Double Coil Resonance Experiment and Partial Reduction of Wave Packet in Quantum Mechanics

Interference and measurement aspects for the double coil resonance experiment are reanalyzed. The resulting situation is analogous to partial reduction of wave packet in quantum mechanics. Using convergence results of relative frequencies, magnitudes of the intensity are calculated when prior probabilities are assigned to the coefficients associated with the states.     

A binary solvent of water and propanol for use in high-average power dye lasers

Water is an inherently safe solvent for laser dyes and posses far better photo thermal characteristics in comparison to the commonly used organic solvents in dye lasers. However, water solution of dye needs a suitable deaggregating additive to suppress non-radiative dimers and to achieve similar laser efficiency. We have carried out systematic studies on comparative performances of dye lasers, pumped by low-repetition-rate Nd-YAG, as well as high-repetition-rate copper vapour lasers using Rhodamine 6G dye solutions in ethanol and various binary solvents of water. Among different additives in water, for the first time, the results of our studies on the application of water solvent in dye lasers could clearly establish that binary solvent comprising of normal or heavy water and about 18% to 25% n-propanol has produced similar efficiency, better photochemical stability and superior thermo-optic properties than ethanol solvent in high-repetition rate oscillator-amplifier operation. PACS 42.55.Mv; 32.50.+d; 42.70.jk     

Eigenmodes for electromagnetic waves propagating in a toroidalcavity

A solution has been attempted by means of the Helmholtz equation for an electromagnetic wave propagating in an empty torus in a system of toroidal coordinates. The electromagnetic fields are expressed in terms of the Hertz vector to obtain a scalar Helmholtz equation. The latter has been solved by making use of an inverse aspect ratio expansion of the solution. Unlike most previous workers, the authors have obtained their solutions in terms of hypergeometric functions whose static limit is the toroidal harmonics. The cylindrical solutions in terms of Bessel functions can also be recovered by taking the appropriate large aspect ratio limit. The eigenmodes, with arbitrary toroidal and poloidal mode numbers, have been obtained by applying the boundary conditions on the metallic walls of infinite conductivity, and they cannot be distinguished as TE or TM modes. Eigenfrequencies for various toroidal and poloidal mode numbers are plotted against the inverse aspect ratio. First-order approximations to the fields in the toroidal cavity have also been derived     

Density functional theory study of the geometry, energetics, and reconstruction process of Si111 surfaces

We report the structures and energies from first principles density functional calculations of 12 different reconstructed (111) surfaces of silicon, including the 3x3 to 9x9 dimer-adatom-stacking fault (DAS) structures. These calculations used the Perdew-Burke-Ernzerhof generalized gradient approximation of density functional theory and Gaussian basis functions. We considered fully periodic slabs of various thicknesses. We find that the most stable surface is the DAS 7x7 structure, with a surface energy of 1.044 eV/1x1 cell (1310 dyn/cm). To analyze the origins of the stability of these systems and to predict energetics for more complex, less-ordered systems, we develop a model in which the surface energy is partitioned into contributions from seven different types of atom environments. This analysis is used to predict the surface energy of larger DAS structures (including their asymptotic behavior for very large unit cells) and to study the energetics of the sequential size change (SSC) model proposed by Shimada and Tochihara for the observed dynamical reconstruction of the Si(111) 1x1 structure. We obtain an energy barrier at the 2x2 cell size and confirm that the 7x7 regular stage of the SSC model (corresponding to the DAS 7x7 reconstruction) provides the highest energy reduction per unit cell with respect to the unreconstructed Si111 1x1 surface.     

Spatiotemporal rheochaos in nematic hydrodynamics

Motivated by recent observations of rheochaos in sheared wormlike micelles, we study the coupled nonlinear partial differential equations for the hydrodynamic velocity and order-parameter fields in a sheared nematogenic fluid. In a suitable parameter range, we find irregular, dynamic shear banding and establish by decisive numerical tests that the chaos we observe in the model is spatiotemporal in nature.     

