Phase-space slice. Force resolution analysis and comparison between Vlasov and PM for the three-sine-wave simulations with ϵ = (3/4, 1/2) and a = 0.035. To have a better view of the fine structures of the system, the x coordinate is represented in logarithmic scale, sgn(x)log₁₀(1 + 512 × |x|). Some values of x are indicated in blue inside each panel, while the two red vertical segments indicate the force resolution scale, L/n_g, which increases from top to bottom. The Vlasov runs are considered in the left panels. In this case, the intersection of the phase-space sheet with the hyperplane y = z = 0 is calculated directly at linear order and represented in (x, v_x) coordinates. The two top left panels consider Vlasov runs with n_g = 512 and n_s = 256. The only difference between the two simulations is the initial shift of half a voxel size imprinted in initial conditions of the simulation considered in the top left panel (VLA-ANI2-HRS in Table 1) compared to the simulation in panel just below (VLA-ANI2-HR). Our highest resolution run, VLA-ANI2-FHR (with n_s = 512 instead of 256), gives nearly identical results to VLA-ANI2-HR, and is not shown here. The two bottom left panels consider lower force resolution Vlasov runs with n_g = 256 (VLA-ANI2-MR) and then n_g = 128 (VLA-ANI2-LR). The PM runs are examined in the right panels. In this case a very thin slice of particles is considered with (y, z) ∈ [−5 × 10⁻⁴,  5 × 10⁻⁴] as tracers of the phase-space sheet. The top right panel shows the results obtained from our highest resolution PM run, PM-ANI2-UHR, with n_g = 1024 and n_p = 1024. The three next panels all have the same number of particles, , but decreasing spatial resolution, n_g = 512, 256, and 128 for PM-ANI2-HR, PM-ANI2-MR, and PM-ANI2-LR, respectively.