An existence theorem for the unmodified Vlasov Equation

The initial value problem for the modified Vlasov equation with a mollification parameter δ > 0, as introduced by Batt, has a unique global solution in the weak sense whenever f₀ ε L¹ and f₀ ≧ 0 λ-a.e. Assuming boundedness of f₀ and boundedness of the kinetic energy, it is shown that, as δ → 0, there are subsequences δ_n → 0 such that the corresponding solutions converge weakly in the measure-theoretical sense. The limits are shown to be global weak solutions of the initial value problem for Vlasov's equation, and these solutions are seen to be weakly continuous with respect to t. For the plasma physical case, boundedness of the kinetic energy is a consequence of energy conservation.     

Moisture permeability of a polymer nanocomposite containing unmodified clay

Results of an investigation into the kinetics of moisture sorption by an unfilled styrene-acrylate copolymer and a nanocomposite containing unmodified montmorillonite clay are reported. The sorption tests were performed at 25°C and different levels of the relative humidity of air up to 80%. The moisture diffusivity was calculated using Fick's equation for one-dimensional diffusion. Data on the influence of montmorillonite concentration on the coefficients of diffusion, solubility, and permeability are obtained. The experimental values of the permeability coefficient are compared with those calculated by using a model taking into account the increased path of a diffusing water molecule caused by the shielding effect of plate like filler particles. Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 5, pp. 723–736, September–October, 2008.     

Laser-induced shock waves in liquids

Summary The interaction of TEA-CO₂-laser pulses with liquids has been investigated using shadowgraphy and high-speed pressure transducers. It is shown that the absorption coefficient of the liquid at the laser wavelength defines the geometry of the shock wave. Peak pressures in the kbar range have been observed.

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Zusammenfassung Die Wechselwirkung von TEA-CO₂-Laserimpulsen mit Flüssigkeiten wurde untersucht mit Hilfe von Schattenphotographien und schnellen Drucksonden. Es wird gezeigt, dass der Absorptionskoeffizient der Flüssigkeit bei der Laserwellenlänge die Geometrie der Stosswelle bestimmt. Es wurden Druckmaxima im kbar-Bereich beobachtet.

     

Long-wave-short-wave interaction in bubbly liquids

The interaction of long and short waves in a rarefied monodisperse mixture of a weakly compressible liquid containing bubbles of gas is considered. It is shown that the equations describing the dynamics of the perturbations in the bubbly liquid admit of the existence of short-wave-long-wave Benney-Zakharov resonance. A special modification of the multiple-scale method is employed to derive the interaction equations. In the non-resonant case, the interaction equations reduce to the non-linear Schrödinger equation in the form of the short-wave envelope while, in the resonance case, they reduce to the well-known system of Zakharov equations. The characteristics of long-wave-short-wave interaction in a bubbly liquid lie in the fact that, at certain values of the frequency of the short wave, the interaction coefficients vanish (“interaction degeneracy”). A class of new interaction models is constructed in the case of “degeneracy”. Degenerate resonance interaction in a bubbly liquid is investigated numerically using these models.