The effect of vertical vibration on the onset of thermocapillary convection in a horizontal liquid layer

The effect of vertical vibration on the onset of Marangoni convection in a horizontal layer of a viscous incompressible uniform liquid with a free surface and a hard (solid) or soft (impermeable and stress-free) wall is investigated. In the case of harmonic vibration, a dispersion relation is constructed in explicit form using continued fractions. From this, equations are obtained for determining the critical values of the parameters for all three main types of loss of stability. Neutral curves of the monotonic and oscillatory instability are constructed, for fixed frequency and amplitude of the vibration, in the form of a graph of the Marangoni number against the wave number. The regions of parametric resonances, corresponding to synchronous and subharmonic modes are determined. The frequency values for which a high-frequency asymptotic form is reached are obtained. The long-wave Marangoni oscillatory instability is investigated, and it is shown that in this case the Marangoni numbers are negative and depend only on the Prandtl and Biot numbers.     

A numerical investigation of the resonance of gas-filled microbubbles: resonance dependence on acoustic pressure amplitude

The general Keller–Herring equation for free gas bubbles is augmented by specific terms to describe the elasticity, viscosity and thickness of the encapsulating shell in ultrasound contrast agent microbubbles. A numerical investigation that analyses the acoustic backscatter from bubbles is employed to identify resonance frequencies that can be compared, for increasing driving pressure amplitude, with linear approximations obtained via analytical considerations. Calculations for bubbles of the size employed in diagnostic ultrasound, between 2 and 6 μm diameter, that are immersed in water and blood and exposed to monochromatic insonation, causing the bubbles to undergo stable cavitation, reveal that the resonance frequency diverges from the linear approximation as the pressure amplitude is increased. The shift in resonance, to lower frequency values, is found to be more pronounced for larger bubbles with the calculated value differing by up to 40% from the linear approximation. The results of this simulation might be potentially useful in preparation of formulations of ultrasound contrast agents with the specifically desired features, such as for instance resonance frequency.     

Low-energy antiproton-neon interaction

By means of a streamer chamber exposed to the LEAR antiproton beams, the total reaction cross sections, the charged-prong multiplicity distributions and lower limits for the production of negative pions and K_s⁰ in the p̄-Ne interaction were measured at 19.6, 48.7 and 179.6 MeV. Annihilation was found to be dominant over all other non-elastic p̄-Ne processes. An analysis of Ne and other nuclei data in the frame of the Glauber theory allowed us to determine the ratio between the p̄-n and the p̄-p cross sections. An analysis in the light of INC model predictions allowed us to show up events which can be interpreted as annihilations having occurred deeply inside the nuclei.     

On minimizing chi-square distances under the hypothesis of homogeneity or independence for a two-way contingency table

The present paper investigates estimation under the hypothesis of homogeneity or independence for a two-way contingency table. A family of optimality criteria (distances) is introduced of which well-known criteria such as maximum likelihood, Pearson- and Neyman chi-square. The Kullback-Liebler distance turn out to be special cases. We look at the convexity properties of this family and provide some general results. Give any member of this family, an analytical solution is provided for the optimal estimator under the hypothesis of homogeneity whereas a simple algorithm solution is given for the optimal row- and column margin estimators under the hypothesis of independence.     

Damping in beams and plates due to slipping at the support boundaries

Dry friction damping due to axial sliding surfaces normal to the principal lateral direction of structural motion is studied. Primary emphasis is on sufficiently large motion that slipping occurs throughout a cycle. Beams with arbitrary support conditions and vibrating in an arbitrary mode are considered; also a pinned-pinned rectangular plate is studied. In all cases, a simple explicit formula is obtained for an equivalent, linear, viscous critical damping ratio.     

Permeability of microscale fibrous porous media using the lattice Boltzmann method

The permeabilities of microscale fibrous porous media were calculated using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). Two models of the microscale fibrous porous media were constructed based on overlapping fibers (simple cubic, body-centered cubic). Arranging the fibers in skew positions yielded two additional models comprising non-overlapping fibers (skewed simple cubic, skewed body-centered cubic). As the fiber diameter increased, the fibers acted as granular inclusions. The effects of the overlapping fibers on the media permeability were investigated. The overlapping fibers yielded permeability values that were a factor of 2.5 larger than those obtained from non-overlapping fibers, but the effects of the fiber arrangement were negligible. Two correlations were obtained for the overlapping and non-overlapping fiber models, respectively. The effects of the rarefaction and slip flow are also discussed. As the Knudsen number increased, the dimensionless permeability increased; however, the increase differed depending on the fiber arrangement. In the slip flow regime, the fiber arrangement inside the porous media became an important factor.