Boundary integral equation for electromagnetic wave scattering by a homogeneous body of arbitrary shape
A. G. Ramm
推导了三维任意形状均匀体对电磁波散射问题的边界积分方程。
Boundary integral equation is derived for the problem of scattering of electromagnetic waves by 3D homogeneous body of arbitrary shape.
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We present a new method for the analysis of electromagnetic scattering from homogeneous penetrable bodies. Our approach is based on a reformulation of the governing Maxwell equations in terms of two uncoupled vector Helmholtz systems: one for the electric feld and one for the magnetic field. This permits the derivation of resonance-free Fredholm equations of the second kind that are stable at all frequencies, insensitive to the genus of the scatterers, and invertible for all passive materials including those with negative permittivities or permeabilities. We refer to these as decoupled field i…
The classification of exact solutions of Maxwell vacuum equations for the case when the electromagnetic fields and metrics of homogeneous spaces are invariant with respect to the motion group G(VII) is completed. All non-equivalent exact solutions of Maxwell vacuum equations for electromagnetic fields and spaces with such symmetry have been obtained. The vectors of the canonical frame of a homogeneous space of type VII according to the Bianchi classification, and the electromagnetic field potentials have been found.
A new proof is given of the existence of the solution to electromagnetic (EM) wave scattering problem for an impedance body of an arbitrary shape. The proof is based on the elliptic systems theory and elliptic estimates for the solutions of such systems.
Maxwell's vacuum equations are integrated for admissible electromagnetic fields in homogeneous spaces. Admissible electromagnetic fields are those for which the space group generates an algebra of symmetry operators ( integrals of motion ) that is isomorphic to the algebra of group operators. Two frames associated with the group of motions are used to obtain systems of ordinary differential equations to which Maxwell's equations reduce. The solutions are obtained in quadratures. The potentials of the admissible electromagnetic fields and the metrics of the spaces contained in the obtained solu…
We prove for generalisations of quasi-homogeneous $n$-body problems with center of mass zero and $n$-body problems in spaces of negative constant Gaussian curvature that if the masses and rotation are fixed, there exists, for every order of the masses, at most one equivalence class of relative equilibria for which the point masses lie on a circle, as well as that there exists, for every order of the masses, at most one equivalence class of relative equilibria for which all but one of the point masses lie on a circle and rotate around the remaining point mass. The method of proof is a generalis…
Canonical equivalence of a charge in a time dependent, spatially-homogeneous electromagnetic field to a time-dependent perturbed oscillator
本文证明了静态或时变空间均匀电磁场中的粒子系统在规范和酉上等价于受微扰的谐振子，通过复合变换可积分初始问题，并指出其本征态表现为谐振子的纠缠态。
Classical and quantum dynamics for 2D-electromagnetic potentials asymptotically homogeneous of degree zero
考虑在电磁势作用下沿平面运动的带电粒子，其径向极限不为零。我们分析的经典和量子动力学的情况下，大的时间（限制）洛伦兹力（定义为纯径向的速度）的角度部分有一个有限数量的零在固定的能量。任何这样的零点都定义了一个通道，我们将量子波算符与“稳定”的通道联系起来。研究了它们在磁通量为零和非零情况下的完备性。在后一种情况下，人们可能需要纳入一个螺旋状态的通道。这些状态类似于最近在\cite {CHS}中研究的符号确定的情况。
Homogeneous attractive Bose-Einstein condensates with repulsive three-body interactions: the one-dimensional case
该研究针对受吸引两体与排斥三体相互作用的均匀一维玻色气体，借助中间哈特利理论推导平均场极限对应的非线性薛定谔泛函，分析排斥三体项对基态能量估计及质量聚集特性的影响。
Homogeneous attractive Bose-Einstein condensates with repulsive three-body interactions: the two-dimensional case
研究由N个全同玻色子组成的、兼具吸引两体与排斥三体相互作用的均匀二维玻色气体，借助哈特利理论推导其平均场极限对应的非线性薛定谔泛函，聚焦系统与两体相互作用的行为。
The electromagnetic self-force on a charged spherical body slowly undergoing a small, temporary displacement from a position of rest
经典电动力学在半径为R的带电“刚性”体上的自作用力对于经历缓慢（即，速度v<c），轻微（即，与R相比较小），以及从初始静止位置的暂时位移。这些结果与玻尔-罗森菲尔德关于电磁场可测性的分析有关，这是最近一个有争议的问题。
In this paper we discuss global existence of the solution of the Maxwell and Newton system of equations, describing the interaction of a rigid charge distribution with the electromagnetic field it generates. A unique solution is proved to exist (for regular charge distributions) on suitable homogeneous and non-homogeneous Sobolev spaces, for the electromagnetic field, and on coordinate and velocity space for the charge; provided initial data belong to the subspace that satisfies the divergence part of Maxwell's equations.
