The continuum gauge field-theory model for low-energy electronic states of icosahedral fullerenes

The low-energy electronic structure of icosahedral fullerenes is studied within the field-theory model. In the field model, the pentagonal rings in the fullerene are simulated by two kinds of gauge fields. The first one, non-abelian field, follows from so-called K spin rotation invariance for the spinor field while the second one describes the elastic flow due to pentagonal apical disclinations. For fullerene molecule, these fluxes are taken into account by introducing an effective field due to magnetic monopole placed at the center of a sphere. Additionally, the spherical geometry of the fullerene is incorporated via the spin connection term. The exact analytical solution of the problem (both for the eigenfunctions and the energy spectrum) is found.Comment: 9 pages, 2 figures, submitted to European Physical Journal

From low-rank approximation to an efficient rational Krylov subspace method for the Lyapunov equation

We propose a new method for the approximate solution of the Lyapunov equation with rank-$1$ right-hand side, which is based on extended rational Krylov subspace approximation with adaptively computed shifts. The shift selection is obtained from the connection between the Lyapunov equation, solution of systems of linear ODEs and alternating least squares method for low-rank approximation. The numerical experiments confirm the effectiveness of our approach.Comment: 17 pages, 1 figure

Nanomechanical displacement detection using coherent transport in ordered and disordered graphene nanoribbon resonators

Graphene nanoribbons provide an opportunity to integrate phase-coherent transport phenomena with nanoelectromechanical systems (NEMS). Due to the strain induced by a deflection in a graphene nanoribbon resonator, coherent electron transport and mechanical deformations couple. As the electrons in graphene have a Fermi wavelength \lambda ~ a_0 = 1.4 {\AA}, this coupling can be used for sensitive displacement detection in both armchair and zigzag graphene nanoribbon NEMS. Here it is shown that for ordered as well as disordered ribbon systems of length L, a strain \epsilon ~ (w/L)^2 due to a deflection w leads to a relative change in conductance \delta G/G ~ (w^2/a_0L).Comment: 4 Pages, 4 figure

Development of High-Efficient, Resource-Saving Technical Solutions for Wastewater Treatment in Galvanochemical Sector

This article presents the results of the analysis of samples of a machine-shop for the content of organic components and heavy metal ions. The proposed modernized technological scheme uses modern technological solutions for a machine-shop. Based on the analysis of sites and sewage treatment plants of galvanic production, as well as analysis of the presence of polluting components, technical solutions, which are going to increase the intensification and efficiency of water treatment and water treatment through the use of modern physical and chemical methods, technological methods and wastewater treatment devices have been developed. The introduction of additional sorption modules with activated carbon will reduce the ingress of toxic organic components (DBP, aniline, solvents: acetone, gasoline, ethyl acetate, polymer epoxy compounds, including: epoxy adhesives, polymer filler, epoxy-phenolic, phenolic-rubber and rubber adhesives, release adhesives) into wastewater. A modernized scheme using modern solutions will comply with Mosvodokanal standards. Keywords: wastewater, water treatment, toxic organic components, heavy metal ion