L. Mahadevan

Abstract Diseases of the (mitral and tricuspid) atrioventricular valves (AVV), which regulate inflow from the atria to the ventricles, can result in severe obstruction to inflow (stenosis) or valvular leakage (regurgitation), requiring surgical intervention. In patients with small annulus diameters ( < 19 mm), valve replacement is a clinical challenge limited by prosthesis size constraints, lack of growth potential, suboptimal durability, and elevated thrombosis and bleeding risk. While living valve transplantation (LVT) has re-opened the possibility of using allogeneic valve tissue capable of growth and remodeling, translating this to the AVV has been challenging given the anatomical complexity of the sub-valvular apparatus. Here, we propose a strategy using a replacement bi-leaflet cylindrical valve fabricated from donor AVV tissue and artificial chordae, with a geometry designed to mimic the native AVV and engineered to satisfy predefined clinical targets. Pulse duplicator experiments allowed characterization of valve dynamics in terms of clinically important attributes framed as dimensionless parameters. A multi-objective optimization allowed us to identify an optimal design which we implemented in porcine AVV replacements (n=6). Our results demonstrated favorable hemodynamics with minimal regurgitation and stenosis, suggesting a promising method for patient-optimized valve replacements.

We introduce an additive approach for the design of a class of transformable structures based on two-bar linkages ("scissor mechanisms") joined at vertices to form a two-dimensional mesh which we call a pantograph lattice. Our approach shows how these lattices unfold from a one-dimensional collapsed state to two-dimensional surfaces of single and double curvature. We provide an algorithm for growing pantograph structures that allows us to explore the full space of possible mechanisms, and we use it to computationally design and physically assemble a series of examples of varying complexity. We finally demonstrate a streamlined method for automated fabrication of pantograph lattices using multimaterial 3D printing.

Natural filaments, such as proteins, plant tendrils, octopus tentacles, and elephant trunks, can transform into arbitrary three-dimensional shapes that carry out vital functions. Their shape-morphing behavior arises from intricate patterning of active and passive regions, which are difficult to replicate in synthetic matter. Here, we introduce a filament-centric strategy for programmable shape morphing in which intrinsic curvature and twist are directly encoded within multimaterial elastomeric filaments during fabrication. By harnessing rotational multimaterial 3D printing, we directly prescribe the filament’s natural curvature–twist field κ(s) through controlled material distribution and helical liquid crystal mesogen alignment. When heated above their nematic-to-isotropic transition temperature ( T NI ), the helically aligned liquid crystal elastomer regions contract along their local director field, while passive regions remain essentially unchanged. This approach enables independent control of bending and torsion at every cross-section along the filament centerline: the principal natural curvatures of the filament along two orthogonal axes as well as the local twist. Next, we printed architected lattices composed of unit cells formed by sinusoidal filaments that either reversibly contract, expand, or exhibit out-of-plane deformations. Discrete elastic rod simulations of Janus filaments with different natural curvatures and twist, which are interconnected within the printed lattices, allow accurate prediction of their observed shape-morphing behavior. By integrating active–passive elastomers, additive manufacturing, and computational modeling, we have created shape-morphing matter with complex programmable responses for applications that rely on adaptive, robotic, or deployable architectures.

Abstract We consider the problem of inverting the artifacts associated with scanning a page from an open book, i.e. ’xeroxing’. The process typically leads to a non-uniform combination of distortion, blurring and darkening owing to the fact that the page is bound to a stiff spine that causes the sheet of paper to be bent inhomogeneously. Complementing purely data-driven approaches, we use knowledge about the geometry and elasticity of the curved sheet to pose and solve a minimal physically consistent inverse problem to reconstruct the image. Our result relies on three dimensionless parameters, all of which can be measured for a scanner and show that we can improve on the data-driven approaches. More broadly, our results might serve as a ‘textbook’ example and a tutorial of how knowledge of generative mechanisms can speed up the solution of inverse problems.

Posture and its control are fundamental aspects of animal behaviour that capture the complex interplay between sensorimotor activity that is driven by muscular forces, and environmental feedback that is mediated by proprioception and active control. An extreme example of this is seen in brown tree snakes and juvenile pythons: they can stand almost upright, with 70% of their body length in the air. We quantify experimental observations of this behaviour and present a minimal theoretical framework for postural stability by modelling the snake as an active elastic filament whose shape is controlled by muscular forces. We explore two approaches to characterize the musculature needed to achieve a specific posture: proprioceptive feedback (whereby the snake senses and reacts to its own shape) and a control-theoretic optimization approach (whereby the snake minimizes the expended energy to stand up). Then we also analyse the dynamic stability of the snake in its upright pose. Our results lead to a three-dimensional postural stability diagram in terms of muscle actuation and strength, and gravity, consistent with experimental observations. In addition to general predictions about posture control in animals, our study suggests design principles for robotic mimics.

