Imperfect Homoclinic Bifurcations

Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics observed in the circuit can be understood by reference to imperfect homoclinic bifurcations without constructing an explicit mathematical model of the system.Comment: 8 pages, 11 figures, submitted to PR

Exclusion Statistics in a two-dimensional trapped Bose gas

We briefly explain the notion of exclusion statistics and in particular discuss the concept of an ideal exclusion statistics gas. We then review a recent work where it is demonstrated that a {\em two-dimensional} Bose gas with repulsive delta function interactions obeys ideal exclusion statistics, with a fractional parameter related to the interaction strength.Comment: 10 pages, RevTeX. Proceedings of the Salerno workshop "Theory of Quantum Gases and Quantum Coherence", to appear in a special issue of J.Phys. B, Dec. 200

On the decay of turbulence in plane Couette flow

The decay of turbulent and laminar oblique bands in the lower transitional range of plane Couette flow is studied by means of direct numerical simulations of the Navier--Stokes equations. We consider systems that are extended enough for several bands to exist, thanks to mild wall-normal under-resolution considered as a consistent and well-validated modelling strategy. We point out a two-stage process involving the rupture of a band followed by a slow regression of the fragments left. Previous approaches to turbulence decay in wall-bounded flows making use of the chaotic transient paradigm are reinterpreted within a spatiotemporal perspective in terms of large deviations of an underlying stochastic process.Comment: ETC13 Conference Proceedings, 6 pages, 5 figure

Classification of phase transitions of finite Bose-Einstein condensates in power law traps by Fisher zeros

We present a detailed description of a classification scheme for phase transitions in finite systems based on the distribution of Fisher zeros of the canonical partition function in the complex temperature plane. We apply this scheme to finite Bose-systems in power law traps within a semi-analytic approach with a continuous one-particle density of states $\Omega(E)\sim E^{d-1}$ for different values of $d$ and to a three dimensional harmonically confined ideal Bose-gas with discrete energy levels. Our results indicate that the order of the Bose-Einstein condensation phase transition sensitively depends on the confining potential.Comment: 7 pages, 9 eps-figures, For recent information on physics of small systems see "http://www.smallsystems.de

Exclusion Statistics in a trapped two-dimensional Bose gas

We study the statistical mechanics of a two-dimensional gas with a repulsive delta function interaction, using a mean field approximation. By a direct counting of states we establish that this model obeys exclusion statistics and is equivalent to an ideal exclusion statistics gas.Comment: 3 pages; minor changes in notation; typos correcte

The inverse-Compton ghost HDF 130 and the giant radio galaxy 6C 0905+3955: matching an analytic model for double radio source evolution

We present new GMRT observations of HDF 130, an inverse-Compton (IC) ghost of a giant radio source that is no longer being powered by jets. We compare the properties of HDF 130 with the new and important constraint of the upper limit of the radio flux density at 240 MHz to an analytic model. We learn what values of physical parameters in the model for the dynamics and evolution of the radio luminosity and X-ray luminosity (due to IC scattering of the cosmic microwave background (CMB)) of a Fanaroff-Riley II (FR II) source are able to describe a source with features (lobe length, axial ratio, X-ray luminosity, photon index and upper limit of radio luminosity) similar to the observations. HDF 130 is found to agree with the interpretation that it is an IC ghost of a powerful double-lobed radio source, and we are observing it at least a few Myr after jet activity (which lasted 5--100 Myr) has ceased. The minimum Lorentz factor of injected particles into the lobes from the hotspot is preferred to be $\gamma\sim10^3$ for the model to describe the observed quantities well, assuming that the magnetic energy density, electron energy density, and lobe pressure at time of injection into the lobe are linked by constant factors according to a minimum energy argument, so that the minimum Lorentz factor is constrained by the lobe pressure. We also apply the model to match the features of 6C 0905+3955, a classical double FR II galaxy thought to have a low-energy cutoff of $\gamma\sim10^4$ in the hotspot due to a lack of hotspot inverse-Compton X-ray emission. The models suggest that the low-energy cutoff in the hotspots of 6C 0905+3955 is $\gamma\gtrsim 10^3$, just slightly above the particles required for X-ray emission.Comment: 9 pages, 3 figure

