Abstract
The second lecture gave an introduction to active matter by presenting Vicsek's model, which is historically the first theoretical model of an active system (1995), describing some active materials or systems in a little more detail, and explaining the basics of a hydrodynamic theory of active matter.
Tamàs Vicsek was interested in the collective behavior of groups of animals (flights of birds, shoals of fish...) He proposed a simplified model in which each component is punctual, but has a spontaneous velocity that gives it a direction. Each component tends to orient its speed in the direction of those of its neighbors, but with a certain amount of noise. The model predicts a global collective movement of all components above a critical density and below a critical noise amplitude.
Active systems can be grouped into three categories : biological systems, synthetic systems and groups of animals. Synthetic active systems are either colloidal systems in which the particles are self-propelled, or biomimetic systems. Animal groups have been studied in the tradition of Vicsek's work. Robot assemblies, which are increasingly being studied, can also be included in this category.
The construction of a hydrodynamic theory of active matter requires the selection of hydrodynamic variables that are relevant on long time scales, and the consideration of system symmetries to write the evolution of these variables. Hydrodynamic variables are associated with conserved quantities (number of particles, momentum, but not energy) and broken symmetries, such as the mean orientation of components or their velocity.
