Supernovae and the Arrow of Time

Supernovae are explosions of stars and are a central problem in astrophysics. Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities develop during the star’s explosion and lead to intense interfacial RT/RM mixing of the star materials. We handle the mathematical challenges of the RT/RM problem based on the group theory approach. We directly link the conservation laws governing RT/RM dynamics to the symmetry-based momentum model, derive the model parameters, and find the analytical solutions and characteristics of RT/RM dynamics with variable accelerations in the linear, nonlinear and mixing regimes. The theory outcomes explain the astrophysical observations and yield the design of laboratory experiments. They suggest that supernova evolution is a non-equilibrium process directed by the arrow of time.     

The Morphology of Liquid-Crystalline Polymers and the Possible Consequences for their Rheological Behaviour

Abstract

Polymer liquid crystals can occur as polydomain materials where the domain size may be tens of microns. While the material within each domain may be characterized by a common order parameter, the directors of the domains can be more or less randomly distributed. Since the transition from polydomain to monodomain material only involves the removal of grain boundaries and the alignment of directors, the free energy change must necessarily be small. Such a transition can readily be achieved, therefore, by the action of any external field: electrical, magnetic, stress or surface. In this work optical photomicrographs of polymeric liquid crystals with widely varying and in some cases well controlled morphologies are presented. Probable dependence of rheological behaviour on morphology is also discussed. Such dependence is expected to be considerable under certain conditions. Due to experimental and sample limitations, however, direct correlations of rheology and morphology are sparse. Morphological consequences for the rheology of liquid-crystalline materials can be exemplified by the following possibilities. In contrast to the case of isotropic melts, wall effects can be non-negligible. Zero shear rate rheological parameters are not expected to be uniquely defined quantities since the domain sizes are large and the director may not be effectively averaged over typical sample dimensions. Non-zero shear-rate measurements of rheological parameters is effected by the propensity of: (1) individual domain directors to align under the influence of a stress field and (2) flow alignment to dominate surface-induced alignment above some critical shear rate. The effects might be manifested by a non-newtonian regime as well as yield stress behaviour and thixotropy. The kinetics of relaxation from mono- to poly-domain material has implications for the dynamic response and rheological hysterises of the material.     

Fibrous twists and turns: early ceramic technology revealed through computed tomography

While the emergence of pottery manufacturing is a wide-spread historical occurrence, and one that has garnered the attention of archaeologists for decades, we know very little about how these ancient vessels were created. Through the application of radiographic scanning and computed tomography this paper provides insights into the manufacturing techniques used by the earliest potters in North America. While x-rays have been used to investigate ceramic manufacturing techniques for decades, this paper provides a reassessment of radiography in light of advances in both computed tomography and reconstructive software.     

Analysis of Carbamates as Fluorescent 1-Dimethylamino-naphthalene-5-sulfonate Esters

The fluorigenic labelling of several N-methyl carbamates is carried out using 1-dimethyl-aminonaphthalene-5-sulfonyl chloride (dansyl chloride). Prior to chromatography the carbamates are reacted in aqueous solution with the dansyl chloride. The derivative is extracted from the solution with n-hexane and subsequently spotted on a thin-layer plate for chromatography. For each N-methyl carbamate, two highly fluorescent spots are obtained. One is common to all N-methyl carbamates studied, whereas the other is characteristic of each individual carbamate. N.m.r. and infrared spectroscopic data indicate that the common spot is the methylamine derivative, and the second spot is the derivative from the phenyl moiety of each carbamate. The sensitivity of the method is less than one nanogram and has been successfully applied to the analysis of natural water samples.     

Synthesis of a (thienylethenyl)benzimidazole platinum acetylide complex

A new platinum acetylide complex based on 6-dialkylaminobenzimidazol-2-yl-vinyl-2-thiophene-5-ylethyne was synthesized in seven steps and 2% overall yield.     

Molecular dynamics simulations of solid state recrystallization I: Observation of grain growth in annealed iron nanoparticles

Molecular dynamics simulations of solid state recrystallization and grain growth in iron nanoparticles containing 1436 atoms were carried out. During the period of relaxation of supercooled liquid drops and during thermal annealing of the solids they froze to, changes in disorder were followed by monitoring changes in energy and the migration of grain boundaries. All 27 polycrystalline nanoparticles, which were generated with different grain boundaries, were observed to recystallize into single crystals during annealing. Larger grains consumed the smaller ones. In particular, two sets of solid particles, designated as A and B, each with two grains, were treated to generate 18 members of each set with different thermal histories. This provided small ensembles (of 18 members each) from which rates at which the larger grain engulfed the smaller one, could be determined. The rate was higher, the smaller the degree of misorientation between the grains, a result contrary to the general rule based on published experiments, but the reason was clear. Crystal A, which happened to have a somewhat lower angle of misorientation, also had a higher population of defects, as confirmed by its higher energy. Accordingly, its driving force to recrystallize was greater. Although the mechanism of recrystallization is commonly called nucleation, our results, which probe the system on an atomic scale, were not able to identify nuclei unequivocally. By contrast, our technique can and does reveal nuclei in the freezing of liquids and in transformations from one solid phase to another. An alternative rationale for a nucleation-like process in our results is proposed.     

Normal families and uniqueness theorems for entire functions

There exists a set S with 3 elements such that if f is a non-constant entire function satisfying E(S,f)=E(S,f′), then f≡f′. The number 3 is best possible. The proof uses the theory of normal families in an essential way.     

An Application of Branch and Cut to Open Pit Mine Scheduling

The economic viability of the modern day mine is highly dependent upon careful planning and management. Declining trends in average ore grades, increasing mining costs and environmental considerations will ensure that this situation will remain in the foreseeable future. The operation and management of a large open pit mine having a life of several years is an enormous and complex task. Though a number of optimization techniques have been successfully applied to resolve some important problems, the problem of determining an optimal production schedule over the life of the deposit is still very much unresolved. In this paper we will critically examine the techniques that are being used in the mining industry for production scheduling indicating their limitations. In addition, we present a mixed integer linear programming model for the scheduling problems along with a Branch and Cut solution strategy. Computational results for practical sized problems are discussed.