Periodic orbit quantization of a Hamiltonian map on the sphere

In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information to explore the semiclassical quantization of one of these maps.

Cell compartmentalisation in planctomycetes: novel types of structural organisation for the bacterial cell

The organisation of cells of the planctomycete species Pirellula marina, Isosphaera pallida, Gemmata obscuriglobus, Planctomyces mat-is and Candidatus Brocadia anammoxidans was investigated based on ultrastructure derived from thin-sections of cryosubstituted cells, freeze-fracture replicas, and in the case of Gemmata obscuriglobus and Pirellllla marina, computer-aided 3-D reconstructions from serial sections of cryosubstituted cells. All planctomycete cells display a peripheral ribosome-free region, termed here the paryphoplasm, surrounding the perimeter of the cell, and an interior region including any nucleoid regions as well as ribosome-like particles, bounded by a single intracytoplasmic membrane (ICM), and termed the pirellulosome in Pirellula species. Immunogold labelling and RNase-gold cytochemistry indicates that in planctomycetes all the cell DNA is contained wholly within the interior region bounded by the ICM, and the paryphoplasm contains no DNA but at least some of the cell's RNA. The ICM in Isosphaera pallida and Planctomyces mat-is is invaginated such that the paryphoplasm forms a major portion of the cell interior in sections, but in other planctomycetes it remains as a peripheral zone. In the anaerobic ammonium-oxidising (anammox process) chemoautotroph Candidatus Brocadia anammoxidans the interior region bounded by ICM contains a further internal single-membrane-bounded region, the anam-moxosome. In Gemmata obscuriglobus. the interior ICM-bounded region contains the nuclear body, a double-membrane-bounded region containing the cell's nucleoid and all genomic DNA in addition to some RNA. Shared features of cell compartmentalisation in different planctomycetes are consistent with the monophyletic nature of the planctomycetes as a distinct division of the Bacteria. The shared organisational plan for the planctomycete cell constitutes a new type not known in cells of other bacteria.

Quantum nonlinear dynamics of continuously measured systems

Classical dynamics is formulated as a Hamiltonian flow in phase space, while quantum mechanics is formulated as unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and classical nonlinear dynamics. Previous solutions have focused on computing quantities associated with a statistical ensemble such as variance or entropy. However a more diner comparison would compare classical predictions to the quantum predictions for continuous simultaneous measurement of position and momentum of a single system, in this paper we give a theory of such measurement and show that chaotic behavior in classical systems fan be reproduced by continuously measured quantum systems.

Structural and morphological anomalies in magnetosomes: possible biogenic origin for magnetite in ALH84001

We report biogenic magnetite whiskers, with axial ratios of 6: 1, elongated in the [1 1 1]. [1 1 2] and [1 0 0] directions, resembling the magnetite whiskers detected in the Martian meteorite ALH84001 by Bradley ct nl., and interpreted by those authors as evidence of vapour-phase (abiogenic) growth. Magnetosomal whiskers with extended defects consistent with screw dislocations and magnetosomes resembling flattened twinned platelets, as well as other twinning phenomena and other structural defects, are also reported here. Magnetosomes with teardrop-shaped. cuboidal. irregular and jagged structures similar to those detected in ALH84001 by McKay et al.. coprecipitation of magnetite possibly with amorphous calcium carbonate, coprecipitation of magnetite possibly with amorphous silica, the incorporation of titanium in volutin inclusions and disoriented arrays of magnetosomes are also described. These observations demonstrate that the structures of the magnetite particles in ALH84001. their spatial arrange ment and coprecipitation with carbonates and proximity to silicates are consistent with being biogenic. Electron-beam-induced flash-melting of magnetosomes produced numerous screw dislocations in the (1 1 1). (1 0 0) and (1 1 0) lattice planes and induced fusion of platelets. From this, the lack of screw dislocations reported in the magnetite particles in ALH84001 (McKay et al.. and Bradley et al.) indicates that they have a low-temperature origin.

Implicit Taylor methods for stiff stochastic differential equations

In this paper we discuss implicit Taylor methods for stiff Ito stochastic differential equations. Based on the relationship between Ito stochastic integrals and backward stochastic integrals, we introduce three implicit Taylor methods: the implicit Euler-Taylor method with strong order 0.5, the implicit Milstein-Taylor method with strong order 1.0 and the implicit Taylor method with strong order 1.5. The mean-square stability properties of the implicit Euler-Taylor and Milstein-Taylor methods are much better than those of the corresponding semi-implicit Euler and Milstein methods and these two implicit methods can be used to solve stochastic differential equations which are stiff in both the deterministic and the stochastic components. Numerical results are reported to show the convergence properties and the stability properties of these three implicit Taylor methods. The stability analysis and numerical results show that the implicit Euler-Taylor and Milstein-Taylor methods are very promising methods for stiff stochastic differential equations.

