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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 Particle Flow Map (PFM) method to enable accurate long-range advection for incompressible fluid simulation. The foundation of our method is the observation that a particle trajectory generated in a forward simulation naturally embodies a perfect flow map. Centered on this concept, we have developed an Eulerian-Lagrangian framework comprising four essential components: Lagrangian particles for a natural and precise representation of bidirectional flow maps; a dual-scale map representation to accommodate the mapping of various flow quantities; a particle-to-grid interpolation scheme for accurate quantity transfer from particles to grid nodes; and a hybrid impulse-based solver to enforce incompressibility on the grid. The efficacy of PFM has been demonstrated through various simulation scenarios, highlighting the evolution of complex vortical structures and the details of turbulent flows. Notably, compared to NFM, PFM reduces computing time by up to 49 times and memory consumption by up to 41%, while enhancing vorticity preservation as evidenced in various tests like leapfrog, vortex tube, and turbulent flow. 

We present an Eulerian vortex method based on the theory of flow maps to simulate the complex vortical motions of incompressible fluids. Central to our method is the novel incorporation of the flow-map transport equations forline elements, which, in combination with a bi-directional marching scheme for flow maps, enables the high-fidelity Eulerian advection of vorticity variables. The fundamental motivation is that, compared to impulsem, which has been recently bridged with flow maps to encouraging results, vorticityωpromises to be preferable for its numerical stability and physical interpretability. To realize the full potential of this novel formulation, we develop a new Poisson solving scheme for vorticity-to-velocity reconstruction that is both efficient and able to accurately handle the coupling near solid boundaries. We demonstrate the efficacy of our approach with a range of vortex simulation examples, including leapfrog vortices, vortex collisions, cavity flow, and the formation of complex vortical structures due to solid-fluid interactions. 

Site-specific placement of unnatural amino acids, particularly those responsive to light, offers an elegant approach to control protein function and capture their fleeting ‘interactome’. Herein, we have resurrected 4-(trifluoromethyldiazirinyl)-phenylalanine, an underutilized photo-crosslinker, by introducing several key features including easy synthetic access, site-specific incorporation by ‘privileged’ synthetases and superior crosslinking efficiency, to develop photo-crosslinkable bromodomains suitable for ‘interactome’ profiling.