Identifying Structural Flow Defects in Disordered Solids Using Machine-Learning Methods

We use machine-learning methods on local structure to identify flow defects—or particles susceptible to rearrangement—in jammed and glassy systems. We apply this method successfully to two very different systems: a two-dimensional experimental realization of a granular pillar under compression and a Lennard-Jones glass in both two and three dimensions above and below its glass transition temperature. We also identify characteristics of flow defects that differentiate them from the rest of the sample. Our results show it is possible to discern subtle structural features responsible for heterogeneous dynamics observed across a broad range of disordered materials.

Figure 1

Snapshot configurations of the two systems studied. Particles are colored gray to red according to their $D_{\min }^2$ value. Particles identified as soft by the SVM are outlined in black. (a) A snapshot of the pillar system. Compression occurs in the direction indicated. (b) A snapshot of the $d=2$ sheared, thermal Lennard-Jones system.

Figure 2

Probability that a particle of a given $D_{\min }^2$ value is soft. The vertical dashed lines are corresponding $D_{\min ,0}^2$ values. (a) The result for the pillar system, where $d_{AA}$ refers to the large grain diameter (since this is a granular system with macroscopic grains, thermal fluctuations are negligible). (b) The result of using an SVM trained at a temperature $T$ ($T=0.1,0.2,0.3$ and 0.4 shown in different colors) to classify data at the same temperature for the $d=2\mathrm{LJ}$ glass. [(c), (d)] Results for species $A$ and $B$, respectively, for the $d=3$ system at $T=0.4,0.5$ and 0.6.

Figure 3

Radial distribution functions averaged over hard (black dark lines) or soft (red light lines) particles. $g_{AB}$ and $g_{BA}$ functions of soft particles are not equal to each other since they refer to different kinds of regions: neighbors of soft particles from species $A$ and neighbors of soft particles from species $B$, respectively.

Figure 4

(a) Distribution of $G_B^A(i;r_{\text{peak}}^{AB})$, proportional to the Gaussian weighted density at $r_{\text{peak}}^{AB}$, for soft (red dark) and hard (blue medium dark and green light) particles; $r_{\text{peak}}^{AB}$ corresponds to the first peak of $g_{AB}$ or $g_{BA}$. (b) Distribution of ${\mathrm{\Psi }}_{AB}^B(i;2.07{\sigma }_{AA},1,2)$, proportional to the density of neighbors with small bond angles near a particle $i$, for soft (red dark) and hard (blue medium dark and green light) particles. The inset shows examples of configurations with corresponding radial and bond orientation properties, where dark (light) gray neighbors are of species $A(B)$.