Final Report Summary - D4PARTICLES (Statistical physics of dense particle systems in the absence of thermal fluctuations) Statistical mechanics was developed by its founders to understand the thermal properties of simple phases of matter. In this project we aimed at extending the tools of equilibrium statistical mechanics to characterize and understand at the microscopic level the physical properties of dense particle systems evolving far from thermal equilibrium. Our work deals with essentially two types of materials. First, we consider dense particle assemblies that evolve at strictly zero temperature under the influence of an external forcing at the macroscopic scale, such as dense suspensions of non-Brownian particles. In another effort, we consider materials where particles are driven at the microscopic level, such as self-propelled or active particles, and self-deformable soft colloidal particles.We have developed novel numerical tools to characterize the rheology of dense suspensions of non-Brownian particles. To this end, we performed computer simulations to analyze the response of a particle-based model of athermal particles to an external shear flow. Starting from simple particle interactions, we progressively added one or several of the following ingredients: thermal motion, frictional forces between particles, inertial forces and analyzed the resulting macroscopic response of the system. In the simplest case, we have been able to determine the growth of the viscosity of non-Brownian particles over an unprecedented dynamic range, thereby establishing the laws obeyed by model systems. Adding thermal fluctuations and inertial forces allowed us to perform detailed comparison to experimental measurements performed in the laboratory. Finally, we have shown that the addition of a small amount of frictional forces produces a spectacular shear-thickening behavior, where the viscosity of the suspension may abruptly increase by several orders of magnitude upon a small change in the driving amplitude. Reproducing numerically this effect within a very simple, minimal model of a suspension paves the way for a detailed understanding of its microscopic origin. In a second part of this project we have considered particle systems where the "particles" are locally driven. Our goal is to develop minimal models to understand the emerging physical properties of dense assemblies of "active" particles, where the activity is either provided by a physical process (such as active colloidal particles), or because particles are actually living entities (such as bacterial colonies or dense epithelial tissues). We have discovered that dense assemblies of particles that should behave as arrested solids can easily flow like a fluid when the level of the "activity" is increased. Using the language of phase transitions, this suggests that active materials undergo a non-equilibrium transition towards a glassy state that is conceptually affected in a deep way as to their equilibrium, thermal counterparts. We have employed advanced statistical mechanical tools to characterize better and understand theoretically this phenomenon. We are also studying the case where the "activity" can actually take the form of a change of the shape of the particles, which we termed "self-deformable" particles. Intuitively, this means that a particle could have the ability to momentarily decrease its size in order to squeeze in a small space. This could then again allow for the macroscopic flow of an otherwise completely jammed material, which could be relevant for dense tissues. Finally, we also study the generic problem of non-Brownian particle systems driven by periodic driving forces, in order to understand how periodic forces differ from ordinary (white-noise) thermal fluctuations, and we related our studies to the broad field of mechanical response of driven amorphous materials.
