A Saint-Venant principle for nonlinear elasticity

This paper proves the global boundedness in time of higher moments to a weak solution of the non-linear space-homogeneous Boltzmann equation for inverse k^th-power forces with k ≧ 5. In the course of the proof a new collisional estimate of is obtained, where v, v_* are the velocities before and v′, v′_* are the velocities after a binary collision.     

Uniqueness of the nonlinear elastic dielectric affine boundary value problem on the whole space and on cone-like regions

Conservation laws derived from the energy–momentum tensor are employed to establish under suitable sufficient conditions uniqueness in affine boundary value problems for the homogeneous nonlinear elastic dielectric on the whole space and on certain cone-like regions. In particular, the electric enthalpy is assumed to be strictly quasi-convex for the whole space, and strictly rank-one convex for cone-like regions. Asymptotic behaviour is also stipulated. Uniqueness results for corresponding affine boundary value problems of homogeneous nonlinear elastostatics are a special case of those derived here.     

Recovery of Stresses in a Beam from those in a Cone

We consider a trapezoidal thin plate, as shown in Figure 1, which has one end loaded by a concentrated transverse unit force and the other clamped at zero displacement. The stress is determined according to a method proposed by Galerkin [1] which involves the superposition of two plane elastic stress distributions. To access the accuracy of the method, the oblique sides of the trapezium are allowed to become parallel so that, in the limit, the trapezium becomes a rectangle of the same area. The limiting values of the maximum stress components are exactly those obtained by the Saint-Venant method for a bar. However, over the clamped end, the displacement vanishes only at three arbitrarily selected points. A similar procedure is applied to the transversely loaded truncated cone, but now the limiting values of the stress do not entirely match those obtained by the Saint-Venant theory for a circular cylinder. We also briefly discuss, for completeness, the same bodies under axial loadings, and arrive at similar conclusions which therefore hold for general loads. This revised version was published online in August 2006 with corrections to the Cover Date.     

On partial weakly clustering states with an application to the Ising model

The concept of partial weak clustering in the mean is defined for states on physical systems which admit amenable (semi-)groups of symmetries. The properties of partial weak clustering states are studied and the relations between these states and (extremal) invariant (partial) states are considered. As an application we discuss the zero field magnetization in the two-dimensional Ising model.     

On universal relations in elasticity theory

Zusammenfassung Es wird eine Methode zur Erhaltung allgemeingültiger Beziehungen für Verzerrungen kompressibler, isotroper, elastischer Körper dargestellt.     

Renormalization connection between the eight-vertex model and the gaussian model

A generalized version of the Villain model is defined which contains the eight-vertex model as a special case. A renormalization pattern is formulated in terms of this Villain model by which critical line(s) in the eight-vertex model are connected with the Gaussian fixed line. Gaussian equivalents are found for various operators along the Baxter line. The relation between the present results and those recently obtained by Kadanoff and Brown is discussed.