Low-Frequency Pulsations of Coronal Magnetic Loops

We analyze low-frequency intensity fluctuations of the microwave emission from solar flares at frequencies 22 and 37 GHz. The three microwave bursts of durations of about 1 h, observed at the Metsähovi Radio Observatory (Finland) with the time resolution of 0.1 and 0.05 s, are studied. To obtain spectral-temporal characteristics of the low-frequency fluctuations, we apply the Wigner-Ville method, i.e., the time-lag Fourier transform of the local autocorrelation function of an analytical signal. As a result, we obtain for the first time the dynamical spectra of the low-frequency fluctuations, which are identified as MHD eigenoscillations of coronal magnetic loops. The features of the dynamical spectra testify that several types of low-frequency pulsations are excited in coronal magnetic loops during solar flares: 1) Fast and slow magnetosonic oscillations with periods of 1-1.5 s and 200-280 s, respectively. Fast magnetosonic oscillations appear as pulse trains of duration 100-200 s and have the positive frequency drift d/ dt 0.125 Hz/min and the frequency splitting 0.05 Hz; 2) The eigenoscillations of a coronal magnetic loop as an equivalent electric circuit. The period of these oscillations is about 1 s during the initial stage of a microwave burst and increases gradually up to 4 s during the decay stage of the radio emission; and 3) Intensity modulation of the microwave radiation by a periodic pulse sequence with a period of about 1 s at the burst onset and about 2 s at its end. The parameters of the dynamical spectra and identification of the MHD pulsations allow us to obtain information on the loop parameters, such as the ratio of the loop radius to its length (r/L 0.1), the ratio of the gas pressure to the magnetic-field pressure inside the loop ( 3· 10^-3), the ratio of plasma densities outside and inside the loop, and the electric current in the coronal loop (I 1.5 · 10¹² A).     

On the normal structure of the general linear group over a ring

The present paper is devoted to the study of normal subgroups of the general linear group over a ring and the centrality of the extension St (n, R) E(n,R). The notions of the standard commutator formula and the standard normal structure of GL(n, R), E(n, R), and St (n,R) and their relationships are discussed. In particular, it is shown that the normality of E(n, R) in GL (n,R) and the standard distribution of subgroups normalized by E (n, R) follow from some conditions of linear dependence in R. Also, it is proved that the standardness of the normal structure of GL (n,R) and the centrality of K₂(n, R) in St (n,R) follow from the same conditions over a quotient ring R/I, provided that si In}-1. Under certain additional assumptions (for example, I is contained in the Jacobson radical of R), the converse is also true. The standard technique due to H. Bass, Z. I. Borevich, N. A. Vavilov, L. N. Vaserstein, W. van der Kallen, A. A. Suslin, M. S. Tulenbaev, and others is used and developed in this paper. Bibliography: 21 titles.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 236, 1997, pp. 166–182.The author gratefully acknowledges the support of the St. Petersburg Mayor's Office for the grant for young scientists and of the SFB 343 in Bielefeld University. The investigation presented in this paper was made possible in part by grant No. JHP100 from the International Science Foundation and the Russian Government.     

Dynamo-optical effects in a plasma

The propagation of electromagnetic waves in a nonuniformally moving cold electron plasma with no external magnetic field and collisions is considered. The motion is assumed to be stationary. It is shown that in the case of smooth variation of the parameters of the medium the trajectories of the rays in the zero approximation of geometric-optics are determined by the concentration distribution, while the motion leads to rotation of the polarization plane in the wave. For plane-stratified flow with a constant velocity gradient an exact solution of the equations is determined which constitutes the superposition of two independent waves that are elliptically polarized in opposite directions. The refraction law of these waves is found, and the corresponding reflection and penetration coefficients are calculated in the case of a layer having a finite thickness.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 15, No. 2, pp. 183–190, February, 1972.     

Estimation of the anisotropy of the short-time and long-time strengths of glass-reinforced plastics

A linear correlation between the tensile stress and the logarithm of the lifetime of a glass-reinforced plastic in various directions in the plane of the sheet has been experimentally established. The parametric introduction of the time factor into the criterion of the short-time strength of anisotropic materials is proposed as a first approximation. The Gol'denblat-Kopnov criterion is used to derive a simple relation describing the strength properties of glass-reinforced plastics in the uniaxial state of stress.Moscow Institute of Chemical Machine-Building. Scientific-Research Institute of Mechanics, Moscow Lomonosov State University. Translated from Mekhanika Polimerov, Vol. 5, No. 2, pp. 243–249, March–April, 1969.     

ε-Expansions in Dyson's Hierarchical Model

We consider Dyson's hierarchical model on a d-dimensional hierarchical lattice and define a renormalization group (RG) transformation for complex values of d as a map in the space of sequences of coupling constants determining the model Hamiltonian. We show that d=4 is a bifurcation value of this transformation for the RG transformation parameter equal to 1+2/d, and we construct a non-Gaussian RG-invariant Hamiltonian in terms of the (4–d)-expansion. We establish that the (–3/2)- and (4–d)-expansion coefficients for a non-Gaussian fixed point in the dimension d=3 have the same asymptotic representation as the size of the elementary cell tends to infinity, thus confirming that both the expansions describe the same nontrivial fixed point in the dimension three.     

Single-Channel and Multi-Channel Planar Free-Electron Masers

We discuss the results of studying generation of powerful millimeter-wave pulses in single-channel and multi-channel planar free-electron masers (FEMs) in which a two-dimensional distributed feedback (DF) is used for synchronization of radiation. Computer simulations show the possibility of the formation of several sheet beams from a single cathode along with the subsequent synchronization of auto-oscillations in different channels. We present the results of experiments in the ELMI facility on generation of powerful microsecond pulses at a wavelength of 4 mm in a single-channel FEM having a two-dimensional distributed feedback and driven by a 1 MeV, 3 kA, 3 s sheet electron beam.     

Low-field magnetic properties of LaMnO3+δ with 0.065≤δ≤0.154

In a weak magnetic field LaMnO_3+δ exhibits at δ=0.065 below the paramagnetic-to-ferromagnetic (FM) Curie temperature, T_C, a mixed (spin-glass and FM) phase followed by a frustrated FM phase at δ between 0.100 and 0.154. The same behavior is observed in La_1−xCa_xMnO₃ with x between 0 and 0.3. This can be understood by the similar variation of the Mn⁴⁺ concentration, c between ≈0.13 and 0.34, in both materials when x or δ is increased. On the other hand, considerable differences are found between these compounds in the values of the magnetic irreversibility, in the dependencies of T_C(c) and the magnetic susceptibility, χ(c), as well as in the critical behavior of χ(T) near T_C. These differences can be explained by distortions of the cubic perovskite structure, by the reduced lattice disorder and by the more homogeneous hole distribution in LaMnO_3+δ than in La_1−xCa_xMnO₃.     

Quantum logic approach to wave packet control

We study control of wave packets with a finite accuracy, approaching it as quantum information processing. For a given control resolution, we define the analogs of several quantum bits within the shape of a single wave packet. These bits are based on wave packet symmetries. Analogs of one- and two-bit gates can be implemented using only free wave packet evolution and coordinate-dependent ac Stark shifts applied at the moments of fractional revivals. As in quantum computation, the gates form a logarithmically small set of basis operations which can be used to approximate any unitary transformation desired for quantum control of the wave packet dynamics. Numerical examples show the application of this approach to control vibrational wave packet revivals.