LaPIV using multigrid warping and proxy regularization

The Lagrangian Particle Image Velocimetry (LAPIV) method was firstly proposed in Yang et al. (2019) as a prototype approach to achieve the goal of accurate and efficient reconstruction of 3D Eulerian velocity field of fluid flow from multi-view particle images. After validating against synthetic datasets, the prototype has already shown significant advantages in revealing more small scale flow structures than other stateof-the-art Eulerian velocity estimation methods, such as TomoPIV (Scarano, 2013) and VIC# (Jeon et al., 2019). However, at this early stage, LAPIV can not be easily applied to other datasets. In the current work, we focus on extending LAPIV to operational search by incorporating several essential and wellestablished paradigms: multi-resolution, warping, and proxy regularization. Recent approaches, Lasinger et al. (2019) and Cornic et al. (2020), function in the same vein as LAPIV, aiming at reconstructs the dense Eulerian volumetric flow directly from multi-view particle-seeded images Another pipeline consists of firstly reconstructing the Lagrangian flow using the Lagrangian Particle Tracking (LPT), then optimally interpolating the Lagrangian flow to Eulerian grids, taking into account the Eulerian dynamics constraints as in Flowfit (Gesemann, 2020) and VIC# (Jeon et al., 2019). If Eulerian flow is required, LAPIV is the preferred approach due to its simplicity and ability to utilize the original rich image features.

Global regularity for a 1D Euler-alignment system with misalignment

We study one-dimensional Eulerian dynamics with nonlocal alignment interactions, featuring strong short-range alignment, and long-range misalignment. Compared with the well-studied Euler-alignment system, the presence of the misalignment brings different behaviors of the solutions, including the possible creation of vacuum at infinite time, which destabilizes the solutions. We show that with a strongly singular short-range alignment interaction, the solution is globally regular, despite the effect of misalignment.

Efficient numerical methods for multiscale crowd dynamics with emotional contagion

In this paper, we develop two efficient numerical methods for a multiscale kinetic equation in the context of crowd dynamics with emotional contagion [A. Bertozzi, J. Rosado, M. Short and L. Wang, Contagion shocks in one dimension, J. Stat. Phys. 158 (2014) 647–664]. In the continuum limit, the mesoscopic kinetic equation produces a natural Eulerian limit with nonlocal interactions. However, such limit ceases to be valid when the underlying microscopic particle characteristics cross, corresponding to the blow up of the solution in the Eulerian system. One method is to couple these two situations — using Eulerian dynamics for regions without characteristic crossing and kinetic evolution for regions with characteristic crossing. For such a hybrid setting, we provide a regime indicator based on the macroscopic density and fear level, and propose an interface condition via continuity to connect these two regimes. The other method is based on a level set formulation for the continuum system. The level set equation shares similar forms as the kinetic equation, and it successfully captures the multi-valued solution in velocity, which implies that the multi-valued solution other than the viscosity solution should be the physically relevant ones for the continuum system. Numerical examples are presented to show the efficiency of these new methods.