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

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

Аспекты обучения работников первичной сети по вопросам контроля туберкулеза в Молдове

Nicolae Testemiţanu State Medical and Pharmaceutical University, Institute of Phthisiopneumology Chiril Draganiuc, Center of Politics and Analysis in Health, Congresul III al Medicilor de Familie din Republica Moldova, 17–18 mai, 2012, Chişinău, Republica Moldova, Conferinţa Naţională „Maladii bronhoobstructive la copii”, consacrată profesorului universitar, doctor habilitat Victor Gheţeul, 27 aprilie, Chişinău, Republica MoldovaTuberculosis is a public health problem in Moldova. Primary health care (PHC) workers play an important role in control of tuberculosis (TB). The article describes the results of PHC workers training on problems of tuberculosis control. About 3720 PHC workers (1355 family physicians and 2365 nurses) from Moldova have been trained in problems of classic TB and TB/MDR control. Continuous medical education in form of short training courses, based on interactive instructional methods for adults, and focused on development of knowledge, abilities and attitudes of trainees are efficient for preparation of work force of health care system. Training of more than 50% of PHC workers resulted in improvement of TB control at primary care level proved by improved of prevention, case detection, and completion treatment in ambulatory conditions. However, the control of classic tuberculosis improved and global incidence of TB cases decreased over the past seven years, the control of TB/MDR remains a major problem.Туберкулез является проблемой публичного здоровья в Молдове. Работники первичной медицинской сети играют важную роль в контроле туберкулеза. Статья описывает результаты обучения работников первичной медицинской сети по вопросам контроля туберкулеза. Около 3720 работников первичной медицинской сети из Молдовы (1355 семейных врачей и 2365 семейных медицинских сестер) были обучены по вопросам контроля классического и полилекарственного устойчивого (ПЛУ) туберкулеза. Непрерывное медицинское обучение в форме коротких курсов, основанных на интерактивных методах обучения для взрослых, ориентированных на развитие знаний, практических навыков и отношений являются эффективной формой подготовки работников первичной медицинской сети. Обучение более 50% работников первичной медицинской сети повысило эффективность контроля туберкулеза на уровне первичной медицинской сети через улучшение предупреждения, раннего выявления и лечения туберкулеза в амбулаторных условиях. Несмотря на улучшение контроля классического туберкулеза и снижение глобальной заболеваемости туберкулезом, продолжает оставаться важной проблемой контроль ПЛУ туберкулеза

Porous medium equation with nonlocal pressure

We provide a rather complete description of the results obtained so far on the nonlinear diffusion equation $u_t=\nabla\cdot (u^{m-1}\nabla (-\Delta)^{-s}u)$, which describes a flow through a porous medium driven by a nonlocal pressure. We consider constant parameters $m>1$ and $0<s<1$, we assume that the solutions are non-negative, and the problem is posed in the whole space. We present a theory of existence of solutions, results on uniqueness, and relation to other models. As new results of this paper, we prove the existence of self-similar solutions in the range when $N=1$ and $m>2$, and the asymptotic behavior of solutions when $N=1$. The cases $m = 1$ and $m = 2$ were rather well known.Comment: 24 pages, 2 figure

Computational modelling elucidates the mechanism of ciliary regulation in health and disease

<p>Abstract</p> <p>Background</p> <p>Ciliary dysfunction leads to a number of human pathologies, including primary ciliary dyskinesia, nephronophthisis, situs inversus pathology or infertility. The mechanism of cilia beating regulation is complex and despite extensive experimental characterization remains poorly understood. We develop a detailed systems model for calcium, membrane potential and cyclic nucleotide-dependent ciliary motility regulation.</p> <p>Results</p> <p>The model describes the intimate relationship between calcium and potassium ionic concentrations inside and outside of cilia with membrane voltage and, for the first time, describes a novel type of ciliary excitability which plays the major role in ciliary movement regulation. Our model describes a mechanism that allows ciliary excitation to be robust over a wide physiological range of extracellular ionic concentrations. The model predicts the existence of several dynamic modes of ciliary regulation, such as the generation of intraciliary Ca²⁺spike with amplitude proportional to the degree of membrane depolarization, the ability to maintain stable oscillations, monostable multivibrator regimes, all of which are initiated by variability in ionic concentrations that translate into altered membrane voltage.</p> <p>Conclusions</p> <p>Computational investigation of the model offers several new insights into the underlying molecular mechanisms of ciliary pathologies. According to our analysis, the reported dynamic regulatory modes can be a physiological reaction to alterations in the extracellular environment. However, modification of the dynamic modes, as a result of genetic mutations or environmental conditions, can cause a life threatening pathology.</p