Contains experimental data, videos, and code for the work "Surface wakes on ultra-soft solids", Chakrabarti et al. 2026. (DOI: https://doi.org/10.1103/lvvp-8pll)

In crowded environments, individuals must navigate around other occupants to reach their destinations. Understanding and controlling traffic flows in these spaces is relevant for coordinating robot swarms and designing infrastructure for dense populations. Here, we use simulations, theory, and experiments to study how adding stochasticity to agent motion can reduce traffic jams and help agents travel more quickly to prescribed goals. A computational approach reveals the collective behavior. Above a critical noise level, large jams do not persist. From this observation, we analytically approximate the swarm's goal attainment rate, which allows us to solve for the agent density and noise level that maximize the goals reached. Robotic experiments corroborate the behaviors observed in our simulated and theoretical results. Finally, we compare simple, local navigation approaches with a sophisticated but computationally costly central planner. A simple reactive scheme performs well up to moderate densities and is far more computationally efficient than a planner, motivating further research into robust, decentralized navigation methods for crowded environments. By integrating ideas from physics and engineering using simulations, theory, and experiments, our work identifies new directions for emergent traffic research.

A mechanistic understanding of neurodevelopment requires us to follow the multiscale processes that connect molecular genetic processes to macroscopic cerebral cortical formations and thence to neurological function. Using MRI of the brain of the ferret, a model organism for studying cortical morphogenesis, we create in vitro physical gel models and in silico numerical simulations of normal brain gyrification. Using observations of genetically manipulated animal models, we identify cerebral cortical thickness and cortical expansion rate as the primary drivers of dysmorphogenesis and demonstrate that in silico models allow us to examine the causes of aberrations in morphology and developmental processes at various stages of cortical ontogenesis. Finally, we explain analogous cortical malformations in human brains, with comparisons with human phenotypes induced by the same genetic defects, providing a unified perspective on brain morphogenesis that is driven proximally by genetic causes and affected mechanically via variations in the geometry of the brain and differential growth of the cortex.

Evolutionary adaptations associated with the formation of a folded cortex in many mammalian brains are thought to be a critical specialization associated with higher cognitive function. The dramatic surface expansion and highly convoluted folding of the cortex during early development is a theme with variations that suggest the need for a comparative study of cortical gyrification. Here, we use a combination of physical experiments using gels, computational morphogenesis, and geometric morphometrics to study the folding of brains across different species. Starting with magnetic resonance images of brains of a newborn ferret, a fetal macaque, and a fetal human, we construct two-layer physical gel brain models that swell superficially in a solvent, leading to folding patterns similar to those seen in vivo. We then adopt a three-dimensional continuum model based on differential growth to simulate cortical folding in silico. Finally, we deploy a comparative morphometric analysis of the in vivo, in vitro, and in silico surface buckling patterns across species. Our study shows that a simple mechanical instability driven by differential growth suffices to explain cortical folding and suggests that variations in the tangential growth and different initial geometries are sufficient to explain the differences in cortical folding across species.

A mechanistic understanding of neurodevelopment requires us to follow the multiscale processes that connect molecular genetic processes to macroscopic cerebral cortical formations and thence to neurological function. Using magnetic resonance imaging of the brain of the ferret, a model organism for studying cortical morphogenesis, we create in vitro physical gel models and in silico numerical simulations of normal brain gyrification. Using observations of genetically manipulated animal models, we identify cerebral cortical thickness and cortical expansion rate as the primary drivers of dysmorphogenesis and demonstrate that in silico models allow us to examine the causes of aberrations in morphology and developmental processes at various stages of cortical ontogenesis. Finally, we explain analogous cortical malformations in human brains, with comparisons with human phenotypes induced by the same genetic defects, providing a unified perspective on brain morphogenesis that is driven proximally by genetic causes and affected mechanically via variations in the geometry of the brain and differential growth of the cortex.

