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Résumé:

The nature of the glass transition is theoretically understood in the mean-field limit of infinite spatial dimensions, but the problem remains totally open in physical dimensions. Nontrivial finite-dimensional fluctuations are hard to control analytically, and experiments fail to provide conclusive evidence regarding the nature of the glass transition. Here, we use Monte Carlo simulations that fully bypass the glassy slowdown, and access equilibrium states in two-dimensional glass-forming liquids at low enough temperatures to directly probe the transition. We find that the liquid state terminates at a thermodynamic glass transition at zero temperature, which is associated with an entropy crisis and a diverging static correlation length.

Commentaires: 23 pages, 18 figures. Réf Journal: Nat. Commun. 10, 1508 (2019)

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DOI: 10.1109/JBHI.2018.2834159
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Diffuse low-grade gliomas (DLGG) are brain tumors of young adults. They affect the quality of life of the inflicted patients and, if untreated, they evolve into higher grade tumors where the patient's life is at risk. Therapeutic management of DLGGs includes chemotherapy, and tumor diameter is particularly important for the follow-up of DLGG evolution. In fact, the main clinical basis for deciding whether to continue chemotherapy is tumor diameter growth rate. In order to reliably assist the doctors in selecting the most appropriate time to stop treatment, we propose a novel clinical decision support system. Based on two mathematical models, one linear and one exponential, we are able to predict the evolution of tumor diameter under Temozolomide chemotherapy as a first treatment and thus offer a prognosis on when to end it. We present the results of an implementation of these models on a database of 42 patients from Nancy and Montpellier University Hospitals. In this database, 38 patients followed the linear model and four patients followed the exponential model. From a training data set of a minimal size of five, we are able to predict the next tumor diameter with high accuracy. Thanks to the corresponding prediction interval, it is possible to check if the new observation corresponds to the predicted diameter. If the observed diameter is within the prediction interval, the clinician is notified that the trend is within a normal range. Otherwise, the practitioner is alerted of a significant change in tumor diameter.

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We numerically analyse the landscape governing the evolution of the vibrational dynamics of hard disk glasses as the density increases towards jamming. We find that the dynamics becomes slow, spatially correlated, and starts to display aging dynamics across an avoided Gardner transition, with a phenomenology that resembles three dimensional observations. We carefully analyse the behaviour of single glass samples, and find that the emergence of aging dynamics is controlled by the apparition of a complex organisation of the landscape that splits into a remarkable hierarchy of minima as jamming is approached. Our results show that the mean-field prediction of a Gardner phase characterized by an ultrametric structure of the landscape provides a useful description of finite dimensional systems, even when the Gardner transition is avoided.

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19 Citations
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It was recently discovered that SWAP, a Monte Carlo algorithm that involves the exchange of pairs of particles of differing diameters, can dramatically accelerate the equilibration of simulated supercooled liquids in regimes where the normal dynamics is glassy. This spectacular effect was subsequently interpreted as direct evidence against a static, cooperative explanation of the glass transition such as the one offered by the random first-order transition (RFOT) theory. We review several empirical facts that support the opposite view, namely, that a local mechanism cannot explain the glass transition phenomenology. We explain the speedup induced by SWAP within the framework of the RFOT theory. We suggest that the efficiency of SWAP stems from a postponed onset of glassy dynamics, which allows the efficient exploration of configuration space even in the regime where the physical dynamics is dominated by activated events across free-energy barriers. We describe this effect in terms of `crumbling metastability' and use the example of nucleation to illustrate the possibility of circumventing free-energy barriers of thermodynamic origin by a change of the local dynamical rules.

Commentaires: 15 pages, 3 figures; v2: improved discussions and clarifications

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