These data sets were studied in:

**"Visualizing free energy landscapes for four hard disks"**

ER Weeks & K Criddle, Phys. Rev. E 102, 062153 (2020)- Abstract / PDF / journal / arXiv:2001.11635v2

**Data from Figs. 5 and 6**:
fig5.txt,
fig6.txt.
Format of data: text file with 15 columns, 400 rows,
corresponding to the trajectories shown in Figs. 5 and 6. Columns 1-8 are
(x1,y1,x2,y2,x3,y3,x4,y4): the real-space coordinates. Columns 9,
10 correspond to (d1,d2) plotted in panel (g). Columns 11-13
are (c1,c2,c3) plotted in panel (f). Columns 14-15 are (u1,u2)
plotted in panel (h).
The locations marked by (b,c,d,e) in Fig. 5
correspond to rows 1, 331, 371, and 554 in the fig5 data.
The locations marked by (b,c,d,e) in Fig. 6
correspond to rows 1, 101, 201, and 400 in the fig6 data.

**Data from Fig. 7**:
fig7a-ep03.txt,
fig7b-ep02.txt,
fig7c-ep01.txt.
Format of data: text file, columns = (time, raw c1, smoothed c1).
The data plotted in the paper are smoothed over a time window
of 10 tau_B, which corresponds to 100, 500, and 10 data points
(as the raw data were sampled differently).

**Data from Fig. 8**: fig8.txt. Format of data: text file,
columns = (epsilon, tau, 0 or 1). The third column is 0 for diffusive dynamics (blue
circles in Fig. 8) or 1 for ballistic dynamics (red triangles in Fig. 8).

**Data from Fig. 9**: fig9.txt. Text file, 4 columns = (x,y,z,F)
where F is the free energy. The minimum free energy is -7.11,
the maximum is 0. As usual, the points with maximum free energy
are nearly all at the edges of the phase space (the borders of
the "holes" that correspond to cube edges). Note that the
(x,y,z) points are not sampled uniformly over the sphere, in part
because there's no straightforward way to do that. Rather, the
points are generated on the surface of a cube and projected down
to a unit sphere. For that matter, the original histogram of
Omega is done based on a cubical surface. We first find the
coordinates (c1,c2,c3) and then, knowing that this is symmetric,
consider the coordinates in the first octant (all positive
values). We then note further symmetry and project the points
onto one face of a cube, so that Omega can be compiled in a 2D
array with square histogram bins. It is this data that then gets
turned back into a spherical projection. In the paper, when
discussing barrier heights, we account for the fact that the
square bins on the cube face become unevenly sized bins in the
spherical phase space (which is what we really care about). That
is, the same number of counts in a bin that's actually narrower
in size sould be counted as a larger value of Omega than those
counts in a bin that is wider.
One more related data file:
fig6f.txt: same thing, but for the 3D
free-energy landscape of Fig. 6(f). The minimum free energy is -8.32,
the maximum is -0.01.

**Data from Fig. 10**: PGM-formatted images, with
contrast stretched. JPEG versions are provided, with quality set
to 100%, although nonetheless JPEG compression has changed some of the
pixel intensities by +/- 1. So for maximum quality, I recommend
using the PGM images if you care about this from a data
standpoint rather than merely wanting a qualitatively correct
image.

- fig10a.pgm: I made a histogram of Omega and took the negative natural log of the data: the results are between -13.23 (bottom of free energy landscape = most likely state) and 0.00 (states with only 1 count; these were found at the very edges of the landscape). The contrast was stretched by adding 13.5 and then multiplying by 18.8, so that the bottom of the free energy landscape has value 5 and the top points have value 253 in the PGM image.
- fig10b.pgm: The units are a bit arbitrary; the contrast was stretched by multiplying the raw values from the simulation by 6400. Note that the contrast was further enhanced in the paper.
- fig10c.pgm: Similar to (a), I made a histogram of Omega and took the negative natural log of the data. In this case, the results are between -14.72 and 0.00. Again, the states with only 1 or 2 counts are at the very edges of the landscape. The contrast was stretched by adding 15.0 and then multiplying by 17.0.
- fig10d.pgm: The units are a bit arbitrary; the contrast was stretched by multiplying the raw values from the simulation by 85000. Note that the contrast was further enhanced in the paper.
- fig10a.jpg -- JPEG version
- fig10b.jpg -- JPEG version
- fig10c.jpg -- JPEG version
- fig10d.jpg -- JPEG version

**Data from Fig. 11**: fig11.txt. Format of data: text file,
columns = (epsilon, u-height [green diamonds], c-height [red squares], d-height [purple
triangles], log(tau) [filled blue circles]). The terms in [] describe the symbols of
Fig. 11. The heights are the free energy barrier heights for the landscapes based on
the u, c, and d variables.

**Trajectory data:**
The trajectory data are in the format [x1,y1,x2,y2,x3,y3,x4,y4]. Note this
format differs from almost all of our other track arrays available
on the Weeks lab data pages. These files are small pieces of
the simulation files, some of which would be larger than 100 MB.
Note also that when we calculated the free energy landscapes by
compiling the microstate counts (Omega), we did this from every
single time step simulated. In contrast, these trajectories aren't
saved every single time step, but rather every dN time steps (for
the diffusive data).

For the ballistic data trajectory files, the data are spaced every 0.01 time increments. The particles are defined to have an initial velocity of 1.0, so that v1^2 + v2^2 + v3^2 + v4^2 = 4.0 holds true for all times due to conservation of kinetic energy. Thus if one takes the displacements from one line of data to the next, and divides by 0.01 to convert to velocity, this relation is essentially true (with the exceptions being times when a collision occurs, so that the displacement is not v*dt.) The units of length are in terms of particle radius (R = 1).

filename | epsilon | data saved every dN steps | dynamics |
---|---|---|---|

traj-ep10j.txt (in a zip file) | 1.0 | 1000 | diffusive |

traj-ep04j.txt (in a zip file) | 0.4 | 10000 | diffusive |

traj-ep02j.txt (in a zip file) | 0.2 | 10000 | diffusive |

traj-ep01j.txt (in a zip file) | 0.1 | 20000 | diffusive |

traj-ep10p.txt (in a zip file) | 1.0 | n/a | ballistic |

traj-ep05p.txt (in a zip file) | 0.5 | n/a | ballistic |

traj-ep03p.txt (in a zip file) | 0.3 | n/a | ballistic |

traj-ep02p.txt (in a zip file) | 0.2 | n/a | ballistic |

**More ballistic data:** The files above are
trajectory files. These files below list the collisions that have
occured, from which one can reconstruct trajectories at any
temporal resolution you wish. These are again text files, with
18 columns of data: [x1, y1, vx1, vy1, x2, y2, vx2, vy2, x3,
y3, vx3, vy3, x4, y4, vx4, vy4, C, time]. The first 16 columns
are the positions and velocities of each particle right before a
collision occurs. Given that the collision is at this moment,
either two particles will be in contact (separation
distance = 2) or one particle will be in contact with the outer
wall. The data "C" indicates which collision is
happening. C = [0,1,2,3] indicates that disk [0,1,2,3] is
colliding with the wall. C = [4,5,6,7,8,9] indicates collisions
between two disks: respectively 0+1, 0+2, 0+3, 1+2, 1+3, or 2+3.
There's nothing really that useful about the variable C, I just
included it for debugging purposes.