Eva Kanso

The complex formations exhibited by schooling fish have long been the object of fascination for biologists and physicists. However, the physical and sensory mechanisms leading to organized collective behavior remain elusive. On the physical side in particular, it is unknown how the flows generated by individual fish influence the collective patterns that emerge in large schools. To address this question, we here present a continuum theory for a school of swimmers in an inline formation. The swimmers are modeled as flapping wings that interact through temporally nonlocal hydrodynamic forces, as arise when one swimmer moves through the lingering vortex wakes shed by the others, leading to a system of time-delay-differential equations. Through coarse-graining, we derive a system of partial differential equations for the evolution of swimmer density and collective vorticity-induced hydrodynamic force. Linear stability analysis of the governing equations shows that there is a range of swimmer densities for which the uniform (constant-density) state is unstable to perturbations. Numerical simulations in periodic domains reveal families of stable traveling wave solutions, where a uniform school destabilizes into a collection of densely populated "subschools" separated by relatively sparse regions that move as a propagating wave. We find that distinct propagating waves may be stable for the same set of kinematic parameters. We also find that finite schools can evolve into packets of coarsening traveling waves whose overall spreading is described by a rarefaction fan moving upstream and a terminating downstream shock. Generally, our results show that temporally nonlocal hydrodynamic interactions can lead to rich collective behavior in schools of swimmers.

Abstract Data-driven modeling of collective dynamics is a challenging problem because emergent phenomena in multi-agent systems are often shaped by short- and long-range interactions among individuals. For example, in bird flocks and fish schools, flow coupling plays a crucial role in emergent collective behavior. Such collective motion can be modeled using graph neural networks (GNNs), but GNNs struggle when graphs become large and often fail to capture long-range interactions. Here, we construct hierarchical and equivariant GNNs, and show that these GNNs accurately predict local and global behavior in systems with collective motion. As representative examples, we apply this approach to simulations of clusters of point vortices and populations of microswimmers. In these systems, our approach is more accurate and faster than a fully-connected GNN. Specifically, only our approach conserves the Hamiltonian for the point vortices and only our approach predicts the transition from aggregation to swirling for the microswimmers.

Schooling fish often self-organize into a variety of collective patterns, from polarized schooling to rotational milling. Mathematical models support the emergence of these large-scale patterns from local decentralized interactions, in the absence of individual memory and group leadership. In a popular model where individual fish interact locally following rules of avoidance, alignment, and attraction, the group exhibits collective memory: changes in individual behavior lead to emergent patterns that depend on the group's past configurations. However, the mechanisms driving this collective memory remain obscure. Here, we combine numerical simulations with tools from bifurcation theory to uncover that the transition from milling to schooling in this model is driven by a noisy transcritical bifurcation where the two collective states intersect and exchange stability. We further show that key features of the group dynamics - the bifurcation character, transient milling, and collective memory - can be captured by a phenomenological model of the group polarization. Our findings demonstrate that collective memory arises from a noisy bifurcation rather than from structural bistability, thus resolving a long-standing ambiguity about its origins and contributing fundamental understanding to collective phase transitions in a prevalent model of fish schooling.

The remarkable cohesion and coordination observed in moving animal groups and their collective responsiveness to threats are thought to be mediated by scale-free correlations, where changes in the behavior of one animal influence others in the group, regardless of the distance between them. But are these features independent of group size? Here, we investigate group cohesiveness and collective responsiveness in computational models of massive schools of fish of up to 50,000 individuals. We show that as the number of swimmers increases, flow interactions destabilize the school, creating clusters that constantly fragment, disperse, and regroup, similar to their biological counterparts. We calculate the spatial correlation and speed of information propagation in these dynamic clusters. Spatial correlations in cohesive and polarized clusters are indeed scale free, much like in natural animal groups, but fragmentation events are preceded by a decrease in correlation length, thus diminishing the group's collective responsiveness, leaving it more vulnerable to predation events. Importantly, in groups undergoing collective turns, the information about the change in direction propagates linearly in time among group members, thanks to the non-reciprocal nature of the visual interactions between individuals. Merging speeds up the transfer of information within each cluster by several fold, while fragmentation slows it down. Our findings suggest that flow interactions may have played an important role in group size regulation, behavioral adaptations, and dispersion in living animal groups.

Phagotrophy, the ability of cells to ingest organic particles, marked a pivotal milestone in evolution, enabling the emergence of single-celled eukaryotes that consume other organisms and leading to multicellular life. However, reliance on food particles also created a mechanical challenge—how to coordinate the transfer of particles from the exterior environment to the cell interior? Here, we investigate this important link using mechanistic models of ciliates, a clade of single-celled eukaryotes that either swim or attach and generate feeding currents to capture prey. We demonstrate that ciliates optimize their feeding efficiency by designating a specific portion of the cell surface as a ‘mouth,’ and optimal cilia coverage varies by life strategy: for sessile ciliates, prey encounter is most efficient when cilia are arranged in bands around oral structures while ciliates that swim display diverse ciliary arrangements that meet the cell’s nutritional needs. Importantly, beyond a threshold of doubling nutrient uptake, further increases in feeding flux do not seem to be a dominant selective force in cell design. The evolution of phagotrophy by microbes required effective particle transport and ingestion, enabling the rise of ciliates as key grazers in aquatic ecosystems. This study shows that the morphological adaptations of ciliates for phagotrophy were shaped by hydrodynamic forces.

