Unveiling the Phase Diagram and Reaction Paths of the Active Model B with the Deep Minimum Action Method

Nonequilibrium phase transitions are notably difficult to analyze because their mechanisms depend on the system's dynamics in a complex way due to the lack of time-reversal symmetry. To complicate matters, the system's steady-state distribution is unknown in general. Here, the phase diagram of the active Model B is computed with a deep neural network implementation of the geometric minimum action method (gMAM). This approach unveils the unconventional reaction paths and nucleation mechanism by which the system switches between the homogeneous and inhomogeneous phases in the binodal region. Our main findings are: (i) the mean time to escape the phase-separated state is (exponentially) extensive in the system size $L$, but it increases non-monotonically with $L$; (ii) the mean time to escape the homogeneous state is always finite, in line with the recent work of Cates and Nardini~[Phys. Rev. Lett. 130, 098203]; (iii) at fixed $L$, the active term increases the stability of the homogeneous phase, eventually destroying the phase separation in the binodal for large but finite systems. Our results are particularly relevant for active matter systems in which the number of constituents hardly goes beyond $10^7$ and where finite-size effects matter.Comment: 5 pages, 4 figures, and Supplemental Materia

Socioeconomic agents as active matter in nonequilibrium Sakoda-Schelling models

How robust are socioeconomic agent-based models with respect to the details of the agents' decision rule? We tackle this question by considering an occupation model in the spirit of the Sakoda-Schelling model, historically introduced to shed light on segregation dynamics among human groups. For a large class of utility functions and decision rules, we pinpoint the nonequilibrium nature of the agent dynamics, while recovering the equilibrium-like phase separation phenomenology. Within the mean field approximation we show how the model can be mapped, to some extent, onto an active matter field description (Active Model B). Finally, we consider non-reciprocal interactions between two populations, and show how they can lead to non-steady macroscopic behavior. We believe our approach provides a unifying framework to further study geography-dependent agent-based models, notably paving the way for joint consideration of population and price dynamics within a field theoretic approach.Comment: 12 pages, 7 figure

Interactions médiées dans la matière molle et tension de surface des fluides actifs

This thesis focuses on two topics ubiquitous in soft matter: first, mediated interactions between nano-to-micrometer sized objects, second, surface tension in out-of-equilibrium systems.The first part of this thesis is devoted to the properties of a system of particles whose interactions are mediated by a fluctuating background. We start with a nonequilibrium study and we show that the combination of mediated interactions and of the nonequilibrium drive leads to complex structures. Our predictions, beyond statistical mechanical methods, rests on extending the methods of nonlinear dynamics in pattern forming systems, to systems with a local conservation law. The second study of this part is dedicated to an equilibrium experimental system of colloidal particles embedded in lyotropic lamellar phases. Relying on a bottom-up approach, we implement the details of the interaction between each colloidal particle and each lamella to come up with an exact description of the effective force emerging between colloids. These analytical results are then used to discriminate between two types of interaction, both being possibly encountered in experiments.The second part of this thesis focuses on the notion of surface tension for interfaces involving active fluids. We will come up with a definition relating macroscopic forces to microscopic ones, either between particles or, when applicable, between particles and a confining medium. When the active fluid is in contact with a solid boundary, the solid-fluid surface tension is, in general, a more complex quantity than its equilibrium counterpart. By this we mean that its value may depend on the geometry or other details of the measuring device. We will also show that a carefully designed probe allows us to access an equation-of-state-abiding surface tension akin to its equilibrium counterpart. Liquid-vapor interfaces can also be encountered in assemblies of self-propelled particles when these undergo a motility-induced phase separation. We show also that the surface tension associated to a liquid-vapor interface possesses a mechanical definition that echoes the equilibrium one.Cette thèse aborde deux thématiques importantes en matière molle, à savoir, l’apparition d’interactions médiées par le milieu entre objets de taille nanométriques ou micrométriques, et la notion de tension de surface dans les systèmes hors de l’équilibre.La première partie de cette thèse est consacrée à l’étude de systèmes dans lesquelles les interactions entre particules sont médiées par un champ fluctuant. Nous étudions dans un premier temps un système hors d’équilibre et nous montrons que l’existence d’interactions médiées associées à l’activité des particules qui place le système hors de l’équilibre conduit à la formation de structures complexes. Nos prédictions s’appuient sur des méthodes de mécanique statistique mais surtout sur des méthodes de dynamique non-linéaire utilisées pour prédire l’apparition de motifs dans les systèmes dans lesquels il existe une quantité conservée. Le seconde étude de cette partie est dédiée à l’explication des interactions émergentes observées expérimentalement dans des systèmes de particules colloïdales insérées dans des phases lamellaires lyotropiques. En partant de la description microscopique des interactions entre particules et couches de surfactants, nous calculons de façon exacte la force effective qui émerge entre particules seulement. Ces résultats analytiques sont ensuite utilisés pour distinguer et identifier, parmi deux types possibles d’interactions entre lamelles et particules, lequel est observé dans notre système expérimental à l’étude.La seconde partie de cette thèse s’attache à identifier la notion de tension de surface dans les fluides actifs. Nous parvenons à proposer une définition de la tension de surface qui relie les forces macroscopiques aux forces microscopiques existant entre particules, ou entre particules et un mur confinant. Lorsque le fluide actif est en contact avec un mur, la tension de surface solide-fluide est en général d’une nature plus complexe que celle que l’on peut définir pour son analogue d’équilibre. Par ceci, nous entendons que la valeur mesurée de la tension de surface peut dépendre de la géométrie ou d’autres détails de l’appareil de mesure utilisé. Nous montrerons également que des appareils de mesure correctement choisis permettent d’accéder à une tension de surface intrinsèque au matériau (et non plus à la géométrie), caractéristique d’une variable d’état d’équilibre. Les séparations de phases de type liquide-vapeur peuvent être également rencontrées dans les assemblées de particules auto-propulsées, lorsque celles-ci sont sujettes à une séparation de phase induite par la motilité. Nous montrons alors que la tension de surface associée à l’interface liquide-vapeur possède une définition mécanique cohérente avec avec son interprétation d’équilibre

