Active matter at high density: collective excitations, entropy production and spatial velocity correlations

Slides

Many systems of biological or technological interest, such as bacterial colonies or cell monolayers, arrange in dense aggregates and show spatial patterns in their velocity field without displaying a global polarization. In this talk, we investigate this phenomenon through a non-equilibrium stochastic dynamics, the so-called Active Brownian Particles (ABP), which is one of the most popular models to describe the behavior of several experimental active particles. We report the first evidence that pure repulsive spherical ABPs, without alignment interactions, spontaneously display spatial velocity correlations in homogeneous dense phases (liquid, hexatic and solid). This observable is analytically predicted and the expression for its correlation length reveals the dynamical origin of this collective phenomenon. In addition, the relation between spatial velocity correlations and entropy production is investigated by exploiting the Harada-Sasa relation. We analyze the energetic properties in the wave vector and frequency domains, finding analytical expressions for the spectral entropy production of the system. Each component of the active force (in frequency and wave vector domains) is able to excite the phonons of the active solid while each phonon dissipates energy in the environment producing entropy similarly to that produced by a monochromatic wave. Differently from the latter case, only the phonons with smaller frequencies provide the main contribution to the entropy and, in general, active systems dissipate energy at frequencies shifted from that of the excited phonon as much as the persistence time increases.

(Non equilibrium) thermodynamics of classical integrable models in their thermodynamic limit

Slides

Motivated by recent experimental developments in atomic physics, a large theoretical effort has been devoted to the analysis of the dynamics of quantum isolated systems after a sudden quench. In this talk I will describe the evolution of a family of classical many-body integrable (Neumann) models after instantaneous quenches of the same kind. The asymptotic dynamics of these models can be fully elucidated, and the stationary properties (in the thermodynamic limit) compared to the ones obtained exactly using a Generalised Gibbs Ensemble. The latter can not only be built but also used to evaluate analytically all relevant observables, a quite remarkable fact for an interacting integrable system with a non-trivial phase diagram.

Acoustic triggering of shear instability in granular media; Geophysical implications

Laboratory studies of granular friction have emerged as a powerful tool for investigating seismic fault slip [1], including dynamic triggering of earthquakes and landslides [2,3]. However, physical origins of triggering by small-amplitude seismic waves still remain a challenging issue.

Here we report two related experiments on the ultrasound-induced unjamming transition in granular media. Firstly, we investigate the quasi-static sliding in sheared dry and wet granular layers, monitored with passive (acoustic emission: AE) and active acoustic detections (wave velocity and coda correlation). Avalanche-like dynamics and quasi-periodic stick-slip behaviour are both observed, accompanied by a decrease of the acoustic velocity and an increase of AE rate (precursors) before fracture-like failure, i.e. mainshock / macroslip.

The acoustic fluidization of sheared granular layers is then investigated by applying high amplitude ultrasound (< 100 nm), which reduces abruptly the critical steady-state stress or/and triggers advanced macroslips in the periodic stick-slip regime, but with reduced magnitude of stress drop and recurrence interval. We show that such acoustic triggering of macroscopic shear instability arises from the acoustic lubrication of grain contacts via microslips [4,5], playing a role of effective temperature.

Secondly, we show that such acoustic lubrication can also explain the triggering of granular flows below the maximal stability angle (failure), by high-amplitude ultrasound (50-100 kHz). As a function of the distance of the slope to failure, we observe a bifurcation of triggered flows, from slow intermittent creep to fast inertial flow [5]. This latter may be delayed, when the cohesion is increased between wet grains, due to the fracture nucleation. These findings help to understand landslides or rockfalls triggered by seismicity [3].

[1] C. Marone, Laboratory-derived friction laws and their application to seismic faulting, Ann. Revs. Earth & Plan. Sci. 26, 643 (1998); C.H. Scholz, The Mechanics of Earthquake and Faulting (3rd edition, Cambridge University Press, 2018)

[2] P. Johnson and X. Jia, Nonlinear dynamics, granular media and dynamic earthquake triggering, Nature 437, 871 (2005)

[3] V. Durand et al, On the link between external forcings and slope instabilities in the Piton de la Fournaise summit crater, Reunion Island, J. Geophys. Res. 123, 2422 (2019)

[4] X. Jia, T. Brunet, and J. Laurent, Elastic weakening of a dense granular pack by acoustic fluidization: Slipping, compaction, and aging Phys. Rev E 84, 020301(R) (2011)

[5] J. Léopoldès, X. Jia, A. Tourin, and A. Mangeney, Triggering granular avalanches with ultrasound, Phys. Rev. E 102, 042901 (2020)

Response of a granular sandwich to external vibrations: How to control the transmitted acoustic frequency

Slides

A mechanical vibration applied to a confined granular system can induce a transition from a solid-like state, able to resist applied stresses, into a flowing fluid-like state. We discuss the influence of frequency vibration on this transition for a granular sandwich. More precisely we show that the system only responds to perturbations around a characteristic frequency $f^*$, which can be associated with attenuated standing waves, bouncing back and forth between the two confining plates. These standing waves are responsible for a change in the rheological properties of the granular sandwich, a phenomenon named "acoustic fluidization". Furthermore, we will also show that $f^*$ represents an optimal frequency at which the system reaches the maximal kinetic energy.

By means of numerical simulations in different dimensions we will show that $f^*$ is fully controlled by sound propagation along the fastest chain, providing evidence that the stiffest force chain acts like a wave-guide which localizes a standing wave between the two plates and fixes the frequency of the sound wave. We will discuss how to use this remarkable property to control the frequency of acoustic attenuation of a wall without changing its thickness or bulk material.

Slow timescales in vibrofluidized granular materials

Vibrofluidized granular materials attain a non-equilibrium steady state through the balance between the energy lost in dissipative collisions and the energy injected with mechanical vibrations.

Such vibrations are typically fast but these systems have a rich phenomenology with much slower characteristic times.

In this talk, I focus on two phenomena: the emergence of collective drifts in disordered granular packings and the spontaneous formation of crystals and quasi-crystals in granular binary mixtures.

In the first case, I report a numerical analysis that shows how a dense granular system is able to convert the unbiased vibrations to which it is subjected into a slow and directed collective motion. I provide many arguments to interpret this behavior as a peculiar instance of the ratchet effect.

In the second case, I present some numerical and (preliminary) experimental results about self-assembly in bidispersed granular monolayers. Following the predictions of an equilibrium phase diagram of non-additive hard disks, the granular medium is able to reach the same structures obtained in the thermal system.

The more general aim of the talk is to highlight that granular systems can exhibit genuine out-of-equilibrium behaviors but also mimic equilibrium ones.

Entropy production in Mechanosensation (and Perception)

This talk will review recent stochastic-thermodynamics approaches to describe the nonequilibrium nature of spontaneous fluctuations in active mechanosensory hair-cell bundles that are responsible of sound transduction. Particular emphasis will be given to coarse-grained experimental data extracted from bullfrog's sacculus --a paradigm of active oscillations in a real biological system. To this aim, different approaches to estimate the underlying dissipation of active fluctuations will be discussed: fluctuation-dissipation theorems [1], irreversibility measures [2], and non-Markovian modelling [3]. If time available, a swift appetizer will be given on how stochastic thermodynamics can be useful in understanding human visual perception of nonequilibrium phenomena [4].

[1] Martin et al, PNAS 98, 14380 (2001); Berger, Hudspeth, bioRxiv (2022)

[2] Roldan et al, NJP 23, 08313 (2021)

[3] Tucci et al, arXiv 2201.1217 (2022) - PRL in press

[4] Durmaz et al, in preparation (2022)