We study rigidity properties of lattices in Isom(H) SOn,1(R), n ≥ 3, and of surface groups in Isom(H2) SL2(R) in the context of integrable measure equivalence. The results for lattices in Isom(H), n ≥ 3, are generalizations of Mostow rigidity; they include a cocycle version of strong rigidity and an integrable measure equivalence classification. Despite the lack of Mostow rigidity for n = 2 we ...

We study the properties of affine rigidity of a hypergraph and prove a variety of fundamental results. First, we show that affine rigidity is a generic property (i.e., depends only on the hypergraph, not the particular embedding). Then we prove that a graph is generically neighborhood affinely rigid in d-dimensional space if it is (d+1)-vertex-connected. We also show neighborhood affine rigidit...

The article shows the effect of torsional rigidity of beam elements onto spatial work of bridges, floorings and other plate-ribbed systems It is shown that, in determining the torsional rigidity using existing methods it is necessary to have spatial spiral cracks, but torsional rigidity when normal cracks is not researched. A method is described for determining the torsional rigidity of reinfor...

In this paper, we introduce new concepts of weak rigidity matrix and infinitesimal weak rigidity for planar frameworks. The weak rigidity matrix is used to directly check if a framework is infinitesimally weakly rigid while previous work can check a weak rigidity of a framework indirectly. An infinitesimal weak rigidity framework can be uniquely determined up to a translation and a rotation (an...

Micellar shape change in an amphiphilic solution is investigated by a molecular dynamics simulation of coarse-grained semiflexible amphiphilic molecules with explicit solvent molecules. Our simulations show that a cylindrical micelle is obtained at small molecular rigidity while a disc-shaped micelle appears at large molecular rigidity. We find that most chains are in an extended conformation a...

In this paper, we present a sufficient condition for the universal rigidity of a generic bar framework G(p) in terms of the Gale matrix Z corresponding to G(p). We also establish a relationship between the stress matrix S and the Gale matrix Z for bar frameworks. This allows us to translate back and forth between S and Z in recently obtained results concerning universal rigidity, global rigidit...

The geometry of cavities in the surfaces of proteins facilitates a variety of biochemical functions. To better understand the biochemical nature of protein cavities, the shape, size, chemical properties, and evolutionary nature of functional and nonfunctional surface cavities have been exhaustively surveyed in protein structures. The rigidity of surface cavities, however, is not immediately ava...

In this paper we provide a Liouville type theorem in the framework of fracture mechanics, and more precisely in the theory of SBV deformations for cracked bodies. We prove the following rigidity result: if u ∈ SBV (Ω, RN ) is a deformation of Ω whose associated crack Ju has finite energy in the sense of Griffith’s theory (i.e., HN−1(Ju) <∞), and whose approximate gradient ∇u is almost everywher...

This article summarizes the presently available general theory of rigidity of 3dimensional structures. We explain how a structure, for instance a bar and joint structure, can fail to be rigid for two quite different types of reasons. First, it may not have enough bars connecting certain sets of nodes. That is, it may faij for topologlcrl reasons. Secondly,. although it may “count” correctly, it...

Rigidity is one of the major signs of P a r k i n s o n ’s disease (PD). However, its pathophysiology has rarely been studied. This appears a little surprising since data obtained from animal physiology, which offers a scheme of neuronal circuits that might be hyperor hypoactive, could be useful in the study of muscle tone problems, a classical area in neurological semiology. Experimental model...