8,060 research outputs found
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
The radial curvature of an end that makes eigenvalues vanish in the essential spectrum II
Under the quadratic-decay-conditions of the radial curvatures of an end, we
shall derive growth estimates of solutions to the eigenvalue equation and show
the absence of eigenvalues.Comment: "" in the conditions and should be replaced by
"". in the conclusion of Theorem 1.3
should be replaced by ; trivial miss-calculatio
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
On the magnitude of spheres, surfaces and other homogeneous spaces
In this paper we define the magnitude of metric spaces using measures rather
than finite subsets as had been done previously and show that this agrees with
earlier work with Leinster in arXiv:0908.1582. An explicit formula for the
magnitude of an n-sphere with its intrinsic metric is given. For an arbitrary
homogeneous Riemannian manifold the leading terms of the asymptotic expansion
of the magnitude are calculated and expressed in terms of the volume and total
scalar curvature of the manifold. In the particular case of a homogeneous
surface the form of the asymptotics can be given exactly up to vanishing terms
and this involves just the area and Euler characteristic in the way conjectured
for subsets of Euclidean space in previous work.Comment: 21 pages. Main change from v1: details added to proof of Theorem
A Spectral Bernstein Theorem
We study the spectrum of the Laplace operator of a complete minimal properly
immersed hypersurface in . (1) Under a volume growth condition on
extrinsic balls and a condition on the unit normal at infinity, we prove that
has only essential spectrum consisting of the half line .
This is the case when , where
is the extrinsic distance to a point of and are the
principal curvatures. (2) If the satisfy the decay conditions
, and strict inequality is achieved at some point
, 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
Local Asymmetry and the Inner Radius of Nodal Domains
Let M be a closed Riemannian manifold of dimension n. Let f be an
eigenfunction of the Laplace-Beltrami operator corresponding to an eigenvalue
\lambda. We show that the volume of {f>0} inside any ball B whose center lies
on {f=0} is > C|B|/\lambda^n. We apply this result to prove that each nodal
domain contains a ball of radius > C/\lambda^n.Comment: 12 pages, 1 figure; minor corrections; to appear in Comm. PDE
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
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
Advanced bladder technology. Gas impermeable protein films and laminates Final report
Gas impermeable and cryogenic flexible protein film
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