Control theory for topological active matter

Experimental techniques have demonstrated the ability to alter the collective dynamics of active systems with various types of external perturbations [1-2]. In many experiments, the spatiotemporal control of activity is often optimised using system-specific procedures. A series of recent theoretical works has strived to go beyond this empirical effort, and systematically guide experiments towards optimal control [3-6]: how to determine the protocol which most efficiently changes the collective properties of the system. Many collective states in active matter feature some non-trivial topological properties [7] which can have important biological functions [8-9]. In this context, promoting and driving defects has emerged as an efficient strategy to regulate internal flows and structures [2, 10]. An important challenge is to examine how existing control theories for active matter [3-6] can be deployed in topological states. To this end, the aim of this project is to reveal how control theories can identify the optimal strategies to manipulate defects, and thus provide an efficient route towards controlling dynamical patterns in active matter.

We will build on previous studies by Golestanian [6, 11-13] and Fodor [5, 14] which have considered minimal models of topological active matter in many-body systems. These models will cover both particle-based models (T1) and stochastic field theories (T3), which represent multicellular assemblies (L3). By building and analysing an effective stochastic dynamic for defects, we will propose a systematic roadmap for the optimal control of topological properties, with a focus on minimising the amount of energy dissipated in driving defects. We will rely on numerical simulations (T9, T10), along with analytical tools of defect topology (T5), optimal control (T6), and stochastic thermodynamics (T7). Our results will shed light on concrete strategies to control patterns in experimental settings.

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