A mechanistic understanding of neurodevelopment requires us to follow the multiscale processes that connect molecular genetic processes to macroscopic cerebral cortical formations and thence to neurological function. Using magnetic resonance imaging of the brain of the ferret, a model organism for studying cortical morphogenesis, we create in vitro physical gel models and in silico numerical simulations of normal brain gyrification. Using observations of genetically manipulated animal models, we identify cerebral cortical thickness and cortical expansion rate as the primary drivers of dysmorphogenesis and demonstrate that in silico models allow us to examine the causes of aberrations in morphology and developmental processes at various stages of cortical ontogenesis. Finally, we explain analogous cortical malformations in human brains, with comparisons with human phenotypes induced by the same genetic defects, providing a unified perspective on brain morphogenesis that is driven proximally by genetic causes and affected mechanically via variations in the geometry of the brain and differential growth of the cortex.

The transformation of a two-dimensional epithelial sheet into various three-dimensional structures is a critical process in generating the diversity of animal forms. Previous studies of epithelial folding have revealed diverse mechanisms driven by epithelium-intrinsic or -extrinsic forces. Yet little is known about the biomechanical basis of epithelial splitting, which involves extreme folding and eventually a topological transition breaking the epithelial tube. Here, we leverage tracheal-esophageal separation (TES), a critical and highly conserved morphogenetic event during tetrapod embryogenesis, as a model system for interrogating epithelial tube splitting. We identify an evolutionarily conserved, compressive force exerted by the mesenchyme surrounding the epithelium, as being necessary to drive epithelial constriction and splitting. The compressive force is mediated by localized convergent flow of mesenchymal cells towards the epithelium. Sonic hedgehog (SHH) secreted by the epithelium functions as an attractive cue for mesenchymal cells. Removal of the mesenchyme, inhibition of cell migration, or loss of SHH signaling all abrogate TES, which can be rescued by externally applied pressure. These results unveil the biomechanical basis of epithelial splitting and suggest plausible mesenchymal origins of tracheal-esophageal birth defects.

Evolutionary adaptations associated with the formation of a folded cortex in many mammalian brains are thought to be a critical specialization associated with higher cognitive function. The dramatic surface expansion and highly convoluted folding of the cortex during early development is a theme with variations that suggest the need for a comparative study of cortical gyrification. Here, we use a combination of physical experiments using gels, computational morphogenesis, and geometric morphometrics to study the folding of brains across different species. Starting with magnetic resonance images of brains of a newborn ferret, a fetal macaque, and a fetal human, we construct two-layer physical gel brain models that swell superficially in a solvent, leading to folding patterns similar to those seen in vivo. We then adopt a three-dimensional continuum model based on differential growth to simulate cortical folding in silico. Finally, we deploy a comparative morphometric analysis of the in vivo, in vitro, and in silico surface buckling patterns across species. Our study shows that a simple mechanical instability driven by differential growth suffices to explain cortical folding and suggests that variations in the tangential growth and different initial geometries are sufficient to explain the differences in cortical folding across species.

Evolutionary adaptations associated with the formation of a folded cortex in many mammalian brains are thought to be a critical specialization associated with higher cognitive function. The dramatic surface expansion and highly convoluted folding of the cortex during early development is a theme with variations that suggest the need for a comparative study of cortical gyrification. Here, we use a combination of physical experiments using gels, computational morphogenesis, and geometric morphometrics to study the folding of brains across different species. Starting with magnetic resonance images of brains of a newborn ferret, a fetal macaque, and a fetal human, we construct two-layer physical gel brain models that swell superficially in a solvent, leading to folding patterns similar to those seen in vivo. We then adopt a three-dimensional continuum model based on differential growth to simulate cortical folding in silico. Finally, we deploy a comparative morphometric analysis of the in vivo, in vitro, and in silico surface buckling patterns across species. Our study shows that a simple mechanical instability driven by differential growth suffices to explain cortical folding and suggests that variations in the tangential growth and different initial geometries are sufficient to explain the differences in cortical folding across species.

