The acoustic niche hypothesis suggests that vocal signals of sympatric animal species are structured so as to minimize acoustic interference and facilitate communication. Accordingly, each species attempts to establish its own acoustic bandwidth so that intra-species signals are not masked. Detecting a non-random partitioning of the frequency spectrum among sympatric species could constitute evidence for the existence of acoustic avoidance behaviour. However, results from previous studies have been mixed or inconclusive, possibly as a consequence of overlooking the importance of physiological and ecological constraints. Here we introduce an improved test that incorporates prior information on body mass to account for the allometric correlation between mass (size) and vocalization frequency. By correcting for the bias induced by this correlation, the new test uncovers evidence of acoustic niche partitioning as a function of frequency in several tropical bird communities that would not be detected under a more standard test. Separately, we introduce a spatial version of the acoustic partitioning test which, in theory, could prove effective when data are collected from multiple sites located in close spatial proximity.

Liquid condensates are membraneless organelles that form via phase separation in living cells. These condensates provide unique heterogeneous environments that have much potential in regulating a range of biochemical processes from gene expression to filamentous protein aggregation—a process linked to Alzheimer's and Parkinson's diseases. Here we theoretically study the physical interplay between protein aggregation, its inhibition, and liquid-liquid phase separation. Our key finding is that the action of protein aggregation inhibitors can be strongly enhanced by liquid condensates. The physical mechanism of this enhancement relies on the partitioning and colocalization of inhibitors with their targets inside the liquid condensate. Our theory uncovers how the physicochemical properties of condensates can be used to modulate inhibitor potency, and we provide experimentally testable conditions under which drug potency is maximal. Our findings suggest design principles for protein aggregation inhibitors with respect to their phase-separation properties.

Biomolecular and physical cues of the extracellular matrix environment regulate collective cell dynamics and tissue patterning. Nonetheless, how the viscoelastic properties of the matrix regulate collective cell spatial and temporal organization is not fully understood. Here we show that the passive viscoelastic properties of the matrix encapsulating a spheroidal tissue of breast epithelial cells guide tissue proliferation in space and in time. Matrix viscoelasticity prompts symmetry breaking of the spheroid, leading to the formation of invading finger-like protrusions, YAP nuclear translocation and epithelial-to-mesenchymal transition both in vitro and in vivo in a Arp2/3-complex-dependent manner. Computational modelling of these observations allows us to establish a phase diagram relating morphological stability with matrix viscoelasticity, tissue viscosity, cell motility and cell division rate, which is experimentally validated by biochemical assays and in vitro experiments with an intestinal organoid. Altogether, this work highlights the role of stress relaxation mechanisms in tissue growth dynamics, a fundamental process in morphogenesis and oncogenesis.

Development is a highly dynamic process in which organisms often experience changes in both form and behavior, which are typically coupled to each other. However, little is known about how organismal-scale behaviors such as body contractility and motility impact morphogenesis. Here, we use the cnidarian Nematostella vectensis as a developmental model to uncover a mechanistic link between organismal size, shape, and behavior. Using quantitative live imaging in a large population of developing animals, combined with molecular and biophysical experiments, we demonstrate that the muscular-hydraulic machinery that controls body movement also drives larva-polyp morphogenesis. We show that organismal size largely depends on cavity inflation through fluid uptake, whereas body shape is constrained by the organization of the muscular system. The generation of ethograms identifies different trajectories of size and shape development in sessile and motile animals, which display distinct patterns of body contractions. With a simple theoretical model, we conceptualize how pressures generated by muscular hydraulics can act as a global mechanical regulator that coordinates tissue remodeling. Altogether, our findings illustrate how organismal contractility and motility behaviors can influence morphogenesis.

A quantitative analysis of human gait patterns in space–time provides an opportunity to observe variability within and across individuals of varying motor capabilities. Impaired gait significantly affects independence and quality of life, and thus a large part of clinical research is dedicated to improving gait through rehabilitative therapies. Evaluation of these paradigms relies on understanding the characteristic differences in the kinematics and underlying biomechanics of impaired and unimpaired locomotion, which has motivated quantitative measurement and analysis of the gait cycle. Previous analysis has largely been limited to a statistical comparison of manually selected pointwise metrics identified through expert knowledge. Here, we use a recent statistical-geometric framework, elastic functional data analysis (FDA), to decompose kinematic data into continuous ‘amplitude’ (spatial) and ‘phase’ (temporal) components, which can then be integrated with established dimensionality reduction techniques. We demonstrate the utility of elastic FDA through two unsupervised applications to post-stroke gait datasets. First, we distinguish between unimpaired, paretic and non-paretic gait presentations. Then, we use FDA to reveal robust, interpretable groups of differential response to exosuit assistance. The proposed methods aim to benefit clinical practice for post-stroke gait rehabilitation, and more broadly, to automate the quantitative analysis of motion.

