Relative equilibria for the generalized rigid body

This paper gives necessary and sufficient conditions for the (n-dimensional) generalized free rigid body to be in a state of relative equilibrium. The conditions generalize those for the case of the three-dimensional free rigid body, namely that the body is in relative equilibrium if and only if its angular velocity and angular momentum align, that is, if the body rotates about one of its principal axes. For the n-dimensional rigid body in the Manakov formulation, these conditions have a similar interpretation. We use this result to state and prove a generalized Saari’s Conjecture (usually stated for the N-body problem) for the special case of the generalized rigid body

Electron impact excitation of N IV: calculations with the DARC code and a comparison with ICFT results

There have been discussions in the recent literature regarding the accuracy of the available electron impact excitation rates (equivalently effective collision strengths $\Upsilon$) for transitions in Be-like ions. In the present paper we demonstrate, once again, that earlier results for $\Upsilon$ are indeed overestimated (by up to four orders of magnitude), for over 40\% of transitions and over a wide range of temperatures. To do this we have performed two sets of calculations for N~IV, with two different model sizes consisting of 166 and 238 fine-structure energy levels. As in our previous work, for the determination of atomic structure the GRASP (General-purpose Relativistic Atomic Structure Package) is adopted and for the scattering calculations (the standard and parallelised versions of) the Dirac Atomic R-matrix Code ({\sc darc}) are employed. Calculations for collision strengths and effective collision strengths have been performed over a wide range of energy (up to 45~Ryd) and temperature (up to 2.0$\times$10$^6$~K), useful for applications in a variety of plasmas. Corresponding results for energy levels, lifetimes and A-values for all E1, E2, M1 and M2 transitions among 238 levels of N~IV are also reported.Comment: This paper with 5 Figs. and 8 Tables will appear in MNRAS (2016

Implementation of a block Lanczos algorithm for Eigenproblem solution of gyroscopic systems

The details of implementation of a general numerical procedure developed for the accurate and economical computation of natural frequencies and associated modes of any elastic structure rotating along an arbitrary axis are described. A block version of the Lanczos algorithm is derived for the solution that fully exploits associated matrix sparsity and employs only real numbers in all relevant computations. It is also capable of determining multiple roots and proves to be most efficient when compared to other, similar, exisiting techniques

Isostatic compression process converts polyaromatics into structural material

Isostatic compression process compacts certain powdered aromatic polymers into homogeneous materials that can be machined to form useful components, such as bearings. It provides for complete removal of air in the interstitial spaces surrounding the granules of the powdered polymer before the powder is subjected to isostatic compression

Solubility of Sulfur Dioxide in Sulfuric Acid

The solubility of sulfur dioxide in 50% (wt./wt.) sulfuric acid was evaluated by regular solution theory, and the results verified by experimental measurements in the temperature range of 25 C to 70 C at pressures of 60 to 200 PSIA. The percent (wt./wt.) of sulfur dioxide in 50% (wt./wt.) sulfuric acid is given by the equation %SO2 = 2.2350 + 0.0903P - 0.00026P 10 to the 2nd power with P in PSIA

Carbon and titanium diboride (TiB2) multilayer coatings.

Titanium Diboride, (TiB2) is a metal-based refractory ceramic material that has been investigated in industrial applications ranging from, cutting tools to wear parts and for use in the aerospace industry. The unique properties which make this material so fascinating are, its high hardness, high melting point and its corrosion resistance. TiB2 is prevented from wider mainstream use because of its inherent brittle nature. With a view to overcome this in coating form and with the aim of providing in addition inherent lubricity, in this study 50 layer TiB2/C multilayer stacks have been fabricated, with varying volume fractions of ceramic, whereby the interfaces of the layers limit crack propagation in the TiB2 ceramic. TiB2 has been multilayered with carbon, to make use of the unique and hybrid nature of the bonding in carbon coatings. DC magnetron sputtering with substrate bias was the preferred route for the fabrication of these coatings. AISI tool steel has been used as the substrate material. By varying the amount of TiB2 ceramic from 50% to 95%, the Hardness of the coating is seen to increase from 5 GPa to 17GPa. The Hardness is observed to decrease as a function of increasing carbon content, agreeing with other studies that the carbon layers are not load-bearing. The graphitic nature of the sp2 bond, however, acts as a lubricant layer

