A note on the derivation of rigid-plastic models

This note is devoted to a rigorous derivation of rigid-plasticity as the limit of elasto-plasticity when the elasticity tends to infinity

Genuinely multipartite entangled quantum states with fully local hidden variable models and hidden multipartite nonlocality

The relation between entanglement and nonlocality is discussed in the case of multipartite quantum systems. We show that, for any number of parties, there exist genuinely multipartite entangled states which admit a fully local hidden variable model, i.e. where all parties are separated. Hence, although these states are entangled in the strongest possible sense, they cannot lead to Bell inequality violation considering general non-sequential local measurements. Then, we show that the nonlocality of these states can nevertheless be activated using sequences of local measurements, thus revealing genuine multipartite hidden nonlocality.Comment: 4 pages + appendix. 1 Figur

Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach

A new approach to irreversible quasistatic fracture growth is given, by means of Young measures. The study concerns a cohesive zone model with prescribed crack path, when the material gives different responses to loading and unloading phases. In the particular situation of constant unloading response, the result contained in [G. Dal Maso, C. Zanini: Quasi-static crack growth for a cohesive zone model with prescribed crack path. Proc. Roy. Soc. Edinburgh Sect. A, 137A (2007), 253–279.] is recovered. In this case, the convergence of the discrete time approximations is improved

Fracture

These notes begin with a review of the mainstream theory of brittle fracture, as it has emerged from the works of Griffi th and Irwin. We propose a re-formulation of that theory within the confi nes of the calculus of variations, focussing on crack path prediction. We then illustrate the various possible minimality criteria in a simple 1d-case as well as in a tearing experiment and discuss in some details the only complete mathematical formulation so far, that is that where global minimality for the total energy holds at each time. Next we focus on the numerical treatment of crack evolution and detail crack regularization which turns out to be a good approximation from the standpoint of crack propagation. This leads to a discussion of the computation of minimizing states for a non-convex functional. We illustrate the computational issues with a detailed investigation of the tearing experiment

On Textile Fragments Found at Karadong, a 3rd to early 4th Century Oasis in the Taklamakan Desert (Xinjiang, China)

In 1993 and 1994, the Sino-French archeological mission in Xinjiang led by Abdurassul Idriss and Corinne Debaine-Francfort,1 excavated the site at Karadong in the heart of the Takalamakan desert, on a former delta of the Keriya River, whose headwaters are in the Kunlun Mountains at the Tibetan border, and which vanishes in the desert sands. At one time, it continued north all the way to the Tarim River, thus forming a communication link with the Kucha region. Older deltas visible on satellite images have been explored and two related archeological sites have been consecutively excavated to the northwest of Karadong: an Iron Age site, Djoumboulak Koum, and a Bronze Age site, the so-called Northern Cemetery (fig. 1).2 Textiles were found on both sites, and especially at Djoumboulak Koum, where several cemeteries as well as a ‘city’, ringed by a thick rampart, revealed the types of woolen fabrics local people valued a few centuries before Karadong. These discoveries have provided important parallels for the interpretation of the textile fragments discovered in the ruins of Karadong dwellings, and in particular, in shedding light on their relationships with regions near and far. Our presentation is divided in three parts. Firstly, we will examine the archeological and historical context of Karadong in order to understand who was living there, and what kinds of relationships these people had with the outside world. Secondly, we shall describe the salient features of the forty-nine small and poorly preserved textile fragments found there. Thirdly, we will show how these textiles—quite sober in appearance—substantiate surprising evidence of the circulation of textiles and ideas over great distances