Propagation of Elastic Waves in Periodically Inhomogeneous Media

The structural theory of waves and vibrations in periodically inhomogeneous media is set out. Relevant research results are presented. Emphasis is on the principles of the theory, surface waves, and other surface effects     

Single-Pulse Echo and Its Secondary Signals in Two-Level Spin Systems

The dependences of the amplitudes of single- and two-pulse spin echoes and their secondary signals in NMR (protons of glycerin in an inhomogeneous magnetic field) in the exciting-pulse repetition period T _r have been compared. The difference in origin of the primary and secondary signals of a single-pulse echo in a two-level spin system has been confirmed. It is shown that only a primary single-pulse echo observed when T _r > T ₁ (T ₁ is the spin lattice relaxation time) results from single-pulse excitation. The secondary single-pulse echo signals are observed for T _r < T ₁ and are due to the multiphase formation mechanism. The results obtained for magnetically ordered substances are analyzed. Based on these data, it was inferred earlier that primary and secondary single-pulse echo signals were formed by one and the same multiphase mechanism.     

Effective dielectric function of a metal-dielectric composite with nonrandomly distributed particles

Summary The optical properties of a metal-dielectric binary composite with nonrandomly distributed particles were studied within the framework of the effective medium theory. All the particles, as usual, were assumed to be spherical and the nonrandomness of their distribution was achieved by forcing onto the system the correlation that prevents the metal particles from touching each other or the one that forces them to aggregate in pairs, either oriented at random or all alike. The drawbacks of the effective medium theory due to the assumption that the particles be very small were overcome by describing the scattering properties of the particles through their exact Mie amplitudes. Both kinds of correlation we considered turned out to have substantial effects on the onset of the percolation phenomena. The transition induced by the correlation of exclusion from a behaviour typical of the Bruggeman model to one more appropriate to the Maxwell-Garnett model was followed as a function of the exclusion radius. In the case of aggregation the onset of the percolation phenomena was found to be strongly influenced by the further introduction of an orientational order of the pairs. Based on work supported in part by the U. S. Army European Research Office through Contract DAJA45-86-C-0003 and in part by the Consiglio Nazionale delle Ricerche through the Gruppo Nazionale Struttura della Materia.     

On the inhomogeneous deformation of rubber-elastic polymers

Measurements in a gas dilatometer on carbon-black filled rubber cross-linked with sulfur show a large pressure drop in the specimen chamber, which to a large extent cannot be explained by a volume change of the specimen. The extension ratio at which the pressure starts to fall depends on the carbon-black content. Comparative measurements in a deformation calorimeter show that crystallisation always begins first at higher strains. It is assumed that the investigated specimens are inhomogeneously deformed even at small strains, depending on the carbon-black content, and that internal voids are formed, onto the surfaces of which gas molecules are deposited. This gas adsorption causes the pressure drop measured in the dilatometer; it is dependent on the nature of the gas. Argon shows no interaction with internal surfaces in the specimen; for measurements in an argon atmosphere, volume increases and strain-induced crystallisation can be properly determined. It is presumed that strain-induced crystallisation sets in earlier for specimens with larger carbonblack content, corresponding to the more inhomogeneous character of the deformation.Dedicated to Prof. Dr. R. Bonart on the occasion of his 60th birthday     

The importance of fully quantitative non-local treatments of exchange energy in Density Functional Theory of atoms,molecules and clusters,characterised by strongly inhomogeneous electron liquids

After a brief summary of some recent work on non-local approximations to the exchange energy and potential in density functional theory, a table is presented for atoms from Be to Ar, with an even number of electrons, having large electron density gradients, which highlights the importance of exchange. Until non-local exchange energy is truly quantitative, refinements of correlation energy may be submerged through ‘noisy’ exchange.     

Oscillations of an inhomogeneous elastic layer

A method is proposed to analyze wave fields in an elastic layer with elastic properties varying arbitrarily with depth. The method is based on reducing the boundary-value problem to a system of Fredholm integral equations of the second kind, which is then analyzed numerically. Some features of the structure of dispersion sets are analyzed and, in particular, their asymptotes are constructed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 157–164, May–June, 2006.     

计算特征向量摄动量的混合基展开法

在结构修改和模型校正中，模态展开法是计算特征向量摄动量的常用方法之一，但当高阶模态被截断时，它会带来很大的截断误差。本文利用已知的有限阶模态，构造了Ｎ维欧氏空间的一个新基－混合基，并将特征向量的摄动量在新基上展开来计算特征向量的一、二阶 摄动量。该方法使得不管截模态个数的多少，其精度总与全模态展开法相同，且计算量都远少于全模记展开法；与改进的部分民开法相比，本方法不要求所截留的模态边连续的低阶模态     

A method of interface inversion in inhomogeneous media

First, an approximate solution of time domain interface scattering field is derived by extending the classical Born approximation in the problem of interface scattering. In accordance with the solution form, a projection density compensation (PDC) inversion method is developed according to the projection slice theorem, which is valid for the cases of inhomogeneous media and wave mode transformation. Finally, in the model of layered media, the calculation algorithm and the simulation inversion comparison results of point defect, crack, and crack on an interface, as well as the experiment method and results in the condition of acoustic wave, are given. The project supported by the National Natural Science Foundation of China (No.19232031) and Chinese Education Commission Science Foundation