Concerning extruder flow

A criterial equation for determining the energy dissipation in the channel of an extruder screw is obtained analytically for a Newtonian model of the extrudate. It is shown that for actual extruders the dissipation does not depend on the pressure in the die.Moscow Region. Translated from Mekhanika Polimerov, No. 5, pp. 924–927, September–October, 1969.     

Coupled problems of thermoviscoelasticity

The author derives a heat flux equation with allowance for the dissipation of internal forces on the basis of the fundamental equations of continuum mechanics and the thermodynamics of irreversible processes.Moscow Lomonosov State University. Translated from Mekhanika Polimerov, No. 3, pp. 415–421, May–June, 1969.     

A higher-order moment method of the lattice Boltzmann model for the conservation law equation

In this paper, we proposed a higher-order moment method in the lattice Boltzmann model for the conservation law equation. In contrast to the lattice Bhatnagar–Gross–Krook (BGK) model, the higher-order moment method has a wide flexibility to select equilibrium distribution function. This method is based on so-called a series of partial differential equations obtained by using multi-scale technique and Chapman–Enskog expansion. According to Hirt’s heuristic stability theory, the stability of the scheme can be controlled by modulating some special moments to design the third-order dispersion term and the fourth-order dissipation term. As results, the conservation law equation is recovered with higher-order truncation error. The numerical examples show the higher-order moment method can be used to raise the accuracy of the truncation error of the lattice Boltzmann scheme for the conservation law equation.     

Thermodynamic analysis of the equations of a linear viscoelastic anisotropic solid

Constraints on the coefficients of the equations of state of anisotropic linear viscoelasticity are obtained using the positive definiteness of two quadratic forms—the potential energy and the energy dissipation rate.Mekhanika Polimerov, Vol. 3, No. 2, pp. 227–235, 1967     

Mathematical model of polytropic polymer extrusion

The basic equations of the statics of the extrusion process have been derived with allowance for viscosity anomaly, heat-transfer effect, and the dependence of the actual length of the metering zone on the regime parameters. The model obtained makes possible the analytic determination of the output and the temperature and pressure of the melt at the screw outlet. The theoretical results are compared with experiment.All-Union Scientific-Research Institute of Agricultural Machine-Building, Moscow. Translated from Mekhanika Polimerov, No. 6, pp. 1095–1101, November–December, 1970.     

On the optimality of velocity averaging lemmas

Studying weak solutions of Burgers' equation with finite entropy dissipation we show the sharpness of recent results of Jabin and Perthame on velocity averaging. Similar arguments give bounds on the regularity of asymptotic finite-energy states for some variational problems of Ginzburg–Landau type.     

Nonlinear evolution of screw modes in finite-conductivity plasma

The paper examines numerical modeling of nonlinear stabilization of screw instability in a plasma with a free surface. The analysis is based on a cylindrical model allowing for finite conductivity of the plasma.Translated from Vychislitel'naya Matematika i Matematicheskoe Obespechenie EVM, pp. 113–122, 1985.     

On the Navier-Stokes Equations with Energy-Dependent Nonlocal Viscosities

We discuss the mathematical modeling of incompressible viscous flows for which the viscosity depends on the total dissipation energy. In the two-dimensional periodic case, we begin with the case of temperature-dependent viscosities with very large thermal conductivity in the heat convective equation, in which we obtain the Navier-Stokes system coupled with an ordinary differential equation involving the dissipation energy as the asymptotic limit. Letting further the latent heat to vanish, we derive the Navier-Stokes equations with a nonlocal viscosity depending on the total dissipation of energy. Bibliography: 7 titles.Dedicated to V. A. Solonnikov on the occasion of his 70th birthday__________Published in Zapiski Nauchnykh Seminarov POMI, Vol. 306, 2003, pp. 71–91.     

