How can we manipulate the topological connectivity of a three-dimensional prismatic assembly to control the number of internal degrees of freedom and the number of connected components in it? To answer this question in a deterministic setting, we use ideas from elementary number theory to provide a hierarchical deterministic protocol for the control of rigidity and connectivity. We then show that it is possible to also use a stochastic protocol to achieve the same results via a percolation transition. Together, these approaches provide scale-independent algorithms for the cutting or gluing of three-dimensional prismatic assemblies to control their overall connectivity and rigidity.

Tissues undergoing morphogenesis impose mechanical effects on one another. How developmental programs adapt to or take advantage of these effects remains poorly explored. Here, using a combination of live imaging, modeling, and microsurgical perturbations, we show that the axial and paraxial tissues in the forming avian embryonic body coordinate their rates of elongation through mechanical interactions. First, a cell motility gradient drives paraxial presomitic mesoderm (PSM) expansion, resulting in compression of the axial neural tube and notochord; second, elongation of axial tissues driven by PSM compression and polarized cell intercalation pushes the caudal progenitor domain posteriorly; finally, the axial push drives the lateral movement of midline PSM cells to maintain PSM growth and cell motility. These interactions form an engine-like positive feedback loop, which sustains a shared elongation rate for coupled tissues. Our results demonstrate a key role of inter-tissue forces in coordinating distinct body axis tissues during their co-elongation.

Channel formation and branching is widely seen in physical systems where movement of fluid through a porous structure causes the spatiotemporal evolution of the medium. We provide a simple theoretical framework that embodies this feedback mechanism in a multiphase model for flow through a frangible porous medium with a dynamic permeability. Numerical simulations of the model show the emergence of branched networks whose topology is determined by the geometry of external flow forcing. This allows us to delineate the conditions under which splitting and/or coalescing branched network formation is favored, with potential implications for both understanding and controlling branching in soft frangible media.

Rectilinear crawling locomotion is a primitive and common mode of loco- motion in slender soft-bodied animals. It requires coordinated contractions that propagate along a body that interacts frictionally with its environment. We propose a simple approach to understand how this coordination arises in a neuromechanical model of a segmented, soft-bodied crawler via an itera- tive process that might have both biological antecedents and technological relevance. Using a simple reinforcement learning algorithm, we show that an initial all-to-all neural coupling converges to a simple nearest-neighbour neural wiring that allows the crawler to move forward using a localized wave of contraction that is qualitatively similar to what is observed in Drosophila melanogaster larvae and used in many biomimetic solutions. The resulting solution is a function of how we weight gait regularization in the reward, with a trade-off between speed and robustness to proprioceptive noise. Overall, our results, which embed the brain–body–environment triad in a learning scheme, have relevance for soft robotics while shedding light on the evolution and development of locomotion.

Understanding the morphology of self-assembled fibrillar bundles and aggregates is relevant to a range of problems in molecular biology, supramolecular chemistry and materials science. Here, we propose a coarse-grained approach that averages over specific molecular details and yields an effective mechanical theory for the spatial complexity of self-assembling fibrillar structures that arises due to the competing effects of (the bending and twisting) elasticity of individual filaments and the adhesive interactions between them. We show that our theoretical framework accounting for this allows us to capture a number of diverse fibril morphologies observed in natural and synthetic systems, ranging from Filopodia to multi-walled carbon nanotubes, and leads to a phase diagram of possible fibril shapes. We also show how the extreme sensitivity of these morphologies can lead to spatially chaotic structures. Together, these results suggest a common mechanical basis for mesoscale fibril morphology as a function of the nanoscale mechanical properties of its filamentous constituents.

Many complex systems experience damage accumulation, which leads to aging, manifest as an increasing probability of system collapse with time. This naturally raises the question of how to maximize health and longevity in an aging system at minimal cost of maintenance and intervention. Here, we pose this question in the context of a simple interdependent network model of aging in complex systems and show that it exhibits cascading failures. We then use both optimal control theory and reinforcement learning alongside a combination of analysis and simulation to determine optimal maintenance protocols. These protocols may motivate the rational design of strategies for promoting longevity in aging complex systems with potential applications in therapeutic schedules and engineered system maintenance.

Animal hearts are soft shells that actively pump blood to oxygenate tissues. Here, we propose an allometric scaling law for the heart rate based on the idea of elastohydrodynamic resonance of a fluid-loaded soft active elastic shell that buckles and contracts axially when twisted periodically. We show that this picture is consistent with numerical simulations of soft cylindrical shells that twist-buckle while pumping a viscous fluid, yielding optimum ejection fractions of 35%–40% when driven resonantly. Our scaling law is consistent with experimental measurements of heart rates over 2 orders of magnitude, and provides a mechanistic basis for how metabolism scales with organism size. In addition to providing a physical rationale for the heart rate and metabolism of an organism, our results suggest a simple design principle for soft fluidic pumps.

Inspired by the jamming in leaky systems that arises in many physiological and industrial settings, we study the propagation of clogs in a leaky microfluidic channel. By driving a colloidal suspension through such a channel with a fluid-permeable wall adjoining a gutter, we follow the formation and propagation of jams and show that they move at a steady speed, in contrast with jams in channels that have impermeable walls. Furthermore, by varying the ratio of the resistance from the leaky wall and that of the gutter, we show that it is possible to control the shape of the propagating jam, which is typically wedge shaped. We complement our experiments with numerical simulations, where we implement an Euler-Lagrangian framework for the simultaneous evolution of both immersed colloidal particles and the carrier fluid. Finally, we show that the particle ordering in the clog can be tuned by adjusting the geometry of the leaky wall. Altogether, the leaky channel serves both as a filter and a shunt with the potential for a range of uses.

When a volatile droplet is deposited on a floating swellable sheet, it becomes asymmetric, lobed and mobile. We describe and quantify this phenomena that involves nonequilibrium swelling, evaporation and motion, working together to realize a self-excitable spatially extended oscillator. Solvent penetration causes the film to swell locally and eventually buckle, changing its shape and the drop responds by moving. Simultaneously, solvent evaporation from the swollen film causes it to regain its shape once the droplet has moved away. The process repeats and leads to complex pulsatile spinning and/or sliding movements. We use a one-dimensional experiment to highlight the slow swelling of and evaporation from the film and the fast motion of the drop, a characteristic of excitable systems. Finally, we provide a phase diagram for droplet excitability as a function of drop size and film thickness and scaling laws for the motion of the droplet.

The ability to infer intention lies at the basis of many social interactions played out via motor actions. We consider a simple paradigm of this ability in humans using data from experiments simulating an antagonistic game between an Attacker and a Blocker. Evidence shows early inference of an Attacker move by as much as 100ms but the nature of the informational cues signaling the impending move remains unknown. We show that the transition to action has the hallmark of a critical transition that is accompanied by early warning signals. These early warning signals occur as much as 130 ms before motion ensues—showing a sharp rise in motion autocorrelation at lag-1 and a sharp rise in the autocorrelation decay time. The early warning signals further correlate strongly with Blocker response times. We analyze the variance of the motion near the point of transition and find that it diverges in a manner consistent with the dynamics of a fold-transition. To test if humans can recognize and act upon these early warning signals, we simulate the dynamics of fold-transition events and ask people to recognize the onset of directional motion: participants react faster to fold-transition dynamics than to its uncorrelated counterpart. Together, our findings suggest that people can recognize the intent and onset of motion by inferring its early warning signals.