Suppose you have a pair of pants you need to wear tomorrow, but they’re still damp after washing. You use a flat iron to dry them, easily handling the flat parts but struggling with uneven areas like the zipper, pockets, seams, and waistband. This difficulty arises because heat from the iron doesn’t reach these rough areas as quickly as it does the flat ones.
Jake Avila of the UPD College of Science Institute of Mathematics developed a theory to model heat propagation through rough surfaces, collaborating with Italian mathematicians. His method, called homogenization, combines the material’s tiny details with its larger properties, providing a more accurate heat propagation model. Avila’s theory can also apply to other phenomena like acoustic wave propagation and turbulence flow. His next goal is to develop a more general version for wider applications.
