Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

Spinor norms of local autometries of generalized quadratic lattices

It is proved that the group of spinor norms of autometries of a generalized quadratic lattice ℒ over the ring of integral elements v _p of a local field k _p , in the case wherep∤2 and ℒ is a generalized translation, is generated by the spinor norms of symmetries contained in the group of autometries of ℒ. As a corollary, an extension to the case of generalized quadratic lattices is given for known sufficient conditions of coincidence of the genus and the spinor genus of a quadratic lattice. Bibliography: 9 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 211, 1994, pp. 161–173. Translated by Yu. G. Teterin.     

Ionic and Phase Compositions of Y2.5Ce0.5Fe2.5Ga2.5O12 Ferrogarnet Powder Produced by Gel Combustion

Doklady Physical Chemistry - The ionic and phase compositions of Y2.5Ce0.5Fe2.5Ga2.5O12 ferrogarnet samples obtained by gel combustion with subsequent vacuum annealing were studied for the first...     

Computer-based calculations for transmetabelian groups of exponent 16, 25, and 27

A new stage of research on 2-generated transmetabelian groups of primary exponent is announced, which makes it possible to investigate groups of exponent 16, 25,and 27.More complete data describing the current state of studies are available via the Internet at http: //www.pdmi.ras.ru/ yuri/transmet. Bibliography: 7titles.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 236, 1997, pp. 162–165.     

Representation of integers by positive-ternary quadratic forms

The discrete ergodic method is applied to the problem mentioned in the title. We obtain estimates (of exact order) of the number of primitive representations in a given cone and a given residue class. The paper is an extension of the work of Peters (M. Peters, Acta Arithm.,34, 57–80 (1977)).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 121, pp. 117–156, 1983.     

Study of gas flow in region of incidence of a shock on a cylinder in high supersonic flow

Some results are presented of a study on the effect of incident shock intensity on the flow field and force effects of a shock incident on a cylinder in the vicinity of the point of incidence (V. K. Kutlikov assisted in obtaining part of the experimental data).     

Computational group theory in St. Petersburg

The paper is devoted to the history of computational group theory in St. Petersburg. Some features of this scientific area are outlined. We mention here some results of A. I. Skopin concerned with computations in Burnside groups of small prime-power exponents, as well as A. V. Rukolaine's work on the computation of ordinary characters of some finite simple groups. The note is dedicated to the 70th anniversary of A. I. Skopin's birth. Bibliography: 24titles.Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 236, 1997, pp. 42–49.     

Cavitation and crystallization in a metastable Lennard-Jones liquid at negative pressures and low temperatures

Molecular dynamics simulations have been used to investigate the kinetics of spontaneous cavitation and crystallization in a Lennard-Jones liquid at negative pressures in the temperature range where these processes compete with each other. The nucleation rate has been calculated in NVE and NpT ensembles by the method of mean lifetime and the transition interface sampling method with parallel path swapping. The data obtained have been used to determine in the framework of classical nucleation theory the value of the ratio of the solid-liquid and the liquid-void interfacial free energy for critical crystals and cavities and the values of their volumes at points where the cavitation rate of the liquid is equal to the rate of its crystallization.