Geometric graph models of systems as diverse as proteins, DNA assemblies, architected materials and robot swarms are useful abstract representations of these objects that also unify ways to study their properties and control them in space and time. While much work has been done in the context of characterizing the behaviour of these networks close to critical points associated with bond and rigidity percolation, isostaticity, etc., much less is known about floppy, underconstrained networks that are far more common in nature and technology. Here, we combine geometric rigidity and algebraic sparsity to provide a framework for identifying the zero energy floppy modes via a representation that illuminates the underlying hierarchy and modularity of the network and thence the control of its nestedness and locality. Our framework allows us to demonstrate a range of applications of this approach that include robotic reaching tasks with motion primitives, and predicting the linear and nonlinear response of elastic networks based solely on infinitesimal rigidity and sparsity, which we test using physical experiments. Our approach is thus likely to be of use broadly in dissecting the geometrical properties of floppy networks using algebraic sparsity to optimize their function and performance.

Grasping, in both biological and engineered mechanisms, can be highly sensitive to the gripper and object morphology, as well as perception and motion planning. Here, we circumvent the need for feedback or precise planning by using an array of fluidically actuated slender hollow elastomeric filaments to actively entangle with objects that vary in geometric and topological complexity. The resulting stochastic interactions enable a unique soft and conformable grasping strategy across a range of target objects that vary in size, weight, and shape. We experimentally evaluate the grasping performance of our strategy and use a computational framework for the collective mechanics of flexible filaments in contact with complex objects to explain our findings. Overall, our study highlights how active collective entanglement of a filament array via an uncontrolled, spatially distributed scheme provides options for soft, adaptable grasping.

Many complex flows such as those arising from the collective motion of ocean plastics in geophysics or motile cells in biology are characterized by sparse and noisy trajectory datasets. We introduce techniques for identifying Lagrangian coherent structures (LCSs) of hyperbolic and elliptic nature in such datasets. Hyperbolic LCSs, which represent surfaces with maximal attraction or repulsion over a finite amount of time, are computed through a regularized least-squares approximation of the flow map gradient. Elliptic LCSs, which identify regions of coherent motion such as vortices and jets, are extracted using DBSCAN – a popular data clustering algorithm – combined with a systematic parameter selection strategy. We deploy these methods on various benchmark analytical flows and real-life experimental datasets ranging from oceanography to biology and show that they yield accurate results, despite sparse and noisy data. We also provide a lightweight computational implementation of these techniques as a user-friendly and straightforward Python code.

Inspired by recent experiments that highlight the role of nematic defects in the morphogenesis of epithelial tissues, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture. Allowing the surface to evolve via relaxational dynamics leads to a theory linking nematic defect dynamics, cellular division rates, and Gaussian curvature. Regions of large positive (negative) curvature and positive (negative) growth are colocalized with the presence of positive (negative) defects. In an ex-vivo setting of cultured murine neural progenitor cells, we show that our framework is consistent with the observed cell accumulation at positive defects and depletion at negative defects. In an in-vivo setting, we show that the defect configuration consisting of a bound +1 defect state, which is stabilized by activity, surrounded by two −1/2 defects can create a stationary ring configuration of tentacles, consistent with observations of a basal marine invertebrate Hydra.