Collective cell migration is critical in a range of biophysical processes spanning wound healing to tumor metastasis. It is therefore important to develop techniques for regulating cell motion, but while we have developed powerful migration tools from optogenetics and bioelectricity, the complex mechanics of collective systems make it difficult to determine where and when to apply these stimuli. For example, here we begin with a circular sheet of skin cells with a central hole, or “wound”, and show that globally stimulating all cells to migrate radially inwards to close the gap through electrotaxis causes catastrophic mechanical damage, emerging from strong cell-cell adhesion, which we explain with an active elasticity model. We propose a solution inspired by sheepherding based on using local stimulation to learn the collective perturbation-response of the group and then drive tissue motion. First, we induce local electrotaxis to characterize the impulse-response function of quasi-1D strips of skin tissue, discovering that hyper-local stimulation triggers long-range tissue response over a length scale set by cell-cell adhesion also predicted by our model. Based on this, we apply local, concentric ring fields to in vitro circular wounds. Continuously driving cells towards the wound core kinetically traps the tissue in a jammed state and freezes healing. Pulsing the stimuli allows the tissue to relax and fluidize again, accelerating migration. Finally, we integrate the key length and timescales of tissue mechanics into a biophysically-informed continuum control model. The model’s predictive framework helps determine where and when to apply stimulation for optimal tissue growth which, when tested, accelerates healing 5-fold.

Inspired by recent experimental observations of a harmonically excited elastic foil hovering near a wall while supporting substantial weight, we develop a theoretical framework that describes the underlying physical effects. Using elastohydrodynamic lubrication theory, we quantify how the dynamic deformation of the soft foil couples to the viscous fluid flow in the intervening gap. Our analysis shows that the soft foil rectifies the reversible forcing, breaking time-reversal symmetry; the spatial distribution of the forcing determines whether the sheet is attracted to or repelled from the wall. A simple scaling law predicts the time-averaged equilibrium hovering height and the maximum weight the sheet can sustain before detaching. Numerical simulations of the governing equation corroborate our theoretical predictions, are in qualitative agreement with experiments, and might explain the behavior of organisms while providing design principles for soft robotics.

We explore the dynamical response of the free surface of an ultrasoft solid driven by a localized moving pressure disturbance. Experiments reveal a steady V-shaped wake analogous to a surface Mach wedge. A simple geometric argument provides a qualitative explanation consistent with observations. A theoretical framework combining elastodynamic, capillary, and gravitational effects yields a generalized dispersion relation that smoothly interpolates between Kelvin's theory of liquid interface wakes and Rayleigh's theory of elastic surface waves. Our analysis explains the observed Mach-like behavior quantitatively while also emphasizing how elastodynamic effects can generate effective damping through radiative leakage. Together, our experiments and theory reveal the existence of a new regime that bridges fluid and solid surface-wave physics, offering new routes for probing the dynamics of soft interfaces.

Epithelial cortinoids, fluid-filled shells formed from induced pluripotent stem cells (iPSCs), must accommodate large deformations during growth and morphogenesis. Using inflation-deflation assays and high-resolution imaging, we find that these fluid-filled shells are weakly pressurized and achieve extreme deformability through reversible soft modes of deformation accommodated by the cytoskeleton. We show that cytoskeletal elements such as actin localized along lateral cell edges undergo tilt and bend instabilities that buffer mechanical load by decoupling apico-basal stretching from lateral extension. These reversible instabilities act as elastic safety valves, permitting large shape changes without loss of epithelial hydraulic and topological integrity. A minimal theoretical and computational model demonstrates how tilt and bend reduce effective resistance to radial thinning and explains the observed pressure-strain softening. Thus, iPSC shells exploit reversible cytoskeletal instabilities as mechanical buffers, enabling robust tolerance of large deformations in developing epithelia.

Ducks display a unique and dramatic sexual dimorphism in their vocal organ, the syrinx. Males have a left-sided bulla that is not present in females and that has been long hypothesized to play a role in courtship vocalizations, though this connection has never been tested. The large, hollow morphology of the bulla and its proximity to the sound-producing vocal folds introduce the possibility that it may work as a Helmholtz resonator, which makes it possible to predict the resonance frequencies enhanced by this structure. We found that during early ontogeny, the distribution of energy across the harmonic spectrum of contact calls is not different between males and females. We then used microcomputed tomography (µCT) scans of duck syringes to estimate resonance frequencies of the bullae and compared these with spectral features of their vocalizations. This comparison overall supports the idea that the bulla resonance may specifically enhance aspects of courtship vocalizations, especially in species that have a tonal courtship whistle. This was further supported when we tested the frequencies produced when air was blown through 3D printed bullae. We also saw potential influence of the bulla in non-courtship vocalizations, which could be explored further with a greater understanding of the input of other vocal tract features that influence vocalization. We observed that, in general, excepting the common eider, bulla size shows a weak positive correlation with male bird body mass. This study provides support for the long-held hypothesis that the adult male duck bulla influences resonance frequencies, in particular in courtship vocalizations.

