156 research outputs found
Rotating superfluids in anharmonic traps: From vortex lattices to giant vortices
We study a superfluid in a rotating anharmonic trap and explicate a rigorous
proof of a transition from a vortex lattice to a giant vortex state as the
rotation is increased beyond a limiting speed determined by the interaction
strength. The transition is characterized by the disappearance of the vortices
from the annulus where the bulk of the superfluid is concentrated due to
centrifugal forces while a macroscopic phase circulation remains. The analysis
is carried out within two-dimensional Gross-Pitaevskii theory at large coupling
constant and reveals significant differences between 'soft' anharmonic traps
(like a quartic plus quadratic trapping potential) and traps with a fixed
boundary: In the latter case the transition takes place in a parameter regime
where the size of vortices is very small relative to the width of the annulus
whereas in 'soft' traps the vortex lattice persists until the width of the
annulus becomes comparable to the vortex cores. Moreover, the density profile
in the annulus where the bulk is concentrated is, in the 'soft' case,
approximately gaussian with long tails and not of the Thomas-Fermi type like in
a trap with a fixed boundary.Comment: Published version. Typos corrected, references adde
Ginzburg-Landau vortex dynamics with pinning and strong applied currents
We study a mixed heat and Schr\"odinger Ginzburg-Landau evolution equation on
a bounded two-dimensional domain with an electric current applied on the
boundary and a pinning potential term. This is meant to model a superconductor
subjected to an applied electric current and electromagnetic field and
containing impurities. Such a current is expected to set the vortices in
motion, while the pinning term drives them toward minima of the pinning
potential and "pins" them there. We derive the limiting dynamics of a finite
number of vortices in the limit of a large Ginzburg-Landau parameter, or \ep
\to 0, when the intensity of the electric current and applied magnetic field
on the boundary scale like \lep. We show that the limiting velocity of the
vortices is the sum of a Lorentz force, due to the current, and a pinning
force. We state an analogous result for a model Ginzburg-Landau equation
without magnetic field but with forcing terms. Our proof provides a unified
approach to various proofs of dynamics of Ginzburg-Landau vortices.Comment: 48 pages; v2: minor errors and typos correcte
The Effects of Negative Legacies on the Adjustment of Parentally Bereaved Children and Adolescents
This is a report of a qualitative analysis of a sample of bereaved families in which one parent died and in which children scored in the clinical range on the Child Behavior Check List. The purpose of this analysis was to learn more about the lives of these children. They were considered to be at risk of developing emotional and behavioral problems associated with the death. We discovered that many of these “high risk” children had a continuing bond with the deceased that was primarily negative and troubling for them in contrast to a comparison group of children not at risk from the same study. Five types of legacies, not mutually exclusive, were identified: health related, role related, personal qualities, legacy of blame, and an emotional legacy. Coping behavior on the part of the surviving parent seemed to make a difference in whether or not a legacy was experienced as negative
Inhomogeneous Vortex Patterns in Rotating Bose-Einstein Condensates
We consider a 2D rotating Bose gas described by the Gross-Pitaevskii (GP)
theory and investigate the properties of the ground state of the theory for
rotational speeds close to the critical speed for vortex nucleation. While one
could expect that the vortex distribution should be homogeneous within the
condensate we prove by means of an asymptotic analysis in the strongly
interacting (Thomas-Fermi) regime that it is not. More precisely we rigorously
derive a formula due to Sheehy and Radzihovsky [Phys. Rev. A 70, 063620(R)
(2004)] for the vortex distribution, a consequence of which is that the vortex
distribution is strongly inhomogeneous close to the critical speed and
gradually homogenizes when the rotation speed is increased. From the
mathematical point of view, a novelty of our approach is that we do not use any
compactness argument in the proof, but instead provide explicit estimates on
the difference between the vorticity measure of the GP ground state and the
minimizer of a certain renormalized energy functional.Comment: 41 pages, journal ref: Communications in Mathematical Physics: Volume
321, Issue 3 (2013), Page 817-860, DOI : 10.1007/s00220-013-1697-
Analysis of Nematic Liquid Crystals with Disclination Lines
We investigate the structure of nematic liquid crystal thin films described
by the Landau--de Gennes tensor-valued order parameter with Dirichlet boundary
conditions of nonzero degree. We prove that as the elasticity constant goes to
zero a limiting uniaxial texture forms with disclination lines corresponding to
a finite number of defects, all of degree 1/2 or all of degree -1/2. We also
state a result on the limiting behavior of minimizers of the Chern-Simons-Higgs
model without magnetic field that follows from a similar proof.Comment: 40 pages, 1 figur
Ginzburg-Landau model with small pinning domains
We consider a Ginzburg-Landau type energy with a piecewise constant pinning
term in the potential . The function is different from
1 only on finitely many disjoint domains, called the {\it pinning domains}.
These pinning domains model small impurities in a homogeneous superconductor
and shrink to single points in the limit ; here, \v is the inverse of
the Ginzburg-Landau parameter. We study the energy minimization in a smooth
simply connected domain with Dirichlet boundary
condition on \d \O, with topological degree {\rm deg}_{\d \O} (g) = d
>0. Our main result is that, for small \v, minimizers have distinct
zeros (vortices) which are inside the pinning domains and they have a degree
equal to 1. The question of finding the locations of the pinning domains with
vortices is reduced to a discrete minimization problem for a finite-dimensional
functional of renormalized energy. We also find the position of the vortices
inside the pinning domains and show that, asymptotically, this position is
determined by {\it local renormalized energy} which does not depend on the
external boundary conditions.Comment: 39 page
Carcinoid heart disease: relationship of circulating vasoactive substances to ultrasound-detectable cardiac abnormalities.
- …