Steering Active Matter.

A layer of self-driven filaments in a loop-shaped channel, seen from above, under a pattern of light that sets how hard the filaments push. Under even light the layer churns into turbulence with no net flow; the question is whether a fixed pattern of light can make it flow one way round.

Colors

The direction the filaments point, as a color wheel: opposite directions along the same line share a color, since a filament has no head or tail. Pale where alignment is weak, brighter where the light is stronger. The walls are dark gray.

Triangles and rings

Defects: points where the filaments can't agree on a direction. Triangles are +½ defects, which swim; rings are −½ defects, which don't. They form in pairs and annihilate in pairs.

Flow round the loop

The mean speed along the channel, clockwise positive (↻), averaged over about the last 1,000 steps; "Now" is the current value. Under even light it wanders around zero.

Defects, typical speed

How many defects are in the channel, and the root-mean-square speed of the flow.

The results

Lower on the page: every design's flow under the conditions it was made for and under eight shifted ones, and three training runs of the two best methods.

Presets

Light patterns from the study, each with a sentence on what to look for. Every preset restarts from a turbulent state (Dim light from a calm one).

Paint light, Paint dark

Drag on the channel to raise or lower the light under a soft round brush; the fluid responds at once. Brush sets its size.

Light

Scales the whole pattern, as a weaker or stronger lamp would. The optimized designs were made at ×1.00.

Speed

Simulation steps per frame (each step is 0.1 time units).

Restart

The same light from the next of four turbulent starting states.

Defects, Pause, Copy share link

Show or hide the defect marks, pause, and copy a link that reopens this preset, light and speed (not painted light).

Try this: start with Uniform light and watch the flow readout wander around zero for a few thousand steps. Then switch to Optimized pump and watch it settle clockwise. Then paint dark over the pump’s brightest patches and see how much flow is left.

Active nematics

A nematic is a phase of rod-like units that line up without forming a lattice, as in a liquid crystal display. In an active nematic, each unit also pushes along its length: microtubule bundles driven by kinesin motors, actin with myosin, dense bacteria. Extensile pushing makes alignment unstable. Above a threshold of activity, the layer breaks into active turbulence: chaotic flow, with defects constantly created and destroyed. Confined to a narrow channel or ring, the same fluid can flow coherently round it, in either direction.

Steering with light

With motors that bind only under light, a projector sets the activity point by point. Earlier work used optimal control to find patterns, changing in space and time, that steer defects and draw flows, but found no stable flow along a channel once the fluid is turbulent. A pump made of triangular posts is known to work. This study asks three narrower things: can a fixed pattern, coarse enough for a projector, pump the turbulent fluid one way round a loop; do gradients through the simulation find better patterns than a search without them; and does designing over a range of conditions protect a pattern from the model being wrong. See Fluids and learned simulators for how fluids are simulated.

The model

A 2D active nematic in the standard continuum form, on a 128 × 128 periodic grid, spacing 1, time step 0.1. The orientation is a tensor Q with components (q1, q2) = S (cos 2θ, sin 2θ), for direction θ and order S. Q is carried and turned by the flow (rotating at half the vorticity, flow-aligning λ = 0.7) and relaxes toward alignment:

with K = 1 and C = 0.5. The rods’ push is an active stress −ζQ, where ζ is the activity the light sets. The flow is Stokes flow with friction, written for the stream function ψ:

with η = 1, friction Γ = 0.02 in the fluid and 5 in the walls, and f the active force. Elastic back-stresses in the flow are left out, as in many minimal models.

• Flow solve: conjugate gradients, preconditioned by the exact Fourier inverse for uniform friction, warm-started from the last step’s flow. The study stops at a relative residual of 10⁻³; the browser runs a fixed 16 iterations, which gives the same accuracy (a largest velocity error of 0.2–0.4% of the typical speed) and the same pumping (0.041 against 0.044 for one design on 16 states).
• Channel: a racetrack, two straights 40 long joined by half circles, 20 wide, centreline perimeter about 243.
• Regimes (uniform light): circulation round the loop below an activity of about 0.11, a transition near 0.18, turbulence from 0.3 with 12–38 defects. The study runs at 0.3.

