Vortex energy and vortex bending for a rotating Bose-Einstein condensate

For a Bose-Einstein condensate placed in a rotating trap, we give a simplified expression of the Gross-Pitaevskii energy in the Thomas Fermi regime, which only depends on the number and shape of the vortex lines. Then we check numerically that when there is one vortex line, our simplified expression leads to solutions with a bent vortex for a range of rotationnal velocities and trap parameters which are consistent with the experiments.Comment: 7 pages, 2 figures. submitte

Ginzburg-Landau model with small pinning domains

We consider a Ginzburg-Landau type energy with a piecewise constant pinning term $a$ in the potential $(a^2 - |u|^2)^2$. The function $a$ 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 $\v\to0$; here, \v is the inverse of the Ginzburg-Landau parameter. We study the energy minimization in a smooth simply connected domain $\Omega \subset \mathbb{C}$ with Dirichlet boundary condition $g$ on \d \O, with topological degree {\rm deg}_{\d \O} (g) = d >0. Our main result is that, for small \v, minimizers have $d$ 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

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 $\Omega$ proportional to (\eps^2|\log\eps|)^{-1} . We prove that if \Omega = \Omega_0 (\eps^2|\log\eps|)^{-1} and $\Omega_0 > 2(3\pi)^{-1}$ 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

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

Vortex Rings in Fast Rotating Bose-Einstein Condensates

When Bose-Eintein condensates are rotated sufficiently fast, a giant vortex phase appears, that is the condensate becomes annular with no vortices in the bulk but a macroscopic phase circulation around the central hole. In a former paper [M. Correggi, N. Rougerie, J. Yngvason, {\it arXiv:1005.0686}] we have studied this phenomenon by minimizing the two dimensional Gross-Pitaevskii energy on the unit disc. In particular we computed an upper bound to the critical speed for the transition to the giant vortex phase. In this paper we confirm that this upper bound is optimal by proving that if the rotation speed is taken slightly below the threshold there are vortices in the condensate. We prove that they gather along a particular circle on which they are evenly distributed. This is done by providing new upper and lower bounds to the GP energy.Comment: to appear in Archive of Rational Mechanics and Analysi

Forecasting Tunisian type 2 diabetes prevalence to 2027: validation of a simple model.

BACKGROUND: Most projections of type 2 diabetes (T2D) prevalence are simply based on demographic change (i.e. ageing). We developed a model to predict future trends in T2D prevalence in Tunisia, explicitly taking into account trends in major risk factors (obesity and smoking). This could improve assessment of policy options for prevention and health service planning. METHODS: The IMPACT T2D model uses a Markov approach to integrate population, obesity and smoking trends to estimate future T2D prevalence. We developed a model for the Tunisian population from 1997 to 2027, and validated the model outputs by comparing with a subsequent T2D prevalence survey conducted in 2005. RESULTS: The model estimated that the prevalence of T2D among Tunisians aged over 25 years was 12.0% in 1997 (95% confidence intervals 9.6%-14.4%), increasing to 15.1% (12.5%-17.4%) in 2005. Between 1997 and 2005, observed prevalence in men increased from 13.5% to 16.1% and in women from 12.9% to 14.1%. The model forecast for a dramatic rise in prevalence by 2027 (26.6% overall, 28.6% in men and 24.7% in women). However, if obesity prevalence declined by 20% in the 10 years from 2013, and if smoking decreased by 20% over 10 years from 2009, a 3.3% reduction in T2D prevalence could be achieved in 2027 (2.5% in men and 4.1% in women). CONCLUSIONS: This innovative model provides a reasonably close estimate of T2D prevalence for Tunisia over the 1997-2027 period. Diabetes burden is now a significant public health challenge. Our model predicts that this burden will increase significantly in the next two decades. Tackling obesity, smoking and other T2D risk factors thus needs urgent action. Tunisian decision makers have therefore defined two strategies: obesity reduction and tobacco control. Responses will be evaluated in future population surveys

A cost effectiveness analysis of salt reduction policies to reduce coronary heart disease in four Eastern Mediterranean countries.

BACKGROUND: Coronary Heart Disease (CHD) is rising in middle income countries. Population based strategies to reduce specific CHD risk factors have an important role to play in reducing overall CHD mortality. Reducing dietary salt consumption is a potentially cost-effective way to reduce CHD events. This paper presents an economic evaluation of population based salt reduction policies in Tunisia, Syria, Palestine and Turkey. METHODS AND FINDINGS: Three policies to reduce dietary salt intake were evaluated: a health promotion campaign, labelling of food packaging and mandatory reformulation of salt content in processed food. These were evaluated separately and in combination. Estimates of the effectiveness of salt reduction on blood pressure were based on a literature review. The reduction in mortality was estimated using the IMPACT CHD model specific to that country. Cumulative population health effects were quantified as life years gained (LYG) over a 10 year time frame. The costs of each policy were estimated using evidence from comparable policies and expert opinion including public sector costs and costs to the food industry. Health care costs associated with CHDs were estimated using standardized unit costs. The total cost of implementing each policy was compared against the current baseline (no policy). All costs were calculated using 2010 PPP exchange rates. In all four countries most policies were cost saving compared with the baseline. The combination of all three policies (reducing salt consumption by 30%) resulted in estimated cost savings of $235,000,000 and 6455 LYG in Tunisia;$39,000,000 and 31674 LYG in Syria; $6,000,000 and 2682 LYG in Palestine and$1,3000,000,000 and 378439 LYG in Turkey. CONCLUSION: Decreasing dietary salt intake will reduce coronary heart disease deaths in the four countries. A comprehensive strategy of health education and food industry actions to label and reduce salt content would save both money and lives

Seroprevalence of Toxoplasma gondii infection in arthritis patients in eastern China

Background: There is accumulating evidence for an increased susceptibility to infection in patients with arthritis. We sought to understand the epidemiology of Toxoplasma gondii infection in arthritis patients in eastern China, given the paucity of data on the magnitude of T. gondii infection in these patients. Methods: Seroprevalence of T. gondii infection was assessed by enzyme-linked immunosorbent assay using a crude antigen of the parasite in 820 arthritic patients, and an equal number of healthy controls, from Qingdao and Weihai cities, eastern China. Sociodemographic, clinical and lifestyle information on the study participants were also obtained. Results: The prevalence of anti-T. gondii IgG was significantly higher in arthritic patients (18.8%) compared with 12% in healthy controls (P < 0.001). Twelve patients with arthritis had anti-T. gondii IgM antibodies comparable with 10 control patients (1.5% vs 1.2%). Demographic factors did not significantly influence these seroprevalence frequencies. The highest T. gondii infection seropositivity rate was detected in patients with rheumatoid arthritis (24.8%), followed by reactive arthritis (23.8%), osteoarthritis (19%), infectious arthritis (18.4%) and gouty arthritis (14.8%). Seroprevalence rates of rheumatoid arthritis and reactive arthritis were significantly higher when compared with controls (P < 0.001 and P = 0.002, respectively). A significant association was detected between T. gondii infection and cats being present in the home in arthritic patients (odds ratio [OR], 1.68; 95% confidence interval [CI]: 1.24 – 2.28; P = 0.001). Conclusions: These findings are consistent with and extend previous results, providing further evidence to support a link between contact with cats and an increased risk of T. gondii infection. Our study is also the first to confirm an association between T. gondii infection and arthritis patients in China. Implications for better prevention and control of T. gondii infection in arthritis patients are discussed. Trial registration: This is an epidemiological survey, therefore trial registration was not required