Mediated interactions in soft matter and surface tension of active fluids

Cette thèse aborde deux thématiques chères à la matière molle, à savoir, l’apparition d’interaction médiées par le milieu entre objets de taille nanométrique ou micrométrique, et la notion de tension de surface dans les systèmes hors de l’équilibre. La première partie de cette thèse est consacrée à l’étude de systèmes dans lesquelles les interactions entre particules sont médiées par un champ fluctuant. Nous étudions dans un premier temps un système hors d’équilibre et nous montrons que l’existence d’interactions médiées associées à l’activité des particules qui place le système hors de l’équilibre conduit à la formation de structures complexes. Nos prédictions s’appuient sur des méthodes de mécanique statistique mais surtout sur des méthodes de dynamique non-linéaire utilisées pour prédire l’apparition de motifs dans les systèmes dans lesquels il existe une quantité conservée. Le seconde étude de cette partie est dédiée à l’explication des interactions émergentes observées expérimentalement dans des systèmes de particules colloidales insérées dans des phases lamellaires lyotropiques. En partant de la description microscopique des interactions entre particules et couches de surfactants, nous calculons de façon exacte la force effective qui émerge entre particules seulement. Ces résultats analytiques sont ensuite utilisés pour distinguer et identifier, parmi deux types possibles d’interactions entre lamelles et particules, lequel est observé dans notre système expérimental à l’étude. La seconde partie de cette thèse s’attache à identifier la notion de tension de surface dans les fluides actifs. Nous parvenons à proposer une définition de la tension de surface qui relie les forces macroscopiques aux forces microscopiques existant entre particules, ou entre particules et un mur confinant. Lorsque le fluide actif est en contact avec un mur, la tension de surface solide-fluide est en général d’une nature plus complexe que celle que l’on peut définir pour son analogue d’équilibre. Par ceci, nous entendons que la valeur mesurée de la tension de surface peut dépendre de la géométrie ou d’autres détails de l’appareil de mesure utilisé. Nous montrerons également que des appareils de mesure correctement choisis permettent d’accéder à une tension de surface intrinsèque au matériau(et non plus à la géométrie), caractéristique d’une variable d’état d’équilibre. Les séparations de phases de type liquide-vapeur peuvent être également rencontrées dans les assemblées de particules auto-propulsées, lorsque celles-ci sont sujettes à une séparation de phase induite par la motilité. Nous montrons alors que la tension de surface associée à l’interface liquide-vapeur possède une définition mécanique cohérente avec avec son interprétation d’équilibre.This thesis focuses on two topics ubiquitous in soft matter: first, mediated interactions between nano-to-micrometer sized objects, second, surface tension in out-of-equilibrium systems. The first part of this thesis is devoted to the properties of a system of particles whose interactions are mediated by a fluctuating background. We start with a nonequilibrium study and we show that the combination of mediated interactions and of the nonequilibrium drive leads to complex structures. Our predictions, beyond statistical mechanical methods, rest on extending the methods of nonlinear dynamics in pattern forming systems, to systems with a local conservation law. The second study of this part is dedicated to an equilibrium experimental system of colloidal particles embedded in lyotropic lamellar phases. Relying on a bottom-up approach, we implement the details of the interaction between each colloidal particle and each lamella to come up with an exact description of the effective force emerging between colloids. These analytical results are then used to discriminate between two types of interaction, both being possibly encountered in experiments. The second part of this thesis focuses on the notion of surface tension for interfaces involving active fluids. We will come up with a definition relating macroscopic forces to microscopic ones, either between particles or, when applicable, between particles and a confining medium. When the active fluid is in contact with a solid boundary, the solid-fluid surface tension is, in general, a more complex quantity than its equilibrium counterpart. By this we mean that its value may depend on the geometry or other details of the measuring device. We will also show that a carefully designed probe allows us to access an equation-of-state-abiding surface tension akin to its equilibrium counterpart. Liquid-vapor interfaces can also be encountered in assemblies of self-propelled particles when these undergo a motility-induced phase separation. We show also that the surface tension associated to a liquid-vapor interface possesses a mechanical definition that echoes the equilibrium one

