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.

• Python code to generate 2D hyperplane intersection process (HIP) point patterns.

  Please cite the following article if you use this code:
  M. A. Klatt, J. Lovrić, D. Chen, S. C. Kapfer, F. M. Schaller, P. W. A. Schönhöfer, B. S. Gardiner, A.-S. Smith, G. E. Schröder-Turk, and S. Torquato, Universal Hidden Order in Amorphous Cellular Geometries, Nature Communications, 10 811 (2019).

• Adaptive Shrinking Cell Monte Carlo Hard-Polyhedron Packing Program.

  Please cite the following articles if you use this code:
  S. Torquato and Y. Jiao. Dense Packings of the Platonic and Archimedean Solids, Nature, 460, 876 (2009).
  S. Torquato and Y. Jiao. Dense Packings of Polyhedra: Platonic and Archimedean Solids, Physical Review E, 80, 041104 (2009).

• 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, 98, 013307 (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).

• 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.

  Please cite the 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).

• Target and inferred potentials that yield low sensitivity of pair statistics on pair potentials.

  Please cite the following paper if you use this data:
  H. Wang, F. H. Stillinger and S. Torquato, Sensitivity of Pair Statistics on Pair Potentials in Many-Body Systems, The Journal of Chemical Physics, 153 124106 (2020).

  Note that the unit distance and energy of the target potentials \(v_0\) are defined in Sec. IIC of the text. The inferred potentials \(v_1\) were obtained using Iterative Boltzmann Inversion or gradient descent optimization of parameters, targeting the pair statistics of \(v_0\) at specified densities and temperatures, as described in the captions of Fig. 3-7 of the text.

Group Affiliations

Department of Chemistry

Princeton Institute for the Science and Technology of Materials

Princeton Center for Theoretical Science

Department of Chemical Engineering

Department of Mechanical Engineering

Program in Applied and Computational Mathematics

Institute for Advanced Study

Useful Links

Crystal Lattice Structures

Bilbao Crystallographic Server