Temperature dependence of the photoelastic behaviour of crystals—Part I

A modified form of Filon’s spectrometer method is used to study the variation of the stress-optical constants (q ₁₁-q ₁₂) andq ₄₄ of KCl, KBr, KI, LiF, MgO and NaCl in the temperature range 30° C. to 400° C. It is found that (q ₁₁-q ₁₂) andq ₄₄ generally increase numerically with the increase of temperature except those of NaCl which show a decrease. In KBr and KI,q ₄₄ first increases and then decreases numerically. The potassium halides show an interesting gradation of variation of these constants. In all the crystals studied, which are of NaCl type, the variation in (q ₁₁-q ₁₂) is greater than that inq ₄₄. Mueller’s ultrasonic method is used for measuring the ratio of strain-optical constantsp ₁₂/p ₁₁, in the temperature range 30°C. to 250°C. Combining the results obtained by these two methods, the absolute strain-optical constantsp ₁₁ andp ₁₂ have been evaluated at different temperatures. Curves are given showing the variation ofp ₁₁ andp ₁₂ with temperature. The variation ofp ₁₁ andp ₁₂ with temperature is discussed in terms of the contributions of the various factors considered by Mueller in his theory of photoelastic effect in cubic crystals.     

Further Revelations on L.S.D.

In a recent paper the author showed that the distribution ofleading significant digits, l.s.d., resulting from successivemultiplications is logarithmic. In this paper these resultsare extended by establishing, still without any assumptionsof invariance to scaling, that this distribution remains invariantunder all further arithmetic operations—both multiplicativeand additive. The fact that 30% of decimal numbers have l.s.d.1 persists.     

On a problem of S.L. Sobolev

In his famous works of 1930 [1,2] Sergey L. Sobolev has proposed a construction of the solution of the Cauchy problem for the hyperbolic equation of the second order with variable coefficients in Rş. Although Sobolev did not construct the fundamental solution, his construction was modified later by Romanov (2002) and Smirnov (1964) to obtain the fundamental solution. However, these works impose a restrictive assumption of the regularity of geodesic lines in a large domain. In addition, it is unclear how to realize those methods numerically. In this paper a simple construction of a function, which is associated in a clear way with the fundamental solution of the acoustic equation with the variable speed in 3-d, is proposed. Conditions on geodesic lines are not imposed. An important feature of this construction is that it lends itself to effective computations.     

O.R.C.S. 1981 Results

Journal of the Operational Research Society -     

Temperature dependence of the strains and stresses in Lavsan fiber

The behavior of heat-stabilized and unstabilized polyester cord fiber at elevated temperatures is described.Mekhanika Polimerov, Vol. 4, No. 2, pp. 369–371, 1968     

Nonlocal regularization of L. C. Young's tacking problem

L. C. Young's tacking problem is a prototype of a nonconvex variational problem for which minimizing sequences for the energy do not attain a minimum. The minimizer of the energy is usually described as a Young-measure or generalized curve. In many studies, the tacking problem is regularized by adding a higher-order viscosity term to the energy. This regularized energy has classical minimizers. In this paper we regularize instead with a spatially nonlocal term. This weakly regularized problem still has measure-valued minimizers, but as the nonlocal term becomes stronger, the measure-valued solutions organize, coalesce, and eventually turn into classical solutions. The information on the measure-valued solutions is obtained by studying equivalent variational problems involving moments of the measures.The research of D. Brandon has been partially supported by the Office of Naval Research under Grant Number N00014-88-K-0417 and by DARPA Grant F4920-87-C-0116, and that of R. C. Rogers has been partially supported by the Office of Naval Research under Grant Number N00014-88-K-0417 and by the National Science Foundation under Grant Number DMS-8801412.     

Eine Verallgemeinerung eines Satzes von L. S. Pontrjagin

Ohne Zusammenfassung     

Temperature dependence of the mechanical properties of polyethylene in fabricated parts

The effect of temperature and aging on the mechanical properties of low-density polyethylene has been investigated. These properties fluctuate both between identical mass-produced parts and within the same part. It is shown that the fluctuations are caused and determined by differences in the nature of the supermolecular structure.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 778–786, September–October, 1969.