Abstract Sea stars use hundreds of tube feet on their oral surface to crawl, climb, and navigate complex environments—all without the coordination of a central brain. While the morphology of tube feet and their role as muscular hydrostats are well described, the dynamics underlying their locomotion remain poorly understood. To investigate these dynamics, we employed an optical imaging method based on frustrated total internal reflection to visualize and quantify tube foot adhesion in real time across individuals of Asterias rubens spanning a wide size range. Our results reveal an inverse relationship between crawling speed and the duration of tube foot contact with the substrate. This suggests that sea stars regulate locomotion by modulating foot-substrate interaction time in response to body load. To test this, we conducted perturbation experiments using 3D-printed backpacks that increased body mass by 25% and 50%, along with numerical simulations based on a mechanistic model incorporating decentralized feedback control of the tube feet. The added load significantly increased adhesion time, supporting the role of a load-dependent mechanical adaptation. We further investigated inverted locomotion, both experimentally and through simulation, and found that tube feet adjust their contact behavior when the animal is oriented upside down relative to gravity. Together, our findings demonstrate that sea stars adapt their locomotion to changing mechanical demands by modulating tube foot-substrate interactions, revealing a robust, decentralized strategy for navigating diverse and challenging terrains.

Many single-celled organisms exhibit both solitary and colonial existence. An important step towards multicellularity, which is associated with benefits such as enhanced nutrient uptake, was the formation of colonies of unicellular organisms. However, the initial drivers that favoured individual cells aggregating into more complex colonies are less clear. Here we show that hydrodynamic coupling between proximate neighbours results in faster feeding flows for neighbouring ciliates, such that individuals within a dynamic colony have stronger average feeding flows than solitary individuals. Flows generated by individuals acting together reach higher velocities, thus allowing access to a wider range of prey resources than individuals acting on their own. Moreover, we find that accrued feeding benefits are typically asymmetric: whereas all individuals benefit from acting together, those with slower solitary currents gain more from partnering than those with faster currents. We find that colonial organization in simple unicellular organisms is beneficial for all its members. This provides fundamental insights into the selective forces favouring the early evolution of multicellular organization. How unicellular organisms evolved into multicellular ones is an open question. Now, using unicellular Stentor coeruleus as a model system, the transition between isolated individuals and a coordinated colony is shown to benefit all colony members.

Aquatic animals are much better at underwater navigation than robotic vehicles. Robots face major challenges in deep water because of their limited access to global positioning signals and flow maps. These limitations, and the changing nature of water currents, support the use of reinforcement learning approaches, where the navigator learns through trial-and-error interactions with the flow environment. But is it feasible to learn underwater navigation in the agent’s Umwelt, without any land references? Here, we tasked an artificial swimmer with learning to reach a specific destination in unsteady flows by relying solely on egocentric observations, collected through on-board flow sensors in the agent’s body frame, with no reference to a geocentric inertial frame. We found that while sensing local flow velocities is sufficient for geocentric navigation, successful egocentric navigation requires additional information of local flow gradients. Importantly, egocentric navigation strategies obey rotational symmetry and are more robust in unfamiliar conditions and flows not experienced during training. Our work expands underwater robot-centric learning, helps explain why aquatic organisms have arrays of flow sensors that detect gradients, and provides physics-based guidelines for transfer learning of learned policies to unfamiliar and diverse flow environments. Aquatic animals outperform robotic vehicles in underwater navigation due to robots’ limited access to GPS and flow maps in deep water. The authors report that to successfully learn navigation, an agent must sense both local flows and flow gradients, enabling adaptable and robust policies under unfamiliar conditions.

Mucociliary clearance is a vital defense mechanism of the human airways, protecting against harmful particles and infections. When this process fails, it contributes to respiratory diseases like chronic obstructive pulmonary disease (COPD) and asthma. While advances in single-cell transcriptomics have revealed the complexity of airway composition, much of what we know about how airway structure impacts clearance relies on animal studies. This limits our ability to create accurate human-based models of airway diseases. Here we show that the airways in female rats and in humans exhibit species-specific differences in the distribution of ciliated and secretory cells as well as in ciliary beat, resulting in significantly higher clearance effectiveness in humans. We further reveal that standard lab-grown cultures exhibit lower clearance effectiveness compared to human airways, and we identify the underlying structural differences. By combining diverse experiments and physics-based modeling, we establish universal benchmarks to assess human airway function, interpret preclinical models, and better understand disease-specific impairments in mucociliary clearance. Mucociliary clearance is crucial for airway defense but its structure-function relationships in humans are not fully understood. Here, the authors show how airway epithelial structure impacts clearance by mapping cilia distribution, comparing human and rat airways, and developing quantitative models to assess function.

