A variational numerical solution of the one‐dimensional wave propagation problem for an inhomogeneous medium

Abstract

Some basic properties of driving point impedance function Z(s) representing a new class of five‐element‐kind RLC‐FDNR networks are derived based on Tellegen's theorem. Any function which possesses these properties is then called a PR2 function (second order positive real function).

The realizability conditions for a PR2 function to be realizable as RLC‐FDNR networks have been described and given in theorems. Analytic tests of PR2 functions with examples using computer aids have been discussed. Furthermore, a modified Brune cycle has been proved successful for realizing this kind of networks. We have solved many typical examples using computer aids and concluded with a conjecture that any PR2 function is realizable with finite Brune cycles.     

Nonlinear grain–grain forces and the width of the solitary wave in granular chains: a numerical study

Any impulse results in the formation of a solitary wave of time averaged width $W$ in a granular chain. If the grain–grain interaction potential $V\sim \delta ^n$ , where $\delta $ is the distance by which the grains approach each other, then it is well established that $n\ge 2$ . Here we present dynamical simulation based results which suggest that $W-1\propto (n-2)^{-\alpha }$ where $\alpha =0.3283$ or $\approx $ 1/3. While in qualitative agreement, the result is quantitatively different from the formula for $W$ proposed earlier by Nesterenko.     

Computation of the Green’s function for the transverse vibration of a composite circular membrane

A new analytical method is suggested for the approximate computation of the time-dependent Green’s function for the equations of the transverse vibration of a composite circular membrane with piecewise constant varying density and tension. The method is based on the derivation of eigenvalues and eigenfunctions for an ordinary differential equation with piecewise constant coefficients and an approximate computation of the Green’s function in the form of the Fourier series with a finite number of terms relative to the orthogonal set of the derived eigenfunctions. A computational experiment confirms the robustness of the method.     

Simulation of the motion and destruction of bolides in the Earth’s atmosphere

Issues of high-temperature interaction of bolides with the Earth’s atmosphere are considered. As an example, the motion and destruction of the Chelyabinsk (Chebarkul) meteorite are studied. The calculation results are compared with data of observations.     

Lamb wave propagation in the functionally graded piezoelectric–piezomagnetic material plate

The propagation behaviour of Lamb waves in the functionally graded piezoelectric–piezomagnetic material plate with material parameters varying continuously along the thickness direction is investigated in this paper. The power series technique is employed to solve these variable coefficient ordinary differential equations. Dispersion equations are given for different boundary conditions. In numerical examples, the influence of the variation of each parameter on dispersion curves and cut-off frequency in electrically and magnetically open cases is discussed in detail. Results show that the elastic parameters and density varying along the thickness direction obviously influence the variation of phase velocity. Some variations in electric and magnetic parameters also affect the phase velocity but the influence is too small, while others almost cannot affect the dispersion curves. Cut-off frequency is closely related to two elastic parameters and to density, whereas other parameters almost cannot influence it. All the results can provide theoretical guidance not only for the analysis and design of a magnetoelectric transducer using functionally graded materials, but also for ultrasonic nondestructive evaluation.     

Use of the Bohm’s formula and its analogues in probe diagnostics

Simple algorithms are developed to proceed the probe characteristics in a number of limiting regimes when the characteristic probe size, r _p, is relatively large (r _p > 10³rD). It relates both to steady plasmas and to movement with the directed velocity, u. We consider the cases of collision-free (the Knudsen number, Kn?1) and collisional (Kn?1) plasmas. The majority of the proposed algorithms are tested in practice and confirm their reliability.     

