The mathematics of burger flipping (Q2167984)

This work seems to be very interesting and structured impressively. The author presents a simple model of cooking by flipping, and some interesting observations emerge. The rate of cooking depends on the spectrum of a linear operator and on the fixed point of a map. If the system has symmetric thermal properties, the rate of cooking becomes independent of the sequence of flips, as long as the last point to be cooked is the midpoint. After numerical optimization, the flipping intervals become roughly equal in duration as their number is increased, though the final interval is significantly longer and found that the optimal improvement in cooking time, given an arbitrary number of flips, is about 29\% over a single flip. The author solves the one-dimensional heat equation with general boundary conditions using Newton's law of cooling and expresses the solution as a generalized Fourier series in Sturm-Liouville eigenfunctions. It is observed that the food might never fully reach its cooked temperature, unless it is flipped.