On exact solutions of a Sobolev equation

A nonlinear Sobolev-type equation that can be used to describe nonstationary processes in the semiconductor medium is studied. A number of families of exact solutions of this equation that can be expressed in terms of elementary functions and quadratures is obtained; some of these families contain arbitrary sufficiently smooth functions of one argument. The qualitative behavior of the resulting solutions is analyzed.     

1H NMR in CaCl2·xH2O nanocrystals and water sorption isobars in a CaCl2-silica gel system

Mobility of water molecules in nanocrystals and other phases of CaCl₂·xH₂O (x=0–12) formed in the nanopores of silica gel during sorption of water vapor is studied by¹H NMR. The sorption properties of calcium chloride impregnated in the pores of micro- and mesoporous silica gels were measured. Institute of Inorganic Chemistry, Siberian Branch, Russian Academy of Sciences. G. K. Boreskov Institute of Catalysis, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 2, pp. 261–266, March–April, 1998. This work was supported by RFFR grants No. 96-03-33069 and 97-03-33533 and NATO grant HTECH LG N 970330.     

Applied computer model of the non-stationary gas flow in a long multilayer-insulated high-pressure subsea gas pipeline

An applied fluid-dynamics model of the non-stationary flow in a long multilayer-insulated high-pressure subsea gas pipeline was developed. Instead of a complex partial differential heat conduction equation, which represents the heat flux between the flowing gas and the environment in the energy balance equation, the model uses a first-order ordinary differential equation. The applied model allows one to significantly increase the speed of numerical computation of the fluid-dynamics parameters of the gas flow in the pipeline, which is necessary for multivariate computations in design and operation of gas pipelines.     

Tunneling into a Luttinger liquid revisited

We study how electron-electron interactions renormalize tunneling into a Luttinger liquid beyond the lowest order of perturbation in the tunneling amplitude. We find that the conventional fixed point has a finite basin of attraction only in the point contact model, but a finite size of the contact makes it generically unstable to the tunneling-induced breakup of the liquid into two independent parts. In the course of renormalization to the nonperturbative-in-tunneling fixed point, the tunneling conductance may show a nonmonotonic behavior with temperature or bias voltage.     

Steady viscous fluid flow near a cylinder subject to longitudinal deformation

Within the framework of the class of exact solutions of the hydrodynamic equations, characterized by the linear dependence of some of the velocity components on the axial coordinate, the axisymmetric and rotationally symmetric regimes are considered for viscous fluid flow in the gap between two cylinders one of which is being longitudinally deformed while the other is rigid. In the investigated region of the Reynolds number spectrum a point at which a rotationally symmetric solution branches off from the solution without swirl is found and the intervals of multiple values of this parameter, within which each fixed Re corresponds to more than one solution of the rotationally symmetric or axisymmetric type, are distinguished.