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arxiv: 2606.24376 · v1 · pith:7QPSM2MDnew · submitted 2026-06-23 · ❄️ cond-mat.dis-nn · cond-mat.mes-hall· cond-mat.mtrl-sci· cond-mat.soft· math.GN

The Physics of Topological Defects in Glasses

Arabinda Bera , Peter Schall , Timothy W. Sirk , Vijayakumar Chikkadi , Alessio Zaccone This is my paper

Pith reviewed 2026-06-25 22:24 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.mes-hallcond-mat.mtrl-scicond-mat.softmath.GN
keywords topological defectsglassesamorphous solidsplasticitynon-affine displacementsvibrational modesshear bands
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The pith

Topological defects appear in glasses and correlate with sites of plastic activity and shear bands.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper reviews recent theoretical, numerical and experimental work identifying topological invariants inside vibrational eigenmodes, non-affine displacement fields and deformation-induced vector fields of amorphous solids. These invariants are reported to coincide with soft spots that undergo localized rearrangements, yielding and shear-band formation. A sympathetic reader would care because the same topological language that organizes plasticity in crystals might now apply to disordered materials, offering a route to predict mechanical failure from defect topology rather than from local stress alone. The review assembles the underlying concepts of Burgers vectors and non-affine plasticity and evaluates the current evidence and open questions.

Core claim

Topological defects play a central role in the mechanical behavior of crystalline materials, yet their relevance to amorphous solids has only recently begun to emerge. Over the last few years, theoretical, computational, and experimental studies have revealed the presence of well-defined topological invariants in vibrational eigenmodes, non-affine displacement fields, and deformation-induced vector fields of glasses. These defects have been shown to correlate strongly with soft spots, localized plastic rearrangements, yielding, and shear-band formation, suggesting a new perspective on the microscopic origins of plasticity in disordered materials.

What carries the argument

Topological invariants defined through Burgers vectors applied to non-affine displacement fields and vibrational eigenmodes.

If this is right

  • Plastic events in glasses can be classified and predicted using the same topological quantities employed for crystals.
  • Shear-band formation is expected to initiate at clusters of these defects.
  • Yielding thresholds become linked to the density and arrangement of topological invariants rather than solely to local stress or free volume.
  • A unified topological description of plasticity and mechanical failure becomes possible for both ordered and disordered solids.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the defects prove causal, targeted annealing protocols might be designed to reduce their density and thereby increase glass toughness.
  • The approach could be tested against existing theories of shear-transformation zones by checking whether topological charge predicts zone activation sites.
  • Direct visualization of the invariants in colloidal glasses under shear would provide an independent experimental check.

Load-bearing premise

The topological invariants identified in modes and displacement fields are mechanistically tied to plastic events rather than incidental correlations.

What would settle it

High-resolution simulations or experiments that find no statistical spatial overlap between the locations of these topological invariants and the sites of subsequent plastic rearrangements or shear-band nucleation.

Figures

Figures reproduced from arXiv: 2606.24376 by Alessio Zaccone, Arabinda Bera, Peter Schall, Timothy W. Sirk, Vijayakumar Chikkadi.

Figure 1
Figure 1. Figure 1: Dislocation in crystal and Burgers circuit. ( [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Topological structure of Eshelby-like plastic rearrangements. ( [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Representative topological defects in two and three spatial dimensions. ( [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 12
Figure 12. Figure 12: [ [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗
Figure 4
Figure 4. Figure 4: Topological defects in vibrational eigenmodes of amorphous solids and their con [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Evolution of the generalized Burgers vector during deformation and its connec [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Collective organization of topological defects during deformation of a three [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Topological organization of defects during shear-band formation in a two [PITH_FULL_IMAGE:figures/full_fig_p021_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Burgers rings as topological signatures of Eshelby-like plastic events in amor [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Hedgehog topological defects (HTDs) in three-dimensional amorphous solids [PITH_FULL_IMAGE:figures/full_fig_p042_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Topology of vibrational eigenmodes in a 2D Colloidal Glass. [PITH_FULL_IMAGE:figures/full_fig_p043_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: A dense colloidal monolayer under shear due to an optical vortex. ( [PITH_FULL_IMAGE:figures/full_fig_p044_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Plastic deformation driven by topological defects during shear and subsequent [PITH_FULL_IMAGE:figures/full_fig_p045_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Elements and correlations of plasticity in 3D sheared colloidal glasses. ( [PITH_FULL_IMAGE:figures/full_fig_p046_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Colloidal glasses under shear in 3D. (a) Schematic of the experimental setup showing a cross-section of shear-cell mounted on top of a confocal microscope. The shear￾cell has two parallel boundaries, and the top boundary is moved relative to the bottom one. (b) A reconstruction of the coarse-grained nonaffine displacement field of particles in a 2D section. (c) A positive and a negative hedgehog defects i… view at source ↗
Figure 15
Figure 15. Figure 15: Percolation of topological defects. (a) Average non-affine displacement mea￾sure D2 min as a function of applied shear strain γ. A change in slope is observed at the yield￾ing transition, indicated by the shaded regions corresponding to the pre-yielding (blue) and yielding (red) regimes, reflecting the onset of enhanced non-affine motion. (b) To￾tal number of hedgehog topological defects, NHTD, extracted … view at source ↗
read the original abstract

