The mathematics of burger flipping

What is the most effective way to grill food? Timing is everything, since only one surface is exposed to heat at a given time. Should we flip only once, or many times? We present 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. We find that the optimal improvement in cooking time, given an arbitrary number of flips, is about 29% over a single flip. This toy problem has some characteristics reminiscent of turbulent thermal convection, such as a uniform average interior temperature with boundary layers.

烤食物最有效的方法是什么？时间是关键，因为在给定时间只有一个面受热。我们应该只翻一次，还是多次呢？我们提出了一个通过翻面来烹饪的简单模型，并得出了一些有趣的观察结果。烹饪速度取决于一个线性算子的频谱以及一个映射的不动点。如果系统具有对称的热学性质，只要最后要烤的点是中点，烹饪速度就与翻面的顺序无关。经过数值优化，随着翻面次数的增加，翻面间隔的时长大致相等，尽管最后一个间隔明显更长。我们发现，在任意翻面次数的情况下，烹饪时间的最佳改善比只翻一次大约提高了29%。这个玩具问题具有一些让人联想到湍流热对流的特征，比如内部平均温度均匀且有边界层。