What is the connection between crumpled paper and marine algae? Saddle-like shapes similar to those found in an Elizabethan "ruff" collar, say the physicists at the Laboratory for Statistical Physics at the Ecole normale supérieure.
They have modeled them and calculated their energy. It turns out that the most stable shape is that adopted by certain marine algae.
A practical experiment
Cut out a disk from a sheet of paper, place it on your coffee cup, and press the tip of your pen down on the center of the disk: the paper curls up, forming a cone-shaped fold. In the language of physics, this is known as a 'conical point'. When you crumple up a sheet of paper, you can also see miniature conical points, which are formed starting out from the folds.
Ice cream cones or ruffs
Two researchers at the Laboratory for Statistical Physics at the Ecole normale supérieure have studied these conical points. Or to be more precise, they tried to see how conical points generate 'e-cones'. What is an e-cone? If you remove a wedge from a disk and stick together the edges of the remaining shape, you get an 'ice-cream cone'. Whereas if you add a wedge that is larger than the one that was removed, you get an e-cone (e stands for excess).
E-cones can take on an infinite number of shapes, without the intervention of any external force. The physicists modeled these e-cones in order to predict their shape and the elastic stresses generated. Their work shows that the symmetrical shape with two folds is the one with the lowest energy. This is found in certain marine algae which spontaneously adopt this shape during growth.
- Martin Michael Müller, Martine Ben Amar, Jemal Guven. Conical Defects in Growing Sheets. Physical Review Letters, 2008; 101 (15): 156104 DOI: 10.1103/PhysRevLett.101.156104
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