#### We have made available several computer codes used in our research projects related to disordered packings of hard spheres and ellipsoids in low dimensions and sphere packings in high dimensions.

- A Matlab function to compute surface correlation functions \(F_{ss}, F_{sv}\) as well as \(F_{vv}\) for two-phase digitized media in three-dimensional Euclidean space \(\mathbb{R}^3\).
Please cite the following article if you use this code:

Z. Ma and S. Torquato, Precise algorithms to compute surface correlation functions of two-phase heterogeneous media and their applications, Physical Review E, in press (2018). - Generate Sphere Packings in Arbitrary Euclidean Dimension. Registration, Instructions and source code are found here.
Please cite the following if you use this code:

M. Skoge, A. Donev, F. H. Stillinger and S. Torquato,*Packing Hyperspheres in High-Dimensional Euclidean Spaces*,**Physical Review E 74**, 041127 (2006). - Event-driven MD Simulation of Nonspherical Particles with Applications to Ellipses and Ellipsoids. Instructions and executables can be found here.
Please cite following if you use this code:

A. Donev, S. Torquato, and F. H. Stillinger,*Neighbor List Collision-Driven Molecular Dynamics for Nonspherical Hard Particles: II. Applications to Ellipses and Ellipsoids*,**Journal of Computational Physics**,**202**, 765 (2005).The most up-to-date instructions and executables are maintained on Aleksandar Donev’s homepage.

- Torquato-Jiao Sequential Linear Programming method for generating jammed packings of spheres. Download here (Github)
Please cite following if you use this code:

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).

## Slides from Recent talks

- Unusual Classical Ground States of Matter, PACM Colloquium, February, 16, 2009.
- Sphere Packings in Low Dimensions, PCCM Summer School, August 11, 2008.
- Sphere Packings in High Dimensions, PCCM Summer School, August 11, 2008.

## Movies

- An animation of the LS algorithm packing a system of 100 monodisperse disks (August 18th, 2014) The Lubachevsky-Stillinger molecular dynamics algorithm is used to produce a dense packing of monodisperse disks within a squarefundamental cell with periodic boundary conditions. The dimensionless growth rate is 0.01. The initial condition was generated via RSA at a packing fraction of 0.10
- An animation of the TJ algorithm packing a system of 100 monodisperse disks (August 18th, 2014) The Torquato-Jiao (“TJ”) sphere packing protocol is used to produce a collectively-jammed packing of 100 monodisperse spheres inside a fixed square fundamental cell with periodic boundary conditions. The initial condition was generated via RSA at a packing fraction of 0.10

## Data

- Representative densest-known (or dense) binary sphere packings with various size ratio and compositions.
Please see the “read_me.txt” for detailed instructions and cite the following work:

A. B. Hopkins, F. H. Stillinger, and S. Torquato, Densest Binary Sphere Packings,**Physical Review E**, 85, 021130 (2012). - Coordinates of strictly jammed MRJ packings of 2000 monodisperse spheres in three dimensions 1000-prt packinkgs as generated by the Torquato-Jiao algorithm described above (August 18th, 2014).

Please cite following paper if you use this data:

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).

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).