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1.
Electromagnetic scattering by a smooth convex impedance cone 总被引:1,自引:0,他引:1
The problem of the diffraction of an electromagnetic planewave by a convex cone of arbitrary smooth cross-section withimpedance (Leontovich) boundary conditions is studied. The vectorproblem is reduced to that for the Debye potentials. By meansof KontorovichLebedev integrals, two spectral functionsare introduced and the corresponding boundary value problemis formulated. The spectral functions for the potentials arefound to satisfy the Helmholtz equations on the unit sphereand to be coupled through non-traditional boundary conditionsof the impedance type with shifts on the spectral variable.The use of the Green theorem permits us to establish an integralformulation of the boundary value problem for the spectral functions.The formal asymptotic solution of the problem is then givenfor the case of a narrow cone. For this, two different methodsare given: a method of perturbation applied to the spectralintegral equations and an adaptation of the method of matchingthe asymptotic series in spectral domain. Both methods leadto the same closed-form result for the leading term of the scatteringdiagram asymptotics. 相似文献
2.
Semyon B. Yakubovich 《Journal of Approximation Theory》2004,131(2):175
We establish analogs of the Hausdorff–Young and Riesz–Kolmogorov inequalities and the norm estimates for the Kontorovich–Lebedev transformation and the corresponding convolution. These classical inequalities are related to the norms of the Fourier convolution and the Hilbert transform in Lp spaces, 1p∞. Boundedness properties of the Kontorovich–Lebedev transform and its convolution operator are investigated. In certain cases the least values of the norm constants are evaluated. Finally, it is conjectured that the norm of the Kontorovich–Lebedev operator is equal to . It confirms, for instance, by the known Plancherel-type theorem for this transform when p=2. 相似文献
3.
The three-dimensional problem of a thin rigid elliptic inclusion in the middle of a composite elastic wedge is investigated. The wedge consists of three connected wedge-shaped layers connected by a sliding clamp, in which the layer containing the inclusion is incompressible. The outer faces of the composite wedge are also under sliding-clamp conditions. The inclusion is completely bonded to the elastic medium in the contact region. Using Fourier and Kontorovich–Lebedev transformations, a system of integral equations of the problems are derived for the shear contact stresses. A regular asymptotic method is used to solve this system. Calculations are carried out. The results can be used for calculations on the strength of rubber-metal articles and structures having a corner line. 相似文献
4.
Christopher Svedberg 《Annales Henri Poincare》2011,12(5):849-917
Ringstr?m managed (in Invent Math 173(1):123–208, 2008) to prove future stability of solutions to Einstein’s field equations when matter consists of a scalar field with a potential
creating an accelerated expansion. This was done for a quite wide class of spatially homogeneous space–times. The methods
he used should be applicable also when other kinds of matter fields are added to the stress-energy tensor. This article addresses
the question whether we can obtain stability results similar to those Ringstr?m obtained if we add an electromagnetic field
to the matter content. Before this question can be addressed, more general properties concerning Einstein’s field equation
coupled to a scalar field and an electromagnetic field have to be settled. The most important of these questions are the existence
of a maximal globally hyperbolic development and the Cauchy stability of solutions to the initial value problem. 相似文献
5.
In this paper we consider second order scalar elliptic boundary value problems posed over three–dimensional domains and their
discretization by means of mixed Raviart–Thomas finite elements [18]. This leads to saddle point problems featuring a discrete
flux vector field as additional unknown. Following Ewing and Wang [26], the proposed solution procedure is based on splitting
the flux into divergence free components and a remainder. It leads to a variational problem involving solenoidal Raviart–Thomas
vector fields. A fast iterative solution method for this problem is presented. It exploits the representation of divergence
free vector fields as s of the –conforming finite element functions introduced by Nédélec [43]. We show that a nodal multilevel splitting of these finite
element spaces gives rise to an optimal preconditioner for the solenoidal variational problem: Duality techniques in quotient
spaces and modern algebraic multigrid theory [50, 10, 31] are the main tools for the proof.
Received November 4, 1996 / Revised version received February 2, 1998 相似文献
6.
The diffraction of a plane electromagnetic wave obliquely incident upon the edge of a coated wedge is considered. The generalized
impedance boundary conditions (GIBC's) on the wedge's faces are used to simulate the effect of the coatings. To insure the well-posedness of the problem, special
contact conditions (CC's) on the edge are additionally imposed. By using Sommerfeld integrals, the problem is reduced to a system of coupled functional
equations, which is solved by the perturbation method. It is shown that, for a certain range of the angles of oblique incidence,
the solution can be represented in the form of convergent series that are Neumann series for linear equations with contracting
operators. Nonuniform asymptotics of the wave field for regions outside a neighborhood of the edge of the wedge are constructed.
Bibliography: 9 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 218, 1994, pp. 72–95.
Translated by L. G. Vardapetyan and M. A. Lyalinov. 相似文献
7.
