The Study of Electromagnetic Scattering by a Non-perfectly Conductor in Chiral Media by Potential Theory

This paper is concerned with the electromagnetic scattering by a nonperfectly conductor obstacle in chiral environment.A two-dimensional mathematical model is established.The existence and uniqueness o...     

ANALYSIS OF TWO-DIMENSIONAL ELECTROMAGNETIC SCATTERING BY A PERFECTLY CONDUCTING OBSTACLE IN A HOMOGENEOUS CHIRAL ENVIRONMENT

The time-harmonic electromagnetic plane waves incident on a perfectly conducting obstacle in a homogeneous chiral environment are considered.A two-dimensional direct scat- tering model is established and the existence and uniqueness of solutions to the problem are discussed by an integral equation approach.The inverse scattering problem to find the shape of scatterer with the given far-field data is formulated.Result on the uniqueness of the inverse problem is proved.     

THE C~(1,α) REGULARITY OF SOLUTIONS TO DOUBLE OBSTACLE PROBLEM OF VARIATIONAL INEQUALITY

In this paper, a double obstacle problem of variational inequalities is considered and its solutions is obtained. The results of one-sided obstacle problem are not required in the analysis of our main results, which is different from the previous works.     

LOCAL REGULARITY RESULT FOR SOLUTIONS OF OBSTACLE PROBLEMS

This paper gives the local regularity result for solutions to obstacle problems of A-harmonic equation divA(x, ξu(x)) = 0, |A.(x,ξ)|≈|?|p-1, when 1 < p < n and the obstacle function (?)≥0.     

ON THE HYPERBOLIC OBSTACLE PROBLEM OF FIRST ORDER

InroductlonThe classical obstacle problem canbe formulated as the     

Approximate acoustic cloaking in inhomogeneous isotropic space

We consider the approximate acoustic cloaking in an inhomogeneous isotropic background space.By employing transformation media,together with the use of a sound-soft layer lining right outside the cloaked region,we show that one can achieve the near-invisibility by the"blow-up-a-small-region"construction.This is based on novel scattering estimates corresponding to multiple multi-scale obstacles located in an isotropic space.We develop a novel system of integral equations to decouple the nonlinear scattering interaction among the small obstacle components,the regular obstacle components and the inhomogeneous background medium.     

周期手性结构电磁散射问题的积分方程方法

In this paper, we consider the electromagnetic scattering by a periodic chiral structure. The media is homogeneous and the structure is periodic in one direction and invariant in another direction. The electromagnetic fields inside the chiral medium are governed by Maxwell equations together with the Drude-BornFedorov equations. We simplify the problem to a two-dimensional scattering problem and discuss the existence and the uniqueness of solutions by an integral equation approach. We show that for all but possibly a discrete set of wave numbers, the integral equation has a unique solution.     

ON THE ERROR ESTIMATE OF NONCONFORMING FINITE ELEMENT APPROXIMATION TO THE OBSTACLE PROBLEM

This paper is devoted to analysis of the nonconforming element approximation to the obstacle problem, and improvement and correction of the results in [11], [12].     

COUPLING OF FINITE ELEMENT AND BOUNDARY ELEMENT METHODS FOR THE SCATTERING BY PERIODIC CHIRAL STRUCTURES

Consider a time-harmonic electromagnetic plane wave incident on a biperiodic structure in R^3. The periodic structure separates two homogeneous regions. The medium inside the structure is chiral and nonhomogeneous. In this paper, variational formulations coupling finite element methods in the chiral medium with a method of integral equations on the periodic interfaces are studied. The well-posedness of the continuous and discretized problems is established. Uniform convergence for the coupling variational approximations of the model problem is obtained.     

OBSTACLE PROBLEMS ON RCD(K,N)METRIC MEASURE SPACES

In this paper,we solve the obstacle problems on metric measure spaces with generalized Ricci lower bounds.We show the existence and Lipschitz continuity of the solutions,and then we establish some regularities of the free boundaries.     

Electromagnetic scattering by a homogeneous chiral obstacle in a chiral environment

Time-harmonic electromagnetic waves are scattered by a homogeneouschiral obstacle embedded in a chiral environment. The correspondingtransmission problem is reduced, via Bohren's decomposition,to an integral equation over the interface between the obstacleand the surrounding medium. This integral equation is shownto be uniquely solvable except for a discrete set of electromagneticparameters of the obstacle.     