Multi-frequency topological derivative for approximate shape acquisition of curve-like thin electromagnetic inhomogeneities
在本文中，我们研究了一种非迭代成像算法的基础上的拓扑导数，以恢复可穿透的电磁夹杂物的形状时，他们的介电常数和/或磁导率不同于嵌入（均匀）空间。主要目标是裂纹状薄夹杂物的成像，但该算法可以应用于任意形状的夹杂物。为此，我们应用多个时间谐波频率，并通过其最大值归一化拓扑导数成像函数。为了验证其有效性，我们将其应用于成像的二维裂纹状薄电磁不均匀性完全隐藏在均匀的材料。相应的数值模拟与噪声数据进行显示所提出的算法的有效性。
Existence of a Unique Local Solution to the Many-body Maxwell-Schrödinger Initial Value Problem
研究带电粒子与自生电磁场相互作用的多体问题。我们通过多体麦克斯韦-薛定谔系统来模拟粒子的动力学，其中粒子被量子力学处理，电磁场是经典量。我们证明了存在一个唯一的本地时间解决这个非线性初值问题，使用压缩映射参数。
Minimizing configurations and Hamilton-Jacobi equations of homogeneous N-body problems
对于具有齐次位势的$N$ -体问题，在齐次弱KAM解的研究中，我们定义了一类特殊的中心构型，这类构型与同素约化有关.对于具有$α\in (0,2)$的$1/r^α$中的位势，我们证明了齐次弱KAM解的存在性.我们证明了这种解与另一个Hamilton-Jacobi方程在正常位形球中的黏性解有关。作为应用，我们证明了牛顿三体问题的临界Hamilton-Jacobi方程不存在光滑齐次解。
The problem of classification of exact solutions of Maxwell's vacuum equations for admissible electromagnetic fields and homogeneous space-time with the group of motions $G_3(VIII)$ according to the Bianchi classification is considered. All non-equivalent solutions are found. The classification problem for remaining groups of motions $G_3(N)$ has already been solved in the other papers. That is why all non-equivalent solutions of empty Maxwell equations for all homogeneous spaces with admissible electromagnetic fields are known now.
Two body problem on two point homogeneous spaces, invariant differential operators and the mass center concept
从不变微分算子理论的角度考虑了两点齐型空间上具有中心相互作用的两体问题。找到了两粒子哈密顿量在对称群上的径向微分算子和不变算子的表示，研究了这些空间的不同质心定义与所得到的哈密顿算子表示的关系。
Recovery of small electromagnetic inhomogeneities from boundary measurements in time-dependent Maxwell's equations
我们考虑的时间相关的麦克斯韦方程组的反问题，确定的位置和某些性质的小电磁不均匀性在均匀的背景介质从动态测量的切向分量的磁场的边界（或边界的一部分）的域。
The classification of exact solutions of Maxwell vacuum equations for the case when the electromagnetic fields and metrics of homogeneous spaces are invariant with respect to the motion group $G_3(IX)$ is done. All appropriate non-equivalent exact solutions of Maxwell vacuum equations are found.
