A note on disturbances in a semi-infinite piezoelectric medium coated with a perfectly conducting thin film

Summary The paper makes use of the constitutive equations of a piezoelectric material and the tool of Laplace transform to investigate the disturbances in a semi-infinite piezoelectric medium coated with a perfectly conducting thin film.     

The plastic indentation of a semi-infinite solid by a perfectly rough circular punch

Zusammenfassung In dieser Arbeit werden das plastische Spannungsfeld und ein zulässiges Geschwindigkeitsfeld für den eben begrenzten Halbraum gegeben, der unter dem Einfluss eines ideal rauhen, starren Stempels mit kreisförmigem Querschnitt steht. Das Material ist als starr-plastisch vorausgesetzt, ohne Verfestigung, und der Fliessbedingung vonTresca genügend. Es wird gezeigt, dass die Hypothese vonHaar undvon Kármán auf dieses Problem anwendbar ist, wonach zwei von den drei Hauptspannungen gleich sind. Es wird auch eine gültige Fortsetzung des plastischen Spannungsfeldes ins starre Gebiet in der Nähe des Stempels erhalten.     

Magnetohydrodynamic flow in a rectangular duct with perfectly conducting electrodes

Zusammenfassung Grenzschichtverfahren werden benutzt, um das Problem der magnetohydrodynamischen Strömung einer leitenden Flüssigkeit durch einen unendlichen rechteckigen Kanal bei grosser Hartmannzahl zu lösen für den Fall, dass die Wände, die parallel zum angelegten Magnetfeld sind, perfekt leiten, während die anderen beiden Wände Isolatoren sind. Das Problem ist als Integralgleichung für die Stromdichte an der Elektrode formuliert. Diese Gleichung besitzt als Lösung eine einfache, geschlossene Form.

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Part of this work was done in partial fulfillment of the degree of Doctor of Philosophy at the University of Minnesota.     

The scattering of electromagnetic waves by a perfectly conducting infinite cylinder

We consider the scattering of a plane time-harmonic electromagnetic wave by a perfectly conducting infinite cylinder with axis in the direction k , where k is the unit vector along the z axis. Suppose the incident wave propagates in a direction perpendicular to the cylinder. For a given observation angle θ, let F_D(θ, α) k be the far-field pattern of the electric field corresponding to an incident wave with direction angle α polarized perpendicular to the axis and let F_N(θ; α) k be the far-field pattern of the magnetic field corresponding to an incident wave with direction angle α polarized parallel to the z axis. Let {α_n}_n=1^∞ be a distinct set of angles in [ ? π, π] and μ a complex number. Then, necessary and sufficient conditions are given for the set {(1 ? μ)F_D(θ;α_n) + μF_N(θ;α_n)}_{n = 1}^∞ to be complete in L²[ ? π, π]. Applications, together with numerical examples, are given to the inverse scattering problem of determining the shape of the cylinder from a knowledge of the far-field data.     

An investigation of acceleration waves in a perfectly conducting magnetohydrodynamic fluid

This paper discusses the propagation of discontinuities in a perfectly conducting magnetohydrodynamic fluid, the model having been proposed by P. H. Roberts [1] in the context of neutron stars. P. H. Roberts [1] obtained a stability criterion which was subsequently reproduced by B. Straughan [3] using a discontinuity analysis but in the process the resulting sixth order secular equation decomposed into a product of quadratic and quartic polynomial factors. The first section of this paper investigates the reason for this factorization and the latter sections examine the nature of the equations governing the behaviour of the discontinuity amplitudes. The presence of the magnetic field effectively makes the fluid non-isotropic and so the determination of amplitude equations is non standard although they finally prove to be of Bernoulli type.     

均匀手性介质中理想导体光栅的电磁散射

§1Introduction Phenomenaofopticalactivityinspecialmaterialshavebeenknownsincethe beginningoflastcentury.Thoughopticalactivityhasbeenconsideredinopticsandin quantummechanicsformanyyears,itsanalysiswithintheframeworkofclassical electromagneticfieldtheoryarosemuchlater.Recently,therehasbeenaconsiderable interestinthestudyofscatteringanddiffractionbychiralmedium.Ingeneral,the electromagneticfieldsinsidethechiralmediumaregovernedbyMaxwellequations togetherwithDrude-Born-Fedorovequationsinwhichth…     

An inverse electromagnetic scattering problem for a bi-periodic inhomogeneous layer on a perfectly conducting plate

This article is concerned with uniqueness for reconstructing a periodic inhomogeneous medium sitting on a perfectly conducting plate. We deal with the problem in the framework of time-harmonic Maxwell systems without TE or TM polarization. An orthogonal relation is obtained for two refractive indices and then used to prove that the refractive index can be uniquely identified from a knowledge of the incident fields and the total tangential electric field on a plane above the inhomogeneous medium, utilizing the eigenvalues and eigenfunctions of a quasi-periodic Sturm–Liouville eigenvalue problem.     

