Steering of Vortices by Magnetic Field Tilting in Open Superconductor Nanotubes

In planar superconductor thin films, the places of nucleation and arrangements of moving vortices are determined by structural defects. However, various applications of superconductors require reconfigurable steering of fluxons, which is hard to realize with geometrically predefined vortex pinning landscapes. Here, on the basis of the time-dependent Ginzburg–Landau equation, we present an approach for the steering of vortex chains and vortex jets in superconductor nanotubes containing a slit. The idea is based on the tilting of the magnetic field (Formula presented.) at an angle (Formula presented.) in the plane perpendicular to the axis of a nanotube carrying an azimuthal transport current. Namely, while at (Formula presented.), vortices move paraxially in opposite directions within each half-tube; an increase in (Formula presented.) displaces the areas with the close-to-maximum normal component (Formula presented.) to the close(opposite)-to-slit regions, giving rise to descending (ascending) branches in the induced-voltage frequency spectrum (Formula presented.). At lower B values, upon reaching the critical angle (Formula presented.), the close-to-slit vortex chains disappear, yielding (Formula presented.) of the (Formula presented.) type ((Formula presented.) : an integer; (Formula presented.) : the vortex nucleation frequency). At higher B values, (Formula presented.) is largely blurry because of multifurcations of vortex trajectories, leading to the coexistence of a vortex jet with two vortex chains at (Formula presented.). In addition to prospects for the tuning of GHz-frequency spectra and the steering of vortices as information bits, our findings lay the foundation for on-demand tuning of vortex arrangements in 3D superconductor membranes in tilted magnetic fields

On Parametrization of the Linear GL(4,C) and Unitary SU(4) Groups in Terms of Dirac Matrices

Parametrization of $4\times 4$-matrices $G$ of the complex linear group $GL(4,C)$ in terms of four complex 4-vector parameters $(k,m,n,l)$ is investigated. Additional restrictions separating some subgroups of $GL(4,C)$ are given explicitly. In the given parametrization, the problem of inverting any $4\times 4$ matrix $G$ is solved. Expression for determinant of any matrix $G$ is found: $\det G = F(k,m,n,l)$. Unitarity conditions $G^{+} = G^{-1}$ have been formulated in the form of non-linear cubic algebraic equations including complex conjugation. Several simplest solutions of these unitarity equations have been found: three 2-parametric subgroups $G_{1}$, $G_{2}$, $G_{3}$ - each of subgroups consists of two commuting Abelian unitary groups; 4-parametric unitary subgroup consisting of a product of a 3-parametric group isomorphic SU(2) and 1-parametric Abelian group. The Dirac basis of generators $\Lambda_{k}$, being of Gell-Mann type, substantially differs from the basis $\lambda_{i}$ used in the literature on SU(4) group, formulas relating them are found - they permit to separate SU(3) subgroup in SU(4). Special way to list 15 Dirac generators of $GL(4,C)$ can be used $\{\Lambda_k\} = \{\alpha_i\oplus\beta_j\oplus(\alpha_iV\beta_j = {\boldsymbol K} \oplus {\boldsymbol L}\oplus{\boldsymbol M})\}$, which permit to factorize SU(4) transformations according to S = e^{i\vec{a}\vec{\alpha}} e^{i\vec{b}\vec\beta}} e^{i{\boldsymbol k}{\boldsymbol K}} e^{i{\boldsymbol l}{\boldsymbol L}} e^{i\boldsymbol m}{\boldsymbol M}}, where two first factors commute with each other and are isomorphic to SU(2) group, the three last ones are 3-parametric groups, each of them consisting of three Abelian commuting unitary subgroups.Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Effect of organic matter release from natural cork used on bisphenol a removal from aqueous solution

The paper presents an experimental study aimed at investigating the mechanism responsible for Bisphenol A adsorption on natural cork, and the role played on process kinetics by the organic matter released from the cork. Obtained data show that natural cork has a good affinity toward Bisphenol A, with removal efficiency being as high as 75% in less than 24 h. The adsorption process is characterized by a fast-initial rate which tends to reduce progressively, and follows a pseudo second order model equation. Statistical physics analysis allows for obtaining a molecular description of the adsorption, which is shown to take place through a single anchorage point, perpendicularly to the adsorbent surface. Nuclear magnetic resonance spectroscopy and fluorescence analysis reveal that the colloidal organic matter released from the cork interacts with Bisphenol A; it also plays a relevant role in the slowing down of the adsorption rate, as it competes with cork adsorption sites for Bisphenol A. Organic matter is found to be highly heterogenous, presenting at the same time carbohydrates, aromatic and aliphatic domains. Such moieties interact stably with the contaminant in the solution probably due the establishment of dispersive forces (e.g. π-stacking) which sequestrate Bisphenol A into the inner hydrophobic core of the organic matter three-dimensional structure