Long term stable integration of a maximally sliced Schwarzschild black hole using a smooth lattice method

We will present results of a numerical integration of a maximally sliced Schwarzschild black hole using a smooth lattice method. The results show no signs of any instability forming during the evolutions to t=1000m. The principle features of our method are i) the use of a lattice to record the geometry, ii) the use of local Riemann normal coordinates to apply the 1+1 ADM equations to the lattice and iii) the use of the Bianchi identities to assist in the computation of the curvatures. No other special techniques are used. The evolution is unconstrained and the ADM equations are used in their standard form.Comment: 47 pages including 26 figures, plain TeX, also available at http://www.maths.monash.edu.au/~leo/preprint

Peptide Sequence and Conformation Strongly Influence Tryptophan Fluorescence

AbstractThis article probes the denatured state ensemble of ribonuclease Sa (RNase Sa) using fluorescence. To interpret the results obtained with RNase Sa, it is essential that we gain a better understanding of the fluorescence properties of tryptophan (Trp) in peptides. We describe studies of N-acetyl-L-tryptophanamide (NATA), a tripeptide: AWA, and six pentapeptides: AAWAA, WVSGT, GYWHE, HEWTV, EAWQE, and DYWTG. The latter five peptides have the same sequence as those surrounding the Trp residues studied in RNase Sa. The fluorescence emission spectra, the fluorescence lifetimes, and the fluorescence quenching by acrylamide and iodide were measured in concentrated solutions of urea and guanidine hydrochloride. Excited-state electron transfer from the indole ring of Trp to the carbonyl groups of peptide bonds is thought to be the most important mechanism for intramolecular quenching of Trp fluorescence. We find the maximum fluorescence intensities vary from 49,000 for NATA with two carbonyls, to 24,400 for AWA with four carbonyls, to 28,500 for AAWAA with six carbonyls. This suggests that the four carbonyls of AWA are better able to quench Trp fluorescence than the six carbonyls of AAWAA, and this must reflect a difference in the conformations of the peptides. For the pentapeptides, EAWQE has a fluorescence intensity that is more than 50% greater than DYWTG, showing that the amino acid sequence influences the fluorescence intensity either directly through side-chain quenching and/or indirectly through an influence on the conformational ensemble of the peptides. Our results show that peptides are generally better models for the Trp residues in proteins than NATA. Finally, our results emphasize that we have much to learn about Trp fluorescence even in simple compounds

Late time behaviour of the maximal slicing of the Schwarzschild black hole

A time-symmetric Cauchy slice of the extended Schwarzschild spacetime can be evolved into a foliation of the $r>3m/2$-region of the spacetime by maximal surfaces with the requirement that time runs equally fast at both spatial ends of the manifold. This paper studies the behaviour of these slices in the limit as proper time-at-infinity becomes arbitrarily large and gives an analytic expression for the collapse of the lapse.Comment: 18 pages, Latex, no figure

Force balance and membrane shedding at the Red Blood Cell surface

During the aging of the red-blood cell, or under conditions of extreme echinocytosis, membrane is shed from the cell plasma membrane in the form of nano-vesicles. We propose that this process is the result of the self-adaptation of the membrane surface area to the elastic stress imposed by the spectrin cytoskeleton, via the local buckling of membrane under increasing cytoskeleton stiffness. This model introduces the concept of force balance as a regulatory process at the cell membrane, and quantitatively reproduces the rate of area loss in aging red-blood cells.Comment: 4 pages, 3 figure