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Attractive versus truncated repulsive supercooled liquids: The dynamics is encoded in the pair correlation function
Statistical Mechanics · Submitted 3 Jun 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We demonstrate that a properly weighted integral of the pair correlation function, which amplifies the subtle differences between the two systems, correctly captures their dynamical differences.
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The abstract, sentence by sentence
We compare glassy dynamics in two liquids that differ in the form of their interaction potentials. Both systems have the same repulsive interactions but one has also an attractive part in the potential. These two systems exhibit very different dynamics despite having nearly identical pair correlation functions. We demonstrate that a properly weighted integral of the pair correlation function, which amplifies the subtle differences between the two systems, correctly captures their dynamical differences. The weights are obtained from a standard machine learning algorithm.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We compare glassy dynamics in two liquids that differ in the form of their interaction potentials. | contribution 0.80 | 0.88 | 0.03 | asserted 0.85 |
| s1 | Both systems have the same repulsive interactions but one has also an attractive part in the potential. | method 0.59 | 0.51 | 0.03 | asserted 1.00 |
| s2 | These two systems exhibit very different dynamics despite having nearly identical pair correlation functions. | result 0.99 | 0.86 | 0.17 | asserted 1.00 |
| s3 | We demonstrate that a properly weighted integral of the pair correlation function, which amplifies the subtle differences between the two systems, correctly captures their dynamical differences. | result 0.76 | 0.95 | 0.85 | asserted 1.00 |
| s4 | The weights are obtained from a standard machine learning algorithm. | method 1.00 | 0.79 | 0.04 | asserted 1.00 |
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The paper
Original abstract
We compare glassy dynamics in two liquids that differ in the form of their interaction potentials. Both systems have the same repulsive interactions but one has also an attractive part in the potential. These two systems exhibit very different dynamics despite having nearly identical pair correlation functions. We demonstrate that a properly weighted integral of the pair correlation function, which amplifies the subtle differences between the two systems, correctly captures their dynamical differences. The weights are obtained from a standard machine learning algorithm.
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How the literature uses it
5 arXiv papers cite this in 14 sentences
Papers citing it · 11 sentences without a confident label
Cites it as support 1 paper
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While on the one hand this sensitivity of the theory means that a high precision is required when measuring the input-$S(k)$, on the other hand this supports the idea that important information about the dynamics is already enclosed in static $2-$point density correlations [ref] .
Multi-component generalized mode-coupling theory: Predicting dynamics from structure in glassy mixtures · From structure to dynamics · 0.96
Cites it as background 1 paper
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This kind of simple transfer-test performance measure was already introduced a few years ago [ref] , while the idea of applying the trained model to other temperatures dates back from the original works on Machine Learning applied to glasses [ref] .
Rotation-equivariant Graph Neural Networks for Learning Glassy Liquids Representations · Temperature generalization · 0.91
What it cites · 22 sentences without a confident label
Uses the method or tool of 8 papers
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In order to determine whether the magnitude of $S$ has physical meaning, we follow [ref] and compute $P(R|S)$ (left panel of Fig. [ref], the probability of observing a local re-arrangement $(P((i,t)>^*))$ for a given range of softness $∈[S, S+0.025]$, for different $1/T$.
The Relationship Between Local Structure and Relaxation in Out-of-Equilibrium Glassy Systems · Introduction · 0.91
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In order to determine whether the magnitude of $S$ has physical meaning, we follow [ref] and compute $P(R|S)$ (left panel of Fig. [ref], the probability of observing a local re-arrangement $(P((i,t)>^*))$ for a given range of softness $∈[S, S+0.025]$, for different $1/T$.
A structural approach to relaxation in glassy liquids · Introduction · 0.91
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Cage-jumps taking place during a time interval $W=[t_1,t_2]$, for a given particle $i$, may be captured by computing the quantity $p_hop(i,t)$ [ref] : [equation] for all $t ∈W$, where averages are performed over the time intervals surrounding time $t$, i.e. $U=[t_1,t]$, $V=[t,t_2]$. $t^* = argmax_t∈W ((i,t))$ is the time that best separates the trajectory $r⃗_i([t_1,t_2])$ into two sub-trajectories $r⃗_i([t_1,t^*])$ and $r⃗_i([t^*,t_2])$.
Evolution of dynamical facilitation approaching the granular glass transition · Introduction · 1.00
Compares with 1 paper
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A comparison of that theory with Schweizer's has recently shown they produce comparable results, although the latter is more precise [ref] .
A Comparative Study of a Class of Mean Field Theories of the Glass Transition · Introduction · 0.92
Cites as background 1 paper
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A number of approaches have attempted to identify these subtle structural signatures in supercooled liquids [ref] .
Understanding fragility in supercooled Lennard-Jones mixtures. I. Locally preferred structures · Introduction · 0.97
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