Discrete innovations in dynamic models of economy

Kalinin. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 4, pp. 47–59, July–August, 1990.     

Existence of a linear selector of a superlinear multivalued mapping

Mathematical Notes -     

Terahertz free-electron lasers with bragg structures based on the coupling between traveling and quasicritical waves

The possibility of creating high-power tunable planar terahertz free-electron lasers based on modified Bragg structures with the coupling of paraxial and transverse (with respect to the velocity of particles) wave fluxes has been demonstrated. In addition to the compatibility with the transport channels of intense electron beams, the advantage of the proposed structures is the spatial coherence of radiation at a large oversize factor of the interaction region in two transverse coordinates.     

Kinetics of Thermal Decomposition of Solid Propellant Based on Aluminum and Ammonium Perchlorate

Kinetic regularities of the mass loss and heat and-gas release were studied in the thermal decomposition of a solid propellant composed of aluminum, ammonium perchlorate, and a polymer binder. It was shown that, under heating from 40 to 340°C under permanent vacuum conditions, propellant samples decompose without ignition, with the limiting mass loss in the decomposition being 48%. When experiments were performed in air, the propellant formulation decomposes with sharp ignition, with the inflammation temperature (270–287°C) and amount of volatiles released by this instant of time (10–16 wt %) dependent on the heating rate. The kinetic regularities of the mass loss in the decomposition of a solid propellant were described in terms of the polychromatic kinetics model that assumes that the reaction system has ensembles of particles differing in reactivity. The distribution functions of the mass fractions of the propellant by activation energies of decomposition were calculated. The heat release kinetics in the decomposition of a propellant formulation in the temperature range 153–270°C in a closed evacuated system is described by a sum of equations for two parallel reactions: 1st-order reaction with a heat effect Q₁ = 200 ± 5 kJ kg^–1 and 1st-order autocatalysis with heat effect Q₂ = 1900 ± 50 kJ kg–1. The rate constants and the activation parameters of the process were determined.

     

Stochastic instability of nonlinear oscillations

Consider a dynamic system whose behavior is described by

$$x'' + \omega ^2 _0 (1 + \alpha x^2 )x + F(t)x = 0$$