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.     

Flow and conduction of inhomogeneous media. II. Variation of the basic model of an inhomogeneous medium

On the basis of a basic model of an inhomogeneous medium, different variations are proposed. Analytical dependences are obtained for the conduction of the in homogeneous medium and the results of calculation and experiment are compared.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 46, No. 2, pp. 247–252, February, 1982.     

A boundary element method for the solution of a class of heat conduction problems for inhomogeneous media

A boundary element method is derived for solving the two-dimensional heat equation for an inhomogeneous body subject to suitably prescribed temperature and/or heat flux on the boundary of the solution domain. Numerical results for a specific test problem is given.     

Instability of a homogeneous plastic flow and strain localization in structurally inhomogeneous media

Changes in the internal structure of a deformed medium are described, in addition to the defect densities, by the kinetic variables (order parameters) related to the collective modes of the macroscopic plastic deformation. The kinetic equations for two order parameters represent a system of nonlinear equations of the reaction-diffusion type. It is demonstrated that instability of a homogeneous solution with respect to inhomogeneous perturbations appears when the characteristic variation lengths of the order parameters markedly differ from each other.     

Heat conduction in a series of inhomogeneous slabs

A general theory is worked out for boundary-value problems of steady-state, two-dimensional heat conduction in a series of inhomogeneous media. Specific examples are discussed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vo. 28, No. 6, pp. 1088–1093, June, 1975.     

Some heat conduction problems in an inhomogeneous body

Solutions are obtained for the heat conduction equation in the case when the thermal conductivity is a homogeneous function of the coordinates.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Theory of fluidized-bed electrical conduction

Mechanisms for the passage of electric current through a fluidized bed are discussed, and corresponding estimates for the effective electrical conductivity are given.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 11, pp. 889–900, November, 1978.     

Heat conduction equation for systems with an inhomogeneous internal structure

Based on the two-temperature model, a heat conduction equation for inhomogeneous systems is suggested. The conditions under which this equation is reduced to a classical transfer equation of the parabolic type or a local-nonequilibrium transfer equation of the hyperbolic type are discussed. The parameters characterizing heat transfer in an inhomogeneous medium are discussed from a physical viewpoint.Institute of Chemical Physics, Russian Academy of Sciences, Chernogolovka. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 4, pp. 492–496, April, 1994.     

An extended method of time-dependent fundamental solutions for inhomogeneous heat conduction

In this paper, the method of time-dependent fundamental solutions is extended to solving transient heat conduction problems in inhomogeneous media. The solution of the problem under investigation is split into two parts, namely the particular and homogenous solutions. The novelty of the proposed approach lies in that an approximation of the particular solution is derived by using the fundamental solutions of the associated eigenvalue equations. Numerical results for one- and two-dimensional geometries are presented to verify the efficacy of the proposed method. The effects of the numbers of source and collocation points, the eigenvalues and the parameter T on the accuracy of the numerical solution are also investigated.