Wednesday, April 12, 2023
04/12/2023 - 1:00pm
The physical properties and structure of materials under nanoscopic confinement can significantly differ from their bulk counterparts. This talk focuses on a class of estimators used to determine the position-dependent diffusivity tensor for a confined fluid. The estimators are suitable for trajectory data obtained from confocal microscopy experiments and molecular dynamics (MD) simulations. We first demonstrate the use of the estimators on trajectories generated from a few toy problems, to highlight some numerical issues associated with them. Specifically, we show that these estimators may lose accuracy near hard boundaries of the simulation domain. To address this issue, we introduce a correction scheme using Diffusion maps. We demonstrate the use of this correction on trajectories obtained from MD simulations of a model system consisting of a pure liquid within a slit pore. The resulting diffusivity profiles yield empirical distributions that are in good agreement with those obtained directly from MD simulations.
04/12/2023 - 4:15pm
In this talk I will explain a new numerical framework, employing physics-informed neural networks, to find a smooth self-similar solution for different equations in fluid dynamics. The new numerical framework is shown to be both robust and readily adaptable to several situations.