Harmonic distrotions under nonlinear periodic deformation of fluid polymers

Conclusions 1. It has been shown for a number of viscoelastic fluid systems that under nonlinear periodic deformation, the contribution of the third harmonic of the stress to the fundamental does not exceed 20% of the amplitude.2. In the case of clay soil and melt of filled polyethylene, the shape of the stress waves is essentially definable by the relative phase angle of the third harmonic of the stress and is practically independent of the deformation amplitude in a growing nonlinear range of deformation.3. In the case of the polyethylene melt, the amplitude dependence of the phase angles of the stress harmonics is in satisfactory agreement with the analysis of model I. With increasing deformation amplitude, the modulus vector of the first harmonic rotates counterclockwise and remains in the first trigonometric quadrant; the modulus vector of the third harmonic passes from the second to the third quadrant, and the modulus vector of the fifth harmonic passes from the second to the fourth quadrant via the third.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 893–898, September–October, 1978.     

Some observations on the performance of balloons from the rate of rotation of the fan in the F-Type radiosonde

If the rate of ascent of the balloon is constant, the rate of rotation of the fan in the F-Type radiosonde should decrease with height, due to the decrease in the density of the air. It was observed from the radiosonde ascents of Minicoy that the rate of rotation of the fan remained almost unchanged up to even 100 mb. It is shown that this is due to the increase in the rate of ascent of the balloon by about 2% of the value near the ground per km. ascent. Positive evidence of turbulence in the stratosphere is provided by the large fluctuations in the rate of rotation of the fan. It is also observed that the balloon whose fabric at the 50 mb. level is about 0·014 mm. thick bursts due to the turbulence.     

An investigation on the influence of slot injection/suction on the spreading of a thin film under gravity on a rotating disk

We investigate the influence of slot injection/suction on the axisymmetric spreading of a thin film under the influence of gravity and rotation. The effects of surface tension are ignored. We allow a very thin film to precede the bulk of the fluid to overcome the singularity which arises as a consequence of applying the no-slip boundary condition. We show how the width of the slot and magnitude of the injection/suction influences the height of ridges and depth of cavities on the profile of the free surface of the thin film. Rotation increases the depth of the cavities and the height of the ridges as compared to the effects of gravity alone. The presence of rotation also results in the formation of a breaking wave.     

Prediction of the deformation properties of a polymeric composite with a granular-fibrous filler

Conclusion A variant of calculation of the characteristics of the deformation properties of a hybrid composite containing a complex disperse filler in the form of granular particles and short fibers was proposed. The effect of aggregation of the granular filler, the statistical distributions of the fibers by lengths and orientation in the material, and the anisotropy of the fibers are taken into consideration in the calculation. The statistical distribution of the orientation of the fibers is given by a function proportional to the distance from the center to the surface of a triaxial ellipsoid in the corresponding direction. The uniform random distribution of the fibers in bulk and in the plane is a special case of this distribution. The results of the analysis of the effect of the parameters of the statistical distributions of the length and orientation of short fibers on the elasticity characteristics of a composite are reported. The dependence of the creep of the composite on the ratio of the concentration of the components of the complex filler was determined, and the efficiency of partial replacement of a granular filler by a short-fiber filler to inhibit creep of the composite was demonstrated. The possibilities of predicting the long-term creep were experimentally confirmed on the example of LDPE filled with ground limestone and short glass fibers.Presented at the Sixth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, November, 1986).Translated from Mekhanika Kompozitnykh Materialov, No. 5, pp. 898–909, September–October, 1987.     