Ciliated microorganisms near the base of the aquatic food chain either swim to encounter prey or attach at a substrate and generate feeding currents to capture passing particles. Here, we represent attached and swimming ciliates using a popular spherical model in viscous fluid with slip surface velocity that affords analytical expressions of ciliary flows. We solve an advection–diffusion equation for the concentration of dissolved nutrients, where the Péclet number ( $Pe$ ) reflects the ratio of diffusive to advective time scales. For a fixed hydrodynamic power expenditure, we ask what ciliary surface velocities maximize nutrient flux at the microorganism's surface. We find that surface motions that optimize feeding depend on $Pe$ . For freely swimming microorganisms at finite $Pe$ , it is optimal to swim by employing a ‘treadmill’ surface motion, but in the limit of large $Pe$ , there is no difference between this treadmill solution and a symmetric dipolar surface velocity that keeps the organism stationary. For attached microorganisms, the treadmill solution is optimal for feeding at $Pe$ below a critical value, but at larger $Pe$ values, the dipolar surface motion is optimal. We verified these results in open-loop numerical simulations and asymptotic analysis, and using an adjoint-based optimization method. Our findings challenge existing claims that optimal feeding is optimal swimming across all Péclet numbers, and provide new insights into the prevalence of both attached and swimming solutions in oceanic microorganisms.

Data-driven modeling of collective dynamics is a challenging problem because emergent phenomena in multi-agent systems are often shaped by long-range interactions among individuals. For example, in bird flocks and fish schools, long-range vision and flow coupling drive individual behaviors across the collective. Such collective motion can be modeled using graph neural networks (GNNs), but GNNs struggle when graphs become large and often fail to capture long-range interactions. Here, we construct hierarchical and equivariant GNNs, and show that these GNNs accurately predict local and global behavior in systems with collective motion. As representative examples, we apply this approach to simulations of clusters of point vortices and populations of microswimmers. For the point vortices, we define a local graph of vortices within a cluster and a global graph of interactions between clusters. For the microswimmers, we define a local graph around each microswimmer and a global graph that groups long-range interactions. We then combine this hierarchy of graphs with an approach that enforces equivariance to rotations and translations. This combination results in a significant improvement over a fully-connected GNN. For point vortices, our method conserves the Hamiltonian over long times, and, for microswimmers, our method predicts the transition from aggregation to swirling.

Sessile ciliates attach to substrates and generate feeding currents to capture passing particulates and dissolved nutrients. Optimal ciliary activity that maximizes nutrient flux at the cell surface while minimizing the rate of hydrodynamic energy dissipation is well characterized in uniform nutrient fields. However, it is unclear how ciliary motion should change when nutrients are non-uniform or patchy. To address this question, we modeled the sessile ciliate and feeding currents using the spherical envelope model, and used an unsteady advection-diffusion equation to describe the nutrient scalar field. In the absence of flows, we calculated the diffusive nutrient uptake analytically in linear nutrient gradients and found no advantage over uptake in uniform fields. With ciliary activity driving feeding currents, we used a spectral method to solve for the unsteady nutrient concentration. We found that, when the axis of symmetry of the ciliary motion is aligned with the nutrient gradient, nutrient uptake at the cell surface increases steadily over time, with highest uptake achieved by the treadmill ciliary motion which is optimal in uniform fields as well. The associated nutrient uptake in concentration gradients scales with the square root of the product of time and Péclet number. In patchy environments, optimal ciliary activity depends on the nature of the patchiness. Our findings highlight strategies that enable sessile ciliates to thrive in environments with fluctuating nutrient availability.

The coordinated motion of animal groups through fluids is thought to reduce the cost of locomotion to individuals in the group. However, the connection between the spatial patterns observed in collectively moving animals and the energetic benefits at each position within the group remains unclear. To address this knowledge gap, we study the spontaneous emergence of cohesive formations in groups of fish, modeled as flapping foils, all heading in the same direction. We show in pairwise formations and with increasing group size that (1) in side-by-side arrangements, the reciprocal nature of flow coupling results in an equal distribution of energy requirements among all members, with reduction in cost of locomotion for swimmers flapping inphase but an increase in cost for swimmers flapping antiphase, and (2) in inline arrangements, flow coupling is non-reciprocal for all flapping phase, with energetic savings in favor of trailing swimmers, but only up to a finite number of swimmers, beyond which school cohesion and energetic benefits are lost at once. We explain these findings mechanistically and we provide efficient diagnostic tools for identifying locations in the wake of single and multiple swimmers that offer opportunities for hydrodynamic benefits to aspiring followers. Our results imply a connection between the resources generated by flow physics and social traits that influence greedy and cooperative group behavior.