There have been a number of pharmaceutical and non-pharmaceutical interventions associated with COVID-19 over the past two years. Various non-pharmaceutical interventions were proposed and implemented to control the spread of the COVID-19 pandemic. Most common of these were partial and complete lockdowns that were used in an attempt to minimize the costs associated with mortality, economic losses and social factors, while being subject to constraints such as finite hospital capacity. Here, we use a minimal model posed in terms of optimal control theory to understand the costs and benefits of such strategies. This allows us to determine top-down policies for how to restrict social contact rates given an age-structured model for the dynamics of the disease. Depending on the relative weights allocated to mortality and socioeconomic losses, we see that the optimal strategies range from long-term social-distancing only for the most vulnerable, partial lockdown to ensure not over-running hospitals, and alternating-shifts, all of which lead to significant reduction in mortality and/or socioeconomic losses. Crucially, commonly used strategies that involve long periods of broad lockdown are almost never optimal, as they are highly unstable to reopening and entail high socioeconomic costs. Using parameter estimates from data available for Germany and the USA early in the pandemic, we quantify these policies and use sensitivity analysis in the relevant model parameters and initial conditions to determine the range of robustness of our policies. Finally we also discuss how bottom-up behavioral changes affect the dynamics of the pandemic and show how they can work in tandem with top-down control policies to mitigate pandemic costs even more effectively.

The remarkable range of biological forms in and around us, such as the undulating shape of a leaf or flower in the garden, the coils in our gut, or the folds in our brain, raise a number of questions at the interface of biology, physics, and mathematics. How might these shapes be predicted, and how can they eventually be designed? We review our current understanding of this problem, which brings together analysis, geometry, and mechanics in the description of the morphogenesis of low-dimensional objects. Starting from the view that shape is the consequence of metric frustration in an ambient space, we examine the links between the classical Nash embedding problem and biological morphogenesis. Then, motivated by a range of experimental observations and numerical computations, we revisit known rigorous results on curvature-driven patterning of thin elastic films, especially the asymptotic behaviors of the solutions as the (scaled) thickness becomes vanishingly small and the local curvature can become large. Along the way, we discuss open problems that include those in mathematical modeling and analysis along with questions driven by the allure of being able to tame soft surfaces for applications in science and engineering.

Understanding the complex patterns in space–time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here, we use optimal control theory to pose the problem of transporting a slender drop of an active fluid and determine the dynamical profile of the active stresses to move it with minimal viscous dissipation. By parametrizing the position and size of the drop using a low-order description based on lubrication theory, we uncover a natural “gather–move–spread” strategy that leads to an optimal bound on the maximum achievable displacement of the drop relative to its size. In the continuum setting, the competition between passive surface tension and active controls generates richer behavior with futile oscillations and complex drop morphologies that trade internal dissipation against the transport cost to select optimal strategies. Our work combines active hydrodynamics and optimal control in a tractable and interpretable framework and begins to pave the way for the spatiotemporal manipulation of active matter.

Adhesive contact between a thin elastic sheet and a substrate arises in a range of biological, physical and technological applications. By considering the dynamics of this process that naturally couples fluid flow, long-wavelength elastic deformations and microscopic adhesion, we analyse a sixth-order thin-film equation for the short-time dynamics of the onset of adhesion and the long-time dynamics of a steadily propagating adhesion front. Numerical solutions corroborate scaling laws and asymptotic analyses for the characteristic waiting time for adhesive contact and for the speed of the adhesion front. A similarity analysis of the governing partial differential equation further allows us to determine the shape of a fluid-filled blister ahead of the adhesion front. Finally, our analysis reveals a near-singular behaviour at the moving elastohydrodynamic contact line with an effective boundary condition that might be useful in other related problems.

Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, for example, it can bend without twisting, but cannot twist without bending. Given the ubiquity of ribbon-like biopolymers in biology and chemistry, here we study the statistical mechanics of microscopic inextensible, fluctuating ribbons loaded by forces and torques. We show that these ribbons exhibit a range of topologically and geometrically complex morphologies exemplified by three phases—a twist-dominated helical phase (HT), a writhe-dominated helical phase (HW), and an entangled phase—that arise as the applied torque and force are varied. Furthermore, the transition from HW to HT phases is characterized by the spontaneous breaking of parity symmetry and the disappearance of perversions (that correspond to chirality-reversing localized defects). This leads to a universal response curve of a topological quantity, the link, as a function of the applied torque that is similar to magnetization curves in second-order phase transitions.

Kirigami, the art of introducing cuts in thin sheets to enable articulation and deployment, has become an inspiration for a novel class of mechanical metamaterials with unusual properties. Here we complement the use of periodic tiling patterns for kirigami designs by showing that quasicrystals can also serve as the basis for designing deployable kirigami structures, and analyze the geometrical, topological, and mechanical properties of these aperiodic kirigami structures.

