Stress relaxation of polybutadiene at large deformation. Measurements of stress and birefringence in shear and elongation

The rheological behavior of an uncrosslinked polybutadiene on sudden application of finite strain was examined. The shear stress σ, two components of birefringence, and the extinction angle were measured in shear (magnitude of shear γ ≤ 3.5) and tensile stress and the birefringence were measured in uniaxial elongation (elongation ratio λ ≤ 3.8). Measurements were performed at 30°C with a tensile tester equipped with appropriate sample holders. The stress-optical coefficient was 3.01 × 10^?9Pa^?1. The first and second normal-stress differences v₁ and v₂ were separately evaluated with the use of stress-optical law. The Lodge—Meissner relation v₁ = γσ held good. The ratio v₂/v₁ was independent of time and varied from about ?0.3 to ?0.2 with increasing γ in the range of measurements. Each of the stress components was factored into a function of strain and one of time, and the latter was common to all the stress components. Simple formulas were proposed to represent stress components in step deformations.     

A scaling method for obtaining kinetic equations from the BBGKY hierarchy

Kinetic equations for the one-particle distribution function of dilute gases and plasmas and evolution equations for the variance of their fluctuations are obtained from the BBGKY hierarchy equations by using Mori's scaling method in an extended form.     

Solvable lattice models related to the vector representation of classical simple Lie algebras

A series of solvable lattice models with face interaction are introduced on the basis of the affine Lie algebraX _n ⁽¹⁾ =A _n ⁽¹⁾ ,B _n ⁽¹⁾ ,C _n ⁽¹⁾ ,D _n ⁽¹⁾ . The local states taken on by the fluctuation variables are the dominant integral weights ofX _n ⁽¹⁾ of a fixed level. Adjacent local states are subject to a condition related to the vector representation ofX _n . The Boltzmann weights are parametrized by elliptic theta functions and solve the star-triangle relation.