Topological defects play a central role in the mechanical behavior of crystalline materials, yet their relevance to amorphous solids has only recently begun to emerge. Over the last few years, theoretical, computational, and experimental studies have revealed the presence of well-defined topological invariants in vibrational eigenmodes, non-affine displacement fields, and deformation-induced vector fields of glasses. These defects have been shown to correlate strongly with soft spots, localized plastic rearrangements, yielding, and shear-band formation, suggesting a new perspective on the microscopic origins of plasticity in disordered materials. In this review, we provide a comprehensive overview of recent developments in the rapidly growing field of topological defects in glasses. We discuss the underlying theoretical concepts, including Burgers vectors, non-affine plasticity, vibrational modes, and topological invariants, and review recent numerical and experimental advances. Finally, we assess the current achievements, limitations, and open questions, and discuss future directions toward a unified topological description of plasticity and mechanical failure in amorphous solids.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript is a review article surveying recent theoretical, computational, and experimental studies on topological defects in glasses. It covers underlying concepts including Burgers vectors, non-affine plasticity, vibrational modes, and topological invariants (such as winding numbers) identified in eigenmodes, displacement fields, and deformation-induced vector fields. The review summarizes reported correlations between these defects and soft spots, localized plastic rearrangements, yielding, and shear-band formation, and suggests this body of work offers a new perspective on the microscopic origins of plasticity in disordered materials. It concludes by assessing achievements, limitations, and open questions while outlining future directions.

Significance. If the correlations summarized from the cited literature prove to be mechanistically relevant rather than incidental, the review could help consolidate an emerging topological framework for plasticity in amorphous solids, analogous to the role of dislocations in crystals. The manuscript's value lies in its synthesis of independent studies across theory, simulation, and experiment, providing a consolidated reference that may guide further work toward a unified description of mechanical failure in glasses.

major comments (1)
  1. [Abstract] Abstract: The claim that the defects 'suggest a new perspective on the microscopic origins of plasticity' rests on correlations reported in the underlying studies. The review should more explicitly evaluate the risk that these invariants are incidental rather than causal, particularly since the abstract and closing sections note that mechanistic relevance remains to be established beyond correlation.
minor comments (2)
  1. [Abstract] Abstract: The phrase 'well-defined topological invariants' is used without immediate enumeration of the specific invariants (Burgers vectors, winding numbers); adding a short parenthetical list would improve immediate clarity for readers.
  2. The review states it assesses limitations and open questions; ensure that the discussion of potential alternative explanations (e.g., that observed correlations arise from shared underlying disorder rather than topology per se) is proportionate to the strength of the cited evidence.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our review and the constructive comment on the abstract. We agree that the language should more explicitly distinguish correlation from potential causality and will revise accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that the defects 'suggest a new perspective on the microscopic origins of plasticity' rests on correlations reported in the underlying studies. The review should more explicitly evaluate the risk that these invariants are incidental rather than causal, particularly since the abstract and closing sections note that mechanistic relevance remains to be established beyond correlation.