Human–wildlife cooperation occurs when humans and free-living wild animals actively coordinate their behavior to achieve a mutually beneficial outcome. These interactions provide important benefits to both the human and wildlife communities involved, have wider impacts on the local ecosystem, and represent a unique intersection of human and animal cultures. The remaining active forms are human–honeyguide and human–dolphin cooperation, but these are at risk of joining several inactive forms (including human–wolf and human–orca cooperation). Human–wildlife cooperation faces a unique set of conservation challenges, as it requires multiple components—a motivated human and wildlife partner, a suitable environment, and compatible interspecies knowledge—which face threats from ecological and cultural changes. To safeguard human–wildlife cooperation, we recommend: (i) establishing ethically sound conservation strategies together with the participating human communities; (ii) conserving opportunities for human and wildlife participation; (iii) protecting suitable environments; (iv) facilitating cultural transmission of traditional knowledge; (v) accessibly archiving Indigenous and scientific knowledge; and (vi) conducting long-term empirical studies to better understand these interactions and identify threats. Tailored safeguarding plans are therefore necessary to protect these diverse and irreplaceable interactions. Broadly, our review highlights that efforts to conserve biological and cultural diversity should carefully consider interactions between human and animal cultures.

Transport of biomaterial in tubular networks is ubiquitous in nature, where examples include the endoplasmic reticulum, leaf venation or vessel networks in vertebrates. Flow feedback by adjustment of the local tube radius in response to a fluid flow is a pivotal mechanism to optimize the transport properties of a network. To describe liquid transport in tubular networks we develop a minimal mathematical model, which includes the interplay of the viscous flow feedback and the tubes elastic bending energy while conserving the network material. Flow feedback in pitted, branched and loopy networks is shown to lower their resistance, as compared to a feedback-free system, by local adaptations without the need for additional network material. Flow feedback in particular reduces the resistance in pitted and branched networks, directly linked with a reduction in the effective number of neighboring tubes. In loopy networks we find a direction-dependent flow resistance, with a prevailing transport direction set by the network geometry.

A common handsaw can be converted into a bowed musical instrument capable of producing exquisitely sustained notes when its blade is appropriately bent. Acoustic modes localized at an inflection point are known to underlie the saw’s sonorous quality, yet the origin of localization has remained mysterious. Here we uncover a topological basis for the existence of localized modes that relies on and is protected by spatial curvature. By combining experimental demonstrations, theory, and computation, we show how spatial variations in blade curvature control the localization of these trapped states, allowing the saw to function as a geometrically tunable high-quality oscillator. Our work establishes an unexpected connection between the dynamics of thin shells and topological insulators and offers a robust principle to design high-quality resonators across scales,from macroscopic instruments to nanoscale devices, simply through geometry.

The body of vertebrate embryos forms by posterior elongation from a terminal growth zone called the tail bud. The tail bud is a source of highly motile cells that eventually constitute the presomitic mesoderm (PSM), a tissue that plays an important role in elongation movements. PSM cells establish an anterior-posterior cell motility gradient that parallels a gradient associated with the degradation of a specific cellular signal (FGF) known to be implicated in cell motility. Here, we combine the electroporation of fluorescent reporters in the PSM with time-lapse imaging in the chicken embryo to quantify cell diffusive movements along the motility gradient. We show that a simple microscopic model for random cell motility induced by FGF activity along with geometric confinement leads to rectified tissue elongation consistent with our observations. A continuum analog of the microscopic model leads to a macroscopic mechano-chemical model for tissue extension that couples FGF activity-induced cell motility and tissue rheology, and is consistent with the experimentally observed speed and extent of elongation. Together, our experimental observations and theoretical models explain how the continuous addition of cells at the tail bud combined with lateral confinement can be converted into oriented movement and drive body elongation

Combing hair involves brushing away the topological tangles in a collective curl, defined as a bundle of interacting elastic filaments. Using a combination of experiment and computation, we study this problem that naturally links topology, geometry and mechanics. Observations show that the dominant interactions in hair are those of a two-body nature, corresponding to a braided homochiral double helix. This minimal model allows us to study the detangling of an elastic double helix driven by a single stiff tine that moves along it and leaves two untangled filaments in its wake. Our results quantify how the mechanics of detangling correlates with the dynamics of a topological quantity, the link density, that propagates ahead of the tine and flows out the free end as a link current. This in turn provides a measure of the maximum characteristic length of a single combing stroke in the many-body problem on a head of hair, producing an optimal combing strategy that balances trade-offs between comfort, efficiency and speed of combing in hair curls of varying geometrical and topological complexity.

