Molecular Dynamics in a curved space: physical motivations, methods, and
parallel implementation.
Fran??ois Sausset
Physics Department, Technion
As it is well known, the dimensionality of the space in which a system
is embedded plays a major role on the physical behaviour of that system.
Another major property of the space is its metric and more particularly
its curvature. During my PhD, I studied a new model of glass-forming
liquids which uses the curvature of the embedding space as a key
ingredient: by curving a plane, the 2D crystal can be avoided and a
glass can be formed. Moreover, by varying the (spatially) constant
curvature of the plane, one can tune the properties of the glass-forming
liquid and thus describe the wide range of glassy behaviours.
This model has been first studied numerically by using Molecular
Dynamics to look at the statics and dynamics of the system when cooling it.
So, I had to generalize the Verlet algorithm to the hyperbolic plane
(plane of constant negative Gaussian curvature), as well as introducing
a way to build generic periodic boundary conditions on such a space
(only a few ways on the infinity of all possible ones where known
previously). I also had to parallelize the simulation code to access
interesting regions of the parameter space.
Finally, I will give a brief summary of the latest results obtained
through these simulations.