    Authors: We agree with the referee that the abstract should frame the claim more cautiously. The manuscript already states in the closing sections that mechanistic relevance remains to be established, but the abstract's phrasing can be tightened to emphasize that the reported correlations do not yet demonstrate causality and that the risk of incidental invariants must be evaluated in future work. We will revise the abstract to read along the lines of: 'These defects have been shown to correlate strongly with soft spots, localized plastic rearrangements, yielding, and shear-band formation; whether these correlations reflect causal mechanisms or incidental associations remains an open question that the field must address.' Parallel clarifications will be ensured in the discussion of limitations. revision: yes

Circularity Check

0 steps flagged

Review paper with no internal derivation chain

full rationale

This is a review article summarizing correlations reported in prior independent studies on topological defects in glasses. It presents no new derivations, equations, predictions, or fitted parameters of its own; the abstract and structure explicitly frame the content as an overview of existing theoretical, computational, and experimental work. No load-bearing steps reduce to self-citations, self-definitions, or fitted inputs called predictions within the manuscript itself. The central suggestion of a 'new perspective' is attributed to the strength of the cited literature rather than any internal argument constructed here.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As a review paper the work introduces no new free parameters, axioms, or invented entities; it aggregates concepts from the cited literature on topological defects in glasses.

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Reference graph

Works this paper leans on

128 extracted references · 90 canonical work pages · 1 internal anchor

  1. [1]

    P. G. Debenedetti and F. H. Stillinger.Supercooled Liquids and the Glass Transi- tion. Nature 410 (2001), 259–267.https://doi.org/10.1038/35065704

    work page doi:10.1038/35065704 2001

  2. [2]

    Berthier \ and\ author G

    L. Berthier and G. Biroli.Theoretical Perspective on the Glass Transition and Amorphous Materials. Rev. Mod. Phys. 83 (2011), 587–645.https://doi.org/ 10.1103/RevModPhys.83.587

    work page doi:10.1103/revmodphys.83.587 2011

  3. [3]

    Nicolas, E

    A. Nicolas, E. E. Ferrero, K. Martens, and J.-L. Barrat.Deformation and flow of amorphous solids: Insights from elastoplastic models. Rev. Mod. Phys. 90 (2018), 045006.https://doi.org/10.1103/RevModPhys.90.045006

    work page doi:10.1103/revmodphys.90.045006 2018

  4. [4]

    J. P. Hirth and J. Lothe.Theory of Dislocations. 2nd. New York: Wiley, 1982

    1982

  5. [5]

    Mura.Micromechanics of Defects in Solids

    T. Mura.Micromechanics of Defects in Solids. 2nd. Dordrecht: Martinus Nijhoff, 1987.https://doi.org/10.1007/978-94-009-3489-4

    work page doi:10.1007/978-94-009-3489-4 1987

  6. [6]

    M. H. Cohen and D. Turnbull.Molecular Transport in Liquids and Glasses. J. Chem. Phys. 31 (1959), 1164–1169.https://doi.org/10.1063/1.1730566

    work page doi:10.1063/1.1730566 1959

  7. [7]

    Spaepen.A Microscopic Mechanism for Steady State Inhomogeneous Flow in Metallic Glasses

    F. Spaepen.A Microscopic Mechanism for Steady State Inhomogeneous Flow in Metallic Glasses. Acta Metall. 25 (1977), 407–415.https://doi.org/10.1016/ 0001-6160(77)90232-2

    1977

  8. [8]

    A. S. Argon.Plastic Deformation in Metallic Glasses. Acta Metallurgica 27 (1979), 47–58.https://doi.org/10.1016/0001-6160(79)90055-5. 32

    work page doi:10.1016/0001-6160(79)90055-5 1979

  9. [9]

    M. L. Falk and J. S. Langer.Dynamics of Viscoplastic Deformation in Amorphous Solids. Physical Review E 57 (1998), 7192–7205.https://doi.org/10.1103/ PhysRevE.57.7192

    1998

  10. [10]

    J. Lin, T. Gueudr´ e, A. Rosso, and M. Wyart.Criticality in the Approach to Failure in Amorphous Solids. Phys. Rev. Lett. 115 (2015), 168001.https://doi.org/ 10.1103/PhysRevLett.115.168001

    work page doi:10.1103/physrevlett.115.168001 2015

  11. [11]

    E. E. Ferrero and E. A. Jagla.Properties of the density of shear transformations in driven amorphous solids. J. Phys.: Condens. Matter 33 (2021), 124001.https: //doi.org/10.1088/1361-648X/abd73a

    work page doi:10.1088/1361-648x/abd73a 2021

  12. [12]

    J. D. Eshelby.The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems. Proc. R. Soc. A 241 (1957), 376–396.https://doi.org/ 10.1098/rspa.1957.0133

    work page doi:10.1098/rspa.1957.0133 1957

  13. [13]

    Picard, A

    G. Picard, A. Ajdari, L. Bocquet, and F. Lequeux.Elastic Consequences of a Single Plastic Event: A Step Towards the Microscopic Modeling of the Flow of Yield Stress Fluids. Eur. Phys. J. E 15 (2004), 371–381.https://doi.org/10. 1140/epje/i2004-10054-8

    2004

  14. [14]

    F. C. Frank.Supercooling of Liquids. Proc. R. Soc. A 215 (1952), 43–46.https: //doi.org/10.1098/rspa.1952.0194

    work page doi:10.1098/rspa.1952.0194 1952

  15. [15]

    Tanaka, H

    H. Tanaka, H. Tong, R. Shi, and J. Russo.Revealing Key Structural Features Hidden in Liquids and Glasses. Nat. Rev. Phys. 1 (2019), 333–348.https://doi. org/10.1038/s42254-019-0053-3

    work page doi:10.1038/s42254-019-0053-3 2019

  16. [16]

    Widmer-Cooper and P

    A. Widmer-Cooper and P. Harrowell.Predicting the Long-Time Dynamic Hetero- geneity in a Supercooled Liquid on the Basis of Short-Time Heterogeneities. Phys. Rev. Lett. 96 (2006), 185701.https://doi.org/10.1103/PhysRevLett.96. 185701

    work page doi:10.1103/physrevlett.96 2006

  17. [17]

    M. L. Manning and A. J. Liu.Vibrational Modes Identify Soft Spots in a Sheared Disordered Packing. Phys. Rev. Lett. 107 (2011), 108302.https://doi.org/10. 1103/PhysRevLett.107.108302

    2011

  18. [18]

    Patinet, D

    S. Patinet, D. Vandembroucq, and M. L. Falk.Connecting Local Yield Stresses with Plastic Activity in Amorphous Solids. Phys. Rev. Lett. 117 (2016), 045501. https://doi.org/10.1103/PhysRevLett.117.045501

    work page doi:10.1103/physrevlett.117.045501 2016

  19. [20]

    Cubuk and et al.Structure-property relationships from universal signatures of plasticity in disordered solids

    E. Cubuk and et al.Structure-property relationships from universal signatures of plasticity in disordered solids. Science 358 (2017), 1033–1037.https://doi.org/ 10.1126/science.aai8830

    work page doi:10.1126/science.aai8830 2017

  20. [21]

    E. D. Cubuk, S. S. Schoenholz, J. M. Rieser, B. D. Malone, J. Rottler, D. J. Durian, E. Kaxiras, and A. J. Liu.Identifying Structural Flow Defects in Disordered Solids Using Machine-Learning Methods. Phys. Rev. Lett. 114 (2015), 108001.https: //doi.org/10.1103/PhysRevLett.114.108001. 33

    work page doi:10.1103/physrevlett.114.108001 2015

  21. [22]

    Bapst, T

    V. Bapst, T. Keck, A. Grabska-Barwi´ nska, C. Donner, E. D. Cubuk, S. S. Schoen- holz, A. Obika, A. W. R. Nelson, T. Back, D. Hassabis, and P. Kohli.Unveiling the predictive power of static structure in glassy systems. Nat. Phys. 16 (2020), 448–454.https://doi.org/10.1038/s41567-020-0842-8

    work page doi:10.1038/s41567-020-0842-8 2020

  22. [23]

    Boattini, S

    E. Boattini, S. Mar´ ın-Aguilar, S. Mitra, G. Foffi, F. Smallenburg, and L. Filion. Autonomously revealing hidden local structures in supercooled liquids. Nat. Com- mun. 11 (2020), 5479.https://doi.org/10.1038/s41467-020-19286-8

    work page doi:10.1038/s41467-020-19286-8 2020

  23. [24]

    Zaccone.Explicit Analytical Solution for Random Close Packing ind= 2and d= 3

    A. Zaccone.Explicit Analytical Solution for Random Close Packing ind= 2and d= 3. Phys. Rev. Lett. 128 (2022), 028002.https : / / doi . org / 10 . 1103 / PhysRevLett.128.028002

    2022

  24. [25]

    Torquato, T

    S. Torquato, T. M. Truskett, and P. G. Debenedetti.Is Random Close Packing of Spheres Well Defined?Phys. Rev. Lett. 84 (2000), 2064–2067.https://doi. org/10.1103/PhysRevLett.84.2064

    work page doi:10.1103/physrevlett.84.2064 2000

  25. [26]

