Multi-Particle Motion Control

In 1787 a German musician named Ernst Chladni, developed to a much greater scale experiments performed by Robert Hooke over a century before. By taking a metal plate, sprinkled with sand, and drawing one of his violin bows over the edge. The result was that under repeated draws, as the plate achieved resonance, the sand grains moved to form definite lines on the surface, looking similar to iron filings placed near a magnet. This occurs because of the standing waves formed on the flat surface. In a single standing wave, the nodes are the places where the medium doesn’t move. The vibration on either side of a node is in perfect phase. On a flat surface, you have to imagine a 3D wave coming out of a page. Instead of just points, the stationary medium forms lines called nodal lines that the sand tends to reach as once there the grains are in no obligation to move. It has been assumed for a long time that the motion of the particles once on the node are random, occasionally leaving just to be bounced back on, and so most manipulation has been based on dynamically changing the nodal lines.

There is, however, a new idea. Through some intense mathematical modelling it appears that the movement of the grains can be modelled statistically based on likely probabilities of movement. By recording the location of all the particles simultaneously a single note can be played to move all particles in their individual desired directions. Since the movement is still random and contains a certain variance the particles will only have a net movement in the right direction. This results in a loss of precision that can be best described by imagining writing, except it now looks like it has been written with someone’s non dexterous hand. To work out which note is to be played a computer takes the information about the location of the particles and then looks through the available frequencies to see which one will move all the particles in a desired direction based on the modes of the surface. This manipulation is very impressive as it only requires a single actuator to produce the vibration when previous examples have used over thirty to achieve a similar result.

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