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Lugantsev L.D.,Moscow State University of Mechanical Engineering
Chemical and Petroleum Engineering | Year: 2016

A method and algorithm for use in computer analysis of the carrying capacity and remaining life of composite shell structures that function under the conditions of thermomechanical and corrosion effects are set forth. © 2016 Springer Science+Business Media New York Source


A solution of the Dirac equation for an electron in the field of a point nucleus (Ze), expressed in terms of an eigenfunction of the operator of the spin projection onto the third axis and the corresponding solution of the Schrödinger equation is derived. This solution is suitable for practical calculations. On the basis of this solution, using ordinary methods of QED and field theory, general principles for the emission of photons, axions, and neutrinos (Ze)*→(Ze)+γ,a,vv¯ by a hydrogen-like atom are formulated which take into account the spin state of the electron and, in the case of photons, their polarization. This range of questions pertaining to a comparative characteristic of processes of emission of massless or almost massless particles has, to this day, not been discussed from this point of view in the literature. Selection rules for γ, a, vv¯ emission processes are also obtained, where for axions and neutrinos they coincide with the existing selection rules in the literature ∆m = 0,±1; with ∆l = ±1 pertaining to photons, but for photon emission a few of them do in fact differ from them with the hypothesis of odd values of ∆l, not established by us and additional to the usual values ∆l = ±1 of variation of the azimuthal quantum number l due to the appearance of “new” integrals over the spherical angle θ for ∆m = ±1, where for ∆m = 0, as before, ∆l = ±1. Moreover, the dependence of the amplitude of the photon emission process on the quantum numbers is in principle different than in the previously adopted approach to the problem although the lifetime in the excited state for small values of the quantum numbers coincides in order of magnitude with the accepted value ~10–9 s. © 2016, Springer Science+Business Media New York. Source


Polyanin A.D.,Russian Academy of Sciences | Vyazmin A.V.,Moscow State University of Mechanical Engineering
Theoretical Foundations of Chemical Engineering | Year: 2013

Differential-difference heat conduction and diffusion models and equations with a finite relaxation time are described that give a finite disturbance propagation rate. The modified Biot-Fourier law with delay is used for the heat flux, which leads to the differential-difference heat-conduction equation ∂T/∂t+τ = aΔ T, where the left-hand side is calculated at t + τ (τ is the relaxation time) and the right-hand side is calculated, as usual, at t (without a time shift). At τ = 0, the differential-difference heat-conduction equation turns into the classical parabolic heat-conduction equation; if the left-hand side is expanded into a series in τ and two main terms of expansion are retained, we obtain the Cattaneo-Vernotte hyperbolic heat-conduction equation. An exact solution to the differential-difference heat-conduction equation is derived for a one-dimensional problem without the initial conditions with an arbitrary periodic boundary condition. The approximate solution is constructed to the general three-dimensional initial-boundary value problem of heat propagation with a finite relaxation time in a bounded domain with arbitrary initial heat distribution and the boundary condition of the third kind. It is shown that the differential-difference model makes it possible to derive the Oldroyd-type differential heat-conduction model. © 2013 Pleiades Publishing, Ltd. Source


Polyanin A.D.,Russian Academy of Sciences | Vyazmin A.V.,Moscow State University of Mechanical Engineering
Theoretical Foundations of Chemical Engineering | Year: 2013

A new exact method of solving general three-dimensional nonstationary linearized equations for viscoelastic fluids is described based on breaking these equations down into several simpler equations. Formulas are given that make it possible to express the solution in the respective systems (consisting of four connected equations) by solving two independent equations. The most widespread rheological models of viscoelastic fluids are considered to illustrate the powerful capabilities of the proposed method. A new differential-difference model for a viscous fluid with a constant relaxation time is proposed that gives a finite disturbance propagation rate and is in good agreement with the Maxwell and Oldroyd differential models of viscoelastic fluids. The axial flows of viscoelastic fluids are studied, and solutions to certain hydrodynamic problems are given. © 2013 Pleiades Publishing, Ltd. Source


Generalov M.B.,Moscow State University of Mechanical Engineering
Theoretical Foundations of Chemical Engineering | Year: 2013

The mechanism of structure formation is proposed in the crystallization of droplets of binary eutectic solutions in cryogenic liquids. Theoretical relationships are derived for calculating the rate of crystallite growth and the size of nanocrystals that form. Calculated values of the size of forming nanocrystals are compared with the experimental data. © 2013 Pleiades Publishing, Ltd. Source

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