    C. S. O’Hern, L. E. Silbert, A. J. Liu, and S. R. Nagel.Jamming at zero temperature and zero applied stress: The epitome of disorder. Phys. Rev. E 68 (2003), 011306. https://doi.org/10.1103/PhysRevE.68.011306

    work page doi:10.1103/physreve.68.011306 2003

  26. [27]

    Zaccone and E

    A. Zaccone and E. Scossa-Romano.Approximate Analytical Description of the Nonaffine Response of Amorphous Solids. Phys. Rev. B 83 (2011), 184205.https: //doi.org/10.1103/PhysRevB.83.184205

    work page doi:10.1103/physrevb.83.184205 2011

  27. [28]

    Zaccone.Complete mathematical theory of the jamming transition: A perspec- tive

    A. Zaccone.Complete mathematical theory of the jamming transition: A perspec- tive. Journal of Applied Physics 137 (2025), 050901.https://doi.org/10.1063/ 5.0245684. [29]Soft Matter Physics: An Introduction. Ed. by M. Kleman and O. D. Lavrentovich. New York, NY: Springer New York, 2003, 434–471.https://doi.org/10.1007/ 978-0-387-21759-8_12

    2025

  28. [29]

    Shankar, A

    S. Shankar, A. Souslov, M. J. Bowick, M. C. Marchetti, and V. Vitelli.Topological Active Matter. Nat. Rev. Phys. 4 (2022), 380–398.https://doi.org/10.1038/ s42254-022-00445-3

    2022

  29. [30]

    G. I. Taylor.The Mechanism of Plastic Deformation of Crystals. Part I. Theoret- ical. Proc. R. Soc. A 145 (1934), 362–387.https://doi.org/10.1098/rspa. 1934.0106

    work page doi:10.1098/rspa 1934

  30. [31]

    Orowan.Zur Kristallplastizit¨ at

    E. Orowan.Zur Kristallplastizit¨ at. III. Zeitschrift f¨ ur Physik 89 (1934), 634–659. https://doi.org/10.1007/BF01341480

    work page doi:10.1007/bf01341480 1934

  31. [32]

    M. Polanyi. ¨Uber eine Art Gitterst¨ orung, die einen Kristall plastisch machen k¨ onnte. Zeitschrift f¨ ur Physik 89 (1934), 660–664.https://doi.org/10.1007/ BF01341481

    1934

  32. [33]

    Volterra.Sur l’´ equilibre des corps ´ elastiques multiplement connexes

    V. Volterra.Sur l’´ equilibre des corps ´ elastiques multiplement connexes. Annales Scientifiques de l’ ´Ecole Normale Sup´ erieure 24 (1907), 401–517.https://doi. org/10.24033/asens.583

    work page doi:10.24033/asens.583 1907

  33. [34]

    J. M. Burgers.Some Considerations on the Fields of Stress Connected with Dis- locations in a Regular Crystal Lattice. Proc. K. Ned. Akad. Wet. 42 (1939), 293– 325

    1939

  34. [35]

    F. C. Frank.The Resultant Content of Dislocations in an Arbitrary Intercrystalline Boundary. Symp. Plast. Deform. Cryst. Solids (1951), 150–154. 34

    1951

  35. [36]

    F. R. N. Nabarro.Dislocations in a Simple Cubic Lattice. Proc. Phys. Soc. 59 (1947), 256–272.https://doi.org/10.1088/0959-5309/59/2/309

    work page doi:10.1088/0959-5309/59/2/309 1947

  36. [37]

    F. C. Frank.On the Theory of Liquid Crystals. Discussions of the Faraday Society 25 (1958), 19–28.https://doi.org/10.1039/DF9582500019

    work page doi:10.1039/df9582500019 1958

  37. [38]

    Kl´ eman.Points, Lines and Walls: In Liquid Crystals, Magnetic Systems and Various Ordered Media

    M. Kl´ eman.Points, Lines and Walls: In Liquid Crystals, Magnetic Systems and Various Ordered Media. New York: Wiley, 1977

    1977

  38. [39]

    Kl´ eman and J

    M. Kl´ eman and J. Friedel.Disclinations, Dislocations, and Continuous Defects: A Reappraisal. Rev. Mod. Phys. 80 (2008), 61–115.https://doi.org/10.1103/ RevModPhys.80.61

    2008

  39. [40]

