Dispersion for the Schr\"odinger Equation on Networks

In this paper we consider the Schr\"odinger equation on a network formed by a tree with the last generation of edges formed by infinite strips. We give an explicit description of the solution of the linear Schr\"odinger equation with constant coefficients. This allows us to prove dispersive estimates, which in turn are useful for solving the nonlinear Schr\"odinger equation. The proof extends also to the laminar case of positive step-function coefficients having a finite number of discontinuities.Comment: 16 pages, 2 figure

Uniqueness results for an ODE related to a generalized Ginzburg-Landau model for liquid crystals

We study a singular nonlinear ordinary differential equation on intervals {[}0, R) with R <= +infinity, motivated by the Ginzburg-Landau models in superconductivity and Landau-de Gennes models in liquid crystals. We prove existence and uniqueness of positive solutions under general assumptions on the nonlinearity. Further uniqueness results for sign-changing solutions are obtained for a physically relevant class of nonlinearities. Moreover, we prove a number of fine qualitative properties of the solution that are important for the study of energetic stability

Symmetry and Multiplicity of Solutions in a Two-Dimensional Landau–de Gennes Model for Liquid Crystals

We consider a variational two-dimensional Landau–de Gennes model in the theory of nematic liquid crystals in a disk of radius R. We prove that under a symmetric boundary condition carrying a topological defect of degree k 2 for some given even non-zero integer k, there are exactly two minimizers for all large enough R. We show that the minimizers do not inherit the full symmetry structure of the energy functional and the boundary data. We further show that there are at least five symmetric critical points

Laparoscopic herniorrhaphy in children.

The authors report their experience in laparoscopic repair of inguinal hernias in children. From May 2010 to November 2013, 122 patients with inguinal hernia underwent laparoscopic herniorrhaphy (92 males and 30 females). Telescope used was 5 mm, while trocars for the operative instruments were 3 or 2 mm. After introducing the camera at the umbilical level and trocars in triangulation, a 4-0 nonabsorbable monofilament suture was inserted directly through the abdominal wall. The internal inguinal ring was then closed by N or double N suture. All operations were performed in one-day surgery setting. In the case of association of inguinal and umbilical hernia an original technique was performed for positioning and fixing the umbilical trocar and for the primary closure of the abdominal wall defect. The postoperative follow-up consisted of outpatient visits at 1 week and 1, 3, and 6 months. The mean age of patients was 38.5 months. Of all patients, 26 were also suffering from umbilical hernia (19 males and 7 females). A total of 160 herniorrhaphies were performed; 84 were unilateral (66 inguinal hernia, 18 inguinal hernia associated with umbilical hernia), 38 bilateral (30 inguinal hernia, 8 inguinal hernia associated with umbilical hernia). Nine of 122 patients (6 males and 3 females) were operated in emergency for incarcerated hernia. A pre-operative diagnosis of unilateral inguinal hernia was performed in 106 cases. Of these patients, laparoscopy revealed a controlateral open internal inguinal ring in 22 cases (20.7%). The mean operative time was 29.9±15.9 min for the monolateral herniorrhaphies, while in case of bilateral repair the mean operative time was 41.5±10.4 min. The mean operative time for the repair of unilateral inguinal hernia associated with umbilical hernia was 30.1±7.4 while for the correction of bilateral inguinal hernia associated with umbilical hernia 39.5±10.6 min. There were 3 recurrences (1.8%): 2 cases in unilateral repair and 1 case a unilateral recurrence in a bilateral repair. No other complications were seen. Laparoscopic repair of inguinal hernia in children performed in this experience resulted a safe and effective procedure

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 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

The Compact Ignition Tokamak and electron cyclotron heating: Description of need; assessment of prospects

The CIT will benefit from auxiliary heating of 10 to 40 MW. The schedules of both the CIT construction project and the operating plan contain adequate time to develop and implement ECH systems based on the gyrotron and the induction free electron laser (IFEL). Each approach has advantages and is the object of R and D at the level of many millions of dollars per year. While the gyrotron is further advanced in terms of power and pulse length achieved, rapid progress is scheduled for the IFEL, including experiments on tokamaks. Plans of CIT, gyrotron, and IFEL make 1992 an appropriate time frame to commit to one or both systems. 12 refs., 8 figs., 2 tabs

Quantifying Collaboration Quality in Face-to-Face Classroom Settings Using MMLA

Producción CientíficaThe estimation of collaboration quality using manual observation and coding is a tedious and difficult task. Researchers have proposed the automation of this process by estimation into few categories (e.g., high vs. low collaboration). However, such categorical estimation lacks in depth and actionability, which can be critical for practitioners. We present a case study that evaluates the feasibility of quantifying collaboration quality and its multiple sub-dimensions (e.g., collaboration flow) in an authentic classroom setting. We collected multimodal data (audio and logs) from two groups collaborating face-to-face and in a collaborative writing task. The paper describes our exploration of different machine learning models and compares their performance with that of human coders, in the task of estimating collaboration quality along a continuum. Our results show that it is feasible to quantitatively estimate collaboration quality and its sub-dimensions, even from simple features of audio and log data, using machine learning. These findings open possibilities for in-depth automated quantification of collaboration quality, and the use of more advanced features and algorithms to get their performance closer to that of human coders.European Union via the European Regional Development Fund and in the context of CEITER and Next-Lab (Horizon 2020 Research and Innovation Programme, grant agreements no. 669074 and 731685)Junta de Castilla y León (Project VA257P18)Ministerio de Ciencia, Innovación y Universidades (Project TIN2017-85179-C3-2-R

Non-alcoholic and craft beer production and challenges

Beer is the most consumed alcoholic beverage in the world and the third most popular beverage after water and tea. Emerging health-oriented lifestyle trends, demographics, stricter legislation, religious prohibitions, and consumers’ preferences have led to a strong and steady growth of interest for non-alcoholic beers (NABs), low-alcohol beers (LABs), as well for craft beers (CBs). Conventional beer, as the worlds most consumed alcoholic beverage, recently gained more recognition also due to its potential functionality associated with the high content of phenolic antioxidants and low ethanol content. The increasing attention of consumers to health-issues linked to alcohol abuse urges breweries to expand the assortment of conventional beers through novel drinks concepts. The production of these beers employs several techniques that vary in performance, efficiency, and usability. Involved production technologies have been reviewed and evaluated in this paper in terms of efficiency and production costs, given the possibility that craft brewers might want to adapt them and finally introduce novel non-alcoholic drinks in the market