Applications of Abel's original integral equation: Determination of potentials

1991 ◽  
pp. 26-34
Author(s):  
Rudolf Gorenflo ◽  
Sergio Vessella
Keyword(s):  
Integral Equation

On the limiting behaviour of a basic stochastic process

1972 ◽  
Vol 9 (1) ◽  
pp. 202-207
Author(s):  
İzzet Şahin ◽  
Oussama Achou
Keyword(s):  
Stochastic Process ◽  
Integral Equation ◽  
Stochastic Processes ◽  
Integral Equations ◽  
Mixed Type ◽  
Limiting Distributions ◽  
State Dependent ◽  
Limiting Behaviour ◽  
Rate Of Decline

Determination of the limiting distributions for a class of mixed-type stochastic processes with state-dependent rates of decline is reduced to the solution of a class of integral equations. For the case where the rate of decline is proportional to the state, some results are obtained by solving the integral equation of the process through Fuchs' method.

Approximation of the Strain Field Associated With an Inhomogeneous Precipitate—Part 1: Theory

1980 ◽  
Vol 47 (4) ◽  
pp. 775-780 ◽  
Author(s):  
W. C. Johnson ◽  
Y. Y. Earmme ◽  
J. K. Lee
Keyword(s):  
Integral Equation ◽  
Strain Field ◽  
Equivalent Stress ◽  
Taylor Series Expansion ◽  
Transformation Strain ◽  
Coherent Precipitate ◽  
Precipitate Shape ◽  
Polynomial Series ◽  
Elastic Strain Field

Two independent methods are derived for the calculation of the elastic strain field associated with a coherent precipitate of arbitrary morphology that has undergone a stress-free transformation strain. Both methods are formulated in their entirety for an isotropic system. The first method is predicated upon the derivation of an integral equation from consideration of the equations of equilibrium. A Taylor series expansion about the origin is employed in solution of the integral equation. However, an inherently more accurate means is also developed based upon a Taylor expansion about the point of which the strain is to be calculated. Employing the technique of Moschovidis and Mura, the second method extends Eshelby’s equivalency condition to the more general precipitate shape where the constrained strain is now a function of position within the precipitate. An approximate solution to the resultant system of equations is obtained through representation of the equivalent stress-free transformation strain by a polynomial series. For a given order of approximation, both methods reduce to the determination of the biharmonic potential functions and their derivatives.

On the harmonic oscillations of a rigid body on a free surface

1965 ◽  
Vol 21 (3) ◽  
pp. 427-451 ◽  
Author(s):  
W. D. Kim
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Rigid Body ◽  
Potential Problem ◽  
Harmonic Oscillation ◽  
Added Mass ◽  
The Body ◽  
Rigorous Solution ◽  
Damping Coefficients

The present paper deals with the practical and rigorous solution of the potential problem associated with the harmonic oscillation of a rigid body on a free surface. The body is assumed to have the form of either an elliptical cylinder or an ellipsoid. The use of Green's function reduces the determination of the potential to the solution of an integral equation. The integral equation is solved numerically and the dependency of the hydrodynamic quantities such as added mass, added moment of inertia and damping coefficients of the rigid body on the frequency of the oscillation is established.

Method of Moment Determination of Current Distribution on Elements of Yagi-Uda Array

2017 ◽  
Vol 2 (9) ◽  
pp. 23-29
Author(s):  
Raji A. Abimbola
Keyword(s):  
Integral Equation ◽  
Method Of Moments ◽  
Current Distribution ◽  
Tangential Component ◽  
The Other ◽  
Induced Current ◽  
Method Of Moment ◽  
Current Distributions ◽  
Complex Coefficients

Presented in this paper is the numerical solution to the current distributions on two forms of Yagi-Uda antenna designs. One form consists of twelve elements while the other consists of fourteen elements. Employing method of moments technique in which the unknown current is expanded in terms of known expansion function and complex coefficients which are to be determined. It is demonstrated that, when the integral equation that expresses tangential component of an impressed field in terms of induced current on the elements of Yagi-Uda array is reduced into matrix form, the current distribution of interest becomes known. The profiles for the current distributions on elements of those arrays represented in graphical forms reveal that, the currents are symmetrical about the length of the element in each case. It is found that the highest magnitude of the current exists on the driven element. Furthermore, the characteristic profiles of the currents on elements of those arrays exhibit sinusoidal type of waveform and are largely similar when the frequencies of operation are 200MHz and 665MHz, respectively.

Reflexion and transmission at a plane screen with periodically arranged circular or elliptical apertures

1973 ◽  
Vol 61 (1) ◽  
pp. 109-127 ◽  
Author(s):  
F. G. Leppington ◽  
H. Levine
Keyword(s):  
Integral Equation ◽  
Asymptotic Solution ◽  
Sound Wave ◽  
Infinite Plane ◽  
Rectangular Array ◽  
Transmission Coefficients ◽  
Single Aperture ◽  
Rigid Plane ◽  
Periodic Arrangement

A plane harmonic sound wave is considered to be incident upon a rigid plane screen that contains a periodic rectangular array of circular or elliptical apertures, and a characterization is sought for the reflexion and transmission coefficients of the scattered waves when the relationships aperture dimension [Lt ] spacing [Lt ] wavelength apply. The problem is analysed with the help of an integral equation over a single aperture and, as a consequence of the determination of the leading terms in its asymptotic solution, some prior results for more general (that is, irregular) aperture spacing are confirmed and specific features of the interaction in the periodic arrangement are established. Similar formulations are devised and given attention for the related problems in which (i) the screen is backed by a rigid infinite plane and (ii) the apertures contain rigid pistons capable of executing normal displacements compatible with an assigned and common impedance. A section is devoted to the solution, based on expansion of its kernel, for an integral equation of the first kind with a plane circular or elliptical domain.

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