Extreme ultraviolet emission lines of Ni XII in laboratory and solar spectra

Wavelengths for emission lines arising from 3s23p5-3s3p6 and 3s23p5-3s23p43d transitions in Ni XII have been measured in extreme ultraviolet spectra of the Joint European Torus(JET) tokamak. The 3s23p5 2P1/2-3s23p4(3P)3d 2D3/2 line is found to lie at 152.90 ± 0.02 A, a significant improvement over the previous experimental determination of 152.95 ± 0.5 A. This new wavelength is in good agreement with a solar identification at 152.84 ± 0.06 A, confirming the presence of this line in the solar spectrum. The Ni XII feature at 152.15 A may be a result only of the 3s23p5 2P3/2-3s23p4(3P)3d 2D5/2 transition, rather than a blend of this line with 3s23p5 2P3/2-3s23p (3P)3d 2P1/2, as previously suggested. Unidentified emission lines at 295.32 and 317.61 A in solar flare spectra from the Skylab mission are tentatively identified as the 3s23p5 2P3/2-3s3p6 2S1/2 and 3s23p5 2P1/2-3s3p6 2S1/2 transitions in Ni XII, which have laboratory wavelengths of 295.33 and 317.50 A, respectively. Additional support for these identifications is provided by the line intensity ratio for the solar features, which shows good agreement between theory and observation

A two-dimensional mathematical model of percutaneous drug absorption

Background When a drug is applied on the skin surface, the concentration of the drug accumulated in the skin and the amount of the drug eliminated into the blood vessel depend on the value of a parameter, r. The values of r depend on the amount of diffusion and the normalized skin-capillary clearence. It is defined as the ratio of the steady-state drug concentration at the skin-capillary boundary to that at the skin-surface in one-dimensional models. The present paper studies the effect of the parameter values, when the region of contact of the skin with the drug, is a line segment on the skin surface. Methods Though a simple one-dimensional model is often useful to describe percutaneous drug absorption, it may be better represented by multi-dimensional models. A two-dimensional mathematical model is developed for percutaneous absorption of a drug, which may be used when the diffusion of the drug in the direction parallel to the skin surface must be examined, as well as in the direction into the skin, examined in one-dimensional models. This model consists of a linear second-order parabolic equation with appropriate initial conditions and boundary conditions. These boundary conditions are of Dirichlet type, Neumann type or Robin type. A finite-difference method which maintains second-order accuracy in space along the boundary, is developed to solve the parabolic equation. Extrapolation in time is applied to improve the accuracy in time. Solution of the parabolic equation gives the concentration of the drug in the skin at a given time. Results Simulation of the numerical methods described is carried out with various values of the parameter r. The illustrations are given in the form of figures. Conclusion Based on the values of r, conclusions are drawn about (1) the flow rate of the drug, (2) the flux and the cumulative amount of drug eliminated into the receptor cell, (3) the steady-state value of the flux, (4) the time to reach the steady-state value of the flux and (5) the optimal value of r, which gives the maximum absorption of the drug. The paper gives valuable information which can be obtained by this two-dimensional model, that cannot be obtained with one-dimensional models. Thus this model improves upon the much simpler one-dimensional models. Some future directions of the work based on this model and the one-dimensional non-linear models that exist in the literature, are also discussed

A Pilot Training Program for Improving Resident Physicians\u27 Teaching Skills

Purpose. The purpose of this study was to design, implement, and evaluate a pilot training program on teaching skills and determine if such a program could significantly improve the teaching behavior of resident physicians in the East Tennessee State University College of Medicine. (Abstract shortened.