On the plasticity of Si-O framawork of alkali zinc silicates

The configuration of the Si-O framework in alkali zinc silicates has been investigated on the basis of recently determined structures. The results have shown that there is a linear correlation between the ionic radii of alkali ions and the molar abundance of ZnO+SiO2 per one alkali ion in the structure. This indicates that in the case of zinc silicates, the configuration of the Si-O frameworks is largely influenced by the ionic radii of alkali ions in the structure. On the contrary, in the case of alumino-silicates, the configuration of the Si-O framework is independent of ionic radii of alkali ions. In the former, the Si-O framework is considered to be plastic, while in the latter, it could be called rigid. The latter extreme cases are those of zeolites. In this case, the configuration on frameworks is not entirely influenced by the ionic radii of alkali atoms present. These results are discussed in connection with the historical investigations of silicate structures

Linkage Mechanisms Governed by Integrable Deformations of Discrete Space Curves

A linkage mechanism consists of rigid bodies assembled by joints which can be used to translate and transfer motion from one form in one place to another. In this paper, we are particularly interested in a family of spacial linkage mechanisms which consist of $n$-copies of a rigid body joined together by hinges to form a ring. Each hinge joint has its own axis of revolution and rigid bodies joined to it can be freely rotated around the axis. The family includes the famous threefold symmetric Bricard6R linkage also known as the Kaleidocycle, which exhibits a characteristic "turning over" motion. We can model such a linkage as a discrete closed curve in $\mathbb{R}^3$ with a constant torsion up to sign. Then, its motion is described as the deformation of the curve preserving torsion and arc length. We describe certain motions of this object that are governed by the semi-discrete mKdV equations, where infinitesimally the motion of each vertex is confined in the osculating plane