Line Plot from Scientific Research

Weak dissipation. Given the velocity correlation function, C ( t ), and its relaxation time, , we can define the shape function as {h(t/)}={-log C(t/)/(t/)}. In the limit t / 0, h ( t / ) 1 for overdamped exponential dynamics, and h ( t / ) 0 for inertial underdamped dynamics 9 . Experiments on natural swarms (orange line) and numerical simulations of near-critical ISM (purple line) both show underdamped inertial relaxation. The Vicsek model, on the other hand, belongs to the overdamped class (green line; data from ref. 9 ).

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