Science Advances

This PDF file includes:

• Particle leakage through the funnels
• Rectification mechanism
• Particle-resolved simulations
• Numerical solution of the continuum model
• Fig. S1. Steady-state density profiles for funnel-wall systems with the funnel
  particles either mobile or fixed.
• Fig. S2. Local polarization around a sawtooth-shaped speed profile, obtained from particle-resolved simulations and the continuum model.
• Fig. S3. Polarization profiles obtained from the continuum model with w₂ = 0 and w₂ > 0.
• Fig. S4. Propulsion speed profiles used in simulations of “active circuits.”

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Other Supplementary Material for this manuscript includes the following:

• Movie S1 (.mov format). Movie showing the self-assembly process of a single chevron-shaped obstacle.