[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

The solution of electromagnetic scattering by a homogeneous prolate (or oblate) spheroidal particle with an arbitrary size and refractive index is obtained for any angle of incidence by solving Maxwell's equations under given boundary conditions. The method used is that of separating the vector wave equations in the spheroidal coordinates and expanding them in terms of the spheroidal wavefunctions. The unknown coefficients for the expansion are determined by a system of equations derived from the boundary conditions regarding the continuity of tangential components of the electric and magnetic vectors across the surface of the spheroid. The solutions both in the prolate and oblate spheroidal coordinate systems result in a same form, and the equations for the oblate spheroidal system can be obtained from those for the prolate one by replacing the prolate spheroidal wavefunctions with the oblate ones and vice versa. For an oblique incidence, the polarized incident wave is resolved into two components, the TM mode for which the magnetic vector vibrates perpendicularly to the incident plane and the TE mode for which the electric vector vibrates perpendicularly to this plane. For the incidence along the rotation axis the resultant equations are given in the form similar to the one for a sphere given by the Mie theory. The physical parameters involved are the following five quantities: the size parameter defined by the product of the semifocal distance of the spheroid and the propagation constant of the incident wave, the eccentricity, the refractive index of the spheroid relative to the surrounding medium, the incident angle between the direction of the incident wave and the rotation axis, and the angles that specify the direction of the scattered wave.

Light Scattering by a Spheroidal Particle

The interaction of waves with obstacles is an everyday phenomenon in science and engineering, arising for example in acoustics, electromagnetism, seismology and hydrodynamics. The mathematical theory and technology needed to understand the phenomenon is known as multiple scattering, and this book is the first devoted to the subject. The author covers a variety of techniques, describing first the single-obstacle methods and then extending them to the multiple-obstacle case. A key ingredient in many of these extensions is an appropriate addition theorem: a coherent, thorough exposition of these theorems is given, and computational and numerical issues around them are explored. The application of these methods to different types of problems is also explained; in particular, sound waves, electromagnetic radiation, waves in solids and water waves. A comprehensive bibliography of some 1400 items rounds off the book, which will be an essential reference on the topic for applied mathematicians, physicists and engineers.

Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles

Graphdiyne nanotube (GDNT) arrays were prepared through an anodic aluminum oxide template catalyzed by Cu foil. The as-grown nanotubes have a smooth surface with a wall thickness of about 40 nm; after annealing, the GDNTs are about 15 nm. The morphology-dependent field emission properties of graphdiyne arrays were measured and display high performance field emission properties. The turn-on field and threshold field of GDNTs annealed decreased to 4.20 and 8.83 V/μm, respectively.

Construction of Tubular Molecule Aggregations of Graphdiyne for Highly Efficient Field Emission

This article reviews Multiple Scattering, Interaction of Time-Harmonic Waves with N Obstacles by P. A. Martin , 2006. 450 pp. Price: $140.00 (hardcover). ISBN: 0-521-86554-9

Multiple Scattering, Interaction of Time-Harmonic Waves with N Obstacles

In this work the scattering from an eccentrically coated infinite metallic cylinder is considered. The problem is solved using classical separation of variables techniques combined with translational addition theorems. For small eccentricities κd, where d is the distance between the two axes and κ the wave number of the dielectric coating, exact closed‐form expressions of the form S(d)=S(0)[1+g′(κd)+g″(κd)2+O(κd)3] are obtained for the scattered field and the various scattering cross sections of the problem. Both polarizations are considered for normal incidence. Numerical and graphical results for various values of the parameters are also discussed.

Electromagnetic scattering from an eccentrically coated infinite metallic cylinder

We have calculated the electric field around and on the surface of an open thick-wall carbon nanotube (CNT) of height h, external radius R, and wall thickness w. To accomplish that we simulate the CNT as a vertical array of touching toroids, each of external radius R and cross section radius w/2, and then we express the problem in toroidal coordinates. From our calculations we obtain the enhancement factor γ as a function of h, R, and w. By fitting to our numerical results we obtain an empirical but simple formula for γ, which extrapolates to that of a closed CNT in the limiting case of w=R.

Enhancement factor of open thick-wall carbon nanotubes

Power series expansions for the even and odd angular Mathieu functions Se m (h, cos θ) and So m (h, cosθ), with small argument h, are derived for general integer values of m. The expansion coefficients that we evaluate are also useful for the calculation of the corresponding radial functions of any kind.

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Power series expansions for Mathieu functions with small arguments

The scattering of a plane acoustic wave from an impenetrable, soft or hard, prolate or oblate spheroid is considered. Two different methods are used for the evaluation. In the first, the pressure field is expressed in terms of spheroidal wave functions. In the second, a shape perturbation method, the field is expressed in terms of spherical wave functions only, while the equation of the spheroidal boundary is given in spherical coordinates. Analytical expressions are obtained for the scattered pressure field and the various scattering cross-sections, when the solution is specialized to small values of the eccentricity h = d/(2a) , where d is the interfocal distance of the spheroid and 2a is the length of its rotation axis. In this case, exact, closed-form expressions are obtained for the expansion coefficients g
 (2) and g
 (4) in the relation S(h) = S(0)[1 + g
 (2)
 h
 2 + g
 (4)
 h
 4 + O(h
 6)] expressing the scattered field and the scattering cross-sections. Numerical results are given for various values of the parameters.

Acoustic scattering by an impenetrable spheroid

The scattering of a plane electromagnetic wave by a perfectly conducting prolate or oblate spheroid is considered analytically by a shape perturbation method. The electromagnetic field is expressed in terms of spherical eigenvectors only, while the equation of the spheroidal boundary is given in spherical coordinates. There is no need for using any spheroidal eigenvectors in our solution. Analytical expressions are obtained for the scattered field and the scattering cross-sections, when the solution is specialized to small values of the eccentricity h = d/(2a), (h 1), where d is the interfocal distance of the spheroid and 2a the length of its rotation axis. In this case exact, closed-form expressions, valid for each small h, are obtained for the expansion coefficients g(2) and g(4) in the relation S(h) = S(0)[1 + g(2)h2 + g(4)h4 + O(h6)] expressing the scattering cross-sections. Numerical results are given for various values of the parameters.

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John A. Roumeliotis

Papers

Electromagnetic scattering from an eccentrically coated infinite metallic cylinder

Enhancement factor of open thick-wall carbon nanotubes

Power series expansions for Mathieu functions with small arguments

Acoustic scattering by an impenetrable spheroid

Electromagnetic Scattering by a Metallic Spheroid Using Shape Perturbation Method