On the chaotic rotation of a liquid-filled gyrostat via the Melnikov-Holmes-Marsden integral

The non-linear motions of a gyrostat with an axisymmetrical, fluid-filled cavity are investigated. The cavity is considered to be completely filled with an ideal incompressible liquid performing uniform rotational motion. Helmholtz theorem, Euler's angular momentum theorem and Poisson equations are used to develop the disturbed Hamiltonian equations of the motions of the liquid-filled gyrostat subjected to small perturbing moments. The equations are established in terms of a set of canonical variables comprised of Euler angles and the conjugate angular momenta in order to facilitate the application of the Melnikov-Holmes-Marsden (MHM) method to investigate homoclinic/heteroclinic transversal intersections. In such a way, a criterion for the onset of chaotic oscillations is formulated for liquid-filled gyrostats with ellipsoidal and torus-shaped cavities and the results are confirmed via numerical simulations. (c) 2006 Elsevier Ltd. All rights reserved.

On the chaotic instability of a nonsliding liquid-filled top with a small spheroidal base via Melnikov-Holmes-Marsden integrals

Chaotic orientations of a top containing a fluid filled cavity are investigated analytically and numerically under small perturbations. The top spins and rolls in nonsliding contact with a rough horizontal plane and the fluid in the ellipsoidal shaped cavity is considered to be ideal and describable by finite degrees of freedom. A Hamiltonian structure is established to facilitate the application of Melnikov-Holmes-Marsden (MHM) integrals. In particular, chaotic motion of the liquid-filled top is identified to be arisen from the transversal intersections between the stable and unstable manifolds of an approximated, disturbed flow of the liquid-filled top via the MHM integrals. The developed analytical criteria are crosschecked with numerical simulations via the 4th Runge-Kutta algorithms with adaptive time steps.

Quantum dynamics of three coupled atomic Bose-Einstein condensates

The simplest model of three coupled Bose-Einstein condensates is investigated using a group theoretical method. The stationary solutions are determined using the SU(3) group under the mean-field approximation. This semiclassical analysis, using system symmetries, shows a transition in the dynamics of the system from self trapping to delocalization at a critical value for the coupling between the condensates. The global dynamics are investigated by examination of the stable points, and our analysis shows that the structure of the stable points depends on the ratio of the condensate coupling to the particle-particle interaction, and undergoes bifurcations as this ratio is varied. This semiclassical model is compared to a full quantum treatment, which also displays a dynamical transition. The quantum case has collapse and revival sequences superimposed on the semiclassical dynamics, reflecting the underlying discreteness of the spectrum. Nonzero circular current states are also demonstrated as one of the higher-dimensional effects displayed in this system.

Hamiltonian mappings and circle packing phase spaces.

We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of the three different phase space geometries (planar, hyperbolic or spherical) and exhibits an infinite number of coexisting stable periodic orbits which appear to ‘pack’ the phase space with circular resonances.

Spatial, temporal, and human dimensions of air pollution in Brisbane

Arriving in Brisbane some six years ago, I could not help being impressed by what may be prosaically described as its atmospheric amenity resources. Perhaps this in part was due to my recent experiences in major urban centres in North America, but since that time, that sparkling quality and the blue skies seem to have progressively diminished. Unfortunately, there is also objective evidence available to suggest that this apparent deterioration is not merely the result of habituation of the senses. Air pollution data for the city show trends of increasing concentrations of those very substances that have destroyed the attractiveness of major population centres elsewhere, with climates initially as salubrious. Indeed, present figures indicate that photochemical smog in unacceptably high concentrations is rapidly becoming endemic also over Brisbane. These regrettable developments should come as no surprise. The society at large has not been inclined to respond purposefully to warnings of impending environmental problems, despite the experiences and publicity from overseas and even from other cities within Australia. Nor, up to the present, have certain politicians and government officials displayed stances beyond those necessary for the maintenance of a decorum of concern. At this stage, there still exists the possibility for meaningful government action without the embarrassment of losing political favour with the electorate. To the contrary, there is every chance that such action may be turned to advantage with increased public enlightenment. It would be more than a pity to miss perhaps the final remaining opportunity: Queensland is one of the few remaining places in the world with sufficient resources to permit both rational development and high environmental quality. The choice appears to be one of making a relatively minor investment now for a large financial and social gain the near future, or, permitting Brisbane to degenerate gradually into just another stagnated Los Angeles or Sydney. The present monograph attempts to introduce the problem by reviewing the available research on air quality in the Brisbane area. It also tries to elucidate some seemingly obvious, but so far unapplied management approaches. By necessity, such a broad treatment needs to make inroads into extensive ranges of subject areas, including political and legal practices to public perceptions, scientific measurement and statistical analysis to dynamics of air flow. Clearly, it does not pretend to be definitive in any of these fields, but it does try to emphasize those adjustable facets of the human use system of natural resources, too often neglected in favour of air pollution control technology. The crossing of disciplinary boundaries, however, needs no apology: air quality problems are ubiquitous, touching upon space, time and human interaction.