Definition of diagonal Poisson’s ratio and elastic modulus for infill masonry walls

The prediction of the response of infilled frames through the simplified approach of substituting the infill with an equivalent pin-jointed strut is treated. In this framework the results of an experimental study for the mechanical characterization of different types of masonry infills having the aim of estimating strength, Young modulus and Poisson’s ratio are presented. Four types of masonry were investigated and subjected to ordinary compressive tests orthogonally to the mortar beds and along the directions of the mortar beds. The experimental campaign confirmed the possibility of using an orthotropic plate model for prediction of the Poisson’s ratio and Young modulus along the diagonal direction of infills (these parameters are requested by a model already known in the literature for the identification of struts equivalent to masonry infills). The experimental campaign made it possible to recognise a correlation between the Poisson’s ratios and the strengths of masonries investigated along the orthotropic axes and to obtain the diagonal Poisson’s ratio without specific experimental tests. Finally, the experimental responses of some infilled frames were used to test the reliability of the model proposed here.     

Experience in polyharmonic analysis of the parameters of the earth’s rotation

A method for approximating time series by an nth degree trigonometric polynomial for a series of parameters of the Earths rotation, calculated from GPS and GLONASS measurements, is tested. Satisfactory agreement is obtained between the model and experimental data. The results can be used for complex modeling and forecasting of the parameters of the Earths rotation.Translated from Izmeritelnaya Tekhnika, No. 12, pp. 40–42, December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Absence of ‘fragility’ and mechanical response of jammed granular materials

We perform molecular dynamic simulations of frictional non-thermal particles driven by an externally applied shear stress. After the system jams following a transient flow, we probe its mechanical response in order to clarify whether the resulting solid is ‘fragile’. We find the system to respond elastically and isotropically to small perturbations of the shear stress, suggesting absence of fragility. These results are interpreted in terms of the energy landscape of dissipative systems. For the same values of the control parameters, we check the behaviour of the system during a stress cycle. Increasing the maximum stress value, a crossover from a visco-elastic to a plastic regime is observed.     

Electrical breakdown in nonuniformly heated gases and the upper temperature limit of the applicability of Paschen’s law

The electrical breakdown of nonuniformly heated gas-discharge gaps with a uniform electric field at temperatures of 1200–3600 K is studied experimentally. It is found that the thermionic emission from the cathode has an effect on the breakdown parameters. This effect starts manifesting itself at the critical density of the emission currentJ _cr ∽ 10⁻⁸ A/cm² attained in experiments with a tungsten cathode at a temperatureT _CT ∼ 1700 K. The increase of the cathode temperature to -2200 K results in a decrease of the breakdown voltageU _br by more than an order of magnitude due to the thermionic emission. The heating of the anode to a temperature of up to 3600 K does not result in a decrease of the breakdown voltage below the values defined by the gas density. In this case, the decrease of the values ofU _br is due only to the change of the gas density distribution along the gap length and obeys the generalized law of similarity. The existence of a critical temperatureT _T is predicted, above which one should expect a drastic decrease of the breakdown voltage due to the thermal ionization of gas. The value ofT _T depends on the configuration of the thermal field between the electrodes and the type of gas. In the thermal fields typical of our experimental conditions involving the heating of one of the electrodes, the critical temperature for xenon is about 4700 K. The studies were carried out in argon, krypton, and xenon.     

Self-diffusion in granular gases: an impact of particles’ roughness

An impact of particles?? roughness on the self-diffusion coefficient D in granular gases is investigated. For a simplified collision model where the normal, ${\varepsilon}$ , and tangential, ??, restitution coefficients are assumed to be constant we develop an analytical theory for the diffusion coefficient, which takes into account non-Maxwellain form of the velocity-angular velocity distribution function. We perform molecular dynamics simulations for a gas in a homogeneous cooling state and study the dependence of the self-diffusion coefficient on ${\varepsilon}$ and ??. Our theoretical results are in a good agreement with the simulation data.     

Yesterday’s dreams and today’s reality in telecommunications

Twenty-five years ago the telecommunications industry had its vision of the future. There were three dreams that, given the right technology, they could achieve: (1) the Dick Tracy wristwatch phone; (2) the Picturephone; and (3) the set-top box for the home television which could access an information store maintained by the telephone company. None of these dreams turned out as planned, but it is interesting to compare the original concepts with what has actually transpired in the last quarter-century. Today, having achieved some form of each of these three dreams, it seems as if, looking ahead to tomorrow’s technology, the industry has no similar vision.