Abstract Evolutionary adaptations associated with the formation of a folded cortex in many mam-malian brains are thought to be a critical specialization associated with higher cognitive function. The dramatic surface expansion and highly convoluted folding of the cortex during early development is a theme with variations that suggest the need for a comparative study of cortical gyrification. Here, we use a combination of physical experiments using gels, computational morphogenesis, and geometric morphometrics to study the folding of brains across different species. Starting with magnetic resonance images of brains of a newborn ferret, a fetal macaque, and a fetal human, we construct two-layer physical gel brain models that swell superficially in a solvent, leading to folding patterns similar to those seen in vivo. We then adopt a three-dimensional continuum model based on differential growth to simulate cortical folding in silico. Finally, we deploy a comparative morphometric analysis of the in vivo, in vitro, and in silico surface buckling patterns across species. Our study shows that a simple mechanical instability driven by differential growth suffices to explain cortical folding and suggests that variations in the tangential growth and different initial geometries are sufficient to explain the differences in cortical folding across species.

Evolutionary adaptations associated with the formation of a folded cortex in many mammalian brains are thought to be a critical specialization associated with higher cognitive function. The dramatic surface expansion and highly convoluted folding of the cortex during early development is a theme with variations that suggest the need for a comparative study of cortical gyrification. Here, we use a combination of physical experiments using gels, computational morphogenesis, and geometric morphometrics to study the folding of brains across different species. Starting with magnetic resonance images of brains of a newborn ferret, a fetal macaque, and a fetal human, we construct two-layer physical gel brain models that swell superficially in a solvent, leading to folding patterns similar to those seen in vivo. We then adopt a three-dimensional continuum model based on differential growth to simulate cortical folding in silico. Finally, we deploy a comparative morphometric analysis of the in vivo, in vitro, and in silico surface buckling patterns across species. Our study shows that a simple mechanical instability driven by differential growth suffices to explain cortical folding and suggests that variations in the tangential growth and different initial geometries are sufficient to explain the differences in cortical folding across species.

A mechanistic understanding of neurodevelopment requires us to follow the multiscale processes that connect molecular genetic processes to macroscopic cerebral cortical formations and thence to neurological function. Using MRI of the brain of the ferret, a model organism for studying cortical morphogenesis, we create in vitro physical gel models and in silico numerical simulations of normal brain gyrification. Using observations of genetically manipulated animal models, we identify cerebral cortical thickness and cortical expansion rate as the primary drivers of dysmorphogenesis and demonstrate that in silico models allow us to examine the causes of aberrations in morphology and developmental processes at various stages of cortical ontogenesis. Finally, we explain analogous cortical malformations in human brains, with comparisons with human phenotypes induced by the same genetic defects, providing a unified perspective on brain morphogenesis that is driven proximally by genetic causes and affected mechanically via variations in the geometry of the brain and differential growth of the cortex.

Evolutionary adaptations associated with the formation of a folded cortex in many mam-malian brains are thought to be a critical specialization associated with higher cognitive function. The dramatic surface expansion and highly convoluted folding of the cortex during early development is a theme with variations that suggest the need for a comparative study of cortical gyrification. Here, we use a combination of physical experiments using gels, computational morphogenesis, and geometric morphometrics to study the folding of brains across different species. Starting with magnetic resonance images of brains of a newborn ferret, a fetal macaque, and a fetal human, we construct two-layer physical gel brain models that swell superficially in a solvent, leading to folding patterns similar to those seen in vivo. We then adopt a three-dimensional continuum model based on differential growth to simulate cortical folding in silico. Finally, we deploy a comparative morphometric analysis of the in vivo, in vitro, and in silico surface buckling patterns across species. Our study shows that a simple mechanical instability driven by differential growth suffices to explain cortical folding and suggests that variations in the tangential growth and different initial geometries are sufficient to explain the differences in cortical folding across species.

A mechanistic understanding of neurodevelopment requires us to follow the multiscale processes that connect molecular genetic processes to macroscopic cerebral cortical formations and thence to neurological function. Using magnetic resonance imaging of the brain of the ferret, a model organism for studying cortical morphogenesis, we create in vitro physical gel models and in silico numerical simulations of normal brain gyrification. Using observations of genetically manipulated animal models, we identify cerebral cortical thickness and cortical expansion rate as the primary drivers of dysmorphogenesis and demonstrate that in silico models allow us to examine the causes of aberrations in morphology and developmental processes at various stages of cortical ontogenesis. Finally, we explain analogous cortical malformations in human brains, with comparisons with human phenotypes induced by the same genetic defects, providing a unified perspective on brain morphogenesis that is driven proximally by genetic causes and affected mechanically via variations in the geometry of the brain and differential growth of the cortex.

