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Scaling Description of Dynamical Heterogeneity and Avalanches of Relaxation in Glass-Forming Liquids
Soft Condensed Matter · Submitted 29 Apr 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This property, related to the nature of the zero-temperature fixed point, directly leads to decoupling of particle diffusion and relaxation time (the so-called Stokes-Einstein violation).
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The abstract, sentence by sentence
We provide a theoretical description of dynamical heterogeneities in glass-forming liquids, based on the premise that relaxation occurs via local rearrangements coupled by elasticity. In our framework, the growth of the dynamical correlation length $\xi$ and of the correlation volume $\chi_4$ are controlled by a zero-temperature fixed point. We connect this critical behavior to the properties of the distribution of local energy barriers at zero temperature. Our description makes a direct connection between dynamical heterogeneities and avalanche-type relaxation associated to dynamic facilitation, allowing us to relate the size distribution of heterogeneities to their time evolution. Within an avalanche, a local region relaxes multiple times, the more the larger is the avalanche. This property, related to the nature of the zero-temperature fixed point, directly leads to decoupling of particle diffusion and relaxation time (the so-called Stokes-Einstein violation). Our most salient predictions are tested and confirmed by numerical simulations of scalar and tensorial thermal elasto-plastic models.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We provide a theoretical description of dynamical heterogeneities in glass-forming liquids, based on the premise that relaxation occurs via local rearrangements coupled by elasticity. | contribution 0.98 | 0.92 | 0.11 | asserted 1.00 |
| s1 | In our framework, the growth of the dynamical correlation length $\xi$ and of the correlation volume $\chi_4$ are controlled by a zero-temperature fixed point. | result 0.77 | 0.81 | 0.14 | asserted 1.00 |
| s2 | We connect this critical behavior to the properties of the distribution of local energy barriers at zero temperature. | contribution 0.56 | 0.82 | 0.08 | asserted 1.00 |
| s3 | Our description makes a direct connection between dynamical heterogeneities and avalanche-type relaxation associated to dynamic facilitation, allowing us to relate the size distribution of heterogeneities to their time evolution. | contribution 0.87 | 0.90 | 0.33 | asserted 1.00 |
| s4 | Within an avalanche, a local region relaxes multiple times, the more the larger is the avalanche. | result 0.82 | 0.61 | 0.09 | asserted 1.00 |
| s5 | This property, related to the nature of the zero-temperature fixed point, directly leads to decoupling of particle diffusion and relaxation time (the so-called Stokes-Einstein violation). | interpretation 0.68 | 0.82 | 0.24 | asserted 1.00 |
| s6 | Our most salient predictions are tested and confirmed by numerical simulations of scalar and tensorial thermal elasto-plastic models. | result 0.50 | 0.93 | 0.17 | asserted 1.00 |
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The paper
Original abstract
We provide a theoretical description of dynamical heterogeneities in glass-forming liquids, based on the premise that relaxation occurs via local rearrangements coupled by elasticity. In our framework, the growth of the dynamical correlation length $\xi$ and of the correlation volume $\chi_4$ are controlled by a zero-temperature fixed point. We connect this critical behavior to the properties of the distribution of local energy barriers at zero temperature. Our description makes a direct connection between dynamical heterogeneities and avalanche-type relaxation associated to dynamic facilitation, allowing us to relate the size distribution of heterogeneities to their time evolution. Within an avalanche, a local region relaxes multiple times, the more the larger is the avalanche. This property, related to the nature of the zero-temperature fixed point, directly leads to decoupling of particle diffusion and relaxation time (the so-called Stokes-Einstein violation). Our most salient predictions are tested and confirmed by numerical simulations of scalar and tensorial thermal elasto-plastic models.
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How the literature uses it
5 arXiv papers cite this in 16 sentences
Papers citing it · 12 sentences without a confident label
Builds on it 1 paper
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In this second regime, studied in detail in [ref] in 2d thermal EPMs, and for which we provide a mean-field analysis, the length increases logarithmically with relaxation time.
Mean-Field Analysis of the Glassy Dynamics of an Elastoplastic Model of Super-Cooled Liquids · Introduction · 0.85
Uses its data or values 1 paper
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For $d=2$, $d̃_f≈2$ and $σ̃≈1/2$ [ref] , leading to $l_c ∼√(χ_4^*) [ln(τ_α/t)]^-1$.
Testing theories of the glass transition with the same liquid, but many kinetic rules · Introduction · 0.90
Cites it as support 1 paper
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Furthermore, dynamical heterogeneity has been seen to emerge naturally in thermal elastoplastic models [ref] , with a spatial length-scale of dynamical correlations and thermal avalanches that grow with decreasing temperature [ref] .
Mean-Field Analysis of the Glassy Dynamics of an Elastoplastic Model of Super-Cooled Liquids · Introduction · 0.97
What it cites · 9 sentences without a confident label
Compares with 1 paper
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Quantitatively, the magnitude of dynamical heterogeneities we simulated is comparable to most super-cooled liquids (as the estimated $χ_4^*$ increases by about two decades as the glass transition is reached [ref] ), whereas the magnitude of the Stoke-Einstein breakdown is comparable to that of rather strong glass-forming liquids [ref] .
The glass transition in molecules, colloids and grains: universality and specificity · Conclusion and discussion · 0.98
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