Tannaka duality on quotient stacks

Let = [X/G] be the quotient stack of a scheme X by an affine group scheme G over a field k. Assume that there is a line bundle on whose underlying line bundle on X is very ample. Let VB() be the category of vector bundles on .We show that is canonically isomorphic to the stack of fiber functors on VB(). This is an analogue of the Tannaka duality for affine groups. Partially supported by CNCSIS contract no. 33079/2004     

Empirical power law for magnetic turbulence spectra of an anisotropic plasma

Three-dimensional dynamic distributions of oscillations of the magnetic field over wave vectors k have been obtained from the plasma and magnetic measurements on four satellites in the Cluster experiment in a turbulent plasma in the outer Earth’s cusp and near it. The resulting k spectra exhibit strong inhomogeneous anisotropy. The dependences of the energy of magnetic oscillations on the wavenumber have been analyzed for 288 three-dimensional spectra in the wavelength interval covering the magnetohydrodynamic and ion scales. It has been shown that the energy density of magnetic fluctuations per unit volume in the wave vector space that is averaged over the total solid angle decreases in the wavelength interval from ～2000 to ～10 km with an increase in according to a power law with an exponent of α = -5.0 ± 0.3 for any magnitude and character of anisotropy.     

Restricting the High-Temperature Growth of Nanocrystalline Tin Oxide

The sensitivity of tin oxide is dependent on various factors, one of which is the grain size. Three methods have been investigated with the aim of stabilising the grain size in the nanometer range, namely; (i) encapsulation within a silica matrix, (ii) coating the crystallites with hexamethyldisilazane and (iii) pinning the grain boundaries with a second metal oxide nanocrystal. The resulting materials have been characterised by X-ray powder diffraction (XRPD), Extended X-ray absorption fine structure (EXAFS) and conductivity measurements.     

Thermal calculation of accelerating structures in electron linacs

The temperature distribution in the accelerating structures of standing-wave and traveling-wave electron linacs is calculated. The objects of consideration in the former and latter cases are, respectively, a circular iris waveguide with magnetic coupling and a biperiodic accelerating structure. Calculation data for steady and transient heating conditions are presented. The variation of the cell’s geometry and resonance frequency with the temperature of the structure is also calculated. Calculations are made for copper structures with allowance for microwave wall losses.     

On some properties of nearly conservative dynamics of Ikeda map and its relation with the conservative case

The behavior of the well-known Ikeda map with very weak dissipation (so-called nearly conservative case) is investigated. The changes in the bifurcation structure of the parameter plane while decreasing the dissipation are revealed. It is shown that when the dissipation is very weak the system demonstrates an “intermediate” type of dynamics combining the peculiarities of conservative and dissipative dynamics. The correspondence between the trajectories in the phase space in the conservative case and the transformations of the set of initial conditions in the nearly conservative case has been obtained. The dramatic increase of the number of coexisting low-period attractors and the extraordinary growth of the transient time while the dissipation decreases have been revealed. The method of plotting a bifurcation tree for the set of initial conditions has been used to classify the existing attractors by their structure. Also it was shown that most of the coexisting attractors are destroyed by rather small external noise, and the transient time in noisy driven systems increases still more. The new method of two-parameter analysis for conservative systems was proposed.     

Bistability of Multiwalled Carbon Nanotubes Arranged on Plane Substrates

Physics of the Solid State - Stationary states of multi-walled carbon nanotubes have been studied. The numerical simulation showed that nanotubes become bistable systems at rather large diameters....