An inhomogeneity problem in couple stress theory

Using Hilbert theory and Mindlin's couple stress theory, the problem of two-dimensional circular inhomogeneity (when the inserted material is of different size than the size of the cavity and having different elastic constants) is studiedin this paper. Stress could be bounded at infinity. The formulation is valid also for regions other then the circular ones when the matrix is finite has also been tackled. Numerical results are in conformity with the fact that the effect of couple stresses is negligible when the ratio of the smallest dimension of the body to the cahracteristic length is large.

Brillouin Scattering by Phonons Renormalized by Two-Magnon Excitations in Ferromagnetic Dielectrics

Brillouin scattering by one-phonon-two-magnon interacting excitations in ferromagnetic dielectrics is discussed. The basic light scattering mechanism is taken to be the modulation of the density-dependent optical dielectric polarizability of the medium by the dynamic strain field generated by the longitudinal acoustic (LA) phonons. The renormalization effects arising from the scattering of phonons by the two-magnon creation-annihilation processes have, however, been taken into account. Via these interactions, the Brillouin components corresponding to the two-magnon excitations are reflected indirectly in the spectrum of the phonon scattered light as line-broadening of the otherwise relatively sharp Brillouin doublet. The present mechanism is shown to be dominant in a clean saturated ferromagnetic dielectric with large magneto-strictive coupling constant, and with the magnetic ions in the orbitally quenched states. Following the linear response theory, an expression has been derived for the spectral density of the scattered light as a function of temperature, scattering angle, and the strength of the externally applied magnetic field. Some estimates are given for the line-width and line-shift of the Brillouin components for certain typical choice of parameters involved. The results are discussed in relation to some available calculations on the ultrasonic attenuation in ferromagnetic insulators at low temperatures.

Self-consistent theory of localization in weakly disordered systems

An analytic treatment of localization in a weakly disordered system is presented for the case where the real lattice is approximated by a Cayley tree. Contrary to a recent assertion we find that the mobility edge moves inwards into the band as disorder increases from zero.

On the theory of polarographic maxima

The theory of polarographic maxima is presented taking into account the interaction of momentum transport, the electrostatic potential field, the adsorption—desorption and the faradaic processes. Several earlier results are generalised. The systems approach employed here is also extended to quasi-linear situations.

Optimal maintenance policy for equipment subject to random deterioration and random failure A modern control theory approach.

The stochastic version of Pontryagin's maximum principle is applied to determine an optimal maintenance policy of equipment subject to random deterioration. The deterioration of the equipment with age is modelled as a random process. Next the model is generalized to include random catastrophic failure of the equipment. The optimal maintenance policy is derived for two special probability distributions of time to failure of the equipment, namely, exponential and Weibull distributions Both the salvage value and deterioration rate of the equipment are treated as state variables and the maintenance as a control variable. The result is illustrated by an example

Orbit perturbation theory of beam-plasma instability

The nonlinear theory of the instability caused by an electron beam-plasma interaction is studied. A nonlinear analysis has been carried out using many-body methods. A general formula for a neutral collisionless plasma, without external fields, is derived. This could be used for calculating the saturation levels of other instabilities. The effect of orbit perturbation theory on the beam-plasma instability is briefly reviewed.

Rapid distortion of axisymmetric turbulence

A generalization of the isotropic theory of Batchelor & Proudman (1954) is developed to estimate the effect of sudden but arbitrary three-dimensional distortion on homogeneous, initially axisymmetric turbulence. The energy changes due to distortion are expressed in terms of the Fourier coefficients of an expansion in zonal harmonics of the two independent scalar functions that describe the axisymmetric spectral tensor. However, for two special but non-trivial forms of this tensor, which represent possibly the simplest kinds of non-isotropic turbulence and specify the angular distribution but not the wavenumber dependence, the energy ratios have been determined in closed form. The deviation of the ratio from its isotropic value is the product of a factor containing R, the initial value of the ratio of the longitudinal to the transverse energy component, and another factor depending only on the geometry of the distortion. It is found that, in axisymmetric and large two-dimensional contractions, the isotropic theory gives nearly the correct longitudinal energy, but (when R > 1) over-estimates the increase in the transverse energy; the product of the two intensities varies little unless the distortion is very large, thus accounting for the stress-freezing observed in rapidly accelerated shear flows.Comparisons with available experimental data for the spectra and for the energy ratios show reasonable agreement. The different ansatzes predict results in broad qualitative agreement with a simple strategem suggested by Reynolds & Tucker (1975), but the quantitative differences are not always negligible.

Application of molecular orbital theory to the interpretation of x-ray absorption spectra of platinum complexes

X-ray LIII-absorption edges of platinum in nine octahedral complexes have been recorded using a bent crystal spectrograph. The edge features of the discontinuities have been interpreted with the help of qualitative molecular orbital diagrams. A correlation between the energy separation of the first two absorption maxima and the spectrochemical series of the ligands has been arrived at.

Theory of CO2-laser induced x-ray emission from high density gaseous targets

Abstract is not available.

Theory of Non-linear Waves in Multi-dimensions: with Special Reference to Surface Water Waves

The surface water waves are "modal" waves in which the "physical space" (t, x, y, z) is the product of a propagation space (t, x, y) and a cross space, the z-axis in the vertical direction. We have derived a new set of equations for the long waves in shallow water in the propagation space. When the ratio of the amplitude of the disturbance to the depth of the water is small, these equations reduce to the equations derived by Whitham (1967) by the variational principle. Then we have derived a single equation in (t, x, y)-space which is a generalization of the fourth order Boussinesq equation for one-dimensional waves. In the neighbourhood of a wave froat, this equation reduces to the multidimensional generalization of the KdV equation derived by Shen & Keller (1973). We have also included a systematic discussion of the orders of the various non-dimensional parameters. This is followed by a presentation of a general theory of approximating a system of quasi-linear equations following one of the modes. When we apply this general method to the surface water wave equations in the propagation space, we get the Shen-Keller equation.

Synthesis, spectral and electrochemical properties of donor/acceptor substituted fluoroarylporphyrins

Spectroscopic and electrochemical redox properties of a series of fluorinated porphyrins bearing donor-acceptor groups and their Zn(II) and Cu(II) derivatives are presented. The magnitude of the ring reduction potentials and charge transfer properties derived from spectral data depend on the nature and position of the substituent(s), (nitro/dimethylamino) and the central metal ions.

Spectral and thermal data on polystyrene peroxide

Poly(styrene peroxide) has been prepared and characterized. Nuclear magnetlc resonance (NMR) spectra Of the polymer show the shift Of aliphatic protons. Differential scanning calorimetric (DSC) and differential thermal analysis (DTA) results show anexothermic peak around 110 OC which is characteristic of peroxide decomposition.

Superoperator formalism and chemisorption theory

It is pointed out that the superoperator formalism, developed for the calculation of ionization potentials in molecular physics, is a very powerful tool in chemisorption theory. This is demonstrated by applying the formalism to the Anderson-Newns model and by showing how the different approximate solutions can be obtained by elegant and systematic procedures. It is also pointed out that using the formalism, solutions for more complicated hamiltonians can easily be obtained.