Theoretical development of the image method for a general magnetic source in the presence of a superconducting sphere or a long superconducting cylinder

Lin, Qiong-Gui

doi:10.1103/physrevb.74.024510

Cited by 29 publications

(39 citation statements)

References 27 publications

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“…(39) positions of the image sources are independent of sound frequency and the boundary conditions on the surface of the cylinder. Positions of two image sources, at the center of the cylinder ð0; 0Þ and at the point ða 2 =b; 0Þ, are determined uniquely and coincide with locations of image charges in corresponding electrostatic 26 and magnetostatic 27 problems. A third image source is necessary to ensure second-order accuracy of the asymptotic solutions for hard and impedance cylinders, and the position ðÀa 2 =2b; 0Þ for the third line source was chosen in deriving Eq.…”

Section: Discussionmentioning

confidence: 99%

“…(26) can be evaluated in a closed form by using the exponential form of the cosine function and separating the total sum into the sum of two independent series. Using the power series representation of Àlnð1 À xÞ ¼ P 1 n¼1 x n =n, for jxj < 1, the sum is written as Sða; bÞ ¼ À0:5lnð1 À 2a cos b þ a 2 Þ; 0 < a < 1: (27) Recognizing that …”

Section: Derivation Of the Asymptotic Solutions Of The Scatteredmentioning

confidence: 99%

“…(31) is consistent with the known exact magnetostatic solution. 27 In the fluid mechanics context, the pressure corresponds to the fluid velocity potential of a mass injection source in the presence of an impenetrable circular cylinder. Like in the soft cylinder case, Eq.…”

Section: Derivation Of the Asymptotic Solutions Of The Scatteredmentioning

confidence: 99%

“…Rayleigh scattering by soft, hard, and impedance cylinders is considered with the goal of developing a simple, accurate, and uniformly valid approximation of the exact solution for arbitrary positions of the source and receiver outside of the cylinder. The developed 2-D Green's functions hold everywhere outside of the cylinder, have a similar structure to the static limits in the electrostatic 26 and magnetostatic 27 solutions, and are represented by the sums of "image sources" within the scatterer. The asymptotic Green's functions allow a clear physical interpretation and lead to a computationally efficient approach to solve more complicated problems for the scattering of sound in underwater waveguides.…”

Section: Introductionmentioning

confidence: 99%

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Rayleigh scattering of a cylindrical sound wave by an infinite cylinder

Baynes

Godin

2017

The Journal of the Acoustical Society of America

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Rayleigh scattering, in which the wavelength is large compared to the scattering object, is usually studied assuming plane incident waves. However, full Green's functions are required in a number of problems, e.g., when a scatterer is located close to the ocean surface or the seafloor. This paper considers the Green's function of the two-dimensional problem that corresponds to scattering of a cylindrical wave by an infinite cylinder embedded in a homogeneous fluid. Soft, hard, and impedance cylinders are considered. Exact solutions of the problem involve infinite series of products of Bessel functions. Here, simple, closed-form asymptotic solutions are derived, which are valid for arbitrary source and receiver locations outside the cylinder as long as its diameter is small relative to the wavelength. The scattered wave is given by the sum of fields of three linear image sources. The viability of the image source method was anticipated from known solutions of classical electrostatic problems involving a conducting cylinder. The asymptotic acoustic Green's functions are employed to investigate reception of low-frequency sound by sensors mounted on cylindrical bodies. https://doi

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Section: Discussionmentioning

confidence: 99%

Section: Derivation Of the Asymptotic Solutions Of The Scatteredmentioning

confidence: 99%

Section: Derivation Of the Asymptotic Solutions Of The Scatteredmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Rayleigh scattering of a cylindrical sound wave by an infinite cylinder

Baynes

Godin

2017

The Journal of the Acoustical Society of America

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“…However, for the Meissner state the question has remained open until these last years. Several models using the method of images to calculate superconducting repulsion forces (Lin, 2006;Yang & Zheng, 2007) have been proposed. However, this method of images is limited to a few geometrical configurations that can be solved exactly, and the physical interpretation of the method is under discussion (Giaro et al, 1990;Perez-Diaz & GarciaPrada, 2007).…”

Section: Introductionmentioning

confidence: 99%