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     

Pseudo-Finsleroid standard model analysis of electroweak interactions

A standard model Lagrangian is constructed making the pseudo-Finsleroid generalization of the Yang-Mills field equation by the conformal method. The Higgs field potential is suggested that ensures generation of particle masses caused by the spontaneous symmetry breaking. After transition to the conformal coordinates, the expressions obtained assume the standard form that in many cases allows the results of pseudo-Euclidean theory to be used in calculations of the Feynman diagrams. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 44–51, April, 2006.     

Electromagnetic form factors of a massive neutrino

Electromagnetic form factors of a massive neutrino are studied in a minimally extended standard model in an arbitrary R_ξ gauge and taking into account the dependence on the masses of all interacting particles. The contribution from all Feynman diagrams to the electric, magnetic, and anapole form factors, in which the dependence of the masses of all particles as well as on gauge parameters is accounted for exactly, are obtained for the first time in explicit form. The asymptotic behavior of the magnetic form factor for large negative squares of the momentum of an external photon is analyzed and the expression for the anapole moment of a massive neutrino is derived. The results are generalized to the case of mixing between various flavors of the neutrino. Explicit expressions are obtained for the electric, magnetic, and electric dipole and anapole transitional form factors as well as for the transitional electric dipole moment.     

Evolution of coupled fermions under the influence of an external axial-vector field

The evolution of coupled fermions interacting with external axial-vector fields is described with the help of the classical field theory. We formulate the initial conditions problem for the system of two coupled fermions in (3+1)-dimensional space-time. This problem is solved using perturbation theory. We obtain in the explicit form the expressions for the leading and next to leading order terms in the expansion over the strength of the external fields. It is shown that in the relativistic limit the intensity of the fermion field coincides with the transition probability in the two neutrinos system interacting with moving and polarized matter. PACS 14.60.Pq; 03.50.-z     

Two-dimensional nonstationary gas dissipation into a vacuum from a plane or axisymmetric channel

The nonstationary escape of an ideal polytropic gas from a plane or axisymmetric channel is investigated. It is hence assumed that the gas is initially at rest, and the diaphragm separating it from the vacuum can be at any section of the channel.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 76–83, January–February, 1976.     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.