Influence of crossed electric and quantizing magnetic fields on the Einstein relation in nonlinear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestion for experimental determination

An attempt is made to study the Einstein relation for the diffusivity-to-mobility ratio (DMR) under crossed fields' configuration in nonlinear optical materials on the basis of a newly formulated electron dispersion law by incorporating the crystal field in the Hamiltonian and including the anisotropies of the effective electron mass and the spin-orbit splitting constants within the framework of kp formalisms. The corresponding results for III-V, ternary and quaternary compounds form a special case of our generalized analysis. The DMR has also been investigated for II-VI and stressed materials on the basis of various appropriate dispersion relations. We have considered n-CdGeAs2, n-Hg1-xCdxTe, n-In1-xGaxAsyP1-y lattice matched to InP, p-CdS and stressed n-InSb materials as examples. The DMR also increases with increasing electric field and the natures of oscillations are totally band structure dependent with different numerical values. It has been observed that the DMR exhibits oscillatory dependences with inverse quantizing magnetic field and carrier degeneracy due to the Subhnikov-de Haas effect. An experimental method of determining the DMR for degenerate materials in the present case has been suggested. (C) 2010 Elsevier B.V. All rights reserved.

High temperature deformation processing maps for boron modified Ti-6Al-4V alloys

The alloy, Ti-6Al-4V is an alpha + beta Ti alloy that has large prior beta grain size (similar to 2 mm) in the as cast state. Minor addition of B (about 0.1 wt.%) to it refines the grain size significantly as well as produces in-situ TiB needles. The role played by these microstructural modifications on high temperature deformation processing maps of B-modified Ti64 alloys is examined in this paper.Power dissipation efficiency and instability maps have been generated within the temperature range of 750-1000 degrees C and strain rate range of 10(-3)-10(+1) s(-1). Various deformation mechanisms, which operate in different temperature-strain rate regimes, were identified with the aid of the maps and complementary microstructural analysis of the deformed specimens. Results indicate four distinct deformation domains within the range of experimental conditions examined, with the combination of 900-1000 degrees C and 10(-3)-10(-2) s(-1) being the optimum for hot working. In that zone, dynamic globularization of alpha laths is the principle deformation mechanism. The marked reduction in the prior beta grain size, achieved with the addition of B, does not appear to alter this domain markedly. The other domains, with negative values of instability parameter, show undesirable microstructural features such as extensive kinking/bending of alpha laths and breaking of beta laths for Ti64-0.0B as well as generation of voids and cracks in the matrix and TiB needles in the B-modified alloys. (C) 2010 Elsevier B.V. All rights reserved.

Gauge theory of a group of diffeomorphisms. III. The fiber bundle description

A new fiber bundle approach to the gauge theory of a group G that involves space‐time symmetries as well as internal symmetries is presented. The ungauged group G is regarded as the group of left translations on a fiber bundle G(G/H,H), where H is a closed subgroup and G/H is space‐time. The Yang–Mills potential is the pullback of the Maurer–Cartan form and the Yang–Mills fields are zero. More general diffeomorphisms on the bundle space are then identified as the appropriate gauged generalizations of the left translations, and the Yang–Mills potential is identified as the pullback of the dual of a certain kind of vielbein on the group manifold. The Yang–Mills fields include a torsion on space‐time.

Theoretical Estimation of Length Dependent In-Plane Stiffness of Single Walled Carbon Nanotubes Using the Nonlocal Elasticity Theory

In the present paper, Eringen's nonlocal elasticity theory is employed to evaluate the length dependent in-plane stiffness of single-walled carbon nanotubes (SWCNTs). The SWCNT is modeled as an Euler-Bernoulli beam and is analyzed for various boundary conditions to evaluate the length dependent in-plane stiffness. It has been found that the nonlocal scaling parameter has a significant effect on the length dependent in-plane stiffness of SWCNTs. It has been observed that as the nonlocal scale parameter increases the stiffness ratio of SWCNT decreases. In nonlocality, the cantilever SWCNT has high in-plane stiffness as compared to the simply-supported and the clamped cases.

