Unexpected stray attractors in confined leader-follower dynamics driven by cone-of-vision interactions.

Experiments with groups of fish inside a circular tank have provided valuable insights into the nature of leadership in social groups. Sophisticated mathematical models were constructed with a view to recovering observed schooling and leadership behavior in such experiments. Here, and with the help of variations on a promising class of such models, we explore a dual set of social concerns, namely the likelihood of permanent evasion from a cohesive group by a controlled individual in confinement.

Shepherding in a Self-gravitating Disk of Trans-Neptunian Objects.

A relatively massive and moderately eccentric disk of trans-Neptunian objects (TNOs) can effectively counteract apse precession induced by the outer planets, and in the process shepherd highly eccentric members of its population into nearly stationary configurations that are antialigned with the disk itself. We were sufficiently intrigued by this remarkable feature to embark on an extensive exploration of the full spatial dynamics sustained by the combined action of giant planets and a massive trans-Neptunian debris disk. In the process, we identified ranges of disk mass, eccentricity, and precession rate that allow apse-clustered populations that faithfully reproduce key orbital properties of the much-discussed TNO population.

The disruption of multiplanet systems through resonance with a binary orbit.

Most exoplanetary systems in binary stars are of S-type, and consist of one or more planets orbiting a primary star with a wide binary stellar companion. Planetary eccentricities and mutual inclinations can be large, perhaps forced gravitationally by the binary companion. Earlier work on single planet systems appealed to the Kozai-Lidov instability wherein a sufficiently inclined binary orbit excites large-amplitude oscillations in the planet's eccentricity and inclination.

Self-organization in two-dimensional swarms.

We undertake a systematic numerical exploration of self-organized states in a deterministic model of interacting self-propelled particles in two dimensions. In the process, we identify various types of collective motion, namely, disordered swarms, rings, and droplets. We construct a "phase diagram," which summarizes our results as it delineates phase transitions (all discontinuous) between disordered swarms and vortical flocks on one hand and bound vortical flocks and expanding formations on the other.