Failure rates of regenerative systems with heavy tails

Let ξ_t be a regenerative process and assume that, at each state x, the process can fail with intensity α(x). If the inter-regeneration times have a finite exponential moment orinf _xα(x)>0, then α(ξ_t) tends to some limiting positive intensity as t→∞ (under mild additional restrictions). This fact is widely used in engineering because the limiting intensity can be employed in various calculations, say, in reliability theory. The paper contains a variety of examples showing that α(ξ_t) provided that inter-regeneration time has no exponential moment andinf _x α(x)=0. The speed of convergence depends, in general, on both the tail of inter-regeneration time and α(x). Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part III.     

Nondegenerate systems and generic properties of the integrable Hamiltonian systems

The goal of the paper is to clarify whether the nondegenerate Hamiltinian systems are “typical” among all integrable systems. The importance of this problem is emphasized by a theorem of Fomenko-Zieschang, in which an isoenergy invariant determining the nondegenerate systems up to topological equivalence is constructed. Bibliography: 12 titles. Published inZapiski Nauchnykh Seminarov POMI, Vol. 234, 1996, pp. 184–192.     

Asymptotic Freedom in the Conformal Quantum Gravity with Matter

The grand unified theory (GUT) based on the O(N) and SU(N)-gauge groups after the conformally invariant gravity being included is investigated. We calculate the one-loop gravity contributions into the renormalization group equations and study their solutions. The analysis performed show that the asymptotic freedom behaviour early established for all GUT's coupling constants is not broken by taking into account this kind of gravity. However all restrictions imposed on the GUT multiplet composition become less firmly and the physical content of the constructed models is more realistic.     

Sensitivity analysis of regenerative queuing models

Queuing models described as regenerative processes driven by several sequences are under investigation. Occurrence times in these sequences are supposed to be asynchronous, in general. Sensitivity coefficients that are derivatives of some stationary performance measures with respect to definite parameters as well as derivatives of higher orders are derived for such queuing models. These sensitivity coefficients can be evaluated by simulation.     

Focusing crystal mirrors for X-ray diagnostics of laser-produced plasma

The paper describes an investigation of the characteristics of spherical focusing Bragg-reflection mirrors. The integral reflectivity of bent crystals at Bragg angles 80–90°, the width of the spectrum of the reflected x-rays, and the spatial resolution of the images formed by the focusing crystals are considered. Results are presented of the calculated integral reflectivity of bent silicon and quartz crystals of different orientation and in different orders of reflection. The feasibility is demonstrated of laser-plasma diagnostics using the images obtained with the aid of a multichannel x-ray microscope based on focusing crystals. Possible schemes of active diagnostics of a dense laser plasma using a monochromatic transilluminating x-ray beam are considered.Laser Plasma Laboratory, Lebedev Physics Institute. Translated from FIAN Preprint No. 143, Lebedev Physics Institute of the Academy of Sciences of the USSR, Moscow, 1989.     

Infrared supercontinuum from a large mode area PCF under extreme picosecond excitation

Evolution of the long-wavelength edge of supercontinuum (SC) in a large mode-area photonic crystal fiber (LMA PCF) under extreme (close to the fiber damage threshold) picosecond excitation is analyzed for the first time to our knowledge. The obtained results are interpreted on the basis of the numerical simulations explaining both spectral and temporal characteristics of SC in dependence on the pulse power and the fiber length. An existence of the minimum LMA PCF length providing the broadest spectrum under the highest picosecond excitations is predicted. The multimode cross-modulation inside the LMA PCF is analyzed, as well.      

Radiation-induced damage in calcium fluoride ionic crystals exposed to high-intensity ultraviolet and vacuum ultraviolet light

An experimental setup for studying optical materials under the action of plasma-emitted intense (up to 10⁵ W/cm²) ultraviolet and vacuum ultraviolet radiation is described, and methods for estimating the radiation damage are developed. The damage produced in calcium fluoride ionic crystals at ～300 K by low (10³ rad) and moderate (10⁶ rad) absorbed doses is experimentally estimated.     

Experiment and modeling of a diode-pumped 1.3 μm Nd:YVO<Subscript>4</Subscript> laser passively Q-switched with PbS-doped glass

A diode-pumped 1.34 m Nd:YVO₄ laser passively Q-switched with PbS quantum dots doped glass is presented. An average output power of 24 mW with a Q-switching efficiency of 13% and a Q-switched pulse width of 15 ns was obtained. A four level spectroscopic model of a PbS quantum dots doped glass saturable absorber is applied to numerically simulate passively Q-switched Nd:YVO₄ laser operation. It has been shown that for the simulation of passive Q-switching of 1.3 m Nd:YVO₄ lasers with PbS doped glasses as the saturable absorbers, it is necessary to take into account intensity dependence of bleaching relaxation times. PACS 42.60.Gd; 42.55.Xi; 42.70.Hj