scholarly journals Electrostatic images and T-matrices for simple geometries

2021 ◽  
Author(s):  
◽  
Matt Majic
Keyword(s):  
Spherical Harmonics ◽  
Electromagnetic Scattering ◽  
Harmonic Functions ◽  
Scattering Problem ◽  
Low Frequency ◽  
Harmonic Series ◽  
Exact Nature ◽  
Linear Relationships ◽  
T Matrix ◽  
Scattered Fields

<p>This thesis is concerned with electrostatic boundary problems and how their solutions behave depending on the chosen basis of harmonic functions and the location of the fundamental singularities of the potential.  The first part deals with the method of images for simple geometries where the exact nature of the image/fundamental singularity is unknown; essentially a study of analytic continuation for Laplace's equation in 3 dimensions. For the sphere, spheroid and cylinder, new deductions are made on the location of the images of point charges and their linear or surface charge densities, by using different harmonic series solutions that reveal the image.  The second part looks for analytic expressions for the T-matrix for electromagnetic scattering of simple objects in the low frequency limit. In this formalism the incident and scattered fields are expanded on an orthogonal basis such as spherical harmonics, and the T-matrix is the transformation between the coefficients of these series, providing the general solution of any electromagnetic scattering problem by a given particle at a given wavelength. For the spheroid, bispherical system and torus, the natural basis of harmonic functions for the geometry of the scatterer are used to determine T-matrix expressed in that basis, which is then transformed onto a basis of canonical spherical harmonics via the linear relationships between different bases of harmonic functions.</p>

scholarly journals Electrostatic images and T-matrices for simple geometries

2021 ◽  
Author(s):  
◽  
Matt Majic
Keyword(s):  
Spherical Harmonics ◽  
Electromagnetic Scattering ◽  
Harmonic Functions ◽  
Scattering Problem ◽  
Low Frequency ◽  
Harmonic Series ◽  
Exact Nature ◽  
Linear Relationships ◽  
T Matrix ◽  
Scattered Fields

<p>This thesis is concerned with electrostatic boundary problems and how their solutions behave depending on the chosen basis of harmonic functions and the location of the fundamental singularities of the potential.  The first part deals with the method of images for simple geometries where the exact nature of the image/fundamental singularity is unknown; essentially a study of analytic continuation for Laplace's equation in 3 dimensions. For the sphere, spheroid and cylinder, new deductions are made on the location of the images of point charges and their linear or surface charge densities, by using different harmonic series solutions that reveal the image.  The second part looks for analytic expressions for the T-matrix for electromagnetic scattering of simple objects in the low frequency limit. In this formalism the incident and scattered fields are expanded on an orthogonal basis such as spherical harmonics, and the T-matrix is the transformation between the coefficients of these series, providing the general solution of any electromagnetic scattering problem by a given particle at a given wavelength. For the spheroid, bispherical system and torus, the natural basis of harmonic functions for the geometry of the scatterer are used to determine T-matrix expressed in that basis, which is then transformed onto a basis of canonical spherical harmonics via the linear relationships between different bases of harmonic functions.</p>

scholarly journals Semi-analytical calculation of the low-frequency electromagnetic scattering from a near-surface spherical inclusion in a conducting half-space

2014 ◽  
Vol 470 (2170) ◽  
pp. 20140269 ◽  
Author(s):  
Anastassios Skarlatos ◽  
Theodoros Theodoulidis
Keyword(s):  
Electromagnetic Scattering ◽  
Formal Solution ◽  
Spherical Inclusion ◽  
Scattering Problem ◽  
Analytical Calculation ◽  
Low Frequency ◽  
Near Surface ◽  
Proposed Model ◽  
Parametric Inversion ◽  
Full Coupling

The low-frequency electromagnetic scattering problem of a near-surface hollow spherical inclusion is solved by means of a modal approach. The primary field is excited using a current-carrying coil. The presented solution addresses the full coupling between the two interfaces of the geometry in a rigorous way. There is a direct physical interpretation of the different occurring terms in the formal solution, which provides a deeper understanding of the underlying phenomena. The calculation is very fast, which makes the proposed model suitable for use with parametric inversion algorithms.

