Harmonic and anharmonic oscillations of a cylindrical plasma in the presence of a uniform axial magnetic field and a steady axial current

In the present note we have studied the harmonic and anharmonic oscillations of cylindrical plasma using Lagrangian formalism. In order to study the harmonic oscillations, the equations are linearized and the resulting equation for the displacement has been numerically solved. For situations present in thermonuclear reactors, the presence of axial magnetic field is found necessary to make the periods of oscillation to become comparable with the time required for the thermonuclear reactions to set in. A detailed analysis of the anharmonic oscillations reveals that the significant interaction is between the first and the second mode. The fundamental period of anharmonic oscillation is more than the corresponding period of harmonic oscillations by 9·2%. Graphs have been drawn for the amplitudes of relative variations in density and magnetic field and of the time-varying part of anharmonic oscillation.

Oscillations of a three-component assembly with or without magnetic field

The plasma is taken to be composed of singly ionized molecules, free electrons and neutral molecules, each of the component being described by the hydromagnetic equations, modified to take into account the displacement current, existence of free charge in the medium, and the modified current equation without involving the scalar conductivity. The basic equations are linearized and only small amplitude waves are considered. In the absence of any external magnetic field, the transverse and longitudinal modes of oscillation separate out. In the transverse part a coupled plasma oscillation occurs which could be propagated only above a certain critical frequency and in the longitudinal part one extraordinary mode of propagation occurs having a forbidden range of frequencies. When there is an external applied magnetic field, ordinary and extraordinary waves are propagated along the direction of the magnetic field, whereas only ordinary waves are propagated transverse to the magnetic field. The critical frequencies above which these waves are propagated are evaluated and, the possible explanation of this medium like behaviour could be the implicit assumption of conductivity being not a scalar.

Polarisation studies on the Raman spectra of cubic crystals - Part II: Calcium fluoride and potassium aluminium sulphate

Polarisation characters of the Raman lines of calcium fluoride (fluorspar) and potassium aluminium sulphate (alum) were investigated under the following conditions. Unpolarised light was incident normally on a face of the crystal making an angle 22.5° with a cubic face and the light scattered transversely along a cubic axis was analysed by a double image prism kept with its principal axes inclined at 45° to the vertical. Under these conditions the depolarisation factors of the Raman lines belonging to the totally symmetric (A), the doubly degenerate (E) and the triply degenerate (F) modes should be respectively =1, >1 and <1. The characteristic Raman line of CaF2 at 322 cm-1 exhibited a depolarisation value less than 1, showing thereby that the corresponding mode is a triply degenerate one (F). The Raman lines observed in the spectrum of K-alum were also classified and the results were compared with those given by previous investigators using standard crystal orientations.

Infrared spectra of trichloroacetates of copper, calcium, strontium and barium

Infrared spectra of trichloroacetates of Cu, Ca, Sr and Ba were studied in order to investigate the effect of coordination on the vibration spectra of the ligand. The shifts of the antisymmetric and symmetric COO- stretching frequencies are explained on the basis of the type of co-ordination of the COO- group to the metal ion. From the spectra it is established that the coordination of the COO- group to metal is different for trichloroacetates and monochloroacetates.

A weighted mean square method of linearization in non-linear oscillations

The paper deals with a linearization technique in non-linear oscillations for systems which are governed by second-order non-linear ordinary differential equations. The method is based on approximation of the non-linear function by a linear function such that the error is least in the weighted mean square sense. The method has been applied to cubic, sine, hyperbolic sine, and odd polynomial types of non-linearities and the results obtained are more accurate than those given by existing linearization methods.

Micellar size and shape in solutions of calcium stearate in cetane from optical depolarization data

Observations at a series of temperatures of the changes in viscosities and depolarization factors of 1% and 18% solutions of calcium stearate in cetane to which varying amounts of water have been added can be interpreted in terms of the existence of anisometric micelles. In general, changes in the size of the micelles inferred from values of ρh agree with those deduced from the viscosity data. The correlation between anisometry of micelles from rheological and optical observations is much poorer in the case of ρν, presumably because of the difficulty in differentiating the contribution of anisometry and anisotropy to ρν.

Consideration on thermal decomposition of calcium hydroxide pellets for energy storage

The reversible chemical reaction of Ca(OH)2/CaO appears to be attractive for storage of solar thermal energy, in view of the nonpolluting and nontoxic nature of the reactants. This paper presents some data on thermal decomposition of calcium hydroxide pellets along with its additives of aluminum, aluminum hydroxide, zinc, and copper. The addition of aluminum and zinc powder enhanced the rate of decomposition considerably at 450°C, but copper had no effect. Considerations on the effect of additives are also discussed in some detail, though their effects are not established with certainty. There is some evidence that heat transfer into the pellet, and the number of potential nucleation sites due to thermal stresses, influence the kinetics and mechanism of decomposition.