    P. J. Steinhardt, D. R. Nelson, and M. Ronchetti.Icosahedral Bond Orientational Order in Supercooled Liquids. Phys. Rev. Lett. 47 (1981), 1297–1300.https:// doi.org/10.1103/PhysRevLett.47.1297

    work page doi:10.1103/physrevlett.47.1297 1981

  40. [41]

    P. J. Steinhardt and P. Chaudhari.Point and line defects in glasses. Philos. Mag. A 44 (1981), 1375–1381.https://doi.org/10.1080/01418618108235816

    work page doi:10.1080/01418618108235816 1981

  41. [42]

    P. J. Steinhardt, D. R. Nelson, and M. Ronchetti.Bond-orientational order in liquids and glasses. Phys. Rev. B 28 (1983), 784–805.https : / / doi . org / 10 . 1103/PhysRevB.28.784

    1983

  42. [43]

    D. R. Nelson.Order, frustration, and defects in liquids and glasses. Phys. Rev. B 28 (1983), 5515–5535.https://doi.org/10.1103/PhysRevB.28.5515

    work page doi:10.1103/physrevb.28.5515 1983

  43. [44]

    P. W. Anderson.Through the Glass Lightly. Science 267 (1995), 1615–1616.https: //doi.org/10.1126/science.267.5204.1615.f

    work page doi:10.1126/science.267.5204.1615.f 1995

  44. [45]

    C. A. Angell.Formation of Glasses from Liquids and Biopolymers. Science 267 (1995), 1924–1935.https://doi.org/10.1126/science.267.5206.1924

    work page doi:10.1126/science.267.5206.1924 1995

  45. [46]

    M. D. Ediger.Spatially Heterogeneous Dynamics in Supercooled Liquids. Annu. Rev. Phys. Chem. 51 (2000), 99–128.https : / / doi . org / 10 . 1146 / annurev . physchem.51.1.99

    2000

  46. [47]

    Tanaka, T

    H. Tanaka, T. Kawasaki, H. Shintani, and K. Watanabe.Critical-like Behaviour of Glass-Forming Liquids. Nat. Mater. 9 (2010), 324–331.https://doi.org/10. 1038/nmat2634

    2010

  47. [48]

    Schall, D

    P. Schall, D. A. Weitz, and F. Spaepen.Structural Rearrangements That Govern Flow in Colloidal Glasses. Science 318 (2007), 1895–1899.https://doi.org/10. 1126/science.1149308

    2007

  48. [49]

    & K¨ ohn, A

    D. Turnbull and M. H. Cohen.Free-Volume Model of the Amorphous Phase: Glass Transition. J. Chem. Phys. 34 (1961), 120–125.https://doi.org/10.1063/1. 1731549

    work page doi:10.1063/1 1961

  49. [50]

    J. S. Langer.Shear-Transformation-Zone Theory of Plastic Deformation Near the Glass Transition. Phys. Rev. E 77 (2008), 021502.https://doi.org/10.1103/ PhysRevE.77.021502

    2008

  50. [51]

    M. L. Manning, J. S. Langer, and J. M. Carlson.Strain Localization in a Shear Transformation Zone Model for Amorphous Solids. Physical Review E 76 (2007), 056106.https://doi.org/10.1103/PhysRevE.76.056106

    work page doi:10.1103/physreve.76.056106 2007

  51. [52]

    A. L. Greer.Metallic Glasses. Science 267 (1995), 1947–1953.https://doi.org/ 10.1126/science.267.5206.1947. 35

    work page doi:10.1126/science.267.5206.1947 1995

  52. [54]

    W. H. Wang.The Elastic Properties, Elastic Models and Elastic Perspectives of Metallic Glasses. Prog. Mater. Sci. 57 (2012), 487–656.https://doi.org/10. 1016/j.pmatsci.2011.07.001

    2012

  53. [55]

    W. L. Johnson and K. Samwer.A Universal Criterion for Plastic Yielding of Metallic Glasses with a(T /T g)2/3 Temperature Dependence. Phys. Rev. Lett. 95 (2005), 195501.https://doi.org/10.1103/PhysRevLett.95.195501

    work page doi:10.1103/physrevlett.95.195501 2005

  54. [56]

    W. H. Wang.Dynamic relaxations and relaxation-property relationships in metallic glasses. Prog. Mater. Sci. 106 (2019), 100561.https://doi.org/10.1016/j. pmatsci.2019.03.006

    work page doi:10.1016/j 2019

  55. [57]

