BRST charges for finite nonlinear algebras

Some ingredients of the BRST construction for quantum Lie algebras are applied to a wider class of quadratic algebras of constraints. We build the BRST charge for a quantum Lie algebra with three generators and ghost-anti-ghosts commuting with constraints. We consider a one-parametric family of quadratic algebras with three generators and show that the BRST charge acquires the conventional form after a redefinition of ghosts. The modified ghosts form a quadratic algebra. The family possesses a nonlinear involution, which implies the existence of two independent BRST charges for each algebra in the family. These BRST charges anticommute and form a double BRST complex.     

Hidden symmetries of integrable conformal mechanical systems

We split the generic conformal mechanical system into a “radial” and an “angular” part, where the latter is defined as the Hamiltonian system on the orbit of the conformal group, with the Casimir function in the role of the Hamiltonian. We reduce the analysis of the constants of motion of the full system to the study of certain differential equations on this orbit. For integrable mechanical systems, the conformal invariance renders them superintegrable, yielding an additional series of conserved quantities originally found by Wojciechowski in the rational Calogero model. Finally, we show that, starting from any N=4 supersymmetric “angular” Hamiltonian system one may construct a new system with full N=4 superconformal D(1,2;α) symmetry.     

Experimental study of the interaction of shock waves with the contact boundary and zone of turbulent mixing of different gases

The interaction of a shock wave with turbulent flow was experimentally investigated. The case where a shock wave formed at one end of the tube, passed through the interface between two quiescent gases with different densities (air–CO2 or air–Ar), was reflected from the end of the tube, and interacted with the zone of turbulent mixing formed at the interface. The Mach number of the shock wave incident on the interface in air was M ≈ 2.37–2.57. The flow field was recorded using the schlieren method and high-speed video recording. It was found that after passing the mixing zone, the shock-wave front was deformed and became unstable.     

Durability of structures of polymer composites affected by static loads and climatic factors

Conclusions We suggested a model of predicting residual strength and durability of structures of CP, jointly acted upon by static loads and environmental factors, by the use of data on short-time and long-time strength obtained under laboratory conditions and of the results of residual strength in aging without load. The methods of accelerated laboratory tests devised for studying the climatic stability of PFC in aging without load cannot be quantitatively applied to the investigation of aging under load.Presented at the Sixth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, November, 1986).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 915–920, September–October, 1987.     

Two-frequency lasing in the Nd:YLF laser with a lens-shaped active element and longitudinal diode pumping

In the laser with lens-shaped Nd:YLF [100] active element, the dependence of polarization and frequency of the radiation on the cavity length is studied under conditions of longitudinal diode pumping. The conditions at which birefringence in the Nd:YLF active element allows two-frequency lasing are determined.