Session P62: Glassy Dynamics: From Simple Models to Biological Tissues

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In infinite dimension, many-body systems of pairwise interacting particles provide exact analytical benchmarks for features of amorphous materials, such as the stress-strain curve of glasses under quasistatic shear. Here, instead of a global shear, we consider an alternative driving protocol as recently introduced in [Morse et al., arXiv:2009.07706], which consists of randomly assigning a constant local displacement field on each particle, with a finite spatial correlation length. We show that, in the infinite-dimension limit, the mean-field dynamics under such a random forcing is strictly equivalent to that under global shear, upon a simple rescaling of the accumulated strain. Moreover, the scaling factor is essentially given by the variance of the relative local displacements on interacting pairs of particles, which encodes the presence of a finite spatial correlation. In this framework, global shear is simply a special case of a much broader family of local forcing, that can be explored by tuning its spatial correlations. These results hint at a unifying framework for establishing rigourous analogies, at the mean-field level, between different driven disordered systems.   

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Our understanding of the glass transition is hampered by the astronomical timescales required to discriminate competing theoretical approaches. Recently, considerable progress has been made in obtaining data at unprecedented degrees of supercooling [1], yet theoretical approaches based on dynamical or thermodynamical standpoints still describe the available data.

Here we make the case that the dynamical phase transition of dynamic facilitation theory, is in fact compatible with thermodynamic interpretations such as random first order transition theory. We use trajectory sampling in experiments and simulations to show that the dynamical transition has a structural character [2,3] and reweight these data to extend the dynamical phase transition to deeper supercooling than previously accessed [4]. The inactive phase exhibits a lower entropy than the active phase (normal supercooled liquid) which falls only slowly as a function of temperature, as noted by Kauzmann in the context of supercooled liquids and their crystal. We find evidence that the dynamical phase transition has a lower critical point close to the Kauzmann temperature where the configurational entropy is predicted to become small in thermodynamic theories. In this picture, the dynamical phase transition of facilitation is thus incorporated into a thermodynamic picture of sub-extensive entropy at low temperature [5].

[1] Royall CP, Turci F, Russo J, Tatsumi S and Robinson JFE, J. Phys.: Condens. Matter 30 363001 (2018).

[2] Speck T, Malins A and Royall CP, Phys. Rev. Lett. 109 195703 (2012).

[3] Pinchaipat R, Campo M, Turci F, Hallet JE, Speck T, and Royall CP, Phys. Rev. Lett. 119 028004 (2017).

[4] Turci F and Royall CP and Speck T, Phys. Rev. X 7 031028 (2017).

[5] Royall CP, Turci F and Speck T, J. Chem. Phys. 153 090901 (2020).   

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To understand why the universal low-temperature properties of glasses
differ dramatically from their crystalline counterparts, it is paramount
to understand what controls the vibrational properties of glasses. Numerical
methods generally create glasses by quenching a mildly supercooled liquid,
which limits the variation of vibrational properties of glasses and the
ability to examine correlations between different quantities.
Due to recent advances in simulation techniques, we are now able to study glasses
with a wide range of stabilities. Additionally, since
there is evidence that the glass transition and vibrational properties of
glasses are different in two and three dimensions, understanding these differences
can aid in the understanding of the low-temperature properties of glasses.
Here, we study vibrational modes and sound attenuation in simulated glasses
that range from very poorly annealed to very stable. Our most
stable glass is comparable to exceptionally-stable, vapor-deposited
laboratory glasses.
In both two and three dimensions we find that the density of the
quasi-localized, low-frequency
modes decrease quickly with increasing stability.
Notably the quasi-localized, low-frequency modes in two dimensions are
nearly absent for the most stable glasses.
Accompanying this large decrease
in quasi-localized, low-frequency modes is a large decrease in sound attenuation with
increasing stability.
We contrast the difference in the scaling of the
boson peak height and frequency in two and three dimensions.   

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In multicellular organisms, properly programmed collective motion is required to form tissues and organs, and this programming breaks down in diseases like cancer. Recent experimental work highlights that some organisms tune the global mechanical properties of a tissue across a fluid-solid transition to allow or prohibit cell motion and control processes such as body axis elongation. What is the physical origin of such rigidity transitions? Is it similar to zero-temperature jamming transitions in particulate matter, or glass transitions in molecular or colloidal materials? Over the past decade, our group and others have shown that models for confluent tissues, where there are no gaps or overlaps between cells, exhibit a rigidity transition due to geometric incompatibility. A similar transition is also seen in models for biopolymer networks. I will use a newly developed framework for “higher-order rigidity” to discuss similarities and differences between rigidity in particulate matter and rigidity in confluent tissues and fiber networks. I will also discuss recent work to test which mechanisms are operating in real biological systems.   

Live

I will first present the dynamical mean-field theory of the glass transition, in particular a derivation of it that highlights connections with MCT and with the infinite dimensional theory of the glass transition. I will then motivate, discuss and present the first results on its cluster extension.