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     

Global nonautonomous Schr?dinger flows on Hermitian locally symmetric spaces

In this paper, we consider the global existence of one-dimensional nonautonomous (inhomogeneous) Schr?dinger flow. By exploiting geometric symmetries, we prove that, given a smooth initial map, the Cauchy problem of the nonautonomous (inhomogeneous) Schr?dinger flow from S¹ into a Hermitian locally symmetric space admits a unique global smooth solution, and then we address the global existence of the Cauchy problem of inhomogeneous Heisenberg spin ferromagnet system.     

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.     

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.     

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.     

String cosmology in inhomogeneous cylindrically symmetric spacetime

String-dust cosmology in an inhomogeneous cylindrically symmetric model is considered. Solutions are obtained only for geometric string with the separability assumption for metric coefficients.     

Time-dependent correlations in an inhomogeneous one-component plasma

Sum rules describing perfect screening at equilibrium in a classical plasma are extended to the time-displaced structure function of an inhomogeneous one-component plasma. We find that there are long-wavelength modes which oscillate undamped with a single frequency , being an angular average of the squared plasma frequency at infinity. Our results are derived heuristically, allowing also for quantum effects, from linear response theory, and rigorously from the classical BBGKY hierarchy under some reasonable assumptions on the spatial decay of correlations. Special cases are investigated, in particular plasmas bounded by walls of varied shapes.This laboratory is associated with the CNRS.     

Topological analysis of some special graphs. III. Regular polyhedra

A regular polyhedron is isomorphic to a cluster on which every face has same number of bonds and every atom has an equal number of coordinating atoms. A general strategy for generating the eigenvectors and the eigenvalues of regular polyhedra is given. Net sign analyses are also performed on the eigenvectors of regular polyhedra. The results provide us a quick way to grasp the topological feature of the electronic structure of clusters having interesting topology.