329 research outputs found
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
Vortex density models for superconductivity and superfluidity
We study some functionals that describe the density of vortex lines in
superconductors subject to an applied magnetic field, and in Bose-Einstein
condensates subject to rotational forcing, in quite general domains in 3
dimensions. These functionals are derived from more basic models via
Gamma-convergence, here and in a companion paper. In our main results, we use
these functionals to obtain descriptions of the critical applied magnetic field
(for superconductors) and forcing (for Bose-Einstein), above which ground
states exhibit nontrivial vorticity, as well as a characterization of the
vortex density in terms of a non local vector-valued generalization of the
classical obstacle problem.Comment: 34 page
Convergence of Ginzburg-Landau functionals in 3-d superconductivity
In this paper we consider the asymptotic behavior of the Ginzburg- Landau
model for superconductivity in 3-d, in various energy regimes. We rigorously
derive, through an analysis via {\Gamma}-convergence, a reduced model for the
vortex density, and we deduce a curvature equation for the vortex lines. In a
companion paper, we describe further applications to superconductivity and
superfluidity, such as general expressions for the first critical magnetic
field H_{c1}, and the critical angular velocity of rotating Bose-Einstein
condensates.Comment: 45 page
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-
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 âhigh riskâ 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
The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate
We study the Gross-Pitaevskii (GP) energy functional for a fast rotating
Bose-Einstein condensate on the unit disc in two dimensions. Writing the
coupling parameter as 1 / \eps^2 we consider the asymptotic regime \eps
\to 0 with the angular velocity proportional to
(\eps^2|\log\eps|)^{-1} . We prove that if \Omega = \Omega_0
(\eps^2|\log\eps|)^{-1} and then a minimizer of
the GP energy functional has no zeros in an annulus at the boundary of the disc
that contains the bulk of the mass. The vorticity resides in a complementary
`hole' around the center where the density is vanishingly small. Moreover, we
prove a lower bound to the ground state energy that matches, up to small
errors, the upper bound obtained from an optimal giant vortex trial function,
and also that the winding number of a GP minimizer around the disc is in accord
with the phase of this trial function.Comment: 52 pages, PDFLaTex. Minor corrections, sign convention modified. To
be published in Commun. Math. Phy
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
Mappings of least Dirichlet energy and their Hopf differentials
The paper is concerned with mappings between planar domains having least
Dirichlet energy. The existence and uniqueness (up to a conformal change of
variables in the domain) of the energy-minimal mappings is established within
the class of strong limits of homeomorphisms in the
Sobolev space , a result of considerable interest in the
mathematical models of Nonlinear Elasticity. The inner variation leads to the
Hopf differential and its trajectories.
For a pair of doubly connected domains, in which has finite conformal
modulus, we establish the following principle:
A mapping is energy-minimal if and only if
its Hopf-differential is analytic in and real along the boundary of .
In general, the energy-minimal mappings may not be injective, in which case
one observes the occurrence of cracks in . Nevertheless, cracks are
triggered only by the points in the boundary of where fails to be
convex. The general law of formation of cracks reads as follows:
Cracks propagate along vertical trajectories of the Hopf differential from
the boundary of toward the interior of where they eventually terminate
before making a crosscut.Comment: 51 pages, 4 figure
Quality of Maternal and Neonatal Care in Albania, Turkmenistan and Kazakhstan: A Systematic, Standard-Based, Participatory Assessment
BACKGROUND: Progress in maternal and neonatal mortality has been slow in many countries despite increasing access to institutional births, suggesting deficiencies in the quality of care. We carried out a systematic assessment of the quality of maternal and newborn care in three CEE/CIS countries, using an innovative approach to identify priority issues and promote action. METHODS: A standard-based tool, covering over 400 items grouped in 13 main areas ranging from support services to case management, was used to assess a sample of ten maternity hospitals in Albania, Kazakhstan and Turkmenistan. Sources of information were visit to services, medical records, observation of cases, and interviews with staff and mothers. A score (range 0 to 3) was attributed to each item and area of care. The assessment was carried out by a multidisciplinary team of international and national professionals. Local managers and staff provided the necessary information and were involved in discussing the findings and the priority actions. RESULTS: Quality of care was found to be substandard in all 13 areas. The lowest scores (between one and two) were obtained by: management of normal labour, delivery, obstetric complications and sick babies; infection prevention; use of guidelines and audits; monitoring and follow-up. Neonatal care as a whole scored better than obstetric care. Interviewed mothers identified lack of information, insufficient support during labour and lack of companionship as main issues. Actions to improve quality of care were identified at facility as well as at central level and framed according to main health system functions. CONCLUSIONS: Quality of care is a key issue to improve maternal and neonatal outcomes, particularly in countries such as CEE/CIS where access to institutional births is nearly universal. Approaches that involve health professionals and managers in comprehensive, action-oriented assessments of quality of care are promising and should be further supported
A perfect correlate does not a surrogate make
BACKGROUND: There is common belief among some medical researchers that if a potential surrogate endpoint is highly correlated with a true endpoint, then a positive (or negative) difference in potential surrogate endpoints between randomization groups would imply a positive (or negative) difference in unobserved true endpoints between randomization groups. We investigate this belief when the potential surrogate and unobserved true endpoints are perfectly correlated within each randomization group. METHODS: We use a graphical approach. The vertical axis is the unobserved true endpoint and the horizontal axis is the potential surrogate endpoint. Perfect correlation within each randomization group implies that, for each randomization group, potential surrogate and true endpoints are related by a straight line. In this scenario the investigator does not know the slopes or intercepts. We consider a plausible example where the slope of the line is higher for the experimental group than for the control group. RESULTS: In our example with unknown lines, a decrease in mean potential surrogate endpoints from control to experimental groups corresponds to an increase in mean true endpoint from control to experimental groups. Thus the potential surrogate endpoints give the wrong inference. Similar results hold for binary potential surrogate and true outcomes (although the notion of correlation does not apply). The potential surrogate endpointwould give the correct inference if either (i) the unknown lines for the two group coincided, which means that the distribution of true endpoint conditional on potential surrogate endpoint does not depend on treatment group, which is called the Prentice Criterion or (ii) if one could accurately predict the lines based on data from prior studies. CONCLUSION: Perfect correlation between potential surrogate and unobserved true outcomes within randomized groups does not guarantee correct inference based on a potential surrogate endpoint. Even in early phase trials, investigators should not base conclusions on potential surrogate endpoints in which the only validation is high correlation with the true endpoint within a group
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