Instabilities in the Chapman-Enskog Expansion and Hyperbolic Burnett Equations

It is well-known that the classical Chapman-Enskog procedure does not work at the level of Burnett equations (the next step after the Navier-Stokes equations). Roughly speaking, the reason is that the solutions of higher equations of hydrodynamics (Burnett's, etc.) become unstable with respect to short-wave perturbations. This problem was recently attacked by several authors who proposed different ways to deal with it. We present in this paper one of possible alternatives. First we deduce a criterion for hyperbolicity of Burnett equations for the general molecular model and show that this criterion is not fulfilled in most typical cases. Then we discuss in more detail the problem of truncation of the Chapman-Enskog expansion and show that the way of truncation is not unique. The general idea of changes of coordinates (based on analogy with the theory of dynamical systems) leads finally to nonlinear Hyperbolic Burnett Equations (HBEs) without using any information beyond the classical Burnett equations. It is proved that HBEs satisfy the linearized H-theorem. The linear version of the problem is studied in more detail, the complete Chapman-Enskog expansion is given for the linear case. A simplified proof of the Slemrod identity for Burnett coefficients is also given.     

Moment Inequalities and High-Energy Tails for Boltzmann Equations with Inelastic Interactions

Journal of Statistical Physics - We study high-energy asymptotics of the steady velocity distributions for model kinetic equations describing various regimes in dilute granular flows. The main...     

Chain decay of low-angle tilt boundaries in nanocrystalline materials

In terms of two-dimensional dislocation-disclination dynamics, a theoretical model is developed to describe the decay of a low-angle tilt boundary in a deformed nanocrystalline material under the action of an externally applied elastic stress and of the elastic field of a neighboring decayed boundary. The critical external stresses are calculated at which the boundary decays and the dislocations making up this boundary either are trapped by the boundary that decayed earlier or break away from both boundaries. The decay of a low-angle tilt boundary is shown to result in a substantial decrease in the critical decay stresses for the neighboring boundaries, which can cause an avalanche-like chain decay of low-angle boundaries yielding high-density ensembles of mobile dislocations capable of carrying substantial plastic deformations and of forming shear bands in deformed nanocrystalline materials.     

Error analysis of surface area determinations by the chromatographic technique

The systematic and random errors in the determination of the surface area of adsorbents and catalysts by argon thermodesorption chromatography are analyzed.

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Complex lanthanide chromate(VI)-phosphates K2R(CrO4)(PO4) (R = Dy-Lu, Y)

The conditions of formation of complex lanthanide chromate(VI)-phosphates K₂R(CrO₄)(PO₄) were found and these compounds were synthesized by solid-state synthesis with variation of the starting compounds, the temperature of synthesis (500–800 °C), and the annealing time (6–200 h). These salts are typical of late lanthanides, R = Dy-Lu, Y. Using lutetium derivatives as examples, it was shown that no similar compounds with lithium or sodium are formed. All the complex chromate(VI)-phosphates obtained decompose under static conditions at temperatures above 550 °C. They are isostructural and crystallize in the monoclinic system. The unit cell parameters for thulium, ytterbium, and lutetium compounds were calculated. It is shown by IR spectroscopy that PO₄ tetrahedra in the crystal lattice of potassium lanthanide chromate(VI)-phosphates are substantially distorted, whereas the CrO₄ tetrahedra retain the regular tetrahedron symmetry (T _d ). Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 622–626, April, 2006.     

Antiferromagnetic fluctuations in water-intercalated YBa2Cu3O6.8

Raman scattering by phononic and electronic excitations, as well as the magnetic susceptibility of water-intercalated YBa₂Cu₃O_6.8, has been studied. Direct evidence of the incorporation of OH^?-groups into the structure of the crystal has been obtained. The observed changes in the phonon spectrum and the appearance of the spectrum of antiferromagnetic fluctuations with an increased exchange coupling constant imply the localization of carriers and suppression of superconductivity. Change in the resonance behavior of the two-magnon scattering of light indicates the transformation of the electronic structure in crystallites absorbing water.     

Effect of Cyclic Hydrocarbon Vapors on the Structure of YBa2Cu3Oy

Russian Journal of Physical Chemistry A - The effect vapors of the simplest cyclic hydrocarbons have on the structure of YBa2Cu3Oy (123) with high (у = 6.96) and low (у = 6.3) oxygen...     

A Novel M8L6 Cubic Cage That Binds Tetrapyridyl Porphyrins: Cage and Solvent Effects in Cobalt-Porphyrin-Catalyzed Cyclopropanation Reactions

Confinement of a catalyst can have a significant impact on catalytic performance and can lead to otherwise difficult to achieve catalyst properties. Herein, we report the design and synthesis of a novel caged catalyst system Co−G@Fe₈(Zn−L ⋅ 1)₆ , which is soluble in both polar and apolar solvents without the necessity of any post-functionalization. This is a rare example of a metal-coordination cage able to bind catalytically active porphyrins that is soluble in solvents spanning a wide variety of polarity. This system was used to investigate the combined effects of the solvent and the cage on the catalytic performance in the cobalt catalyzed cyclopropanation of styrene, which involves radical intermediates. Kinetic studies show that DMF has a protective influence on the catalyst, slowing down deactivation of both [Co(TPP)] and Co−G@Fe₈(Zn−L ⋅ 1)₆ , leading to higher TONs in this solvent. Moreover, DFT studies on the [Co(TPP)] catalyst show that the rate determining energy barrier of this radical-type transformation is not influenced by the coordination of DMF. As such, the increased TONs obtained experimentally stem from the stabilizing effect of DMF and are not due to an intrinsic higher activity caused by axial ligand binding to the cobalt center ([Co(TPP)(L)]) . Remarkably, encapsulation of Co−G led to a three times more active catalyst than [Co(TPP)] (TOF_ini) and a substantially increased TON compared to both [Co(TPP)] and free Co−G . The increased local concentration of the substrates in the hydrophobic cage compared to the bulk explains the observed higher catalytic activities.     

Rivulet flow on the outer surface of an inclined cylinder

A study of the three-dimensional flow of a liquid film (rivulet) over the external part of an inclined cylinder was conducted for liquids with various physical properties. Patterns of the flow regimes were constructed. Good agreement is observed between the experimental data on the thickness and wall friction with the calculation with an asymptotic model in the case of a waveless rivulet. A comparison of the evolution of natural waves on rivulets with the theory of waves of maximal growth shows good agreement for small Re numbers. During the experiments, the wave characteristics of excited waves on a rivulet were investigated. The thickness, amplitude, frequency, and phase velocity of the waves over a wide range of variable parameters are given. Phase velocity integrated functions of the amplitude are constructed for various liquids. The friction on the cylinder wall is measured in the presence of natural and excited waves. The effects of wave regimes on the average values and RMS (root-mean-square) friction pulsations are studied.