Wavelets and adaptive grids for the discontinuous Galerkin method

In this paper, space adaptivity is introduced to control the error in the numerical solution of hyperbolic systems of conservation laws. The reference numerical scheme is a new version of the discontinuous Galerkin method, which uses an implicit diffusive term in the direction of the streamlines, for stability purposes. The decision whether to refine or to unrefine the grid in a certain location is taken according to the magnitude of wavelet coefficients, which are indicators of local smoothness of the numerical solution. Numerical solutions of the nonlinear Euler equations illustrate the efficiency of the method.     

Electron-Optical System of a High-Power Gyrotron with Nonadiabatic Electron Gun

We describe a nonadiabatic electron gun operated in the mode of a currentconfined by spatial charge and intended for producing helical electron beams for high-power gyroresonantdevices.Results of numerical simulation of electron trajectories and electron-beam parameters arepresented. It is shown that for a high operating current, the pitch factor and the electronvelocity spread can be significantly better than in the conventional adiabatic systems. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48,No. 6, pp. 517–522, June 2005     

Energetics of an adiabatically-loaded excited anharmonic oscillator

The dependence of the energy characteristics on an adiabatically slowly increasing external force is determined analytically for an anharmonic oscillator. The analytical results are confirmed by a numerical calculation. The nature of the force dependences of the energy characteristics are determined and discussed. Fiz. Tverd. Tela (St. Petersburg) 39, 153–157 (January 1997)     

Resistance peak and giant magnetoresistance of degenerate ferromagnetic semiconductors with arbitrary spin polarization

The temperature peak of the resistance and the giant magnetoresistance of degenerate ferromagnetic semiconductors with an arbitrary degree of electron spin polarization are investigated. The spin-wave and paramagnetic domains are considered. The calculations are based on the notion of the magnetic-impurity scattering of carriers. Fiz. Tverd. Tela (St. Petersburg) 39, 1589–1593 (September 1997)     

Colossal magnetoresistance of the Sm1−x SrxMnO3 system

The results of investigating the temperature dependence of the resistivity, the differential magnetic susceptibility, and the magnetoresistance of a partially substituted perovskite Sm_1−x Sr_xMnO₃ (x=0.16–0.4) are presented. Colossal intrinsic magnetoresistance, reaching 90% in an external magnetic field of 30 kOe, is discovered in the compound with x=0.30 at 77 K. Fiz. Tverd. Tela (St. Petersburg) 39, 1831–1832 (October 1997)     

On edge states in superconductors with time inversion symmetry breaking

The efficiency of conversion of the heat flux into hard x radiation (HXR) is analyzed, via time-dependent two-temperature one-dimensional non-LTE-radiation-hydrodynamic numerical modeling, for a heat-to-radiation flux converter linked to the edge of a low-atomic-number hot Z-pinch. The domain of parameters in this scheme is found where about the same HXR yield can be achieved at values of input energy which are an order of magnitude lower than in the conventional scheme of a radially imploding plasma. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 7, 502–506 (10 April 1997) Published in English in the original Russian Journal. Edited by Steve Torstveit.     

A Lieb-Thirring Bound for a Magnetic Pauli Hamiltonian

A Lieb-Thirring-Sobolev type inequality for Pauli Hamiltonians with magnetic fields is derived. The bound is in terms of an effective field, whose energy is comparable to that of the magnetic field itself. An application to the stability of matter in magnetic fields is given. Received: 19 September 1996 / Accepted: 3 January 1997