Numerical simulation of the unsteady aerodynamic interaction of two plane airfoil cascades

A method for the calculation of unsteady aerodynamic interaction of two plane airfoil cascades that are in relative motion in a subsonic flow of ideal gas is developed. This interaction provides a two-dimensional approximation of the flow in a stage of an axial turbomachine. The method is based on the reduction of the problem to the calculation of the unsteady flow in a single interblade passage of each of the cascades. The calculation uses generalized space-time periodicity relations corresponding to the unsteady process of interest. The calculation is based on the direct numerical integration of the non-stationary gas dynamics equations with the use of the finite difference Godunov-Kolgan-Rodionov scheme of the second approximation order with respect to time and space. The calculation procedure includes the determination of the acoustic fields that are generated by the stage in the incident flow and in the flow behind it. The results of the calculations that illustrate the accuracy of the numerical solution and the capabilities of the method are presented.     

Description of bimolecular fluorescence-quenching processes on the surface of pyrogenic silica

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 55, No. 6, pp. 966–971, December, 1991.     

Propagation of three-dimensional acoustic perturbations in channels of variable cross sectional area at frequencies near the cutoff frequency

A study is made of the propagation of three-dimensional acoustic perturbations in a two-dimensional gas flow in axisymmetric channels of variable cross sectional area at frequencies near the cutoff frequency. The cross sectional area of the channel is assumed to vary slowly along its length. The obtained results are of interest, for example, from the point of view of estimating the level of noise carried through the gas ducts of a jet engine. The singularities of a solution found earlier in [1] (essentially the analog of the WKB approximation) are investigated. These singularities are due to the existence of turning points in the theory of the WKB approximation. The formalism of this theory [2] is used to develop a method for calculating the reflection coefficient of acoustic perturbations; in this approximation, reflection is found to be appreciable only at the channel sections where the frequency is near the cutoff frequency. Calculated examples are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 149–159, November–December, 1980.I am grateful to A. N. Kraiko, who pointed out the connection between the singularities investigated in the present paper and turning points in the theory of the WKB approximation and suggested that the formalism of this theory should be used to calculate the reflection coefficient. Discussions that I had with Kraiko during the work were very helpful.     

Recent Advances on the Total Syntheses of Communesin Alkaloids and Perophoramidine

The communesin alkaloids are a diverse family of Penicillium‐derived alkaloids. Their caged‐polycyclic structure and intriguing biological profiles have made these natural products attractive targets for total synthesis. Similarly, the ascidian‐derived alkaloid, perophoramidine, is structurally related to the communesins and has also become a popular target for total synthesis. This review serves to summarize the many elegant approaches that have been developed to access the communesin alkaloids and perophoramidine. Likewise, strategies to access the communesin ring system are reviewed.     

Flow in the zones of separation of a turbulent boundary layer in front of a subsonic jet injected through a circular nozzle

Flow taking place in the three-dimensional region of separation formed by the interaction of a subsonic stream with a single subsonic jet emerging from a circular hole in a plate perpendicular to the stream is considered. The aim of the investigation is to discover the physical characteristics of the flow in the three-dimensional separation zone in front of a subsonic jet obstacle and to determine the principal laws governing the geometrical and hydrodynamic characteristics of the flow as functions of the parameters of the driving stream and jet.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 34–41, May–June, 1973.     

Lax Pairs for Linear Hamiltonian Systems

Siberian Mathematical Journal - We construct Lax pairs for linear Hamiltonian systems of differential equations. In particular, the Gröbner bases are used for computations. It is proved that...     

On the Quasinormal Convergence of Functions

Mathematical Notes - In the paper, it is proved that a topological space $$X$$ is a $$QN$$ -space if and only if every image of the space $$X$$ under a Baire mapping to the Baire space...     

Feedback in a Control Problem for a System with Discontinuous Right-Hand Side

Differential Equations - On a finite time horizon, we consider a control system described by a vector differential equation with right-hand side that changes its structure at some times spaced by a...     

Immunocytochemical Localization of XRCC1 and γH2AX Foci Induced by Tightly Focused Femtosecond Laser Radiation in Cultured Human Cells

To assess the prospects for using intense femtosecond laser radiation in biomedicine, it is necessary to understand the mechanisms of its action on biological macromolecules, especially on the informational macromolecule—DNA. The aim of this work was to study the immunocytochemical localization of DNA repair protein foci (XRCC1 and γH2AX) induced by tightly focused femtosecond laser radiation in human cancer A549 cells. The results showed that no XRCC1 or γH2AX foci tracks were observed 30 min after cell irradiation with femtosecond pulses of 10¹¹ W∙cm⁻² peak power density. An increase in the pulse power density to 2 × 10¹¹ W∙cm⁻² led to the formation of linear tracks consisting both of XRCC1 and γH2AX protein foci localized in the places where the laser beam passed through the cell nuclei. A further increase in the pulse power density to 4 × 10¹¹ W∙cm⁻² led to the appearance of nuclei with total immunocytochemical staining for XRCC1 and γH2AX on the path of the laser beam. Thus, femtosecond laser radiation can be considered as a tool for local ionization of biological material, and this ionization will lead to similar effects obtained using ionizing radiation.