Velocity, energy and helicity of vortex knots and unknots

In this paper we determine the velocity, the energy and estimate writhe and twist helicity contributions of vortex filaments in the shape of torus knots and unknots (toroidal and poloidal coils) in a perfect fluid. Calculations are performed by numerical integration of the Biot-Savart law. Vortex complexity is parametrized by the winding number $w$, given by the ratio of the number of meridian wraps to that of the longitudinal wraps. We find that for $w<1$ vortex knots and toroidal coils move faster and carry more energy than a reference vortex ring of same size and circulation, whereas for $w>1$ knots and poloidal coils have approximately same speed and energy of the reference vortex ring. Helicity is dominated by the writhe contribution. Finally, we confirm the stabilizing effect of the Biot-Savart law for all knots and unknots tested, that are found to be structurally stable over a distance of several diameters. Our results also apply to quantized vortices in superfluid $^4$He.Comment: 17 pages, 8 figures, 2 table

Kelvin Wave Cascade and Decay of Superfluid Turbulence

Kelvin waves (kelvons)--the distortion waves on vortex lines--play a key part in the relaxation of superfluid turbulence at low temperatures. We present a weak-turbulence theory of kelvons. We show that non-trivial kinetics arises only beyond the local-induction approximation and is governed by three-kelvon collisions; corresponding kinetic equation is derived. On the basis of the kinetic equation, we prove the existence of Kolmogorov cascade and find its spectrum. The qualitative analysis is corroborated by numeric study of the kinetic equation. The application of the results to the theory of superfluid turbulence is discussed.Comment: 4 pages, RevTe

Nasal immunization with the c-terminal domain of bcla3 induced specific igg production and attenuated disease symptoms in mice infected with clostridioides difficile spores

Clostridioides difficile is a Gram-positive, spore-forming bacterium that causes a severe intestinal infection. Spores of this pathogen enter in the human body through the oral route, interact with intestinal epithelial cells and persist in the gut. Once germinated, the vegetative cells colonize the intestine and produce toxins that enhance an immune response that perpetuate the disease. Therefore, spores are major players of the infection and ideal targets for new therapies. In this context, spore surface proteins of C. difficile, are potential antigens for the development of vaccines targeting C. difficile spores. Here, we report that the C-terminal domain of the spore surface protein BclA3, BclA3CTD, was identified as an antigenic epitope, over-produced in Escherichia coli and tested as an immunogen in mice. To increase antigen stability and efficiency, BclA3CTD was also exposed on the surface of B. subtilis spores, a mucosal vaccine delivery system. In the experimental conditions used in this study, free BclA3CTD induced antibody production in mice and attenuated some C. difficile infection symptoms after a challenge with the pathogen, while the spore-displayed antigen resulted less effective. Although dose regimen and immunization routes need to be optimized, our results suggest BclA3CTD as a potentially effective antigen to develop a new vaccination strategy targeting C. difficile spores

Performance of a Tungsten-Cerium Fluoride Sampling Calorimeter in High-Energy Electron Beam Tests

A prototype for a sampling calorimeter made out of cerium fluoride crystals interleaved with tungsten plates, and read out by wavelength-shifting fibres, has been exposed to beams of electrons with energies between 20 and 150 GeV, produced by the CERN Super Proton Synchrotron accelerator complex. The performance of the prototype is presented and compared to that of a Geant4 simulation of the apparatus. Particular emphasis is given to the response uniformity across the channel front face, and to the prototype's energy resolution.Comment: 6 pages, 6 figures, Submitted to NIM

Definition of analytical cleaning procedures for archaeological pottery from underwater environments: The case study of samples from Baia (Naples, South Italy)

