Active matter is a rapidly growing field that has potential applications to biological systems especially in cell mechanics and developmental biology, e.g. epithelial cell sheet dynamics in early embryogenesis. A key outstanding question remains the behaviour of active particle systems at high density. We perform numerical studies of a dense collection of self-propelled particles with soft repulsive interactions in two dimensions. In a first system with alignment, we observe a jammed phase at high density and low self-propulsion speed. The dynamics of this phase is controlled by the low-frequency modes of the underlying jammed packing. The second, non-aligning system was recently shown to exhibit active phase separation in two dimensions in the absence of any attractive interaction or breaking of the orientational symmetry. We construct a phase diagram in terms of activity and packing fraction and identify three distinct regimes: a homogeneous liquid with anomalous cluster size distribution, a phase-separated state both at high and at low density, and a frozen phase. We provide a physical interpretation of the different regimes and develop scaling arguments for the boundaries separating them.
What happens to the collective motion of an aligning flock once it is confined to move on the surface of a sphere? We build the first numerical model of active matter, that is independently driven particles, on the
surface of a sphere. For polar symmetry, instead of the aligned flocks of flat geometry, we find complex defect dynamics at low driving, and an equatorial travelling band forming at higher driving. For nematic symmetry, defects at low driving follow active elasticity theory and choose either tetrahedral or flat configurations.