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Identifying Structural Flow Defects in Disordered Solids Using Machine-Learning Methods University of Pennsylvania ScholarlyCommons Department of Physics Papers Department of Physics 3-9-2015 Identifying Structural Flow Defects in Disordered Solids Using Machine-Learning Methods E. D. Cubuk Harvard University Samuel Schoenholz University of Pennsylvania, [email protected] Jennifer M. Rieser University of Pennsylvania, [email protected] B. D. Malone Harvard University J. Rottler University of British Columbia See next page for additional authors Follow this and additional works at: https://repository.upenn.edu/physics_papers Part of the Physics Commons Recommended Citation Cubuk, E. D., Schoenholz, S., Rieser, J. M., Malone, B. D., Rottler, J., Durian, D. J., Kaxiras, E., & Liu, A. J. (2015). Identifying Structural Flow Defects in Disordered Solids Using Machine-Learning Methods. Physical Review Letters, 114 (10), 108001-1-108001-5. http://dx.doi.org/10.1103/ PhysRevLett.114.108001 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/physics_papers/592 For more information, please contact [email protected]. Identifying Structural Flow Defects in Disordered Solids Using Machine-Learning Methods Abstract 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. Disciplines Physical Sciences and Mathematics | Physics Author(s) E. D. Cubuk, Samuel Schoenholz, Jennifer M. Rieser, B. D. Malone, J. Rottler, Douglas J. Durian, E. Kaxiras, and Andrea J. Liu This journal article is available at ScholarlyCommons: https://repository.upenn.edu/physics_papers/592 week ending PRL 114, 108001 (2015) PHYSICAL REVIEW LETTERS 13 MARCH 2015 Identifying Structural Flow Defects in Disordered Solids Using Machine-Learning Methods † E. D. Cubuk,1,* S. S. Schoenholz,2, J. M. Rieser,2 B. D. Malone,1 J. Rottler,3 D. J. Durian,2 E. Kaxiras,1 and A. J. Liu2 1Department of Physics and School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA 2Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA 3Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T1Z4, Canada (Received 25 September 2014; published 9 March 2015) 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. DOI: 10.1103/PhysRevLett.114.108001 PACS numbers: 45.70.-n, 61.43.-j, 62.20.F-, 83.50.-v All solids flow at high enough applied stress and melt at The results for Lennard-Jones systems show that the high enough temperature. Crystalline solids flow [1] and correlation between structure and irreversible rearrange- premelt [2] via localized particle rearrangements that occur ments does not degrade with increasing temperature, even preferentially at structural defects known as dislocations. above the dynamical glass transition, and is equally strong The population of dislocations therefore controls both how in two and three dimensions. Finally, we exploit the method crystalline solids flow and how they melt. In disordered to discover which structural properties distinguish soft solids, it has long been hypothesized that localized particle particles from the rest of the system and to understand rearrangements [3] induced by stress or temperature also why previous attempts to identify them by structural occur at localized flow defects [4–6]. Like dislocations in analysis have failed. crystals [7], flow defects in disordered solids are particu- Physically motivated quantities such as free volume or larly effective in scattering sound waves, so analyses of bond orientational order correlate with flow defects [12] but the low-frequency vibrational modes [8] have been used are insufficient to identify them a priori. We introduce a successfully to demonstrate the existence of localized flow large set of quantities that are each less descriptive, but defects [7,9–17]. However, all attempts to identify flow when used as a group provide a more complete and defects [18,19] directly from the structure, without using unbiased description of local structure. These quantities knowledge of the interparticle interactions, have failed have been used to represent the potential energy landscape [18,19]. Likewise, in supercooled liquids, purely structural of complex materials from quantum mechanical calcula- measures correlate only weakly with kinetic heterogeneities tions [25]. For a system composed of multiple species of particles, we define two families of structure