The effects of copper on the microbial community of a coral reef sponge

Marine sponges often harbour communities of symbiotic microorganisms that fulfil necessary functions for the well-being of their hosts. Microbial communities associated with the sponge Rhopaloeides odorabile were used as bioindicators far sublethal cupric ion (Cu2+) stress. A combined strategy incorporating molecular, cultivation and electron microscopy techniques was adopted to monitor changes in microbial diversity. The total density of sponge-associated bacteria and counts of the predominant cultivated symbiont (alpha -proteobacterium strain NW001) were significantly reduced in response to Cu2+ concentrations of 1.7 mug l(-1) and above after 14 days of exposure. The number of operational taxonomic units (OTUs) detected by restriction fragment length polymorphism (RFLP) decreased by 64% in sponges exposed to 223 mug l(-1) Cu2+ for 48 h and by 46% in sponges exposed to 19.4 mug l(-1) Cu2+ for 14 days. Electron microscopy was used to identify 17 predominant bacterial morphotypes, composing 47% of the total observed cells in control sponges. A reduction In the proportion of these morphotypes to 25% of observed cells was evident in sponges exposed to a Cu2+ concentration of 19.4 mug l(-1). Although the abundance of most morphotypes decreased under Cu2+ stress, three morphotypes were not reduced in numbers and a single morphotype actually increased in abundance. Bacterial numbers, as detected using fluorescence in situ hybridization (FISH), decreased significantly after 48 h exposure to 19.4 mug l(-1) Cu2+. Archaea, which are normally prolific in R. odorabile, were not detected after exposure to a Cu2+ concentration of 19.4 mug l(-1) for 14 days, indicating that many of the microorganisms associated with R. odorabile are sensitive to free copper. Sponges exposed to a Cu2+ concentration of 223 mug l(-1) became highly necrosed after 48 h and accumulated 142 +/- 18 mg kg(-1) copper, whereas sponges exposed to 19.4 mug l(-1) Cu2+ accumulated 306 +/- 15 mg kg(-1) copper after 14 days without apoptosis or mortality. Not only do sponges have potential for monitoring elevated concentrations of heavy metals but also examining changes in their microbial symbionts is a novel and sensitive bioindicator for the assessment of pollution on important microbial communities.

Izergin-Korepin model with a boundary

The Izergin-Korepin model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the twisted quantum affine algebra U-q[((2))(2)]. We give the bosonization of the vacuum state with zero particle content. Excitation states are given by the action of the vertex operators on the vacuum state. We derive the boundary S-matrix. We give an integral expression of the correlation functions of the boundary model, and derive the difference equations which they satisfy. (C) 2001 Elsevier Science B.V. All rights reserved.

An electron microscopic study of nickel sulfide inclusions in toughened glass

It has been known since the early sixties that nickel sulfide inclusions cause spontaneous fracture of toughened (thermally tempered) glass, but despite the considerable amount of work done on this problem in the last four decades, failures still occur in the field with regularity. In this study we have classified (by viewing through a 60x optical microscope) inclusions into two groups, which are classic and atypical nickel sulfides. The classics look like the nickel sulfide inclusions found at the initiation-of-fracture of windows that have broken spontaneously. We have compared the structure and composition of the atypical inclusions with the structure and composition of the classics. All of the classic and atypical nickel sulfide inclusions studied in this work were found to have a composition in the range of Ni52S48 to Ni48S52. Inclusions on the nickel rich side of stoichiometric NiS were found to be two-phase assemblies, and inclusions on the sulphur rich side of NiS were single phase. It had been proposed that the atypicals were passive, and of a different composition to the classics. However, we found that the difference between passive and dangerous nickel sulfide inclusions was not a difference in composition but rather a difference in the type of material in the internal pore space. The passive's had carbon char in their internal pore space, whereas the pore space of dangerous inclusions contained Na2O. The presence of Na2O and carbon char with the inclusions indicates that the formation of the inclusions results from a reaction of a nickel-rich phase with sodium sulphate and carbon. (C) 2001 Kluwer Academic Publishers.

