Shear-flow transition: the basin boundary

The structure of the basin of attraction of a stable equilibrium point is investigated for a dynamical system (W97) often used to model transition to turbulence in shear flows. The basin boundary contains not only an equilibrium point Xlb but also a periodic orbit P, and it is the latter that mediates the transition. Orbits starting near Xlb relaminarize. We offer evidence that this is due to the extreme narrowness of the region complementary to basin of attraction in that part of phase space near Xlb. This leads to a proposal for interpreting the 'edge of chaos' in terms of more familiar invariant sets.Comment: 11 pages; submitted for publication in Nonlinearit

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

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

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

Static non-reciprocity in mechanical metamaterials

Reciprocity is a fundamental principle governing various physical systems, which ensures that the transfer function between any two points in space is identical, regardless of geometrical or material asymmetries. Breaking this transmission symmetry offers enhanced control over signal transport, isolation and source protection. So far, devices that break reciprocity have been mostly considered in dynamic systems, for electromagnetic, acoustic and mechanical wave propagation associated with spatio-temporal variations. Here we show that it is possible to strongly break reciprocity in static systems, realizing mechanical metamaterials that, by combining large nonlinearities with suitable geometrical asymmetries, and possibly topological features, exhibit vastly different output displacements under excitation from different sides, as well as one-way displacement amplification. In addition to extending non-reciprocity and isolation to statics, our work sheds new light on the understanding of energy propagation in non-linear materials with asymmetric crystalline structures and topological properties, opening avenues for energy absorption, conversion and harvesting, soft robotics, prosthetics and optomechanics.Comment: 19 pages, 3 figures, Supplementary information (11 pages and 5 figures

Reduction and Emergence in Bose-Einstein Condensates

A closer look at some proposed Gedanken-experiments on BECs promises to shed light on several aspects of reduction and emergence in physics. These include the relations between classical descriptions and different quantum treatments of macroscopic systems, and the emergence of new properties and even new objects as a result of spontaneous symmetry breaking

Numerical and Experimental Investigation of Circulation in Short Cylinders

In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we explore Couette flows having height comparable to the gap between cylinders, centrifugally stable rotation, and high Reynolds number. Experiments in water are compared with numerical simulations. Simulations show that endcaps corotating with the outer cylinder drive a strong poloidal circulation that redistributes angular momentum. Predicted azimuthal flow profiles agree well with experimental measurements. Spin-down times scale with Reynolds number as expected for laminar Ekman circulation; extrapolation from two-dimensional simulations at $Re\le 3200$ agrees remarkably well with experiment at $Re\sim 10^6$. This suggests that turbulence does not dominate the effective viscosity. Further detailed numerical studies reveal a strong radially inward flow near both endcaps. After turning vertically along the inner cylinder, these flows converge at the midplane and depart the boundary in a radial jet. To minimize this circulation in the MRI experiment, endcaps consisting of multiple, differentially rotating rings are proposed. Simulations predict that an adequate approximation to the ideal Couette profile can be obtained with a few rings

Bose-Einstein condensation in a two-dimensional, trapped,interacting gas

We study Bose-Einstein condensation phenomenon in a two-dimensional (2D) system of bosons subjected to an harmonic oscillator type confining potential. The interaction among the 2D bosons is described by a delta-function in configuration space. Solving the Gross-Pitaevskii equation within the two-fluid model we calculate the condensate fraction, ground state energy, and specific heat of the system. Our results indicate that interacting bosons have similar behavior to those of an ideal system for weak interactions.Comment: LaTeX, 4 pages, 4 figures, uses grafik.sty (included), to be published in Phys. Rev. A, tentatively scheduled for 1 October 1998 (Volume 58, Number 4

Fox Squirrels (Sciurus niger) Develop West Nile Virus Viremias Sufficient for Infecting Select Mosquito Species

The West Nile virus (WNV) viremia and shedding profiles of 11 adult fox squirrels (Sciurus niger) infected by needle inoculation or mosquito bite were characterized. Daily mean titers (95% confidence intervals) for all squirrels on days 1 through 6 postexposure (p.e.) were: 10(1.7 (1.32.1)), 10(4.4 (4.04.8)), 10(5.3 (5.05.6)), 10(4.4 (3.94.9)), 10(2.7 (2.03.4)), and 10(1.1 (0.52.1)) plaque-forming units (PFU)/mL. The highest WNV serum titers of individual squirrels infected by needle inoculation or mosquito bite ranged from 10(4.5) to 10(6.1) and from 10(5.1) to 10(5.3) PFU/mL, respectively. Nine (82%) squirrels, including all 4 squirrels infected by mosquito bite, had WNV serum titers \u3e or =10(5.1) PFU/mL that persisted on average for 1.6 +/- 0.3 days. Infection and dissemination rates of Culex pipiens (L.) that fed on squirrels with serum titers of 10(4.4 +/- 0.1) PFU/mL were 56% and 13%, respectively. Both of these rates increased to over 80% when fed on squirrels with a mean WNV titer of 10(5.5 +/- 0.1) PFU/mL. Infection and dissemination also occurred in Aedes triseriatus (Say) but at a much lower rate. WNV was isolated from the oral and rectal cavities of all squirrels and from urine that was opportunistically collected from 5 squirrels. The largest quantity of WNV recovered from swabs of the oral cavity and urine was 10(3.1) PFU. The longest periods after exposure that WNV was isolated from the oral cavity and urine from a squirrel were 22 and 17 days p.e., respectively. WNV RNA was also detected in kidney tissue in 1 squirrel 29 days p.e., suggesting that fox squirrels can be persistently infected. Collectively these observations provide further evidence that squirrels can contribute to the natural history and epidemiology of WNV, especially in peridomestic environments