The collective patterns that emerge in schooling fish are often analyzed using models of self-propelled particles in unbounded domains. However, while schooling fish in both field and laboratory settings interact with domain boundaries, these effects are typically ignored. Here, we propose a model that incorporates geometric confinement, by accounting for both flow and wall interactions, into existing data-driven behavioral rules. We show that new collective phases emerge where the school of fish "follows the tank wall" or "double mills." Importantly, confinement induces repeated switching between two collective states, schooling and milling. We describe the group dynamics probabilistically, uncovering bistable collective states along with unintuitive bifurcations driving phase transitions. Our findings support the hypothesis that collective transitions in fish schools could occur spontaneously, with no adjustment at the individual level, and opens venues to control and engineer emergent collective patterns in biological and synthetic systems that operate far from equilibrium.

Abstract Motility endows microorganisms with the ability to swim to nutrient-rich environments, but many species are sessile. Existing hydrodynamic arguments in support of either strategy, to swim or to attach and generate feeding currents, are often built on a limited set of experimental or modeling assumptions. Here, to assess the hydrodynamics of these “swim” or “stay” strategies, we propose a comprehensive methodology that combines mechanistic modeling with a survey of published shape and flow data in ciliates. Model predictions and empirical observations show small variations in feeding rates in favor of either motile or sessile cells. Case-specific variations notwithstanding, our overarching analysis shows that flow physics imposes no constraint on the feeding rates that are achievable by the swimming versus sessile strategies – they can both be equally competitive in transporting nutrients and wastes to and from the cell surface within flow regimes typically experienced by ciliates. Our findings help resolve a long-standing dilemma of which strategy is hydrodynamically optimal and explain patterns occurring in natural communities that alternate between free swimming and temporary attachments. Importantly, our findings indicate that the evolutionary pressures that shaped these strategies acted in concert with, not against, flow physics.

Motility endows microorganisms with the ability to swim to nutrient-rich environments, but many species are sessile. Existing hydrodynamic arguments in support of either strategy, to swim or to attach and generate feeding currents, are often built on a limited set of experimental or modeling assumptions. Here, to assess the hydrodynamics of these “swim” or “stay” strategies, we propose a comprehensive methodology that combines mechanistic modeling with a survey of published shape and flow data in ciliates. Model predictions and empirical observations show small variations in feeding rates in favor of either motile or sessile cells. Case-specific variations notwithstanding, our overarching analysis shows that flow physics imposes no constraint on the feeding rates that are achievable by the swimming versus sessile strategies – they can both be equally competitive in transporting nutrients and wastes to and from the cell surface within flow regimes typically experienced by ciliates. Our findings help resolve a long-standing dilemma of which strategy is hydrodynamically optimal and explain patterns occurring in natural communities that alternate between free swimming and temporary attachments. Importantly, our findings indicate that the evolutionary pressures that shaped these strategies acted in concert with, not against, flow physics.

Mucociliary clearance (MCC) is a key mechanical defense mechanism of the human airways, and clearance failure is linked to major respiratory diseases. However, our understanding of MCC mainly stems from animal models, limiting crucial insights into human barrier function and in-vitro modeling of airway diseases. Our study (Fig. 1 and 2) fills this knowledge gap and(1) maps the luminal distribution of ciliated and secretory cell types along the proximo-distal axis of the rat and human airway epithelium, (2) identifies species-specific differences in cilia properties and MCC, and (3) elucidates quantitative structural parameters of airway epithelia that predict MCC. Our broad range of experimental approaches and physics-based modeling translate into generalizable parameters to quantitatively benchmark the human-relevancy of MCC in different in vitro airway models, and to characterize distinct disease states. Fig 1: Graphical Abstract <fig><object-id>erj;64/suppl_68/PA2654/F1</object-id><object-id>F1</object-id><object-id>F1</object-id><graphic></graphic></fig> Fig 2: Key metrics for comparing MCC in human branching generation (BG) 0-6 and in vitro ALI epi cultures differentiated in different media. A, luminal cell type composition; B, Measured and modeled clearance distance per ciliary beat. <fig><object-id>erj;64/suppl_68/PA2654/F2</object-id><object-id>F2</object-id><object-id>F2</object-id><graphic></graphic></fig>

Abstract The coordinated motion of animal groups through fluids is thought to reduce the cost of locomotion to individuals in the group. However, the connection between the spatial patterns observed in collectively moving animals and the energetic benefits at each position within the group remains unclear. To address this knowledge gap, we study the spontaneous emergence of cohesive formations in groups of fish, modeled as flapping foils, all heading in the same direction. We show in pairwise formations and with increasing group size that (1) in side-by-side arrangements, the reciprocal nature of flow coupling results in an equal distribution of energy re-quirements among all members, with reduction in cost of locomotion for swimmers flapping inphase but an increase in cost for swimmers flapping antiphase, and (2) in inline arrangements, flow coupling is non-reciprocal for all flapping phase, with energetic savings in favor of trailing swimmers, but only up to a finite number of swimmers, beyond which school cohesion and energetic benefits are lost at once. We explain these findings mechanistically and we provide efficient diagnostic tools for identifying locations in the wake of single and multiple swimmers that offer op-portunities for hydrodynamic benefits to aspiring followers. Our results imply a connection between the resources generated by flow physics and social traits that influence greedy and cooperative group behavior.

