Improved experimental tracking techniques for validating discrete element method simulations of tumbling mills

We report on further developments in the three-dimensional tracking of a particle deep within the tumbling ball charge of an experimental mill. The experimental X-ray program employing the use of bi-planar X-ray angiography now includes the tracking of a typical 6 mm bulk charge particle in three dimensions with a spatial resolution that is accurate to within 0.15 mm. The improved experimental tracking techniques presented were developed for the purpose of generating accurate three-dimensional particle trajectory data against which to validate a numerical method for the simulation of discrete media, namely the discrete element method (DEM). These improvements are complimented with techniques for comparing charge profiles between numerical DEM simulations and three-dimensional experimental trajectory data.     

On Ultrasmall Nanocrystals

Ultrasmall nanocrystals are a growing sub-class of traditional nanocrystals that exhibit new properties at diameters typically below 2 nm. In this review, we define what constitutes an ultrasmall nanoparticle while distinguishing between ultrasmall and magic-size nanoparticles. After a brief overview of ultrasmall nanoparticles, including ultrasmall gold clusters, our recent work is presented covering the optical properties, structure, and application of ultrasmall CdSe nanocrystals. This unique material has potential application in solid state lighting due to its balanced white emission. This section is followed by a discussion on the blurring boundary between what can be considered a nanoparticle and a molecule.     

Derivations and spectral triples on quantum domains II: Quantum annulus

Science China Mathematics - Continuing our study of spectral triples on quantum domains, we look at unbounded invariant and covariant derivations in the quantum annulus. In particular, we...     

Gårding's Theory of Hyperbolic Polynomials

This paper presents a simple, self‐contained account of Gårding's theory of hyperbolic polynomials, together with a recent convexity result of Bauschke‐Güler‐Lewis‐Sendov and an inequality of Gurvits. This account begins by establishing some new results. The first concerns the existence of a pointwise arrangement of the eigenvalues so that they become global real analytic functions. The second asserts that the associated “branches” are independent of the choice of hyperbolic direction. © 2013 Wiley Periodicals, Inc.     

Condensation of zinc vapor in a supersonic carrier gas

A study of the condensation of a metal vapor in an inert carrier gas is made. Superheated zinc vapor is generated in a hot shot wind tunnel in a helium carrier gas and expanded in a converging-diverging nozzle. Static pressure measurements along the length of the nozzle are made to determine the location of the onset of condensation. A conical nominal Mach 5 (helium) nozzle is employed. The amount of supercooling before the onset of condensation is found to be approximately 430 K, measured along the isentrope over a range of initial zinc mass fractions of .35 to .70 for saturation partial pressures of zinc between 10 psia and 70 psia. The measurements are compared with results of an analysis based on the classical liquid drop model of nucleation. The computed results agree reasonably well with the measurements.     

Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion

Surfaces can have a significant influence on the overall response of a continuum body but are often neglected or accounted for in an ad hoc manner. This work is concerned with a nonlinear continuum thermomechanics formulation which accounts for surface structures and includes the effects of diffusion and viscoelasticity. The formulation is presented within a thermodynamically consistent framework and elucidates the nature of the coupling between the various fields, and the surface and the bulk. Conservation principles are used to determine the form of the constitutive relations and the evolution equations. Restrictions on the jump in the temperature and the chemical potential between the surface and the bulk are not a priori assumptions, rather they arise from the reduced dissipation inequality on the surface and are shown to be satisfiable without imposing the standard assumptions of thermal and chemical slavery. The nature of the constitutive relations is made clear via an example wherein the form of the Helmholtz energy is explicitly given.     

Optically Anomalous Crystals

The optical symmetry of many crystals is lower than would be expected from their external form and X-ray diffraction data. Recently such optical anomalies have been attributed to nonequilibrium structures resulting from kinetically controlled crystal growth. Impurities are incorporated to different extents at various surface sites that would otherwise have become symmetry-related within the bulk crystal. After their discovery by Brewster in 1815, optically anomalous crystals were the subject of lively debate throughout the 19th century among some of the most distinguished contributors to the development of crystallography including Biot, Berzelius, Herschel, Mitscherlich, Frankenheim, Pasteur, Mallard, Klein, Groth, Wyrouboff, Barlow, Brauns, Rinne, Pockels, and Friedel. From a sea of wild speculation two conflicting postulates emerged: that the symmetric form resulted from accidental twinning of segments with lower symmetry, or that the optical peculiarities resulted from stress due to impurities or external perturbations. Neither postulate expresses the present view. Interest in this research waned at the turn of the century, and after 1917 no one pursued Tammann's alternative correct insight. The problem of anomalous double refraction attracted no attention for more than half a century until its recent solution. This review discusses both mineral and organic systems with particular emphasis on the phyllosilicate apophyllite and on 1,5-dichloro-2,3-dinitrobenzene. These nonequilibrium structures relate to questions of crystal order, crystal growth, molecular recognition, and the design of new materials. The review provides a reminder of the enduring value of the polarizing microscope as a research tool in chemistry.