This repository contains Matlab code for the paper "The Mathematics of Burger Flipping" by Jean-Luc Thiffeault.
The following MATLAB functions are part of this repository:
- heat - Temperature profile for the heat equation.
- heatsteady - Steady temperature profile for heat equation.
- heateigval - Eigenvalues (spectrum) of the heat operator.
- heateigfun - Eigenfunctions of the heat operator.
- tcookthru - The time to cook food through without flipping.
- flipheatfix - The fixed point of the flip-heat operation for fixed time.
- tcooksym - Time to cook for equal flips and symmetric boundary conditions.
- cooktime - Cooking time on a hot plate for several flips of the food.
- mincooktime - Minimize cooking time for given number of flips of the food.
- flipheatbl - Boundary layer for the flip-heat operator for rapid flip time.
- flipheatop - The flip-heat operator.
- flipop - The "flipping" operator acting on eigenfunctions.
Thiffeault, J.-L. "The Mathematics of burger flipping," Physica D: Nonlinear Phenomena 439, 133410 (2022). DOI: 10.1016/j.physd.2022.133410
BibTeX entry:
@Article{Thiffeault2022,
title = {The mathematics of burger flipping},
journal = {Physica D: Nonlinear Phenomena},
volume = 439,
pages = 133410,
year = 2022,
issn = {0167-2789},
doi = {10.1016/j.physd.2022.133410},
url = {https://doi.org/10.1016/j.physd.2022.133410},
author = {Jean-Luc Thiffeault},
keywords = {Heat equation, Optimization, Cooking},
abstract = {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.}
}This code is released under the MIT License. See the file LICENSE for copying permission.