The coordinated motion of animal groups through fluids is thought to reduce the cost of locomotion to individuals in the group. However, the connection between the spatial patterns observed in collectively moving animals and the energetic benefits at each position within the group remains unclear. To address this knowledge gap, we study the spontaneous emergence of cohesive formations in groups of fish, modeled as flapping foils, all heading in the same direction. We show in pairwise formations and with increasing group size that (1) in side-by-side arrangements, the reciprocal nature of flow coupling results in an equal distribution of energy re-quirements among all members, with reduction in cost of locomotion for swimmers flapping inphase but an increase in cost for swimmers flapping antiphase, and (2) in inline arrangements, flow coupling is non-reciprocal for all flapping phase, with energetic savings in favor of trailing swimmers, but only up to a finite number of swimmers, beyond which school cohesion and energetic benefits are lost at once. We explain these findings mechanistically and we provide efficient diagnostic tools for identifying locations in the wake of single and multiple swimmers that offer op-portunities for hydrodynamic benefits to aspiring followers. Our results imply a connection between the resources generated by flow physics and social traits that influence greedy and cooperative group behavior.

Organs that pump luminal fluids by the coordinated beat of motile cilia are integral to animal physiology. Such organs include the human airways, brain ventricles and reproductive tracts. Although cilia organization and duct morphology vary drastically in the animal kingdom, ducts are typically classified as carpet or flame designs. The reason behind the appearance of these two different designs and how they relate to fluid pumping remain unclear. Here, we demonstrate that two structural parameters—lumen diameter and cilia-to-lumen ratio—organize the observed duct diversity into a continuous spectrum that connects carpets to flames across all animal phyla. Using a unified fluid model, we show that carpets and flames represent trade-offs between flow rate and pressure generation. We propose that the convergence of ciliated organ designs follows functional constraints rather than phylogenetic distance and offer guiding design principles for synthetic ciliary pumps. The ducts of many fluid-pumping organs feature cilia. Two structural parameters organize the different types of ducts into a continuous spectrum between ciliary carpet and flame designs depending on the fluid-pumping requirements.

Fish often swim in schools. Flow interactions are thought to be beneficial for schooling. Recent work shows that flow interactions cause a pair of free inline swimmers, flapping at the same frequency, to passively stabilize at discrete locations relative to each other and that these passively stable formations are energetically beneficial. However, the stability of these formations is sensitive to finite mismatch in flapping frequencies. Here, we propose a local flow sensing model and feedback controller that stabilize a pair of frequency-uncoordinated swimmers into a cohesive formation. Our findings bear relevance to understanding fish collective behavior and for designing bio-inspired underwater robotics.

Motility endows microorganisms with the ability to swim to nutrient-rich environments, but many species are sessile. Existing hydrodynamic arguments in support of either strategy, to swim or to attach and generate feeding currents, are often built on a limited set of experimental or modeling assumptions. Here, to assess the hydrodynamics of these 'swim' or 'stay' strategies, we propose a comprehensive methodology that combines mechanistic modeling with a survey of published shape and flow data in ciliates. Model predictions and empirical observations show small variations in feeding rates in favor of either motile or sessile cells. Case-specific variations notwithstanding, our overarching analysis shows that flow physics imposes no constraint on the feeding rates that are achievable by the swimming versus sessile strategies - they can both be equally competitive in transporting nutrients and wastes to and from the cell surface within flow regimes typically experienced by ciliates. Our findings help resolve a long-standing dilemma of which strategy is hydrodynamically optimal and explain patterns occurring in natural communities that alternate between free swimming and temporary attachments. Importantly, our findings indicate that the evolutionary pressures that shaped these strategies acted in concert with, not against, flow physics.

Motility endows microorganisms with the ability to swim to nutrient-rich environments, but many species are sessile. Existing hydrodynamic arguments in support of either strategy, to swim or to attach and generate feeding currents, are often built on a limited set of experimental or modeling assumptions. Here, to assess the hydrodynamics of these “swim” or “stay” strategies, we propose a comprehensive methodology that combines mechanistic modeling with a survey of published shape and flow data in ciliates. Model predictions and empirical observations show small variations in feeding rates in favor of either motile or sessile cells. Case-specific variations notwithstanding, our overarching analysis shows that flow physics imposes no constraint on the feeding rates that are achievable by the swimming versus sessile strategies – they can both be equally competitive in transporting nutrients and wastes to and from the cell surface within flow regimes typically experienced by ciliates. Our findings help resolve a longstanding dilemma of which strategy is hydrodynamically optimal and explain patterns occurring in natural communities that alternate between free swimming and temporary attachments. Importantly, our findings indicate that the evolutionary pressures that shaped these strategies acted in concert with, not against, flow physics.

