Partial synchronization in inhomogeneous autooscillatory media

Investigation of the phenomenon of partial synchronization in a continuous medium with natural frequency detuning depending on a spatial coordinate revealed frequency synchronization cluster formation previously known only in discrete models of distributed systems. The frequency cluster formation and the evolution of the cluster structures depending on the system parameters have been studied.     

Spatial coherence in strongly scattering media

We study the spatial coherence of an optical beam in a strongly scattering medium confined in a slab geometry. Using the radiative transfer equation, we study numerically the behavior of the transverse spatial coherence length in the different transport regimes. Transitions from the ballistic to the diffusive regimes are clearly identified.     

Pulse propagation in finite elastic inhomogeneous media

The transfer matrix of a finite elastic bar is derived and the reflection and transmission functions are obtained. The matrix formalism is combined with Fourier component decomposition and applied to simulate acoustic pulse propagations in elastic inhomogeneous periodic and finite media. The numerical results are compared with experimental data to conclude about the validity of this method.     

Dispersion of elastic waves in periodically inhomogeneous media

Propagation of time-harmonic elastic waves through periodically inhomogeneous media is considered. The material inhomogeneity exists in a single direction along which the elastic waves propagate. Within the period of the linear elastic and isotropic medium, the density and elastic modulus vary either in a continuous or a discontinuous manner. The continuous variations are approximated by staircase functions so that the generic problem at hand is the propagation of elastic waves in a medium whose finite period consists of an arbitrary number of different homogeneous layers. A dynamic elasticity formulation is followed and the exact phase velocity is derived explicitly as a solution in closed form in terms of frequency and layer properties. Numerical examples are then presented for several inhomogeneous structures.     

Propagation of inhomogeneous waves in anisotropic piezo-thermoelastic media

A mathematical model for the propagation of harmonic plane waves in an anisotropic piezo-thermoelastic medium is explained through three relations. Two of them relate the stress-induced harmonic variations in temperature and electric potential to mechanical displacement of material particles. The third is a system that defines modified Christoffel equations for wave propagation in the medium. The solution of this system is ensured by a quartic equation whose complex roots explain the existence and propagation of four attenuating waves in the medium. The effects of piezoelectricity and thermoelasticity on the wave propagation are analyzed in the discussion of special cases. An angle between propagation direction and direction of maximum attenuation defines the attenuated wave as inhomogeneous wave. The complex slowness vector for each of the four attenuated waves in the medium is resolved to calculate the phase velocity and the attenuation factor for its propagation as an inhomogeneous wave along a general direction in three-dimensional space. The variations in phase velocities and attenuation factors with propagation direction are computed, for a realistic numerical model.     

Poisson's and Laplace's equations in inhomogeneous magnetic media

Poisson's equation in inhomogeneous static magnetic media is derived for the magnetic vector potential and for the magnetic scalar potential. A modified three-dimensional seven-point finite-difference operator to be used in numerical solutions is presented. The special case of discrete inhomogeneity as discussed.     

Material symmetries and inhomogeneous waves in piezoelectric media

Summary This study is an experimental investigation on a novel oscillation phenomenon of a water rivulet on a smooth hydrophobic surface. It is found that the water rivulet running down on a smooth Plexiglass plate exhibits all together four distinctive patterns with increasing either the Froude number, the Weber number or the Reynolds number. Once either the Froude number, the Weber number or the Reynolds number exceeds the third critical value, the rivulet on a smooth Plexiglass plate is restabilized, and becomes almost straight. However, in the restable rivulet, several beads of a rosary are formed following immediately downstream of the pipe mouth. This is no more than the novel oscillation phenomenen of the water rivulet on a smooth Plexiglass plate. The oscillatory motion is steady in the hydrodynamical sense, because the phase of the oscillation is always the same at each point in space.It is found that with increasing either the Froude number, the Weber number or the Reynolds number, not only the wave-length and width of the beads in the restable rivulet increase, but also the rivulet itself becomes more straight and stable. On one hand, with increasing distance from the pipe mouth along the central axis of the rivulet, the local maximum width of each of the beads decreases, but its wave-length increases.It is suggested that the oblique surface waves generated at the left and right contact lines of the rivulet play a primary role in the contraction process of the novel oscillation phenomenon of the restable rivulet.     