New family of thallium cuprate superconductors not containing calcium or barium: TlSrn+1−xLnxCunO2n+3+δ (Ln=La, Pr, or Nd)

The first two members of the new TlSrn+1−xLnxCunO2n+3+δ (Ln=La, Pr, or Nd) series of superconducting cuprates possessing 1021 and 1122 type structures are described. The n=1 (1021) members with Tcs around 40 K have electrons or holes as the majority charge carriers depending on x. The n=2 (1122) cuprate (Ln=Pr or Nd) shows a Tc in the 80–90 K range.

Undamped Oscillations of Collisionless Stellar Systems: Spheres,Spheroids and Discs.

The collisionless Boltzmann equation governing self-gravitating systems such as galaxies has recently been shown to admit exact oscillating solutions with planar and spherical symmetry. The relation of the spherically symmetric solutions to the Virial theorem, as well as generalizations to non-uniform spheres, uniform spheroids and discs form the subject of this paper. These models generalize known families of static solutions. The case of the spheroid is worked out in some detail. Quasiperiodic as well as chaotic time variation of the two axes is demonstrated by studying the surface of section for the associated Hamiltonian system with two degrees of freedom. The relation to earlier work and possible implications for the general problem of collisionless relaxation in self gravitating systems are also discussed.

Effect of calcium deficiency on the mechanical properties of hydroxyapatite crystals

The deterioration of the mechanical properties of bone with age is related to several factors including the structure, organization and chemistry of the constituent phases; however, the relative contribution of each of these factors is not well understood. In this study, we have investigated the effect of chemistry (calcium deficiency) on the mechanical properties of single crystals of hydroxyapatite. Single crystals of stoichiometric crystals grown by the flux method and calcium-deficient platelet crystals grown using wet chemical methods were used as model systems. Using nanoindentation, we show that calcium deficiency leads to an 80% reduction in the hardness and elastic modulus and at least a 75% reduction in toughness in plate-shaped hydroxyapatite crystals. Measurement of local mechanical properties using nanoindentation and nanoscale chemistry through elemental mapping in a transmission electron microscope points to a direct correlation between the observed spatial variation in composition and the large scatter in the measured hardness and modulus values. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Redistribution of subcellular calcium in rat liver on administration of vanadate

Mitochondria isolated from the livers of rats administered with sodium meta-, ortho-, or polyvanadate, but not vanadyl sulphate, exhibited enhanced Ca2+ — stimulated respiration and uptake of calcium. These effects were shown also by mitochondria isolated from livers perfused with polyvanadate. The concentration of acid-soluble calcium decreased significantly in the mitochondrial fraction on vanadate treatment, while that in the cytosol showed a corresponding increase. Phenoxybenzamine, an antagonist to a-adrenergic receptors, effectively inhibited vanadate-induced Ca2+ mobilization, but surgical sympathectomy was without effect. This is the first demonstration of vanadate mimicking agr-adrenergic agonists in vivo.

Novel organic porous solids with channel and layered structures from 1,3,5-triazine-2,4,6-triaminehexaacetic acid and its calcium salt

Single crystals of a symmetrically substituted molecule, 1,3,5-triazine-2,4,6-triaminehexaacetic acid, (TTHA) and its Ca2+ salt have been synthesized, the analysis of which reveals the existence of novel channel type cavities and helical packing organizations in the crystals.

Undamped oscillations of homogeneous collisionless stellar systems

The Lewis (1968) invariant of the time-dependent harmonic oscillator is used to construct exact time-dependent, uniform density solutions of the collisionless Boltzmann equation. The spatially bound solutions are time-periodic.

ESR studies of X-irradiated strontium mixed calcium tartrate crystals

The electron spin resonance spectra of X-ray irradiated single crystals of strontium doped calcium tartrate tetrahydrate (CST) with molecular formula Ca0.88Sr0.12C4H4O6.4H(2)O grown in gels has been investigated. Only one species of free radical but with two magnetically unequivalent sites was observed at room temperature. The free radical was found to be the result of the splitting of a C-II bond adjacent to both the hydroxyl and carboxyl groups. The a factor was found to be slightly anisotropic. Couplings with two H nuclei, believed to be the proton of the OH group attached directly to the unsaturated asymmetric carbon atom and the proton attached directly to the: other asymmetric carbon atom of the molecule were observed. The principal g-values were found to be 2.0030, 2.0017, 2.0027. The principal elements of the nuclear coupling are 7.45, 6.59, 4.28 and 8.56, 7.22, 18.71 G, respectively. The radical was found to be very stable. (C) 2000 Elsevier Science Ltd. All rights reserved.

Adsorption behaviour of an oxidised starch onto haematite in the presence of calcium

The adsorption behaviour of an oxidised starch AP as well as that of calcium onto haematite have been studied both individually and together. While the adsorption density of starch AP onto haematite is enhanced in the presence of calcium, the adsorption of calcium onto haematite is not promoted by starch AP. Flocculation tests on haematite ore fines in the presence of starch AP and calcium chloride reveal that the sequence in which calcium and starch are added governs the settling rates and turbidity values. Zeta potential, viscosity and conductivity measurements, and calcium ion binding studies with starch AP indicate calcium-starch interactions. Possible mechanisms involved in such interactions with respect to haematite flocculation have been discussed.