Sunday, 12 April 2009
Go on..... go here.... look around. It's always nice to find out I'm not going completely mad, and that there are others who also "think outside the box". I sometimes get the feeling that if this box was in a room in a house, in a street somewhere, then I would probably find myself in a different town.
What is a soliton? You might ask.
"In mathematics and physics, a soliton is a self-reinforcing solitary wave (a wave packet or pulse) that maintains its shape while it travels at constant speed."
And there's a lovely description of the phenomenon of a soliton, as given by John Scott Russell (1808 – 1882) who observed a solitary wave in the Union Canal in Scotland. He reproduced the phenomenon in a wave tank and named it the "Wave of Translation".
"I was observing the motion of a boat which was rapidly drawn along a narrow channel by a pair of horses, when the boat suddenly stopped - not so the mass of water in the channel which it had put in motion; it accumulated round the prow of the vessel in a state of violent agitation, then suddenly leaving it behind, rolled forward with great velocity, assuming the form of a large solitary elevation, a rounded, smooth and well-defined heap of water, which continued its course along the channel apparently without change of form or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles (14 km) an hour, preserving its original figure some thirty feet long and a foot to a foot and a half in height. Its height gradually diminished, and after a chase of one or two miles (3 km) I lost it in the windings of the channel. Such, in the month of August 1834, was my first chance interview with that singular and beautiful phenomenon which I have called the Wave of Translation".
Now there's something about the description of how the boat sets-up the wave - it sounds a bit like a plunger being pulled on a pinball machine; better yet, the rubber diaphragm at the back of a box which creates smoke rings. Smoke rings are great for school experiments. I am quoting from an amiable site which promotes school experiments:
"The box is placed on its side, and the side with the sheet is given a tap with the hand as one would beat a drum. A smoke ring vortex should be emitted from the hole and travel across the room. The process can be repeated as often as desired so long as some smoke remains. After a while the whole room becomes smokey, and visibility is impaired. The first few rings are usually the most dramatic. A fast-moving ring can be produced immediately after a slower one so that it catches up and overtakes the slower one. Two such vortex generators can be constructed and the rings projected toward one another to study their interaction. It should be pointed out that the vortices are there even in the absence of the smoke, whose sole purpose is to render them visible. This can be illustrated by blowing out a candle from across the room.
The mechanism whereby the vortex ring is generated is easy to understand. When the air exits the hole, it is retarded by friction with the rim of the hole causing the air in the center to move forward faster than the air at the edge. If you imagine riding along with the vortex, the air at the center is moving forward and the air at the edge is moving backwards. This leaves a region of reduced pressure in front of the ring at the edge and behind the ring in the center. The extra air in the center front curves outward, and the extra air at the edge in back curves inward to equalize the pressure thus forming the ring.
Vortex rings are quite a common occurrence in nature. Flowing liquids form vortices when they flow too fast down a narrow channel as can be seen by watching a fast-flowing river. Vortices off the wing tips of fast-moving aircraft are a hazard to other planes that inadvertently fly through them. Most people have seen someone who smokes make vortex rings by shaping the mouth in the form of a circle and exhaling gently. It was once thought (incorrectly) that the interaction of atoms and their spectral emission could be understood in terms of vortex motion inside the atom."
It was Helmholtz who first started to experiment with smoke rings. He was interested in how they might explain the behaviour of vortices in the aether. Thomson, Maxwell and Tait all took an interest in further trying to understand vortex rings, and their infinite mathematical ramifications:
"In 1858 Helmholtz published his important paper in Crelle's Journal on the motion of a perfect fluid. Helmholtz's paper Uber Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen began by decomposing the motion of a perfect fluid into translation, rotation and deformation. It was this aspect which first interested Tait who saw that by using Hamilton's quaternions he could express the fluid velocity as a "vector function". However the ideas in the paper which eventually led the Scottish mathematical physicists to topological considerations concerned vortex lines and vortex tubes. Helmholtz defined vortex lines as lines coinciding with the local direction of the axis of rotation of the fluid, and vortex tubes as bundles of vortex lines through an infinitesimal element of area. Helmholtz showed that the vortex tubes had to close up and also that the particles in a vortex tube at any given instant would remain in the tube indefinitely so no matter how much the tube was distorted it would retain its shape. "
And you just know that this all has something to do with electricity, and matter, and electromagnetic radiation.... and everything else. Indeed, it appears we could relate a pinball machine plunger to an AC circuit, where the generator is compressing, and expanding an electric grid to create shockwaves in the aether. A U-shaped pinball machine plunger; a plunger with no ball and two ends. I thought the timing of the next paragraph impeccable (If it was a cowboy in a movie it would be swinging those saloon doors wide open, right about now):
"By 1839 Faraday was able to bring forth a new and general theory of electrical action. Electricity, whatever it was, caused tensions to be created in matter. When these tensions were rapidly relieved (i.e., when bodies could not take much strain before “snapping” back), then what occurred was a rapid repetition of a cyclical buildup, breakdown, and buildup of tension that, like a wave, was passed along the substance. Such substances were called conductors. In electrochemical processes the rate of buildup and breakdown of the strain was proportional to the chemical affinities of the substances involved, but again the current was not a material flow but a wave pattern of tensions and their relief. Insulators were simply materials whose particles could take an extraordinary amount of strain before they snapped. Electrostatic charge in an isolated insulator was simply a measure of this accumulated strain. Thus, all electrical action was the result of forced strains in bodies."
Many thanks also: