Canonical Problems in Scattering and Potential Theory Part 1

Vinogradov, S. S.; Smith, P.D.; Vinogradova, E. D.

doi:10.1201/9780849387074

Cited by 45 publications

(47 citation statements)

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“…The ISLAE are solved by the truncation method and numerical matrix inversion. Due to the limit of space, readers are referred to [12,13] for more detailed description of the MoR. The two ISLAE obtained have the following matrix form:…”

Section: Appendix a The Methods Of Regularization -From Ill-posed Duamentioning

confidence: 99%

A Comparison of the Performance of Cylindrical Lens Reflectors and Stepped-Indexed Cylindrical Luneburg Lens Reflectors: Simpler Is Better?

Lock¹,

Vynogradov²

2012

PIER B

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Abstract-This paper studies the characteristics of a constant-K lens when considered as a possible substitute for a Luneburg lens in a reflector. The competitiveness of the substitute lens is investigated in its 2D analogue, by comparing the backscattering radar cross section for the range of D/λ ∈ (0, 200). The performance of cylindrical reflectors with either a constant-K lens or a cylindrical Luneburg lens (approximated by a finite number of stepped-index dielectric layers) when illuminated by an electromagnetic plane wave is studied using the semi-analytic Method of Regularization. Because of similar underlying physical principles, these studies provide an insight into the 3D analogue. The radar cross section calculations of the two reflectors for incidence angles varying from normal to grazing incidence show that the cheaper-to-manufacture constant-K lens reflector is able to provide a more powerful and stable backscattering performance than the cylindrical Luneburg lens reflector, for electrical sizes in the range considered.

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Section: Appendix a The Methods Of Regularization -From Ill-posed Duamentioning

confidence: 99%

A Comparison of the Performance of Cylindrical Lens Reflectors and Stepped-Indexed Cylindrical Luneburg Lens Reflectors: Simpler Is Better?

Lock¹,

Vynogradov²

2012

PIER B

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“…Theoretical derivations in this Letter are extended from discussions on the capacitance between axially slotted open circular cylinders in free space. 14 Figure 1 shows the configuration of the problem. The capacitor consists of two infinitely long curved patches that are symmetric with respect to the x axis.…”

Section: -11mentioning

confidence: 99%

Analytical solution for capacitance calculation of a curved patch capacitor that conforms to the curvature of a homogeneous cylindrical dielectric rod

Chen

Bowler

2014

Applied Physics Letters

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This Letter presents an analytical expression for the capacitance of a curved patch capacitor whose electrodes conform to the curvature of a long, homogeneous, cylindrical dielectric rod. The capacitor is composed of two infinitely long curved electrodes, symmetrically placed about a diameter of the cylinder cross-section. The resulting capacitance per unit length depends on both the dielectric properties of the material under test and the capacitor configuration. A practical capacitance measurement is also presented, with appropriately guarded finite electrodes. Very good agreement between measured and theoretically predicted capacitances were observed, to within 2.4 percent. The analytical result presented in this Letter can be applied for extremely rapid evaluation of rod permittivity from measured capacitance.

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“…Our algorithm is based on the method of analytical regularization; details of this method applied to scattering problems for canonical structures are presented in [13,14].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Our algorithm we developed to address this issue is based on method of analytical regularization (MAR). This method has previously been applied successfully in [13,14] to the integral equations associated with potential and wave scattering problems involving single conductors of the canonical shape (with circular, elliptic or rectangular cross-section). The main idea of MAR is in transforming Fredholm integral equations of the first kind into the well-conditioned and fast converging Fredholm equations of the second kind in a matrix formulation.…”

Section: Introductionmentioning

confidence: 99%

Rigorous Approach to Calculation of Capacitance Images of Metallic Samples for Use in Capacitance Microscopy

Safonova¹,

Vinogradova²

2013

PIER B

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Abstract-A high-efficiency rigorous approach for the solution of the two-dimensional Laplace equation with Dirichlet's boundary conditions is developed to tackle electrostatic problems involving metallic cylinders of arbitrarily cross-sections. In this paper, we demonstrate how this novel algorithm can be used to address the problems arising in the capacitance microscopy to provide a higher resolution in studies of micro-cavities and whiskers on the surface of metallic samples. The precise capacitance images of the probe/sample systems are presented.

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Canonical Problems in Scattering and Potential Theory Part 1

Cited by 45 publications

References 0 publications

A Comparison of the Performance of Cylindrical Lens Reflectors and Stepped-Indexed Cylindrical Luneburg Lens Reflectors: Simpler Is Better?

A Comparison of the Performance of Cylindrical Lens Reflectors and Stepped-Indexed Cylindrical Luneburg Lens Reflectors: Simpler Is Better?

Analytical solution for capacitance calculation of a curved patch capacitor that conforms to the curvature of a homogeneous cylindrical dielectric rod

Rigorous Approach to Calculation of Capacitance Images of Metallic Samples for Use in Capacitance Microscopy

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