On the fall of a heavy rigid body in an ideal fluid

We consider a problem about the motion of a heavy rigid body in an unbounded volume of an ideal irrotational incompressible fluid. This problem generalizes a classical Kirchhoff problem describing the inertial motion of a rigid body in a fluid. We study different special statements of the problem: the plane motion and the motion of an axially symmetric body. In the general case of motion of a rigid body, we study the stability of partial solutions and point out limiting behaviors of the motion when the time increases infinitely. Using numerical computations on the plane of initial conditions, we construct domains corresponding to different types of the asymptotic behavior. We establish the fractal nature of the boundary separating these domains.     

One-stage synthesis of benzoacridine and benzophenanthroline functionalized derivatives

A one-stage procedure was developed for preparing new partially hydrogenated derivatives of benzoacridine and benzophenanthroline. The procedure was a triple condensation of 6-aminoquinoline or 2-naphthylamine with formaldehyde and hydroxycyclohexylidenepropanedinitriles, functionalized analogs of cyclic β-diketones.     

Steady streaming around a spherical drop displaced from the velocity antinode in an acoustic levitation field

The steady (acoustic) streaming associated with a sphericaldrop displaced from the velocity antinode of a standing waveis studied. The ratio of the particle size to the acoustic wavelengthis treated as small but non-zero, and the solution is developedin the form of a two-term expansion in terms of the correspondingsmallness parameter. The drop viscosity is assumed to be muchhigher than that of the surrounding fluid, which is the casefor a drop in a gas medium. There are essentially three distinctregions where the steady streaming flow is analysed: insidethe drop (internal circulation), in the Stokes shear-wave layerat the surface on the gas side, and the gas outside the Stokeslayer (the outer streaming region). Solutions for the internalcirculation and the outer streaming are obtained in the limitof small Reynolds number. Despite the gas-to-liquid viscosity ratio being small, the outerstreaming may be dramatically affected by the fact that thesphere is liquid as opposed to solid. The parameter that measuresthe effect of liquidity is essentially the viscosity ratio dividedby the relative (to the particle size) thickness of the Stokeslayer. The case of a solid sphere is recovered by letting thisparameter go to zero.     

Experimental investigation of the shape of a heavy-current air discharge without blowing

The results of investigating experimentally the shape of an are discharge burning between two electrodes in air at atmospheric pressure in the absence of blowing when the currents are less than 100 A are reported. In certain experiments the distance between the electrodes was varied in order to solve special problems. The effect of the electrode material on the shape of the discharge is investigated. It is found that the electrode material does not have a qualitative effect on the shape of the discharge but can lead to a significant variation in the parameter distribution over the discharge gap. The study is a continuation of the research described in [1].     

Spectroscopic Detection of Sulfur Oxides in the Aircraft Wake

The absorption/emission spectral regions of SO, SO₂, SO₃, S₂O and HSO are analyzed for the range from UV (λ ≥ 0.2 μm) to IR (λ < 30 μm) and are compared with the atmospheric transmission spectrum. It is shown that many vibrational bands of the compounds considered fall into atmospheric transmission windows. For the vibrational bands of SO, SO₂, SO₃, S₂O, and HSO molecules there are some gases which hinder the absorption diagnostics of the indicated compounds. These interfering gases are natural components of atmospheric air as well as specific gases of aircraft engine exhaust. It is found that the least influence of the interference takes place in the 2400–2700 cm⁻¹ IR region. The spectroscopic techniques used for the detection of aircraft engine exhaust compounds are briefly reviewed, with much consideration given to SO₂. The IR absorption spectra of SO₂ and other gases are calculated for the conditions of the aircraft engine nozzle exit. Narrow spectral intervals suitable for SO₂ detection in a hot flow are determined. An analysis is made for the detection capabilities of CO₂ lasers (including isotope CO₂ lasers) and CO lasers (both fundamental band and first-overtone ones) as applied to SO₂ detection in aircraft engine exhaust. Published in English as Preprint No. 5 of the P. N. Lebedev Physical Institute, Moscow (2004).