Data-Driven Discovery of Active Nematic Hydrodynamics

Optimal Control of Short-Time Attractors in Active Nematics

Objective Eulerian coherent structures (OECSs) and instantaneous Lyapunov exponents (iLEs) govern short-term material transport in fluid flows as Lagrangian coherent structures and the finite-time Lyapunov exponent do over longer times. Attracting OECSs and iLEs reveal short-time attractors and are computable from the Eulerian rate-of-strain tensor. Here, we devise for the first time an optimal control strategy to create short-time attractors in compressible, viscosity-dominated active nematic flows. By modulating the active stress intensity, our framework achieves a target profile of the minimum eigenvalue of the rate-of-strain tensor, controlling the location and shape of short-time attractors. We show that our optimal control strategy effectively achieves desired short-time attractors while rejecting disturbances. Combining optimal control and coherent structures, our work offers a new perspective to steer material transport in compressible active nematics, with applications to morphogenesis and synthetic active matter.

Physics-informed and data-driven discovery of governing equations for complex phenomena in heterogeneous media

Rapid evolution of sensor technology, advances in instrumentation, and progress in devising data-acquisition software and hardware are providing vast amounts of data for various complex phenomena that occur in heterogeneous media, ranging from those in atmospheric environment, to large-scale porous formations, and biological systems. The tremendous increase in the speed of scientific computing has also made it possible to emulate diverse multiscale and multiphysics phenomena that contain elements of stochasticity or heterogeneity, and to generate large volumes of numerical data for them. Thus, given a heterogeneous system with annealed or quenched disorder in which a complex phenomenon occurs, how should one analyze and model the system and phenomenon, explain the data, and make predictions for length and time scales much larger than those over which the data were collected? We divide such systems into three distinct classes. (i) Those for which the governing equations for the physical phenomena of interest, as well as data, are known, but solving the equations over large length scales and long times is very difficult. (ii) Those for which data are available, but the governing equations are only partially known, in the sense that they either contain various coefficients that must be evaluated based on the data, or that the number of degrees of freedom of the system is so large that deriving the complete equations is very difficult, if not impossible, as a result of which one must develop the governing equations with reduced dimensionality. (iii) In the third class are systems for which large amounts of data are available, but the governing equations for the phenomena of interest are not known. Several classes of physics-informed and data-driven approaches for analyzing and modeling of the three classes of systems have been emerging, which are based on machine learning, symbolic regression, the Koopman operator, the Mori-Zwanzig projection operator formulation, sparse identification of nonlinear dynamics, data assimilation combined with a neural network, and stochastic optimization and analysis. This perspective describes such methods and the latest developments in this highly important and rapidly expanding area and discusses possible future directions.

Probing active nematics with in situ microfabricated elastic inclusions

In this work, we report a direct measurement of the forces exerted by a tubulin/kinesin active nematic gel as well as its complete rheological characterization, including the quantification of its shear viscosity, η, and its activity parameter, α. For this, we develop a method that allows us to rapidly photo-polymerize compliant elastic inclusions in the continuously remodeling active system. Moreover, we quantitatively settle long-standing theoretical predictions, such as a postulated relationship encoding the intrinsic time scale of the active nematic in terms of η and α. In parallel, we infer a value for the nematic elasticity constant, K, by combining our measurements with the theorized scaling of the active length scale. On top of the microrheology capabilities, we demonstrate strategies for defect encapsulation, quantification of defect mechanics, and defect interactions, enabled by the versatility of the microfabrication strategy that allows to combine elastic motifs of different shapes and stiffnesses that are fabricated in situ.

Machine learning methods for liquid crystal research: phases, textures, defects and physical properties

Liquid crystal materials, with their unique properties and diverse applications, have long captured the attention of researchers and industries alike. From liquid crystal displays and electro-optical devices to advanced sensors and emerging technologies, the study and application of liquid crystals continue to be of paramount importance in the fields of materials science, chemistry and physics. With the ever-increasing complexity and diversity of liquid crystal materials, researchers face new challenges in understanding their behaviors, properties, and potential applications. On the other hand, machine learning, a rapidly evolving interdisciplinary field at the intersection of computer science and data analysis, has already become a powerful tool for unraveling implicit correlations and predicting new properties of a wide variety of physical and chemical systems and structures. Here we aim to consider how machine learning methods are suitable for solving fundamental problems in the field of liquid crystals and what are the advantages of this artificial intelligence based approach.

Machine learning interpretable models of cell mechanics from protein images

Cellular form and function emerge from complex mechanochemical systems within the cytoplasm. Currently, no systematic strategy exists to infer large-scale physical properties of a cell from its molecular components. This is an obstacle to understanding processes such as cell adhesion and migration. Here, we develop a data-driven modeling pipeline to learn the mechanical behavior of adherent cells. We first train neural networks to predict cellular forces from images of cytoskeletal proteins. Strikingly, experimental images of a single focal adhesion (FA) protein, such as zyxin, are sufficient to predict forces and can generalize to unseen biological regimes. Using this observation, we develop two approaches-one constrained by physics and the other agnostic-to construct data-driven continuum models of cellular forces. Both reveal how cellular forces are encoded by two distinct length scales. Beyond adherent cell mechanics, our work serves as a case study for integrating neural networks into predictive models for cell biology.

Rectified Rotational Dynamics of Mobile Inclusions in Two-Dimensional Active Nematics

We investigate the dynamics of mobile inclusions embedded in 2D active nematics. The interplay between the inclusion shape, boundary-induced nematic order, and autonomous flows powers the inclusion motion. Disks and achiral gears exhibit unbiased rotational motion, but with distinct dynamics. In comparison, chiral gear-shaped inclusions exhibit long-term rectified rotation, which is correlated with dynamics and polarization of nearby +1/2 topological defects. The chirality of defect polarities and the active nematic texture around the inclusion correlate with the inclusion's instantaneous rotation rate. Inclusions provide a promising tool for probing the rheological properties of active nematics and extracting ordered motion from their inherently chaotic motion.