Just as light rays can be focussed to a point to achieve strong concentration of energy, so too can stress and curvature conspire to concentrate stress and elastic energy in a thin sheet or membrane. The mechanism for these concentrations of stress differ greatly from the familiar one of optics. This talk reviews the variety of forms that this focusing takes, from the familiar case of crumpled paper to the emerging evidence for induced focusing in a conically deformed sheet. Fluid films also show focusing phenomena when capillary flow is created by evaporation as in the stain left by a dried drop of coffee. Here the quantity focused is the concentration of advected solute. The form of this focusing can be controlled widely by varying the boundary shape of the film. The characteristic fadeout of density from edge to interior is governed by a power law that depends strongly on the evaporation conditions.

Chicago