Thermal and chemical nanofractal relaxation

We studied shape relaxation of nano-fractal islands, during annealing, after their growth from antimony cluster deposition on graphite surface. Annealing at 180^°C shows evidence of an increase of the fractal branch width with time followed by branch fragmentation, without changing the fractal dimension. The time evolution of the width of the arm suggests the surface self-diffusion mechanism as the main relaxation process. With Monte Carlo simulations, we confirmed the observed behavior. Comparison is done with our previous results on fragmentation of nano-fractal silver islands when impurity added to the incident cluster promotes rapid fragmentation by surface self-diffusion enhancement [1].     

Spatial amplification of a laser wave and the transverse spread of electrons in an undulator with a noncollinear configuration

The spatial amplification of a wave in a magnetostatic undulator with noncollinear electron and laser beams is studied in the framework of the dispersion relation for single-frequency and collective regimes. The dependence of the gain on the electron beam width is estimated with regard to the spatial boundedness of the beams. The laser power threshold at which the selection with respect to the transverse velocity is possible is obtained for a free-electron laser without inversion.     

A manifestation of magnetism of bismuth in iron garnet films

Bismuth iron garnet films prepared through electron-beam and laser-induced evaporation on (001)-oriented substrates of scandium gallium gadolinium garnet are investigated using ferromagnetic resonance. It is assumed that the additional minima observed in the angular dependence of the resonance field can be associated with the magnetic moment of bismuth ions.     

Domain wall dynamics in a two-layer uniaxial film

Numerical solution of the Slonczewski equations were used to study the motion of an individual domain wall in a two-layer uniaxial film in which the damping parameter and the gyromagnetic ratio depend on the specific layer.     

The structure of alternative superbimodules

Let A be a semisimple alternative superalgebra over a field of characteristic not 2, 3 which contains no sub-superalgebras of type (M₁(F), M₁(F)) in its decomposition into prime ideals. Then each superbimodule of A is merely an alternative A-bimodule. The case where A = (M₁(F),M₁(F)) produces, however, a series of indecomposable A-superbimodules. In the present article, we describe such superbimodules over an algebraically closed field.Translated fromAlgebra i Logika, Vol. 33, No. 6, pp. 689–707, November–December, 1994.Partially supported by the International Science Foundation (ISF), grant No. RB 6000.     

Propagation of thickness-twist waves in a multi-sectioned piezoelectric plate of 6 mm crystals

We study thickness-twist vibrations and waves in an unbounded, multi-sectioned piezoelectric plate of crystals with 6 mm symmetry or polarized ceramics. An exact solution from the three-dimensional equations of piezoelectricity is obtained. Basic vibration and wave propagation characteristics are calculated based on the solution. The results are useful in the understanding and design of plate resonators, filters and acoustic wave sensors of ZnO, AlN and polarized ceramics.     

The exterior magnetic field for the multilayer ellipsoidal model of the brain

The magnetic induction field in the exterior of an ellipsoidallyinhomogeneous, four-conducting-layer model of the human headis obtained analytically up to its quadrupole approximation.The interior ellipsoidal core represents the homogeneous brainwhile each one of the shells represents the cerebrospinal fluid,the skull and the scalp, all characterized by different conductivities.The inhomogeneities of these four domains, together with theanisotropy imposed by the use of the ellipsoidal geometry, providethe most realistic physical and geometrical model of the brainfor which an analytic solution of the biomagnetic forward problemis possible. It is shown that in contrast to the spherical model,where shells of different conductivity are magnetically invisible,the magnetic induction field in ellipsoidal geometry is stronglydependent on the conductivity supports. The fact that sphericalshells of different conductivity are invisible has enhancedthe common belief that the biomagnetic forward solution doesnot depend on the conductivity profiles. As we demonstrate inthe present work, this is not true. Hence, the proposed multilayeredellipsoidal model provides a qualitative improvement of therealistic interpretation of magnetoencephalography (MEG) measurements.We show that the presence of the shells of different conductivitycan be incorporated in the form of the dipole vector for thehomogeneous model. Numerical investigations show that the effectsof shell inhomogeneities are almost as sound as the level ofMEG measurements themselves. The degenerate cases, where eitherthe differences of the conductivities within the shells disappear,or the ellipsoidal geometry is reduced to the spherical one,are also considered.     

New methods for proving the existence and stability of periodic solutions in singularly perturbed delay systems

We carry out a detailed analysis of the existence, asymptotics, and stability problems for periodic solutions that bifurcate from the zero equilibrium state in systems with large delay. The account is based on a specific meaningful example given by a certain scalar nonlinear second-order differential-difference equation that is a mathematical model of a single-circuit RCL oscillator with delay in a feedback loop. Original Russian Text ? A.Yu. Kolesov, E.F. Mishchenko, N.Kh. Rozov, 2007, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Vol. 259, pp. 106–133.     

Terminal control in flat systems

The article considers the application of dynamical feedback control to a special class of nonlinear dynamical systems — so-called flat systems. Flat system, linearizing output, and Lie-Backlund isomorphism are among the concepts reviewed. A man-machine algorithm is proposed for solving the terminal control problem for an arbitrary flat system with known linearizing outputs. __________ Translated from Nelineinaya Dinamika i Upravlenie, No. 3, pp. 191–200, 2003.