Ball Stacking on Constant Curvature Torus

This work scored 99 points in the soft matter course.

Introduction

Figure 1. A bitorus in 3d space

A bitorus shown in the picture above is a closed surface with a genus of 2. While there is no constant negative curvature surface in three-dimensional space, I constructed a bitorus with constant negative curvature using intrinsic geometry method. I found that a generalized periodic boundary condition is equivalent to a closed surface with constant curvature.

Figure 2. Simulated annealing

In order to study the stacking problem under the LJ potential situation, I used both Monte Carlo algorithm and Langevin dynamics for simulated annealing.

Get paper and source code

See this article for details.

Source code on bhcao/balls-on-surface.