On the particle paths and the stagnation points in small-amplitude deep-water waves

In order to obtain quite precise information about the shape of the particle paths below small-amplitude gravity waves travelling on irrotational deep water, analytic solutions of the nonlinear differential equation system describing the particle motion are provided. All these solutions are not closed curves. Some particle trajectories are peakon-like, others can be expressed with the aid of the Jacobi elliptic functions or with the aid of the hyperelliptic functions. Remarks on the stagnation points of the small-amplitude irrotational deep-water waves are also made.Comment: to appear in J. Math. Fluid Mech. arXiv admin note: text overlap with arXiv:1106.382

Quartz crystal microbalance genosensing of brettanomyces bruxellensis yeast in wine using a rapid and efficient drop and collect protocol

A miniaturized quartz crystal microbalance (QCM) genosensor is proposed for sensitive and real-time detection of short ssDNA sequences (53 bp) or DNA extracted from Brettanomyces bruxellensis (Brett) yeast cells. The presence of Brett yeast causes a depreciation of the quality of aged fine wines, producing molecules of unpleasant odors and biogenic amines that are harmful to human health. More specifically, standard quartz crystal (S-QCM) and homemade 4 nm gold transmission electron microscopy (TEM)-grid patterned quartz (multi-TEM QCM) are herein proposed for biofunctionalization steps with different ssDNA sequences. By employing a rapid and efficient drop and collect protocol, the specific detection of 1 pg/\ub5L ssDNA Brett of a short sequence and 100 ng/\ub5L DNA of B. bruxellensis extracted from a wine sample (VR2008) is reported

Acoustic multi-detection of Gliadin using QCM crystals patterned with controlled sectors of tem grid and annealed Nanoislands on gold electrode

Celiac diseases are a group of gluten ingestion-correlated pathologies that are widespread and, in some cases, very dangerous for human health. The only effective treatment is the elimination of gluten from the diet throughout life. Nowadays, the food industries are very interested in cheap, easy-to-handle methods for detecting gluten in food, in order to provide their consumers with safe and high-quality food. Here, for the first time, the manufacture of controlled micropatterns of annealed gold nanoislands (AuNIs) on a single QCM crystal (QCM-color) and their biofunctionalization for the specific detection of traces of gliadin is reported. In addition, the modified quartz crystal with a TEM grid and 30 nm Au (Q-TEM grid crystal) is proposed as an acoustic sensitive biosensing platform for the rapid screening of the gliadin content in real food products

Rotational symmetry of self-similar solutions to the Ricci flow

Let (M,g) be a three-dimensional steady gradient Ricci soliton which is non-flat and \kappa-noncollapsed. We prove that (M,g) is isometric to the Bryant soliton up to scaling. This solves a problem mentioned in Perelman's first paper.Comment: Final version, to appear in Invent. Mat

In vitro evaluation of antibacterial properties and smear layer removal/sealer penetration of a novel silver-citrate root canal irrigant

This study aimed at evaluating the efficacy of a novel silver-citrate root canal irrigation solution (BioAKT) on smear layer removal, sealer penetration after root canal instrumentation and antibacterial activity. Single-root teeth were endodontically treated, sealed with an epoxi-amine resin sealer and irrigated using: Group I: 5.25% sodium hypochlorite (NaOCl). Group II: silver-citrate solution (BioAKT). Group III: phosphate buffer solution (PBS). Group IV: 17% ethylenediaminetetraacetic acid (EDTA). Smear layer removal and silver deposition at the coronal, middle and apical portion of each canal were analyzed using scanning electron microscopy (SEM) and energy-dispersive x-ray spectroscopy (EDS). Sealer penetration into dentinal tubules at coronal, middle and apical portion was assessed through dye-assisted confocal microscopy (CSM). Both SEM and CSM micrographs were evaluated by two examiners (\u3ba = 0.86), who were blind to the irrigation regimens. scores were given according to the degree of penetration of the sealer. Data analysis included Pearson's x2 and Sidak's multiple comparisons. Dentin discs were polished and sterilized. Enterococcus faecalis biofilms were grown using a continuous-flow bioreactor under anaerobic conditions for 72 h. Specimens were irrigated with the tested solutions, and bacterial viability was assessed using a tetrazolium salt assay (MTT). Statistical analysis included one-way ANOVA and Student's post-hoc t-test (p<0.05). BioAKT and EDTA were the most efficient solutions both in removing the smear layer and allowing sealer penetration. However, at the apical portion BioAKT performed significantly better compared to EDTA both in smear layer removal and sealer penetration (p<0.05). BioAKT and NaOCl showed comparable antibacterial effect (p = 0.53). In conclusion, BioAKT represents a suitable smear layer removal agent, which allows for reliable sealer penetration at the apical portion of the root canal system and offers significant antibacterial properties

