Nonlinear power attenuation of the radiation of a pulsed CO2 laser in the atmosphere near the ground

Conclusion Thus, as a result of the natural investigations performed on the propagation of short (microsecond) pulses of CO₂ laser radiation in the near-ground atmosphere, quantitative data are obtained on the nonlinear power attenuation of powerful radiation by the atmosphere in the range of energy densities w = 3–18 J/cm² as a function of the meteorological conditions and the turbulent state of the atmosphere. It has been shown that the principal mechanism of nonlinearity of the medium along a 100–250 m path is the origin of low-threshold optical breakdown centers on solid aerosol particles. The initiation conditions and the main characteristics of an extended laser flash in the atmosphere have been investigated.Future work of interest is to obtain statistically justified dependences of the nonlinear power attenuation and distortions of the structure of beams of powerful pulsed radiation along extended paths on the basic opticometeorological parameters of the state of the atmosphere.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 5–13, February, 1983.     

Cooperative Parametric Instability of Natural Modes and Coherent Mechanism of Self-Mode-Locking in a Ring Class-B Laser

Based on recent experimental observations and numerical simulations [1-4], we develop an analytical theory of spontaneous low-threshold mode-locking in a long homogeneously-broadened fiber laser with slow relaxation of inversion. We show that the phenomenon originates from the self-consistent parametric resonance and beat-frequency-locking of paired hot modes taking place due to coherent nonlinear effects in the system of active two-level centers. An important role of the Risken-Nummedal-Graham-Haken [5-7] multimode instability is discussed.     

Spontaneous Polarization of a Gas of Two-Level Molecules and the Gibbs Quasi-Energy Distribution

We study the possibility of spontaneous formation of a polarization structure in a thermodynamically equilibrium gas of dipolarly interacting two-level molecules. Using the Maxwell-Bloch equations within the framework of the mean-field theory, we find that the antiferroelectric phase transition in a gas with a weak relaxation of the polarization is always a second-order transition. It is shown that if relaxation is neglected, then in the quasi-classical consideration of the translational motion of molecules in the polarization wave, the energy levels of a separate molecule coincide with its quasi-energies that are well known in quantum optics. Thus, to study the statistical properties of the antiferroelectric phase, we apply the generalized Gibbs distribution over quasi-energy states of the molecules. As a result, we determine the characteristic features and the possible parameters of the antiferroelectric state of a gas. In particular, it is found that, owing to the Doppler resonance of part of the molecules with the polarization wave, the properties of the gas antiferroelectrics behind the phase-transition point may radically differ from the properties of the conventional ferroelectrics in the Ginzburg-Landau theory. We also analyze the influence of polarization fluctuations for the case of a ferroelectric transition in a gas.     

Properties of the block BFGS update and its application to the limited-memory block BNS method for unconstrained minimization

Numerical Algorithms - A block version of the Broyden–Fletcher–Goldfarb–Shanno (BFGS) variable metric update formula and its modifications are investigated. In spite of the fact...     

Limit distributions arising in branching random walks on integer lattices

The paper completes the investigation of limit distribution of the number of particles at the source of branching in the model of critical catalytic branching random walk on ^dd N {{mathbb Z}^d};d in {mathbb N} . Limit theorems of such kind were established only for d = 1, 2, 3, 4 under the assumption that, at the initial moment, there is a single particle at the source of branching. We prove their analog for d geqslant 5 d geqslant 5 . Moreover, in any dimension, we generalize the previous results by permitting the initial particle to start at an arbitrary point of the lattice.     

Radical Intermediates in the Decomposition of Substituted Coumarins

Summary. A series of coumarin derivatives containing substituents with an acidic CH₂ group in 3-position was decomposed on the surface of PbO₂. The radical intermediates were identified by EPR spectroscopy. Although the occurrence of several tautomeric forms is possible, the application of the spin trapping technique confirmed the formation of only one radical product, namely the C-radical resulting from the homolytic splitting of the C–H bond of the methylene group.     

New quasi-Newton method for solving systems of nonlinear equations

We propose a new Broyden method for solving systems of nonlinear equations, which uses the first derivatives, but is more efficient than the Newton method (measured by the computational time) for larger dense systems. The new method updates QR or LU decompositions of nonsymmetric approximations of the Jacobian matrix, so it requires O(n ²) arithmetic operations per iteration in contrast with the Newton method, which requires O(n ³) operations per iteration. Computational experiments confirm the high efficiency of the new method.     

Modeling of spectral features in the dynamic spectra of neutron stars

Modeling of atomic and cyclotron lines in the emergent spectra of rotating neutron stars with various distributions of temperature over the star surface is carried out. General and special relativity effects are taken into account in the radiation transfer calculations. A novel method of analysis based on the Fourier series expansion of the observed spectra over rotation frequencies is proposed. It is shown that the mutual influence of the gravitational bending of light rays and rotation of the star leads to the formation of strong features (sometimes several features at once) in the Fourier-harmonic spectrum, whereas these features remain almost invisible in both the integrated and dynamic spectra. Possible application of the obtained results to the interpretation of absorption features in the spectrum of the single neutron star 1E 1207.4 − 5209 is discussed.