Active matter (AM) represents a fascinating system where continuous energy flow enables persistent dynamics like locomotion in inert materials and may lead to fascinating collective behaviors resembling those of living agents such as bird flocks or bacterial vortices. In particular, collective order in AM stands to enable the realization of a new generation of materials with customizable dynamic functions such as targeted transport, self-healing, sensing among others, and is a rapidly expanding field both at the theoretical and experimental level. However, how these collective behaviors emerge and how they correlate to the underlying energy flow remains an open challenge, especially at the small scales where top-down manipulation is often impracticable or unfeasible. It further bears important implication to living systems which stand as a paradigmatic example of how finely controlled programs of energy flow result in robust dynamical functions and diverse collective behavior.
In IDAM we aim to address key areas of this question via the study of a more general class of active matter systems at the particle and field level via discovered and directed strategies for collective control. This approach follows in the spirit of inverse design strategies where desirable collective structures are realized as the stable state from an otherwise disorganized system. These efforts typically combine theory and numerics to formulate an optimization problem from sound physical principles and solve it via a combination of numerics and simulations. For instance, colloidal structures with specific structures (e.g. crystals), materials properties (elastic response, wave propagation etc) or condensed behavior (fluid porosity) have been successfully designed this way via equilibrium, free-energy principles.
However, extending such an approach to AM is non-trivial given its inherent non-equilibrium character via continuous energy consumption. In this project we therefore advance large deviation theory (LDT) as a powerful framework to discover collective phase transitions in AM via control of the underlying dynamics. In particular, LDT allows to alter a system’s dynamics via calculation of internal dynamic observables such as a time average by biasing (hence directing) energy-flows. Indeed, similar approaches to systems of self-propelling particles show that biasing with respect to its energy flow resulted in the formation of well known collective phases such as clustering and flocking of particles, which respectively, represent low and high forms of energy flow in these systems. In IDAM our main goal is to develop a general LDT framework which we apply to a system of particles with continuous size pulsation to explore their emergent collective phases.
We additionally look at a more general class of control problems and consider the case of phase transformations between an initial and final state in finite time. Examples of such processes take place, for instance, in the folding-unfolding transition of a DNA-hair pin motif upon stretching or release from an externally controlled force, or the optimal flipping of a spin state in a magnetic material. From the second law of thermodynamics, we know such transformation energy cost is minimal in the quasistatic limit i.e. as the protocol duration goes to infinity and given by a free-energy difference. However, realistic experimental transitions must necessarily take place in finite time and therefore imply an inevitable energy loss when carried out. Nonetheless, one may consider a protocol which minimizes such a loss and which, from this perspective, represents an optimal control between the two state transition process.
IDAM therefore develops and explores two distinct strategies of control via the following major objectives:
1) Development of a numerical LDT framework which to study collective phase transitions of dynamical systems like active matter models
2) Application of the framework to a system of pulsating active particles in context of collective phase transitions and consideration to continuum active matter models
3) Development of an optimal control optimizer in finite time from a variational formulation of a minimum dissipation protocols
4) Application of a liquid-state transformation via tuning of particle size and interactions in a paradigmatic model of liquids with Lennard-Jones interactions
