Strong temperature-field discontinuities in a nonlinear medium

The conditions for the appearance of temperature discontinuities in a nonlinear medium with finite relaxation times of the heat flux are analyzed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 46, No. 5, pp. 832–836, May, 1984.     

Solitary stress waves in a nonlinear thermoelastic medium

The propagation process of solitary stress waves in a medium with five thermoelastic characteristics is investigated within the one-dimensional statement. Existence conditions and geometric characteristics of solitary waves are obtained, and restrictions are found for the elastic and thermal constants.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 61, No. 3, pp. 493–498, September, 1991.     

Causality in propagation of a pulse in a nonlinear dispersive medium

We investigate the causal propagation of the pulse through dispersive media by very precise numerical solution of the coupled Maxwell–Bloch equations without any approximations about the strength of the input field. We study full nonlinear behaviour of the pulse propagation through solid state media like ruby and alexandrite. We have demonstrated that the information carried by the discontinuity, i.e. front of the pulse, moves inside the media with velocity c even though the peak of the pulse can travel either with sub-luminal or with super-luminal velocity. Our numerical demonstration is subject to the condition that the background refractive index of the medium is unity. We extend the argument of Levi-Civita to prove that the discontinuity would travel with velocity c even in a nonlinear medium.     

Fock states generation in a kicked cavity with a nonlinear medium

Abstract

We discuss a model of a cavity filled with a passive nonlinear ?Kerr‘ medium and periodically kicked by a series of ultra-short laser pulses. The nonlinear medium is described by the (2q ? 1)th nonlinearity X ^(2q?1). We find analytical formulas describing the field states inside the cavity. We show that such a system can produce, depending on the order of the nonlinearity, superpositions of several Fock states with the small photon numbers (0,1; 0,1,2; etc). In particular, the one-photon state can be approached during the evolution of the system with X ⁽³⁾ nonlinearity provided the cavity losses are negligible. The purity of states generated in this process, however, can be seriously degraded by the cavity damping. We perform numerical calculations to validate our analytical results.     

Propagation of a planar shock thermal wave in a nonlinear medium

Conditions are analyzed for a strong discontinuity of a thermal field in a nonlinear medium, possessing thermal relaxation. The solution of the heattransfer equations is obtained in the region between the mobile boundaries and the front of the strong discontinuity.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 49, No. 3, pp. 436–443, September, 1985.     

Light propagation in a multilayered medium for three-dimensional optical memory

We report on the optimization of film thicknesses in a multilayered medium to increase readout signal intensity. The multilayered medium consists of a stack of photosensitive and transparent films, arranged alternately. The thicknesses of the photosensitive and transparent films in the multilayered medium were optimized for a reflection confocal system to read out data by analyzing the propagation of light focused into a multilayered medium.     

Reciprocity relations for nonlinear plasmalike medium in a magnetic field

We consider nonlinear reciprocity of plasmalike medium in a homogeneous magnetic field, which is described by the Vlasov equation in the relaxation approximation. Reciprocal relations for the tensor of nonlinear conductivity are derived. A method of increasing the accuracy of nonlinear functional electronic devices with the aid of obtained reciprocal relations is proposed.

     

Convective heat transfer for a nonlinear viscoplastic medium in a circular pipe

Heat transfer is considered for a viscoplastic material of nonlinear type flowing with dissipation in a circular tube with developed laminar flow and boundary conditions of the first kind.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 19, No. 5, pp. 850–860, November, 1970.     

Motion of a thermal wave front in a nonlinear medium with absorption

We study the evolution of a thermal perturbation in a nonlinear medium whose thermal conductivity depends on the temperature and the temperature gradient according to a power law.Notation u temperature - k coefficient of thermal conductivity - t time - x spatial variable - x₊ a point on the thermal wave front - a ² generalized coefficient of thermal diffusivity - , , , and s parameters of the process - (x^s) Dirac delta-function - B[, ] a beta function - v(, x), (t) auxiliary functions - A, C, T_o, T_m, T*, R, r, p, and _m constants and parameters Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 728–731, October, 1980.     

Light scattering by a coated infinite cylinder in an absorbing medium

The scattering formulation for a coated infinite cylinder in an absorbing medium is presented in this paper. The cylinder is subjected to an arbitrarily polarized plane wave propagating in a general direction at the cylinder. The refractive index and magnetic permeability of the host medium, as well as those for the core and coating of the cylinder, can be real or complex. The scattering and extinction efficiencies and the scattering amplitudes are derived for both the near field and the far field. As the medium is absorbing, the "true" extinction and scattering efficiencies are derived based on the radiative energy outflow at the surface of the cylinder. The radiative efficiencies in the far field are denoted as "apparent" properties because they include absorption by the intervening medium. The influence of the refractive index and permeability of the host medium on the scattering properties of a coated cylinder is illustrated by numerical examples.     

