Volume 13, Issue 4
October 1979, pages 337-455
pp 337-352 October 1979 Statistical Physics
On an interpolation model for the transition operator for Markov and non-Markov processes
A phenomenological interpolation model for the transition operator of a stationary Markov process is shown to be equivalent to the simplest difference approximation in the master equation for the conditional density. Comparison with the formal solution of the Fokker-Planck equation yields a criterion for the choice of the correlation time in the approximate solution. The interpolation model is shown to be form-invariant under an iteration-cum-rescaling scheme. Next, we go beyond Markov processes to find the effective time-development operator (the counterpart of the conditional density) in the following very general situation: the stochastic interruption of the systematic evolution of a variable by an arbitrary stationary sequence of randomizing pulses. Continuous-time random walk theory with a distinct first-waiting-time distribution is used, along with the interpolation model for the transition operator, to obtain the solution. Convenient closed-form expressions for the ‘averaged’ time-development operator and the autocorrelation function are presented in various special cases. These include (i) no systematic evolution, but correlated pulses; (ii) systematic evolution interrupted by an uncorrelated (Poisson) sequence of pulses.
pp 353-365 October 1979 Plasma Physics
Microwave propagation through modulated air plasma
When a microwave propagates through a plasma in which electron density and electron collision frequency periodically vary, the propagating wave is modulated in amplitude and phase. An approximate theory is derived to suit the laboratory experimental conditions. Introducing the amplitude and phase difference, the dependence of electron density and electron collision frequency has been derived for different radio frequency modulation and frequency parameter. A scanning double probe technique is used to measure the exact time variation in the plasma parameters at any fixed position during a single cycle of the applied field. Theoretical values agree with those of experiment.
pp 367-371 October 1979 Liquids
Equilibrium properties of a semiclassical fluid with square-well plus hard core potential
A cluster expansion theory, in which the quantum hard sphere system is taken as a reference system and the attractive interactions as a perturbation, is applied to calculate the equilibrium properties of the square-well fluid in the semiclassical limit. The radial distribution function and direct correlation function are obtained using the exponential approximation. The isothermal compressibility is also evaluated.
pp 373-386 October 1979 Solids
The electron-ion interactions in tetragonal metals
The electron-ion interactions are evaluated exactly over the actual shape of the atomic polyhedron, instead of approximating it by a sphere or an ellipsoid, by making use of simple co-ordinate axes transformations and lattice symmetry in the case of fct and bct structures. It is shown that there are several alternative ways of expressing the interference factor,S(q), one of which was obtained by Sharan and others in the case of indium. By comparing these expressions with the latter, with those of corresponding cubic structures as well as with those obtained under spherical approximation respectively, the crystallographic equivalence and stability of tetragonal structures as well as the validity of Wigner-Seitz approximation are discussed.
pp 387-391 October 1979 Solids
Origin of accidental degeneracy in ligand-field splittings of substituted octahedral complexes
Accidental degeneracy seems to be the rule rather than an exception amongst thed orbital energies of substituted octahedral complexes ofd^{1} configuration. By using symmetry and physical arguments, in conjunction with first-order and second-order degenerate perturbation theory, it is shown that such accidental degeneracies arise in crystal-field theory due to the choice of an inflexible basis set of metal orbitals which neglects the polarisation of metal orbitals by the ligand charges.
pp 393-403 October 1979 Solids
Electron paramagnetic resonance of NH_{3}^{+} radical in potassium sulphate
S Subramanian P Narayana Murty C R K Murty
Room temperature EPR spectra of (NH_{4})_{2}SO_{4} doped K_{2}SO_{4} monocrystals irradiated with x-rays show the presence of NH_{3}^{+} radicals. The EPR parameters areg ‖=2.0037 andg ⊥ = 2.0068;^{14}NA_{XX}=13.75;A_{YY}=24.5;A_{ZZ}=25.5 gauss;^{1}HA_{XX}=A_{YY}=22 andA_{ZZ}=25 gauss. From the^{14}N and^{1}H coupling constants it has been inferred that at room temperature the planar NH_{3}^{+} radical undergoes rotation about theC_{3} axis which corroborates with the equivalence of the protons, but the radical itself is in an asymmetric crystal field environment. The 77K spectra indicate a considerable reduction in the motion of the radical with the free motion almost completely stopped.
pp 405-411 October 1979 Solids
Electrical properties of molybdenite single crystals
M K Agarwal K Nagi Reddy P A Wani
Molybdenite crystals used in the present work were grown by direct vapour transport or sublimation method. The electrical resistivities and I-V characteristics were measured at different temperatures in the symmetry plane. The room temperature resistance of a specimen annealed for different periods has also been measured. These results are described and discussed.
pp 413-422 October 1979 Solids
C Radhakrishnamurty N G Nanadikar
It is shown that hysteresis and susceptibility studies at various temperatures could provide an idea whether a magnetic sample contains multidomain, single-domain or superparamagnetic particles. Our results on titanomagnetites with those of others on cobalt substituted magnesium ferrites suggest that domain wall formation is inhibited in some of them whereby only single-domain or superparamagnetic particles occur irrespective of the physical grain size of such materials. At high concentration of titanium in titanomagnetites, the magnetic behaviour is similar to a spin glass, which we interpret as a transition of optimum single-domains going over to superparamagnetic state.
pp 423-445 October 1979 Spectrescopy
Model for infrared and Raman studies of molecular rotations in liquids and gases
Experimental infrared and Raman data for molecular rotations in dense phases often lie in between the results predicted by theJ- andM-diffusion models of Gordon. In this paper, we present a theory which is similar in its basic approach to Gordon’s extended diffusion models (EDM) but in which the restrictions of theJ andM limits are removed. The outcome is a scheme which allows one to describe situations which fall between the two extreme pictures of theJ andM models. Application of this scheme to experiments is discussed.
pp 447-449 October 1979 Spectrescopy
Pressure broadened calculations of the OCSJ = 1 → 2 line by non-polar perturbers
G K Johri R P Rishishwar S C Mehrotra
Microwave spectral line widths of the transitionJ = 1 → 2 of OCS perturbed by non-polar perturbers,n-hexane, cyclohexane,n-heptane, carbon disulphide, carbon tetrachloride and benzene have been calculated using a recent theory of Mehrotra and Boggs.
pp 451-455 October 1979 Nuclear and Particle Physics
A Thomas-Fermi type picture and the electromagnetic structure of the nucleon
Using a Thomas-Fermi type picture of the nucleon as a dense system of quarks and antiquarks, we give a rationale for the ‘dipole’ nature, scaling and other characteristics of the nucleon electromagnetic form factors. Similar considerations are then given for the electromagnetic structure of the pion.
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