We present experiments on oscillating hydrofoils undergoing combined heaving and pitching motions, paying particular attention to connections between propulsive efficiency and coherent wake features extracted using modal analysis. Time-averaged forces and particle image velocimetry measurements of the flow field downstream of the foil are presented for a Reynolds number of $Re=11\times 10^3$ and Strouhal numbers in the range $St=0.16\unicode{x2013}0.35$ . These conditions produce 2S and 2P wake patterns, as well as a near-momentumless wake structure. A triple decomposition using the optimized dynamic mode decomposition method is employed to identify dominant modal components (or coherent structures) in the wake. These structures can be connected to wake instabilities predicted using spatial stability analyses. Examining the modal components of the wake provides insightful explanations into the transition from drag to thrust production, and conditions that lead to peak propulsive efficiency. In particular, we find modes that correspond to the primary vortex development in the wakes. Other modal components capture elements of bluff body shedding at Strouhal numbers below the optimum for peak propulsive efficiency and characteristics of separation for Strouhal numbers higher than the optimum.

The coordinated motion of animal groups through fluids is thought to reduce the cost of locomotion to individuals in the group. However, the connection between the spatial patterns observed in collectively moving animals and the energetic benefits at each position within the group remains unclear. To address this knowledge gap, we study the spontaneous emergence of cohesive formations in groups of fish, modeled as flapping foils, all heading in the same direction. We show in pairwise formations and with increasing group size that (1) in side-by-side arrangements, the reciprocal nature of flow coupling results in an equal distribution of energy requirements among all members, with reduction in cost of locomotion for swimmers flapping inphase but an increase in cost for swimmers flapping antiphase, and (2) in inline arrangements, flow coupling is non-reciprocal for all flapping phase, with energetic savings in favor of trailing swimmers, but only up to a finite number of swimmers, beyond which school cohesion and energetic benefits are lost at once. We explain these findings mechanistically and we provide efficient diagnostic tools for identifying locations in the wake of single and multiple swimmers that offer opportunities for hydrodynamic benefits to aspiring followers. Our results imply a connection between the resources generated by flow physics and social traits that influence greedy and cooperative group behavior.

The coordinated motion of animal groups through fluids is thought to reduce the cost of locomotion to individuals in the group. However, the connection between the spatial patterns observed in collectively moving animals and the energetic benefits at each position within the group remains unclear. To address this knowledge gap, we study the spontaneous emergence of cohesive formations in groups of fish, modeled as flapping foils, all heading in the same direction. We show in pairwise formations and with increasing group size that (1) in side-by-side arrangements, the reciprocal nature of flow coupling results in an equal distribution of energy requirements among all members, with reduction in cost of locomotion for swimmers flapping inphase but an increase in cost for swimmers flapping antiphase, and (2) in inline arrangements, flow coupling is non-reciprocal for all flapping phase, with energetic savings in favor of trailing swimmers, but only up to a finite number of swimmers, beyond which school cohesion and energetic benefits are lost at once. We explain these findings mechanistically and we provide efficient diagnostic tools for identifying locations in the wake of single (and multiple) swimmers that offer opportunities for hydrodynamic benefits to aspiring followers. Our results imply a connection between the resources generated by flow physics and social traits that influence greedy and cooperative group behavior.

Animals and robots exist in a physical world and must coordinate their bodies to achieve behavioral objectives. With recent developments in deep reinforcement learning, it is now possible for scientists and engineers to obtain sensorimotor strategies (policies) for specific tasks using physically simulated bodies and environments. However, the utility of these methods goes beyond the constraints of a specific task; they offer an exciting framework for understanding the organization of an animal sensorimotor system in connection to its morphology and physical interaction with the environment, as well as for deriving general design rules for sensing and actuation in robotic systems. Algorithms and code implementing both learning agents and environments are increasingly available, but the basic assumptions and choices that go into the formulation of an embodied feedback control problem using deep reinforcement learning may not be immediately apparent. Here, we present a concise exposition of the mathematical and algorithmic aspects of model-free reinforcement learning, specifically through the use of \textit{actor-critic} methods, as a tool for investigating the feedback control underlying animal and robotic behavior.

Abstract Motility endows microorganisms with the ability to swim to nutrient-rich environments, but many species are sessile. Existing hydrodynamic arguments in support of either strategy, to swim or to attach and generate feeding currents, are often built on a limited set of experimental or modeling assumptions. Here, to assess the hydrodynamics of these “swim” or “stay” strategies, we propose a comprehensive methodology that combines mechanistic modeling with a survey of published shape and flow data in ciliates. Model predictions and empirical observations show small variations in feeding rates in favor of either motile or sessile cells. Case-specific variations notwithstanding, our overarching analysis shows that flow physics imposes no constraint on the feeding rates that are achievable by the swimming versus sessile strategies – they can both be equally competitive in transporting nutrients and wastes to and from the cell surface within flow regimes typically experienced by ciliates. Our findings help resolve a long-standing dilemma of which strategy is hydrodynamically optimal and explain patterns occurring in natural communities that alternate between free swimming and temporary attachments. Importantly, our findings indicate that the evolutionary pressures that shaped these strategies acted in concert with, not against, flow physics.