Exact solutions of the cubic-quintic nonlinear optical transmission equation with higher-order dispersion terms and self-steepening term

By using the subsidiary ordinary differential equation method, many explicit Jacobian elliptic periodic solutions of the cubic-quintic nonlinear optical transmission equation with higher-order dispersion nonlinear terms and self-steepening term are obtained. The results are discussed.     

Methods for solving one-dimensional boundary-value problems in a nonlinear elastic medium

Summary One-dimensional problems connected with a mechanical exposure to the boundary of a nonlinear elastic half-space, which leads to a constantly accelerated motion of this boundary, are considered. The value , equal to the square root of the ratio between the velocity of the boundary motion and the velocity of longitudinal wave propagation in a linear elastic medium, is used as the value characterizing the intensity of this exposure. It is shown that as a result of such an exposure shock waves of small or finite amplitude may propagate in the half-space. The asymptotic matching principle and the ray method are used as methods of solution. The merits and demerits of each method are analyzed. It has been inferred that the matched asymptotic method can be applied to waves of small amplitude, and the ray method is usable when investigating the propagation of shock waves not only of small amplitude, but of finite amplitude as well if the time of a consideration of the shock process is not long. The results obtained by the two methods for shock waves of small amplitude are in close agreement. It has been demonstrated that the ray method is adaptable for solving more intricate boundary-value problems resulting in the propagation of several shock waves of finite amplitude at a time. The problem connected with the constantly accelerated motion of one of the boundaries of an initially deformed elastic layer provides an example.     

Entropy squeezing of a degenerate two-photon process with a nonlinear medium

Abstract

This paper presents new results on some aspects of the properties of the entropy squeezing in the time development of a degenerate two-photon of a single-mode interacting with a two-level system with a nonlinear medium. A general analytic expression for the density matrix is obtained on the basis of a Hamiltonian generalized in that it includes nonlinear effects and Stark shifts, by means of which we identify and numerically demonstrate the region of parameters where significantly large squeezing can be obtained. The influence of various parameters on the entropy squeezing are explored. It is shown that features of the entropy squeezing were influenced significantly by changing the nonlinear medium, Stark shift and the detuning. The results show that, certain amounts of the nonlinear effect yield the superstructure of atomic Rabi oscillation and changes the quasiperiod of the entropy evolution and atomic inversion.     

The fixed point theorem in computing magnetostatic fields in a nonlinear medium

In the paper, a concept of a new method for computing reluctivity distribution in the nonlinear media using Brouwer's fixed point theorem is presented.     

Existence of solitary waves in a nonlinear thermoelastic medium with prior deformations

In a geometrically one-dimensional nonlinear formulation, the existence of solitary waves of deformations in nonlinear thermoelastic previously stressed medium is studied. The speed of propagation of the waves is shown to depend on the initial deformations.Translated from Inzhernerno-fizicheskii Zhurnal, Vol. 61, No. 4, pp. 685–689, October, 1991.     

Unconditional nonlinear stability for convection in a porous medium with vertical throughflow

Summary Linear and nonlinear stability analyses of vertical throughflow in a fluid saturated porous layer, which is modelled using a cubic Forchheimer model, are studied. To ensure unconditional nonlinear results are obtainable, and to avoid the loss of key terms, a weighted functional is used in the energy analysis. The linear instability and nonlinear stability thresholds show considerable agreement when the vertical throughflow is small, although there is substantial deterioration of this agreement as the vertical throughflow increases.     

On a certain wave motion in the spatially nonlocal and nonlinear medium

The aim of this paper is to prove the existence of a finite amplitude circularly polarized plane progressive wave in the complex, nonlocal, nonlinear, homogeneous, transversely isotropic and elastic continuum consisting of two strictly interpenetrating ionic continua (in Tiersten's sense [1]). We show that if the Lennard-Jones 6–12 potential is taken into account, then as the deformation increases (the nonlinear effects), a rise in the square of the frequency occurs because of the repulsive part of the interactions.     

Geometric phase in cavity QED containing a nonlinear optical medium and a quantum well

The geometric phase (GP) in cavity QED filled with a nonlinear medium and containing a quantum well is analyzed. We observe collapses and revivals. The optical nonlinearity leads to high frequency oscillations of the GP. The GP is very sensitive not only to the dissipation rates but also to the amplitude of the laser pump.