The thermodynamically consistent equations of a thermoelastic saturated porous medium

A phenomenological model of a porous medium saturated with fluid is considered with in the framework of the hypothesis of interpenetrating continua. Assuming that there are no phase transitions, that the contribution of pulsations to the stress tensor and kinetic energy is small, and the components of the medium are in thermal equilibrium, mass, momentum and energy equations and a law of conservation of compatibility of the deformations and velocities are formulated. Using a representation of the force of interaction of the components in the form of the sum of equilibrium and dissipative components, a new form of inequality is obtained for the rate of entropy production. A definition of a thermoelastic saturated porous medium is given. The symmetry group of such a medium is considered as a set of two groups, corresponding to the symmetry of the skeleton and the fluid. It is shown that, in the class of thermoelastic porous media with an arbitrary type of symmetry of the skeleton, the saturating fluid can only be an ideal fluid, while the thermodynamic potentials and the porosity, stresses and entropies determined by them do not depend on the temperature gradient and the relative fluid velocity. It is found that the condition of incompressibility of only one of the components of the medium leads to the elimination of the porosity from the governing relations, rather than to kinematic limitations. The limitations imposed on the governing relations by the principle of thermodynamic consistency and the requirement of independence of the choice of the frame of reference are investigated. A form of the governing relations, necessary and sufficient to satisfy these principles, is obtained. It is shown that the Biot equations are one of the forms of thermodynamically consistent governing relations. A thermodynamic validation of the effective-stress tensor is given.     

Identification and orbit determination of a tethered satellite system

Orbital motion of a tethered satellite system, composed of two satellites and an inextensible tether, is considered by using a perturbed two-body model. This approach is adopted so that the determination of the orbit of one of the satellites can be attempted without using observations of the motion of the other satellite in the system. The identification of the tethered condition of the system using observations of only one of the satellites in the tethered satellite system is considered. The characteristics of the `tether perturbed' motion of the observed satellite are investigated. Estimation of the state of the system using near perfect data is also illustrated. Observations of one satellite provide the entire state of the system and a parameter involving the ratio of the masses of satellites and the tether length.     

State of stress and strain of brake-class parachutes

The article describes the special features of the operation of brake-class parachutes. It substantiates the possibility of replacing the solution of the dynamic problem of opening of a brake parachute by the static calculation of its state of stress and strain (SSS). The derivation of the equation of motion of a soft carcassed shell is based on the finite element method. The steady-state solution is obtained by the method of adjustment. As an example the results of calculation of the characteristics of the SSS of a cross-shaped brake parachute are presented. It is shown that in the zone of its lower edge considerable concentrations of tension arise in the tissue, the tissue gradually joins the operation of the carcass; the transverse carcass is unsubstantially loaded. The results of the calculations agree with the experimental data.Translated from Dinamicheskie Sistemy, No. 5, pp. 32–36, 1986.     

On the “genetic memory” of chaotic attractor of the barotropic ocean model

The structure of attractor of barotropic ocean model is studied in this paper. Theorems of the existence of the attractor for the finite dimensional approximation of this model are proved as well as its convergence to the attractor of the model itself. Some properties of stationary solutions of this model and their stability are discussed.The structure of the attractor is partially explained by the sequence of bifurcations the system is subjected to by variations of leading parameters. The principal feature of the studied system is the existence of two “almost invariant” basins of chaotic attractor with very rare transitions between them. This is related to the rise of a couple of non-symmetric stable stationary solutions in the model with symmetric forcing.The “memory” of chaos appears also in the presence of maxima in the spectrum of energy. These maxima correspond either to the principal frequency of the limit cycle which arose in the Hopf bifurcation, or to the frequencies of the Feigenbaum phenomenon.     

Free vibrations of a cantilevered plate with a polymer coating

The article considers some of the special characteristics of the free vibrations of a steel cantilevered plate, with the formation of a polymer coating on the plate. It compares the results of an experimental investigation of the effect of internal stresses in the coating on the vibrations and on the static bending of the plate. It demonstrates the possibility of determining the internal stresses in the coating from the change in the frequency of the natural vibrations of a plate with a coating.Institute for the Mechanics of Metal-Polymer Systems, Academy of Sciences of the Belorussian SSR, Gomel'. Translated from Mehanika Polimerov, No. 3, pp. 541–544, May–June, 1970.     

