Piecewise rigidity

Piecewise Rigidity

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...

Piecewise monotone maps without periodic points: Rigidity, measures and complexity.

Piecewise monotone maps without periodic points : Rigidity , measures and complexity

We consider piecewise monotone maps of the interval with zero entropy or no periodic points. First, we give a rigid model for these maps: the interval translations mappings, possibly with ips. It follows, e.g., that the complexity of a piecewise monotone map of the interval is at most polynomial if and only if this map has a nite number of periodic points up to monotone equivalence. Second, we ...

Cumulative Chords, Piecewise-quadratics and Piecewise-cubics

Cumulative chord piecewise-quadratics and piecewise-cubics are examined in detail, and compared with other low degree interpolants for unparameterized data from regular curves in , especially piecewise-4-point quadratics. Orders of approximation are calculated and compared with numerical experiments. Good performance of the interpolant is also confirmed experimentally on sparse data. This work ...

Structural Rigidity

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...