Transformation equations in polarization optics of inhomogeneous birefringent media

The quaternion formalism has been used to derive new systems of equations that describe transformation of the polarization of light in inhomogeneous birefringent media. In quaternion algebra the problem of parametric representation of the unitary transformation matrix reduces to the problem of formulation of the quaternion in trigonometric form. It is shown that this can be done in 30 different ways and that to each trigonometric form corresponds its own system of transformation equations. The six simplest systems of transformation equations have been derived.     

Propagation of inhomogeneous plane waves in anisotropic viscoelastic media

A new technique is explained to study the propagation of inhomogeneous waves in a general anisotropic medium. The harmonic plane waves are considered in a viscoelastic anisotropic medium. The complex slowness vector is decomposed into propagation vector and attenuation vector for the given directions of propagation and attenuation of waves in an unbounded medium. The attenuation is further separated into the contributions from homogeneous and inhomogeneous waves. A non-dimensional inhomogeneity parameter is defined to represent the deviation of an inhomogeneous wave from its homogeneous version. Such a partition of slowness vector of a plane wave is obtained with the help of an algebraic method for solving a cubic equation and a numerical method for solving a real transcendental equation. Derived specifications enable to study the 3D propagation of inhomogeneous plane waves in a viscoelastic medium of arbitrary anisotropy. The whole procedure is wave-specific and obtains the propagation characteristics for each of the three inhomogeneous waves in the anisotropic medium. Numerical examples analyze the variations in propagation characteristics of each of the three waves with propagation direction and inhomogeneity strength.     

Green dyadic calculations for inhomogeneous optical media

A difference equation obtained for the reassociated Green dyadic formalism is exploited to obtain solutions for the case of a multilayered dielectric medium: Computation of limits as layers become progressively thinner leads to a parallel development for the case of a dielectric varying continuously in a single direction. A demonstration example then shows how discrete and continuous techniques can be combined into a hybrid formulation. Finally, numerical computations are presented for the simple case of a dipole, illustrating convergence of the difference equation solutions to the differential equation solution.     

Stokes-vector evolution in a weakly anisotropic inhomogeneous medium

The equation for evolution of the four-component Stokes vector in weakly anisotropic and smoothly inhomogeneous media is derived on the basis of a quasi-isotropic approximation of the geometrical optics method, which provides the consequent asymptotic solution of Maxwell's equations. Our equation generalizes previous results obtained for the normal propagation of electromagnetic waves in stratified media. It is valid for curvilinear rays with torsion and is capable of describing normal mode conversion in inhomogeneous media. Remarkably, evolution of the four-component Stokes vector is described by the Bargmann-Michel-Telegdi equation for relativistic spin precession, whereas the equation for the three-component Stokes vector resembles the Landau-Lifshitz equation describing spin precession in ferromagnetic systems. The general theory is applied for analysis of polarization evolution in a magnetized plasma. We also emphasize fundamental features of the non-Abelian polarization evolution in anisotropic inhomogeneous media and illustrate them by simple examples.     

Ray analysis for shear transients in inhomogeneous viscoelastic media

Summary Formal ray methods are developed for generating asymptotic wavefront expansions for rotary shear stress transients in inhomogeneous viscoelastic media whose behaviour is governed by integral stress-strain laws expressed in terms of either creep or relaxation functions. General results are obtained for arbitrary creep functions which depend on the radial distance from the axis of a cylindrical hole. Specific solutions are then presented for a creep functionJ(r, t) which is an analogue, for inhomogeneous media, of that first introduced by Jeffreys [1]. As a check on our results we show, how, in various limiting cases, they reduce to known exact and asymptotic results obtained previously by other investigators.This work was carried out while the first author was a recipient of a McCalla Research Professorship.     