Asymptotic description of stochastic neural networks. I. Existence of a large deviation principle

We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. The dynamics of the neurons is described by a set of stochastic differential equations in discrete time. The neurons interact through the synaptic weights that are Gaussian correlated random variables. We describe the asymptotic law of the network when the number of neurons goes to infinity. Unlike previous works which made the biologically unrealistic assumption that the weights were i.i.d. random variables, we assume that they are correlated. We introduce the process-level empirical measure of the trajectories of the solutions into the equations of the finite network of neurons and the averaged law (with respect to the synaptic weights) of the trajectories of the solutions into the equations of the network of neurons. The result ( Theorem 3.1 below) is that the image law through the empirical measure satisfies a large deviation principle with a good rate function. We provide an analytical expression of this rate function in terms of the spectral representation of certain Gaussian processes.     

Some laws of the elastic properties of oriented fibrous polymers and fibers

The author considers the results of calculations of the limiting values of the elastic properties (modulus of elasticity and load-extension diagram) of the main types of chemical fibers, using a model with "ideal orientation" of the molecules and the derived laws of deformation of polymer chains. A method is proposed for calculating the elastic properties of "ideally oriented" polymers from the velocity of propagation of an elastic deformation pulse and the effective density of the "skeletons" of the polymer chains. Values of the moduli of elasticity of the amorphous regions of the structure of oriented polymers are calculated. The calculated results are compared with experimental data on the elastic properties of fibers.Mekhanika Polimerov, Vol. 2, No. 1, pp. 34–42, 1966Paper read at the XIV All-Union Conference on High-Molecular Compounds, Oriented State.     

科研设备共享平台的配套服务水平决策

为解决我国科研转化率低的难题, 科研设备共享平台应运而生, 这类平台不仅可以优化科研设备的社会配置, 同时还可以通过提高服务水平进而提升设备的使用效率。然而服务水平的提升可能会导致用户设备租赁时间的减少, 从而可能导致设备共享机制的有效性得不到充分发挥。为了制定合理的服务水平, 以兼顾服务质量以及设备共享机制的有效性的双重目标, 本文在传统的双边共享平台模型中引入了平台的服务决策。研究发现:制定合理的服务水平可以提高社会效率; 当平台的租金分成比例较小时, 提高服务水平可以提高社会福利; 当平台设置的租赁价格较高时, 平台利润对服务水平的变化具有较强的敏感性; 平台持有少量自有设备可以在一定程度上增加收入, 但过量持有设备会导致共享机制的失灵。     

Three-dimensional manifestly Poincaré-invariant approach to the relativistic three-body problem

A three-dimensional manifestly Poincaré-invariant approach to the relativistic three-body problem is developed that satisfies the requirement of cluster separability and at the same time does not lead to so-called spurious states devoid of physical meaning. It is shown that these requirements make it possible to fix the form of the operators of the two-body interactions. The problem is solved with allowance for the dependence of the interaction operators on the spectral parameter. This dependence is a manifestation of the structure of the particles in the three-body system (i.e., it reflects the circumstance that the complete Hilbert space of state vectors of the system includes not only three-body configurations of the original particles) and leads to the appearance of certain factors in the cross sections of physical processes. Two alternative formulations of the method are investigated. In the first formulation, equations are written down for the amplitudes of transitions between free-particle states. In the second formulation, the states of interacting particles in the two-body scattering channels are used as complete orthogonal bases. Partial-wave expansions of the equations with respect to states with given total angular momentum of the system in the helicity basis are made.Institute of Nuclear Physics of the State University, Moscow. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 103, No. 2, pp. 200–232, May, 1995.     

