Solution of the H-plane problem of radiation from a two-dimensional horn with a complex piecewise linear contour

Conclusions The method presented here is highly algorithmic and permits computerizing the calculation of the characteristics of two-dimensional H-phane horns with piecewise linear contours within a broad range of geometrical parameters. The resultant program can be used for analyzing and selecting the optimal geometry of specific radiative assemblies.The data derived in the analysis of the radiation and matching characteristics of thickwalled sectorial horns and of box horns will be useful in the design of antenna assemblies.Zaporozhe Mechanical Engineering Institute. Translated from Izvestiya Vysshikh Uchebnikh Zavedenii, Radiofizika, Vol. 33, No. 5, pp. 604–610, May, 1990.     

On the general structure of nonlinear equations integrable by the general linear spectral problem

Two beams of indistinguishable fermions from independent sources cannot produce an interference pattern that changes when the wavefunction of each single-fermion state for one beam is multiplied by — 1; they cannot produce interference the way photons from independent sources can. This means the changes in neutron interference caused by a magnetic field applied to one of the beams cannot be interpreted as equivalent to changes that could be made by rotating the source of one beam by 2π radians. If it is assumed that rotation by 2π radians cannot be observed, the argument made here becomes a simple proof that particles with half-integral spin cannot be bosons.     

Phase-space solution of the linear mode-conversion problem

The problem of linear mode conversion in a weakly inhomogeneous medium is posed and solved by phase-space methods. The PDEs for the two coupled modes are transformed to a simple first-order ordinary differential equation by a canonical transformation, wherein the two dispersion functions become essentially a locally conjugate pair of coordinates.     

A contribution to the linear magnetoresistance problem

It is shown that semi-classical transport theory provides an extremely accurate prediction of the limiting high field transverse magnetoresistivities of the compensated metals Cd, Pb and W. These results invalidate those theoretical models based on scattering effects which have been proposed to explain the linear term in the magnetoresistivities of K, Al and In. We argue that the only remaining viable models are those based on the effects of sample imperfections and inhomogeneities.     

无限长均匀带电直线组电场分布的复势解法

给出无限长均匀带电直线的复势,接着讨论平行直线排列与平行环形排列两种情况下,无限长均匀带电直线组的复势与电场,并由此得出相应的电场线与等势线方程.     

On extending the trace as a linear functional

A method is given for extending the trace from the trace class to a more general class of Hilbert-Schmidt operators, depending on a fixed projection. Of course no new positive operators are introduced, but the new class is significantly larger than the trace class (provided both the kernel and range of the fixed projection have infinite dimension), and has interesting properties.     

On linear electromagnetic constitutive laws that define almost‐complex structures

It is shown that not all linear electromagnetic constitutive laws will define almost‐complex structures on the bundle of 2‐forms on the spacetime manifold when composed with the Poincaré duality isomorphism, but only a restricted class of them that includes linear spatially isotropic and some bi‐isotropic constitutive laws. Although this result does not trivialize the formulation of the basic equations of pre‐metric electromagnetism, it does affect their reduction to metric electromagnetism by its effect on the types of media that are reducible, and possibly its effect on the way that such media support the propagation of electromagnetic waves.     

Well-posedness of the time-varying linear electro-magnetic initial-boundary value problem

The well-posedness of the initial-boundary value problem of the time-varying linear electromagnetic field in a multi-medium region is investigated. Function spaces are defined, with Faraday's law of electromagnetic induction and the initial-boundary conditions considered as constraints. Gauss's formula applied to a multi-medium region is used to derive the energy-estimating inequality. After converting the initial-boundary conditions into homogeneous ones and analysing the characteristics of an operator introduced according to the total current law, the existence, uniqueness and stability of the weak solution to the initial-boundary value problem of the time-varying linear electromagnetic field are proved.     

A linear problem in diffusion in a region with a mobile boundary

The speed V(t) of the boundary is an arbitrary, continuous, and bounded function of time t. A mathematical model is derived, and a general method of solution based on thermal potentials is given. The particular case of V constant is considered. The solution is obtained as a sum of thermal potentials with unknown densities, which is reduced to a system of integral equations, which are solved by operational methods. The expression for the density of the potentials is obtained in a form suitable for further use.I am indebted to Professor G. M. Bartenev for direction and to Professor V. I. Levin and Dr. I. V. Razumovskaya for discussions of the results.     

Cooperative influence of H2 and C2H4 molecules on theb-a anda-X transitions in the O2 molecule in a ternary complex

Moments of the b-a and a-X transitions induced in an oxygen molecule by collision in the O₂ + C₂H₄ + H₂ complex are calculated by the semiempirical MINDO/3 method with allowance for the spin-orbital interaction. On the basis of two collisional models it is shown that the cooperative influence of C₂H₄ and H₂ molecules can be both enhancing and weakening as compared with their individual influence. Here, the relative location of the oxygen molecule and its surroundings plays an important role. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 4, pp. 453–456, July–August, 2000.     

On the two-component Benard problem a numerical solution

A numerical solution for the two-component Bénard problem is presented, taking into account the contribution of thermal diffusion to the total density gradient. The results are compared with the approximate solution obtained by the variational technique of the local potential introduced some years ago by Glansdorff and Prigogine. The results calculated by the two methods are in agreement when the Soret coefficient is not too large. But when the gradients become important, the exact numerical solution presented here shows a small divergence from the variational method.The critical Rayleigh number is also compared with the one extrapolated from the analytical solution obtained for free boundary conditions.     

On the linear relaxation of a one-dimensional bonded fluid model

The linear relaxation of a one-dimensional bonded fluid model is studied in the dynamical mean field approximation at the pair level. The results are compared with simulation data. Relaxation at low temperatures shows a cooperative character that can be understood in terms of a simple diffusion picture.     

On mode shapes of a stability problem

This paper presents data of mode shapes of some stable and unstable modes of a free-free beam under direction controlled thrusts. These mode shapes are pertinent in understanding this basic problem and hitherto were not available in the literature. It has been found that the node number of the mode shape corresponding to the first divergence mode increases with the magnitude of the thrust. The main feature of the solution method is given. The instability of a free-free beam under a thrust fixed in direction is pointed out.     

On the lyman problem

This paper attempts to answer Lyman's question (1990) on the non-uniqueness in defining the 3D measure of the boundary vorticity-creation rate. Firstly, a straightforward analysis of the vorticity equation introduces a definition of a general vorticity flux-density tensor and its ‘effective’ part. The approach is strictly based on classical field theory and is independent of the constitutive structure of continuous medium. Secondly, the fundamental question posed by Lyman dealing with the ambiguity of the 3D measure of the boundary vorticity-creation rate for incompressible flow is discussed. It is shown that the original 3D measure (for an incompressible Newtonian fluid defined by Panton 1984), which is reminiscent of an analogy to Fourier's law, is in its character ‘effective’ and plays a crucial role in the prognostic vorticity transport equation. The alternative 3D measure proposed by Lyman includes, on the other hand, a ‘non-effective’ part, which plays a role in the local determination of the ‘effective’ measure as well as in a certain diagnostic integral boundary condition.