Illustrated Physics
physics, drawn
Concept

Symmetry breaking — where it appears

A situation in which a system settles into a state with less symmetry than the laws or the setup that govern it. Either a small imposed asymmetry picks the outcome, or an instability makes the symmetric state unstable and chance decides.

Named by 4 essays across 3 fields — each of them below, with the objects they name alongside it.

Shake more gently and the grains choose a side. The steady share of the grains in each of two shaken compartments joined by a slot, against B, the parameter that grows as the shaking gets gentler. Below B = 4 the only steady state is an equal share, and it is stable. At B = 4 it becomes unstable and two clustered states appear, continuously, one with each compartment full: the fuller compartment holds 0.855 of the grains at B = 5, 0.929 at 6 and 0.979 at 8. Which compartment fills is decided by the first fluctuation. Nothing in the rules prefers either side, and the equal state that the rules would suggest is the one the grains avoid.

The sand that chooses a side

Divide a box of grains into two compartments with a slot in the wall between them and shake it from below. Shaken hard, the grains share themselves equally, as molecules of a gas would. Shaken a little more gently, they gather in one compartment and leave the other almost empty, and the crowded side is cold and the empty side hot. Nothing sorted them. Every collision between grains loses energy, and a compartment that happens to hold a few more grains loses more of it and stops throwing grains over the wall.

fluids · Granular matter The self-bias set by a phase alone. The dc self-bias against the phase between the fundamental and its second harmonic, each of amplitude A, for three chambers: symmetry parameter ε = 0.5, 1, 2, where ε = 1 is a chamber with equal sheaths on both sides. In the symmetric chamber the bias runs from −0.438 A at 0° through zero at 45° to 0.438 at 90°, and back — −43.8 V to 43.8 V at A = 100 V — staying within 0.011 A of a straight line between 0° and 90°. An asymmetric chamber adds a fixed offset of the kind unequal electrodes produce and leaves the phase control in place, so the geometry and the waveform add rather than compete.

The bias a waveform can choose

A plasma between two identical electrodes, driven by a sine wave, has no reason to prefer either side, and it does not: no direct voltage appears. Add the second harmonic and it does, although the chamber is still symmetric, no direct current flows and the power spectrum does not depend on the phase between the two. The phase alone sets a bias of up to 0.44 of each harmonic's amplitude, of either sign, and moves the energy of the ions from one electrode to the other while their number stays put.

astrophysics · Plasma oscillation Water drops that charge two cans to a spark. The voltage between the two cans of a Kelvin water dropper against time, on a logarithmic axis, starting from a stray difference of 1 V, for 10, 20, 40 drops a second in each stream; drops 3 mm across, each with a capacitance of 0.17 pF to its ring, cans of 20 pF. Each drop carries a charge induced by the opposite can's potential into its own can, which raises the opposite can's induced charge on the next drop: the difference grows exponentially, multiplying by e every 6.0 s at 20 drops a second. It passes the 10 kV that will jump a few millimetres of air after 55 s — from one volt to a spark, with nothing but falling water.

The water drops that charge themselves to a spark

Two streams of water drip from one earthed pipe through two metal rings into two metal cans, and each ring is wired to the opposite can. Nothing is charged to begin with, nothing is rubbed, nothing is plugged in. Within a minute a spark cracks between the cans at ten thousand volts. A stray volt between them makes the drops forming in one ring pick up a slight charge, which they carry to the can that makes the other ring's drops pick up the opposite charge — a loop in which every drop strengthens the imbalance that charged it. Kelvin built it in 1867; it is a dynamo made of water and gravity.

electromagnetism · Potential A disc that makes its own field once it turns fast enough. A self-exciting disc dynamo started from rest, its motor's torque set so that, with no current, the disc would run at 0.8, 1.5, 2.5 times the critical speed R/M. Dashed: the disc's speed, in units of the critical speed. Solid: the current in its coil, in units of √(G/M), starting from a stray seed of a millionth, of either sign. Time is in units of the circuit's own L/R. At 0.8 the disc settles at its free-running speed, below critical, and the seed dies. Above it the disc spins up past the critical speed and nothing happens for a while — the current is growing exponentially from a millionth — until it reaches a tenth, at t ≈ 29 for 1.5 and 11 for 2.5 and becomes large enough to brake the disc. Speed and current then ring and settle at exactly the critical speed and a current of ±√(g − 1): 0.71 and 1.22, of the sign the seed happened to have.

The dynamo that reverses with nothing pushing it

A copper disc spinning in a magnetic field drives a current from its axle to its rim. Wire that current through a coil wound round the disc and the coil supplies the field the disc needs — and above one definite speed, a resistance divided by an inductance, the arrangement makes its own field out of any stray one, with nothing else magnetic anywhere. It cannot choose which way the field points; the stray field chooses. Couple two such discs, each feeding the other's coil, and with the motors' torque held perfectly steady the field flips direction again and again at intervals that follow no pattern. The simplest dynamo that works is also the simplest one that reverses.

astrophysics · Flux freezing

Named alongside it

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

BifurcationCapacitanceCapacitive dischargeChaosDielectric breakdownDynamoElectric potentialElectrostatic inductionExponential growthFourier seriesGeomagnetic reversalGranular matter

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