There exists a variety of theories of the glass transition and many more numerical models. But because the models need built-in complexity to prevent crystallization, comparisons with theory can be difficult. We study the dynamics of a deeply supersa
turated emph{monodisperse} four-dimensional (4D) hard-sphere fluid, which has no such complexity, but whose strong intrinsic geometrical frustration inhibits crystallization, even when deeply supersaturated. As an application, we compare its behavior to the mode-coupling theory (MCT) of glass formation. We find MCT to describe this system better than any other structural glass formers in lower dimensions. The reduction in dynamical heterogeneity in 4D suggested by a milder violation of the Stokes-Einstein relation could explain the agreement. These results are consistent with a mean-field scenario of the glass transition.
We recently found that crystallization of monodisperse hard spheres from the bulk fluid faces a much higher free energy barrier in four than in three dimensions at equivalent supersaturation, due to the increased geometrical frustration between the s
implex-based fluid order and the crystal [J.A. van Meel, D. Frenkel, and P. Charbonneau, Phys. Rev. E 79, 030201(R) (2009)]. Here, we analyze the microscopic contributions to the fluid-crystal interfacial free energy to understand how the barrier to crystallization changes with dimension. We find the barrier to grow with dimension and we identify the role of polydispersity in preventing crystal formation. The increased fluid stability allows us to study the jamming behavior in four, five, and six dimensions and compare our observations with two recent theories [C. Song, P. Wang, and H. A. Makse, Nature 453, 629 (2008); G. Parisi and F. Zamponi, Rev. Mod. Phys, in press (2009)].
We discuss an implementation of molecular dynamics (MD) simulations on a graphic processing unit (GPU) in the NVIDIA CUDA language. We tested our code on a modern GPU, the NVIDIA GeForce 8800 GTX. Results for two MD algorithms suitable for short-rang
ed and long-ranged interactions, and a congruential shift random number generator are presented. The performance of the GPUs is compared to their main processor counterpart. We achieve speedups of up to 80, 40 and 150 fold, respectively. With newest generation of GPUs one can run standard MD simulations at 10^7 flops/$.
