Abstract

Flocks of birds, schools of fishes, or bacterial colonies constitute examples of living systems that coordinate their motion. In all these systems their constituent elements generate motion due to energy consumption and can exchange information or react sensitively to chemical cues to move together or to react collectively to external signals. Artificial systems, such as nanorobots, exploit the heterogeneous compositions of their surface to displace because of the heterogeneous chemical processes that take place in the presence of appropriate chemical substances.These systems are intrinsically out of equilibrium in the absence of any external driving, and their collective properties result as a balance between their direct interactions and the indirect coupling to the medium in which they displace. This balance leads usually to the emergence of long-range spatial correlations and slow relaxation times.  These correlations have strong implications on the sensitivity of active systems to external perturbations and disorder, or to the properties of the effective interactions  that determine the emergent phases that characterize them.In order to understand the basic principles underlying the emergence and self-assembly on active systems I will introduce simple statistical   models, and will  show the relevance of shape and symmetries in the non-equilibrium phase transitions of active systems, as well as their response to localized perturbations and the implications this has on the effective interactions of suspension of inclusions embedded in an active bath.