Thermal conductivities of polymers at various temperatures and pressures

The authors describe an apparatus and method for investigating the coefficient of thermal conductivity of high-density and low-density polyethylene, polypropylene, polyorthochlorostyrene, and polyparachlorostyrene in relation to temperature and pressure.     

Coupled motion of a rigid body and point vortices on a two-dimensional spherical surface

The paper is concerned with a class of problems which involves the dynamical interaction of a rigid body with point vortices on the surface of a two-dimensional sphere. The general approach to the 2D hydrodynamics is further developed. The problem of motion of a dynamically symmetric circular body interacting with a single vortex is shown to be integrable. Mass vortices on S ² are introduced and the related issues (such as equations of motion, integrability, partial solutions, etc.) are discussed. This paper is a natural progression of the author’s previous research on interaction of rigid bodies and point vortices in a plane.     

The effect of heat flow on the contact area between a continuous rigid punch and a frictionless elastic half-space

A general proof is given of the theorem that, if a continuous rigid punch indenting an elastic half space is heated, the separation of the solids will increase and part of the contact area will be lost. It is also shown that if the punch is convex, the contact area cannot be multiply-connected.

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Résumé On donne une preuve générale du théorème que, si un poinçon continu rigid, pénétrant un demi-espace élastique, est chauffé, la séparation des solides grandira et une partie de la région de contact sera perdue. On montre également que la région de contact ne peut pas être multiplement connexe si le poinçon est convexe.

     

Formation of the true contact area between high-elastic materials and a hard smooth surface

The change in the true contact area between rubber and glass on passing from static to dynamic friction has been studied experimentally. The extent of this change depends on the applied normal load and the contact time. The change of friction force is determined by the conditions of formation of the true contact area under the action of normal and tangential forces.Mekhanika Polimerov, Vol. 2, No. 2, pp. 263–268, 1966     

On the contact of a rigid sphere and a thin plate

We consider the problem of the contact between a rigid sphere and a thin initially flat plate. After reviewing some plate theory, we establish that a deformation where a finite piece of the plate takes the shape of the sphere is physically unrealisable, and that the contact region must be a ring. However, for both small deflections using classical linear elastic theory and large deflections using von Kármán theory, looking at some typical parameter values we find that the radius of the ring is so small that for practical purposes it should be considered as a point load.     

Dispersion of the mechanical characteristics of plastics at various temperatures

The results of an investigation of the dispersion (standard deviation s and coefficient of variation V) of the static and dynamic strengths of plastics are described. The effect of temperature, state of stress, and type of plastic on the dispersion characteristics is considered.Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 29–34, January–February, 1970.     

Use of the total internal reflection method for measuring the actual contact area of polymeric bodies

An estimate is obtained for the errors of the total internal reflection method associated with penetration of the electromagnetic vibrations into the air gaps formed between rough contact surfaces. Certain recommendations for improving test instrument design are formulated.Institute of Mechanics of Metal-Polymer Systems, Academy of Sciences of the Belorussian SSR, Gomel'. Translated from Mekhanika Polimerov, No. 4, pp. 710–714, July–August, 1974.     

Breakage of the polymer chains in Kapron oriented at various temperatures

Infrared spectroscopy has been used to detect a considerable reduction in the number of broken macromolecules in Kapron oriented at elevated temperatures, particularly in the region above 140°C. This is a consequence of weakening of the hydrogen bonds and an increase in the mobility of the amide groups in the crystalline parts of the polymer as the temperature rises.Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 4, pp. 649–653, July–August, 1971.     

Iterative algorithm for minimizing a convex function at the intersection of a spherical surface and a convex compact set

A numerical algorithm for minimizing a convex function on the set-theoretic intersection of a spherical surface and a convex compact set is proposed. The idea behind the algorithm is to reduce the original minimization problem to a sequence of convex programming problems. Necessary extremum conditions are examined, and the convergence of the algorithm is analyzed.     

Investigation of the thermophysical properties of polymethyl methacrylate at high hydrostatic pressures

Conclusions 1. The experimentally observed course of heat capacity is explained by competition of contributions from the lattice and defects, on one hand, and from retarded rotators, on the other.2. An equation is proposed which describes the dependence of the thermal conductivity of polymers on pressure and which agrees with experimental data to an accuracy of ±1%.Moscow Chemical Engineering Institute. Translated from Mekhanika Polimerov, No. 5, pp. 845–851, September–October, 1976.     

The dynamics of a rigid body with a sharp edge in contact with an inclined surface in the presence of dry friction

In this paper we consider the dynamics of a rigid body with a sharp edge in contact with a rough plane. The body can move so that its contact point is fixed or slips or loses contact with the support. In this paper, the dynamics of the system is considered within three mechanical models which describe different regimes of motion. The boundaries of the domain of definition of each model are given, the possibility of transitions from one regime to another and their consistency with different coefficients of friction on the horizontal and inclined surfaces are discussed.     

On the Heegaard Floer homology of a surface times a circle

We make a detailed study of the Heegaard Floer homology of the product of a closed surface Σg of genus g with S¹. We determine HF⁺(Σg×S¹,s;C) completely in the case c₁(s)=0, which for g?3 was previously unknown. We show that in this case HF^∞ is closely related to the cohomology of the total space of a certain circle bundle over the Jacobian torus of Σg, and furthermore that HF⁺(Σg×S¹,s;Z) contains nontrivial 2-torsion whenever g?3 and c₁(s)=0. This is the first example known to the authors of torsion in Z-coefficient Heegaard Floer homology. Our methods also give new information on the action of H₁(Σg×S¹) on HF⁺(Σg×S¹,s) when c₁(s) is nonzero.     

Modelling of the motion of a disk rolling on a smooth rigid surface

This letter deals with the modelling of the motion of a disk rolling without slipping on a rigid surface.     

Effect of the structure of a polymer matrix and its area of contact with the surface of the filler on the rigidity of a polyethylene composite

The distribution of the orientation of the macromolecules over the wall cross section of a filled polyethylene tube is analyzed. A direct proportionality is established between the degree of orientation (estimated from the shrinkage) and the elastic modulus. The effect of various fillers on the melting and crystallization of low-density polyethylene is considered. For a specified filler concentration the elastic modulus of the composites depends very considerably on the relative area of contact between the polymer matrix and the surface of the filler.Institute of the Mechanics of Polymers, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 387–391, May–June, 1974.