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

Finite temperature Casimir effect for graphene

We adopt the Dirac model for quasiparticles in graphene and calculate the finite temperature Casimir interaction between a suspended graphene layer and a parallel conducting surface. We find that at high temperature the Casimir interaction in such system is just one half of that for two ideal conductors separated by the same distance. In this limit single graphene layer behaves exactly as a Drude metal. In particular, the contribution of the TE mode is suppressed, while one of the TM mode saturates the ideal metal value. Behaviour of the Casimir interaction for intermediate temperatures and separations accessible for an experiment is studied in some detail. We also find an interesting interplay between two fundamental constants of graphene physics: the fine structure constant and the Fermi velocity.Comment: 13 pages, 2 figures, to appear in Physical Review

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

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

Current functionality and potential improvements of non-alcoholic fermented cereal beverages

Fermentation continues to be the most common biotechnological tool to be used in cereal-based beverages, as it is relatively simple and economical. Fermented beverages hold a long tradition and have become known for their sensory and health-promoting attributes. Considering the attractive sensory traits and due to increased consumer awareness of the importance of healthy nutrition, the market for functional, natural, and non-alcoholic beverages is steadily increasing all over the world. This paper outlines the current achievements and technological development employed to enhance the qualitative and nutritional status of non-alcoholic fermented cereal beverages (NFCBs). Following an in-depth review of various scientific publications, current production methods are discussed as having the potential to enhance the functional properties of NFCBs and their safety, as a promising approach to help consumers in their efforts to improve their nutrition and health status. Moreover, key aspects concerning production techniques, fermentation methods, and the nutritional value of NFCBs are highlighted, together with their potential health benefits and current consumption trends. Further research efforts are required in the segment of traditional fermented cereal beverages to identify new potentially probiotic microorganisms and starter cultures, novel ingredients as fermentation substrates, and to finally elucidate the contributions of microorganisms and enzymes in the fermentation process

Functionality of special beer processes and potential health benefits

Consumers’ demand for functional fermented food that can fulfill nutritional needs and help maintain a balanced diet while also having a positive impact on one’s health status is increasing all over the world. Thus, healthy choices could include beverages with nutrients and bioactive compounds which can be used as an effective disease-prevention strategy. Regular beer has certain health benefits which inspire further research with the prospect of obtaining special functional beers with little or no alcohol content. As observed, the special beer market remains highly dynamic and is predicted to expand even further. Therefore, brewers need to keep up with the consumers’ interests and needs while designing special beers, namely nonalcoholic beers (NABs), low-alcohol beers (LABs), and craft beers (CBs). Thus, understanding the potential uses of bioactive compounds in special beer, the wide range of therapeutic effects, and the possible mechanisms of action is essential for developing healthier beverages. This review aimed to evaluate the nutritional features of special beers, and their proven or potential beneficial actions on one’s health status and in preventing certain diseases

Antibacterial, antioxidant and anti-proliferative properties and zinc content of five south Portugal herbs

Context: Crataegus monogyna L. (Rosaceae) (CM), Equisetum telmateia L. (Equisataceae) (ET), Geranium purpureum Vil. (Geraniaceae) (GP), Mentha suaveolens Ehrh. (Lamiaceae) (MS), and Lavandula stoechas L. spp. luisieri (Lamiaceae) (LS) are all medicinal. Objective: To evaluate the antioxidant, antiproliferative and antimicrobial activities of plant extracts and quantify individual phenolics and zinc. Material and methods: Aerial part extracts were prepared with water (W), ethanol (E) and an 80% mixture (80EW). Antioxidant activity was measured with TAA, FRAP and RP methods. Phenolics were quantified with a HPLC. Zinc was quantified using voltammetry. Antibacterial activity (after 48 h) was tested using Enterococcus faecalis, Bacillus cereus, Escherichia coli, Staphylococcus aureus, Pseudomonas aeruginosa and Listeria monocytogenes. Antiproliferative activity (after 24 h) was tested using HEP G2 cells and fibroblasts. Results: Solvents influenced results; the best were E and 80EW. GP had the highest antioxidant activity (TAA and FRAP of 536.90mg AAE/g dw and 783.48mg TE/g dw, respectively). CM had the highest zinc concentration (37.21 mg/kg) and phenolic variety, with neochlorogenic acid as the most abundant (92.91 mg/100 g dw). LS was rich in rosmarinic acid (301.71 mg/100 g dw). GP and LS inhibited the most microorganisms: B. cereus, E. coli and S. aureus. GP also inhibited E. faecalis. CM had the lowest MIC: 5830 mu g/mL. The antibacterial activity is explained by the phenolics present. LS and CM showed the most significant anti-proliferative activity, which is explained by their zinc content. Conclusion: The most promising plants for further studies are CM, LS and GP.FCT, Fundacao para a Ciencia e a Tecnologia of Portugal [SFRH/BSA/139/2014

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

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