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## "Producing an Optimal Can," Friday, December 6, 12n, MH 606

### Michael Campbell

Mike was a CSUF double major physics/math class of 1991 who went on to finish his PhD in math at UCLA in 1999 and then on to postdocs at UCI and UC Berkeley.

ABSTRACT:

It turns out that the calculus problem of producing an optimal can, i.e. one with minimal surface area and therefore at minimum price, becomes much more interesting when material

*and storage*costs are included. The problem then displays features in“phase transition” phenomena (like a piece of metal magnetizing at low temperature). That is pretty amazing, since it takes some heavy-duty tools to get to the discontinuities that characterize phase transitions, in say, a magnetic system. The can problem has discontinuity built in, so we bypass functional analysis, operator algebras, measure/probability theory, stochastic pde’s and all the other inaccessible tools to cut right to the chase. All that is needed is an understanding of first-semester calculus. As the price for storage increases, the optimal can changes from one with a square profile to one with a rectangular profile. This is essentially “symmetry breaking” in statistical mechanics. This talk will explore this open problem.