Illustrated Physics
physics, drawn
Concept

Feedback — where it appears

The use of a system's output to adjust its own input. Negative feedback opposes deviations and stabilises a speed, a temperature or an amplifier's gain; too much of it, applied too late, overcorrects and makes the system oscillate, which is the central problem of control.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

A current that falls by a decade for every ångström. Tunnelling current against the width of a vacuum gap, on a logarithmic scale, for three work functions covering the range of clean metal surfaces. The curves are straight because the transmission is an exponential in the gap, and their slopes are 0.833, 0.944, 1.044 decades per ångström — fitted to the drawn curves and agreeing with 2κ/ln 10 to a part in a million. At 4.5 electronvolts a change of ten picometres, a tenth of an atomic radius, changes the current by 24 per cent. That is the sensitivity a scanning tunnelling microscope lives on, and it is why the instrument measures height by holding the current fixed and recording what the piezo had to do: the current is far too steep a function of height to be read as one.

The last atom does all the seeing

A tunnelling rate falls by a factor of eight for every tenth of a nanometre of extra barrier, which is normally quoted as the reason nothing ever tunnels anywhere. Read the other way it is a microscope: the second-nearest atom of a blunt metal tip carries a two-hundredth of the current the nearest one does, so a tip nobody sharpened resolves a single atom, and the resolution comes from an exponential rather than from any piece of engineering.

quantum · Tunnelling A governor that hunts. The speed of an engine with a centrifugal governor after its load is suddenly increased, against time in units of √(ℓ/g), for three amounts of friction in the governor's linkage: damping 0, 0.25, 0.6, against Vyshnegradsky's minimum for this governor, 0.397. With no friction the speed oscillates about its new, slightly lower value with a growing swing — the governor hunts, opening and closing the throttle out of step with the engine — until the arms hit their stops and the curve ends. At damping 0.25, below the minimum, it still hunts, more slowly. At damping 0.6, above the minimum, the oscillation dies away and the engine settles at its new speed. The friction that seems to spoil the mechanism is what makes it work.

The governor that needed friction to work

James Watt's steam engines were kept at a steady speed by two heavy balls on hinged arms, spun by the engine itself: run faster and the balls fly out and close the steam valve; run slower and they drop and open it. The balls stand at a height set by the speed alone. As engines grew and governors were made more sensitive, many began to hunt — speeding and slowing in a growing rhythm, the governor always too late. In 1868 James Clerk Maxwell wrote the equations down and showed why: a governor with no friction cannot settle at all, and the more precisely it is meant to hold the speed, the more friction it needs.

mechanics · Circular motion

Named alongside it

The objects these essays reach for when they reach for this one.

Centripetal forceCircular motionConical pendulumControl theoryDampingDecay lengthDensity of statesEvanescent waveExponential sensitivityPiezoelectricResolutionRouth hurwitz criterion

All concepts