A note on non-separable solutions of linear partial differential equation

A method has been presented for constructing non-separable solutions of homogeneous linear partial differential equations of the type F(D, D′)W = 0, where D = ∂/∂x, D′ = ∂/∂y, Image where crs are constants and n stands for the order of the equation. The method has also been extended for equations of the form Φ(D, D′, D″)W = 0, where D = ∂/∂x, D′ = ∂/∂y, D″ = ∂/∂z and Image As illustration, the method has been applied to obtain nonseparable solutions of the two and three dimensional Helmholtz equations.

Vibration of rectangular orthotropic plates

An approximate analytical procedure has been given to solve the problem of a vibrating rectangular orthotropic plate, with various combinations of simply supported and clamped boundary conditions. Numerical results have been given for the case of a clamped square plate. Nomenclature 2a, 2b sides of the rectangular plate h plate thickness Eprime x , Eprime y , EPrime, G elastic constants of te orthotropic material D x Eprime x h 3/12 D y Eprime y h 3/12 H xy EPrimeh 3/12+Gh 3/6 D x , D y and H xy are rigidity constants of the orthotropic platergr mass of the plate per unit area ngr Poisson's ratio W deflection of the plate p circular frequency gamma b/a ratio X m , Y characteristic functions of the vibrating beam problem -lambda rgrp 2 a 2 b 2/H xy the frequency parameter.

Raman spectrum of sodium iodide

Raman spectrum of a single crystal of sodium iodide has been recorded for the first time using lambda 2537 excitation. The general features of the spectrum are discussed in the light of the existing theories on the dynamics of the alkali halides. The authors wish to thank Professor D.Y.Phadke of the Tata Institute of Fundamental Research, Bombay, for presenting the crystal of Nal used in the present investigation.

First-principles electronic structure of the delafossites ABO(2) (A=Cu, Ag, Au; B=Al, Ga, Sc, In, Y): evolution of d(10)-d(10) interactions

While bonding between d(10) atoms and ions in molecular systems has been well studied, less attention has been paid to interactions between such seemingly closed shell species in extended inorganic solids. In this contribution, we present visualizations of the electronic structures of the delafossites ABO(2) (A = Cu, Ag, Au) with particular emphasis on the nature of d(10)-d(10) interactions in the close packed plane of the coinage metal ion. We find that on going from Cu to Ag to Au, the extent of bonding between A and A increases. However, the structures (in terms of distances) of these compounds are largely determined by the strongly ionic 13,11 0 interaction and for the larger B ions Sc, In and Y, the A atoms are sufficiently well-separated that A-A bonding is almost negligible. We also analyze some interesting differences between Ag and Au, including the larger A-O covalency of the Au. The trends in electronic structure suggest that the Ag and Au compounds are not good candidate transparent conducting oxides. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.