Low-frequency scattering by a slit in an impedance plane

1979 ◽  
Vol 57 (7) ◽  
pp. 1039-1045
Author(s):  
R. A. Hurd
Keyword(s):  
Electromagnetic Scattering ◽  
Plane Surface ◽  
Low Frequency ◽  
Lower Surface ◽  
Impedance Boundary Condition ◽  
Narrow Slit ◽  
Infinite Plane ◽  
Impedance Boundary ◽  
Impedance Condition ◽  
Scattered Fields

A study is made of electromagnetic scattering by a narrow slit in an infinite plane. On the upper plane surface an impedance boundary condition is assumed; on the lower surface a different impedance condition obtains. Two types of incident wave are treated—a plane space wave and a surface wave. Expressions are found for the scattered fields and the field in the slit.

scholarly journals Estimation of permeability and saturation based on imaginary component of complex resistivity spectra: A laboratory study

2020 ◽  
Vol 12 (1) ◽  
pp. 299-306
Author(s):  
Jiang Jia ◽  
Shizhen Ke ◽  
Junjian Li ◽  
Zhengming Kang ◽  
Xuerui Ma ◽  
...  
Keyword(s):  
Water Saturation ◽  
Pore Space ◽  
Evaluation Model ◽  
Low Frequency ◽  
Petroleum Exploration ◽  
Western China ◽  
Imaginary Component ◽  
Estimation Model ◽  
Complex Resistivity ◽  
Linear Relationships

AbstractLow-frequency resistivity logging plays an important role in the field of petroleum exploration, but the complex resistivity spectrum of rock also contains a large amount of information about reservoir parameters. The complex resistivity spectra of 15 natural sandstone cores from western China, with different water saturations, were measured with an impedance analyzer. The pore space of each core was saturated with NaCl solution, and measurements were collected at a frequency range of 40–15 MHz. The results showed a linear relationship between the real resistivity at 1 kHz and the maximum values of imaginary resistivity for each core with different water saturations. The slopes of the linear best-fit lines had good linear relationships with the porosity and the permeability of cores. Based on this, a permeability estimation model was proposed and tested. In addition, the maxima of imaginary resistivity had power exponential relationships with the porosity and the water saturation of the cores. A saturation evaluation model based on the maxima of imaginary resistivity was established by imitating Archie’s formula. The new models were found to be feasible for determining the permeability and saturation of sandstone based on complex resistivity spectrum measurements. These models advance the application of complex resistivity spectrum in petrophysics.

scholarly journals A study of coupling interactions in finite arbitrarily-shaped grooves in electromagnetic scattering problem

2010 ◽  
Vol 18 (3) ◽  
pp. 2743 ◽  
Author(s):  
M. A. Basha ◽  
S. Chaudhuri ◽  
S. Safavi-Naeini
Keyword(s):  
Electromagnetic Scattering ◽  
Scattering Problem

scholarly journals Approximate T matrix and optical properties of spheroidal particles to third order with respect to size parameter

2020 ◽  
Author(s):  
MRA Majić ◽  
L Pratley ◽  
D Schebarchov ◽  
Walter Somerville ◽  
Baptiste Auguié ◽  
...  
Keyword(s):  
Cross Sections ◽  
Electromagnetic Scattering ◽  
Taylor Expansion ◽  
Particle Surface ◽  
Size Parameter ◽  
Nonspherical Particle ◽  
Rayleigh Approximation ◽  
Boundary Condition Method ◽  
T Matrix ◽  
American Physical

© 2019 American Physical Society. In electromagnetic scattering, the so-called T matrix encompasses the optical response of a scatterer for any incident excitation and is most commonly defined using the basis of multipolar fields. It can therefore be viewed as a generalization of the concept of polarizability of the scatterer. We calculate here the series expansion of the T matrix for a spheroidal particle in the small-size, long-wavelength limit, up to third lowest order with respect to the size parameter, X, which we will define rigorously for a nonspherical particle. T is calculated from the standard extended boundary condition method with a linear system involving two infinite matrices P and Q, whose matrix elements are integrals on the particle surface. We show that the limiting form of the P and Q matrices, which is different in the special case of spheroid, ensures that this Taylor expansion can be obtained by considering only multipoles of order 3 or less (i.e., dipoles, quadrupoles, and octupoles). This allows us to obtain self-contained expressions for the Taylor expansion of T(X). The lowest order is O(X3) and equivalent to the quasistatic limit or Rayleigh approximation. Expressions to order O(X5) are obtained by Taylor expansion of the integrals in P and Q followed by matrix inversion. We then apply a radiative correction scheme, which makes the resulting expressions valid up to order O(X6). Orientation-averaged extinction, scattering, and absorption cross sections are then derived. All results are compared to the exact T-matrix predictions to confirm the validity of our expressions and assess their range of applicability. For a wavelength of 400 nm, the new approximation remains valid (within 1% error) up to particle dimensions of the order of 100-200 nm depending on the exact parameters (aspect ratio and material). These results provide a relatively simple and computationally friendly alternative to the standard T-matrix method for spheroidal particles smaller than the wavelength, in a size range much larger than for the commonly used Rayleigh approximation.

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