The elusive synchrotron precursor of collisionless shocks

Context. Most of the plasma microphysics which shapes the acceleration process of particles at collisionless shock waves takes place in the cosmic-ray precursor, upstream of the shock front, through the interaction of accelerated particles with the unshocked plasma. Aims. Detecting directly or indirectly the synchrotron radiation of accelerated particles in this synchrotron precursor would open a new window on the microphysics of acceleration and of collisionless shock waves. Whether such a detection is feasible is discussed in the present paper. Methods. To this effect, we provide analytical estimates of the spectrum and of the polarization fraction of the synchrotron precursor for both relativistic and non-relativistic collisionless shock fronts, accounting for the self-generation or amplification of magnetic turbulence. Results. In relativistic sources, the spectrum of the precursor is harder than that of the shocked plasma because the upstream residence time increases with particle energy, leading to an effectively hard spectrum of accelerated particles in the precursor volume. At high frequencies, typically in the optical to X-ray range, the contribution of the precursor becomes sizeable, but we find that in most cases studied, it remains dominated by the synchrotron or inverse Compton contribution of the shocked plasma; its contribution might be detectable only in trans-relativistic shock waves. Non-relativistic sources offer the possibility of spectral imaging of the precursor by viewing the shock front edge-on. We calculate this spectro-morphological contribution for various parameters. The synchrotron contribution is also sizeable at the highest frequencies (X-ray range), corresponding to maximum energy electrons propagating on distance scales ~1016 cm away from the shock front. If the turbulence is tangled in the plane transverse to the shock front, the resulting synchrotron radiation should be nearly maximally linearly polarized; polarimetry thus arises as an interesting tool to reveal this precursor

Minimum Action Method for Nonequilibrium Phase Transitions

First-order nonequilibrium phase transitions observed in active matter, fluid dynamics, biology, climate science, and other systems with irreversible dynamics are challenging to analyze because they cannot be inferred from a simple free energy minimization principle. Rather the mechanism of these transitions depends crucially on the system's dynamics, which requires us to analyze them in trajectory space rather than in phase space. Here we consider situations where the path of these transitions can be characterized as the minimizer of an action, whose minimum value can be used in a nonequilibrium generalization of the Arrhenius law to calculate the system's phase diagram. We also develop efficient numerical tools for the minimization of this action. These tools are general enough to be transportable to many situations of interest, in particular when the fluctuations present in the microscopic system are non-Gaussian and its dynamics is not governed by the standard Langevin equation. As an illustration, first-order phase transitions in two spatially-extended nonequilibrium systems are analyzed: a modified Ginzburg-Landau equation with a chemical potential which is non-gradient, and a reaction-diffusion network based on the Schl\"ogl model. The phase diagrams of both systems are calculated as a function of their control parameters, and the paths of the transitions, including their critical nuclei, are identified. These results clearly demonstrate the nonequilibrium nature of the transitions, with differing forward and backward paths.Comment: 18+9 pages, 10+4 figure