functions for [17], although correlations between structure and dynamics each particle i, have been established indirectly [20–24]. X Here we introduce a novel application of machine- − −μ 2 2 X ; μ ðRij Þ =L learning (ML) methods to identify “soft” particles that GY ði Þ¼ e ; ð1Þ are susceptible to rearrangement or, equivalently, that j X X belong to flow defects, from the local structural geometry − R2 R2 R2 =ξ2 ζ ΨX ; ξ λ ζ ð ijþ ikþ jkÞ 1 λ θ alone. Note that our goal is not to identify particles that YZði ; ; Þ¼ e ð þ cos ijkÞ ; undergo rearrangements—this requires studying their j k dynamics. Rather, our goal is to identify the structural ð2Þ characteristics that distinguish particles that are susceptible to rearrangement from those that are not. We apply the where Rij is the distance between particles i and j; θijk is method to two very different systems of an experimental the angle between particles i, j, and k; L, μ, ξ, λ, and ζ are frictional granular packing under uniaxial compression and constants; X,Y,Z are labels that identify the different a model thermal Lennard-Jones glass in both two and three species of particles in the system, with the correspondence dimensions (see Fig. 1). The analysis of granular packing i ↔ X, j ↔ Y, k ↔ Z. By using many different values of shows that our method succeeds even when previous the constants μ, ξ, λ, and ζ we generate many structure methods based on vibrational modes [12] are inapplicable. functions in each family that characterize different aspects 0031-9007=15=114(10)=108001(5) 108001-1 © 2015 American Physical Society week ending PRL 114, 108001 (2015) PHYSICAL REVIEW LETTERS 13 MARCH 2015 of a particle’s local configuration; for a list, see the 1 X D2 ðiÞ ≡ min ½R ðt þ ΔtÞ − ΛR ðtÞ2 ; ð3Þ Supplemental Material [26]. The first family of structure min Λ ij ij z j functions G characterizes radial density properties of the Ψ neighborhood, while the second family characterizes which characterizes the magnitude of nonaffine displace- bond orientation properties. The sums are taken over ment during a time interval Δt. Here, the sum runs over particle pairs whose distance is within a large cutoff neighbors j within a distance of RD of particle i, R is the S c ij Rc. Our results are qualitatively insensitive to the center-center displacement between particles i and j, and z S choice of Rc as long as it includes several neighbor shells. is the number of neighbors within RD. The quantity is X ; μ c Having characterized local structure through GY ði Þ minimized over choices of the local strain tensor Λ. We find and ΨX ði; ξ; λ; ζÞ, we introduce a method to infer from 2 D Δ YZ that Dmin is insensitive to the choice of Rc and t so long this information the location of flow defects in disordered D as Rc is large enough to capture the particles local solids. Generically, we begin with a set of N particles to be neighborhood and Δt is longer than the ballistic time classified as “soft” or “hard.” Each particle is described by scale. A particle is said to have undergone a rearrangement 2 2 2 asetofM variables derived from the two families of if D ≥ D 0. We choose D 0 such that approximately X ΨX μ ξ λ min min; min; functions GY and YZ by varying the constants , , , 0.15% of the particles from each species in each system and ζ (here M ¼ 160); this is represented by the set of has gone through a rearrangement, although the results 2 vectors fF1; …; F g,whereF constitutes an embedding N i depend little on the specific choice of Dmin;0 (Supplemental of the local environment of a particle i, constructed at a Material [26]). RM time ti,in . We select at random a subset of n of these We first test our approach on an experimental system of particles (the “training set”) and label the particles with an two-dimensional (d ¼ 2) “pillars” of particles. A bidisperse 0 1 1 index r ¼ ; . A particle i is labeled as ri ¼ if it pillar made up of grains (plastic cylinders resting upright on rearranges (the details of which will be discussed below) a horizontal substrate) is situated between two plates in a between a time ti, when the structure is characterized, and custom-built apparatus. The bottom plate is fixed, and the a time ti þ Δt and with ri ¼ 0 if it does not rearrange in top plate is driven into the pillar at a constant speed of this time interval.
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