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.     

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.     

A finite-difference algorithm for an inverse Sturm-Liouville problem

We study a method for approximating a potential q(x) in y(0)=y()=0 from finite spectral data. When the potential is symmetric,the data are the first M Dirichlet eigenvalues. In the generalcase, the first M terminal velocities are also specified. Acentred finite-difference scheme reduces the inverse Sturm-Liouvilleproblem to a matrix inverse eigenvalue problem. Our approachis motivated by the work of Paine, de Hoog and Anderssen, whoinvestigated the discrepancy between continuous and matrix eigenvaluesunder finite differences. Our modified Newton scheme is basedon choosing the number of interior mesh points in the discretizationto be 2M. The modified Newton scheme is shown to be convergentfor both the case of a symmetric and general potential. Somenumerical experiments are given. Supported in part by Institute for Scientific Computation,Texas A&M University.     

INTRAVENOUS vs INTRAPERITONEAL SENSITIZER: IMPLICATIONS FOR INTRAPERITONEAL PHOTODYNAMIC THERAPY

Photodynamic therapy (PDT) is a potential treatment for peritoneal carcinomatosis. However, little data is available regarding the relative distribution of sensitizer to tumor and intra-abdominal organs, optimal route of sensitizer administration, and maximal tolerated light dose. Tumor and normal tissue sensitizer levels were measured by tissue extraction 3, 24, 48 and 72 h after 10 mg/kg of Photofrin II was given intraperitoneally (IP) or intravenously (IV) in a mouse peritoneal tumor model, and the maximal tolerated PDT light dose determined. Equivalent tumor sensitizer levels were obtained regardless of the route of sensitizer administration. Route of administration, however, did affect the kinetics of tumor sensitizer elimination, with the half-time for elimination (T1/2) 113.6 h for IP drug and 60.6 h for IV drug. Route of administration also affected sensitizer levels in several intra-abdominal organs, resulting in somewhat higher tumor to liver and kidney levels at 24 and 72 h after IP sensitizer administration. Despite these tissue distribution differences, route of sensitizer administration did not significantly affect PDT toxicity or mortality when mice were treated with 630 nm light. The maximum tolerated light dose was 1.04 J/cm2. These parameters will prove helpful in designing large scale animal trials assessing the efficacy and safety of intra-abdominal PDT.     

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.