Yeonsu Jung

• PDE-constrained optimization
• differentiable simulation
• periodic LQR

A 3 m tapered whip of 40 elastic links on a five-axis shoulder (three slides and two hinges), the only motors. A 0.25 s open-loop drive, found by differentiating through the simulation, sends a wave down the whip: the tip passes 5.8 mm from the target at 68 m/s, 6.8 times the hand's top speed.

The other runs put the same rig on a periodic orbit, one crack a second at 58 m/s. The orbit is unstable (a deviation grows 52-fold per period), so a periodic LQR on the shoulder motors holds it. Without feedback, rounding error alone grows the miss from 2.7 µm to 25.7 mm in eight periods.

• holonomy
• PDE-constrained optimization
• differentiable simulation

The falling-cat problem at its smallest: two links on one ball joint, floating with no angular momentum. The joint bends 90°, the plane of the bend is carried 273° around the body, and the joint straightens. The body comes out rolled 180° about its long axis although the joint never twists. The rotation is a holonomy: it comes from the loop the joint traces, not from any spin.

Executed by motors bounded at 12 N m, the same gait lands at 179.9°; four times faster the motors saturate and it overshoots to 192.9°. A smooth gait found by optimization comes within 2° of the half turn with torques that peak at 0.75 N m.

• reinforcement learning
• PPO

A chain of 16 links, 1.44 m long, lies on the floor, with a motor at each of its 15 ball joints and the rod's elastic law between the links. A policy trained by reinforcement learning (PPO, 400 iterations) rears the far end into a cobra pose and holds it: over the second half of the 18 s episode the head stays 0.56 m up, with 6 links off the floor.

• contact
• entanglement

Rods entangling in a shaken box: 125 rods of aspect ratio 25, and 1,500 rods of aspect ratio 300, five seconds each. A second pair of runs is the vibration test, a pile of each kind on an open, vibrating floor: the short rods spread flat, the long ones stay a pile. Follow the contacts per rod, the largest cluster or the mean speed over time.

In the paper, X-ray tomography and simulation show that as rods get longer, regions of strong entanglement spread until they percolate through the packing, together with a sharp change in its mechanical stability.

• optimization
• linking number
• non-penetration

Fifteen rods of aspect ratio 30 start parallel with their centres on a ring. A minimiser then raises the total linking number between them, while a stiff repulsion pushes apart any pair that comes closer than one rod diameter. The run stops by the solver's own rule after 111,620 iterations, with Σ|Lk| up from 0 to 45.2 over the 105 pairs. The repulsion is a penalty, not a hard constraint, so the rods end up pressed 1–2% into each other.

In the paper, packings that maximize the average crossing number under non-penetration turn out to be self-caged: held together by repulsion and friction alone.

• inverse design
• Newton's method
• ongoing work

Two ways to choose the change in curvature. Two levels: one value for the inner spans and the opposite for the outer ones, up to ±30%. Optimized: one value per span, fitted to a target surface. Drag the slider to apply the change gradually, starting from the exact flat lattice, and watch the height and the two principal curvatures of the surface respond.

Lattices of 5 × 5 and 7 × 7 crossings. The model has no contact, and a small transverse load, released at the end, picks the side the sheet buckles to.

• X-ray tomography
• segmentation

Every rod the cylinder-matching pipeline found in one image stack: 4,582 rods in 2000 × 2000 × 741 voxels, from 4,664 traces made in 722 s, then cut at kinks and joined into whole rods. Press Play to watch them appear in the order they were found. Colour them by direction or length, cut a slab through the pack, or click a rod to read its numbers.

• optimization
• trimmed PCA (SVD)
• direct search

A 201³-voxel crop from the dense centre of a packing, 442,435 rod voxels, segmented by four versions of the pipeline. Play runs two of them on the same clock, at their measured speeds.

Further down the page, one cylinder fit is taken step by step. A trimmed principal-component fit and a direct search (fminsearch) start from the same deliberately poor guess, 1.5 voxels off centre and 12° tilted, and each tries to fill the cylinder with voxels.