Force-driven parallel shear flow in a spatially periodic domain is shown to be linearly unstable
with respect to both the Reynolds number and the domain aspect ratio. This finding is confirmed
by computer simulations, and a simple expression is derived to determine stable flow conditions.
Periodic extensions of Couette and Poiseuille flows are unstable at Reynolds numbers two orders
of magnitude smaller than their aperiodic equivalents because the periodic boundaries impose
fundamentally different constraints. This instability has important implications for designing computational models of nonlinear dynamic processes with periodicity.
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.
