Pattern Formation, Stability and Collapse For Self-Propelled Interacting Particles In Two Dimensions
Maria D'Orsogna, Applied Mathematics Laboratory, UCLA
Interacting biological systems offer an intriguing platform
from which to study multi-agent aggregation, swarming and
pattern formation. We consider a non linear system of self propelled
particles interacting via pairwise potentials,
generating flocks, vortex structures or dispersing in space.
Connections between the interaction potential, its H-stable nature, and the resulting structures are discussed. Coarse graining the model using the Kirkwood-Irving approach yields the appropriate continuum description and we show that in certain limits there is very good agreement between the two models.
Understanding collective properties of driven particle systems is
significant for naturally occurring aggregates and because the knowledge gained can be used as building blocks for the design of artificial ones.
We model self propelling biological or artificial individuals
interacting through pairwise attractive and repulsive forces.
For the first time, we are able to predict stability and morphology
of organization starting from the shape of the two-body
interaction. We present a coherent theory, based on fundamental
statistical mechanics, for all possible phases of collective motion.