Lines on projective varieties and applications

The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined by quadratic equations the base locus of the projective second fundamental form at a general point coincides, as a scheme, with the variety of lines. The second part concerns the problem of extending embedded projective manifolds, using the geometry of the variety of lines. Some applications to the case of homogeneous manifolds are included.Comment: 15 pages. One example removed; one remark and some references added; typos correcte

Continuum viscoplastic simulation of a granular column collapse on large slopes: μ(I) rheology and lateral wall effects

We simulate here dry granular flows resulting from the collapse of granular columns on an inclined channel (up to 22°) and compare precisely the results with laboratory experiments. Incompressibility is assumed despite the dilatancy observed in the experiments (up to 10%). The 2-D model is based on the so-called μ(I) rheology that induces a Drucker-Prager yield stress and a variable viscosity. A nonlinear Coulomb friction term, representing the friction on the lateral walls of the channel, is added to the model. We demonstrate that this term is crucial to accurately reproduce granular collapses on slopes ≳10°, whereas it remains of little effect on the horizontal slope. Quantitative comparison between the experimental and numerical changes with time of the thickness profiles and front velocity makes it possible to strongly constrain the rheology. In particular, we show that the use of a variable or a constant viscosity does not change significantly the results provided that these viscosities are of the same order. However, only a fine tuning of the constant viscosity (η=1 Pa s) makes it possible to predict the slow propagation phase observed experimentally at large slopes. Finally, we observed that small-scale instabilities develop when refining the mesh (also called ill-posed behavior, characterized in the work of Barker et al. [“Well-posed and ill-posed behaviour of the μ(I)-rheology for granular flow,” J. Fluid Mech. 779, 794–818 (2015)] and in the present work) associated with the mechanical model. The velocity field becomes stratified and the bands of high velocity gradient appear. These model instabilities are not avoided by using variable viscosity models such as the μ(I) rheology. However we show that the velocity range, the static-flowing transition, and the thickness profiles are almost not affected by them

Deformation of canonical morphisms and the moduli of surfaces of general type

In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite map can be deformed to a one--to--one map. We use this criterion to construct new simple canonical surfaces with different $c_1^2$ and $\chi$. Our general results enable us to describe some new components of the moduli of surfaces of general type. We also find infinitely many moduli spaces $\mathcal M_{(x',0,y)}$ having one component whose general point corresponds to a canonically embedded surface and another component whose general point corresponds to a surface whose canonical map is a degree 2 morphism.Comment: 32 pages. Final version with some simplifications and clarifications in the exposition. To appear in Invent. Math. (the final publication is available at springerlink.com

Steady water waves with multiple critical layers: interior dynamics

We study small-amplitude steady water waves with multiple critical layers. Those are rotational two-dimensional gravity-waves propagating over a perfect fluid of finite depth. It is found that arbitrarily many critical layers with cat's-eye vortices are possible, with different structure at different levels within the fluid. The corresponding vorticity depends linearly on the stream function.Comment: 14 pages, 3 figures. As accepted for publication in J. Math. Fluid Mec