During reproductive swarming, honeybee clusters of more than 10,000 individuals that hang from structures in the environment (e.g. tree branches) are exposed to diurnal variations in ambient temperature for up to a week. Swarm clusters collectively modulate their morphology in response to these variations (i.e. expanding/ contracting in response to heating/cooling) to maintain their internal temperature within a tolerable range and to avoid exhausting their honey stores prematurely. To understand the spatiotemporal aspects of thermoregulatory morphing, we measured the change in size, shape and internal temperature profiles of swarm clusters in response to dynamic temperature ramp perturbations. Swarm clusters showed a two-fold variation in their volume/density when heated from 15°C to 30°C. However, they did not reach an equilibrium size or shape when held at 30°C for 5 h, long after the core temperature of the cluster had stabilized. Furthermore, the changes in cluster shape and size were hysteretic, contracting in response to cooling faster than expanding in response to heating. Although the base contact diameter of the cluster increased continuously when the swarm was heated, the change in length of the swarm (base to tip) over time was non- monotonic. Consequently, the aspect ratio of the swarm fluctuated continuously even when held at a constant temperature. Taken together, our results quantify the hysteretic and anisotropic morphological responses of swarm clusters to ambient temperature variations while suggesting that both mechanical constraints and heat transfer govern their thermoregulatory morphodynamics.

Euclidean geometry has formed the foundation of architecture, science, and technology for millennia, yet the development of human’s intuitive reasoning about Euclidean geometry is not well understood. The present study explores the cognitive processes and representations that support the development of humans’ intuitive reasoning about Euclidean geometry. One-hundred-twenty-five 7- to 12-year-old children and 30 adults completed a localization task in which they visually extrapolated missing parts of fragmented planar triangles and a reasoning task in which they answered verbal questions about the general properties of planar triangles. While basic Euclidean principles guided even young children’s visual extrapolations, only older children and adults reasoned about triangles in ways that were consistent with Euclidean geometry. Moreover, a relation beteen visual extrapolation and reasoning appeared only in older children and adults. Reasoning consistent with Euclidean geometry may thus emerge when children abandon incorrect, axiomatic-based reasoning strategies and come to reason using mental simulations of visual extrapolations.

Accretion of mineralized thin wall-like structures via localized growth along their edges is observed in physical and biological systems ranging from molluscan and brachiopod shells to carbonate–silica composite precipitates. To understand the shape of these mineralized structures, we develop a mathematical framework that treats the thin-walled shells as a smooth surface left in the wake of the growth front that can be described as an evolving space curve. Our theory then takes an explicit geometric form for the prescription of the velocity of the growth front curve, along with compatibility relations and a closure equation related to the nature of surface curling. Solutions of these equations capture a range of geometric precipitate patterns seen in abiotic and biotic forms across scales. In addition to providing a framework for the growth and form of these thin-walled morphologies, our theory suggests a new class of dynamical systems involving moving space curves that are compatible with non-Euclidean embeddings of surfaces.

Locomotion of soft robots typically relies on control of multiple inflatable actuators by electronic computers and hard valves. Soft pneumatic oscillators can reduce the demand on controllers by generating complex movements required for locomotion from a single, constant input pressure, but either have been constrained to low rates of flow of air or have required complex fabrication processes. Here, we describe a pneumatic oscillator fabricated from flexible, but inextensible, sheets that provides high rates of airflow for practical locomotion by combining three instabilities: out-of-plane buckling of the sheets, kinking of tubing attached to the sheets, and a system-level instability resulting from connection of an odd number of pneumatic inverters made from these sheets in a loop. This device, which we call a “buckling-sheet ring oscillator” (BRO), directly generates movement from its own interaction with its surroundings and consists only of readily available materials assembled in a simple process— specifically, stacking acetate sheets, nylon film, and double-sided tape, and attaching an elastomeric tube. A device incorporating a BRO is capable of both translational and rotational motion over varied terrain (even without a tether) and can climb upward against gravity and downward against the buoyant force encountered under water.

