Figure 1

We implement a relaxation algorithm in Fourier space with $128\times 128$ modes to find a local minima in a square cell of $96\times 96$ units for different values of $U_{0}n$; the potential range is $a=4.3$. (a) The $\mathrm{NCRIF}\equiv 1-L_z^{\prime }(\omega )/⟨I_{\mathrm{rb}}⟩$ vs the local maximum speed $v_{\max }=\omega L/\sqrt{2}$ for $n{U}_0=0.069$, 0.084, 0.099, and 0.114. Here $⟨I_{\mathrm{rb}}⟩$ is the converging inertia moment computed numerically for large $n{U}_0$ at $\omega =0$. Note that the jump in NCRIF for $n{U}_0=0.069$ corresponds to the nucleation of a vortex in the system. (b) NCRIF at $\omega =0$ as a function of $n{U}_0$. We have verified that (a) and (b) are almost independent of the box size.Reuse & Permissions

Figure 2

The density modulations $|\psi {|}^2$ (the dark points denote large mass concentration) of a numerical simulation of Eq. (1) with Dirichlet boundary conditions (the boundaries are in black) in a form of a $u$ tube with roughness. We use a Crank-Nicholson scheme that conserves the total energy and mass. The mesh size is $dx=1$, the nonlocal interaction parameters are chosen as $U_0=0.01$ and $a=8$ (physical constants $\hslash$ and $m$ are 1), and the initial condition is an uniform solution $\psi =1$ plus small fluctuations. We use the protocol described in the text with $\mathcal{G}=0.01$ and a tilted angle of 45°. After 2000 time units the system has reached the stationary situation shown in (b), demonstrating that the mass flow is only a transient. See a movie in Ref. 18 for further detail.Reuse & Permissions