Hydrodynamic and hydromagnetic stability of black holes with radiative transfer

Subrahmanyan Chandrasekhar (Chandra) was just eight years old when the first astrophysical jet was discovered in M87. Since then, jets have been uncovered with a wide variety of sources including accretion disks orbiting stellar and massive black holes, neutron stars, isolated pulsars, γ-ray bursts, protostars and planetary nebulae. This talk will be primarily concerned with collimated hydromagnetic outflows associated with spinning, massive black holes in active galactic nuclei. Jets exhibit physical processes central to three of the major research themes in Chandrasekhar’s research career – radiative transfer, magnetohydrodynamics and black holes. Relativistic jets can be thought of as ‘exhausts’ from both the hole and its orbiting accretion disk, carrying away the energy liberated by the rotating spacetime and the accreting gas that is not radiated. However, no aspect of jet formation, propagation and radiation can be regarded as understood in detail. The combination of new γ-ray, radio and optical observations together with impressive advances in numerical simulation make this a good time to settle some long-standing debates.     

Production planning towards the end of a product life cycle

Previously published papers have derived optimal policies forreplenishing stock when demand is declining according to somedeterministic law. Here we elaborate on that work, providinga full analysis, and extend the analysis back in time by consideringthe period of relatively level demand which is likely to havepreceded the period of decline in demand. We show how optimalinventory replenishment policies extending back to this periodof level demand can be derived.     

Crystalline forms of cellulose in the silver tree fern Cyathea dealbata

Solid-state ¹³C NMR spectroscopy was used to characterize fibrous material cut from the midrib of a fern frond. Signals associated with cellulose crystallites were separated from those associated with the lignin--hemicellulosic matrix by exploiting differences in proton rotating-frame relaxation time constants. Heights of signals at 90.2 and 88.5 ppm, assigned to C-4 in cellulose I_α and I_β, indicated similar proportions of the two crystalline forms. This observation conflicts with a suggestion that plant celluloses can be grouped into the two categories of I_α-rich and I_β-rich. This revised version was published online in August 2006 with corrections to the Cover Date.     

Computing Derivatives of Eigensystems by the Vector {varepsilon}-Algorithm

Rudisill & Chu proposed a (slowly converging) iterativemethod for computing partial derivatives of eigenvalues andeigenvectors of parameter-dependent matrices. It is shown that,with exact computation, application of the vector -algorithmto this method produces the exact solution in a small numberof steps. Numerical results demonstrate the viability of thismethod. A refinement process is suggested which makes the methodespecially effective for subdominant eigenvalues.     

Electrolysis and isoelectric focusing

This paper consists of two parts. In the first part, the authorsprove the existence of steady-state solutions for a three-specieselectrolyte. The species are subject to both dissociation-associationreactions inside the electrolyte and electrochemical reactionsat the boundary electrodes. This is a common occurrence in electrolysis.In the second part, the authors investigate how to use thismodel to describe isoelectric focusing, which is a common techniqueused to separate large protein molecules. In particular, theisoelectric focusing point for a particular type of proteinmolecule is calculated using formal perturbation analysis.     

Simulation of hydrogen adsorption in carbon nanotubes

Computer simulations are reported of hydrogen adsorption in multi-walled carbon nanotubes (MWNTs) and single-walled carbon nanotubes (SWNTs). The gas-solid interaction was modelled both as pure dispersion forces and also with a hypothetical model for chemisorption introduced in a previous paper (CRACKNELL, R., F., 2001, Phys. Chem. chem. Phys., 3, 2091). A two-centre model for hydrogen was employed and the grand canonical Monte Carlo methodology was used throughout. Uptake of hydrogen in the internal space of a carbon nanotube is predicted to be lower than in the optimal graphitic nanofibre with slitlike pores (provided the gas-solid potential is consistent). Part of the difference arises from the assumption of pore surface area used in converting the raw simulation data to gravimetric adsorption; however, the majority of the differences can be attributed to the curvature of the pore. This reduces the uptake of hydrogen (on a gravimetric basis) in spite of deepening the potential minimum inside the pore associated with dispersion forces. It is concluded that for the uptake of hydrogen in SWNTs of 5–10% reported by Heben (DILLON, A. C., JONES, K. M., BEKKEDAHL, T. A., KIANG, C. H., BETHUNE, D. S., AND HEBEN, M. J., 1997, Nature, 386, 377), gas-solid forces other than dispersion forces are required and most of the adsorption must occur in the interstices between SWNTs.