This work is focused on a multidisciplinary study of 13 pottery fragments collected in the submerged archaeological site of Baia (Naples, Italy). Founded by the Romans in the 1st century B.C., this archaeological area represents one of the greatest evidences of Roman architecture and it includes ancient ruins whose structures range from maritime villas and imperial buildings. Several diagnostic tests were carried out in order to characterize the archaeological materials, their structure and properties, as well as the alteration and degradation products. Degradation forms in seawater imply not only a variation in the physico-mechanical and chemical properties of the material but also an aesthetic damage, due to superficial deposits, which can lead to the illegibility of the artefacts. In this context, it is crucial to determine to what extent these decay factors, mainly attributable to biological growth, could affect the durability of pottery and what are the effects of cleaning procedures. The work offers further elements to obtain new insights into the underwater cultural heritage field and in the function of ceramic matter, especially related to several applications in technology and in the adoption of strategies for suitable conservation procedures. (c) 2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Localized induction equation and pseudospherical surfaces

We describe a close connection between the localized induction equation hierarchy of integrable evolution equations on space curves, and surfaces of constant negative Gauss curvature.Comment: 21 pages, AMSTeX file. To appear in Journal of Physics A: Mathematical and Genera

Gradient catastrophe and flutter in vortex filament dynamics

Gradient catastrophe and flutter instability in the motion of vortex filament within the localized induction approximation are analyzed. It is shown that the origin if this phenomenon is in the gradient catastrophe for the dispersionless Da Rios system which describes motion of filament with slow varying curvature and torsion. Geometrically this catastrophe manifests as a rapid oscillation of a filament curve in a point that resembles the flutter of airfoils. Analytically it is the elliptic umbilic singularity in the terminology of the catastrophe theory. It is demonstrated that its double scaling regularization is governed by the Painlev\'e-I equation.Comment: 11 pages, 3 figures, typos corrected, references adde

Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations

We study the topology of quasiperiodic solutions of the vortex filament equation in a neighborhood of multiply covered circles. We construct these solutions by means of a sequence of isoperiodic deformations, at each step of which a real double point is "unpinched" to produce a new pair of branch points and therefore a solution of higher genus. We prove that every step in this process corresponds to a cabling operation on the previous curve, and we provide a labelling scheme that matches the deformation data with the knot type of the resulting filament.Comment: 33 pages, 5 figures; submitted to Journal of Nonlinear Scienc

Stability of vortices in rotating taps: a 3d analysis

We study the stability of vortex-lines in trapped dilute gases subject to rotation. We solve numerically both the Gross-Pitaevskii and the Bogoliubov equations for a 3d condensate in spherically and cilyndrically symmetric stationary traps, from small to very large nonlinearities. In the stationary case it is found that the vortex states with unit and $m=2$ charge are energetically unstable. In the rotating trap it is found that this energetic instability may only be suppressed for the $m=1$ vortex-line, and that the multicharged vortices are never a local minimum of the energy functional, which implies that the absolute minimum of the energy is not an eigenstate of the $L_z$ operator, when the angular speed is above a certain value, $\Omega > \Omega_2$.Comment: 10 pages, 7 figures in EPS forma

New insights to assess the consolidation of stone materials used in built heritage: the case study of ancient graffiti (Tituli Picti) in the archaeological site of Pompeii

Tituli Picti are an ancient form of urban graffiti very common in the archaeological site of Pompeii (Naples, South—Italy). They are generally made of red pigments applied on walls of Campanian ignimbrite. This paper deals with a scientific investigation aimed to their conservation. This is a challenging task since it requires a multidisciplinary approach that includes restorers, archaeologists and conservation scientists. The study has provided suggestions on the proper way to conserve Tituli Picti over time. In the present work, several specimens of Campanian ignimbrite were painted with red earth pigment; lime and Arabic gum have been used as binders as well. Such painted stones were treated with three consolidants: a suspension of reactive nanoparticles of silica, ethyl silicate and an acrylic microemulsion. Treated and untreated specimens were subjected to thermal aging, artificial solar radiation and induced crystallization decay. It has been assessed the colorimetric variations induced by treatments. Moreover, the micromorphologic features of the consolidated surfaces have been highlighted by means of electron microscope observations. The scotch tape test allowed to compare the superficial cohesion induced by the three used products. According to the results, ethyl silicate seems to represent the most successful product