An algorithm for ultrasonic tomography based on inversion of the Helmholtz equation

1981 ◽  
pp. 371-406
Author(s):  
F. Stenger
Keyword(s):  
Helmholtz Equation ◽  
Ultrasonic Tomography

A preconditioned method for the solution of the Robbins problem for the Helmholtz equation

2011 ◽  
Vol 51 ◽  
pp. 87
Author(s):  
Jiang Le ◽  
Huang Jin ◽  
Xiao-Guang Lv ◽  
Qing-Song Cheng
Keyword(s):  
Helmholtz Equation

A Novel Electrical Cpacitance Sensor Design For Dual Modality Tomography Multiphase Measurement

2013 ◽  
Vol 64 (5) ◽  
Author(s):  
Muhammad Jaysuman Pusppanathan ◽  
Fazlul Rahman Yunus ◽  
Nor Muzakkir Nor Ayob ◽  
Ruzairi Abdul Rahim ◽  
Fatin Aliah Phang ◽  
...  
Keyword(s):  
Multiphase Flow ◽  
Flow Measurement ◽  
Ultrasonic Tomography ◽  
Pipe Surface ◽  
Dual Modality ◽  
Tomography System ◽  
Imaging Result ◽  
Process Tomography ◽  
Single Sensor ◽  
Capacitance Tomography

Electrical capacitance tomography (ECT) is one of process tomography technique which is developed rapidly in recent years. ECT is an imaging technique to obtain the internal permittivity distribution of a vessel or pipe by using capacitance electrodes sensor. This method has been integrated with ultrasonic tomography as multimodality system to perform multiphase flow measurement such as crude oil separation and oil process industry. In the present paper, a novel type of ECT sensor was developed using copper FR4 material. The electrode sensors can be flexibly bend or curve to fit the pipe surface for optimum measurement. Thus, every single sensor strip is designed to be functioned independently. Such system has lower sensing capability in the central of the sensing area which often contributes to poor imaging result. This problem can be overcome by combining the ECT with ultrasonic tomography to form a dual modality tomography system. By implementing the new ECT sensor, multiphase flow measurement image results can be achieved. The reconstructed image results are presented in this paper.

scholarly journals Gravitational Interaction in the Chimney Lattice Universe

Universe ◽  
2021 ◽  
Vol 7 (4) ◽  
pp. 101
Author(s):  
Maxim Eingorn ◽  
Andrew McLaughlin ◽  
Ezgi Canay ◽  
Maksym Brilenkov ◽  
Alexander Zhuk
Keyword(s):  
Helmholtz Equation ◽  
Gravitational Potential ◽  
Fourier Expansion ◽  
Gravitational Interaction ◽  
Alternative Solution ◽  
The Third ◽  
Present Universe ◽  
Delta Functions ◽  
Yukawa Potentials ◽  
The Universe

We investigate the influence of the chimney topology T×T×R of the Universe on the gravitational potential and force that are generated by point-like massive bodies. We obtain three distinct expressions for the solutions. One follows from Fourier expansion of delta functions into series using periodicity in two toroidal dimensions. The second one is the summation of solutions of the Helmholtz equation, for a source mass and its infinitely many images, which are in the form of Yukawa potentials. The third alternative solution for the potential is formulated via the Ewald sums method applied to Yukawa-type potentials. We show that, for the present Universe, the formulas involving plain summation of Yukawa potentials are preferable for computational purposes, as they require a smaller number of terms in the series to reach adequate precision.

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