Electromagnetic wave scattering by a thin layer in which many small particles are embedded

Asymptotic properties of MUSIC-type imaging in two-dimensional inverse scattering from thin electromagnetic inclusions

The main purpose of this paper is to study the structure of the well-known non-iterative MUltiple SIgnal Classification (MUSIC) algorithm for identifying the shape of extended electromagnetic inclusions of small thickness located in a two-dimensional homogeneous space. We construct a relationship between the MUSIC-type imaging functional for thin inclusions and the Bessel function of integer order of the first kind. Our construction is based on the structure of the left singular vectors of the collected multistatic response matrix whose elements are the measured far-field pattern and the asymp…

Analysis of multi-frequency subspace migration weighted by natural logarithmic function for fast imaging of two-dimensional thin, arc-like electromagnetic inhomogeneities

The present study seeks to investigate mathematical structures of a multi-frequency subspace migration weighted by the natural logarithmic function for imaging of thin electromagnetic inhomogeneities from measured far-field pattern. To this end, we designed the algorithm and calculated the indefinite integration of square of Bessel function of order zero of the first kind multiplied by the natural logarithmic function. This is needed for mathematical analysis of improved algorithm to demonstrate the reason why proposed multi-frequency subspace migration contributes to yielding better imaging p…

Scattering of electromagnetic waves by many thin cylinders

Electromagnetic wave scattering by many parallel infinite cylinders is studied asymptotically as $a\to 0$. Here $a$ is the radius of the cylinders. It is assumed that the points $\hat{x}_m$ are distributed so that $\mathcal{N}(Δ)=\frac{1}{a}\int_ΔN(x)dx[1+o(1)], $ where $\mathcal{N}(Δ)$ is the number of points $\hat{x}_m=(x_{m1},x_{m2})$ in an arbitrary open subset of the plane $xoy$, the axes of the cylinders are passing through points $\hat{x}_m$, these axes are parallel to the z-axis. The function $N(x)\geq 0$ is a given continuous function. An equation for the self-consistent (efficient) f…

Electromagnetic Wave Scattering by Small Impedance Particles of an Arbitrary Shape

Scattering of electromagnetic (EM) waves by one and many small ($ka\ll 1$) impedance particles $D_m$ of an arbitrary shape, embedded in a homogeneous medium, is studied. Analytic formula for the field, scattered by one particle, is derived. The scattered field is of the order $O(a^{2-κ})$, where $κ\in [0,1)$ is a number. This field is much larger than in the Rayleigh-type scattering. An equation is derived for the effective EM field scattered by many small impedance particles distributed in a bounded domain. Novel physical effects in this domain are described and discussed.

Scattering of electromagnetic waves by many nanowires

Electromagnetic wave scattering by many parallel to $z-$axis, thin, impedance, circular infinite cylinders is studied asymptotically as $a\to 0$. Let $D_m$ be the crossection of the $m-$th cylinder, $a$ be its radius, and $\hat{x}_m=(x_{m1},x_{m2})$ be its center, $1\le m \le M$, $M=M(a)$. It is assumed that the points $\hat{x}_m$ are distributed so that $$\mathcal{N}(Δ)=\frac 1{2πa}\int_ΔN(\hat{x})d\hat{x}[1+o(1)], $$ where $\mathcal{N}(Δ)$ is the number of points $\hat{x}_m$ in an arbitrary open subset $Δ$ of the plane $xoy$. The function $N(\hat{x})\geq 0$ is a given continuous function. An…

小物体对电磁波的散射

Electromagnetic wave scattering by small bodies

本文将Maxwell系统约化为一个具有弱奇异核的Fredholm第二类积分方程，求解了电磁波被单个和多个小物体散射的问题。当物体的特征尺寸趋于零时，该方程渐近求解。开发的技术是用于解决多体电磁波散射问题，通过严格减少它来解决线性代数系统，完全绕过积分方程的使用。本文导出了含有许多小粒子的介质中的有效场方程。概述了一种用于创建所需折射系数的方法。

Symmetries of spacetimes embedded with an Electromagnetic String Fluid

The electromagnetic string fluid (EMSF) is an anisotropic charged string fluid interacting with a strong magnetic field. In this fluid we consider the double congruence defined by the 4-velocity of the fluid $u^a$ and the unit vector $n^a$ along the magnetic field. Using the standard 1+3 decomposition defined by the vector $u^a$ and the 1+1+2 decomposition defined by the double congruence ${u^a,n^a}$ we determine the kinematic and the dynamic quantities of an EM string fluid in both decompositions. In order to solve the resulting field equations we consider simplifying assumptions in the form …

Trapped modes and resonances for thin horizontal cylinders in a two-layer fluid

Exact solutions of the linear water-wave problem describing oblique waves over a submerged horizontal cylinder of small (but otherwise fairly arbitrary) cross-section in a two-layer fluid are constructed in the form of convergent series in powers of the small parameter characterizing the "thinness" of the cylinder. The terms of these series are expressed through the solution of the exterior Neumann problem for the Laplace equation describing the flow of unbounded fluid past the cylinder. The solutions obtained describe trapped modes corresponding to discrete eigenvalues of the problem (lying c…