Running tails as codimension two quasi-solitons in excitation taxis waves with negative refractoriness

Using a Lindblad dissipation dynamics [Lindblad G. On the generators of quantum dynamical semigroups. Commun Math Phys 1976;48:119–130 and see also Gorini V, Frigerio A, Verri M, Kossakowski A, Sudarshan ECG. Properties of quantum Markovian master equations. Rep Math Phys 1978;13:149–173; Alicki R, Messer J. Nonlinear quantum dynamical semigroups for many-body open systems. J Stat Phys 1983;32:299–312.] for biological rate equations we derive a one-component discrete dynamics for the spread of Avian Influenza. Numerical solutions of the difference equations are calculated and compared with measurement data.     

Theory of one-dimensional waves in nonlinear dissipative media

A unified approach is made to the construction of mathematical models describing discontinuous processes, and their analogs in the region of continuous solutions are presented; this makes it possible to distinguish between idealized and actual discontinuities and to classify media on the basis of model equations. The media considered are characterized by physical and geometric nonlinearity and by dissipation due to either viscosity or to the coupling of strain and temperature fields.Institute of Cybernetics, Academy of Sciences of the Estonian SSR, Tallin. Translated from Mekhanika Polimerov, No. 1, pp. 41–48, January–February, 1976.     

Acoustic fatigue of polymer materials

Methods are proposed for experimentally estimating the temperature-time aging of a filled rubber and the degree of damage accumulation in high-frequency fatigue tests. A procedure for experimentally determining the energy dissipation function of a material from the specimen temperature kinetics is described. The results of an investigation of the fatigue properties of two series of filled rubbers at a vibration frequency of 20 kHz are presented. It is shown that the fatigue failure of the materials tested is thermal in character. No accumulation of mechanical damage in the material in the course of intense vibration could be detected.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 662–668, July–August, 1969.     

Terminal defects in crystalline polyethylene

Conclusions 1. It was shown that the terminal defect in polyethylene contains a set of partial twist disclinations with different Frank vectors for different chains.2. It was found that the structure of the terminal defect changes during elongation of the chain and outward from the crystallite. It was also found that the volume of the void formed by the presence of the chain and remains constant; the elongation process is accompanied by a conservative motion of the disclination loops along the chains, which causes creep of the screw dislocations.3. The conformational changes were calculated for a segment moving in the crystal field of neighboring chains in regular and high-pressure PE; the values of the energy of activation of the chain and motion were obtained (10.3·10^–16 and 3.6·10^–16 erg/monomer for the regular and high-pressure PE, respectively), indicating a higher rate of annealing of PE in the high-pressure phase.For communication II, see [2].Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 793–798, September–October, 1978.     

Thermodynamic Equilibrium in the System of Chaotic Quantized Vortices in a Weakly Imperfect Bose Gas

In the example of a weakly imperfect Bose gas, we discuss the mechanism of establishing thermodynamic equilibrium for a chaotic set of quantum vortex filaments. We assume that the dynamics of the Bose condensate is described by the Gross–Pitaevsky equation with an additional noise satisfying the fluctuation–dissipation theorem. In considering a vortex filament as the intersection line of surfaces on which the real and imaginary parts of the order parameter (x,t) vanish, we obtain an equation of the Langevin type for elements of the vortex filament with an appropriately transformed random force. The Fokker–Planck equation for the probability density has a solution given by the Gibbs distribution at the temperature of the Bose condensate. In other words, when the Bose condensate is in thermal equilibrium and no other random actions exist, the system of vortices is also in thermal equilibrium.     

Energy dissipation in a glass laminate stressed in cyclic tension-compression

An experimental investigation has established that in a glass laminate most of the mechanical losses are converted into thermal energy. The sum of the mechanical losses increases with increase in the fatigue life of the material, the ratio of thermal losses remaining constant under given deformation conditions. Quantitative data are presented for the energy dissipation in various phases of the fatigue fracture process.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 4, pp. 655–661, July–August, 1969.     