On estimates for the Green's function for a multipoint boundary problem

We obtain new estimates for the Green's function G(t, s) for a boundary problem of the Vallée-Poussin type: under certain hypotheses we prove the existence of non-negative functions g(t), h(t), u(t) such that g(t) h(s)¦G(t, s)¦g(t) and ¦G(t, s)¦u(t) ¦G(, s)¦, where h(t) and u(t) are positive on sets of positive measure. These estimates allow us to apply effectively the methods of the theory of cones to investigate non-linear boundary problems.Translated from Matematicheskie Zametki, Vol. 4, No. 5, pp. 533–540, November, 1968.The author profoundly thanks M. A. Krasnosel'skii and A. Yu. Levin for their valuable advice and interest in this work.     

On the convergence of a smoothed penalty algorithm for semi-infinite programming

For semi-infinite programming (SIP), we consider a class of smoothed penalty functions, which approximate the exact $l_\rho (0<\rho \le 1)$ penalty functions. On base of the smoothed penalty function, we present a feasible penalty algorithm for solving SIP. Without any boundedness condition or coercive condition, we establish the global convergence theorem. Then we present a perturbation theorem for this algorithm and obtain a necessary and sufficient condition for the convergence to the optimal value of SIP. Under Mangasarian–Fromovitz constrained qualification condition, we further discuss the convergence properties for the algorithm based upon a subclass of smooth approximations to the exact $l_\rho $ penalty function. Finally, numerical results are given.     

On Green's function for the Helmholtz equation in a wedge

It is found that, in the spherical coordinate system, the fundamental solution of the Helmholtz equation in a wedge satisfies the Sommerfeld radiation conditions at infinity uniformly in angle coordinates.Deceased.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 9, pp. 1312–1314, September, 1993.     

Pointwise estimates for Green's kernel of a mixed boundary value problem to the Stokes system in a polyhedral cone

The paper deals with a mixed boundary value problem for the Stokes system in a polyhedral cone. Here different boundary conditions (in particular, Dirichlet, Neumann, free surface conditions) are prescribed on the sides of the polyhedron. The authors obtain regularity results for weak solutions in weighted L ₂ Sobolev spaces and prove point estimates of Green's matrix. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the steady propagation of a semi-infinite crack

We consider the rectilinear propagation of a semi-infinite crack with constant velocity in a crystal structure. We obtain the solutions of homogeneous boundary-value problems for the corresponding difference-differential operators in spaces of one and two dimensions. We give a justification of the computational aspect of the problem. Bibliography: 8 titles.Translated fromProblemy Matematicheskogo Analiza, No. 12, 1992, pp. 127–153.     

On singularity confinement for the pentagram map

The pentagram map, introduced by R. Schwartz, is a birational map on the configuration space of polygons in the projective plane. We study the singularities of the iterates of the pentagram map. We show that a “typical” singularity disappears after a finite number of iterations, a confinement phenomenon first discovered by Schwartz. We provide a method to bypass such a singular patch by directly constructing the first subsequent iterate that is well-defined on the singular locus under consideration. The key ingredient of this construction is the notion of a decorated (twisted) polygon, and the extension of the pentagram map to the corresponding decorated configuration space.     

Robust and high-order effective boundary conditions for perfectly conducting scatterers coated by a thin dielectric layer

A new approach is considered to construct effective boundaryconditions for the solution of problems related to the scatteringof electromagnetic waves by perfectly conducting cylinders coatedby a thin dielectric shell. These boundary conditions aim tobe both robust and of high order while remaining set in termsof surface differential operators involving at most second-orderderivatives. Error estimates yield a theoretical basis for theuse of these boundary conditions in practical computations.Some numerical experiments at frequencies beyond the range ofvalidity of the usual impedance boundary conditions validatethe efficiency of the approach.     

On a generalization of perfectly normal spaces

The notion of quasi-perfect normality which generalizes the notion of usual perfect normality is introduced and the behavior of the dimension functions in this class of spaces is investigated.     

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.