Electromagnetic diffraction on a moving half-plane
研究了均匀各向同性介质中运动半平面上电磁波的绕射问题。它示出，与静止的情况下，入射和反射波的阴影边界是不平行于这些波的传播方向。其他衍射现象报告较早的对象与移动的边缘，也观察到这里。
Full Poincare-invariant equation of motion for an extended charged particle in an electromagnetic field
对于任意电磁场中扩展电荷的刚性非旋转运动，通过对作用在电荷上的4-洛伦兹力=外力4+自身力4的洛仑兹不变式计算，导出了其运动方程。运动方程在任何完整的庞加莱变换下都是不变的。这是一个微分积分方程的粒子的4-中心在闵可夫斯基空间作为一个函数的适当的时间。在给定初始条件和外电磁场且迭代过程收敛的情况下，运动方程的二重真时积分形式适于迭代求解。各种近似的自我力，也与运动方程，推导出来。近似的运动方程求解了两个例子：（1）在均匀电场中的直线双曲运动。(2)均匀磁场中的螺旋（非相对论）运动。在这两种情况下，结果都非常简单。讨论了该运动方程相对于其他运动方程（如Lorentz-Dirac方程）的优越性。关键词：运动方程，扩展带电粒子，自作用力，有效惯性质量。
Electromagnetic wave scattering by many small particles
将电磁波与任意形状的小粒子散射问题严格地归结为求解线性代数方程组，而不需要求解积分方程。该线性代数系统的矩阵元具有物理意义。它们用电和磁极化率张量来表示。分析公式给出计算这些张量与任何所需的精度为均匀体的任意形状。提出了一种通过在给定区域内嵌入许多小颗粒来制造"智能"材料的想法。
Radiative correction in approximate treatments of electromagnetic scattering by point and body scatterers
过渡矩阵（$T$ -matrix）方法提供了一种通用的形式体系来研究物理学各个领域中的散射问题，包括声学（标量场）和电磁学（矢量场），并且与量子力学和量子场论中使用的散射矩阵（$S$ -matrix）理论有关。专注于电磁散射，我们突出了另一种配方的$T$ -矩阵的方法，基于使用的电抗矩阵或$K$ -矩阵，这是更适合于正式研究的能量守恒约束（如光学定理）。我们特别表明，静电或准静态近似可以在此框架内进行校正，以满足与辐射相关的能量守恒约束。一个这样的辐射校正的一般公式，明确获得，并在早期的研究中提出的经验表达式被证明是这个一般公式的特殊情况。因此，这项工作提供了一个理由的经验辐射校正的偶极极化率和概括的任何类型的点或体散射体的任意形状，包括更高的多极阶。
Local Density Approximation and Other Limit Regimes for a Homogeneous Bose Gas with Repulsive Three-Body Interactions in Low-Dimensional Space
针对低维空间中含两体吸引、三体排斥的均匀玻色气体，研究其能量泛函极小化子的存在性，推导类托马斯-费米有效模型并分析其他极限 regime。
Solution of the equations of electromagnetic self-consistency in a plasma
本文在非相对论近似下，对均匀二分量等离子体的电磁自洽方程组进行了解析求解。
On a quaternionic Maxwell equation for the time-dependent electromagnetic field in a chiral medium
将均匀手征媒质中含时电磁场的麦克斯韦方程组化为一个四元数方程。得到了满足因果原理的基本解，从而可以求解含时手征麦克斯韦系统。
Electromagnetic wave scattering by many small particles and creating materials with a desired permeability
研究了均匀介质中多个小粒子（体）对电磁波的散射问题。粒子的物理性质由它们的边界阻抗来描述。在极限$a\to 0$中，得到了极限介质中有效电磁场的极限方程，其中$a$是粒子的特征尺寸，粒子数$M(a)$以适当的速率趋于无穷大.所提出的理论允许一个创建一个不均匀的渗透性的介质。主要的新物理结果是限制介质渗透率$μ(x)$的显式解析公式。当初始介质具有恒定的磁导率$μ_0$时，由于嵌入了许多具有预定边界阻抗的小颗粒而获得的限制介质具有非均匀的磁导率，该非均匀的磁导率根据小颗粒的分布密度和它们的边界阻抗来解析地表示。
On the Essential Spectrum of N-Body Systems with Asymptotically Homogeneous of Order Zero Interactions
我们概述了我们最近的一些结果的本质谱的N体哈密顿与功能定义的潜在的径向极限在无穷远。这些结果推广了描述一般N体哈密顿量本质谱的HVZ定理。证明是基于一个认真研究代数所产生的潜在的和他们的交叉产品。我们还描述了这些代数的谱上的拓扑，从而将A.马杰拉我们的技术适用于更一般的类的潜在的平移不变代数的有界一致连续的函数在有限维向量空间。
Recovery of small electromagnetic inhomogeneities from boundary measurements on part of the boundary
研究利用部分边界测量数据，通过求解最小化问题构造背景解作为权重，基于平均化方法识别小介电不均匀性的位置和性质。
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