Figure 2
(a) The dependence of dv/dt on v for different force strengths (from top to bottom): \(f=0\), \(f=f_c\) and \(|f|>|f_c|\). The stable points towards the system evolves are shown. For \(|f|\le |f_c|\) there are two stable points \(dv/dt=0\) – one with the velocity in the direction of the force and another in the opposite direction. For \(|f|\ge |f_c|\) the only solution corresponds to the velocity in the direction of the force. (b) Illustration of the derivation of the average force \(f_{\rm av}\) that keeps the particles within the initially occupied area (the circle of radius R). Due to symmetry the average force is directed towards the center of the circle.