Numerical study of the spherically-symmetric Gross-Pitaevskii equation in two space dimensions

We present a numerical study of the time-dependent and time-independent Gross-Pitaevskii (GP) equation in two space dimensions, which describes the Bose-Einstein condensate of trapped bosons at ultralow temperature with both attractive and repulsive interatomic interactions. Both time-dependent and time-independent GP equations are used to study the stationary problems. In addition the time-dependent approach is used to study some evolution problems of the condensate. Specifically, we study the evolution problem where the trap energy is suddenly changed in a stable preformed condensate. In this case the system oscillates with increasing amplitude and does not remain limited between two stable configurations. Good convergence is obtained in all cases studied.Comment: 9 latex pages, 7 postscript figures, To appear in Phys. Rev.

Collective excitations of a two-dimensional interacting Bose gas in anti-trap and linear external potentials

We present a method of finding approximate analytical solutions for the spectra and eigenvectors of collective modes in a two-dimensional system of interacting bosons subjected to a linear external potential or the potential of a special form $u(x,y)=\mu -u \cosh^2 x/l$, where $\mu$ is the chemical potential. The eigenvalue problem is solved analytically for an artificial model allowing the unbounded density of the particles. The spectra of collective modes are calculated numerically for the stripe, the rare density valley and the edge geometry and compared with the analytical results. It is shown that the energies of the modes localized at the rare density region and at the edge are well approximated by the analytical expressions. We discuss Bose-Einstein condensation (BEC) in the systems under investigations at $T\ne 0$ and find that in case of a finite number of the particles the regime of BEC can be realized, whereas the condensate disappears in the thermodynamic limit.Comment: 10 pages, 2 figures include

Patterns of in situ Mineral Colonization by Microorganisms in a ~60°C Deep Continental Subsurface Aquifer

The microbial ecology of the deep biosphere is difficult to characterize, owing in part to sampling challenges and poorly understood response mechanisms to environmental change. Pre-drilled wells, including oil wells or boreholes, offer convenient access, but sampling is frequently limited to the water alone, which may provide only a partial view of the native diversity. Mineral heterogeneity demonstrably affects colonization by deep biosphere microorganisms, but the connections between the mineral-associated and planktonic communities remain unclear. To understand the substrate effects on microbial colonization and the community response to changes in organic carbon, we conducted an 18-month series of in situ experiments in a warm (57°C), anoxic, fractured carbonate aquifer at 752 m depth using replicate open, screened cartridges containing different solid substrates, with a proteinaceous organic matter perturbation halfway through this series. Samples from these cartridges were analyzed microscopically and by Illumina (iTag) 16S rRNA gene libraries to characterize changes in mineralogy and the diversity of the colonizing microbial community. The substrate-attached and planktonic communities were significantly different in our data, with some taxa (e.g., Candidate Division KB-1) rare or undetectable in the first fraction and abundant in the other. The substrate-attached community composition also varied significantly with mineralogy, such as with two Rhodocyclaceae OTUs, one of which was abundant on carbonate minerals and the other on silicic substrates. Secondary sulfide mineral formation, including iron sulfide framboids, was observed on two sets of incubated carbonates. Notably, microorganisms were attached to the framboids, which were correlated with abundant Sulfurovum and Desulfotomaculum sp. sequences in our analysis. Upon organic matter perturbation, mineral-associated microbial diversity differences were temporarily masked by the dominance of putative heterotrophic taxa in all samples, including OTUs identified as Caulobacter, Methyloversatilis, and Pseudomonas. Subsequent experimental deployments included a methanogen-dominated stage (Methanobacteriales and Methanomicrobiales) 6 months after the perturbation and a return to an assemblage similar to the pre-perturbation community after 9 months. Substrate-associated community differences were again significant within these subsequent phases, however, demonstrating the value of in situ time course experiments to capture a fraction of the microbial assemblage that is frequently difficult to observe in pre-drilled wells