Partially conserved axial-vector current inS-matrix theory

Mandelstam�s argument that PCAC follows from assigning Lorentz quantum numberM=1 to the massless pion is examined in the context of multiparticle dual resonance model. We construct a factorisable dual model for pions which is formulated operatorially on the harmonic oscillator Fock space along the lines of Neveu-Schwarz model. The model has bothm ? andm ? as arbitrary parameters unconstrained by the duality requirement. Adler self-consistency condition is satisfied if and only if the conditionm?2?m?2=1/2 is imposed, in which case the model reduces to the chiral dual pion model of Neveu and Thorn, and Schwarz. The Lorentz quantum number of the pion in the dual model is shown to beM=0.

Parametrized tests of post-Newtonian theory using Advanced LIGO and Einstein Telescope

General relativity has very specific predictions for the gravitational waveforms from inspiralling compact binaries obtained using the post-Newtonian (PN) approximation. We investigate the extent to which the measurement of the PN coefficients, possible with the second generation gravitational-wave detectors such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and the third generation gravitational-wave detectors such as the Einstein Telescope (ET), could be used to test post-Newtonian theory and to put bounds on a subclass of parametrized-post-Einstein theories which differ from general relativity in a parametrized sense. We demonstrate this possibility by employing the best inspiralling waveform model for nonspinning compact binaries which is 3.5PN accurate in phase and 3PN in amplitude. Within the class of theories considered, Advanced LIGO can test the theory at 1.5PN and thus the leading tail term. Future observations of stellar mass black hole binaries by ET can test the consistency between the various PN coefficients in the gravitational-wave phasing over the mass range of 11-44M(circle dot). The choice of the lower frequency cutoff is important for testing post-Newtonian theory using the ET. The bias in the test arising from the assumption of nonspinning binaries is indicated.

Superconformal transformations of theN=4 supersymmetric Yang-Mills theory

We obtain the superconformal transformation laws of theN=4 supersymmetric Yang-Mills theory and explicitly demonstrate the closure of the algebra.

Confirmation of pauling's theory that vitamin C improves immunity to infection

It is pointed out that the complement Clq, associated with the immune response system, has a part containing about 80 residues with a collagen-like sequence, with Gly at every third location and having also a number of Hyp and Hyl residues in locations before Gly, and that it takes the triple-helical conformation characteristic of collagen. As with collagen biosynthesis, ascorbic acid is therefore expected to be required for its production. Also, collagen itself, in the extracellular matrix, is connected with the fibroblast surface protein (FSP), whose absence leads to cell proliferation, and whose addition leads to suppression of malignancy in tissue culture. All these show the great importance of vitamin C for resistance to diseases, and even to cancer, as has been widely advocated by Pauling.

A Comprehensive Theory of Erosive Burning in Solid Rocket Propeilants

The theory of erosive burning has been constructed front first principles using turbulent boundary layer concepts. It is shown that the problem constitutes one of solution of flame propagation equation for turbulent flow. The final approximate solution for the case of single step overall kinetics reveals the combined effects of fluid mechanics and chemical kinetics. The results obtained from this theory are compared with earlier experimental results. The dependence of erosive burning characteristics on various parameters has been elucidated.

Topological defects in crystals: A density-wave theory

A new approach for describing dislocations and other topological defects in crystals, based on the density wave theory of Ramakrishnan and Yussouff is presented. Quantitative calculations are discussed in brief for the order parameter profiles, the atomic configuration and the free energy of a screw dislocation with Burgers vector b = (a/2, a/2,a/2 ) in a bcc solid. Our results for the free energy of the dislocation in a crystal of sizeR, when expressed as (λb 2/4π) ln (αR/|b|) whereλ is the shear elastic constant, yield, for example, the valueα ⋍ 1·85 for sodium at its freezing temperature (371°K). The density distribution in the presence of the dislocation shows that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order parameter theory incorporating thermal effects.