Fig. 2.

Rolling ring. (A) Snapshots of an initially circular ring with radius $R=1/\left(2\pi \right)$ subjected to illumination at angle ${\theta }_I$ and of intensity $\mathrm{\Lambda }$ at times $T=\left\{\mathrm{0,11.83},23.68,35.48\right\}$. The point that is initially in contact with the ground is marked with a black dot, while the center of mass is the blue dot. The incident arrows indicate the direction of incoming light. Self-shadowing is taken into account thanks to the choice of $f$ in Eq. 11; this is depicted by the absence of arrows in the lower part of the ring. (B) Distance traveled by the rolling ring vs. time for various intensities $\mathrm{\Lambda }=\left\{0.01,0.1,\mathrm{1,10}\right\}$. Note that a steady velocity is reached in all cases, after an initial transient. (C) Steady-state velocity as a function of illumination angle and intensity $\mathrm{\Lambda }=\left\{0.01,0.1,\mathrm{1,10}\right\}$. The velocity increases when the illumination angle moves away from the vertical, but is relatively insensitive to the intensity of illumination. (D) Scaled change of spontaneous curvature induced by illumination along the beam for ${\theta }_I=0.2$ (indicated by dot in C), for various illumination intensities $\mathrm{\Lambda }=\left\{0.01,0.1,\mathrm{1,10}\right\}$. This quantity appears to be largely insensitive to the intensity of illumination. Simulation data are shown as solid black lines, while the analytical solution given by solving Eq. 29 is shown as a red dashed line. The Inset is at higher magnification.