Explosionlike boiling of a viscous liquid in a high-intensity ultrasonic beam

The effect accompanying the propagation of high-intensity focused ultrasound in a viscous liquid, namely, medical gel, is studied. It is found that, under the action of continuous focused ultrasound (with an intensity of about 13000 W/cm²), in the area close to the waist of the caustic of the ultrasound beam, gas bubbles 10–15 mm in diameter periodically arise in an explosionlike way and then collapse with a lifetime of about 2 ms. The emergence of bubbles is accompanied by short pops with a duration of about 1 ms. An increase in the sound intensity leads to an increase in the frequency of the bubble generation (a decrease in the period from several seconds to fractions of a second) with practically the same shape of formations and the same dynamics of their development and collapse. Theoretical estimates adequately describe the size of the bubbles. The comparison of the effects produced by an intense focused ultrasonic beam on a gel and on biological tissue shows that the development of caverns (cavities) in tissues under the action of intense focused ultrasound is the manifestation of the effect of explosionlike boiling of the liquid.     

Following gluonic world lines to find the QCD coupling in the infrared

Using a parametrization of the Wilson loop with the minimal-area law, we calculate the polarization operator of a valence gluon, which propagates in the confining background. This enables us to obtain the infrared freezing (i.e. finiteness) of the running strong coupling in the confinement phase, as well as in the deconfinement phase up to the temperature of dimensional reduction. The momentum scale defining the onset of freezing is found both analytically and numerically. The nonperturbative contribution to the thrust variable, originating from the freezing, makes the value of this variable closer to the experimental one.     

Stability and accuracy functions in multicriteria linear combinatorial optimization problems

We consider a vector linear combinatorial optimization problem in which initial coefficients of objective functions are subject to perturbations. For Pareto and lexicographic principles of efficiency we introduce appropriate measures of the quality of a given feasible solution. These measures correspond to so-called stability and accuracy functions defined earlier for scalar optimization problems. Then we study properties of such functions and calculate the maximum norms of perturbations for which an efficient solution preserves the efficiency. This work was partially supported through NATO Science Fellowship grant.     

On Nikol’skii classes for double trigonometric series with monotone coefficients

The paper is devoted to the investigation of the relationship between the rate of decay of the coefficients of a trigonometric sum in two variables and the smoothness of the sum of the double series in the L _p spaces.     

Rare-earth complexes of mesomorphic Schiff's base ligands

Rare-earth complexes of mesomorphic Schiff 's bases, 4-[(alkylimino)methyl]-3-hydroxyphenyl 4-alkyloxybenzoates, were synthesized. Whereas the ligands LH display a nematic and/or a smectic C phase, the metal complexes show a viscous smectic A phase and decompose at the clearing point. The mesophase was investigated by hot-stage polarizing optical microscopy, by differential scanning calorimetry and by high temperature X-ray diffraction. Two types of complex were found, [Ln(LH)₃ (NO₃)₃] and [Ln(LH)₂L(NO₃)₂], depending on the ligand or the central metal ion. The first coordination sphere of the rare-earth ion in these metallomesogens is comparable to that in the structure of complexes with 4-alkoxy-N-alkyl2-hydroxybenzaldimine ligands.     

Rheological properties of crystallizing polylactide: Detection of induction time and modeling the evolving structure and properties

Linear viscoelastic properties of polymer melts are highly sensitive to any structural changes, including molecular weight changes and the formation and growth of crystallites. Here, we make use of this sensitivity to study the homogeneous crystallization of polylactide. As this polymer is rather quickly susceptible to thermal degradation even at moderate temperatures, it is essentially impossible to study homogeneous crystallization in the absence of degradation. Thus, the evolution of complex viscosity of a polylactide due to thermal degradation in the absence of crystallization was studied. A simple empirical model is used to characterize the variation of complex viscosity due to thermal degradation and to determine the induction time of homogeneous crystallization at wide range of degrees of supercooling. Next, the evolution of complex viscosity due to crystallization was measured at several temperatures. Based on the results, a phenomenological model describing the viscosity evolution during homogeneous crystallization is proposed and validated. Finally, the linear viscoselastic data in the early stages of crystallization are shown to be consistent with gelation due to the formation of a network of tie molecules between spherulites. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 812–822, 2010     

Molybdenum and Tungsten Combined Oxidation by Dissociative Evaporation of Products during Refractory Oxides Crystal Growth from the Melt

The main chemical reactions and composition of gas and solid phases have been determined for the equimolar ratio Mo: W: O₂ = 1: 1: 2 at T = 2400 K in the pressure range of 1-1 x 10^-5 bar. It is established that the character of the main processes of combined oxidation depends significantly on the pressure and state of the oxidant (oxygen): at P > 7.52 x 10^-5 bar, oxidation reactions involve mainly molecular oxygen, whereas atomic oxygen dominates at lower pressures. At P ≥ 0.424 bar, the solid phase contains not only Mo but also MoO₂. At P = 1 x 10^-5 bar, the concentration of lower Mo and W oxides and elementary Mo and W in the gas phase sharply increases, which can negatively affect the main crystallization units.     

Resolution approaches to enantiomers of 4-formyl[2.2]paracyclophane

Three techniques for the resolution of 4-formyl[2.2]paracyclophane were examined with the separation of the diastereomeric derivatives with (R)- and (S)-2-hydrazino-2-oxo-N-(1-phenylethyl)acetamide followed by their hydrolysis being found to be the most efficient, allowing (Rp)- and (Sp)-4-formyl[2.2]paracyclophanes to be obtained with 99.5% and 98.7% ee, respectively.     

The rearrangement of cyclopropylketone arylhydrazones. Synthesis of tryptamines and tetrahydropyridazines

The cyclopropyliminium rearrangement of cyclopropylketone arylhydrazones may result in two possible products. The first one forms via cyclopropane ring-opening and ring-closure to give six-membered tetrahydropyridazines. The second is formed via ring-closure resulting in a five-membered ring and subsequent Grandberg rearrangement into a tryptamine. The product ratio depends on the nature of the starting hydrazones.