Darwin’s finches are a classic example of adaptive radiation, exemplified by their adaptive and functional beak morphologies. To quantify their form, we carry out a morphometric analysis of the three-dimensional beak shapes of all of Darwin’s finches and find that they can be fit by a transverse parabolic shape with a curvature that increases linearly from the base toward the tip of the beak. The morphological variation of beak orientation, aspect ratios, and curvatures allows us to quantify beak function in terms of the elementary theory of machines, consistent with the dietary variations across finches. Finally, to explain the origin of the evolutionary morphometry and the developmental morphogenesis of the finch beak, we propose an experimentally motivated growth law at the cellular level that simplifies to a variant of curvature-driven flow at the tissue level and captures the range of observed beak shapes in terms of a simple morphospace. Altogether, our study illuminates how a minimal combination of geometry and dynamics allows for functional form to develop and evolve.

When a thin stream of aqueous sodium alginate is extruded into a reacting calcium chloride bath, it polymerizes into a soft elastic tube that spontaneously forms helical coils due to the ambient fluid drag. We quantify the onset of this drag-induced instability and its nonlinear evolution using experiments, and explain the results using a combination of scaling, theory and simulations. By co-extruding a second (internal) liquid within the aqueous sodium alginate jet and varying the rates of co-extrusion of the two liquids, as well as the diameter of the jet, we show that we can tune the local composition of the composite filament and the nature of the ensuing instabilities to create soft filaments of variable relative buoyancy, shape and mechanical properties. All together, by harnessing the fundamental varicose (jetting) and sinuous (buckling) instabilities associated with the extrusion of a jelling filament, we show that it is possible to print complex three-dimensional filamentous structures in the ambient fluid.

Inspired by the quest for shape-shifting structures in a range of applications, we show how to create morphable structural materials using a neutrally stable unit cell as a building block. This unit cell is a self-stressed hinged structure with a one-parameter family of morphing motions that are all energetically equivalent. However, unlike kinematic mechanisms, the unit cell is not infinitely floppy and instead exhibits a tunable mechanical response akin to that of an ideal rigid-plastic material. Theory and simulations allow us to explore the properties of planar and spatial assemblies of neutrally stable elements, and solve the inverse problem of designing assemblies that can morph from one given shape into another. Simple experimental prototypes of these assemblies corroborate our theoretical results and show that the addition of switchable hinges allows us to create load-bearing structures. Altogether, totimorphs pave the way for structural materials whose geometry and deformation response can be controlled independently and at multiple scales.

Kirigami involves cutting a flat, thin sheet that allows it to morph from a closed, compact configuration into an open deployed structure via coordinated rotations of the internal tiles. By recognizing and generalizing the geometric constraints that enable this art form, we propose a design framework for compact reconfigurable kirigami patterns, which can morph from a closed and compact configuration into a deployed state conforming to any prescribed target shape, and subsequently be contracted into a different closed and compact configuration. We further establish a condition for producing kirigami patterns and mechanisms which are reconfigurable and rigid deployable allowing us to connect the compact states via a zero-energy family of deployed states. All together, our inverse design framework lays out a path for the creation of shape-morphing material structures.

Singularities are common in diverse physical systems1 and lead to universal structures. This universality suggests that they should also naturally arise in biological systems, where active growth, autonomous motion, kinesis and taxis focus deformations in spacetime, as exemplified in the morpho- genetic processes determining biological size and shape4. A familiar example of a morphogenetic singularity is seen in the humble apple, which forms in the neighbourhood of the stalk as the apple grows. Here we study the geometry and morpho- genesis of the cusp of an apple by combining observations of fruit growth with a simple theory, finite element simulations and controlled swelling experiments using a physical gel sim- ulacrum. Our observations show that the axisymmetric cusp develops into a self-similar form, which can be understood in terms of a mechanical theory for the inhomogeneous growth of a soft sphere. Physical experiments using local inhibition in swelling gels corroborate our theoretical predictions. These experiments further show that axisymmetric cusps can lose stability and become lobed. We use simulations to show that the number of cuspidal lobes depends on the ratio of the size of the stalk to the size of the sphere, as well as the amplitude and periodicity of perturbations that mimic the role of fruit anatomy, consistent with observations of multi-cusped fruits.