Two-step melting of the vortex solid in layered superconductors with random columnar pins

We consider the melting of the vortex solid in highly anisotropic layered superconductors with a small concentration of random columnar pinning centers. Using large-scale numerical minimization of a free-energy functional, we find that melting of the low-temperature, nearly crystalline vortex solid (Bragg glass) into a vortex liquid occurs in two steps as the temperature increases: the Bragg glass and liquid phases are separated by an intermediate Bose glass phase. A suitably defined local melting temperature exhibits spatial variation similar to that observed in experiments.     

Masking of manganese in relation to stepwise complexometric determination of calcium, magnesium and manganese

A critical study has been made of the masking of manganese with potassium cyanide in alkaline medium for complexometric titration of calcium and magnesium. It has been found that there is incomplete oxidation to manganese(III) unless the solution is aged for a sufficient period or air is bubbled through the solution at 35 ± 5° for 10 min. The manganese(III) complex can be reduced with ascorbic acid for titration with EDTA. Procedures are given for stepwise titration of magnesium, manganese and calcium in silicate materials. Mixed indicators are used, to improve the end-points.     

Synthetic studies towards complex diterpenoids—VI : New synthetic routes to tetracyclic bridged-bicyclo[3.2.1]octane intermediates by intramolecular alkylation reactions through α-diazomethyl ketones of hydroaromatic γ,δ-unsaturated acids

Two new synthetic routes to a number of tetracyclic intermediates, for the total synthesis of some diterpenoids incorporating the bicyclo[3.2.1]octane moiety, are described. The syntheses of the bicyclo[3,2,1]octane derivatives begin with preparation of the hydroaromatic γ,δ-unsaturated acids 6, 15 and 17, and proceed via the α-diazomethyl ketones to the corresponding pentacyclic ketones 20, 24 and 26 by an intramolecular carbenoid insertion reaction, followed by a regiospecific acid-catalysed cleavage of the aromatic conjugated cyclopropane bond to the respective unsaturated ketones 27, 29 and 30. The second route to these unsaturated ketones involves a single step boron trifluoride etherate catalysed intramolecular alkylation in the corresponding α-diazomethyl ketones. The tetracyclic ketones 31, 34 and 35 were obtained in quantitative yields by a regiostereospecific hydrogenolytic cleavage of the aromatic conjugated cyclopropane bond in the respective pentacyclic precursors with PdC in ethanol. Under the same conditions, reduction of the styrenoid bond in the ketones 29 and 30 proceeds stereospecifically leading to 34 and 35 respectively, whereas the unsaturated ketone 27 gave a mixture of epimeric ketones 31 and 32 in a ratio of 69:31.     

Axisymmetric shrink fit problems of the elastic cylinder of finite length

The general case of the axisymmetric shrink fit problems of a solid elastic cylinder whose ends are free from tractions is formulated in terms of the Fredholm integral equation of the second kind. This is accomplished by the use of Papkovich-Fadle eigenfunction and the calculus of residues. Indentation by three types of sleeve is considered; (i) Edge Sleeve, (ii) Symmetrical central Sleeve and, (iii) Two identical edge sleeves. For each case, numerical results of effective resistance and contact pressure are reported for various values of the Poisson's ratio, radius of the cylinder and the sleeve width.

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Zusammenfassung Der allgemeingültige Fall achsensymmetrischer Schrumpf-Anpassungs probleme eines elastischen Festzylinders dessen Enden zugkraftfrei sind wird in der Form der zweiten Integral-gleichung von Fredholm ausgedrückt. Dies wird durch die Anwendung der Papkovich-Fadle Eigenfunktion und der Residuenrechung erreicht. Drei Arten von Manteleinkerbungen werden untersucht: (i) einseitige Endeinkerbung, (ii) symmetrische Zentraleinkerbung, (iii) zweiseitige Endeinkerbung. Für jeden Testfall werden die Zahlenergbnisse des effektiven Winderstandes und des Berührungsdruckes für verschieden Werter der Poisson Ratio, des Zylinderradius und der Mantelkerbweite berichtet.

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The present results were obtained in the course of research supported by NSF Grand GK-25604.