Examples of active systems, formed of units that are able to extract energy from the environment and dissipate it to self-propel, are found everywhere in nature: flocks of birds, animal swarms, suspensions of bacteria or tissues are all biological active systems. Scientists are able to build synthetic active systems using catalytic colloidal particles or micro-robots.

Active systems have theoretically fascinating properties, a fact that drove a very intense research activity lately. Future applications may encompass the engineering self-assembling materials using active units, considered as a defining agenda in the community.

Large assemblies of active units display collective phenomena that are absent in equilibrium. One of the most ubiquitous is phase separation, where even repulsive but active particles phase separate into dense and dilute phases. In some cases, this phenomena resemble to liquid-vapor phase separation of standard fluids. Due to broken time-reversibility, however, active systems can show novel forms of phase separation, comprising a state where the liquid state comprises mesoscopic vapor bubbles (thus resembling to a boiling liquid), or active foams states, where thin liquid filaments are dispersed in the vapor.

Furthermore, in most experimental realization, active systems are `wet’, meaning that particles move in a fluid which itself can mediate interactions among particles, a feature whose consequences are so far little understood theoretically.

The main open theoretical question is how to control these novel states of matter in terms of microscopically tunable parameters. The main goal of this PhD is to fill this gap. This will require both analytical and computational work done on agent based models and continuous descriptions of active systems. If successful, the work will provide a guide for experimentalists to design novel self-assembling materials using active units. Given the ubiquity of phase separation in non-equilibrium contexts, we will further explore the relevance of these results to other out-of-equilibrium systems, such as biological tissues and granular materials.