Quantifying hydrodynamic collective states of magnetic colloidal spinners and rollers

Ferromagnetic microparticles energized by an alternating magnetic field exhibit fascinating collective behavior ranging from the emergent self-assembled spinners to a variety of self-organized rolling states. Despite their simplicity, quantifying their essentially multibody collective behavior remains elusive due to a multitude of relevant interactions, from short-range collisions to long-range magnetic and hydrodynamic forces. Here we develop a high-performance computational algorithm based on smoothed particle hydrodynamics to quantify the role of individual interactions in the emergent collective state. The computational model provides insight into the role of hydrodynamic interaction on the onset of collective behavior and allows characterization of dynamic regimes that are hard to access experimentally. Comparison with high-resolution experimental data allows validation of the algorithm. Our work expands the scope of modern computational tools for predictive modeling of microscopic active systems and provides insight into the intricate role of hydrodynamic interactions on the onset of collective behavior in living and synthetic active matter.