Our study focuses on the intricate connection between tissue-level organization and ciliated organ function in humans, particularly in understanding the morphological organization of airways and their role in mucociliary clearance. Mucociliary clearance is a key mechanical defense mechanism of human airways, and clearance failure is associated with many respiratory diseases, including chronic obstructive pulmonary disease (COPD) and asthma. While single-cell transcriptomics have unveiled the cellular complexity of the human airway epithelium, our understanding of the mechanics that link epithelial structure to clearance function mainly stem from animal models. This reliance on animal data limits crucial insights into human airway barrier function and hampers the human-relevant in vitro modeling of airway diseases. This study, for the first time, maps the distribution of ciliated and secretory cell types along the airway tree in both rats and humans, noting species-specific differences in ciliary function and elucidates structural parameters of airway epithelia that predict clearance function in both native and in vitro tissues alike. By uncovering how tissue organization influences ciliary function, we can better understand disruptions in mucociliary clearance, which could have implications for various ciliated organs beyond the airways.

It is unclear how animals with radial symmetry control locomotion without a brain. Using a combination of experiments, mathematical modeling, and robotics, we tested the extent to which this control emerges in sea stars (Protoreaster nodosus) from the local control of their hundreds of feet and their mechanical interactions with the body. We discovered that these animals compensate for an experimental increase in their submerged weight by recruiting more feet that synchronize in the power stroke of the locomotor cycle during their bouncing gait. Mathematical modeling of the mechanics of a sea star replicated this response to loading without a central controller. A robotic sea star was found to similarly recruit more actuators under higher loads through purely decentralized control. These results suggest that an array of biological or engineered actuators are capable of cooperative transport where the actuators are dynamically recruited by the mechanics of the body. In particular, the body's vertical oscillations serve to recruit feet in greater numbers to overcome the weight to propel the body forward. This form of distributed control contrasts the conventional view of animal locomotion as governed by the central nervous system and offers inspiration for the design of engineered devices with arrays of actuators.

A hydrostatic skeleton allows a soft body to transmit muscular force via internal pressure. A human's tongue, an octopus' arm and a nematode's body illustrate the pervasive presence of hydrostatic skeletons among animals, which has inspired the design of soft engineered actuators. However, there is a need for a theoretical basis for understanding how hydrostatic skeletons apply mechanical work. We therefore modeled the shape change and mechanics of natural and engineered hydrostatic skeletons to determine their mechanical advantage (MA) and displacement advantage (DA). These models apply to a variety of biological structures, but we explicitly consider the tube feet of a sea star and the body segments of an earthworm, and contrast them with a hydraulic press and a McKibben actuator. A helical winding of stiff, elastic fibers around these soft actuators plays a critical role in their mechanics by maintaining a cylindrical shape, distributing forces throughout the structure and storing elastic energy. In contrast to a single-joint lever system, soft hydrostats exhibit variable gearing with changes in MA generated by deformation in the skeleton. We found that this gearing is affected by the transmission efficiency of mechanical work (MA×DA) or, equivalently, the ratio of output to input work. The transmission efficiency changes with the capacity to store elastic energy within helically wrapped fibers or associated musculature. This modeling offers a conceptual basis for understanding the relationship between the morphology of hydrostatic skeletons and their mechanical performance.

ABSTRACT A hydrostatic skeleton allows a soft body to transmit muscular force via internal pressure. A human’s tongue, an octopus’ arm, and a nematode’s body illustrate the pervasive presence of hydrostatic skeletons among animals, which has inspired the design of soft engineered actuators. However, there is a need for a theoretical basis for understanding how hydrostatic skeletons apply mechanical work. We therefore model the shape change and mechanics of natural and engineered hydrostatic skeletons to determine their mechanical advantage (MA) and displacement advantage (DA). These models apply to a variety of biological structures, but we explicitly consider the tube feet of a sea star and the body segments of an earthworm, and contrast them with a hydraulic press and a McKibben actuator. A helical winding of stiff, elastic fibers around these soft actuators plays a critical role in their mechanics by maintaining a cylindrical shape, distributing forces throughout the structure, and storing elastic energy. In contrast to a single-joint lever system, soft hydrostats exhibit variable gearing with changes in MA generated by deformation in the skeleton. We found that this gearing is affected by the transmission efficiency of mechanical work (MA × DA) or, equivalently, the ratio of output to input work), which changes with the capacity to store elastic energy within helically wrapped fibers or associated musculature. This modeling offers a conceptual basis for understanding the relationship between the morphology of hydrostatic skeletons and their mechanical performance.