On the theory of non-Newtonian polymer flow

Shear flow of polymers is examined on the assumption that the main contribution to polymer viscosity is made by the dissipation of energy in the destruction of the fluctuation network. A simple physicomechanical model of the flow process is proposed and used to obtain an expression for the polymer viscosity in terms of certain functions reflecting the influence of the molecular structure.Mekhanika Polimerov, Vol. 2, No. 3, pp. 429–434, 1966     

A joint SSPDF–CMC method for simulating turbulent methane–air jet combustion

A joint single scalar probability density function and conditional moment closure (SSPDF–CMC) method is proposed for modeling a turbulent methane–air jet flame. In general, the probability density function (PDF) of passive scalar (such as mixture fraction) is non-Gaussian and not fully determined by the advecting velocity field, therefore the presumed shape of PDF of mixture fraction assumed as clipped Gaussian distribution or beta function in normal conditional moment closure (CMC) method is incorrect. In SSPDF–CMC method, the PDF of mixture fraction is obtained using a Monte-Carlo method to solve a PDF transport equation. An assumption that the averaged scalar advection is approximately equal to the averaged scalar dissipation in the wake of a grid-generated turbulence flow is adopted to model the averaged scalar dissipation. The predictions using the proposed method are compared with those using the conventional CMC method and the experimental data. It is seen that the predicted Favre conditional averaged statistics and Favre unconditional averaged statistics using the proposed method are in better agreement with the measurement data than those using the conventional CMC method. The predicted conditional or unconditional mean NO even using the SSPDF model is only in fair agreement with the experiments. It shows that the first-order closure for the conditional reaction rate of NO should be improved.     

Experimental study of the contribution of interfacial friction to the deformation resistance of particle-reinforced polymers

A study has been made of the dissipative properties of heavily filled elastomers as influenced by friction of the elastic matrix on the surface of the solid filler particles. In order to model the frictional surface, specimens were predamaged by cyclic deformation, with strain amplitudes sufficient to cause separation of the matrix from the filler. The predeformation operation was performed by means of a mechanical system having individual particle-matrix bonds, so that it was possible to evaluate the contribution of interfacial friction to the resistance of the polymer. When external pressure was applied to the specimens, the width of the hysteresis loop increased with increasing pressure, obviously reflecting an increase of the surface friction in the matrix. It was established that for a given volumetric fill, the dissipation of mechanical energy increased with decreasing particle size (with increasing frictional surface area). The significant influence of interfacial friction on the level and rate of strain relaxation was demonstrated experimentally.Paper presented at the 9th International Conference on the Mechanics of Composite Materials (Riga, October 1995).Translated from Mekhanika Kompositnykh Materialov, Vol. 31, No. 5, pp. 579–583, September–October, 1995.     

Damping by dry friction of dynamic loads in a fiber-reinforced composite

Conclusions The accurate analytical solutions of a number of nonlinear problems of impacts on semiinfinite and finite fibers, interacting with the matrix in accordance with the dry friction law, were obtained. We examined the cases of both unidirectional motions and reversed motions caused by unloading, and also oscillatory motions. The results can be used to calculate the energy dissipated in the separating sections of the composite in shock effects. It was shown that the amount of energy dissipated in the dynamic effect is considerably greater than in the quasistatic effect. Thus, dissipation in the system with friction depends strongly on the nature of load application with time.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 28–37, January–February, 1986.     

Effect of two photon absorption on nonlinear pulse propagation in gain medium

The effects of two photon absorption (TPA) and gain dispersion on soliton propagation in amplified medium are investigated. For finite gain bandwidth, the effect of gain dispersion becomes significant along with TPA and is treated as perturbation in fundamental soliton propagation. Including these perturbing effects an analytical expression of integrated intensity is formulated applying a completely new methodology by adopting Rayleigh’s dissipation function in the framework of variational approach. With classical analogy, the Euler–Lagrange equation in non-conservative system is used to solve the problem analytically. In order to justify the analytical prediction a numerical verification is made by split-step beam propagation method following Ginzburg–Landau equation.     

Boussinesq-type system of equations in the Bénard-Marangoni system

A system of coupled evolution equations for the bulk velocity and the surface displacement is found to govern the longwavelength perturbations in a Bénard-Marangoni system. This system of equations, involving nonlinearity, dispersion, and dissipation, is a generalization of the usual Boussinesq system.Instituto de Física Teórica, Universidade Estadual, Paulista, Rua Pamplona 145, 01405-900 São Paulo SP, Brazil. Laboratoire de Physique Mathématique, Université de Montpellier II, 34095 Montpellier Cedex 05, France. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 3, pp. 419–427, June, 1994.