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.     

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.     

Time-resolved fluorescence study of the single tryptophan in thiocyanate and azide derivatives of horseradish peroxidase: Implication for a p H-induced conformational change in the heme cavity

Detailed pH-dependent steady state and picosecond time-resolved tryptophan fluorescence studies on thiocyanate and azide complexes of horseradish peroxidase have been carried out. The fluorescence decay of the single tryptophan in these species was fitted to a discrete three exponential model. Maximum entropy method analysis also gave three distinct regions of lifetime distributions. The fast subnanosecond lifetime component was found to have > 97% amplitude contribution while other two longer lifetime components have small contributions. Small contributions from the nanosecond lifetime components possibly arise from apoprotein impurity or some small amount of disordered heme conformer of the protein. pH dependence of the fast picosecond lifetime components was found to show a systematic behavior which has been interpreted in the light of obligatory conformation change associated with activation of the enzyme at low pH.     

Theoretical and experimental investigation of the linear optical response of YBa2Cu4O8 The relevance of LDA calculations

We report results of ellipsometric measurements of the dielectric tensor of YBa₂Cu₄O₈ as well as calculations employing density functional theory in the local density approximation (LDA). For the computation of the one-electron eigenvalues and states the linear-muffin-tin-orbital method (LMTO) was used. Measured and calculated results show good agreement. In particular, the calculation predicts different band structures for YBa₂Cu₃O₇ and YBa₂Cu₄O₈ in the vicinity of the Fermi energy which lead to significant differences in the optical spectra. One such difference is a region of small ε₂ in the near infrared which is a fingerprint of the high (relative to the top of the highest fully occupied band) Fermi energy as compared to the situation in YBa₂Cu₃O₇. Our experimental results confirm the theoretical findings.     

Structure of thin block copolymer films studied by X-ray reflectivity

Summary X-ray reflectivity may be used to determine the internal structure of thin polymer films. An electron density difference of 10% for polystyrene and polyisoprene is sufficient to distinguish between a random distribution of lamellae, complete orientation parallel to the substrate surface and a surface induced formation of lamellae. The disappearance of the lamellar Bragg-peaks, with heating of the film, shows the transition into the disordered state.     

Influence of layer and anisotropic fluctuations of the refractive index on the beyond-the-horizon SHF propagation in the troposphere over the sea when there is an evaporation duct

On the basis of the invariant imbedding method the disturbance theory for complex constants of propagation is proposed. This approach allows us to consider the influence of layer and anisotropic fluctuations of refractive index on the beyond-the-horizon propagation in the adiabatic approximation with the existence of an evaporation duct. Finally, the authors consider some examples of the calculations and investigate stochastic effects connected with the interaction between fluctuating and regular waveguides.     

On exact order estimates of N-widths of classes of functions analytic in a simply connected domain

In the spaces E _q(Ω), 1 < q < ∞, introduced by Smirnov, we obtain exact order estimates of projective and spectral n-widths of the classes W ^r E _p(Ω) and W ^r E _p(Ω)Ф in the case where p and q are not equal. We also indicate extremal subspaces and operators for the approximative values under consideration.     

Linear optical switching in a FLC/waveguide composite device

A fast electrooptic modulation in a polymer waveguide using a ferroelectric liquid crystal has been proposed. In this device, the surface stabilized ferroelectric liquid crystal and the soft mode ferroelectric liquid crystal are used as an active material on the passive polymer waveguide, and electrooptic switching is realized by controlling the total reflection at the polymer waveguide-liquid crystal interface. The response time is of the order of several microseconds. The analogue electrooptic modulation in the waveguide is realized using the field induced linear molecular tilt of the electroclinic effect in the soft mode ferroelectric liquid crystal.