Vortex ring generation due to the coalescence of a water drop at a free surface

 Results are presented of an experimental investigation of vortex ring formation by a fluid drop contacting a free surface with negligible velocity. The pool fluid is mixed with fluorescein dye, and a laser sheet is used to illuminate a plane of the flow. A series of representative images is recorded by a CCD camera and speculation is made regarding specific sources of vorticity flux through the free surface. Two scaling analyses previously presented by other investigators are demonstrated to be equivalent under the assumptions of this experiment, and they provide the motivation for a series of test runs in which the duration of the coalescence process, τ_*, is related to variations in drop diameter L and fluid surface tension σ. Experimental results are in agreement with the analyses, showing τ_*∼σ^-1/2 and τ_*∼L ^3/2. Received: 22 December 1995 / Accepted: 15 October 1996     

On the dispersion of a solute in oscillating flow of a non-Newtonian fluid in a channel

The paper presents an exact analysis of the dispersion of an immiscible solute in a non-Newtonian fluid (known as an incompressible second-order fluid which shows viscoelastic behaviour) flowing slowly in a parallel plate channel in the presence of a periodic pressure gradient. Using a generalized dispersion model which is valid for all times after the solute injection, the diffusion coefficients K _i (τ)(i=1,2,3,…) are obtained as functions of time τ in the case when the initial solute distribution is in the form of a slug of finite extent. The analysis leads to the novel result that K ₂(τ) (which is a measure of the longitudinal dispersion coefficient of the solute) has a steady part S in addition to a fluctuating part D ₂(τ) due to the pulsatility of the flow. It is found that S decreases with increase in the viscoelastic parameter M for given values of the amplitude λ and frequency ω of the pressure pulsation. On the other hand, it is found that at a fixed instant τ, the amplitude of D ₂(τ) increases with increase in M for given values of λ and ω. Further it is shown that at a given instant τ, the amplitude of D ₂(τ) decreases with increase in ω for given λ and M and the profile for D ₂(τ) becomes progressively flatter with increase in ω. Finally the axial distribution of the average concentration θ _m of the solute over the channel cross-section is determined at different instants after the solute injection for several values of M, λ and ω. The present study is likely to have important bearing on the problem of dispersion of tracers in blood flow through arteries.     

Carleman problem for two pairs of functions in a ring

We consider a particular case of the matrix Carleman problem for two pairs of functions in a ring and find a constructive solution of this problem. In addition, we propose an algorithm for the construction of solutions for two infinite systems of smooth transition and for a system of two singular equations of special type. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 5, pp. 662–671, May, 1997     

On the embedding problem with noncommutative kernel of order p4. VI

In the case of number fields the embedding problem of a p-extension with non-Abelian kernel of order p⁴ is studied. The two kernels of order 3⁴ with generators α, γ and relations α⁹ = 1, [α,α]³=1,[α,αγγ]==1,[αγγ]=α³,γ³=1 or γ³=α³ and the kernel of order 2⁴ with generators α, β, γ and relations α⁴=1 β²,[αγ]=1, [α,γ]=1,[βγ]=α² are considered. For kernels of odd order the embedding problem is always solvable. For the kernel of order 16 the solvability conditions are reduced to those for the associated problems at the Archimedean points, and to the compatibility condition. Bibliography: 9 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 227, 1995, pp. 74–82.     

H2 CARS thermometry in a fuel-rich,premixed, laminar CH4/air flame in the pressure range between 5 and 40 bar

To establish H₂ CARS thermometry at high pressure, accumulated H₂ Q-branch CARS spectra were recorded in the exhaust of a fuel-rich CH₄/air flame at pressures between 5 and 40 bar. Temperatures were deduced by fitting theoretical spectra to experimental data points. The Energy-Corrected Sudden (ECS) scaling law was employed to set up an empirical model for the calculation of H₂ linewidths in high-pressure hydrocarbon flames with H₂ as a minority species. Experimental H₂ CARS spectra could be simulated very accurately with this model. The evaluated temperatures agreed well with reference temperatures obtained by spontaneous rotational Raman scattering of N₂.     

Anderson transition in dilute systems with pure exponential interactions

Summary Assuming a completely disordered lattice it is shown that all the states are localized when the disorder parameterx=a ₀/0 reachesthe value 0.31, wherea is the mean atomic separation anda ₀ is the Bohr radius.     

Exact solutions of a nonlinear sigma-model in a curved space and the theory of magnetically ordered media with variable saturation magnetization

Stationary solitons are found to occur in two-dimensional media with a variable saturation magnetization whose square is a harmonic function of the coordinates. It is shown in this case that the Landau-Lifshits equation can be reduced to the integrable O(3) sigma-model in curved space. Some properties of the solutions obtained are discussed. Bibliography: 15 titles. Translated by V. D. Lipovskii.     

Integral manifolds and the reduction principle in stability theory. III

It is shown how, with the help of approximate integral manifolds, to solve the reduction problem in stability theory in the nonsingular critical case. A generalization of the first fundamental Lyapunov-Malkin theorem in critical cases is obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 10, pp. 1324–1329, October, 1991.     

Anisotropic alpha-emission in the223Ra decay chain

Anisotropic α-emission from nuclei in the decay chain from²²³Ra to²⁰⁷Tl has been observed using low temperature nuclear orientation in combination with high resolution α-detection at 4.2 K. Information on partial wave amplitudes as well as hyperfine interactions has been extracted.