Energy dissipation from an extrudate in the gap between the screw rib and the extruder shell

A dimensionless equation is derived for determining the energy dissipation between the screw rib and the sleeve of an extruder for a Newtonian model extrudate. The parameter ranges, within which the pressure at the exit from the screw and some geometrical parameters do not affect the dissipation, are indicated.Moscow Institute of Chemical Engineering. Translated from Mekhanika Polimerov, No. 4, pp. 746–749, July–August, 1972.     

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.     

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.     

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.     

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     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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     

On stationary flows with energy dependent nonlocal viscosities

A nonlocal constitutive law for an incompressible viscous flow in which the viscosity depends on the total dissipation energy of the fluid is obtained as the limit case of very large thermal conductivity when the viscosity varies with the temperature. A rigorous analysis is illustrated within the Hilbertian framework for unidirectional stationary flows of Newtonian and Bingham fluids with heating by viscous dissipation. An extension to quasi-Newtonian fluids of power law type and with temperature dependent viscosities is obtained in the context of the heat equation with an L¹-term. The nonlocal model proposed by Ladyzhenskaya in 1966 as a modification of Navier-Stokes equations can be, in particular, obtained with this procedure. Bibliography: 14 titles.Dedicated to O. A. Ladyzhenskaya on the occasion of her 80th birthday__________Published in Zapiski Nauchnykh Seminarov POMI, Vol. 295, 2003, pp. 99–117.     

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.     

stresses and reversible deformations during shear flow of polymer solutions and melts

The influence of the accumulated elastic energy on the relationships between tangential stresses, the first difference between the normal stresses and the reversible deformations during isothermal shearing steady-state flow of polymer solutions and melts, is analyzed. It is shown that the reversible deformation in the non-Newtonian flow region is related to the tangential and normal stresses by Lodge's formula, if the thixotropic disruption of the structural flow units is accompanied by the dissipation of the elastic energy accumulated in them; the conservation of the elastic energy accumulated during the flow causes exceeding of the reversible deformation values as compared with the values calculated by Lodge's formula.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 886–895, September–October, 1972.     

An interphase layer in organic fibrous composites

Conclusions In this work, it was attempted to demonstrate the special features of polymer fibers manifested primarily in a special mechanism of formation of the interphase layer during formation of the composite material. The role of the interphase layer in this case is not reduced just to dissipation of the energy generated during rupture of a fiber. It can also play the role of an element of the structure of the composite acting as a possible source of initial cracks. From this viewpoint it would be useful to re-examine the micromechanics of failure of the composite and attempt to take into account the role of the interphase layer in a real system of many fibers, not just in the fiber-interphase layer-matrix triad.Translated from Mekhanika Kompozitnykh Materialov, Vol. 29, No. 1, pp. 10–18, January–February, 1993.     

An Efficient Geometric Integrator for Thermostatted Anti-/Ferromagnetic Models

(Anti)-/ferromagnetic Heisenberg spin models arise from discretization of Landau–Lifshitz models in micromagnetic modelling. In many applications it is essential to study the behavior of the system at a fixed temperature. A formulation for thermostatted spin dynamics was given by Bulgac and Kusnetsov, which incorporates a complicated nonlinear dissipation/driving term while preserving spin length. It is essential to properly model this term in simulation, and simplified schemes give poor numerical performance, e.g., requiring an excessively small timestep for stable integration. In this paper we present an efficient, structure-preserving method for thermostatted spin dynamics.     

Galvanic-approximation investigation of magnetoacoustic dissipation in a viscoelastic weakly conducting cylinder

The radial oscillations of a viscoelastic, weakly conducting, nonmagnetic cylinder are studied. The oscillations are excited by a contact-free induction method in the presence of a constant axial magnetic field. The Joule heating and viscous heating densities are calculated for two types of boundary conditions. The effect of electric conductivity on the dissipation of the energy of magnetoacoustic disturbances is compared with the effect of viscosity. The spectra of resonance oscillations of the cylinder are investigated.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 5, pp. 44–49, 1987.