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This paper introduces a two-phase interfacial fluid model based on the impulse variable to capture complex vorticity-interface interactions. Our key idea is to leverage bidirectional flow map theory to enhance the transport accuracy of both vorticity and interfaces simultaneously and address their coupling within a unified Eulerian framework. At the heart of our framework is an impulse ghost fluid method to solve the two-phase incompressible fluid characterized by its interfacial dynamics. To deal with the history-dependent jump of gauge variables across a dynamic interface, we develop a novel path integral formula empowered by spatiotemporal buffers to convert the history-dependent jump condition into a geometry-dependent jump condition when projecting impulse to velocity. We demonstrate the efficacy of our approach in simulating and visualizing several interface-vorticity interaction problems with cross-phase vortical evolution, including interfacial whirlpool, vortex ring reflection, and leapfrogging bubble rings. 

We propose a novel solid-fluid interaction method for coupling elastic solids with impulse flow maps. Our key idea is to unify the representation of fluid and solid components as particle flow maps with different lengths and dynamics. The solid-fluid coupling is enabled by implementing two novel mechanisms: first, we developed an impulse-to-velocity transfer mechanism to unify the exchanged physical quantities; second, we devised a particle path integral mechanism to accumulate coupling forces along each flow-map trajectory. Our framework integrates these two mechanisms into an Eulerian-Lagrangian impulse fluid simulator to accommodate traditional coupling models, exemplified by the Material Point Method (MPM) and Immersed Boundary Method (IBM), within a particle flow map framework. We demonstrate our method's efficacy by simulating solid-fluid interactions exhibiting strong vortical dynamics, including various vortex shedding and interaction examples across swimming, falling, breezing, and combustion. 

Abstract Machine learning (ML) is emerging as a powerful tool to predict the properties of materials, including glasses. Informing ML models with knowledge of how glass composition affects short-range atomic structure has the potential to enhance the ability of composition-property models to extrapolate accurately outside of their training sets. Here, we introduce an approach wherein statistical mechanics informs a ML model that can predict the non-linear composition-structure relations in oxide glasses. This combined model offers an improved prediction compared to models relying solely on statistical physics or machine learning individually. Specifically, we show that the combined model accurately both interpolates and extrapolates the structure of Na₂O–SiO₂glasses. Importantly, the model is able to extrapolate predictions outside its training set, which is evidenced by the fact that it is able to predict the structure of a glass series that was kept fully hidden from the model during its training.