Mathematicians prove melting ice stays smooth
After decades of effort, mathematicians now have a complete understanding of the complicated equations that model the motion of free boundaries, like the one between ice and water.
Drop an ice cube into a glass of water. You can probably picture the way it starts to melt. You also know that no matter what shape it takes, you’ll never see it melt into something like a snowflake, composed everywhere of sharp edges and fine cusps.
Mathematicians model this melting process with equations. The equations work well, but it’s taken 130 years to prove that they conform to obvious facts about reality. Now, in a paper posted in March, Alessio Figalli and Joaquim Serra and Xavier Ros-Oton of the University of Barcelona have established that the equations really do match intuition. Snowflakes in the model may not be impossible, but they are extremely rare and entirely fleeting.
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