The self-assembly of peptides and proteins into amyloid fibrils plays a causative role in a wide range of increasingly common and currently incurable diseases. The molecular mechanisms underlying this process have recently been discovered, prompting the development of drugs that inhibit specific reaction steps as possible treatments for some of these disorders. A crucial part of treatment design is to determine how much drug to give and when to give it, informed by its efficacy and intrinsic toxicity. Since amyloid formation does not proceed at the same pace in different individuals, it is also important that treatment design is informed by local measurements of the extent of protein aggregation. Here, we use stochastic optimal control theory to determine treatment regimens for inhibitory drugs targeting several key reaction steps in protein aggregation, explicitly taking into account variability in the reaction kinetics. We demonstrate how these regimens may be updated “on the fly” as new measurements of the protein aggregate concentration become available, in principle, enabling treatments to be tailored to the individual. We find that treatment timing, duration, and drug dosage all depend strongly on the particular reaction step being targeted. Moreover, for some kinds of inhibitory drugs, the optimal regimen exhibits high sensitivity to stochastic fluctuations. Feedback controls tailored to the individual may therefore substantially increase the effectiveness of future treatments.

some detail, along with other important factors, such as private patronage from wealthy figures who were unhealthily obsessed with the hypothetical phenom-enon of antigravity. The renaissance of general relativity rovides a rich case study for thinking about fundamental problems of scien-tific change. How are theories used and not used? What is the difference between healthy and withering research pro-grams? Can the resurgence of a heory be explained by new observational discov-eries? Technological advances? Individ-ual personalities? Social and political de-velopments? The book is a great cross section of those different approaches, which will make it valuable to scholars in history and sociology of physics—although it might set a fairly high methodological barrier to entry for non-specialist readers. Nevertheless, The Re - naissance of General Relativity in Context will ickly become a classic in the his-tory of the field, and it will perhaps spur new research programs of its own.

Inspired by the allure of additive fabrication, we pose the problem of origami design from a different perspective: How can we grow a folded surface in three dimensions from a seed so that it is guaranteed to be isometric to the plane? We solve this problem in two steps: by first identifying the geometric conditions for the compatible completion of two separate folds into a single developable fourfold vertex, and then showing how this foundation allows us to grow a geometrically compatible front at the boundary of a given folded seed. This yields a complete marching, or additive, algorithm for the inverse design of the complete space of developable quad origami patterns that can be folded from flat sheets. We illustrate the flexibility of our approach by growing ordered, disordered, straight, and curved-folded origami and fitting surfaces of given curvature with folded approximants. Overall, our simple shift in perspective from a global search to a local rule has the potential to transform origami-based metastructure design.

Pattern formation driven by differential strain in constrained elastic systems is a common motif in many technological and biological systems. Here we introduce a biologically motivated case of elastic patterning that allows us to explore the conditions for the existence of local puckering and global wrinkling patterns: a soft growing composite ring adhered elastically to a constraining rigid ring. We explore how differential growth of the soft ring and the elastic resistance to shear and stretching deformations induced by soft adherence lead to a range of phenomena that include uniform aperture-like modes, localized puckers that are Nambu–Goldstone-like modes and global wrinkles in the system. Our analysis combines computer simulations of a discrete rod model with a nonlinear stability analysis of the differential equations in the continuum limit. We provide phase diagrams and scaling relations that reveal the nature and extent of the deformation patterns. Overall, our study reveals how geometry and mechanics conspire to yield a rich phenomenology that could serve as a guide to the design of programmable localized elastic deformations while being relevant for the mechanical basis of biological morphogenesis.

Interactions with animal pollinators have helped shape the stunning diversity of flower morphologies across the angiosperms. A common evolutionary consequence of these interactions is that some flowers have converged on suites of traits, or pollination syndromes, that attract and reward specific pollinator groups. Determining the genetic basis of these floral pollination syndromes can help us understand the processes that contributed to the diversification of the angiosperms. Here, we characterize the genetic architecture of a bee-to-hummingbird pollination shift in Aquilegia (columbine) using QTL mapping of 17 floral traits encompassing color, nectar composition, and organ morphology. In this system, we find that the genetic architectures underlying differences in floral color are quite complex, and we identify several likely candidate genes involved in anthocyanin and carotenoid floral pigmentation. Most morphological and nectar traits also have complex genetic underpinnings; however, one of the key floral morphological phenotypes, nectar spur curvature, is shaped by a single locus of large effect.

