This is the supplemental material for the manuscript "Verification, validation, and results of an approximate model for the stress of a Tokamak toroidal field coil at the inboard midplane" submitted to Fusion Engineering and Design. This material includes PDF writeups of the derivations of the axisymmetric extended plane strain model, the elastic properties smearing model, and 20+ MATLAB scripts and functions which implement the model and generate the figures in the paper.
The data are 4554 light curves derived from images taken of the globular cluster M4 by the Kepler space telescope during the K2 portion of its mission, specifically during Campaign 2 of that mission, which occurred in 2014. A total of 3856 images were taken over approximately three months at a cadence of approximately half an hour. The purpose of these observations was to find stars and other objects that vary in brightness over time --- variable stars. Also included is a table with associated information for each of the 4554 objects and their light curves.
Ant colonies regulate activity in response to changing conditions without using centralized control. Harvester ant colonies forage in the desert for seeds, and their regulation of foraging manages a tradeoff between spending and obtaining water. Foragers lose water while outside in the dry air, but the colony obtains water by metabolizing the fats in the seeds they eat. Previous work shows that the rate at which an outgoing forager leaves the nest depends on its recent experience of brief antennal contact with returning foragers that carry a seed. We examine how this process can yield foraging rates that are robust to uncertainty and responsive to temperature and humidity across minutes to hour-long timescales. To explore possible mechanisms, we develop a low-dimensional analytical model with a small number of parameters that captures observed foraging behavior. The model uses excitability dynamics to represent response to interactions inside the nest and a random delay distribution to represent foraging time outside the nest. We show how feedback of outgoing foragers returning to the nest stabilizes the incoming and outgoing foraging rates to a common value determined by the ``volatility’’ of available foragers. The model exhibits a critical volatility above which there is sustained foraging at a constant rate and below which there is cessation of foraging. To explain how the foraging rates of colonies adjust to temperature and humidity, we propose a mechanism that relies on foragers modifying their volatility after they leave the nest and get exposed to the environment. Our study highlights the importance of feedback in the regulation of foraging activity and points to modulation of volatility as a key to explaining differences in foraging activity in response to conditions and across colonies. Our results present opportunities for generalization to other contexts and systems with excitability and feedback across multiple timescales.