Nonlinear Diffusion Processes

We study elliptic systems of strongly nonlinear first-order differential equations in complex form on the plane. For such systems we develop the theory of Hilbert boundary value problems which is very much similar to the well-known theory for a holomorphic vector. Systems of nonlinear elliptic equations describe problems of interaction of several nonlinear stationary processes in the diffusive and convective mass and heat transport by hydrodynamic fluid flows.     

High pressure elastic and plastic deformations of silica: In situ diamond anvil cell Raman experiments

Normal silica glass is usually referred to as low density amorphous silica as it can be converted to high density amorphous silica by a hydrostatic pressure (polyamorphic transition). In this work in situ Raman experiments are performed in a diamond anvil cell up to 18 GPa. The pressure effects on the structure of silica after successive compression decompression experiments are analyzed. The mode Grüneisen parameters corresponding to the elastic compression of high density amorphous silica are obtained and compared with those of normal silica. A reorganization of the high density amorphous silica below 3 GPa is evidenced.     

Dense amorphous packing of binary hard sphere mixtures with chemical order: The stability of a solute ordered approximant

Recently, Miracle proposed that the intermediate structure in metallic glasses could be usefully characterized as an ordered face centered cubic packing of solute-centered coordination clusters. In this paper we examine the stability of such solute ordered arrangements in binary hard sphere mixtures subject to density maximization through local particle moves.     

Averaging method in the motion stability problem for a rotating body suspended on a long rigid string

We use the averaging method to study the stability of the vertical rotation of a rigid body suspended on a long rigid string.     

Predicting the onset of DNA supercoiling using a non-linear hemitropic elastic rod

Elastic rod models provide a means to interpret single molecule DNA experiments as well as predict DNA behavior under physiological conditions. Here we use an elastic rod model to predict the stability boundary (critical torque vs. applied tension) for single molecule DNA experiments in which the molecule is subjected to applied tension and twist. We discuss the shortcomings of the usual isotropic rod model. We then derive a consistent non-linear material law from the general representation for a hemitropic (chiral) rod. Finally, we present results of a standard bifurcation analysis predicting the stability boundary. We find results from the non-linear hemitropic rod to match the data closely.     

Geometry and electronic structure of a heterometallic cluster Mo<Subscript>2</Subscript>Mg<Subscript>2</Subscript> in different oxidation states of Mo: a DFT study

Reduction of tetranuclear heterometallic complex Mo₂Mg₂ was simulated using the B3LYP and PBE density functional methods. The results of geometry calculations of the initial complex [Mo^VIO₂Mg(MeOH)₂(OMe)₄]₂ and a partially reduced Mo^V complex are in good agreement with experimental data. The reduced Mo^III complex is characterized by a decrease in the binding energy of aqua ligands. Structural rearrangement of the complex with release of a coordination position at the Mo atoms requires small energy expenditure. One can assume that the reduction of the polynuclear complex causes overcrowding of its coordination sphere, which favors formation of dinitrogen complexes. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 441–457, March, 2008.     

Thermal degradation of composites of poly(methyl methacrylate) with alkoxysilane hydrolyzates

Organic-inorganic composites of poly(methyl methacrylate) with alkoxysilane hydrolyzates form transparent films. Their thermal and oxidative thermal degradation were studied by differential scanning calorimetry and thermogravimetric analysis.     

On calculation of the distribution coefficient from the results of continuous gas extraction of a volatile component from a liquid mixture

Distribution coefficient of a volatile component among the liquid and gas phases was calculated from equidistant data on continuous gas extraction by using an equation generalizing the relations available in the literature.