Figure 2. (*a*) Predicted emergence of solid-like and fluid-like behaviours. Distributions of positions, *P*_{x}, and velocities, *P*_{u}, at times *t* = 2T (red lines), *t* = 4T (green lines), *t* = 6T (yellow lines) and *t* = 8T (blue lines) after at swarm at equilibrium and centred on *x* = 0 is suddenly displaced to *x* = 5. Predictions for speed-dependent forces (lower panel) and speed-independent forces were obtained using equations (2.5) and (2.6). A fluid-like ‘sloshing’ behaviour is predicted to arise when forces are speed-dependent, and a solid-like ‘sliding’ behaviour is predicted to arise when forces are speed-independent. Predictions were obtained for *σ*_{x} = 1, *σ*_{u} = 1 and *T* = 1 a.u. (*b*) Predicted emergence of solid-like and fluid-like behaviours. Distributions of positions, *P*_{x}, and velocities, *P*_{u}, at times *t* = 2T (red lines), *t* = 4T (green lines), *t* = 6T (yellow lines) and *t* = 8T (blue lines) after a swarm at equilibrium and centred on *x* = 0 is suddenly displaced to *x* = 5. A fluid-like ‘sloshing’ behaviour is predicted to occur as the swarm returns to equilibrium. Predictions were obtained using equation (2.7) for a swarm containing 10 midges with a Gaussian density profile and exponential velocity correlations, , and characterized by *σ*_{x} = 1, *σ*_{u} = 1, *σ*_{c} = 1 and *b* = 1 a.u. Fluid-like behaviours are also predicted to emerge when correlations are weaker, i.e. when , and when they are shorter-ranged, i.e. when *σ*_{c} = 1/2.