Self-organization of active mixtures

Self-organization is ubiquitous in biological systems at all scales, from the animal world down to the intra-cellular environment. In all these systems, the dynamics of micro-constituents can lead to emergent large-scale behaviours, such as static patterns or collective motion. Active matter provides a solid framework to explain the physics behind these processes at many different scales. So far, the literature on the subject has mostly focused on single-component active systems; nonetheless, monodispersity imposes strong limitations on the complexity of the emergent macroscopic phases. In order to obtain less idealised self-assembling structures like the ones encountered in biology, heterogeneity must be included. In this work we study the macroscopic phenomenology of N-component active mixtures of run-and-tumble particles (RTPs) interacting via quorum-sensing (QS), with both numerical and analytical tools. Microscopic simulations are employed to study the macroscopic phases of binary active mixtures, with a special focus on dynamic patterns. To explain the emergence of the observed phases, we coarse-grain the microscopic theory to derive the macroscopic dynamics of the density fields. Via mean-field approximation and linear stability analysis of the field theory, we relate the microscopic parameters to the emergent large-scale patterns. Finally, we study under which conditions on the microscopic dynamics an active mixture of RTPs exhibits time-reversal symmetry (TRS) at the macroscopic level. When this occurs, the active mixture is macroscopically equivalent to an equilibrium passive system. In particular, we show that such a mapping to equilibrium can exist only if microscopic QS-interactions between different strains are reciprocal.