P. Malits 《Acta Appl Math》2007,98(2):135-152
This paper deals with a new class of Fredholm integral equations of the first kind associated with Hankel transforms of integer
order. Analysis of the equations is based on operators transforming Bessel functions of the first kind into kernels of Weber–Orr
integral transforms. Their inverse operators are established by means of new inversion theorems for the Hankel and Weber–Orr
integral transforms of functions belonging to L
1 and L
2. These operators together with the proven Paley–Wiener’s theorem for the Weber–Orr transform enable to regularize the equations
and, in special cases, to derive explicit solutions. The integral equations analyzed in this paper can be employed instead
of dual integral equations usually treated with the Cooke–Lebedev method. An example manifests that it may be preferable because
of the possibility to control norms of operators in the regularized equations.
相似文献
8.
V. R. Khalilov 《Theoretical and Mathematical Physics》1999,119(1):481-492
In the problem of a two-dimensional hydrogen-like atom in a magnetic field background, we construct quasi-classical solutions
and the energy spectrum of the Dirac equation in a strong Coulomb field and in a weak constant homogeneous magnetic field
in 2+1 dimensions. We find some “exact” solutions of the Dirac and Pauli equations describing the “spinless” fermions in strong
Coulomb fields and in homogeneous magnetic fields in 2+1 dimensions.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 1, pp. 105–118, April, 1999. 相似文献
9.
N. V. Mokeeva 《Journal of Mathematical Sciences》2007,142(6):2597-2604
The problem of diffraction of a plane wave by a transparent wedge is considered (the wave numbers inside the wedge and outside
it are different). Absorption in a medium is assumed to occur. The existence of a solution satisfying the limiting absorption
principle is proved. The existence theorem and the fact that the limit passage can be performed are proved for the corresponding
system of equations. Bibliography: 3 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 332, 2006, pp. 138–148. 相似文献
10.
S. E. Stepanov 《Theoretical and Mathematical Physics》1997,111(1):419-427
Based on the classical problem for decomposition of the tensor product of representations into irreducible components, which
is considered in the elementary representation theory for orthogonal groups, a partial classification of the Einstein equations
is carried out. A new class of Maxwell equations for relativistic electrodynamics is singled out and studied. Pointwise-irreducible
decompositions for the energy-momentum and electromagnetic field tensors are obtained and a physical interpretation of the
decomposition components is given.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 1, pp. 32–43, April, 1997. 相似文献
11.
We consider a problem of wedging of an elastic wedge by a rigid plate along an edge crack that is located on the axis of symmetry
of the wedge and reaches its vertex. The detachment of the crack faces from the surfaces of the plate is taken into account.
Using the Wiener–Hopf method, we obtain an analytic solution of the problem. The size of the detachment zone, the stress intensity
factor, the distribution of stresses on the line of continuation of the crack and in the contact domain, and circular displacements
of the crack faces are determined. 相似文献
12.
V. A. Solonnikov 《Journal of Mathematical Sciences》2011,176(3):475-504
We analyze the simplest free boundary problem of magnetohydrodynamics governing the evolution of an isolated mass of a viscous
incompressible liquid in the presence of the magnetic field. The motion of the liquid is governed by the Navier–Stokes equations,
and for the magnetic field we have the Maxwell equations with an excluded displacement current. The magnetic field should
be determined not only in the domain filled with the liquid, but also in the surrounding vacuum region. On the free boundary
of the liquid standard jump conditions for the magnetic field are prescribed, as well as kinematic and dynamic boundary conditions,
where the magnetic stress tensor is taken into account. We prove that the solution corresponding to a rigid rotation of the
fluid and to zero magnetic field is stable if the functional of potential energy has a positive second variation. Bibliography:
11 titles. 相似文献
13.
In the paper it is proved that the problem of scattering of the plane wave by a transparent wedge has a unique solution, provided
that the radiation condition should be meant in the following form: if one subtracts from the solution the incident wave and
all reflected and refracted waves, then the remainder satisfies the radiation condition in integral form. The problem is scalar,
the velocities of the wave inside and outside the wedge are not equal, the wave process is described by the classical Helmholtz
equations, and the conjugation boundary condition is satisfied on the sides of the wedge. Bibliography: 8 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 354, 2008, pp. 5–18. 相似文献
14.
Belkacem Said-Houari 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2011,110(1):115-133
This work is concerned with a system of nonlinear viscoelastic wave equations with nonlinear damping and source terms acting
in both equations. We will prove that the energy associated to the system is unbounded. In fact, it will be proved that the
energy will grow up as an exponential function as time goes to infinity, provided that the initial data are large enough.
The key ingredient in the proof is a method used in Vitillaro (Arch Ration Mech Anal 149:155–182, 1999) and developed in Said-Houari
(Diff Integr Equ 23(1–2):79–92, 2010) for a system of wave equations, with necessary modification imposed by the nature of
our problem. 相似文献
15.
