Phase-space singularities in planar Couette flow

The spectrum of singularities in the steady-state phase-space distribution function for two-dimensional two-body planar Couette flow is characterized by calculating numerically the generalized dimension $D_q$ and the Legendre transform of (1-q)$D_q$. The discrete probabilities $p_i$(ε), where ε is the discretization length, scale with the dimension of the initial phase space at equilibrium. Away from equilibrium the $p_i$(ε) scale with a range of indices, extending from the full accessible phase-space dimension to a lower limit which is controlled by the value of the shear rate γ. We compare these results with the Kawasaki nonequilibrium-distribution-function approach.