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

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

Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system

Recent work in the literature has shown that the one-loop long distance quantum corrections to the Newtonian potential imply tiny but observable effects in the restricted three-body problem of celestial mechanics, i.e., at the Lagrangian libration points of stable equilibrium the planetoid is not exactly at equal distance from the two bodies of large mass, but the Newtonian values of its coordinates are changed by a few millimeters in the Earth-Moon system. First, we assess such a theoretical calculation by exploiting the full theory of the quintic equation, i.e., its reduction to Bring-Jerrard form and the resulting expression of roots in terms of generalized hypergeometric functions. By performing the numerical analysis of the exact formulas for the roots, we confirm and slightly improve the theoretical evaluation of quantum corrected coordinates of Lagrangian libration points of stable equilibrium. Second, we prove in detail that also for collinear Lagrangian points the quantum corrections are of the same order of magnitude in the Earth-Moon system. Third, we discuss the prospects to measure, with the help of laser ranging, the above departure from the equilateral triangle picture, which is a challenging task. On the other hand, a modern version of the planetoid is the solar sail, and much progress has been made, in recent years, on the displaced periodic orbits of solar sails at all libration points, both stable and unstable. The present paper investigates therefore, eventually, a restricted three-body problem involving Earth, Moon and a solar sail. By taking into account the one-loop quantum corrections to the Newtonian potential, displaced periodic orbits of the solar sail at libration points are again found to exist

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-

Prescribing the Jacobian in critical spaces

International audienceWe consider the Sobolev space $X=W^{s,p}({\mathbb S}^m ; {\mathbb S}^{k-1})$. We prove the existence of a robust distributional Jacobian $Ju$ for $u\in X$ provided $sp\ge k-1$. This generalizes a result of Bourgain, Brezis and the second author (Comm. Pure Appl. Math. 2005), where the case $m=k$ is considered. In the critical case where $sp=k-1$, we identify the image of the map $X\ni u\mapsto Ju$. This extends a result of Alberti, Baldo and Orlandi (J. Eur. Math. Soc. 2003) for $s=1$ and $p=k-1$. We also present a new, analytical, dipole construction method

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

Establishment of the 1st World Health Organization International Standard for Plasmodium falciparum DNA for nucleic acid amplification technique (NAT)-based assays

BACKGROUND: In order to harmonize results for the detection and quantification of Plasmodium falciparum DNA by nucleic acid amplification technique (NAT)-based assays, a World Health Organization (WHO) collaborative study was performed, evaluating a series of candidate standard preparations. METHODS: Fourteen laboratories from 10 different countries participated in the collaborative study. Four candidate preparations based upon blood samples parasitaemic for P. falciparum were evaluated in the study. Sample AA was lyophilized, whilst samples BB, CC and DD were liquid/frozen preparations. The candidate standards were tested by each laboratory at a range of dilutions in four independent assays, using both qualitative and quantitative NAT-based assays. The results were collated and analysed statistically. RESULTS: Twenty sets of data were returned from the participating laboratories and used to determine the mean P. falciparum DNA content for each sample. The mean log10 "equivalents"/ml were 8.51 for sample AA, 8.45 for sample BB, 8.35 for sample CC, and 5.51 for sample DD. The freeze-dried preparation AA, was examined by accelerated thermal degradation studies and found to be highly stable. CONCLUSION: On the basis of the collaborative study, the freeze-dried material, AA (NIBSC code No. 04/176) was established as the 1st WHO International Standard for P. falciparum DNA NAT-based assays and has been assigned a potency of 10(9) International Units (IU) per ml. Each vial contains 5 x 10(8) IU, equivalent to 0.5 ml of material after reconstitution

Central blood pressure and pulse wave velocity: relationship to target organ damage and cardiovascular morbidity-mortality in diabetic patients or metabolic syndrome. An observational prospective study. LOD-DIABETES study protocol

<p>Abstract</p> <p>Background</p> <p>Diabetic patients show an increased prevalence of non-dipping arterial pressure pattern, target organ damage and elevated arterial stiffness. These alterations are associated with increased cardiovascular risk.</p> <p>The objectives of this study are the following: to evaluate the prognostic value of central arterial pressure and pulse wave velocity in relation to the incidence and outcome of target organ damage and the appearance of cardiovascular episodes (cardiovascular mortality, myocardial infarction, chest pain and stroke) in patients with type 2 diabetes mellitus or metabolic syndrome.</p> <p>Methods/Design</p> <p><b>Design</b>: This is an observational prospective study with 5 years duration, of which the first year corresponds to patient inclusion and initial evaluation, and the remaining four years to follow-up.</p> <p><b>Setting</b>: The study will be carried out in the urban primary care setting.</p> <p><b>Study population</b>: Consecutive sampling will be used to include patients diagnosed with type 2 diabetes between 20-80 years of age. A total of 110 patients meeting all the inclusion criteria and none of the exclusion criteria will be included.</p> <p><b>Measurements</b>: Patient age and sex, family and personal history of cardiovascular disease, and cardiovascular risk factors. Height, weight, heart rate and abdominal circumference. Laboratory tests: hemoglobin, lipid profile, creatinine, microalbuminuria, glomerular filtration rate, blood glucose, glycosylated hemoglobin, blood insulin, fibrinogen and high sensitivity C-reactive protein. Clinical and 24-hour ambulatory (home) blood pressure monitoring and self-measured blood pressure. Common carotid artery ultrasound for the determination of mean carotid intima-media thickness. Electrocardiogram for assessing left ventricular hypertrophy. Ankle-brachial index. Retinal vascular study based on funduscopy with non-mydriatic retinography and evaluation of pulse wave morphology and pulse wave velocity using the SphygmoCor system. The medication used for diabetes, arterial hypertension and hyperlipidemia will be registered, together with antiplatelet drugs.</p> <p>Discussion</p> <p>The results of this study will help to know and quantify the prognostic value of central arterial pressure and pulse wave velocity in relation to the evolution of the subclinical target organ damage markers and the possible incidence of cardiovascular events in patients with type 2 diabetes mellitus.</p> <p>Trial Registration</p> <p>ClinicalTrials.gov Identifier: NCT01065155</p