Acoustic oscillations in the combustion of an aerosol

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 32–41, May–June, 1989.     

Kazhdan-Lusztig polynomials for certain varieties of incomplete flags

We give explicit formulas for the Kazhdan-Lusztig P- and R-polynomials for permutations coming from the variety F_1,n−1 of incomplete flags consisting of a line and a hyperplane.     

Surfatron acceleration in electromagnetic waves with a low phase velocity

The possibility of unlimited surfatron acceleration of nonrelativistic charged particles by slow electromagnetic waves has been revealed. The capture into such an acceleration regime has been described. The region of the parameters in which the effect of the capture and acceleration exists has been considered. The contribution of this mechanism to an increase in the energy of charged particles in the Earth’s magnetosphere has been estimated.     

Linear stationary control systems over the Boolean semiring and their graphs of modules

We consider linear stationary dynamical systems over the Boolean semiring. We analyze the properties of complete observability, identifiability, attainability, and controllability of a system. We define the notion of the “graph of modules” of totally controllable totally attainable Boolean linear stationary systems by analogy with spaces of modules in the case of systems over fields. The above-mentioned graph is described in the simplest case of one-dimensional inputs and outputs. We prove the weak connectedness of this oriented graph.     

On the spectrum of magnetic field and scalar impurity fluctuations in acoustic turbulence

The fluctuations of a magnetic field in acoustic turbulence are examined. An equation is derived for the spectral tensor of homogeneous magnetic field fluctuations. In a certain limit case the spectrum of steady-state pulsations is obtained in the presence of an external source. It is shown that three kinds of spectra exist in an inertial subdomain, each of which corresponds to a definite domain in wave space. Analogous results have been obtained for the fluctuations of a homogeneous scalar impurity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 26–31, March–April 1971.In conclusion, the author grateful to R. Z. Sagdeev for discussing the results obtains at a seminar.