions. We show that many of the properties of the resulting functions, including functional equations and reciprocity laws, are direct consequences of transformation formulae of hypergeometric functions. Interest in these results is reinforced by the fact that polynom...
متن کامل