481 research outputs found
Majorana-Oppenheimer approach to Maxwell electrodynamics in Riemannian space-time
The Riemann -- Silberstein -- Majorana -- Oppengeimer approach to the Maxwell
electrodynamics in presence of electrical sources and arbitrary media is
investigated within the matrix formalism. The symmetry of the matrix Maxwell
equation under transformations of the complex rotation group SO(3.C) is
demonstrated explicitly. In vacuum case, the matrix form includes four real matrices . In presence of media matrix form requires two
sets of matrices, and -- simple and
symmetrical realization of which is given. Relation of and
to the Dirac matrices in spinor basis is found. Minkowski
constitutive relations in case of any linear media are given in a short
algebraic form based on the use of complex 3-vector fields and complex
orthogonal rotations from SO(3.C) group. The matrix complex formulation in the
Esposito's form, based on the use of two electromagnetic 4-vector, is studied
and discussed. Extension of the 3-vector complex matrix formalism to arbitrary
Riemannian space-time in accordance with tetrad method by
Tetrode-Weyl-Fock-Ivanenko is performed.Comment: 32pages. Proccedings of the 14th Conference-School "Foundation &
Advances in Nonlinear Science", Minsk, September 22-25, 2008. P. 20-49; ed.
V.I. Kuvshinov, G.G. Krylov, Minsk, 200
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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
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