Ternary numbers and algebras. Reflexive numbers and Berger graphs

The Calabi-Yau spaces with SU(m) holonomy can be studied by the algebraic way through the integer lattice where one can construct the Newton reflexive polyhedra or the Berger graphs. Our conjecture is that the Berger graphs can be directly related with the $n$-ary algebras. To find such algebras we study the n-ary generalization of the well-known binary norm division algebras, ${\mathbb R}$, ${\mathbb C}$, ${\mathbb H}$, ${\mathbb O}$, which helped to discover the most important "minimal" binary simple Lie groups, U(1), SU(2) and G(2). As the most important example, we consider the case $n=3$, which gives the ternary generalization of quaternions and octonions, $3^p$, $p=2,3$, respectively. The ternary generalization of quaternions is directly related to the new ternary algebra and group which are related to the natural extensions of the binary $su(3)$ algebra and SU(3) group. Using this ternary algebra we found the solution for the Berger graph: a tetrahedron.Comment: Revised version with minor correction

A note on the breathing mode of an elastic sphere in Newtonian and complex fluids

Experiments on the acoustic vibrations of elastic nanostructures in fluid media have been used to study the mechanical properties of materials, as well as for mechanical and biological sensing. The medium surrounding the nanostructure is typically modeled as a Newtonian fluid. A recent experiment however suggested that high-frequency longitudinal vibration of bipyramidal nanoparticles could trigger a viscoelastic response in water-glycerol mixtures [M. Pelton et al., "Viscoelastic flows in simple liquids generated by vibrating nanostructures," Phys. Rev. Lett. 111, 244502 (2013)]. Motivated by these experimental studies, we first revisit a classical continuum mechanics problem of the purely radial vibration of an elastic sphere, also called the breathing mode, in a compressible viscous fluid, and then extend our analysis to a viscoelastic medium using the Maxwell fluid model. The effects of fluid compressibility and viscoelasticity are discussed. Although in the case of longitudinal vibration of bipyramidal nanoparticles, the effects of fluid compressibility were shown to be negligible, we demonstrate that it plays a significant role in the breathing mode of an elastic sphere. On the other hand, despite the different vibration modes, the breathing mode of a sphere triggers a viscoelastic response in water-glycerol mixtures similar to that triggered by the longitudinal vibration of bipyramidal nanoparticles. We also comment on the effect of fluid viscoelasticity on the idea of destroying virus particles by acoustic resonance

An Automatic Control System for Conditioning 30 GHz Accelerating Structures

A software application programme has been developed to allow fast and automatic high-gradient conditioning of accelerating structures at 30 GHz in CTF3. The specificity of the application is the ability to control the high-power electron beam which produces the 30 GHz RF power used to condition the accelerating structures. The programme permits operation round the clock with minimum manpower requirements. In this paper the fast control system, machine control system, logging system, graphical user control interface and logging data visualization are described. An outline of the conditioning control system itself and of the feedback controlling peak power and pulse length is given. The software allows different types of conditioning strategies to be programme

Vibrational modes of metal nanoshells and bimetallic core-shell nanoparticles

We study theoretically spectrum of radial vibrational modes in composite metal nanostructures such as bimetallic core-shell particles and metal nanoshells with dielectric core in an environment. We calculate frequencies and damping rates of fundamental (breathing) modes for these nanostructures along with those of two higher-order modes. For metal nanoshells, we find that the breathing mode frequency is always lower than the one for solid particles of the same size, while the damping is higher and increases with reduction of the shell thickness. We identify two regimes that can be characterized as weakly damped and overdamped vibrations in the presence of external medium. For bimetalllic particles, we find periodic dependence of frequency and damping rate on the shell thickness with period determined by mode number. For both types of nanostructures, the frequency of higher modes is nearly independent of the environment, while the damping rate shows strong sensitivity to outside medium.Comment: 7 pages, 8 figure

Simple model for the vibrations of embedded elastically cubic nanocrystals

The purpose of this work is to calculate the vibrational modes of an elastically anisotropic sphere embedded in an isotropic matrix. This has important application to understanding the spectra of low-frequency Raman scattering from nanoparticles embedded in a glass matrix. First some low frequency vibrational modes of a free cubically elastic sphere are found to be nearly independent of one combination of elastic constants. This is then exploited to obtain an isotropic approximation for these modes which enables to take into account the surrounding isotropic matrix. This method is then used to quantatively explain recent spectra of gold and copper nanocrystals in glasses.Comment: 6 pages, 5 figure

Comment on "Estimate of the vibrational frequencies of spherical virus particles"

This comment corrects some errors which appeared in the calculation of an elastic sphere eigenenergies. As a result, the symmetry of the mode having the lowest frequency is changed. Also a direction for calculating the damping of these modes for embedded elastic spheres is given.Comment: comment L. H. Ford Phys. Rev. E 67 (2003) 05192

Pinning Enhancement by Heterovalent Substitution in Y1−x_{1-x}REx_{x}Ba2_{2}Cu3_{3}O7−δ_{7-\delta}

The intragrain pinning in high-$T_c$ superconductor compounds Y$_{1-x}$RE$_{x}$Ba$_{2}$Cu$_{3}$O$_{7-\delta}$ with low concentration of RE (La, Ce, Pr) was investigated. Magnetic and transport measurements reveal that the pinning is maximal for the concentration of heterovalent RE such that the average distance between the impurity ions in the plane of rare-earth elements close to the diameter of Abrikosov vortices in YBCO.Comment: 11 pages, 6 figures, will be published in SUS