Regularized extremal shift in problems of stable control

We discuss a technical approach, based on the method of regularized extremal shift (RES), intended to help solve problems of stable control of uncertain dynamical systems. Our goal is to demonstrate the essence and abilities of the RES technique; for this purpose we construct feedback controller for approximate tracking a prescribed trajectory of an inaccurately observed system described by a parabolic equation. The controller is "resource-saving" in a sense that control resource spent for approximate tracking do not exceed those needed for tracking in an "ideal" situation where the current values of the input disturbance are fully observable. © 2013 IFIP International Federation for Information Processing.German Sci. Found. (DFG) Eur. Sci. Found. (ESF);Natl. Inst. Res. Comput. Sci. Control France (INRIA);DFG Research Center MATHEON;Weierstrass Institute for Applied Analysis and Stochastics (WIAS);European Patent Offic

On the theory of magnetic field dependence of heat conductivity in dielectric in isotropic model

Phonon polarization in a magnetic field is analyzed in isotropic model. It is shown, that at presence of spin-phonon interaction phonon possess circular polari-zation which causes the appearance of heat flux component perpendicular both to temperature gradient and magnetic field.Comment: 5 pages, 0 figure

Critical temperature and giant isotope effect in presence of paramagnons

We reconsider the long-standing problem of the effect of spin fluctuations on the critical temperature and isotope effect in a phonon-mediated superconductor. Although the general physics of the interplay between phonons and paramagnons had been rather well understood, the existing approximate formulas fail to describe the correct behavior of $$ for general phonon and paramagnon spectra. Using a controllable approximation, we derive an analytical formula for $T_{c}$ which agrees well with exact numerical solutions of the Eliashberg equations for a broad range of parameters. Based on both numerical and analytical results, we predict a strong enhancement of the isotope effect when the frequencies of spin fluctuation and phonons are of the same order. This effect may have important consequences for near-magnetic superconductors such as MgCNi$_{3}$Comment: 5 pages, 2 figure

Smith–Purcell radiation of a vortex electron

A wide variety of emission processes by electron wave packets with an orbital angular momentum ℓhbar, called the vortex electrons, can be influenced by a nonparaxial contribution due to their intrinsic electric quadrupole moment. We study Smith–Purcell radiation from a conducting grating generated by a vortex electron, described as a generalized Laguerre–Gaussian packet, which has an intrinsic magnetic dipole moment and an electric quadrupole moment. By using a multipole expansion of the electromagnetic field of such an electron, we employ a generalized surface-current method, applicable for a wide range of parameters. The radiated energy contains contributions from the charge, from the magnetic moment, and from the electric quadrupole moment, as well as from their interference. The quadrupole contribution grows as the packet spreads while propagating, and it is enhanced for large ℓ. In contrast to the linear growth of the radiation intensity from the charge with a number of strips N, the quadrupole contribution reveals an N3 dependence, which puts a limit on the maximal grating length for which the radiation losses stay small. We study spectral-angular distributions of the Smith–Purcell radiation both analytically and numerically and demonstrate that the electron's vorticity can give rise to detectable effects for non-relativistic and moderately relativistic electrons. On a practical side, preparing the incoming electron's state in a form of a non-Gaussian packet with a quadrupole moment—such as the vortex electron, an Airy beam, a Schrödinger cat state, and so on—one can achieve quantum enhancement of the radiation power compared to the classical linear regime. Such an enhancement would be a hallmark of a previously unexplored quantum regime of radiation, in which non-Gaussianity of the packet influences the radiation properties much stronger than the quantum recoil

On reconstructing an unknown coordinate of a nonlinear system of differential equations

The paper discusses a method of auxiliary controlled models and the application of this method to solving problems of dynamical reconstruction of an unknown coordinate in a nonlinear system of differential equations. The solving algorithm, which is stable with respect to informational noises and computational errors, is presented. © AGH University of Science and Technology Press, Krakow 2014.Russian Academy of Sciences, RAS Russian Foundation for Basic Research, RFB