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