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 in dimensions 1, 2, and 3, 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 nonmonotonically with L in dimension 1; (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 (2023)PRLTAO0031-900710.1103/PhysRevLett.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.

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 an 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. Finally, we consider nonreciprocal interactions between two populations and show how they can lead to nonsteady 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.

Push-pull mechanics of E-cadherin ectodomains in biomimetic adhesions.

E-cadherin plays a central role in cell-cell adhesion. The ectodomains of wild-type cadherins form a crystalline-like two-dimensional lattice in cell-cell interfaces mediated by both trans (apposed cell) and cis (same cell) interactions. In addition to these extracellular forces, adhesive strength is further regulated by cytosolic phenomena involving α and ß catenin-mediated interactions between cadherin and the actin cytoskeleton. Cell-cell adhesion can be further strengthened under tension through mechanisms that have not been definitively characterized in molecular detail. Here we quantitatively determine the role of the cadherin ectodomain in mechanosensing. To this end, we devise an E-cadherin-coated emulsion system, in which droplet surface tension is balanced by protein binding strength to give rise to stable areas of adhesion. To reach the honeycomb/cohesive limit, an initial emulsion compression by centrifugation facilitates E-cadherin trans binding, whereas a high protein surface concentration enables the cis-enhanced stabilization of the interface. We observe an abrupt concentration dependence on recruitment into adhesions of constant crystalline density, reminiscent of a first-order phase transition. Removing the lateral cis interaction with a "cis mutant" shifts this transition to higher surface densities leading to denser, yet weaker adhesions. In both proteins, the stabilization of progressively larger areas of deformation is consistent with single-molecule experiments that show a force-dependent lifetime enhancement in the cadherin ectodomain, which may be attributed to the "X-dimer" bond.

Spatial organization of active particles with field-mediated interactions.

We consider a system of independent pointlike particles performing a Brownian motion while interacting with a Gaussian fluctuating background. These particles are in addition endowed with a discrete two-state internal degree of freedom that is subjected to a nonequilibrium source of noise, which affects their coupling with the background field. We explore the phase diagram of the system and pinpoint the role of the nonequilibrium drive in producing a nontrivial patterned spatial organization. We are able, by means of a weakly nonlinear analysis, to account for the parameter-dependence of the boundaries of the phase and pattern diagram in the stationary state.

Interaction and structuration of membrane-binding and membrane-excluding colloidal particles in lamellar phases.

Within the framework of a discrete Gaussian model, we present analytical results for the interaction induced by a lamellar phase between small embedded colloidal particles. We consider the two limits of particles strongly adherent to the adjacent membranes and of particles impenetrable to the membranes. Our approach takes into account the finite size of the colloidal particles, the discrete nature of the layers, and includes the Casimir-like effect of fluctuations, which is very important for dilute phases. Monte Carlo simulations of the statistical behavior of the membrane-interacting colloidal particles account semi-quantitatively, without any adjustable parameters, for the experimental data measured on silica nanospheres inserted within lyotropic smectics. We predict the existence of finite-size and densely packed particle aggregates originating from the competition between attractive interactions between colloidal particles in the same layer and repulsion between colloidal particles one layer apart.

Field-Embedded Particles Driven by Active Flips.

Systems of independent active particles embedded into a fluctuating environment are relevant to many areas of soft-matter science. We use a minimal model of noninteracting spin-carrying Brownian particles in a Gaussian field and show that activity-driven spin dynamics leads to patterned order. We find that the competition between mediated interactions and active noise alone can yield such diverse behaviors as phase transitions and microphase separation, from lamellar up to hexagonal ordering of clusters of opposite magnetization. These rest on complex multibody interactions. We find regimes of stationary patterns, but also dynamical regimes of relentless birth and growth of lumps of magnetization opposite of the surrounding one. Our approach combines Monte Carlo simulations with analytical methods based on dynamical density functional approaches.