A mechanistic understanding of neurodevelopment requires us to follow the multiscale processes that connect molecular genetic processes to macroscopic cerebral cortical formations and thence to neurological function. Using magnetic resonance imaging of the brain of the ferret, a model organism for studying cortical morphogenesis, we create in vitro physical gel models and in silico numerical simulations of normal brain gyrification. Using observations of genetically manipulated animal models, we identify cerebral cortical thickness and cortical expansion rate as the primary drivers of dysmorphogenesis and demonstrate that in silico models allow us to examine the causes of aberrations in morphology and developmental processes at various stages of cortical ontogenesis. Finally, we explain analogous cortical malformations in human brains, with comparisons with human phenotypes induced by the same genetic defects, providing a unified perspective on brain morphogenesis that is driven proximally by genetic causes and affected mechanically via variations in the geometry of the brain and differential growth of the cortex.

Abstract The archetypal instability of a structure is associated with the eponymous Euler beam, modelled as an inextensible curve which exhibits a supercritical bifurcation at a critical compressive load. In contrast, a soft compressible beam is capable of a subcritical instability, a problem that is far less studied, even though it is increasingly relevant in the context of soft materials and structures. Here, we study the stability of a soft extensible elastic beam on an elastic foundation under the action of a compressive axial force, using the Lyapunov–Schmidt reduction method which we corroborate with numerical calculations. Our calculated bifurcation diagram differs from those associated with the classical Euler–Bernoulli beam, and shows two critical loads, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>p</mml:mi> <mml:mrow> <mml:mtext>cr</mml:mtext> </mml:mrow> <mml:mo>±</mml:mo> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> , for each buckling mode n . The beam undergoes a supercritical pitchfork bifurcation at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>p</mml:mi> <mml:mrow> <mml:mtext>cr</mml:mtext> </mml:mrow> <mml:mo>+</mml:mo> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> for all n and slenderness. Due to the elastic foundation, the lower order modes at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>p</mml:mi> <mml:mrow> <mml:mtext>cr</mml:mtext> </mml:mrow> <mml:mo>−</mml:mo> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> exhibit subcritical pitchfork bifurcations, and perhaps surprisingly, the first supercritical pitchfork bifurcation point occurs at a higher critical load. The presence of the foundation makes it harder to buckle the elastic beam. Overall, our study has uncovered the subtle interplay between elasticity and foundation effects in a minimal setting for an extensible beam with experimentally testable predictions.

When navigating complex environments, animals often combine multiple strategies to mitigate the effects of external disturbances. These modalities often correspond to different sources of information, leading to speed - accuracy trade-offs. Inspired by the intermittent reorientation strategy seen in the behaviour of the dung beetle, we consider the problem of the navigation strategy of a correlated random walker moving in two dimensions. We assume that the heading of the walker can be reoriented to the preferred direction by paying a fixed cost as it tries to maximize its total displacement in a fixed direction. Using optimal control theory, we derive analytically and confirm numerically the strategy that maximizes the walker's speed, and show that the average time between reorientations scales inversely with the magnitude of the environmental noise. We then extend our framework to describe execution errors and sensory acquisition noise. As a result, we provide a range of testable predictions and suggest new experimental directions. Our approach may be amenable to other navigation problems involving multiple sensory modalities that require switching between egocentric and geocentric strategies.

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

Synthetic active collectives, made of nonliving individuals that cooperatively change group shape and dynamics, hold promise for practical applications and understanding of their natural analogs. We investigate how simple steric interaction constraints between active individuals produce a versatile and functional system using the link-bot: a V-shape-based, single-stranded chain composed of active bots whose dynamics are defined by geometric linking constraints. A variety of emergent properties arises from this active polymer-like system, including locomotion, navigation, transportation, and competitive or cooperative interactions. By adjusting a few link parameters, we show how link-bots can perform diverse tasks, including traversing or obstructing narrow spaces, passing by or enclosing objects, and propelling loads in different directions. Overall, the reconfigurability of link-bots indicates their potential in developing programmable soft robotic systems with simple components and materials at any scale.

