Comparison of four different versions of the variable metric method for solving inverse heat conduction problems

In this study, four different versions of the variable metric method (VMM) are investigated in solving standard one-dimensional inverse heat conduction problems in order to evaluate their efficiency and accuracy. These versions include Davidon–Fletcher–Powell (DFP), Broydon–Fletcher–Goldfarb–Shanno (BFGS), Symmetric Rank-one (SR1), and Biggs formula of the VMM. These investigations are carried out using temperature data obtained from numerical simulations.     

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 Range of Applicability of the Reissner–Mindlin and Kirchhoff–Love Plate Bending Models

We show that the Reissner–Mindlin plate bending model has a wider range of applicability than the Kirchhoff–Love model for the approximation of clamped linearly elastic plates. Under the assumption that the body force density is constant in the transverse direction, the Reissner–Mindlin model solution converges to the three-dimensional linear elasticity solution in the relative energy norm for the full range of surface loads. However, for loads with a significant transverse shear effect, the Kirchhoff–Love model fails. This revised version was published online in June 2006 with corrections to the Cover Date.     

Approach to the investigation of the occurrence of turbulence in the flow of a viscous fluid in closed volumes

Moscow. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 64–72, January–February, 1995.     

Effect of shear strength on the development of instability during the deceleration of imploding casings

Arzamas-16. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 4, pp. 163–167, July–August, 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.     

Energy approach to the solution of the nonlinear boundary-value problems of the nonclassical theory of anisotropic stratified shells with slit-cracks

Kiev. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 3, pp. 131–135, May–June, 1994.     

On the extendability of solutions of a difference equation “to the left”

We give sufficient conditions for the extendability of solutions of a nonlinear difference equation “to the left” in a Banach space. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 3, pp. 298–302, July–September, 2007.     

Non-Ergodicity of the Nosé–Hoover Thermostatted Harmonic Oscillator

The Nosé–Hoover thermostat is a deterministic dynamical system designed for computing phase space integrals for the canonical Gibbs distribution. Newton’s equations are modified by coupling an additional reservoir variable to the physical variables. The correct sampling of the phase space according to the Gibbs measure is dependent on the Nosé–Hoover dynamics being ergodic. Hoover presented numerical experiments to show that the Nosé–Hoover dynamics are non-ergodic when applied to the harmonic oscillator. In this article, we prove that the Nosé–Hoover thermostat does not give an ergodynamical system for the one- dimensional harmonic oscillator when the “mass” of the reservoir is large. Our proof of non-ergodicity uses KAM theory to demonstrate the existence of invariant tori for the Nosé–Hoover dynamical system that separate phase space into invariant regions. We present numerical experiments motivated by our analysis that seem to show that the dynamical system is not ergodic even for a moderate thermostat mass.     

Temperature dependence of the interfacial tension of PS/PMMA, PS/PE, and PMMA/PE blends

The effect of temperature on the interfacial tension for PS/PMMA, PS/PE, and PMMA/PE was measured using the imbedded fiber retraction method. Interfacial tensions for PS/PMMA, PS/PE, and PMMA/PE were measured over temperature ranges of 160–250 °C, 140–220 °C, and 140–220 °C, respectively. The interfacial tension was found to follow a dependence of 3.6–0.013 T dyn/cm, 7.6–0.051 T dyn/cm and 11.8–0.017 T dyn/cm for PS/PMMA, PS/PE, and PMMA/PE, respectively. Comparison of the data with the mean field theory of Helfand and Sapse were made; however, a simple linear fit to the data described the temperature dependence in the experimental window as well as the predictions of the mean field theory. Received: 6 July 1999 Accepted: 23 March 2000     

Influence of the gas flow rate on the drawing of optical fibers from fluoride glasses

Angarsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 84–87, September–October, 1994.     

On the Justification of Plate Models

In this paper, we will consider the modelling of problems in linear elasticity on thin plates by the models of Kirchhoff–Love and Reissner–Mindlin. A fundamental investigation for the Kirchhoff plate goes back to Morgenstern (Arch. Ration. Mech. Anal. 4:145–152, 1959) and is based on the two-energies principle of Prager and Synge. This was half a century ago.     

Singular solutions of the problems of the nonlinear theory of elastic dislocations

Rostov State University, Rostov-on-Don 344000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 36, No. 5, pp. 173–180, September–October, 1995.     

Determination of the kinetic strength constants and of the critical size of destruction of composite materials on the basis of recording of pulse electromagnetic radiation during their destruction

Kemerovo. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 4, pp. 153–159, July–August, 1994.     

Evaluation of the seismic effect of an underground explosion

Tashkent. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 6, pp. 3–11, November–December, 1994.     

Numerical method of solving the problem of the contact of an elastic plate with an obstacle

Novosibirsk. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 5, pp. 142–146, September–October, 1994.     

Enhancing the controllability of a composite dielectric

The possibility of increasing the control coefficient of a nonlinear dielectric is studied. Composite structures are designed for which the control coefficient of the composite is considerably (5–20 times) higher than the control coefficients of its components are developed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 143–152, September–October, 2008.     

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.     

A double-front structure of detonation wave as the result of phase transitions

Using thermochemical code calculations, we show that the nanographite–nanodiamond phase transition, which may occur in the detonation products of a number of carbon containing explosives, can affect the detonation properties and can cause a specific detonation regime with some unusual peculiarities. Among them, we first note the failure of the Chapman–Jouguet condition and the presence of the sonic plane, where the Mach number is equal to unity, in a detonation product expansion wave at a lower pressure than that at the Chapman–Jouguet point. The peculiarities of this detonation regime are demonstrated by the example of TNT, HNS, and RDX. The computed detonation velocities are in excellent agreement with experiments over a wide range of initial charge densities for all of the investigated explosives. The results of this work allow one to explain, e.g., contradictory experimental data on the detonation pressure and on the length of the reaction zone for TNT. We believe that some other solid–solid, solid–liquid, and liquid–liquid phase transformations in the detonation products may also cause a detonation regime with the same features as shown here for the nanographite–nanodiamond transition. We suggest a computational study that should facilitate proposing detonation experiments strongly arguing in favor of the model presented. PACS 47.40.-x; 47.40.Rs; 64.70.-p; 64.70.Kb; 05.70.-a; 05.70-.CeThis paper was based on the work that was presented at the 19th International Colloquium on the Dynamics of Explosions and Reactive Systems, Hakone, Japan, July 27–August 1, 2003.     

Numerical analysis of the asymptotic representation of solitary waves

Novosibirsk. Translated from Prikladnaya Mekhanika i Technicheskaya Fizika, No. 5, pp. 44–54, September–October, 1994.