A Monster Lie algebra?

This paper defines a remarkable Lie algebra of infinite dimension and rank, and conjectures that it may be related to the Fischer-Griess Monster group.     

Finite-dimensional points of continuity of Lat

Associated with every linear transformation A on a finite-dimensional vector space V there is a collection Lat A of subspaces of V, namely the subspaces invariant under A. The collection lat A always contains the (trivial) subspace 0 and the (improper) subspace V. Since, moreover, it is closed under the formation of intersections and spans, it forms a lattice with respect to those operations (whence its name). The purpose of this paper is to interpret and to prove the following assertion: anecessary and sufficient condition that a linear transformation on a finite-dimensionalcomplex vector space be a point of continuity of Lat is that it be non-derogatory. The assumption that the underlying coefficient field is the set of complex numbers is maintained throughout.     

Free surface waves in wall-bounded granular flows

We report free-surface waves in granular flows near boundaries in an inclined chute. The chevron-shaped traveling waves spontaneously develop at inclinations close to the angle of repose for both steady and accelerating flows. Two distinct regimes are characterized by internal angle and frequency variations. Experimental measurements indicate that subsurface circulation driven by velocity gradients near frictional walls plays a central role in the pattern formation mechanism, suggesting that wave generation is controlled by the granular analog of a fluid boundary layer.     

Carbon nanotubes formed in graphite after mechanical grinding and thermal annealing

Multi-walled carbon nanotubes with cylindrical and bamboo-type structures are produced in a graphite sample after mechanical milling at ambient temperature and subsequent thermal annealing up to 1400 °C. The ball milling produces a precursor structure and the thermal annealing activates the nanotube growth. Different nanotubular structures indicate different formation mechanisms: multi-wall cylindrical carbon nanotubes are probably formed upon micropores and the bamboo tubes are produced because of the metal catalysts. A two-dimensional growth governed by surface diffusion is believed to be one important factor for the nanotube growth. A potential industrial production method is demonstrated with advantages of large production quantity and low cost. Received: 17 May 2002 / Accepted: 12 September 2002 / Published online: 4 December 2002 RID="*" ID="*"Corresponding author. Fax: +61-2/6125-8338, E-mail: ying.chen@anu.edu.au     

Suppression of plasma turbulence during optimized shear configurations in JET

Correlation of density turbulence suppression and reduced plasma transport is observed in the internal transport barrier (ITB) region of JET tokamak discharges with optimized magnetic shear. The suppression occurs in two stages. First, low frequency turbulence and ion transport are reduced across the plasma core by a toroidal velocity shear generated by intense auxiliary heating. Then with the ITB formation, high frequency turbulence and electron transport are reduced locally within the steep pressure gradient region of the ITB.     

The formation and decay of shocks for a conservation law in several dimensions

Archive for Rational Mechanics and Analysis -     

Indefinite integrals of products of special functions

A method is given for deriving indefinite integrals involving squares and other products of functions which are solutions of second-order linear differential equations. Several variations of the method are presented, which applies directly to functions which obey homogeneous differential equations. However, functions which obey inhomogeneous equations can be incorporated into the products and examples are given of integrals involving products of Bessel functions combined with Lommel, Anger and Weber functions. Many new integrals are derived for a selection of special functions, including Bessel functions, associated Legendre functions, and elliptic integrals. A number of integrals of products of Gauss hypergeometric functions are also presented, which seem to be the first integrals of this type. All results presented have been numerically checked with Mathematica.     

Scattered-light analysis of a surface-flawed plate subjected to cylindrical bending

The scattered-light photoelastic technique was utilized to determine Mode I stress-intensity factors associated with a semi-elliptical surface flaw in a plate subjected to cylindrical bending. Stress-intensity factors were experimentally determined for the point of maximum flaw penetration and the point of intersection of the flaw border with the free surface of the plate. Experimental results compare favorably with those obtained in a three-dimensional finite-element analysis.     

Service life of counter-current chromatography coils

A multilayer coil of PTFE tubing, which failed after being used each workday for about 3 years in a type J centrifuge, was examined. Two types of defects were found. One, called crazes, occurs throughout the coil and does not leak initially, but may eventually lead to a short, axially oriented slit. Another, called indentations, is seen primarily in the innermost and other nearby layers. They are elongated, about 5 mm, indentations, usually on the central side of the tubing. These eventually crack and leak. PTFE tubing is permeable to air and hexane and expands by more than 1% when immersed in hexane, heptane or chloroform for a few days. It is suggested that the crazes result from exposure of the somewhat flexible tubing to the undulating centripetal force field in the coil-planet centrifuge, especially when further softened by solvent absorption. The indentations may result from carriage of the excess tubing length, created by solvent absorption, from the coil periphery to the coil center by the centripetal force field, which continuously travels from the peripheral tail to the central head of the coil. A 1% increase in coil length creates 74 cm of excess tubing in the 160-ml coils examined in this study. It is suggested that fluorinated ethylene propylene (FEP) tubing, especially when etched on the outside, may provide more stable CCC coils, since its expansion when exposed to organic solvents is 0.1 or less than that of PTFE.