Vortex damping of sloshing in tanks with baffles

The problem of damping the sloshing in tanks with sharp-edged baffles (thin inserts which partially span a longitudinal or transverse cross-section) is considered. Separation of the boundary layer and the formation of vortices occur at these sharp edges. It is assumed that the domains where there is significant vortex motion of the fluid are localized in small neighbourhoods of the sharp edges of the baffles. The non-linear vortex damping is determined from the distribution of the velocity intensity factors at these sharp edges in the same way as the linear damping, caused by the dissipation of energy in a boundary layer close to a wall, is determined from the fluid velocity distribution on the walls of a cavity. Both of the above-mentioned distributions are calculated by solving the same boundary-value problem on the oscillations of an ideal fluid. The second of the distributions characterizes the singular properties of the solutions of this problem on particular lines. A method based on the variation of the area of the baffles, which simplifies the calculation of the velocity intensity factors is described. The distinctive features arising when the method of finite elements is used are considered. The results of numerical calculations of the damping of sloshing in a cylindrical tank with a ring baffle are compared with experimental data.     

Riemannian Submersions with Discrete Spectrum

We prove some estimates on the spectrum of the Laplacian of the total space of a Riemannian submersion in terms of the spectrum of the Laplacian of the base and the geometry of the fibers. When the fibers of the submersions are compact and minimal, we prove that the spectrum of the Laplacian of the total space is discrete if and only if the spectrum of the Laplacian of the base is discrete. When the fibers are not minimal, we prove a discreteness criterion for the total space in terms of the relative growth of the mean curvature of the fibers and the mean curvature of the geodesic spheres in the base. We discuss in particular the case of warped products.     

多次分组会议安排的最佳混合方案

本文在仔细分析问题条件和要求的基础上,运用了运筹学、图论、矩阵理论和置换等方面的知识和技巧,建立了一个布尔规划模型。     

Analysis of hydrodynamic losses for various types of aortic valves

Conclusions The creation of an automated computer-controlled hydraulic stand made it possible to measure the main hydrodynamic parameters of the flow through the investigated HVP and to determine the coefficients of Eq. (2) of fluid flow in the test chamber of the stand. The coefficients found can serve as a criterion of a comparative assessment of the hydrodynamics of HVPs. An analysis of the coefficients showed that the main contribution to pressure losses across ball and disc valves is made by viscous and convective effects. An analysis of inertial losses confirmed the presence of oscillations of the ball closing elements of the AKCh-3-06 valve around the props of the stroke limiters and made it possible to assess them quantitatively. For leaflet valves the contribution of inertial losses to the total pressure losses is more considerable than in the case of disc and ball valves both in the regime of an increase of power of the output and in the regime of a constant power. The mechanical properties of the material of leaflet valves have an effect on the hydrodynamic characteristics. The advantage of the investigated leaflet valves consists not only in that they have smaller total hydraulic losses compared with the other valves, but also in that they provide a high amplitude of pulsations of the blood stream in the case of insufficient contractility of the heart.Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 506–512, May–June, 1985.     

The increasingly complex structure of the bifurcation tree of a piecewise-smooth system

A new approach to the study of the dynamics of a piecewise-smooth system is proposed, which uses the a priori known possible bifurcation structures of the parameter space. In Section 1 the synthesis of the structures of the bifurcation tree of the system is considered, namely, the local structures, bifurcation bands, sources and nodes. It is shown that a node corresponding to a doubling bifurcation with reorientation of the domain of existence can generate a sequence of increasingly complex structures. Then the increasing number of unstable orbits serves as one of the mechanisms giving rise to the chaotic behaviour of the dynamical system. In Section 2 the procedure for synthesizing the structures of the bifurcation tree of a piecewise-smooth system proposed in the first part of the paper is applied to the problem of the forced vibrations of a linear oscillator with impacts against a stopping device. Period-doubling cascades are discovered, which are accompanied by the reorientation of the domain of existence of a solution relative to some bifurcation surface, namely, the trunk of the tree. A set of frequency intervals is distinguished on the bifurcation trunk, each containing an infinite sequence of increasingly complex local structures appearing and disappearing at the nodes. This specific mechanism, giving rise to the chaotic motion of the oscillator, is realized in neighbourhoods of the limiting nodal bifurcation points.