Zoom recording session 1: Julien Tailleur, Cécile Cottin-Bizonne.
Zoom recording session 2: Clément Erignoux, Liesbeth M. C. Janssen.

Vincent Calvez (Lyon), Mike Cates (Cambridge), Cécile Cottin-Bizonne (Lyon), Clément Erignoux (Lille), Martin Evans (Edinburgh), Liesbeth M. C. Janssen (Eindhoven), Yariv Kafri (Haifa),

Vincent Calvez (Lyon): A simple go-or-grow model of self-generated aerotaxis.

I will present recent experimental results of self-generated hypoxia triggering the expansion of a ring of amoebae Dictyostelium discoideum at constant speed in the long range. We introduced a simple reaction-diffusion-advection model. Relevant modeling assumptions enabled computing the speed of expansion, extending the standard Fisher wave speed of classical reaction-diffusion equations. We focused on the contribution of directed motion towards oxygen gradients (aerotaxis) in the wave speed. We predicted a transition between small and large aerotactic bias, with opposite behaviours regarding the mixing of cells during the front expansion.
This is joint work with Mete Demircigil (Institut Camille Jordan, Lyon), and a team of biophysicists : Christophe Anjard, Olivier Cochet-Escartin and Jean-Paul Rieu (Institut Lumière Matière, Lyon).

Mike Cates (Cambridge): Entropy Production Rate in Active Field Theories. pdf

The entropy production rate (EPR) is often considered a measure of microscopic heat production, but it can also be defined directly in terms of forward and time-reversed path weights for coarse-grained variables such as the continuous density or polarization fields used to describe active matter. This 'informatic' entropy production is a direct measure of irreversibility in the coarse-grained dynamics and in some cases can be given a local meaning. The local EPR can have different scalings with the noise level depending on whether the breaking of time-reversal symmetry is associated with a deterministic feature (such as a steady current circulation or a static interface) or with the dynamics of fluctuations. These scalings can also depend on whether fields such as polarization are taken to have even or odd parity under time-reversal (that is, whether a particle-scale vector represents orientation or velocity). The EPR is not conserved under coarse-graining so that reversible or near-reversible behaviour can emerge at large scales or if certain degrees of freedom are not monitored. Under RG flow, it is possible for an active model to be in the same universality class as a passive one but still maintain nontrivial scaling of the EPR as the fixed point is approached.

Cécile Cottin-Bizonne (Lyon): An introduction to active matter in real (laboratory) life.

Clément Erignoux (Lille): Scaling limits and behavior for microscopic stochastic models of active matter. pdf

Most attempts to understand the behavior of active matter models from a mathematical standpoint have been focused on some form of mean field interactions between particles, meaning that the interaction of each individual particle with the system is averaged out over a large number of its neighbors. In this talk, I will share a few attempts to model active matter by lattice gases of particles interacting at a microscopic level. I will talk about the mathematical challenges involved in such microscopic models. I will also present results in (finished and ongoing) work with T. Bodineau, M. Kourbane-Houssène and J. Tailleur, in which we show the emergence of two classical phenomena for active matter, namely Motility induced phase separation (MIPS), and alignment phase transitions.

Martin Evans (Edinburgh): Interacting Persistent Random Walkers. pdf

In this talk I will consider persistent random walkers, also known as run and tumble particles, which are emerging as a fundamental microscopic model of active matter. I will review the properties of a single persistent walker then consider the case of two persistent random walkers that interact through an exclusion interaction. An exact expression for the stationary state of two such walkers on a periodic lattice reveals how the particles jam and generate an effective attractive potential. The full spectrum of the two-particle problem can also be computed and exhibits exceptional points, which correspond to dynamical transitions in the relaxation time.
Jamming and attraction of interacting run-and-tumble random walkers, AB Slowman, MR Evans, RA Blythe, Physical review letters 116 (21), 218101 (2016)
Exact spectral solution of two interacting run-and-tumble particles on a ring lattice, E Mallmin, RA Blythe, MR Evans, Journal of Statistical Mechanics: Theory and Experiment 2019 (1), 013204

Liesbeth M. C. Janssen (Eindhoven): The physics of glass formation: from liquids to living cells.

