Characterizing dynamic length scales in glass-forming liquids

Reply to Comment by Flenner and Szamel on our paper in Nature Physics 8, 164 (2012).Comment: 1 pag

Locally nilpotent derivations on affine surfaces with a \C^*-action

We give a classification of normal affine surfaces admitting an algebraic group action with an open orbit. In particular an explicit algebraic description of the affine coordinate rings and the defining equations of such varieties is given. By our methods we recover many known results, e.g. the classification of normal affine surfaces with a `big' open orbit of Gizatullin and Popov or some of the classification results of Danilov-Gizatullin, Bertin and others.Comment: Date of writing: 2/03/200

Lifetime of dynamic heterogeneities in a binary Lennard-Jones mixture

A four-time correlation function was calculated using a computer simulation of a binary Lennard-Jones mixture. The information content of the four-time correlation function is similar to that of four-time correlation functions measured in NMR experiments. The correlation function selects a sub-ensemble and analyzes its dynamics after some waiting time. The lifetime of the sub-ensemble selected by the four-time correlation function is calculated, and compared to the lifetimes of slow sub-ensembles selected using two different definitions of mobility, and to the $\alpha$ relaxation time.Comment: accepted for publication in Phys. Rev.

On a result of Miyanishi-Masuda

Let $X$ be an affine surface admitting a unique affine ruling and a $\mathbb C^*$-action. Assume that the ruling has a unique degenerate fibre and that this fibre is irreducible. In this paper we give a short proof of the following result of Miyanishi and Masuda: the universal covering of $X$ is a hypersurface in the affine 3-space given by the equation $x^my=z^d-1$, where $m>1$.Comment: 3 page