Temporal imaging of biological epithelial structures yields shape data at discrete-time points, leading to a natural question: how can we reconstruct the most likely path of growth patterns consistent with these discrete observations? We present a physically plausible framework to solve this inverse problem by creating a framework that generalizes quasi-conformal maps to quasi-conformal flows. By allowing the spatio-temporal variation of the shear and dilation fields during the growth process, subject to regulatory mechanisms, we are led to a type of generalized Ricci flow. When guided by observational data associated with surface shape as a function of time, this leads to a constrained optimization problem. Deploying our data-driven algorithmic approach to the shape of insect wings, leaves and even sculpted faces, we show how optimal quasi-conformal flows allow us to characterize the morphogenesis of a range of surfaces.

systems of cells and extra-cellular matrix (ECM) systems are well known to form ordered patterns of orientationally aligned fibers. Here, we interpret them as active analogs of the (disordered) isotropic to the (ordered) nematic phase transition seen in passive liquid crystalline elastomers. A minimal theoretical framework that couples cellular activity (embodied as mechanical stress) and the finite deformation elasticity of liquid crystal elastomers sets the stage to explain these patterns. Linear stability analysis of the governing equations about simple homogeneous isotropic base states shows how the onset of periodic morphologies depends on the activity, elasticity, and applied strain, provides an expression for the wavelength of the instability, and is qualitatively consistent with observations of cell-ECM experiments. Finite element simulations of the nonlinear problem corroborate the results of linear analysis. These results provide quantitative insights into the onset and evolution of nematic order in cell-matrix composites.

Perturbation theory plays a central role in the approximate solution of nonlinear differential equations. However, its naïve application often yields divergent series solutions. While these can be made convergent using singular perturbation methods of various types, the procedures used can be subtle owing to the lack of globally applicable algorithms. Inspired by the fact that all exact solutions of differential equations are consequences of their (Lie) symmetries, we reformulate perturbation theory for differential equations as a series expansion of their solutions’ symmetries. This is a change in perspective from the usual method of obtaining series expansions of the solutions themselves. We show that these approximate symmetries are straightforward to calculate and are never singular; their integration is therefore an easier way of constructing uniformly convergent solutions. This geometric viewpoint naturally subsumes the renormalization group-inspired approach of Chen, Goldenfeld and Oono, the method of multiple scales and the Poincare–Lindstedt method, by exploiting a fundamental class of symmetries that we term ‘hidden scale symmetries’. It also clarifies when and why these singular perturbation methods succeed and just as importantly, when they fail. More broadly, direct, algorithmic identification and integration of these hidden scale symmetries permits solution of problems where other methods are impractical.

Abstract Evolutionary adaptations associated with the formation of a folded cortex in many mammalian brains are thought to be a critical specialization associated with higher cognitive function. The dramatic surface expansion and highly convoluted folding of the cortex during early development is a theme with variations that suggest the need for a comparative study of cortical gyrification. Here, we use a combination of physical experiments using gels, computational morphogenesis, and geometric morphometrics to study the folding of brains across different species. Starting with magnetic resonance images of brains of a newborn ferret, a fetal macaque, and a fetal human, we construct two-layer physical gel brain models that swell superficially in a solvent, leading to folding patterns similar to those seen in vivo . We then adopt a three-dimensional continuum model based on differential growth to simulate cortical folding in silico . Finally, we deploy a comparative morphometric analysis of the in vivo, in vitro , and in silico surface buckling patterns across species. Our study shows that a simple mechanical instability driven by differential growth suffices to explain cortical folding and suggests that variations in the tangential growth and different initial geometries are sufficient to explain the differences in cortical folding across species.

Abstract A mechanistic understanding of neurodevelopment requires us to follow the multiscale processes that connect molecular genetic processes to macroscopic cerebral cortical formations and thence to neurological function. Using magnetic resonance imaging of the brain of the ferret, a model organism for studying cortical morphogenesis, we create in vitro physical gel models and in silico numerical simulations of normal brain gyrification. Using observations of genetically manipulated animal models, we identify cerebral cortical thickness and cortical expansion rate as the primary drivers of dysmorphogenesis and demonstrate that in silico models allow us to examine the causes of aberrations in morphology and developmental processes at various stages of cortical ontogenesis. Finally, we explain analogous cortical malformations in human brains, with comparisons with human phenotypes induced by the same genetic defects, providing a unified perspective on brain morphogenesis that is driven proximally by genetic causes and affected mechanically via variations in the geometry of the brain and differential growth of the cortex. Impact statement Physical gel models and numerical simulations are created to study ferret brain gyrification and cortical malformations, and comparisons with human phenotypes are presented to link genetics and brain morphogenesis.

