Casimir stress in an inhomogeneous medium

The Casimir effect in an inhomogeneous dielectric is investigated using Lifshitz’s theory of electromagnetic vacuum energy. A permittivity function that depends continuously on one Cartesian coordinate is chosen, bounded on each side by homogeneous dielectrics. The result for the Casimir stress is infinite everywhere inside the inhomogeneous region, a divergence that does not occur for piece-wise homogeneous dielectrics with planar boundaries. A Casimir force per unit volume can be extracted from the infinite stress but it diverges on the boundaries between the inhomogeneous medium and the homogeneous dielectrics. An alternative regularization of the vacuum stress is considered that removes the contribution of the inhomogeneity over small distances, where macroscopic electromagnetism is invalid. The alternative regularization yields a finite Casimir stress inside the inhomogeneous region, but the stress and force per unit volume diverge on the boundaries with the homogeneous dielectrics. The case of inhomogeneous dielectrics with planar boundaries thus falls outside the current understanding of the Casimir effect.     

Dislocations in an inhomogeneous anisotropic medium

The general expressions for the stress field of a dislocation situated near a welded, slipping and free boundary are derived employing the method of Fourier transformations. As an example the stress field of a screw dislocation near a simple type of welded boundary is explicitly given.     

Buildup of an electron-photon avalanche in a layered medium with a random-distributed density

This is a study concerning the buildup of an electron—photon avalanche in a medium with a random-distributed density. The formulas derived here describe the avalanche characteristics, averaged over fluctuations of the medium, in terms of the corresponding avalanche characteristics for a medium with a deterministically distributed density. Numerical results are shown pertaining to an avalance in the atmosphere.     

Migration of particles in an inhomogeneous medium

The migration of particles in a one-dimensional inhomogeneous crystalline structure is considered. Some general properties of the migration process are found. Exact results are obtained for structures with linear and periodic inhomogeneity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 13–17, July, 1980.     

非均匀可激介质中的螺旋波

以Barkley模型为对象,研究了可激介质的非均匀性对螺旋波斑图形成的影响.该模型中各参数与可激介质的属性密切相关,通过参数涨落的正态分布来刻画非均匀性,数值研究了单参数以及多参数涨落的正态分布情形下螺旋波斑图的形成.研究表明,可激介质的非均匀性对于螺旋波波纹的粗细及疏密程度有较大影响.参数涨落分布的方差越大,形成的螺旋波波纹越粗糙.对于两参数均匀分布的极端情形,当参数分布大于某一范围,无法形成螺旋波.这些都与螺旋波旋转的角频率密切相关.螺旋波旋转的角频率越大,螺旋波波纹越粗,同时波纹越密集;反之,螺旋波 关键词： 螺旋波 非均匀介质 Barkley模型     

Eigenwaves in an inhomogeneous azimuthally bigyrotropic medium

The problem of natural electromagnetic waves in an azimuthally magnetized bigyrotropic medium which is inhomogeneous in the radial direction is solved analytically. A system of generalized wave equations is obtained in the longitudinal components of the electrical and magnetic fields. Particular solutions of the system are represented in the form of generalized power series. The series exponents are determined and recursion formulas are built up for calculating their coefficients. The passage to particular cases of a homogeneous gyrotropic and inhomogeneous isotropic medium is realized, and the results are compared with known data from the literature.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 46–49, November, 1982.     

Evolution of polarization in an inhomogeneous isotropic medium

The depolarization and rotation of the polarization plane of radiation propagating in a two-dimensional graded-index medium is investigated on the basis of the quantum-mechanical method of coherent states. It is shown that the degree of polarization of both linearly and circularly polarized radiation decreases with increasing distance as a result of interaction between the polarization (spin) and the path (orbital angular momentum) of the beam. The wave nature of the depolarization is emphasized. The depolarization decreases as the radiation wavelength decreases. It is found that the degree of polarization exhibits oscillations of pure diffraction origin during the propagation of light in a single-mode optical fiber. It is shown that the rotation of the polarization plane is nonuniform in character and depends on the offset and the tilt angle of the incident-beam axis relative to the fiber axis. The Berry phase is found to undergo oscillations of a wave nature during the propagation of radiation in an inhomogeneous medium. It is shown that the spread in the angle of rotation of the polarization plane increases with distance and can be determined from measurements of the degree of polarization of the radiation. Zh. éksp. Teor. Fiz. 112, 1985–2000 (December 1997)     

Nonlinear resonant two-wave interaction in an inhomogeneous medium

A one-dimensional steady-state nonlinear resonant two-wave interaction in a lossless periodically inhomogeneous medium is investigated. It is shown that the amplitudes and the phases of the waves vary in a stochastic manner.     

Parton energy loss in an inhomogeneous color medium

The contribution of stochastic inhomogeneities to the parton collisional loss in a color medium is considered.     

An inhomogeneous dielectric as an anisotropic medium

These dielectrics are widely used at cm and mm wavelengths, and it is shown for fiberglass materials that these can behave as homogeneous anisotropic materials described by a dielectric-constant tensor {}, whose components are calculated. The calculations are tested against experiment.     

Helmholtz integral in the acoustics of an inhomogeneous medium

Integral relations that generalize the Helmholtz integral for an inhomogeneous medium with arbitrary gradients of its density and the sound velocity in it are obtained. Expressions that determine the Helmholtz integral for problems related to the diffraction and radiation of sound in an inhomogeneous medium are derived. It is shown that, in the case of an inhomogeneous medium, an additional factor depending on the density distribution in the medium appears in the integrand.