Vol 103, No 3 (2016)

Multiple small-angle neutron scattering by a high-density system of inhomogeneities has been considered. A combined approach to the analysis of multiple small-angle neutron scattering has been proposed on the basis of the synthesis of the Zernike–Prince and Moliére formulas. This approach has been compared to the existing multiple small-angle neutron scattering theory based on the eikonal approximation. This comparison has shown that the results in the diffraction limit coincide, whereas differences exist in the refraction limit because the latter theory includes correlations between successive scattering events. It has been shown analytically that the existence of correlations in the spatial position of scatterers results in an increase in the number of unscattered neutrons. Thus, the narrowing of spectra of multiple small-angle neutron scattering observed experimentally and in numerical simulation has been explained.

The ionization of the final ³He⁺ ion during the nuclear β^–-decay of the tritium atom is discussed. The velocity spectrum of the emitted secondary electrons is derived in the explicit form. This method allows determining the relative and absolute probabilities of formation of the final states in few-electron atoms, which include “free” secondary electrons moving at different velocities.

The GdCoO_3–δ perovskite is a semiconductor with the energy gap E_g ≈ 0.5 eV from electrical transport measurements. It reveals unusual optical absorption spectra without transparency window expected for semiconductors. Instead we have measured the narrow transmittance peak at the photon energy ε₀ = 0.087 eV. To reconcile the transport and optical data we have studied the effect of oxygen vacancies on the electronic structure of the GdCoO_3–δ. We have found that oxygen vacancies result in the in-gap states inside the charge-transfer energy gap of the GdCoO₃. It is a multielectron effect due to strong electron correlations forming the electronic structure of the GdCoO_3–δ. These in-gap states decrease the transparency window and result in a narrow absorption minimum. The predicted temperature dependence of the absorption spectra has been confirmed by our measurements.

A two-stage model of the capture of electrons and holes in traps in amorphous silicon nitride Si₃N₄ has been proposed. The electronic structure of a “Si–Si bond” intrinsic defect in Si₃N₄ has been calculated in the tight-binding approximation without fitting parameters. The properties of the Si–Si bond such as a giant cross section for capture of electrons and holes and a giant lifetime of trapped carriers have been explained. It has been shown that the Si–Si bond in the neutral state gives shallow levels near the bottom of the conduction band and the top of the valence band, which have a large cross section for capture. The capture of an electron or a hole on this bond is accompanied by the shift of shallow levels by 1.4–1.5 eV to the band gap owing to the polaron effect and a change in the localization region of valence electrons of atoms of the Si–Si bond. The calculations have been proposed with a new method for parameterizing the matrix elements of the tightbinding Hamiltonian taking into account a change in the localization region of valence electrons of an isolated atom incorporated into a solid.

A compact spatial Hamiltonian equation for gravity waves on deep water has been derived. The equation is dynamical and can describe extreme waves. The equation for the envelope of a wave train has also been obtained.

A formula for computing the temperature dependence of the London penetration depth of a magnetic field in the regime of coexistence of charge density waves and superconductivity has been proposed taking into account the dependence of both order parameters on the wave vector. It has been shown that an anomalously high diamagnetic response of the system and a finite value of the superconducting current persist even at T_c ≤ T ≤ T_CDW.

We analyze a solenoidal motion in a vertically vibrated freely suspended thin smectic film. We demonstrate analytically that transverse oscillations of the film generate two-dimensional vortices in the plane of the film owing to hydrodynamic nonlinearity. An explicit expression for the vorticity of the in-plane film motion in terms of the film displacement is obtained. The air around the film is proven to play a crucial role, since it changes the dispersion relation of transverse oscillations and transmits viscous stresses to the film, modifying its bending motion. We propose possible experimental observations enabling to check our predictions.

The stabilization of avalanches on dynamical networks has been studied. Dynamical networks are networks where the structure of links varies in time owing to the presence of the individual “activity” of each site, which determines the probability of establishing links with other sites per unit time. An interesting case where the times of existence of links in a network are equal to the avalanche development times has been examined. A new mathematical model of a system with the avalanche dynamics has been constructed including changes in the network on which avalanches are developed. A square lattice with a variable structure of links has been considered as a dynamical network within this model. Avalanche processes on it have been simulated using the modified Abelian sandpile model and fixed-energy sandpile model. It has been shown that avalanche processes on the dynamical lattice under study are more stable than a static lattice with respect to the appearance of catastrophic events. In particular, this is manifested in a decrease in the maximum size of an avalanche in the Abelian sandpile model on the dynamical lattice as compared to that on the static lattice. For the fixed-energy sandpile model, it has been shown that, in contrast to the static lattice, where an avalanche process becomes infinite in time, the existence of avalanches finite in time is always possible.