    D. R. Nelson.Liquids and Glasses in Spaces of Incommensurate Curvature. Phys. Rev. Lett. 50 (1983), 982–985.https://doi.org/10.1103/PhysRevLett.50.982

    work page doi:10.1103/physrevlett.50.982 1983

  56. [58]

    Kivelson, S

    D. Kivelson, S. A. Kivelson, X. L. Zhao, Z. Nussinov, and G. Tarjus.A Ther- modynamic Theory of Supercooled Liquids. Physica A 219 (1995), 27–38.https: //doi.org/10.1016/0378-4371(95)00140-3

    work page doi:10.1016/0378-4371(95)00140-3 1995

  57. [59]

    Tarjus and D

    G. Tarjus and D. Kivelson.Breakdown of the Stokes-Einstein Relation in Super- cooled Liquids. J. Chem. Phys. 103 (1995), 3071–3073.https://doi.org/10. 1063/1.470495

    1995

  58. [60]

    Tarjus, D

    G. Tarjus, D. Kivelson, Z. Nussinov, and P. Viot.The Frustration-Based Approach of Supercooled Liquids and the Glass Transition: A Review and Critical Assess- ment. J. Phys.: Condens. Matter 17 (2005), R1143–R1182.https://doi.org/ 10.1088/0953-8984/17/50/R01

    work page doi:10.1088/0953-8984/17/50/r01 2005

  59. [61]

    D. B. Miracle.A Structural Model for Metallic Glasses. Nat. Mater. 3 (2004), 697– 702.https://doi.org/10.1038/nmat1219

    work page doi:10.1038/nmat1219 2004

  60. [62]

    H. W. Sheng, W. K. Luo, F. M. Alamgir, J. M. Bai, and E. Ma.Atomic Packing and Short-to-Medium-Range Order in Metallic Glasses. Nature 439 (2006), 419– 425.https://doi.org/10.1038/nature04421

    work page doi:10.1038/nature04421 2006

  61. [63]

    Hirata, P

    A. Hirata, P. Guan, T. Fujita, Y. Hirotsu, A. Inoue, A. R. Yavari, T. Sakurai, and M. W. Chen.Direct observation of local atomic order in a metallic glass. Nat. Mater. 10 (2011), 28–33.https://doi.org/10.1038/nmat2897

    work page doi:10.1038/nmat2897 2011

  62. [64]

    Coslovich.Locally preferred structures and many-body static correlations in viscous liquids

    D. Coslovich.Locally preferred structures and many-body static correlations in viscous liquids. Phys. Rev. E 83 (2011), 051505.https://doi.org/10.1103/ PhysRevE.83.051505

    2011

  63. [65]

    Malins, S

    A. Malins, S. R. Williams, J. Eggers, and C. P. Royall.Identification of structure in condensed matter with the topological cluster classification. The Journal of chemical physics 139 (2013)

    2013

  64. [66]

    C. P. Royall and S. R. Williams.The Role of Local Structure in Dynamical Arrest. Phys. Rep. 560 (2015), 1–75.https://doi.org/10.1016/j.physrep.2014.11. 001

    work page doi:10.1016/j.physrep.2014.11 2015

  65. [67]

    J. D. Eshelby.The Elastic Field Outside an Ellipsoidal Inclusion. Proc. R. Soc. A 252 (1959), 561–569.https://doi.org/10.1098/rspa.1959.0173. 36

    work page doi:10.1098/rspa.1959.0173 1959

  66. [68]

    A. Bera, I. Regev, A. Zaccone, and M. Baggioli.Burgers rings as topological sig- natures of Eshelby-like plastic events in glasses. arXiv preprint arXiv:2505.23069 (2025).https://doi.org/10.48550/arXiv.2505.23069

    work page doi:10.48550/arxiv.2505.23069 2025

  67. [69]

    C. E. Maloney and A. Lemaˆ ıtre.Subextensive Scaling in the Athermal, Quasistatic Limit of Amorphous Matter in Plastic Shear Flow. Phys. Rev. Lett. 93 (2004), 016001.https://doi.org/10.1103/PhysRevLett.93.016001

    work page doi:10.1103/physrevlett.93.016001 2004

  68. [71]

    Tanguy, F

    A. Tanguy, F. Leonforte, and J.-L. Barrat.Plastic Response of a 2D Lennard- Jones Amorphous Solid: Detailed Analysis of the Local Rearrangements at Very Slow Strain Rate. Eur. Phys. J. E 20 (2006), 355–364.https://doi.org/10. 1140/epje/i2006-10024-2