Light patterns

• Activity ζ = 0.3 (1 + tanh g), between 0 and 0.6, where g is a sum of smooth shapes in the loop’s own coordinates: position along it u and across it ρ. With K modes, g uses cos and sin of 2πku (k = 1…K), each alone and times (ρ − ½), plus (ρ − ½) alone: 33 settings for K = 8, 17 for K = 4. The shortest wavelength is an eighth of the loop (33 settings) or a quarter (17), about 30 or 60 grid cells.
• Hand designs: a sawtooth with 8 teeth, and 6 dark triangles along the centre sized like the best physical posts. Each was run both ways round on training states and the better orientation kept.

Optimizers

• The score is the mean clockwise velocity along the loop over the second half of a 500-step run, averaged over 16 starting states drawn afresh each step from a training pool of 64.
• Gradient: the derivative of the score with respect to the 33 settings, through all 500 steps (the flow solve differentiated implicitly, memory bounded by checkpointing), followed by Adam for 150 steps. Gradients from single starting states barely agree with each other; the batch carries the signal.
• Robust gradient: the same, with each starting state run under its own random conditions: activity and K each ×0.75–1.25, and noise during the run of strength 0–0.1.
• Search without gradients (an evolution strategy): 8 random directions tried both ways each iteration, 60 iterations, with 33 or 17 settings; about as many simulation runs as the gradient’s cost.

Evaluation and pre-registration

• 32 held-out starting states, 4,000 steps, flow averaged over the last 2,000. Every design runs from the same states (paired comparisons). Nine conditions: as designed; activity ×0.75, ×1.25, ×0.6, ×1.4; K ×0.75, ×1.25; noise 0.05; a shorter channel (straights 24 long). Shifted states are made under the shifted condition.
• A design pumps if its flow is at least 3 standard errors above zero and 3 above uniform light, paired.
• The system, designs, seeds, conditions, questions, decision rules and predictions were fixed on 6 November 2026, before any of these runs. The repeat training runs were added afterwards and are exploratory.

Optimized designs pump

Gradient 0.033 ± 0.003, robust gradient 0.036 ± 0.003, search with 17 settings 0.035 ± 0.004, search with 33 settings 0.014 ± 0.003: all pass the pumping rule. The turbulence's typical speed is about 0.25.

Hand designs don't

The ratchet reaches 0.010 ± 0.003, but only 2.5 standard errors above uniform light; the triangles 0.007. Uniform light: 0.002 ± 0.003.

Gradients weren't decisive

The gradient beats the 33-setting search by 0.019 ± 0.005, but the 17-setting search matches it (−0.002 ± 0.005).

Training runs vary

Trained three times, the gradient's designs reach 0.012–0.033 and the 17-setting search's 0.022–0.035. Every run pumps; four of six beat the ratchet.

Robustness is free

The robust design loses nothing as designed (+0.003 ± 0.005 against the nominal one) and keeps more under seven of eight shifts: 111% of its flow at activity ×1.25 against 79%, and 78% at K ×0.75 against 46%. At activity ×0.6 it keeps 38% against 52%.

A new channel

In the shorter channel the main study's two gradient designs keep 87% and 94% of their flow; across all six repeat-test designs, 24–95%.

Against the predictions made before the test: pumping was larger than predicted (0.033, not 0.02); the 17-setting search was expected to stay below the gradient and didn’t; robustness was expected to cost up to a third of the flow and cost nothing; the shorter channel was expected to lose most of the flow and didn’t. See Reading the results for standard errors and pre-registration.

• One simplified 2D model at one resolution (128 × 128), with no elastic back-stress; a model, not an experiment.
• One channel family. The shorter channel is the only geometry test.
• Fixed patterns only. Light that moves or responds to the flow could do more, and is how most experiments steer.
• The repeat training runs show that a single run can overstate a method by about a third; the comparison of methods rests on three runs each.
• Open: whether a pattern designed this way pumps a real microtubule nematic, and how much robustness to build in when the parameters are known only roughly.