The physics of the frog and the lily pad

A resting frog can deform the lily pad on which it sits. The weight of the frog applies a localised load to the lily pad (which is supported by the buoyancy of the liquid below), thus deforming the pad. Whether or not the frog knows it, the physical scenario of a floating elastic sheet subject to an applied load is present in a diverse range of situations spanning a spectrum of length scales. At global scales the gravitational loading of the lithosphere by mountain ranges and volcanic sea mounts involve much the same physical ingredients.

Why shells behave unexpectedly when poked - Oxford Mathematics Research

The classic picture of how spheres deform (e.g. when poked) is that they adopt something called 'mirror buckling' - this is a special deformation (an isometry) that is geometrically very elegant. This deformation is also very cheap (in terms of the elastic energy) and so it has long been assumed that this is what a physical shell (e.g. a ping pong ball or beach ball) will do when poked. However, experience shows that actually many shells don’t adopt this state - instead, beach balls wrinkle and ping pong balls crumple.

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