Quantum manifestations of closed orbits in the photoexcitation scaled spectrum of the hydrogen atom in crossed fields

The scaled photoexcitation spectrum of the hydrogen atom in crossed electric and magnetic fields has been obtained by means of accurate quantum mechanical calculation using a new algorithm. Closed orbits in the corresponding classical system have also been obtained, using a new, efficient and practical searching procedure. Two new classes of closed orbit have been identified. Fourier transforming each photoexcitation quantum spectrum to yield a plot against scaled action has allowed direct comparison between peaks in such plots and the scaled action values of closed orbits, Excellent agreement has been found with all peaks assigned.

The closed orbits and the photo-excitation scaled spectrum of the hydrogen atom in crossed fields

In a recent Letter to the Editor (J Rao, D Delande and K T Taylor 2001 J. Phys. B: At. Mol. Opt. Phys. 34 L391-9) we made a brief first report of our quantal and classical calculations for the hydrogen atom in crossed electric and magnetic fields at constant scaled energy and constant scaled electric field strength. A principal point of that communication was our statement that each and every peak in the Fourier transform of the scaled quantum photo-excitation spectrum for scaled energy value epsilon = -0.586 538 871028 43 and scaled electric value (f) over tilde = 0.068 537 846 207 618 71 could be identified with a scaled action value of a found and mapped-out closed orbit up to a scaled action of 20. In this follow-up paper, besides presenting full details of our quantum and classical methods, we set out the scaled action values of all 317 closed orbits involved, together with the geometries of many.

The spectrum of endogenous human chromogranin A-derived peptides identified using a modified proteomic strategy.

The hypothesis that chromogranin A (CgA), a protein of neuroendocrine cell secretory granules, may be a precursor of biologically active peptides, rests on observed activities of peptide fragments largely produced by exogenous protease digestion of the bovine protein. Here we have adopted a modified proteomic strategy to isolate and characterise human CgA-derived peptides produced by endogenous prohormone convertases. Initial focus was on an insulinoma as previous studies have shown that CgA is rapidly processed in pancreatic beta cells and that tumours arising from these express appropriate prohormone convertases. Eleven novel peptides were identified arising from processing at both monobasic and dibasic sites and processing was most evident in the C-terminal domain of the protein. Some of these peptides were identified in endocrine tumours, such as mid-gut carcinoid and phaeochromocytoma, which arise from endocrine cells of different phenotype and in different anatomical sites. Two of the most interesting peptides, GR-44 and ER-37, representing the C-terminal region of CgA, were found to be amidated. These data would imply that the intact protein is C-terminally amidated and that these peptides are probably biologically active. The spectrum of novel CgA-derived peptides, described in the present study, should provide a basis for biological evaluation of authentic entities.

How optimal life history changes with the community size-spectrum

This paper derives optimal life histories for fishes or other animals in relation to the size spectrum of the ecological community in which they are both predators and prey. Assuming log-linear size-spectra and well known scaling laws for feeding and mortality, we first construct the energetics of the individual. From these we find, using dynamic programming, the optimal allocation of energy between growth and reproduction as well as the trade-off between offspring size and numbers. Optimal strategies were found to be strongly dependent on size spectrum slope. For steep size spectra (numbers declining rapidly with size), determinate growth was optimal and allocation to somatic growth increased rapidly with increasing slope. However, restricting reproduction to a fixed mating season changed optimal allocations to give indeterminate growth approximating a von Bertalanffy trajectory. The optimal offspring size was as small as possible given other restrictions such as newborn starvation mortality. For shallow size spectra, finite optimal maturity size required a decline in fitness for large size or age. All the results are compared with observed size spectra of fish communities to show their consistency and relevance.