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Collective Phenomena in dense Active Matter: phase transitions and non-equilibrium dynamics.

Periodic Reporting for period 1 - COLPHAM (Collective Phenomena in dense Active Matter: phase transitions and non-equilibrium dynamics.)

Reporting period: 2015-07-15 to 2017-07-14

The main goal of this project was to elucidate the general principles governing the collective behavior of self-propelled (or active) particles (i.e. any ‘biomimetic’ units able to convert energy into motion, like bacteria, birds or synthetic Janus colloids). Active matter, made of large assemblies of interacting active particles, evolves out-of-equilibrium, offering new promises in organizing elementary units at different scales in ways that are unreachable to traditional equilibrium passive systems. As such, the understanding of the emergent collective behavior of active systems has direct applications in a broad range of disciplines, ranging from material science and biology.

The collective phenomena in active matter has been mostly understood in terms of simplified particle models using the framework of statistical mechanics, which allow to identify the key ingredients giving rise to such non-equilibrium behaviour. We followed this strategy in order to tackle the main objectives of the project:
1) To understand the phase behavior of self-propelled particles: Can we describe non-equilibrium phase transitions induced by self-propulsion in terms of equilibrium-like concepts?
2) How does an active fluid flow?
3) Can we use effective thermodynamic concepts to describe the dynamics of active systems?
4) How is the collective behavior of active matter affected by velocity alignment interactions?

The project addressed all initial objectives and opened new directions of research that where not initially foreseen. Important new research results have been attained. We clarified the nature of several phase transitions in active systems, showing to what extent ideas from equilibrium systems can be borrowed to describe them. We elucidated the generic mechanisms by which self-propelled agents synchronize and found new routes for pattern formation. The project also allowed initiating collaborations with other academic institutions in the EU. The collaboration between the fellow (in Spain), its German and British partners initiated in the framework of the project, contributed to develop lasting relations and increase the scientific excellence of the fellow and the ERA. Overall, the completion of this project has advanced in the state-of-the-art by contributing with original results and has consolidated the fellow as a leading expert in the field.
I quantified deviations from equilibrium in an active fluid and show that a unique effective temperature does not in general characterize its dynamics, but it does at very high density due to the collective freezing occurring at non-equilibrium glass transitions.
I designed a versatile computer code to simulate active particles that allows to study its phase behavior and long time dynamics in the presence of an external shear flow.
First, I carried out the investigation of the pressure and the equations of state. I clarified the nature of the activity-induced phase separation generically found in these systems and showed that it verifies the characteristic properties of an equilibrium liquid-gas transition.
Then, I adapted a analytical formalism and performed numerical simulations of Active Brownian Particles under shear. I found that the shear response depends on the coupling between the self-propulsion mechanism and the flow profile.
I investigated the impact of self-propulsion on the synchronization of mobile units. I combined Monte Carlo simulations with analytical calculations to analyze the synchronization dynamics.
I developed a simulation code to investigate the competition between velocity alignment and steric interactions. In collaboration with two master and one graduate students, we established a phase diagram showing how alignment promotes phase separation and the formation of different kinds of coherently moving structures.
During the second year I started considering self-propelled particles with an active torque. Using numerical simulations and analytical calculations based on continuum field equations, we showed that rotations provide a generic new route to pattern formation.

Overall, our results provide a complete picture of the collective behavior of simple models of self-propelled particles. We elucidated the impact of the different kind of interactions and self-propulsion mechanisms in the phase transitions and structure formation. We showed to what extent the static phase behavior and long-time dynamics of active fluids might be described using equilibrium-like concepts and opened new lines of research about the control of particles' self-assembly using rotations.
The possibility to characterize the phase behavior of active matter by thermodynamic measurements is a matter of debate. To move forward in our ability to exploit active systems, it is crucial to provide a consistent interpretation of macroscopic measurements. We showed that the phase behavior of Active Brownian Particles can be described by its equations of state and the slow glassy dynamics by an effective temperature, providing a firm basis to interpret experiments and simulations using thermodynamic-like ideas.

Despite its experimental relevance, the rheology of suspensions of active particles has not yet been investigated in depth yet. We have established a framework to investigate it, together with a numerical simulation code that allows us to compute the viscosity.

To date, most studies of synchronization involve static structures, despite that many interesting synchronization phenomena involve self-propelled agents. We showed that mobile oscillators synchronize through an equilibrium-like coarsening mechanism. Connections to equilibrium have become a main tool to characterize active systems. However, such connections have never been made to describe the relaxation of an internal variable.

Our understanding of the universal character of phase transitions in active matter is based on the analysis of two paradigmatic models: the Vicsek model and the Active Brownian Particles model. In realistic situations, the interaction mechanisms - velocity alignment and excluded volume - of both models are usually at play. However, their interplay has not been explored yet. We analyzed how the structures found in both models are affected affected by excluded volume and velocity alignment interactions.

Despite the recent boost in research on circle swimmers- like bacteria suspensions in two dimensions or asymmetric L-shaped chiral self-propelled colloids- their collective behavior has not been carefully studied yet. Using numerical simulations and an analytic theory we show that rotations provide a novel generic route to pattern formation. Most remarkably, we show that the size of these patterns can be directly controlled by the microscopic parameters of the model in a simple way. These results constitute a significant step in the present quest for controlling the ability of active systems to self-assemble.
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