Adhesive interactions between elastic structures such as graphene sheets, carbon nanotubes, and microtubules have been shown to exhibit hysteresis due to irrecoverable energy loss associated with bond breakage, even in static (rate-independent) experiments. To understand this phenomenon, we start with a minimal theory for the peeling of a thin sheet from a substrate, coupling the local event of bond breaking to the nonlocal elastic relaxation of the sheet and show that this can drive static adhesion hysteresis over a bonding/debonding cycle. Using this model we quantify hysteresis in terms of the adhesion and elasticity parameters of the system. This allows us to derive a scaling relation that preserves hysteresis at different levels of granularity while resolving a seeming paradox of lattice trapping in the continuum limit of a discrete fracture process. Finally, to verify our theory, we use new experiments to demonstrate and measure adhesion hysteresis in bundled microtubules.

Locomotion of an organism interacting with an environment is the consequence of a symmetry-breaking action in space-time. Here we show a minimal instantiation of this principle using a thin cir- cular sheet, actuated symmetrically by a pneumatic source, using pressure to change shape nonlinearly via a spontaneous buckling instability. This leads to a polarized, bilaterally symmetric cone that can walk on land and swim in water. In either mode of loco- motion, the emergence of shape asymmetry in the sheet leads to an asymmetric interaction with the environment that generates movement––via anisotropic friction on land, and via directed iner- tial forces in water. Scaling laws for the speed of the sheet of the actuator as a function of its size, shape, and the frequency of ac- tuation are consistent with our observations. The presence of eas- ily controllable reversible modes of buckling deformation further allows for a change in the direction of locomotion in open arenas and the ability to squeeze through confined environments––both of which we demonstrate using simple experiments. Our simple approach of harnessing elastic instabilities in soft structures to drive locomotion enables the design of novel shape-changing ro- bots and other bioinspired machines at multiple scales.

Kirigami, the art of paper cutting, has become a paradigm for mechanical metamaterials in recent years. The basic building blocks of any kirigami structures are repetitive deployable patterns that derive inspiration from geometric art forms and simple planar tilings. Here, we complement these approaches by directly linking kirigami patterns to the symmetry associated with the set of 17 repeating patterns that fully characterize the space of periodic tilings of the plane. We start by showing how to construct deployable kirigami patterns using any of the wallpaper groups, and then design symmetry-preserving cut patterns to achieve arbitrary size changes via deployment. We further prove that different symmetry changes can be achieved by controlling the shape and connectivity of the tiles and connect these results to the underlying kirigami-based lattice structures. All together, our work provides a systematic approach for creating a broad range of kirigami-based deployable structures with any prescribed size and symmetry properties.

The termite nest is one of the architectural wonders of the liv- ing world, built by the collective action of workers in a colony. Each nest has several characteristic structural motifs that allow for efficient ventilation, cooling, and traversal. We use tomography to quantify the nest architecture of the African termite Apicotermes lamani, consisting of regularly spaced floors connected by scattered linear and helicoidal ramps. To understand how these elaborate structures are built and arranged, we formulate a minimal model for the spatiotemporal evolution of three hydrodynamic fields—mud, termites, and pheromones— linking environmental physics to collective building behavior using simple local rules based on experimental observations. We find that floors and ramps emerge as solutions of the governing equations, with statistics consistent with observations of A. lamani nests. Our study demonstrates how a local self-reinforcing biotectonic scheme is capable of generating an architecture that is simultaneously adaptable and functional, and likely to be relevant for a range of other animal-built structures.

Walking is a common bipedal and quadrupedal gait and associated with terrestrial and aquatic organisms. Inspired by recent evidence of the neural underpinnings of primitive aquatic walking in the little skate Leucoraja erinacea, we introduce a theoretical model of aquatic walking that reveals robust and efficient gaits with modest requirements for body morphology and control. The model predicts undulatory behaviour of the system body with a regular foot placement pattern, which is also observed in the animal, and additionally predicts the existence of gait bistability between two states, one with a large energetic cost for locomotion and another associated with almost no energetic cost. We show that these can be discovered using a simple reinforcement learning (RL) scheme. To test these theoretical frameworks, we built a bipedal robot and show that its behaviours are similar to those of our minimal model: its gait is also periodic and exhibits bistability, with a low efficiency gait separated from a high efficiency gait by a ‘jump’ transition. Overall, our study highlights the physical constraints on the evolution of walking and provides a guide for the design of efficient biomimetic robots.

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.

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.

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.