The liquid-to-glass transition remains one of the deepest unsolved problems in condensed matter science, and has recently found renewed interest in the context of active and living matter. In this talk, I will present a novel first-principles theory of glass formation, referred to as Generalized Mode-Coupling Theory, that can shed new light on glassy phenomena. I will demonstrate that the theory can be successfully applied not only to ordinary glass-forming materials, but also to more complex systems such as dense collectives of living cells. Ultimately, this work can help to elucidate the fundamental link between structure and dynamics in disordered matter, and may even find applications in medical diagnostics to distinguish healthy from pathological cell tissue.

Yariv Kafri (Haifa): The long-ranged influence of disorder on active systems. pdf

The talk will describe the impact of random quenched potentials and torques on scalar active matter. This class of systems is known to undergo motility induced phase separation even in the absence of attractive interactions between the particles. By building on insights on the effects of a localized speck of disorder on scalar active systems it will be argued that: 1) The lower critical dimension below which phase separation is not observed asymptotically is dc=4. 2) The system has a weak-disorder regime in which the structure factor scales as S(q) ~ 1/q^2. In d = 2 we predict that, at larger scales, the behavior should cross over to a strong-disorder regime. In d>2, these two regimes exist separately, depending on the strength of the potential. Time permitting I will also describe results for the one-dimensional system.

Julien Tailleur (Paris): First-order fluctuation-induced phase transitions to collective motion. pdf

The transition to collective motion is paradigmatic of active matter. Self-propelled particles that stochastically align undergo a transition between a disordered state, at low density and large noise, and an ordered one, at high density and low noise. In the latter phase, particles travel together in a randomly selected direction of space, hence spontaneously breaking its isotropy. The nature of this transition has been at the center of a long-standing debate. Numerical simulations and mean-fieldish continuous descriptions have led to the common belief that, depending on the type of microscopic interactions between particles, two types of transitions could be observed. When particles interact with their neighbours within a finite-distance, the transition is first order, with a coexistence phase separating the disordered gas and the ordered liquid. On the contrary, when particles interact with `toplogical' neighbours, the transition is believed to be continuous. In this talk I will show how dressing mean-field hydrodynamic descriptions with noise systematically lead to first-order phase transitions. This holds for metric models but, more surprisingly, also for topological hydrodynamic theories that retain the non-local nature of the aligning interactions at the macroscopic scale. These results have been confirmed using numerical simulations of microscopic models in which particles interact with their k nearest neighbours, a model which is claimed to be relevant for animal-behaviour studies.

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Zoom recording session 1: Julien Tailleur, Cécile Cottin-Bizonne.
Zoom recording session 2: Clément Erignoux, Liesbeth M. C. Janssen.

Vincent Calvez (Lyon), Mike Cates (Cambridge), Cécile Cottin-Bizonne (Lyon), Clément Erignoux (Lille), Martin Evans (Edinburgh), Liesbeth M. C. Janssen (Eindhoven), Yariv Kafri (Haifa),

Vincent Calvez (Lyon): A simple go-or-grow model of self-generated aerotaxis.

I will present recent experimental results of self-generated hypoxia triggering the expansion of a ring of amoebae Dictyostelium discoideum at constant speed in the long range. We introduced a simple reaction-diffusion-advection model. Relevant modeling assumptions enabled computing the speed of expansion, extending the standard Fisher wave speed of classical reaction-diffusion equations. We focused on the contribution of directed motion towards oxygen gradients (aerotaxis) in the wave speed. We predicted a transition between small and large aerotactic bias, with opposite behaviours regarding the mixing of cells during the front expansion.
This is joint work with Mete Demircigil (Institut Camille Jordan, Lyon), and a team of biophysicists : Christophe Anjard, Olivier Cochet-Escartin and Jean-Paul Rieu (Institut Lumière Matière, Lyon).

Mike Cates (Cambridge): Entropy Production Rate in Active Field Theories. pdf

The entropy production rate (EPR) is often considered a measure of microscopic heat production, but it can also be defined directly in terms of forward and time-reversed path weights for coarse-grained variables such as the continuous density or polarization fields used to describe active matter. This 'informatic' entropy production is a direct measure of irreversibility in the coarse-grained dynamics and in some cases can be given a local meaning. The local EPR can have different scalings with the noise level depending on whether the breaking of time-reversal symmetry is associated with a deterministic feature (such as a steady current circulation or a static interface) or with the dynamics of fluctuations. These scalings can also depend on whether fields such as polarization are taken to have even or odd parity under time-reversal (that is, whether a particle-scale vector represents orientation or velocity). The EPR is not conserved under coarse-graining so that reversible or near-reversible behaviour can emerge at large scales or if certain degrees of freedom are not monitored. Under RG flow, it is possible for an active model to be in the same universality class as a passive one but still maintain nontrivial scaling of the EPR as the fixed point is approached.

