Features of the change in the frequency spectrum of electromagnetic radiation during the fracture of rock specimens

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 160–165, September–October, 1994.     

On the nature of the relaxation time,the Maxwell–Cattaneo and Fourier law in the thermodynamics of a continuous medium,and the scale effects in thermal conductivity

We present the theory of space–time elasticity and demonstrate that it is the extended reversible thermodynamics and gives the coupled model of thermoelasticity and heat conductivity and involves traditional thermoelasticity. We formulate the generally covariant variational model’s dynamic thermoelasticity and heat conductivity in which the basic kinematic and static variables are unified tensor objects (subject, matter). Variation statement defines the whole set of the initial-boundary problems for the 4D vector governing equation (Euler equation), the spatial projections of which define motion equations and the time projection gives the heat conductivity equation. We show that space–time elasticity directly implies the Fourier and the Maxwell–Cattaneo laws of heat conduction. However, space–time elasticity is richer than classical thermoelasticity, and it advocates its own equations of motion for coupled thermoelasticity. Moreover, we establish that the Maxwell–Cattaneo law and Fourier law can be defined for the reversible processes as compatibility equations without introducing dissipation. We argue that the present framework of space–time elasticity should prove adequate to describe the thermoelastic phenomena at low temperatures for interpreting the results of molecular simulations of heat conduction in solids and for the optimal heat and stress management in the microelectronic components and the thermoelectric devices.     

Modeling of the dynamics of the change in the index of refraction during resonance interaction of radiation with vibrational-rotational transitions

Moscow. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 21–29, January–February, 1994.     

Microwave radiation in the electrical explosion of conductors

Moscow. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 3–5, January–February, 1995     

Stability of Detonation Profiles in the ZND Limit

Confirming a conjecture of Lyng–Raoofi–Texier–Zumbrun, we show that stability of strong detonation waves in the ZND, or small-viscosity, limit is equivalent to stability of the limiting ZND detonation together with stability of the viscous profile associated with the component Neumann shock. Moreover, on bounded frequencies the nonstable eigenvalues of the viscous detonation wave converge to those of the limiting ZND detonation, while on frequencies of order one over viscosity, they converge to one over viscosity times those of the associated viscous Neumann shock. This yields immediately a number of examples of instability and Hopf bifurcation of reacting Navier–Stokes detonations through the extensive numerical studies of ZND stability in the detonation literature.     

Energy-wave approach in the mechanics of brittle dynamic fracture

Moscow. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 2, pp. 118–123, March–April, 1994.     

Mathematical modeling of the slider-disk interaction in disk units of the Winchester type

Rostov State University, Rostov-on-Don 344000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 36, No. 4, pp. 45–51, July–August, 1995.     

Toward a theory of the propagation of elastoplastic waves in strain-hardening media

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 166–172, September–October, 1994.     

Acoustic resonance in turbomachinery with aerodynamic interaction of the cascades in subsonic gas flow

Sergiev Posad, Moscow Oblast. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 4, pp. 78–85. July–August, 1994.     

Experimental study of the transition to turbulence at a single stationary disturbance in the boundary layer of an oblique aerofoil

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 72–84, January–February, 1995.     

Analysis of flow changes in a diffuser boundary layer in terms of the maximum stability of averaged turbulent flows

Moscow. Translated from Prikladnaya Mekhanika i Technicheskaya Fizika, No. 1, pp. 52–64, January–February, 1995.     

Planar problem of hydrodynamic shaking of a submerged body in the presence of motion in a two-layered fluid

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 32–44, Septerm–October, 1994.     

Hydraulic jump in the shear flow of an ideal incompressible fluid

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 11–20, January–February, 1995.     

Kinetics of the collision of metallic plates in a multilayer packet during explosion welding

Volgograd. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 173–175, September–October, 1994     

On a Serrin-Type Regularity Criterion for the Navier–Stokes Equations in Terms of the Pressure

We prove a Serrin-type regularity result for Leray–Hopf solutions to the Navier–Stokes equations, extending a recent result of Zhou [28].     

Measurement and chemical kinetic model predictions of detonation cell size in methanol–oxygen mixtures

In this study, detonation cell sizes of methanol–oxygen mixtures are experimentally measured at different initial pressures and compositions. Good agreement is found between the experiment data and predictions based on the chemical length scales obtained from a detailed chemical kinetic model. To assess the detonation sensitivity in methanol–oxygen mixtures, the results are compared with those of hydrogen–oxygen and methane–oxygen mixtures. Based on the cell size comparison, it is shown that methanol–oxygen is more detonation sensitive than methane–oxygen but less sensitive than hydrogen–oxygen.     

Mechanism of the initial stage of bubble growth in a liquid close to the superheat limit

Institute of Thermophysics, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 36, No. 3, pp. 130–133, May–June, 1995.     

Asymptotic properties of solutions of the Cauchy problem for a degenerate singularly perturbed system of differential equations in the case of the multiple spectrum of the principal operator

We prove the asymptotic character of a solution of the Cauchy problem for a singularly perturbed linear system of differential equations with degenerate matrix of the coefficients of derivatives in the case where the limit matrix pencil is regular and has multiple “finite” and “infinite” elementary divisors. We establish conditions under which the constructed formal solutions are asymptotic expansions of the corresponding exact solutions. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 2, pp. 247–257, April–June, 2007.     

Generation of long waves by the bottom contour in a two-layer flow

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 3, pp. 34–47, May–June, 1993.     

Method of local approximations in the nonlinear theory of shells

S. A. Chaplygina, Siberian Scientific-Research Institute of Aviation, 630051 Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 2, pp. 150–158, March–April, 1995.