Reflections on mathematical research towards a doctorate of philosophy.

Showing posts with label soliton. Show all posts
Showing posts with label soliton. Show all posts

Thursday, October 12, 2006

applications of solitons

For more than 130 years solitary waves where considered rare curiosities. Not until the 1960's did it become clear that such waves could form in the ocean as seismic waves of enormous wavelengths generated by shocks in the ocean's floor. Moreover, soliton waves are common in a great variety of other physical systems. In some circumstances it is almost impossible ot prevent them from forming.
There are endless examples. When a double-helix molecule of DNA is put into solvent, there is an exchange of hydrogen atoms betwenn the solvent and the DNA. A break forms between the two helices and moves along the molecule as a stable wave. Similar energy pulses are solitons that traverse the helix of other protein molecules. Many solitons exhibit periodicity, fluctuating between extreme values of one or more properties. Such "second order" solitons turn up as pulses in laser light moving along a glass fiber. Energy travels along nerves in solitons pulses. Pressure waves can form solitons, such as the sound of an explosion or the movement of certain mechanical vibrations through solids.
Magnetic fields trapped in superconductors and superfluids form soliton vortices. It seems likely that Jupiter's famous red spot is a long-lasting soliton in the giant planet's turbulent atmposphere.
The most promising application of solitons is in fiber optics. Fibers have a natural tendency to keep light pulses from dispersing, and various techniques are being devised to keep the pulses even more uniform.
Recent years have seen a major trend towards constructing soliton models of elementary particles.


Gardner, Martin, 1914-
Title The ambidextrous universe : mirror asymmetry and time-reversed worlds / Martin Gardner ; illustrated by John Mackey.
Edition 2nd ed.
Published Harmondsworth : Penguin, 1982, c1979.

Wednesday, September 27, 2006

On solitons

The soliton fad is a catchy mixture of operator algebra and explicitlly solvable differential equations. How can anyone resist such temptation? So much for the good news. The bad news is that solitons seem unbudgingly one-dimensional, despite the insinuations of computer simulators. Chalk one up to one-dimensional physics.

Gian-Carlo Rota

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