Salvatore Torquato (Princeton University)

New Algorithm to Generate Jammed Sphere Packings

I describe a new algorithm to generate a diverse class of jammed disordered and ordered sphere packings with very high fidelity across Euclidean space dimensions. The task is posed as an optimization problem that is solved using linear programming techniques [1]. I will discuss how the algorithm leads to efficient generation of the densest sphere packings in high dimensions [2], a problem of importance in digital communications, and its ability to produce maximally random jammed sphere packings that are exactly isostatic in two and three dimensions with novel characteristics that have heretofore not been observed [3].

References:

1. S. Torquato and Y. Jiao, “Robust Algorithm to Generate a Diverse Class of Dense Disordered and Ordered Sphere Packings Via Linear Programming,” Physical Review E, 82, 061302 (2010).

2. E. Marcotte and S. Torquato, “Efficient Linear Programming Algorithm to Generate the Densest Lattice Sphere Packings,” Physical Review E, 87,
063303 (2013).

3. S. Atkinson, F. H. Stillinger, and S. Torquato, “Detailed Characterization of Rattlers in Exactly Isostatic, Strictly Jammed Sphere Packings,” Physical Review E, 88, 062208 (2013).