This webpage contains source codes of C++ programs to generate hard-particle packings in a Euclidean space of arbitrary dimension. If you use these codes, please reference this paper:

"Packing hard spheres in high dimensional Euclidean spaces", by M. Skoge, A. Donev, F. H. Stillinger, and S. Torquato, 2006

Disclaimer: The programs given here are general molecular-dynamics codes. They can be used to prepape disordered jammed packings of hard particles, if used with the appropriate options. The programs do not automatically generate packings, yet alone jammed packings. The above paper should provide background on the algorithm and appropriate parameters to use.

Please read the following instructions carefully before asking questions, and contact Monica Skoge (mskoge at domain  princeton.edu) for help.

All the files are in the zip archive spheres.zip. The files needed to compile are neighbor.C, spheres.C, box.C, sphere.C, event.C, heap.C, and read_ input.C along with corresponding header (.h) files. The main program is spheres.C and calls the core computational functions in box.C. Simply compile with 
	g++ -O neighbor.C spheres.C box.C sphere.C event.C heap.C read_input.C
The codes use
The dimension of the packing is defined through the constant DIM in vector.h and the input file containing the parameters and input/output file names is in input. In this file, the user can either specify to read in an existing configuration of hard spheres from a file by specifying the appropriate file name in readfile or the user can create a new configuration by setting readfile to new. In the latter case, a configuration of N spheres is created at density initialpf  by random sequential addition.
If the temperature temp is set to zero, then all spheres are given zero initial velocities; otherwise velocities are initially chosen from a Maxwell-Boltzman distribution. The expansion rate growthrate governs the rate at which the sphere diameter increases in units of the simulation box size divided by the sphere velocity. Due to expansion, the kinetic energy increases after collisions. Therefore velocities are rescaled to 1 after every "cycle". The user specifies the number of events per sphere in one cycle with the parameter eventspercyle. Statistics, such as pressure, are calculated after every cycle and outputted to datafile. The simulation runs until reaching either the maximum allowed packing fraction maxpf or the maximum allowed pressure maxpressure. Before terminating, the positions of all spheres are outputted to writefile.

The program produces two output files:
  1. writefile contains the final positions of all the spheres. Its format is explained below.
  2. datafile contains the statistics calculated after each cycle. The statistics include (as columns in this order) the current packing fraction, pressure, total change in kinetic energy before rescaling and the total number of MD events processed.

The ASCII file formats used for storing sphere packing configurations is as follows (in three dimensions):
______________________
n_dims ! Euclidian space dimensionality d
N 1 ! Total number of particles
N ! Same as above
D ! Sphere diameter
Lambda ! Lattice vectors for unit cell, here a unit cube
T T T ! Periodic boundary conditions along all dimensions
x1 y1 z1 ! Coordinates of first sphere center
x2 y2 z2 ! second, etc...
...
______________________
The format may seem weird, but it is chosen to conform to the format for monodisperse packings (i.e. packings where all particles have the same shape and size) described at http://atom.princeton.edu/Packing/Fortran.