Regular and chaotic precession of magnetization in magnetic films with a stripe domain structure

Based on a numerical solution of the equations of motion found over a wide range of frequencies of an alternating magnetic field, the nonlinear precession dynamics of magnetization are studied in thin-film structures of the (100) type with a stripe domain structure in a perpendicular bias field. The conditions are determined under which high-amplitude regular and chaotic dynamic regimes occur. Bifurcational variations in the precession of coupled magnetic moments and dynamic-bistability states are detected. The specific features of the spectrum of Lyapunov exponents and of time analogs of Poincaré cross sections of trajectories in chaotic regimes are considered.     

A raman scattering study of the phase transition in the ammonium oxyfluoride (NH4)3TiOF5

Raman spectra of a polycrystalline sample of the perovskite-like oxyfluoride (NH₄)₃TiOF₅ are measured in the frequency region 100–3600 cm^?1 at temperatures ranging from 91 to 370 K under hydrostatic pressures of up to 9 GPa, which include the range of the phase transition from the orientationally disordered cubic phase to the low-symmetry phase. Anomalies in the spectral parameters due to the phase transition are revealed in the range of vibrations of TiOF₅ octahedral groups.     

An axiomatization for the linear logic of knowledge and time LTK r with intransitive time relation

We study the problem of the axiomatization of the linear multimodal logic of knowledge and time LTK _r with reflexive intransitive time relation. The logic is defined semantically as the set of formulas true on frames of a special kind. The LTK _r -frames are linear chains of clusters connected by a reflexive intransitive relation R _T which simulates time. Elements inside a cluster are connected by several equivalence relations imitating the knowledge of different agents. The main result of the article is the proof of the fact that the finite set of formulas proposed by the authors is an axiomatization of the logic LTK _r with reflexive intransitive time relation.     

Generalized normal homogeneous Riemannian metrics on spheres and projective spaces

In this paper, we develop new methods to study generalized normal homogeneous Riemannian manifolds. In particular, we obtain a complete classification of generalized normal homogeneous Riemannian metrics on spheres ${S^n}$ . We prove that for any connected (almost effective) transitive on $S^n$ compact Lie group $G$ , the family of $G$ -invariant Riemannian metrics on $S^n$ contains generalized normal homogeneous but not normal homogeneous metrics if and only if this family depends on more than one parameters and $n\ge 5$ . Any such family (that exists only for $n=2k+1$ ) contains a metric $g_\mathrm{can}$ of constant sectional curvature $1$ on $S^n$ . We also prove that $(S^{2k+1}, g_\mathrm{can})$ is Clifford–Wolf homogeneous, and therefore generalized normal homogeneous, with respect to $G$ (except the groups $G={ SU}(k+1)$ with odd $k+1$ ). The space of unit Killing vector fields on $(S^{2k+1}, g_\mathrm{can})$ from Lie algebra $\mathfrak g $ of Lie group $G$ is described as some symmetric space (except the case $G=U(k+1)$ when one obtains the union of all complex Grassmannians in $\mathbb{C }^{k+1}$ ).     

Anomalous isotopic effect in multibubble sonoluminescence of aqueous solutions of terbium chloride

An anomalously low isotope effect has been discovered in 20-kHz sonoluminescence of terbium chloride solutions in H₂O-D₂O mixtures. The intensity of luminescence in the characteristic 488-and 545-nm lines of the Tb³⁺ ion, which are observed against the solvent continuum (230–700 nm), increases with the content of D₂O to a maximum value of 4.0 ± 0.4, whereas the isotope effect in photoluminescence of the same solutions reaches 10 ± 1.0. The result is explained using the model of nonexponential decay of sonoluminescence of Tb³⁺ ions. These ions, which are formed in an excited state in cavitation bubbles, first undergo radiative and radiationless deactivation in the gas phase. However, some excited ions enter the solution bulk, because the excitation lifetime is longer than the average bubble lifetime. At the first stage, the isotope effect is small, because the density of the gas phase is low and quenching by solvent molecules is weak. At the second stage, the isotope effect coincides with the effect in usual photoluminescence in the solution. The total decrease in the effect in sonoluminescence depends on the weight of the “gas” stage of deactivation of excited Tb³⁺ ions.     

Classification of ultrahigh-energy extensive air showers in terms of the muon content

Ultrahigh-energy extensive air showers detected at the Yakutsk array are analyzed. Showers different in the muon content are revealed. Four classes of showers are separated.     

Emission in the final state in processes with the production of charged pions and light leptons

The Drell-Yan form is proposed for the decay widths of heavy quarks and cross sections for high-energy scattering with the production of charged pions and light leptons including radiative corrections in the final state in the leading logarithmic approximation. The corresponding spectral distributions are given in terms of the convolution of the cross section (decay width) in the Born approximation with the structure functions of pions and leptons. The pion structure function is given in the explicit form.