Mathematical modeling of flows through inelastic porous solids

We propose a framework, based on classical mixture theory, to describe the isothermal flow of an incompressible fluid through a deformable inelastic porous solid. The modeling of the behavior of the inelastic solid takes into account changes in the elastic response due to evolution in the microstructure of the material. We apply the model to a compression layer problem. The mathematical problem generated by the model is a free boundary problem.     

Generalized lattice model of liquid state and its relation to Ginzburg–Landau theory

Basic principles of the generalized lattice model of multicomponent condensed systems are formulated. Short-range parts of interatomic interactions are taken into account by means of the geometric constraints method. Long-range parts of the interactions are taken into account in mean field approximation. The expression for Helmholtz free energy is obtained. A system of integral equations for the equilibrium distributions of components is derived. The asymptotic properties of its solutions are investigated. Moment expansion of interatomic interactions and localization of integral terms in free energy is obtained. A Ginzburg–Landau-like functional of free energy is derived.     

Fluoroalkylation of aromatics: An intramolecular radical cyclization of 4-chloro-1,1,2,2,3,3,4,4-octafluorobutylbenzenes

In the presence of sodium dithionite and DMSO, the intramolecular radical cyclization of 4-chloro-1,1,2,2,3,3,4,4-octafluorobutylbenzenes is achieved to give the corresponding cyclic compounds in moderate to good yields.     

Liquid-phase noncatalytic butene oxidation with nitrous oxide

The kinetics and mechanism of noncatalytic liquid-phase oxidation of but-1-ene and but-2-ene with nitrous oxide in a benzene solution in the temperature range from 180 to 240°C were studied. Oxidation proceeds via the 1,3-dipolar cycloaddition mechanism to form carbonyl compounds. Both of these reactions occur with close rates and activation energies and have the first orders with respect to the alkene and N₂O. A considerable fraction (39%) of but-1-ene involved in oxidation undergoes cleavage at the double bond yielding propanal and an equivalent amount of methylene, the latter producing ethylcyclopropane and cycloheptatriene. The oxidation of but-2-ene proceeds with a minimum bond cleavage and affords methyl ethyl ketone with 84% selectivity. Regularities of the oxidation of terminal and internal alkenes C₂—C₈ with nitrous oxide were analyzed using the previously published data. __________ Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 925–933, April, 2005.     

On a free boundary problem for the Reynolds equation derived from the Stokes system with Tresca boundary conditions

The asymptotic behaviour of a Stokes flow with Tresca free boundary friction conditions when one dimension of the fluid domain tends to zero is studied. A specific Reynolds equation associated with variational inequalities is obtained and uniqueness is proved.     

Dicyclopentadienyl complexes of titanium,niobium, and tungsten in the controlled synthesis of poly(methyl methacrylate)

Organometallic compounds Cp₂TiCl₂, (EtC₅H₄)₂NbCl₂, and (PrⁱC₅H₄)₂WCl₂ were assessed as additives that control polymer chain growth in the polymerization of methyl methacrylate. In the presence of compounds mentioned in amounts comparable with that of the initiator, a uniform process with no gel-effect occured and respective linear increase in the molecular weight of the polymer up to high degrees of the monomer conversion was observed.     

一种新的永久周期磁铁聚焦的高功率宽带放大器

 提出了一种新的高功率宽带放大器，它由速调管和自由电子脉塞组成，用永久周期磁铁聚焦。研究了这种器件的电子束聚焦、群聚和辐射。在速调管提供一阶调制系数为30%，波导管的半径1.51cm，摇摆器的磁场振幅0.16T，周期7.92cm，电子束的电压490kV，电流50A和半径0.368cm的条件下，预估这种器件的辐射波频率为11.4GHz，输出辐射功率为18MW，输出辐射带宽为44%。