Elastic Material Properties
Liquid crystalline materials play a prominent role in the thriving sector of electronic devices. Historically, they have found widespread use in display technologies. However, they are also being increasingly recognized for possessing tremendous potential as materials for nanoscale and colloidal templating, organic electronics, and biosensing. To precisely engineer the behavior of such new devices, it is imperative to understand exactly the elastic behavior of the underlying liquid crystalline phases. I work on developing techniques to estimate these elastic properties using molecular simulation.
Through my work, we have demonstrated the first quantitative predictions of molecular liquid crystal elastic constants from simulation. We are further able to probe surface-like elastic constants which are not directly accessible through experiment.
Despite decades of research, the precise mechanism of chromonic formation is poorly understood. We developed a coarse-grained model capable of capturing all features of the chromonic phase and helps shed light on the molecular organization and emergence of the nematic phase.
Liquid crystal mixtures
Elastic stress and confinement induces elastic segregation and defect formation in binary LC mixtures. We characterize these effects using density-of-states simulations and enhanced sampling. Understanding these effects will help guide LC-driven nanoparticle self- assembly or templated polymerization.
Advances in machine learning have revolutionized the way we interact with data. Statistical mechanics has also played an important role in understanding and developing probabilistic learning. I am interested in adapting Bayesian machine learning and deep learning techniques to enhance sampling in molecular simulation and accelerate molecular pathway discovery. In the process, I hope these methods can help us understand the explicit relationship between molecular conformations and emergent dynamics.
Artificial Neural Network Sampling
Existing adaptive bias methods, which estimate free energies from molecular simulations, rely on fixed kernels or basis sets which hinder their ability to efficiently conform to varied free energy landscapes. They also require user-specified parameters which are in general non-intuitive, yet significantly affect the convergence rate and accuracy of the free energy estimate. I developed a deep learning-based approach which uses Bayesian regularized artificial neural networks to learn free energy landscapes. It's fast, robust to hyperparameters, and will hopefully make it easier to study computationally expensive systems.
Numerical Algebraic Geometry
Fluid Phase Equilibria
Evaluating thermodynamic stability, mixture composition, and critical points often involve finding the global minimum of highly nonlinear equations. Numerical algebraic geometry can be very helpful in developing entirely deterministic or heuristic-driven algorithms that yield global optimality. In particular, numerical polynomial homotopy continuation can find all solutions to a system of nonlinear (polynomial) equations. Formulating such methods facilitates efficient and reliable solutions to problems in classical thermodynamic modeling.