Electromagnetic scattering by a homogeneous chiral obstacle: scattering relations and the far‐field operator

Time‐harmonic electromagnetic waves are scattered by a homogeneous chiral obstacle. The reciprocity principle, the basic scattering theorem and an optical theorem are proved. These results are used to prove that if the chirality measure of the obstacle is real, then the far‐field operator is normal. Moreover, it is shown that the eigenvalues of the far‐field operator are the same as the eigenvalues of Waterman's T‐matrix. Copyright © 1999 John Wiley & Sons, Ltd.     

手性障碍电磁散射的PML有限元计算

该文建立了手性障碍电磁散射问题的二维模型, 给出问题的有限元分析, 并利用结合PML(perfectly matched layers)技术的有限元法进行数值模拟.     

The Atkinson-Wilcox expansion theorem for electromagnetic chiral waves

Consider the problem of scattering of a time-harmonic electromagnetic wave by a three-dimensional bounded and smooth obstacle. The infinite space outside the obstacle is filled by a homogeneous isotropic chiral medium. In the region exterior to a sphere that includes the scatterer, any solution of the generalized Helmholtz's equation that satisfies the Silver-Müller radiation condition has a uniformly and absolutely convergent expansion in inverse powers of the radial distance from the center of the sphere. The coefficients of the expansion can be determined from the leading coefficient, “the radiation pattern”, by a recurrence relation.     

Scattering relations for point‐source excitation in chiral media

A spherical electromagnetic wave propagating in a chiral medium is scattered by a bounded chiral obstacle which can have any of the usual properties. Reciprocity and general scattering theorems, relating the scattered fields due to scattering of waves from a point source put in any two different locations are established. Applying the general scattering theorem for appropriate locations and polarizations of the point source we prove an associated forward scattering theorem. Mixed scattering relations, relating the scattered fields due to a plane wave and the far‐field patterns due to a spherical wave, are also established. Copyright © 2005 John Wiley & Sons, Ltd.     

Electromagnetic scattering by a perfectly conducting obstacle in a homogeneous chiral environment: solvability and low‐frequency theory

The scattering of plane time‐harmonic electromagnetic waves propagating in a homogeneous isotropic chiral environment by a bounded perfectly conducting obstacle is studied. The unique solvability of the arising exterior boundary value problem is established by a boundary integral method. Integral representations of the total exterior field, as well as of the left and right electric far‐field patterns are derived. A low‐frequency theory for the approximation of the solution to the above problem, and the derivation of the far‐field patterns is also presented. Copyright © 2002 John Wiley & Sons, Ltd.     

Obstacle Numbers of Graphs

An obstacle representation of a graph G is a drawing of G in the plane with straight-line edges, together with a set of polygons (respectively, convex polygons) called obstacles, such that an edge exists in G if and only if it does not intersect an obstacle. The obstacle number (convex obstacle number) of G is the smallest number of obstacles (convex obstacles) in any obstacle representation of G. In this paper, we identify families of graphs with obstacle number 1 and construct graphs with arbitrarily large obstacle number (convex obstacle number). We prove that a graph has an obstacle representation with a single convex k-gon if and only if it is a circular arc graph with clique covering number at most k in which no two arcs cover the host circle. We also prove independently that a graph has an obstacle representation with a single segment obstacle if and only if it is the complement of an interval bigraph.     

On a class of nonlinear obstacle problems with measure data

We study the notion of solution to an obstacle problem for a strongly monotone and Lipschitz operator A, when the forcing term is a bounded Radon measure. We obtain existence and uniqueness results. We study also some properties of the obstacle reactions associated with the solutions of the obstacle problems, obtaining the Lcwy­Stampacchia inequality. Moreover we investigate the interaction between obstacle and data and the complementarity conditions     

Motion of a vibrating string in the presence of a convex obstacle: A free boundary problem

Here we study the motion of a vibrating string in the presence of an arbitrary obstacle. We show that if the string always rebounds on the concave parts of the obstacle, it can either rebound or roll on the convex parts. The latter is the case if the velocity of the string is null at the contact point just before contact, or if the contact point propagates at a characteristic speed. Four examples are given. The three first correspond to the same obstacle, a sinusoidal arc, but with different initial conditions. In the first case, the string rebounds on the whole of the obstacle and the motion is explicitly determined when it is periodic. In the second case, the string rolls on the convex part of the obstacle up to the inflexion point and then rebounds on the concave part and unwinds on the convex part. In the third case, the string is initially at rest on the obstacle; then it instantaneously leaves the concave part while it unwinds progressively on the convex part. The fourth case is similar to the third but with a different obstacle; the motion, which is periodic, is determined explicitly.