Elastic Effects in Disordered Nematic Networks

Elastic effects in a model of disordered nematic elastomers are numerically investigated in two dimensions. Networks crosslinked in the isotropic phase exhibit unusual soft mechanical response against stretching. It arises from gradual alignment of orientationally correlated regions that are elongated along the director. A sharp crossover to a macroscopically aligned state is obtained on further stretching. The effect of random internal stress is also discussed.Comment: 5 pages, 5 figure

Twisted Morita-Mumford classes on braid groups

Evaluating the twisted Morita-Mumford classes bar(h)_p on the Artin braid group B_n, we give the stable algebraic independence of the bar(h)_p's on the automorphism group of the free group, Aut(F_n). This is sharper than the results we obtained by restricting them to the mapping class group.Comment: This is the version published by Geometry & Topology Monographs on 25 February 200

Surface topology and involutive bimodules

We remark some basic facts on homological aspects of involutive Lie bialgebras and their involutive bimodules, and present some problems on surface topology related to these facts.Comment: 19 page