When placed on an inclined plane, a perfect 2D disk or 3D sphere simply rolls down in a straight line under gravity. But how is the rolling affected if these shapes are irregular or random? Treating the terminal rolling speed as an order parameter, we show that there are qualitative transitions in the speed as a function of the dimension of the state space and inertia. We calculate the scaling exponents and the macroscopic lag time associated with the presence of first- and second-order transitions and describe the regimes of coexistence of stable states and the accompanying hysteresis. Experiments with rolling cylinders corroborate our theoretical results on the scaling of the lag time. Experiments with spheres reveal closed orbits and their period-doubling in the overdamped and inertial limits, respectively, providing visible manifestations of the hairy ball theorem and the doubly connected nature of [Formula: see text], the space of 3D rotations. Going beyond simple curiosity, our study might shed light on a number of natural and artificial systems that involve the rolling of irregular objects, ranging from nanoscale cellular transport to robotics.

To investigate real-time decision-making in a simplified context, we analyze the trade-offs individuals make using a game of Roulette. In this game, players observe a ball that gradually decelerates as it moves around a circular track, and the participants must predict where the ball will ultimately stop. Players are rewarded for making rapid, accurate predictions, while slower but accurate predictions, or fast yet inaccurate ones, result in lower rewards. In this speed-accuracy trade-off setup we can calculate the optimal timing for placing a bet based on the ball’s initial speed and the deceleration rate, given the capacity of an individual’s tracking abilities. We find that the participants improve their performance by accruing more reward with each trial and saturates close to the optimal performance, indicating that individuals learn the parameters of the physical model as well as a representation of the form of the reward under constrained time. Looking at the correlation between the bet time of the participant and the optimal betting time, the response delay and reward accrued, we find that the participant can be classified on a novice-expert spectrum. Our study offers ways to quantify human adaptation in competitive and dynamic environments such as sports, which may be helpful in enhancing participant performance.

Random packings of stiff rods are self-supporting mechanical structures stabilized by long-range interactions induced by contacts. To understand the geometrical and topological complexity of the packings, we first deploy X-ray computerized tomography to unveil the structure of the packing. This allows us to directly visualize the spatial variations in density, orientational order, and the entanglement, a mesoscopic field that we define in terms of a local average crossing number, a measure of the topological complexity of the packing. We find that increasing the aspect ratio of the constituent rods in a packing leads to a proliferation of regions of strong entanglement that eventually percolate through the system and correlated with a sharp transition in the mechanical stability of the packing. To corroborate our experimental findings, we use numerical simulations of contacting elastic rods and characterize their stability to static and dynamic loadings. Our experiments and computations lead us to an entanglement phase diagram which we also populate using published experimental data from pneumatically tangled filaments, worm blobs, and bird nests along with additional numerical simulations using these datasets. Together, these show the regimes associated with mechanically stable entanglement as a function of the statistics of the packings and loading, with lessons for a range of systems from reconfigurable architectures and textiles to active morphable filamentous assemblies.

SUMMARY The vertebrate bauplan is primarily established via the formation of embryonic tissues in a head-to-tail progression. The mechanics of this elongation, which requires the presomitic mesoderm (PSM), remain poorly understood. Here, we find that avian PSM explants can elongate autonomously when physically confined in vitro, producing a pushing force promoting posterior elongation of the embryo. This tissue elongation is caused by volumetric expansion, which results from an increase in the extracellular fraction accompanied by graded cellular motility. We show that fibroblast growth factor (FGF) signaling promotes glycolysis-dependent production of hyaluronic acid (HA), which is required for expansion of the posterior PSM. Our findings link body axis elongation to tissue expansion through the metabolic control of extracellular matrix production downstream of FGF signaling.

Inspired by recent experimental observations of a harmonically excited elastic foil hovering near a wall while supporting substantial weight, we develop a theoretical framework that describes the underlying physical effects. Using elastohydrodynamic lubrication theory, we quantify how the dynamic deformation of the soft foil couples to the viscous fluid flow in the intervening gap. Our analysis shows that the soft foil rectifies the reversible forcing, breaking time-reversal symmetry; the relative spatial support of the forcing determines whether the sheet is attracted to or repelled from the wall. A simple scaling law predicts the time-averaged equilibrium hovering height and the maximum weight the sheet can sustain before detaching from the surface. Numerical simulations of the governing equation corroborate our theoretical predictions, are in qualitative agreement with experiments, and might explain the behavior of organisms while providing design principles for soft robotics.