Robert M. Yamaleev 《Advances in Applied Clifford Algebras》2006,16(2):167-190
In Refs. [2]–[7] we suggested generalized dynamic equations of motion of relativistic charged particles inside electromagnetic
fields. The dynamic equations had been formulated in terms of external as well as internal momenta. Evolution equations for
external momenta, the Lorentz-force equations, had been derived from evolution equations for internal momenta. In this paper,
along with relativistic dynamics we generalize electromagnetic fields within the scope of ternary algebras. The full theory
is constructed in 4D euclidean space. This space possesses an advantage to build ternary mappings from three vectors onto
one. The dynamics is given by non-linear evolution equations with cubic characteristic polynomial. In polar representation
the internal momenta obey the Jacobi equations whereas external momenta obey the Weierstrass equations for elliptic functions.
The generalized electromagnetic fields are defined by the triple fields where the first one has properties of the electric
field and the other two have properties of the magnetic field. The field equations for the triple fields analogous to the
Maxwell equations are suggested. 相似文献
16.
The paper investigates model reduction techniques that are based on a nonlocal quasi-continuum-like approach. These techniques
reduce a large optimization problem to either a system of nonlinear equations or another optimization problem that are expressed
in a smaller number of degrees of freedom. The reduction is based on the observation that many of the components of the solution
of the original optimization problem are well approximated by certain interpolation operators with respect to a restricted
set of representative components. Under certain assumptions, the “optimize and interpolate” and the “interpolate and optimize”
approaches result in a regular nonlinear equation and an optimization problem whose solutions are close to the solution of
the original problem, respectively. The validity of these assumptions is investigated by using examples from potential-based
and electronic structure-based calculations in Materials Science models. A methodology is presented for using quasi-continuum-like
model reduction for real-space DFT computations in the absence of periodic boundary conditions. The methodology is illustrated
using a basic Thomas–Fermi–Dirac case study. 相似文献
17.
The geometric form of a conjecture associated with the names of Loewner and Carathéodory states that near an isolated umbilic
in a smooth surface in ℝ3, the principal line fields must have index ≤ 1. Real solutions of the differential equation ∂ 2/z ω = g, where the complex
function g is given only up to multiplication by a positive function, are intimately related to umbilics. We determine necessary
and sufficient conditions of an integral nature for real solvability of this equation, which is really a system of two wave
equations. We then construct germs of line fields of every index j ∈ 1/2 ℤ on S2 that cannot be realized as the Gauss image of the principal line fields near an isolated umbilic of positive curvature on
any smooth surface in ℝ3. These include the standard dipole line field of index two and controlled distortions of it. 相似文献
18.
A. S. Kosmodamianskii D. Bardzokas M. L. Fil'shtinskii 《Journal of Mathematical Sciences》1998,92(5):4164-4169
We study the two-dimensional electroelastic problem for an unbounded compound plate with an arbitrary hole located in both
components of the plate. The corresponding boundary-value problem is reduced to a system of singular integral equations of
second kind, which for the case of an elliptic hole can be solved numerically by the method of quadratures. We give the data
of computations that characterize the concentration of the electroelastic fields near the hole subject to action at infinity
by fields of mechanical stresses and electric tension. It is noted that in the case of the inverse piezoelectric effect the
influence of inhomogeneities of the plate on the stress concentrations is sharply expressed.
Six figures. Bibliography: 7 titles.
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 67–75. 相似文献
19.
O. V. Baburova V. Ch. Zhukovsky B. N. Frolov 《Theoretical and Mathematical Physics》2008,157(1):1420-1432
Based on the requirement that the gauge invariance principle for the Poincaré-Weyl group be satisfied for the space-time manifold,
we construct a model of space-time with the geometric structure of a Weyl-Cartan space. We show that three types of fields
must then be introduced as the gauge (“compensating”) fields: Lorentz, translational, and dilatational. Tetrad coefficients
then become functions of these gauge fields. We propose a geometric interpretation of the Dirac scalar field. We obtain general
equations for the gauge fields, whose sources can be the energy-momentum tensor, the total momentum, and the total dilatation
current of an external field. We consider the example of a direct coupling of the gauge field to the orbital momentum of the
spinor field. We propose a gravitational field Lagrangian with gauge-invariant transformations of the Poincaré-Weyl group.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 1, pp. 64–78, October, 2008. 相似文献
20.
An infinite row of periodically spaced, identical rigid circularcylinders is excited by an acoustic line source which is parallelto the generators of the cylinders. A method for calculatingthe scattered field accurately and efficiently is presented.When the cylinders are sufficiently close together, Rayleigh–Blochsurface waves that propagate energy to infinity along the arrayare excited. An expression is derived which enables the amplitudesof these surface waves to be computed without requiring thesolution to the full scattering problem. 相似文献