A phase space approach to generalized Hamilton–Jacobi theory

Generalizations of H–J theory have been discussed before in the literature. The present approach differs from others in that it employs geometrical ideas on phase space and classical transformation theory to derive the basic equations. The relation between constants of motion and symmetries of the generalized H–J equations is then clarified. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

A note on the effective medium theory of random resistive-reactive medium

The effective medium theory for a system with randomly distributed point conductivity and polarisability is reformulated, with attention to cross-terms involving the two disorder parameters. The treatment reveals a certain inconsistency of the conventional theory owing to the neglect of the Maxwell-Wagner effect. The results are significant for the critical resistivity and dielectric anomalies of a binary liquid mixture at the phase separation point.

The non-planar peptide unit II. Comparison of theory with crystal structure datastar, open

The theoretical results derived in Part I (Ramachandran, G.N., Lakshminarayan, A.V. and Kolaskar, A.S. (1973) Biochim. Biophys. Acta 303, 8–13) that the three bonds of the peptide unit meeting at N can have a pyramidal structure is confirmed by an analysis of 14 published crystal structures of small peptides. It is shown that the dihedral angles θN and Δω are correlated, while θC, is small and is uncorrelated with Δω, showing that the non-planar distortion at C′ is generally small.

A theory of the upper critical field in antiferromagnetic superconductors

A generalized Ginzburg-Landau approach is used to study the nonmonotonic temperature dependence of the upper critical field H c 2(T) in antiferromagnetic superconductors RE(Mo)6S8; RE = Dy, Tb, Gd. It is found that electrodynamic effects incorporated through screening and indirect coupling between the staggered magnetization M Q (T) and superconducting order parameter psgr cannot explain the observed nonmonotonicity. This suggests that the direct coupling between the two order parameters should be considered to understand the experimental results, a finding which is consistent with recent microscopic calculations.

Theory of the non-planar peptide unitstar, open

By means of CNDO/2 calculations on N-methyl acetamide, it is shown that the state of minimum energy of the trans-peptide unit is a non-planar conformation, with the NH and NC2α bonds being significantly out of the plane formed by the atoms C1α, C′, O and N.

Einstein relation in n-i-p-i and microstructures of nonlinear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestions for an experimental determination

We investigate the Einstein relation for the diffusivity-mobility ratio (DMR) for n-i-p-i and the microstructures of nonlinear optical compounds on the basis of a newly formulated electron dispersion law. The corresponding results for III-V, ternary and quaternary materials form a special case of our generalized analysis. The respective DMRs for II-VI, IV-VI and stressed materials have been studied. It has been found that taking CdGeAs2, Cd3As2, InAs, InSb, Hg1−xCdxTe, In1−xGaxAsyP1−y lattices matched to InP, CdS, PbTe, PbSnTe and Pb1−xSnxSe and stressed InSb as examples that the DMR increases with increasing electron concentration in various manners with different numerical magnitudes which reflect the different signatures of the n-i-p-i systems and the corresponding microstructures. We have suggested an experimental method of determining the DMR in this case and the present simplified analysis is in agreement with the suggested relationship. In addition, our results find three applications in the field of quantum effect devices.

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.

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.

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations.

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.