"Green" noise in quasistationary stochastic systems

We consider the behavior of stochastic systems driven by noise with a zero value of spectral density at zero frequency ("green" noise). For this purpose we propose the version of the Krylov-Bogoliubov averaging method to study the systems which are not stationary in the case of an external white noise. We use the ergodicity of a nonlinear random function in the method, and obtain equations for any approximation of the theory. In particular, it is shown in the first approximation that there is an effective potential to describe the averaged motion of the system. We consider a phase-locked loop as an example and show that metastable states are possible. The lifetime of these states essentially increases if the form of a green noise spectrum becomes sharper in the low-frequency region. The high stability of the system driven by green noise is confirmed by numerical simulation. It is important that the theoretical result obtained by the averaging method and the one obtained in the simulation coincide with sufficient accuracy. In conclusion, we discuss some of the unsolved green noise problems. (c) 2001 American Institute of Physics.     

Mechanochemical synthesis of nonstoichiometric fluorite Ca1?xLaxF2+x nanocrystals from CaF2 and LaF3 single crystals

The nonstoichiometric Ca_1−x La_xF_2+x phase (x ≥ 0.1) is obtained by mechanochemical synthesis from CaF₂ and LaF₃ single crystals. This phase is the first representative of fluorite fluorides obtained by mechanochemical synthesis in the MF_m-RF_n systems (m < n ≤ 4). The average grain size ranges within 10–30 nm. The temperature dependence of ionic conductivity of the mechanochemically synthesized phase pressurized at 600 MPa (at its high-temperature portion at temperatures exceeding 200–250°C) coincides with the conductivity of the single crystals of the same composition (Ca_0.8La_0.2F_2.2). The activation energy of ionic conductivity (0.95 eV) corresponds to migration of interstitial fluoride ions in the crystal bulk. Mechanochemical synthesis of a multicomponent fluoride material with nanometer grains opens a new chapter in the chemistry of inorganic fluorides. A decrease of the sintering temperature of the powders with nanometer grains is very important for preparing dense fluoride ceramics of complicated compositions and other polycrystalline forms of fluoride materials. __________ Translated from Kristallografiya, Vol. 50, No. 3, 2005, pp. 524–531. Original Russian Text Copyright ? 2005 by Sobolev, Sviridov, Fadeeva, Sul’yanov, Sorokin, Zhmurova, Herrero, Landa-Canovas, Rojas.