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The CUSP: From Finite Time Singularities to Breaking Waves
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234 Leonardo Gallery Scientific Delirium Madness 4.0 Gallery The CUSP: From Finite Time Singularities to Breaking Waves Patrice Le Gal We all know the sound of a Ping-Pong ball bouncing repeatedly faster and faster off the ground before it comes to a halt. This phenomenon of divergence in a finite duration of a physical quantity—here the frequency of rebounds—is known in physics as “singularity in finite time.” Another example of a singularity in finite time is the wave breaking phenomenon. In the vicinity of this subtle instant preceding breaking, the temporal derivative of the free surface of water diverges as the inverse of the square root of time. A geometric representation of this singular behavior is the cusp, the simplest catastrophe depending on two parameters in René Thom’s catastrophe theory. The cusp example shows that for certain time and space positions, the surface is a single valued function, whereas outside this domain, it takes three possible values. Therefore , the cusp gives a useful representation of the tilting of a wave before breaking. The delimiting curves between these two behaviors are called caustics and merge at the singularity point. These lines share the exact mathematical description with the pattern drawn by focusing light at the bottom of a cup after reflecting off the cup wall. My hope during my Scientific Delirium Madness residency was to create an art piece in order to share the contemplation of this subtle and fragile instant where the singularity arises, where the curvature of forms changes sign, where waves overturn. To extend this infinitely small duration, the singularity will be unfolded—as mathematicians say. My result is an array of wooden rods whose arrangement makes straight rays cooperate and interfere in an apparent continuous and smooth motion, giving rise to a regular but cusped surface that sifts and transforms our own perception of the world around it. Like a filter, the CUSP will let wind, sound, light and thoughts to go through its beams. Patrice Le Gal Email: Web: The CUSP under the full moon at Djerassi. (© Patrice Le Gal. Photo © Kristen Stipanov.) ...

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