Анализ фокусировки волн в усеченной линзе Гутмана

The problem of scattering of a plane electromagnetic wave by a truncated axisymmetric Gutman lens including calculation of the field inside the lens is considered. The problem is solved numerically using the hybrid projection method developed earlier for the general case of wave scattering by inhomogeneous bodies of revolution. New results are presented that demonstrate the accuracy of the method, as well as the field distribution in the Gutman lens, which characterize the features of wave focusing depending on the lens size, focal length, and position of the truncation plane.

The exterior gravitational potential of toroids

ABSTRACT We perform a bivariate Taylor expansion of the axisymmetric Green function in order to determine the exterior potential of a static thin toroidal shell having a circular section, as given by the Laplace equation. This expansion, performed at the centre of the section, consists in an infinite series in the powers of the minor-to-major radius ratio e of the shell. It is appropriate for a solid, homogeneous torus, as well as for inhomogeneous bodies (the case of a core stratification is considered). We show that the leading term is identical to the potential of a loop having the same main radius and the same mass – this ‘similarity’ is shown to hold in the ${\cal O}(e^2)$ order. The series converges very well, especially close to the surface of the toroid where the average relative precision is ∼10−3 for e = 0.1 at order zero, and as low as a few 10−6 at second order. The Laplace equation is satisfied exactly in every order, so no extra density is induced by truncation. The gravitational acceleration, important in dynamical studies, is reproduced with the same accuracy. The technique also applies to the magnetic potential and field generated by azimuthal currents as met in terrestrial and astrophysical plasmas.

The Method of Separation of Variables in the Problem of Theory of Elasticity for Radially Inhomogeneous Cylinder

The article deals with the numerical-analytical method of solving problems in the theory of elasticity of inhomogeneous bodies in terms of displacements for a circular cylinder. We consider two-and three-dimensional problems. After separation of variables, the problem is reduced to the numerical solution of the system of differential equations of the first order.

Integrodifferential Equations of the Vector Problem of Electromagnetic Wave Diffraction by a System of Nonintersecting Screens and Inhomogeneous Bodies

The vector problem of electromagnetic wave diffraction by a system of bodies and infinitely thin screens is considered in a quasi-classical formulation. The solution is sought in the classical sense but is defined not in the entire spaceR3but rather everywhere except for the screen edges. The original boundary value problem for Maxwell’s equations system is reduced to a system of integrodifferential equations in the regions occupied by the bodies and on the screen surfaces. The integrodifferential operator is treated as a pseudodifferential operator in Sobolev spaces and is shown to be zero-index Fredholm operator.