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-

Screening of antioxidant properties of the apple juice using the front-face synchronous fluorescence and chemometrics

Fluorescence spectroscopy is gaining increasing attention in food analysis due to its higher sensitivity and selectivity as compared to other spectroscopic techniques. Synchronous scanning fluorescence technique is particularly useful in studies of multi-fluorophoric food samples, providing a further improvement of selectivity by reduction in the spectral overlapping and suppressing light-scattering interferences. Presently, we study the feasibility of the prediction of the total phenolics, flavonoids, and antioxidant capacity using front-face synchronous fluorescence spectra of apple juices. Commercial apple juices from different product ranges were studied. Principal component analysis (PCA) applied to the unfolded synchronous fluorescence spectra was used to compare the fluorescence of the entire sample set. The regression analysis was performed using partial least squares (PLS1 and PLS2) methods on the unfolded total synchronous and on the single-offset synchronous fluorescence spectra. The best calibration models for all of the studied parameters were obtained using the PLS1 method for the single-offset synchronous spectra. The models for the prediction of the total flavonoid content had the best performance; the optimal model was obtained for the analysis of the synchronous fluorescence spectra at Delta lambda = 110 nm (R (2) = 0.870, residual predictive deviation (RPD) = 2.7). The optimal calibration models for the prediction of the total phenolic content (Delta lambda = 80 nm, R (2) = 0.766, RPD = 2.0) and the total antioxidant capacity (Delta lambda = 70 nm, R (2) = 0.787, RPD = 2.1) had only an approximate predictive ability. These results demonstrate that synchronous fluorescence could be a useful tool in fast semi-quantitative screening for the antioxidant properties of the apple juices.info:eu-repo/semantics/publishedVersio

Handling Disturbance and Awareness of Concurrent Updates in a Collaborative Editor

International audienceWhen people work collaboratively on a shared document, they have two contradictory requirements on their editors that may affect the efficiency of their work. On the one hand, they would like to know what other people are currently doing on a particular part of the document. On the other hand, they would like to focus their attention on their own current work, with as little disturbance from the concurrent activities as possible. We present some features that help the user handle disturbance and awareness of concurrent updates. While collabora-tively editing a shared document with other people, a user can create a focus region. The user can concentrate on the work in the region without being interfered with the concurrent updates of the other people. Occasionally, the user can preview the concurrent updates and select a number of these updates to be integrated into the local copy. We have implemented a collaborative editing subsystem in the GNU Emacs 5 text editor with the described features

Control and stabilization of waves on 1-d networks

We present some recent results on control and stabilization of waves on 1-d networks.The fine time-evolution of solutions of wave equations on networks and, consequently, their control theoretical properties, depend in a subtle manner on the topology of the network under consideration and also on the number theoretical properties of the lengths of the strings entering in it. Therefore, the overall picture is quite complex.In this paper we summarize some of the existing results on the problem of controllability that, by classical duality arguments in control theory, can be reduced to that of observability of the adjoint uncontrolled system. The problem of observability refers to that of recovering the total energy of solutions by means of measurements made on some internal or external nodes of the network. They lead, by duality, to controllability results guaranteeing that L 2-controls located on those nodes may drive sufficiently smooth solutions to equilibrium at a final time. Most of our results in this context, obtained in collaboration with R. Dáger, refer to the problem of controlling the network from one single external node. It is, to some extent, the most complex situation since, obviously, increasing the number of controllers enhances the controllability properties of the system. Our methods of proof combine sidewise energy estimates (that in the particular case under consideration can be derived by simply applying the classical d'Alembert's formula), Fourier series representations, non-harmonic Fourier analysis, and number theoretical tools.These control results belong to the class of the so-called open-loop control systems.We then discuss the problem of closed-loop control or stabilization by feedback. We present a recent result, obtained in collaboration with J. Valein, showing that the observability results previously derived, regardless of the method of proof employed, can also be recast a posteriori in the context of stabilization, so to derive explicit decay rates (as) for the energy of smooth solutions. The decay rate depends in a very sensitive manner on the topology of the network and the number theoretical properties of the lengths of the strings entering in it.In the end of the article we also present some challenging open problems