A new twist on soap films

Soap films with complex shapes shed light on the formation of mathematical singularities, which occur in a broad range of fields. This is an example of experimental mathematics, in the sense that we are using laboratory studies to inform conjectures on mathematical connections - Raymond Goldstein The way in which soap films collapse and re-form when twisted or stretched could hold the key to predicting the formation and location of mathematical singularities, which can be seen in the motion of solar flares and other natural phenomena. Research on the processes by which soap films undergo transitions from one stable state to another has led to conjectures on the nature and location of the singular events that occur during the change of form, connecting two previously separate areas in mathematics. In mathematics, singularities occur when an equation or surface breaks down and 'explodes'. In surfaces such as soap films, singularities occur when the surface collides with itself, changing shape in the blink of an eye. Researchers from the University of Cambridge have shown that identifying a special type of curve on the surface can help predict where these singularities are likely to occur in soap films, which could in turn aid in the understanding of singularities in the natural world. The results are published in the journal Proceedings of the National Academy of Sciences (PNAS) .