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We propose theadaptive hybrid particle-grid flow mapmethod, a novel flow-map approach that leverages Lagrangian particles to simultaneously transport impulse and guide grid adaptation, introducing a fully adaptive flow map-based fluid simulation framework. The core idea of our method is to maintain flow-map trajectories separately on grid nodes and particles: the grid-based representation tracks long-range flow maps at a coarse spatial resolution, while the particle-based representation tracks both long and short-range flow maps, enhanced by their gradients, at a fine resolution. This hybrid Eulerian-Lagrangian flow-map representation naturally enables adaptivity for both advection and projection steps. We implement this method inCirrus, a GPU-based fluid simulation framework designed for octree-like adaptive grids enhanced with particle trackers. The efficacy of our system is demonstrated through numerical tests and various simulation examples, achieving up to 512 × 512 × 2048 effective resolution on an RTX 4090 GPU. We achieve a 1.5 to 2× speedup with our GPU optimization over the Particle Flow Map method on the same hardware, while the adaptive grid implementation offers efficiency gains of one to two orders of magnitude by reducing computational resource requirements. The source code has been made publicly available at: https://wang-mengdi.github.io/proj/25-cirrus/. 

We propose theVortexParticleFlowMap (VPFM) method to simulate incompressible flow with complex vortical evolution in the presence of dynamic solid boundaries. The core insight of our approach is that vorticity is an ideal quantity for evolution on particle flow maps, enabling significantly longer flow map distances compared to other fluid quantities like velocity or impulse. To achieve this goal, we developed a hybrid Eulerian-Lagrangian representation that evolves vorticity and flow map quantities on vortex particles, while reconstructing velocity on a background grid. The method integrates three key components: (1) a vorticity-based particle flow map framework, (2) an accurate Hessian evolution scheme on particles, and (3) a solid boundary treatment for no-through and no-slip conditions in VPFM. These components collectively allow a substantially longer flow map length (3–12times longer) than the state-of-the-art, enhancing vorticity preservation over extended spatiotemporal domains. We validated the performance of VPFM through diverse simulations, demonstrating its effectiveness in capturing complex vortex dynamics and turbulence phenomena. 

We propose a novel framework for simulating ink as a particle-laden flow using particle flow maps. Our method addresses the limitations of existing flow-map techniques, which struggle with dissipative forces like viscosity and drag, thereby extending the application scope from solving the Euler equations to solving the Navier-Stokes equations with accurate viscosity and laden-particle treatment. Our key contribution lies in a coupling mechanism for two particle systems, coupling physical sediment particles and virtual flow-map particles on a background grid by solving a Poisson system. We implemented a novel path integral formula to incorporate viscosity and drag forces into the particle flow map process. Our approach enables state-of-the-art simulation of various particle-laden flow phenomena, exemplified by the bulging and breakup of suspension drop tails, torus formation, torus disintegration, and the coalescence of sedimenting drops. In particular, our method delivered high-fidelity ink diffusion simulations by accurately capturing vortex bulbs, viscous tails, fractal branching, and hierarchical structures. 

We propose a neural particle level set (Neural PLS) method to accommodate tracking and evolving dynamic neural representations. At the heart of our approach is a set of oriented particles serving dual roles of interface trackers and sampling seeders. These dynamic particles are used to evolve the interface and construct neural representations on a multi-resolution grid-hash structure to hybridize coarse sparse distance fields and multi-scale feature encoding. Based on these parallel implementations and neural-network-friendly architectures, our neural particle level set method combines the computational merits on both ends of the traditional particle level sets and the modern implicit neural representations, in terms of feature representation and dynamic tracking. We demonstrate the efficacy of our approach by showcasing its performance surpassing traditional level-set methods in both benchmark tests and physical simulations. 

ABSTRACT Research Experiences for Teachers (RET) programs are a burgeoning approach to engage teachers in STEM (science, technology, engineering, mathematics) research that they can translate into their K‐12 classrooms. Despite an increase in studies of RETs, there is a need for comparison of RET and non‐RET teachers' student outcomes. This mixed methods, quasi‐experimental comparison study, using a revised third‐generation activity theory framework, investigates how an RET program for preservice and early career STEM teachers impacted participating teachers and their students up to 8 years after RET participation. Specifically, we conducted a matched comparison of student achievement data from students of nine RET teachers versus many non‐RET comparison teachers within the same districts (n = 830–1132 students). We also investigated student and teacher perceptions of classroom practices through surveys (n = 576 students) and interviews (15 teacher interviews). Omnibus tests revealed no statistically significant differences by treatment in math or science achievement. However, students of the RET teachers reported stronger perceptions of STEM career awareness, greater value for learning STEM subjects, and a greater propensity to persist in STEM course tasks (three of the five constructs measured). This was consistent with teacher interview responses in which RET teachers spoke about STEM career awareness in a broader context for understanding the value of STEM in society, and also discussed struggles in research and attempts to bring this mindset to their students, which may have resulted in greater student engagement in their courses. Implications for teacher education and for supporting science and engineering practices in STEM classrooms are discussed along with recommendations for further research on the impacts of RET programs guided by a revised third‐generation activity theory framework informed by this work.