Knot good

It’s one of those pet hates; when you pop you headphones in your pocket and the tangle elves get to work tying all sorts of knots in them, meaning that listening to music the following day takes 10 minutes longer than you had planned.

Well, it’s not your fault. I’ve recently learned that you can blame PHYSICS!

A duo at the University of California found no elves (durr – they’re invisible!) but they did find some PHYSICS!

It is well known that a jostled string tends to become knotted; yet the factors governing the “spontaneous” formation of various knots are unclear. We performed experiments in which a string was tumbled inside a box and found that complex knots often form within seconds.

From that initial line, maybe the best way to avoid this difficulty is not to jostle your pockets. Some men may find this rather taxing.

We used mathematical knot theory to analyse the knots. Above a critical string length, the probability P of knotting at first increased sharply with length but then saturated below 100%. This behaviour differs from that of mathematical self-avoiding random walks, where P has been proven to approach 100%. Finite agitation time and jamming of the string due to its stiffness result in lower probability, but P approaches 100% with long, flexible strings.

Basically, all other factors (and basically, this means trouser jostling) being equal, the longer your cable, the more likely it is to knot.

There are graphs, photos and a whole raft of other formulae and statistical explanation in the paper. I did my best to work my way through it and, despite falling asleep twice, managed to get to the end.

Imagine my disappointment when I found that they had not even bothered to provide a solution for this horrible phenomenon.

Science is amazing and science can be used to demonstrate amazing things. You only have to look at some Austrian bloke jumping from what appeared to be a large, old-fashioned kettle on the edge of space to see this. But all those amazing things are no use if they can’t be put to practical use. Lest we forget, Felix’s freefall allegedly taught us that we could safely eject from spaceplanes of the future (ok, bit of a stretch there in attempting to justify their expense sheet by the guys at Red Bull perhaps, but still).

But this, for all their efforts:

The experiment was repeated hundreds of times with each string length to collect statistics.

gives us just that. Statistics. And they are statistics that say that if you put your headphones in your pocket and you jostle (or even if you don’t), you are going to end up with knotted cable.

This is no help whatsoever and I feel that I must apologise on behalf of science. In my humble opinion, experiments with no practical application should be banned. Physics should be banned. Raymer and Smith have dragged its name through the mud.

And if those bans leave us with no more skydives from space, well so be it. The likelihood of me ever having to evacuate a spaceplane seems rather small when compared with the likelihood of me having to untie another sodding knot in my Sennheiser CX300II’s every time I take them out of my pocket. And no, I am not a serial jostler.

Science must provide answers and solutions. Otherwise we might as well just all study the arts.

93 seconds you’ll never get back

Remember Leonhard Euler from the Satan’s Arithmetic post? Of course you do.
Now behold Euler’s Disc – probably the most hypnotic thing ever.

Look into the eyes, look into the eyes, not around the eyes… and you’re under…

The physics behind this “scientific toy” can be found here, but basically, it comes down to this:

A spinning/rolling disk ultimately comes to rest; and it does so quite abruptly, the final stage of motion being accompanied by a whirring sound of rapidly increasing frequency. As the disk rolls, the point P of rolling contact describes a circle that oscillates with a constant angular velocity w. If the motion is non-dissipative, w is constant and the motion persists forever, contrary to observation (since w is not constant in real life situations). In fact, precession rate of the axis of symmetry approaches a finite-time singularity modeled by a power law with exponent approximately -1/3 (depending on specific conditions).

So there you have it. Obviously,  it’s important that you remember that rolling friction is the primary mechanism for kinetic energy dissipation in this scenario and not air resistance.

Physics of a tsunami

With my parents still in New Zealand and on the coast in Greymouth (in the direct line for any tsunami emanating from the Honshu earthquake) I was reading around the speed of Tsunamis with some personal interest. However, I didn’t have to, since the Pacific Tsunami Warning Center [sic] has all the predicted “hit” times for the arrival of the wave or, more often, waves.

SEA LEVEL READINGS CONFIRM THAT A TSUNAMI HAS BEEN GENERATED WHICH COULD CAUSE WIDESPREAD DAMAGE. AUTHORITIES SHOULD TAKE APPROPRIATE ACTION IN RESPONSE TO THIS THREAT. THIS CENTER WILL CONTINUE TO MONITOR SEA LEVEL DATA TO DETERMINE THE EXTENT AND SEVERITY OF THE THREAT.

ESTIMATED INITIAL TSUNAMI WAVE ARRIVAL TIMES AT FORECAST POINTS WITHIN THE WARNING AND WATCH AREAS ARE GIVEN BELOW. ACTUAL ARRIVAL TIMES MAY DIFFER AND THE INITIAL WAVE MAY NOT BE THE LARGEST. A TSUNAMI IS A SERIES OF WAVES AND THE TIME BETWEEN SUCCESSIVE WAVES CAN BE FIVE MINUTES TO ONE HOUR.

Apologies for the SHOUTING, but this is obviously a rather important message.
UPDATE HERE and again HERE

And there is NZ on the list, with a predicted arrival time of 1930 GMT this evening. That’s 2130 SA time and 0830 tomorrow local time: over 12 hours after the earthquake hit. And that gives you an idea of how massive the scale of this is, because tsunami waves can top 900kph.

The wave speed is the square root of the product of the gravity constant (g) and water depth.

Tsunamis are normally produced by an earthquake or displacement of the seafloor due to plate shifts, etc. This produces a very large wave very rapidly, which then possesses significant energy.

The energy is distributed through the depth of the water initially, as it is displaced, but because of gravity and friction with the seabed, tends to decrease with increasing depth after a short while.
In deep water, the frictional affect on the wave speed is negligible near the surface. The more shallow the water (for instance as it approaches shore), the greater the affect of friction in slowing the mass of water above the seabed; most of the energy of the wave is transferred to the seabed, a small portion is lost to the atmosphere and in heating of the water.

Therefore, the more shallow the water, the slower the wave speed.

And with the Pacific generally being rather deep, the waves are travelling rather fast.

Thankfully, given the distances involved, that still gives my parents significant time to ensure their safety. Sadly, others nearer the epicentre, or without access to this information will probably not be so lucky.