Lie group analysis of a generalized Krichever-Novikov differential-difference equation

The symmetry algebra of the differential--difference equation $$\dot u_n = [P(u_n)u_{n+1}u_{n-1} + Q(u_n)(u_{n+1}+u_{n-1})+ R(u_n)]/(u_{n+1}-u_{n-1}),$$ where $P$, $Q$ and $R$ are arbitrary analytic functions is shown to have the dimension 1 \le \mbox{dim}L \le 5. When $P$, $Q$ and $R$ are specific second order polynomials in $u_n$ (depending on 6 constants) this is the integrable discretization of the Krichever--Novikov equation. We find 3 cases when the arbitrary functions are not polynomials and the symmetry algebra satisfies \mbox{dim}L=2. These cases are shown not to be integrable. The symmetry algebras are used to reduce the equations to purely difference ones. The symmetry group is also used to impose periodicity $u_{n+N}=u_n$ and thus to reduce the differential--difference equation to a system of $N$ coupled ordinary three points difference equations

Molecular beam epitaxy of InAs nanowires in SiO2 nanotube templates: challenges and prospects for integration of III-Vs on Si

Guided growth of semiconductor nanowires in nanotube templates has been considered as a potential platform for reproducible integration of III-Vs on silicon or other mismatched substrates. Herein, we report on the challenges and prospects of molecular beam epitaxy of InAs nanowires on SiO2/Si nanotube templates. We show how and under which conditions the nanowire growth is initiated by In-assisted vapor-liquid-solid growth enabled by the local conditions inside the nanotube template. The conditions for high yield of vertical nanowires are investigated in terms of the nanotube depth, diameter and V/III flux ratios. We present a model that further substantiates our findings. This work opens new perspectives for monolithic integration of III-Vs on the silicon platform enabling new applications in the electronics, optoelectronics and energy harvesting arena

Evidence for the naphthalene cation in a region of the interstellar medium with anomalous microwave emission

We report high resolution spectroscopy of the moderately reddened (A$_V$=3) early type star Cernis 52 located in a region of the Perseus molecular cloud complex with anomalous microwave emission. In addition to the presence of the most common diffuse interstellar bands (DIBs) we detect two new interstellar or circumstellar bands coincident to within 0.01% in wavelength with the two strongest bands of the naphthalene cation (C$_{10}$H$_{8}^+$) as measured in gas-phase laboratory spectroscopy at low temperatures and find marginal evidence for the third strongest band. Assuming these features are caused by the naphthalene cation, from the measured intensity and available oscillator strengths we find that 0.008 % of the carbon in the cloud could be in the form of this molecule. We expect hydrogen additions to cause hydronaphthalene cations to be abundant in the cloud and to contribute via electric dipole radiation to the anomalous microwave emission. The identification of new interstellar features consistent with transitions of the simplest polycyclic aromatic hydrocarbon adds support to the hypothesis that this type of molecules are the carriers of both diffuse interstellar bands and anomalous microwave emission.Comment: Accepted for publication in The Astrophysical Journa

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

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

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

Is baryon number violated when electroweak strings intercommute?

We reexamine the self-helicity and the intercommutation of electroweak strings. A plausible argument for baryon number conservation when electroweak strings intercommute is presented. The connection between a segment of electroweak strings and a sphaleron is also discussed.Comment: CALT-68-1948, 11 pages, 5 figures available upon request. Replaced with revised version. (Request should be sent to [email protected]

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