The Physics of Flocking
Francesco Ginelli
University of Insubria, Italy
Abstract
These lectures mainly discuss the large scale behavior of active systems undergoing polar collective motion, the so-called Vicsek class whose introduction almost 30 years ago marked the birth of active matter. In order to understand its properties, we will discuss numerical results obtained from microscopic models and analyze the corresponding hydrodynamic description, comparing our results with experimental observations. We will both review classical results, insisting on the role played by symmetries and conservation roles in shaping the physics of flocking, and discuss new developments at the forefront of current research.
Outline
1. Phenomenology and experiments
- Aligning forces and spontaneous symmetry breaking
- The Vicsek model (VM):
The transition to collective motion and (micro)-phase separation
The Toner & Tu phase: scale free correlations, giant number fluctuations and how flocks circumvent Mermin-Wagner & Hohenberg
- Flocking without scale free correlations: the active Ising model
- Experimental observations
Motility assays and phase separation
Starling flocks and topological interactions
Confluent epithelial cells and the Vicsek class
Active colloids
- Nematic interactions in the dry dilute limit
2. Hydrodynamic theory
-Preliminaries: the XY model and spontaneous symmetry breaking at equilibrium
-Symmetries, conservation laws and slow fields
-Toner & Tu theory
Linearised hydrodynamics
Threshold long wavelength instability and phase separation
Nonlinearities and the breakdown of linear theory
Exact scaling exponents: recent results
-Topological interactions
-Malthusian and incompressible flocks.
3. Boundaries and perturbations
- Flocking with no boundaries: social cohesion
- Linear response to an external perturbation
Stationary perturbations
Dynamical perturbations
- Confined flocking
Extensive boundary layers
Casimir-like forces
- Flocking in the dirt, or the role of quenched disorder (only if time allows)