Abstract The coordinated motion of animal groups through fluids is thought to reduce the cost of locomotion to individuals in the group. However, the connection between the spatial patterns observed in collectively moving animals and the energetic benefits at each position within the group remains unclear. To address this knowledge gap, we study the spontaneous emergence of cohesive formations in groups of fish, modeled as flapping foils, all heading in the same direction. We show in pairwise formations and with increasing group size that (1) in side-by-side arrangements, the reciprocal nature of flow coupling results in an equal distribution of energy re-quirements among all members, with reduction in cost of locomotion for swimmers flapping inphase but an increase in cost for swimmers flapping antiphase, and (2) in inline arrangements, flow coupling is non-reciprocal for all flapping phase, with energetic savings in favor of trailing swimmers, but only up to a finite number of swimmers, beyond which school cohesion and energetic benefits are lost at once. We explain these findings mechanistically and we provide efficient diagnostic tools for identifying locations in the wake of single and multiple swimmers that offer op-portunities for hydrodynamic benefits to aspiring followers. Our results imply a connection between the resources generated by flow physics and social traits that influence greedy and cooperative group behavior.

Abstract Scyphomedusae are widespread in the oceans and their swimming has provided valuable insights into the hydrodynamics of animal propulsion. Most of this research has focused on symmetrical, linear swimming. However, in nature, medusae typically swim circuitous, nonlinear paths involving frequent turns. Here we describe swimming turns by the scyphomedusa Aurelia aurita during which asymmetric bell margin motions produce rotation around a linearly translating body center. These jellyfish ‘skid’ through turns and the degree of asynchrony between opposite bell margins is an approximate predictor of turn magnitude during a pulsation cycle. The underlying neuromechanical organization of bell contraction contributes substantially to asynchronous bell motions and inserts a stochastic rotational component into the directionality of scyphomedusan swimming. These mechanics are important for natural populations because asynchronous bell contraction patterns are common in situ and result in frequent turns by naturally swimming medusae.

Mucociliary clearance is a vital defense mechanism of the human airways, protecting against harmful particles and infections. When this process fails, it contributes to respiratory diseases like chronic obstructive pulmonary disease (COPD) and asthma. While advances in single-cell transcriptomics have revealed the complexity of airway composition, much of what we know about how airway structure impacts clearance relies on animal studies. This limits our ability to create accurate human-based models of airway diseases. Here we show that the airways in female rats and in humans exhibit species-specific differences in the distribution of ciliated and secretory cells as well as in ciliary beat, resulting in significantly higher clearance effectiveness in humans. We further reveal that standard lab-grown cultures exhibit lower clearance effectiveness compared to human airways, and we identify the underlying structural differences. By combining diverse experiments and physics-based modeling, we establish universal benchmarks to assess human airway function, interpret preclinical models, and better understand disease-specific impairments in mucociliary clearance.

Abstract Aquatic animals offer compelling evidence that flow sensing alone, without vision, is sufficient to guide a swimming organism to the source of an unsteady hydrodynamic trail. However, the sensory feedback strategies that allow these remarkable trail tracking abilities remain opaque. Here, by integrating mechanistic flow simulations with reinforcement learning techniques, we discovered two simple and equally effective strategies for hydrodynamic trail following. Though not a priori obvious, these strategies possess parsimonious interpretations, analogous to Braitenberg’s simplest vehicles, where the agent senses local flow signals and turns away from or toward the direction of stronger signals. A rigorous stability analysis shows that the effectiveness of these strategies in robustly tracking flow currents is independent of the type of sensor but depends on sensor placement and the traveling nature of the flow signal. Importantly, these results inform a suite of versatile strategies for hydrodynamic trail following applicable to both vortical and turbulent flows. These insights support the future design and implementation of adaptive real-time sensory feedback strategies for autonomous robots in dynamic flow environments.

Many biological and engineered systems, from the Venus flytrap to mechanical metamaterials, exploit elastic instabilities and snap-through transitions to achieve a targeted function. Elastic strips, that buckle into one of two stable equilibrium states and snap from one state to the other as that state becomes unstable or suddenly disappears, have emerged as canonical systems for analyzing shape transitions. Here, we review recent advances that explain how geometric symmetries and symmetry-breaking mechanisms govern shape transitions in boundary-actuated elastic strips and provide universal rules for predicting or designing such transitions. We highlight the opportunities that this geometric understanding offers to emerging research areas, such as multi-functional metamaterials, morphological computing, and mechanical intelligence.

We present experiments on oscillating hydrofoils undergoing combined heaving and pitching motions, paying particular attention to connections between propulsive efficiency and coherent wake features extracted using modal analysis. Time-averaged forces and particle image velocimetry (PIV) measurements of the flow field downstream of the foil are presented for a Reynolds number of Re=11$\times$10$^3$ and Strouhal numbers in the range St=0.16-0.35. These conditions produce 2S and 2P wake patterns, as well as a near-momentumless wake structure. A triple decomposition using the optimized dynamic mode decomposition (opt-DMD) method is employed to identify dominant modal components (or coherent structures) in the wake. These structures can be connected to wake instabilities predicted using spatial stability analyses. Examining the modal components of the wake provides insightful explanations into the transition from drag to thrust production, and conditions that lead to peak propulsive efficiency. In particular, we find modes that correspond to the primary vortex development in the wakes. Other modal components capture elements of bluff body shedding at Strouhal numbers below the optimum for peak propulsive efficiency and characteristics of separation for Strouhal numbers higher than the optimum.