Patterns of species diversity in the gastrointestinal helminths of a coral reef fish, Epinephelus merra (Serranidae), from French Polynesia and the south Pacific Ocean

Large-scale patterns of species diversity in the gastrointestinal helminth faunas of the coral reef fish Epinephelus merra (Serranidae) were investigated in French Polynesia and the South Pacific Ocean. The richer barrier reef community in French Polynesia supported richer parasite communities in E. merra than that on the fringing reef. While parasite communities among fish from the same archipelago were similar, differences in potential host species and the distance between archipelagos may have contributed to a qualitative difference in parasite communities between archipelagos. Digenean community diversity in coral reef fishes was greater in the western South Pacific, following similar patterns in free-living species. However, overall species diversity of camallanid nematodes of coral reef fishes does not appear to have been similarly affected.

Quantum and classical chaos for a single trapped ion

In this paper we investigate the quantum and classical dynamics of a single trapped ion subject to nonlinear kicks derived from a periodic sequence of Gaussian laser pulses. We show that the classical system exhibits: diffusive growth in the energy, or heating,'' while quantum mechanics suppresses this heating. This system may be realized in current single trapped-ion experiments with the addition of near-field optics to introduce tightly focused laser pulses into the trap.

Helminth parasite communities of the water-rat, Hydromys chrysogaster, from Queensland

The helminth fauna from 124 water-rats, Hydromys chrysogaster, collected from 33 localities in Queensland was analysed. A total of 45 species of helminths was found, comprising 2 acanthocephalans, 2 cestodes, 13 nematodes and 28 trematodes. The helminth community of the water-rats in the region north of latitude 18 degrees (far north) was different from that of water-rats south of 18 degrees (central); Sorensen's Index 45.8% similarity, whereas Holmes and Podesta's Index gave 32.1% similarity. Comparisons with data from water-rats from southern and Tasmanian regions showed that they were different from each other and from both Queensland regions. The helminth communities were characterised by high diversity, dominated by trematodes in the central and Tasmanian regions, but with nematodes becoming more prominent in the far northern and southern regions. No core or secondary species were found in the Queensland helminth communities, the southern community was suggestive of a bimodal distribution and the Tasmanian had two core species. A checklist of helminth species occurring in water-rats from eastern Australia is provided.

Quantum signatures of chaos in the dynamics of a trapped ion

We show how a nonlinear chaotic system, the parametrically kicked nonlinear oscillator, may be realized in the dynamics of a trapped, laser-cooled ion, interacting with a sequence of standing-wave pulses. Unlike the original optical scheme [G. J. Milburn and C.A. Holmes, Phys. Rev. A 44, 4704 (1991)], the trapped ion enables strongly quantum dynamics with minimal dissipation. This should permit an experimental test of one of the quantum signatures of chaos: irregular collapse and revival dynamics of the average vibrational energy.

A. W. Campbells Australian career: 1905-1937

The Australian Alfred Walter Campbell (1868-1937) is remembered as one of the two chief pioneers of the study of the cytoarchitectonics of the primate cerebral cortex. He had worked in Britain carrying out neuroanatomical and neuropathological research for almost two decades before his famous monograph on Histological Studies on the Localisation of Cerebral Function appeared in 1905. In that year he returned to his native Australia and practiced for over 30 years in Sydney as a neurologist rather than a neuropathologist, publishing mainly clinical material though he was involved in the investigation of the epidemic of Australian X disease, a viral encephalitis. His abrupt change in both the nature and the location of his career at a time when he was well established in Britain appears to have been a consequence of his marriage and the need to provide for a family. His simultaneous apparent abandonment of research seems not to have really been the case. As judged from the contents of a paper presented to a local medical congress in Sydney in 1911, it appears that, in Australia, Campbell did carry out a major comparative anatomical and histological investigation of the possibility of localization of function in the cerebellar cortex. He never published this work in detail. His investigation let him to conclude that no such localization of function existed, a view contrary to the then topical interpretation of Bolk (1906), but one in accordance with Gordon Holmes' views a decade later. Campbell's circumstances in Sydney, his extremely reticent nature and the essentially negative outcome of his investigation probably explain his failure to make his study more widely known.

Multiple bifurcations in atom optics

We report the observation of multiple bifurcations in a nonlinear Hamiltionian system: laser-cooled atoms in a standing wave with single-frequency intensity modulation. We provide clear evidence of the occurrence of bifurcations by analyzing the atomic momentum distributions.

An evaluation of two indices of red fox (Vulpes vulpes) abundance in an arid environment

The suitability of spotlight counts to index red fox abundance was assessed in an arid environment through a comparison with a scat deposition index (active attractant). In most cases there was a high degree of correlation between the two indices, suggesting that the spotlight counts were accurately documenting fluctuations in population size. However, the precision of the spotlight index was often low (c.v. = 0.07-0.46), suggesting that the technique may not allow the statistical detection of small changes in abundance. During periods when there was an influx of new individuals into the population, the seasonal scat index displayed a three-month time lag in documenting abundance while foxes accustomed themselves to the presence of the regular food supply. The level of precision of the scat index was also found to be relatively low (c.v. = 0.21-0.48). Nevertheless, further refinements of this technique may produce a suitable measure of fox abundance.