Kinetics of Formation and Curing of Oligoether Urethane Allyl Ester

Kinetic parameters of formation of P-9AD oligoether urethane allyl ester with terminal double bonds and of its curing with dinitrile oxide were determined. The dependence of the rate constant on the allyl alcohol concentration and temperature was studied. The mechanism of reaction of P-9A prepolymer with allyl alcohol was proposed. The kinetic and thermodynamic parameters of curing of oligoether urethane allyl ester with dinitrile oxide were determined. The mechanism of reaction of P-9AD oligoether urethane allyl ester with dinitrile oxide was proposed.     

Stability of the cylindrical flame front in an annular combustion chamber

Using small perturbations, within the framework of phenomenological theory of mixture combustion we study stability of the cylindrical front of deflagration combustion in an annular combustion chamber. The flame front is described as a discontinuity of gasdynamic parameters. It is discovered that the flame front is unstable for some types of small perturbations of the mainstream flow of the fuel mixture and the flame front. The mechanics of instability is examined using both numerical and analytical methods. The cases are presented of evolution of the instabilities rotating in the annular channel.     

On Bellman’s approach to optimal control theory

A theorem published earlier by the author is strengthened and a more informative necessary condition for an extremum in optimal control problems is obtained. The result is illustrated by a simple optimal control problem. Translated fromMatematicheskie Zametki, Vol. 66, No. 5, pp. 770–776, November, 1999.     

Acoustic resonance phenomena in air bleed channels in aviation engines

The existence of axial–radial acoustic resonance oscillations of the basic air flow in bleed channels of aviation engines is demonstrated theoretically and experimentally. Numerical and analytical methods are used to determine the frequency of acoustic resonance oscillations for the lowest modes of open and closed bleed channels of the PS-90A engine. Experimental investigations reveal new acoustic resonance phenomena arising in the air flow in bleed channel cavities in the core duct of this engine owing to instability of the basic air flow. The results of numerical, analytical, and experimental studies of the resonance frequencies reached in the flow in bleed channel cavities in the core duct of the PS-90A engine are found to be in reasonable agreement. As a result, various types of resonance oscillations in bleed channels can be accurately described.     

The whispering surface effect

The representation theory of symmetry groups, together with variational and functional-topological methods, are used in a two-dimensional formulation to investigate the waveguide properties of one-dimensionally periodic surfaces (OPS) and interfaces. It is established that all surfaces on which the Neumann condition is satisfied possess the waveguide property—they are open waveguides. This means that there are waves localized in the neighbourhood of the surface which propagate along it without attenuation—waveguide modes. It is shown that for any hard OPS there is always a transmission band of waveguide frequencies, localized in the neighbourhood of zero—the whispering surface effect. Anomalous oscillations localized around OPSs on which the Neumann condition is satisfied are observed and investigated. Examples of surfaces for which anomalous oscillations exist and others for which none exist are presented. It is proved that OPSs on which the Dirichlet condition holds do not have a transmission band for waveguide frequencies in the neighbourhood of zero, and for some frequency bands they do not have waveguide and anomalous properties. It is shown that one-dimensionally periodic interfaces of two media possess waveguide and anomalous properties, provided that the parameters satisfy certain relationships. It is established that if the interface has the waveguide property, then transmission band of frequencies will always exist localized in the neighbourhood of zero—the whispering interface effect. An example is presented in which anomalous oscillations are investigated, dispersion relations are derived and pass and stop bands for waveguide modes are determined.     

Waveguiding and anomalous properties of a periodic knife-type grating

It is shown that periodic knife-type gratings always have waveguiding and anomalous properties. The dispersion relations for waveguide modes are obtained and the passbands are determined. The asymptotical form of the dispersion relations is obtained with an infinite increase in the length of the cascade elements and a decrease in the wave number. The effect of the geometrical characteristics and the type of grating on its waveguiding and anomalous properties is investigated. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirisk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 46–56, November–December, 1998.     

Solvability of nonlinear stationary transfer equation

On the basis of a theorem on the global solvability of abstract equations that generalizes earlier results of the author, theorems on the solvability of the nonlinear stationary one-velocity transfer equation for the general and periodic cases are obtained.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 1, pp. 23–31, April, 1995.     

Effect of ion mean free path length on plasma polarization behind a dust particle in an external electric field

In this paper, a self‐consistent numerical model that describes the behavior of plasma around an isolated, highly charged dust particle is presented. Using the developed model, self‐consistent distributions of the space charge density and plasma potential in the presence of an external electric field are obtained. These distributions are thoroughly analysed though Legendre decomposition. For different dust plasma parameters, such as the radius of the dust particle, the amplitude of the external field, and the mean free path of ions, the dipole moment of the ion cloud surrounding the dust particle is calculated. It turns out that the dependencies of the dipole moment on the value of the external electric field obtained for different parameters are reduced to a single curve by simple scaling.