Improvement of the spatial Hankel transform method to determine the impedance of outdoor ground surfaces

1993 ◽  
Vol 93 (4) ◽  
pp. 2290-2290
Author(s):  
C. Verhaegen ◽  
W. Lauriks ◽  
A. Cops
Keyword(s):  
Hankel Transform ◽  
Transform Method

scholarly journals Laminar pipe flow with time-dependent viscosity

2010 ◽  
Vol 13 (4) ◽  
pp. 729-740 ◽  
Author(s):  
Alan E. Vardy ◽  
James M. B. Brown
Keyword(s):  
General Solution ◽  
Hankel Transform ◽  
Temporal Variations ◽  
Time Dependent ◽  
Pressure Gradients ◽  
Newtonian Viscosity ◽  
Transform Method ◽  
Dependent Viscosity ◽  
Laminar Pipe Flow ◽  
Selection Of

A general solution is obtained for laminar flow in axisymmetric pipes, allowing for prescribed timedependent viscosity and time-dependent pressure gradients. In both cases, the only restriction on the prescribed time dependence is that it must vary continuously; it is not necessary for rates of change to be continuous. The general solution is obtained using the Finite Hankel Transform method. This makes it possible to allow explicitly for time-dependent viscosity, but it does not permit the spatial dependence of viscosity. This contrasts with Laplace transforms, which allow spatial, but not general, temporal variations. The general solution is used to study a selection of particular flows chosen to illustrate distinct forms of physical behaviour and to demonstrate the ease with which solutions are obtained. The methodology is also applied to the simple case of constant (Newtonian) viscosity. In this case, it yields the same solutions as previously published methods, but it does so in a much simpler manner.

Further Consideration of the Thick-Plate Problem With Axially Symmetric Loading

1962 ◽  
Vol 29 (1) ◽  
pp. 91-98 ◽  
Author(s):  
C. W. Nelson
Keyword(s):  
Approximate Method ◽  
Numerical Evaluation ◽  
Thick Plate ◽  
Hankel Transform ◽  
Integral Approach ◽  
Axially Symmetric ◽  
Transform Method ◽  
Thick Plates ◽  
Symmetric Loading ◽  
Special Case

The Fourier-Bessel integral approach was first applied to thick-plate problems of elasticity by Lamb and later by Dougall. Still later, the method, now known as the Hankel transform method, was applied to several cases of the thick-plate problem by Sneddon who, apparently, was the first to obtain numerical results for the stresses in thick plates by this method. Sneddon devised an approximate method for evaluating the integrals; i.e., inverting the transforms, which he encountered. The main contribution of the present paper consists in the more precise numerical evaluation of the integrals involved for a special case previously considered by Sneddon, but for values of parameters outside the range studied by Sneddon. In particular, it is hoped that the formulation of integration procedures presented will be found useful in other thick-plate problems.

scholarly journals Axisymmetric stationary heat conduction problem for half-space with temperature-dependent properties

2020 ◽  
Vol 24 (3 Part B) ◽  
pp. 2137-2150
Author(s):  
Dariusz Perkowski ◽  
Piotr Sebestianiuk ◽  
Jakub Augustyniak
Keyword(s):  
Heat Conduction ◽  
Half Space ◽  
Heat Conduction Problem ◽  
Hankel Transform ◽  
Heating Zone ◽  
Temperature Dependent ◽  
Transform Method ◽  
Special Cases ◽  
Temperature Dependent Properties ◽  
Method Model

The study examines problems of heat conduction in a half-space with a thermal conductivity coefficient that is dependent on temperature. A boundary plane is heated locally in a circle zone at a given temperature as a function of radius. A solution is obtained for any function that describes temperature in the heating zone. Two special cases are investigated in detail, namely Case 1 with given constant temperature in the circle zone and Case 2 with temperature given as a function of radius, r. The temperature of the boundary on the exterior of the heating zone is assumed as zero. The Hankel transform method is applied to obtain a solution for the formulated problem. The effect of thermal properties on temperature distributions in the considered body is investigated. The obtained results were compared with finite element method model.

On the Reconstruction of NQR Nutation Spectra in Solids with Powder Geometry

1994 ◽  
Vol 49 (1-2) ◽  
pp. 35-41 ◽  
Author(s):  
H. Robert ◽  
D. Pusiol ◽  
E. Rommel ◽  
R. Kimmich
Keyword(s):  
Single Crystals ◽  
Maximum Entropy Method ◽  
Hankel Transform ◽  
Entropy Method ◽  
Reconstruction Method ◽  
Zero Field ◽  
Axially Symmetric ◽  
Transform Method ◽  
The Fourier Transform

Abstract In single crystals the NQR nutation frequency depends on the relative orientation of the coil and the quadrupole axes. In powders the nutation lineshape is a superposition of spectra from the randomly oriented single crystals, so that powder patterns appear in such experiments if the recon­struction is performed by the Fourier transform method. In this paper an alternative reconstruction method of nutation spectra is suggested making use of the Hankel Transform. In this way the nutation spectra are simplified. Singularities arising with experiments for the determination of the asymmetry parameter η can easily be resolved. In the particular case of an axially symmetric quadrupolar tensor and a homogeneous radiofrequency field one can reduce the powder pattern to a single line without heterogeneous broadening with respect to orientation. Further improvement o f the nutation spectra can be achieved by taking advantage of the maximum entropy method, which strongly reduces apodisation and noise problems. Applications of the new data manipulation techniques to N Q R imaging methods published elsewhere and 2D zero-field N Q R spectroscopy are reported.

The electromagnetic response of an azimuthally anisotropic half‐space

Geophysics ◽  
1991 ◽  
Vol 56 (9) ◽  
pp. 1462-1473 ◽  
Author(s):  
Xiaobo Li ◽  
Laust B. Pedersen
Keyword(s):  
Half Space ◽  
Transfer Functions ◽  
Hankel Transform ◽  
Electromagnetic Response ◽  
Dipole Source ◽  
Impedance Tensor ◽  
Fracture Zones ◽  
Transform Method ◽  
Homogeneous Half Space ◽  
Horizontal Electric Dipole

Fracture zones are pervasive in crystalline areas. When the earth is seen over a sufficiently large volume fracture zones may be too thin to be individually identified. If they have preferred directions in that volume, the volume can be considered to be an azimuthally anisotropic medium. We have formulated the electromagnetic fields induced by a horizontal electric dipole on the surface of a homogeneous half‐space with azimuthally anisotropic conductivity. The field components are expressed by the two‐dimensional Fourier transform which can be computed by a fast Hankel transform method. The impedance tensor and tipper functions of controlled source tensor magnetotellurics are derived by exciting the dipole source in two different directions. We show the behavior of impedance tensor, tipper functions and their derived quantities: rotational invariants and Parkinson vectors. All transfer functions clearly show anisotropic characteristics. Contours of rotationally invariant apparent resistivities and phases for fixed frequencies are elongated in the direction of maximum conductivity, and Parkinson’s vectors tend to point in the same direction.

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