Abstract
Active nematics are a class of non-equilibrium systems with constituents that consume energy at the molecular level to generate motion at macroscopic scales. In bulk, these materials exhibit turbulent behavior, and the active energy is not converted into meaningful work. One way of taming the turbulence is via confinement in regular geometries, which requires understanding the effect of boundaries on the active flows. Other approaches might involve strategies like optimal control or model-predictive control to steer the flows as desired. These methods require either an accurate knowledge of the underlying model or a robust way of forecasting its behavior in real time. In this dissertation, we address these problems using computations, data-driven model identification and machine learning methods.
Firstly, we use a postulated hydrodynamic model to examine the dynamical behavior of confined 2D active nematics using finite element simulations. Studying an annulus geometry, we uncover an interplay between the confinement and the boundary curvature, while also bridging the observed behaviors in the disk and channel geometries. Next, we employ a data-driven method to automatically identify the optimal continuum models, along with their parameters, directly from the experimental data of active nematics. This approach puts the existing theories to test and helps in developing control protocols that drive the system to desired outcomes. Lastly, we engineer a deep learning forecasting model of active nematics. Our model is able to predict key dynamical events using minimal input data. Such a model can be the backbone of a model predictive control strategy.