Cécile Cottin-Bizonne (Lyon): An introduction to active matter in real (laboratory) life.

Clément Erignoux (Lille): Scaling limits and behavior for microscopic stochastic models of active matter. pdf

Most attempts to understand the behavior of active matter models from a mathematical standpoint have been focused on some form of mean field interactions between particles, meaning that the interaction of each individual particle with the system is averaged out over a large number of its neighbors. In this talk, I will share a few attempts to model active matter by lattice gases of particles interacting at a microscopic level. I will talk about the mathematical challenges involved in such microscopic models. I will also present results in (finished and ongoing) work with T. Bodineau, M. Kourbane-Houssène and J. Tailleur, in which we show the emergence of two classical phenomena for active matter, namely Motility induced phase separation (MIPS), and alignment phase transitions.

Martin Evans (Edinburgh): Interacting Persistent Random Walkers. pdf

In this talk I will consider persistent random walkers, also known as run and tumble particles, which are emerging as a fundamental microscopic model of active matter. I will review the properties of a single persistent walker then consider the case of two persistent random walkers that interact through an exclusion interaction. An exact expression for the stationary state of two such walkers on a periodic lattice reveals how the particles jam and generate an effective attractive potential. The full spectrum of the two-particle problem can also be computed and exhibits exceptional points, which correspond to dynamical transitions in the relaxation time.
Jamming and attraction of interacting run-and-tumble random walkers, AB Slowman, MR Evans, RA Blythe, Physical review letters 116 (21), 218101 (2016)
Exact spectral solution of two interacting run-and-tumble particles on a ring lattice, E Mallmin, RA Blythe, MR Evans, Journal of Statistical Mechanics: Theory and Experiment 2019 (1), 013204

Liesbeth M. C. Janssen (Eindhoven): The physics of glass formation: from liquids to living cells.

The liquid-to-glass transition remains one of the deepest unsolved problems in condensed matter science, and has recently found renewed interest in the context of active and living matter. In this talk, I will present a novel first-principles theory of glass formation, referred to as Generalized Mode-Coupling Theory, that can shed new light on glassy phenomena. I will demonstrate that the theory can be successfully applied not only to ordinary glass-forming materials, but also to more complex systems such as dense collectives of living cells. Ultimately, this work can help to elucidate the fundamental link between structure and dynamics in disordered matter, and may even find applications in medical diagnostics to distinguish healthy from pathological cell tissue.

Yariv Kafri (Haifa): The long-ranged influence of disorder on active systems. pdf

The talk will describe the impact of random quenched potentials and torques on scalar active matter. This class of systems is known to undergo motility induced phase separation even in the absence of attractive interactions between the particles. By building on insights on the effects of a localized speck of disorder on scalar active systems it will be argued that: 1) The lower critical dimension below which phase separation is not observed asymptotically is dc=4. 2) The system has a weak-disorder regime in which the structure factor scales as S(q) ~ 1/q^2. In d = 2 we predict that, at larger scales, the behavior should cross over to a strong-disorder regime. In d>2, these two regimes exist separately, depending on the strength of the potential. Time permitting I will also describe results for the one-dimensional system.

Julien Tailleur (Paris): First-order fluctuation-induced phase transitions to collective motion. pdf

The transition to collective motion is paradigmatic of active matter. Self-propelled particles that stochastically align undergo a transition between a disordered state, at low density and large noise, and an ordered one, at high density and low noise. In the latter phase, particles travel together in a randomly selected direction of space, hence spontaneously breaking its isotropy. The nature of this transition has been at the center of a long-standing debate. Numerical simulations and mean-fieldish continuous descriptions have led to the common belief that, depending on the type of microscopic interactions between particles, two types of transitions could be observed. When particles interact with their neighbours within a finite-distance, the transition is first order, with a coexistence phase separating the disordered gas and the ordered liquid. On the contrary, when particles interact with `toplogical' neighbours, the transition is believed to be continuous. In this talk I will show how dressing mean-field hydrodynamic descriptions with noise systematically lead to first-order phase transitions. This holds for metric models but, more surprisingly, also for topological hydrodynamic theories that retain the non-local nature of the aligning interactions at the macroscopic scale. These results have been confirmed using numerical simulations of microscopic models in which particles interact with their k nearest neighbours, a model which is claimed to be relevant for animal-behaviour studies.