Title: Glassy dynamics on the sphere

Abstract:
We studied a model based on a simple ingredient in order to describe
 the dynamics of a supercooled liquid. Starting from a monodisperse
 Lennard-Jones system on the euclidean plane, we added frustration by
 curving the space to form a sphere of arbitrary radius.

 Using a molecular dynamics algorithm, we showed that this system
 indeed behaves like a glassy liquid.
 The dynamics, caracterized by the self-intermediate scattering
 function Fs(k,t), slows down strongly and changes shape at low
 temperature, for a small variation of the statics, which we tried 
 to explain theoretically  through the study of the mode coupling 
 theory (MCT) on the sphere.

 We derived the dynamical equation of spherical MCT and studied the
 long time limit of its solution. The spherical MCT predicts a dynamic
 transition similar to the one predicted by euclidean MCT, which does
 not allow us to explain the effect of curvature on Fs(k,t), though the
 curvature has an influence on the value of the transition temperature.

 Finally, we took interest in the role of "defects", among which a
 minimal number of 12 is imposed by topology. At low temperature, the
 defects tend to form linear structures, which is predicted
 theoretically and observed in some experiments. The defects have a
 strong contribution in the relaxation, but the role of other particles
 is however not negligible.