    2006

  69. [72]

    E. P. Willmarth, W. Jin, D. Wang, A. Datye, U. D. Schwarz, M. D. Shattuck, and C. S. O’Hern.Particle-scale origin of quadrupolar nonaffine displacement fields in granular solids. Phys. Rev. E 112 (2025), 055402.https://doi.org/10.1103/ 42dk-54hl

    2025

  70. [73]

    Bouchbinder and J

    E. Bouchbinder and J. S. Langer.Nonequilibrium Thermodynamics of Driven Amorphous Materials. I. Internal Degrees of Freedom and Volume Deformation. Phys. Rev. E 80 (2009), 031131.https : / / doi . org / 10 . 1103 / PhysRevE . 80 . 031131

    2009

  71. [74]

    Lerner and I

    E. Lerner and I. Procaccia.Locality and Nonlocality in Elastoplastic Responses of Amorphous Solids. Phys. Rev. E 79 (2009), 066109.https://doi.org/10.1103/ PhysRevE.79.066109

    2009

  72. [75]

    Dasgupta, O

    R. Dasgupta, O. Gendelman, P. Mishra, I. Procaccia, and C. A. B. Z. Shor. Shear localization in three-dimensional amorphous solids. Phys. Rev. E 88 (2013), 032401.https://doi.org/10.1103/PhysRevE.88.032401

    work page doi:10.1103/physreve.88.032401 2013

  73. [76]

    Dasgupta, H

    R. Dasgupta, H. G. E. Hentschel, and I. Procaccia.Yield Strain in Shear Banding Amorphous Solids. Phys. Rev. Lett. 109 (2012), 255502.https://doi.org/10. 1103/PhysRevLett.109.255502

    2012

  74. [77]

    H. G. E. Hentschel, S. Karmakar, E. Lerner, and I. Procaccia.Do Athermal Amor- phous Solids Exist?Phys. Rev. E 83 (2011), 061101.https://doi.org/10.1103/ PhysRevE.83.061101

    2011

  75. [78]

    Alexander.Amorphous Solids: Their Structure, Lattice Dynamics and Elasticity

    S. Alexander.Amorphous Solids: Their Structure, Lattice Dynamics and Elasticity. Phys. Rep. 296 (1998), 65–236.https://doi.org/10.1016/S0370- 1573(97) 00069-0

    work page doi:10.1016/s0370- 1998

  76. [79]

    Bianco and R

    A. Tanguy, J. P. Wittmer, F. Leonforte, and J.-L. Barrat.Continuum Limit of Amorphous Elastic Bodies: A Finite-Size Study of Low-Frequency Harmonic Vi- brations. Phys. Rev. B 66 (2002), 174205.https://doi.org/10.1103/PhysRevB. 66.174205

    work page doi:10.1103/physrevb 2002

  77. [80]

    Leonforte, R

    F. Leonforte, R. Boissi` ere, A. Tanguy, J. P. Wittmer, and J.-L. Barrat.Continuum Limit of Amorphous Elastic Bodies. III. Three-Dimensional Systems. Phys. Rev. B 72 (2005), 224206.https://doi.org/10.1103/PhysRevB.72.224206. 37

    work page doi:10.1103/physrevb.72.224206 2005

  78. [81]

    B. A. DiDonna and T. C. Lubensky.Nonaffine Correlations in Random Elastic Media. Phys. Rev. E 72 (2005), 066619.https://doi.org/10.1103/PhysRevE. 72.066619

    work page doi:10.1103/physreve 2005

  79. [82]

    W. G. Ellenbroek, Z. Zeravcic, W. van Saarloos, and M. van Hecke.Non-affine Re- sponse: Jammed Packings vs. Spring Networks. Europhys. Lett. 87 (2009), 34004. https://doi.org/10.1209/0295-5075/87/34004

    work page doi:10.1209/0295-5075/87/34004 2009

  80. [83]

    Zaccone and E

    A. Zaccone and E. M. Terentjev.Disorder-Assisted Melting and the Glass Tran- sition in Amorphous Solids. Phys. Rev. Lett. 110 (2013), 178002.https://doi. org/10.1103/PhysRevLett.110.178002

    work page doi:10.1103/physrevlett.110.178002 2013

Showing first 80 references.