When navigating complex environments, animals often combine multiple strategies to mitigate the effects of external disturbances. These modalities often correspond to different sources of information, leading to speed – accuracy trade-offs. Inspired by the intermittent reorientation strategy seen in the behaviour of the dung beetle, we consider the problem of the navigation strategy of a correlated random walker moving in two dimensions. We assume that the heading of the walker can be reoriented to the preferred direction by paying a fixed cost as it tries to maximize its total displacement in a fixed direction. Using optimal control theory, we derive analytically and confirm numerically the strategy that maximizes the walker’s speed, and show that the average time between reorientations scales inversely with the magnitude of the environmental noise. We then extend our framework to describe execution errors and …

All-solid-state lithium metal batteries enable high-energy-density applications, such as electric aviation, but suffer from instabilities during operation that lead to rough interfaces between the metal and electrolyte. These cause void formation and dendrite growth that degrades performance and safety. Inspired by the morphogenetic control of thin lamina such as tree leaves that robustly grow into flat shapes, we propose a range of approaches to control lithium metal stripping and plating via a range of feedback mechanisms. A minimal model that captures the coupling between interface motion, thermodynamics, electrochemistry and mechanics shows that local feedback cannot stop the formation of rough interfaces, while long-range feedback allows us to stabilize the interface and keep it flat. Our theoretical study suggests various approaches to achieve this, and provides the beginning of a practical framework for …

Perturbation theory plays a central role in the approximate solution of nonlinear differential equations. However, its naïve application often yields divergent series solutions. While these can be made convergent using singular perturbation methods of various types, the procedures used can be subtle owing to the lack of globally applicable algorithms. Inspired by the fact that all exact solutions of differential equations are consequences of their (Lie) symmetries, we reformulate perturbation theory for differential equations as a series expansion of their solutions’ symmetries. This is a change in perspective from the usual method of obtaining series expansions of the solutions themselves. We show that these approximate symmetries are straightforward to calculate and are never singular; their integration is therefore an easier way of constructing uniformly convergent solutions. This geometric viewpoint naturally …

In crowded environments, individuals must navigate around other occupants to reach their destinations. Understanding and controlling traffic flows in these spaces is relevant to coordinating robot swarms and designing infrastructure for dense populations. Here, we combine simulations, theory, and robotic experiments to study how noisy motion can disrupt traffic jams and enable flow as agents travel to individual goals. Above a critical noise level, large jams do not persist. From this observation, we analytically approximate the goal attainment rate as a function of the noise level, then solve for the optimal agent density and noise level that maximize the swarm's goal attainment rate. We perform robotic experiments to corroborate our simulated and theoretical results. Finally, we compare simple, local navigation approaches with a sophisticated but computationally costly central planner. A simple reactive scheme performs well up to moderate densities and is far more computationally efficient than a planner, suggesting lessons for real-world problems.

Starting from a three-dimensional description of an active nematic layer, we employ an asymptotic theory to derive a series of low-dimensional continuum models that capture the coupled dynamics of flat and curved films, including variations in film thickness, shape deformations, internal velocity fields, and the dynamics of orientational order. Using this asymptotic theory, we investigate instabilities driven by activity in both the nematic and isotropic phases for cylindrical and flat films. In the flat case, we demonstrate that incorporating shape and thickness variations fundamentally alters the bend and splay nature of instabilities compared to conventional two dimensional nematic instabilities. In the isotropic phase, we find that both extensile and contractile activity can induce nematic order, in contrast with active nematics on fixed surfaces, where only extensile activity leads to ordering. For the case of curved geometries such as a cylindrical film, we reveal that thickness and shape instabilities are inherently coupled. In the isotropic phase, the emergence of nematic order triggers both thickness and shape instabilities. In the nematic phase, contractile activity induces thickness instabilities, which in turn drive geometric deformations. Our results highlight the crucial interplay between activity, thickness variations, and curvature, providing new insights into the behavior of active nematic films beyond the conventional two dimensional paradigm that has been studied to date.

Soft valves serve to modulate and rectify flows in complex vasculatures across the tree of life, e.g. in the heart of every human reading this. Here we consider a minimal physical model of the heart mitral valve modeled as a flexible conical shell capable of flow rectification via collapse and coaptation in an impinging (reverse) flow. Our experiments show that the complex elastohydrodynamics of closure features a noise-activated rectification mechanism. A minimal theoretical model allows us to rationalize our observations while illuminating a dynamical bifurcation driven by stochastic hydrodynamic forces. Our theory also suggests a way to trigger the coaptation of soft valves on demand, which we corroborate using experiments, suggesting a design principle for their efficient operation.