Energy Loss from Reconnection with a Vortex Mesh

Experiments in superfluid 4He show that at low temperatures, energy dissipation from moving vortices is many orders of magnitude larger than expected from mutual friction. Here we investigate other mechanisms for energy loss by a computational study of a vortex that moves through and reconnects with a mesh of small vortices pinned to the container wall. We find that such reconnections enhance energy loss from the moving vortex by a factor of up to 100 beyond that with no mesh. The enhancement occurs through two different mechanisms, both involving the Kelvin oscillations generated along the vortex by the reconnections. At relatively high temperatures the Kelvin waves increase the vortex motion, leading to more energy loss through mutual friction. As the temperature decreases, the vortex oscillations generate additional reconnection events between the moving vortex and the wall, which decrease the energy of the moving vortex by transfering portions of its length to the pinned mesh on the wall.Comment: 9 pages, 10 figure

Avoided intersections of nodal lines

We consider real eigen-functions of the Schr\"odinger operator in 2-d. The nodal lines of separable systems form a regular grid, and the number of nodal crossings equals the number of nodal domains. In contrast, for wave functions of non integrable systems nodal intersections are rare, and for random waves, the expected number of intersections in any finite area vanishes. However, nodal lines display characteristic avoided crossings which we study in the present work. We define a measure for the avoidance range and compute its distribution for the random waves ensemble. We show that the avoidance range distribution of wave functions of chaotic systems follow the expected random wave distributions, whereas for wave functions of classically integrable but quantum non-separable wave functions, the distribution is quite different. Thus, the study of the avoidance distribution provides more support to the conjecture that nodal structures of chaotic systems are reproduced by the predictions of the random waves ensemble.Comment: 12 pages, 4 figure

Penetration of a vortex dipole across an interface of Bose-Einstein condensates

The dynamics of a vortex dipole in a quasi-two dimensional two-component Bose-Einstein condensate are investigated. A vortex dipole is shown to penetrate the interface between the two components when the incident velocity is sufficiently large. A vortex dipole can also disappear or disintegrate at the interface depending on its velocity and the interaction parameters.Comment: 7 pages, 9 figure

Spontaneous squeezing of a vortex in an optical lattice

We study the equilibrium states of a vortex in a Bose-Einstein condensate in a one-dimensional optical lattice. We find that quantum effects can be important and that it is even possible for the vortex to be strongly squeezed, which reflects itself in a different quantum mechanical uncertainty of the vortex position in two orthogonal directions. The latter is observable by measuring the atomic density after an expansion of the Bose-Einstein condensate in the lattice.Comment: 8 pages, 3 figures, more details added, some new citation

Using the GrassGro Decision Support Tool to Evaluate the Response in Grazing Systems to Pasture Legume or a Grass Cultivar With Improved Nutritive Value

Decision support tools (DST) based on models of grazing systems allow the evaluation of changes in enterprise management on productivity and profitability. The Grassgro DST (Moore et al., 1997) uses historical weather data on a daily time step to simulate pasture growth and the resultant productivity of either grazing sheep or cattle. Different pasture species are represented within a parameter set that describes the response of pasture species to their environment. Manipulation of these parameters provides a means of evaluating, a priori, the likely responses of livestock production to ‘improved cultivars’. We report the results of simulations conducted within grazing enterprises at three locations in southern Australia: a breeding ewe enterprise at Benalla; a wool-producing enterprise at Hamilton; and a beef breeding enterprise at Corryong

Modeling Solar Lyman Alpha Irradiance

Solar Lyman alpha irradiance is estimated from various solar indices using linear regression analyses. Models developed with multiple linear regression analysis, including daily values and 81-day running means of solar indices, predict reasonably well both the short- and long-term variations observed in Lyman alpha. It is shown that the full disk equivalent width of the He line at 1083 nm offers the best proxy for Lyman alpha, and that the total irradiance corrected for sunspot effect also has a high correlation with Lyman alpha

Vortex density spectrum of quantum turbulence

The fluctuations of the vortex density in a turbulent quantum fluid are deduced from local second-sound attenuation measurements. These measurements are performed with a micromachined open-cavity resonator inserted across a flow of turbulent He-II near 1.6 K. The power spectrum of the measured vortex line density is compatible with a (-5/3) power law. The physical interpretation, still open, is discussed.Comment: Submitted to Europhys. Let

Lower bounds for nodal sets of Dirichlet and Neumann eigenfunctions

Let \phi\ be a Dirichlet or Neumann eigenfunction of the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We prove lower bounds for the size of the nodal set {\phi=0}.Comment: 7 page

Vortex signatures in annular Bose-Einstein condensates

We consider a Bose-Einstein condensate confined in a ``Mexican hat'' potential, with a quartic minus quadratic radial dependence. We find conditions under which the ground state is annular in shape, with a hole in the center of the condensate. Rotation leads to the appearance of stable multiply-quantized vortices, giving rise to a superfluid flow around the ring. The collective modes of the system are explored both numerically and analytically using the Gross-Pitaevskii and hydrodynamic equations. Potential experimental schemes to detect vorticity are proposed and evaluated, which include measuring the splitting of collective mode frequencies, observing expansion following release from the trap, and probing the momentum distribution of the condensate.Comment: 11 pages, 7 figure

A Spectral Bernstein Theorem

We study the spectrum of the Laplace operator of a complete minimal properly immersed hypersurface $M$ in $\R^{n+1}$. (1) Under a volume growth condition on extrinsic balls and a condition on the unit normal at infinity, we prove that $M$ has only essential spectrum consisting of the half line $[0, +\infty)$. This is the case when $\lim_{\tilde{r}\to +\infty}\tilde{r}\kappa_i=0$, where $\tilde{r}$ is the extrinsic distance to a point of $M$ and $\kappa_i$ are the principal curvatures. (2) If the $\kappa_i$ satisfy the decay conditions $|\kappa_i|\leq 1/\tilde{r}$, and strict inequality is achieved at some point $y\in M$, then there are no eigenvalues. We apply these results to minimal graphic and multigraphic hypersurfaces.Comment: 16 pages. v2. Final version: minor revisions, we add Proposition 3.2. Accepted for publication in the Annali di Matematica Pura ed Applicata, on the 05/03/201