Quantum manifestations of scattering orbits in the scaled spectrum of a non-hydrogenic atom in crossed fields

Evidence for scattering closed orbits for the Rydberg electron of the singly excited helium atom in crossed electric and magnetic fields at constant scaled energy and constant scaled electric field strength has been found through a quantum calculation of the photo-excitation spectrum. A particular 3D scattering orbit in a mixed regular and chaotic region has been investigated and the hydrogenic 3D closed orbits composing it identified. To the best of our knowledge, this letter reports the first quantum calculation of the scaled spectrum of a non- hydrogenic atom in crossed fields.

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.

Orbits of operators commuting with the Volterra operator

Asymptotic estimates of the norms of orbits of certain operators that commute with the classical Volterra operator V acting on L-P[0,1], with 1 0, but also to operators of the form phi (V), where phi is a holomorphic function at zero. The method to obtain the estimates is based on the fact that the Riemann-Liouville operator as well as the Volterra operator can be related to the Levin-Pfluger theory of holomorphic functions of completely regular growth. Different methods, such as the Denjoy-Carleman theorem, are needed to analyze the behavior of the orbits of I - cV, where c > 0. The results are applied to the study of cyclic properties of phi (V), where phi is a holomorphic function at 0.

Satellite flies (Leucophora personata, Diptera : Anthomyiidae) and other dipteran parasites of the communal bee Andrena agilissima (Hymenoptera : Andrenidae) on the island of Elba, Italy

Solitary and presocial aculueate Hymenoptera are parasitized by a range of dipteran species in the families Axithomyiidae, Bombyliidae, Conopidae, Phoridae, and Sarcophagidae that are likely to impact on their hosts. We undertook a study over several years of a univoltine and communal bee, Andrena agilissima, and its main dipteran parasites, in particular the satellite fly Leucophora personata (Diptera: Anthomyiidae). Behavioural and ecological data were collected from one nesting aggregation of the host bee on the island of Elba, Italy, from 1993 to 2003, and from a foraging site of the bee, ca 5 km from the nesting aggregation. Other Diptera associated with A. agilissmia at the field site were the bee fly Bombylius fimbriatus (Bombyliidae), the conopid fly Zodion cinereum (Conopidae), and the scuttle fly Megaselia andrenae (Phoridae). The phenology of the Diptera broadly overlapped with that of their host across the season of activity (end of April and all of May). Diurnal activity patterns differed slightly; L. personata in particular was active at the host's nesting site before A. agilissima. Female satellite flies also showed a range of behaviours in gaining entry to a host nest. We summarize published data on this and other Leucophora species that parasitize Andrena host bees. Host bees returning to their nests occasionally undertook zig-zag flight manoeuvres if followed by a satellite fly that were generally successful in evading the fly. Satellite flies that entered a nest, presumably to oviposit, were less likely to remain therein if another host bee entered the same nest, suggesting that one advantage to communal nesting for this host is a reduction in brood cell parasitism by L. personata. We provide the first clear evidence for parasitism by a Zodion of any Andrena host. Both L. personata and M. andrenae concentrated their parasitic activities in the zone of the host nesting aggregation with highest nest densities. Three of the Diptera, L. personata, B. fimbriatus, and Z. cinereum, seemed to have extremely low rates of parasitism whilst that of M. andrenae appeared low. Though they have refined parasitic behaviour that allows them to gain entry into host nests (L. personata, B. fimbriatus, and M. andrenae) or to parasitize adults (Z. cinercum), these parasites seem not to impact upon the dynamics of the host A. agilissima at the nesting aggregation, and the host possesses traits to reduce parasitism.

Satellite tracking of the World's largest bony fish, the ocean sunfish (Mola mola L.) in the North East Atlantic

Satellite-linked archival transmitters were used to record the movements of three ocean sunfish (Mola mola) in the North East Atlantic. Patterns of depth use and temperature experienced by individual fish were integrated into 4-hour intervals throughout the tracking period and relayed via the Argos system. Data were recorded for 42, 90 and 54 days respectively from the three fish. The first two were tagged off southern Portugal at the end of February 2007 and travelled principally northward, while the third fish was tagged off west Ireland in August 2007 and travelled southward. These patterns are consistent with seasonal migration of ocean sunfish to high latitudes and their Subsequent return south. Maximum depths recorded by the three fish were 432 m, 472 m and 320 m respectively. All three individuals showed a diel pattern in depth use, occurring deeper during the day and shallower at night, a pattern consistent with sunfish tracking normally vertically migrating prey. Sunfish sometimes remained continuously at deeper (>200 m) depths during the day, but at other times they showed extensive movement through the water column typically travelling between their maximum depth and the surface within each 4-h period. The overall pattern to emerge was that ocean sunfish travel extensively in both horizontal and vertical dimensions, presumably in search of their patchily-distributed jellyfish prey.