论文标题
汉堡翻转的数学
The mathematics of burger flipping
论文作者
论文摘要
烤食物的最有效方法是什么？时间是一切，因为在给定时间只有一个表面暴露于热量。我们应该只翻一次一次，还是多次？我们通过翻转提出了一个简单的烹饪模型，并出现了一些有趣的观察结果。烹饪速度取决于线性操作员的光谱，以及地图的固定点。如果系统具有对称的热性能，则烹饪速率与翻转序列无关，只要最后一个要烹饪的点就是中点。在数值优化之后，随着数量的增加，翻转间隔在持续时间大致相等，尽管最终间隔明显更长。我们发现，鉴于任意数量的翻转数量，烹饪时间的最佳改善在一个翻转上约为29％。这个玩具问题具有一些让人联想到湍流热对流的特征，例如带边界层的平均内部温度均匀。
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.
