Fluid threshold
Wind directly lifts grains from a resting bed.
The Physics of Healing
VI · Sand Dunes
Dunes, exercise, and why the same force can meet a different system.
The wind that starts a dune moving is not always the wind that keeps it moving.
At first, every grain is seated. Neighbours press against it. Moisture or electrostatic force may hold it. To lift the grain, air must supply enough drag and lift to beat weight, friction, and cohesion. The bed waits.
Then one grain flies. It falls in an arc and strikes the surface. The impact may rebound that grain and kick several others into motion. Those grains strike elsewhere. Wind no longer has to start every hop from rest. Moving sand recruits moving sand.1,2
Wind directly lifts grains from a resting bed.
Striking grains eject replacements and sustain saltation.
This creates hysteresis. Wind can rise through an onset threshold and start saltation. It can then fall below that starting value while impacts keep transport alive. The same wind can meet two dunes: one quiet because nothing began, one streaming because grains are already aloft.
On Earth, turbulence and surface variation can blur the gap. On Mars, thin air makes direct lifting difficult while fast grains strike hard, so models predict a much wider hysteresis band.2 The principle is cleanest there; the numbers stay there.
A second hysteresis lives on the slip face. Add sand and a slope can steepen while staying still. At an upper angle, failure begins. Grains avalanche. Motion may continue until the slope falls to a lower stopping angle.3,4
Increase slope along the quiet branch. Cross the upper threshold. Return along the moving branch. Stop at the lower threshold. One slope between those lines can support either rest or flow.
The same input can meet a different bed because the bed remembers how it arrived.
This is not indecision. Contact networks differ when grains are locked and when they collide. Friction, packing, shape, size, cohesion, and gravity shift the angles. “The angle of repose” is not one sacred number printed inside sand.
Exercise-induced hypoalgesia means a decrease in pain sensitivity after exertion. In pain-free groups, one bout often produces a brief hypoalgesic response. In chronic-pain groups, results are more varied: hypoalgesia, a smaller response, no mean change, or hyperalgesia have all been reported.5,6
A cycling bout and an isometric contraction do not load the same tissue. Local pain at a working muscle can rise while thresholds elsewhere change in another direction. A measure taken at minute five can disagree with one taken the next morning.
Berardi and colleagues followed 47 people with fibromyalgia and 47 controls after 10 minutes of low-intensity elbow exercise. The fibromyalgia group had clinically relevant increases in local pain and fatigue through the three-day recovery; whole-body changes did not reach that clinical threshold.7 The recovery curve—not only the immediate rating—was the result.
A crossover study of 32 women compared prescribed and self-selected resistance loads. Pain rose immediately after all four sessions and then declined over 96 hours; no loading scheme produced a different pain trajectory.8 Choosing the load did not turn the bout into instant analgesia.
Another experiment found that a short isometric bout improved conditioned pain modulation among participants who began with attenuated modulation, regardless of whether they had fibromyalgia.9 Diagnostic label alone did not determine the change. Starting state mattered.
Longer training asks another question. Reviews of fibromyalgia exercise programs report average reductions in pain and gains in function after repeated aerobic, strength, or mixed training. Programs differ in frequency, intensity, duration, supervision, adherence, and progression.
A 2025 meta-analysis included 17 aerobic-exercise trials and 1,095 participants. The pooled effect favored aerobic exercise by 0.49 points on a 0–10 pain scale, with 62% heterogeneity and low certainty in its main GRADE table.10 The average effect was small, and the programs were not one uniform dose.
Adaptation changes the system that receives the next bout. Capacity, motor skill, expectation, sleep, confidence, autonomic response, and pain modulation can change over weeks. The person at session twelve is not simply the person at session one with eleven more loads added.
Let q be sand flux and τ wind stress. A hysteretic model uses one threshold to switch q on and a lower one to switch it off. For exercise, we can write response R as a function of dose D and state z:
State z may include recent load, baseline symptoms, sleep, recovery, expectation, and adaptation. This is bookkeeping, not a validated clinical equation.
The model rules out two bad arguments. First: pain rose after one bout, so regular exercise cannot help. Second: training helps on average, so any acute dose should feel better. Both erase the path between input and outcome.
The dune does not argue for rest. Without transport, it would not be a dune. It argues for trajectories. Ask what started the motion, what now sustains it, how long grains remain aloft, and what changed in the bed after they landed.
At dusk the wind weakens. Sand still hisses along the crest. Each flying grain spends its last momentum by launching another. Then the chain breaks. The slope holds below the angle that made it fail. Final wind speed alone cannot tell you the route home.