Theory of flow in the conductivity problem of inhomogeneous media

Based on flow theory, we provide the basis of the geometric structure of inhomogeneous materials, including phase transitions, and we suggest methods of calculating the conductivity of these systems.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 59, No. 3, pp. 522–539, September, 1990.     

Energy flux characteristics of inhomogeneous waves in anisotropic thermoviscoelastic media

This study aims to calculate the wave-field characteristics of four attenuating waves in anisotropic thermoviscoelastic medium. An energy balance equation relates the complex-valued energy flux vector to the time-averaged densities of kinetic energy, strain energy and dissipated energy of plane harmonic waves in the medium. A complex slowness vector defines the inhomogeneous propagation of an attenuating wave in the medium. This slowness vector is specified with the phase velocity and the two non-dimensional attenuation parameters of the wave. One of the attenuation parameter defines the inhomogeneity strength of the wave as a measure of its deviation from homogeneous propagation. The phase velocity, attenuation parameters, polarizations of particles, propagation direction are combined to define the group velocity, ray direction and quality factor of attenuation of an inhomogeneous wave in the medium. Numerical examples are considered to study the variations of these characteristics of energy flux with propagation direction and inhomogeneity strength for each of the four attenuating waves in the medium. The effects of anisotropic symmetries are analyzed on the velocities of waves. The decay-rate of energy densities is exhibited with offset in the propagation-attenuation plane.     

Conversion of the high-mode solitons in strongly nonlocal nonlinear media

The conversion of high-mode solitons propagating in Strongly Nonlocal Nonlinear Media (SNNM) in three coordinate systems, namely, the elliptic coordinate system, the rectangular coordinate system and the cylindrical coordinate system, based on the Snyder–Mitchell Model that describes the paraxial beam propagating in SNNM, is discussed. Through constituting the trial solution with modulating the Gaussian beam by Ince polynomials, the closed-solution of Gaussian beams in elliptic coordinate is accessed. The Ince–Gaussian (IG) beams constitute the exact and continuous transition modes between Hermite–Gaussian beams and Laguerre–Gaussian (LG) beams, which is controlled by the elliptic parameter. The conditions of conversion in the three types of solitons are given in relation to the Gouy phase invariability in stable propagation. The profiles of the IG breather at a different propagating distance are numerically obtained, and the conversions of a few IG solitons are illustrated. The difference between the IG soliton and the corresponding LG soliton is remarkable from the Poynting vector and phase plots at their profiles along the propagating axis.     

Theory of the flow and conduction of inhomogeneous media

A basic model of an inhomogeneous medium is outlined and, by a combination of the methods of flow theory and reduction to an elementary cell, an analytic dependence is obtained for the conduction of such a medium.     

Structure of inhomogeneous media within the random fractal model

The porosity of inhomogeneous media is treated within the random fractal model. Analytic expressions are obtained for the size distribution curves of bulk mesopores.Translated from Inzhenerno Fizicheskii Zhurnal, Vol. 57, No. 2, pp. 291–298, August, 1989.     

Statistics of inhomogeneous media formed by nucleation and growth

Important statistical properties of inhomogeneous microstructures formed by nucleation and growth are established using line transects. A fundamental time-dependent equation has been derived for the probability of sampling only matrix phase by a random line transect in a system containing growing Poisson-distributed spherical nuclei.It is established that the probability of sampling matrix phase only measures simultaneously the product of two fundamental characteristics of inhomogeneity: the volume fraction of the matrix phase and the probability of existence in the matrix of a free path of specified minimum length. Increasing the number density of the nuclei and decreasing the size of the mean projection of the nuclei on a plane perpendicular to the line transect by the same factor does not change the mean and the variance of the free paths.It is also demonstrated that the distribution of the intercepts from the weaker phase is an important indicator regarding the risk of poor properties. Accordingly, a new approach is suggested for setting MFFOP reliability requirements which minimise the risk from premature fracture.