A nanometre-scale non-periodic structural variation in high temperature superconducting ceramics and the implications for properties

Non-periodic structural variation has been found in the high T-c cuprates, YBa2Cu3O7-x and Hg0.67Pb0.33Ba2Ca2Cu3O8+delta, by image analysis of high resolution transmission electron microscope (HRTEM) images. We use two methods for analysis of the HRTEM images. The first method is a means for measuring the bending of lattice fringes at twin planes. The second method is a low-pass filter technique which enhances information contained by diffuse-scattered electrons and reveals what appears to be an interference effect between domains of differing lattice parameter in the top and bottom of the thin foil. We believe that these methods of image analysis could be usefully applied to the many thousands of HRTEM images that have been collected by other workers in the high temperature superconductor field. This work provides direct structural evidence for phase separation in high T-c cuprates, and gives support to recent stripes models that have been proposed to explain various angle resolved photoelectron spectroscopy and nuclear magnetic resonance data. We believe that the structural variation is a response to an opening of an electronic solubility gap where holes are not uniformly distributed in the material but are confined to metallic stripes. Optimum doping may occur as a consequence of the diffuse boundaries between stripes which arise from spinodal decomposition. Theoretical ideas about the high T-c cuprates which treat the cuprates as homogeneous may need to be modified in order to take account of this type of structural variation.

The strain-driven pyrochlore to "defect fluorite" phase transition in rare earth sesquioxide stabilized cubic zirconias

The relationship between the ordering characteristic of the pyrochlore structure type and that characteristic of the defect fluorite structure type (immediately on either side of two phase regions separating the two structure types) in a range of rare eath sesquioxide stabilized cubic zirconias is investigated via electron diffraction and imaging. Systematic structural change as a function of composition and relative size of the constituent metal ions is highlighted and a multi-q to single-q = 1/2 [111]* model proposed for the observed pyrochlore to defect fluorite phase transition. Strain introduced into the close-packed {111} metal ion planes of the defect fluorite average structure by the local cation and oxygen vacancy distribution is pointed to as the likely origin of the observed behavior. (C) 2001 Academic Press

Analytical solution and numerical model for the interface in a stratified long wave system

For a two layered long wave propagation, linearized governing equations, which were derived earlier from the Euler equations of mass and momentum assuming negligible friction and interfacial mixing are solved analytically using Fourier transform. For the solution, variations of upper layer water level is assumed to be sinosoidal having known amplitude and variations of interface level is solved. As the governing equations are too complex to solve it analytically, density of upper layer fluid is assumed as very close to the density of lower layer fluid to simplify the lower layer equation. A numerical model is developed using the staggered leap-forg scheme for computation of water level and discharge in one dimensional propagation having known amplitude for the variations of upper layer water level and interface level to be solved. For the numerical model, water levels (upper layer and interface) at both the boundaries are assumed to be known from analytical solution. Results of numerical model are verified by comparing with the analytical solutions for different time period. Good agreements between analytical solution and numerical model are found for the stated boundary condition. The reliability of the developed numerical model is discussed, using it for different a (ratio of density of fluid in the upper layer to that in the lower layer) and p (ratio of water depth in the lower layer to that in the upper layer) values. It is found that as ‘CX’ increases amplification of interface also increases for same upper layer amplitude. Again for a constant lower layer depth, as ‘p’ increases amplification of interface. also increases for same upper layer amplitude.

Quasi-stationarity in populations that are subject to large-scale mortality or emigration

We shall examine a model, first studied by Brockwell et al. [Adv Appl Probab 14 (1982) 709.], which can be used to describe the longterm behaviour of populations that are subject to catastrophic mortality or emigration events. Populations can suffer dramatic declines when disease, such as an introduced virus, affects the population, or when food shortages occur, due to overgrazing or fluctuations in rainfall. However, perhaps surprisingly, such populations can survive for long periods and, although they may eventually become extinct, they can exhibit an apparently stationary regime. It is useful to be able to model this behaviour. This is particularly true of the ecological examples that motivated the present study, since, in order to properly manage these populations, it is necessary to be able to predict persistence times and to estimate the conditional probability distribution of population size. We shall see that although our model predicts eventual extinction, the time till extinction can be long and the stationary exhibited by these populations over any reasonable time scale can be explained using a quasistationary distribution. (C) 2001 Elsevier Science Ltd. All rights reserved.

Three-point boundary value problems for second-order, ordinary, differential equations

We establish existence results for solutions to three-point boundary value problems for nonlinear, second-order, ordinary differential equations with nonlinear boundary conditions. (C) 2001 Elsevier Science Ltd. All rights reserved.

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.