DOI: 10.5061/dryad.9kd51c5wm
title: Data from: Non-equilibrium dynamics of hard spheres in the fluid, crystalline, and glassy regimes

description: We investigate the response of a system of hard spheres to two classes of
 perturbations over a range of densities spanning the fluid, crystalline,
 and glassy regimes within a molecular dynamics framework. First, we
 consider the relaxation of a “thermal inhomogeneity,” in which a central
 region of particles is given a higher temperature than its surroundings
 and is then allowed to evolve under Newtonian dynamics. In this case, the
 hot central “core” of particles expands and collides with the cold
 surrounding material, creating a transient radially expanding “compression
 wave,” which is rapidly dissipated by particle-particle collisions and
 interactions with periodic images at the boundary, leading to a rapid
 relaxation to equilibrium. Second, we consider a rapid compression of the
 spheres into a disordered glassy state at high densities. Such rapidly
 compressed systems exhibit very slow structural relaxation times, many
 orders of magnitude longer than thermalization times for simple
 temperature inhomogeneities. We find that thermal relaxation of the
 velocity distribution is determined simply by the total collision rate,
 whereas structural relaxation requires coordinated collective motion,
 which is strongly suppressed at high density, although some particle
 rearrangement nevertheless occurs. We further find that collisions
 propagate significantly faster through glassy systems than through
 crystalline systems at the same density, which leads to very rapid
 relaxation of velocity perturbations, although structural relaxation
 remains very slow. These results extend the validity of previous
 observations that glassy systems exhibit a hybrid character, sharing
 features with both equilibrium and nonequilibrium systems. Finally, we
 introduce the hard-sphere causal graph, a network-based characterization
 of the dynamical history of a hard-sphere system, which encapsulates
 several useful metrics for characterizing hard-sphere systems within a
 single structure, and which emphasizes the role of causality in these
 systems.
description: # Data from: Non-equilibrium dynamics of hard spheres in the fluid,
 crystalline, and glassy regimes Dataset DOI:
 [10.5061/dryad.9kd51c5wm](10.5061/dryad.9kd51c5wm) ## Description of the
 data and file structure Data were prepared from molecular dynamic
 simulations of hard spheres. All datasets are included to reproduce the 12
 figures in the manuscript "Non-Equilibrium Dynamics of Hard Spheres
 in the Fluid, Crystalline, and Glassy Regimes" by Kafker et al.,
 accepted for publication in *Physical Review E*. File names contain the
 relevant quantities, including the figure to which the data belongs. If a
 figure contains an inset, the word inset is included in the file name. All
 files are text files. The relationship between the contents of the figures
 and the contents of the files will be obvious, but are also listed below
 for completeness. ### Files and variables #### File: Fig1.txt
 **Description:**  First column is packing fraction. Second column is
 average collision rate. #### File: Fig1InsetTimes.txt **Description:** 
 Times at which collision rates are all evaluated for inset of Fig. 1. ####
 File: Fig2.txt **Description:**  First column is time. Second column is
 equilibrium collision rate. Third column is inhomogeneous collision rate.
 #### File: Fig5.txt **Description:**  First column is packing fraction.
 Second column is relaxation time. #### File: Fig1InsetGammas.txt
 **Description:**  Each row represents the particle-averaged collision rate
 over time. #### File: Fig6Times.txt **Description:**  Times at which
 collision rates are evaluated. #### File: Fig3Gammas.txt **Description:** 
 Each row represents the collision rate as a function of time for each
 density. #### File: Fig4.txt **Description:**  First column is time,
 second column is rate for solid system, third column is rate for fluid
 system. #### File: Fig7RapidCompression.txt **Description:**  First column
 is time, second column is collision rate. #### File: Fig7Equilibrium.txt
 **Description:**  First column is time, second column is collision rate.
 #### File: Fig3Times.txt **Description:**  Times at which all collision
 rates are evaluated. #### File: Fig6Gammas.txt **Description:**  Each row
 corresponds to the collision rate over time at the appropriate density.
 #### File: Fig8Equilibrium.txt **Description:**  For equilibrium systems,
 first column is packing fraction, second column is mean collisional
 contact number, third column is standard deviation. #### File:
 Fig2Inset.txt **Description:**  Each row represents the location of a
 sphere in the box. #### File: Fig7Inset.txt **Description:**  Each row
 represents the location of a sphere in the box. #### File:
 Fig9AdjacencyMatrix.txt **Description:**  Adjacency matrix of the directed
 acyclic graph. #### File: Fig9Vertices.txt **Description:**  Vertex labels
 of the directed acyclic graph. #### File: Fig10FullAdjacencyMatrix.txt
 **Description:**  Adjacency matrix of the full directed acyclic graph.
 #### File: Fig8RapidCompression.txt **Description:**  For rapidly
 compressed systems, first column is packing fraction, second column is
 mean collisional contact number, third column is standard deviation. ####
 File: Fig10FullVertices.txt **Description:**  Vertex labels of the full
 directed acyclic graph. #### File: Fig10HighlightedVertices.txt
 **Description:**  Vertex labels of the highlighted subgraph. #### File:
 Fig11_Crystal1.txt **Description:**  Sphere locations for the first frame
 of the crystal time series. #### File: Fig11_Crystal3.txt
 **Description:**  Sphere locations for the third frame of the crystal time
 series. #### File: Fig11_Crystal5.txt **Description:**  Sphere locations
 for the fifth frame of the crystal time series. #### File:
 Fig10HighlightedAdjacencyMatrix.txt **Description:**  Adjacency matrix for
 the highlighted subgraph. #### File: Fig11_Glassy3.txt **Description:** 
 Sphere locations for the third frame of the glassy time series. #### File:
 Fig11_Glassy4.txt **Description:**  Sphere locations for the fourth frame
 of the glassy time series. #### File: Fig11_Crystal4.txt **Description:** 
 Sphere locations for the fourth frame of the crystal time series. ####
 File: Fig11_Glassy1.txt **Description:**  Sphere locations for the first
 frame of the glassy time series. #### File: Fig11_Crystal2.txt
 **Description:**  Sphere locations for the second frame of the crystal
 time series. #### File: Fig12Crystal.txt **Description:**  Sphere
 locations for the crystalline configuration. #### File: Fig11_Glassy2.txt
 **Description:**  Sphere locations for the second frame of the glassy time
 series. #### File: Fig11_Glassy5.txt **Description:**  Sphere locations
 for the fifth frame of the glassy time series. #### File: Fig12Glassy.txt
 **Description:**  Sphere locations for the glassy configuration.