1. Spontaneous exfoliation of a drying gel J. Y. Chung, I. Regev and L. Mahadevan,  Soft Matter , 12, 7855-62, 2016.
    [View PDF] [Download PDF] Wet starch cracks when it dries inhomogeneously, while hot glass cracks when it cools non-uniformly. In both cases, differential shrinkage induced by drying/cooling from the surface causes superficial cracks to grow perpendicular to the surface in different patterns. In contrast with these observations of bulk cracking in brittle materials, when a soft and homogeneously swollen polymer gel dries, differential strains lead to the peeling of a thin layer that spontaneously tears away from the bulk. Continued drying leads to the process repeating itself, forming a peeled-layered structure. The emergent thickness of the exfoliated layer is a function of both the geometry of the original gel and the physical parameters associated with the drying rate and external temperature. We characterize the experimental conditions under which layer peeling can arise, and use simulations to corroborate these observations. Finally, a minimal theory explains the scaling of the peel thickness, consistent with our experiments
  2. Bending and buckling of wet paper M. Lee, S. Kim, H-Y. Kim, and L. Mahadevan  Physics of Fluids  28, 042101, 2016.
    [View PDF] [Download PDF] Flat paper stained with water buckles and wrinkles as it swells and deforms out of the original plane. Here we quantify the geometry and mechanics of a strip of paper that swells when it imbibes water from a narrow capillary. Characterizing the hygroexpansive nature of paper shows that thickness-wise swelling is much faster than in-plane water imbibition, leading to a simple picture for the process by which the strip of paper bends out of the plane. We model the out-of-plane deformation using a quasi-static theory and show that our results are consistent with quantitative experiments. C
  3. Similarity and singularity in adhesive elastohydrodynamic touchdown A. Carlson and L. Mahadevan  Physics of Fluids  28, 011702, 2016.
    [View PDF] [Download PDF] We consider the dynamics of an elastic sheet as it starts to adhere to a wall, a process that is limited by the viscous squeeze flow of the intervening liquid. Elastohydrodynamic lubrication theory allows us to derive a partial di↵erential equation coupling the elastic deformation of the sheet, the microscopic van der Waals adhesion, and viscous thin film flow. We use a combination of numerical simulations of the governing equation and a scaling analysis to describe the self-similar touchdown of the sheet as it approaches the wall. An analysis of the equation in terms of similarity variables in the vicinity of the touchdown event shows that only the fundamental similarity solution is observed in the time-dependent numerical simulations, consistent with the fact that it alone is stable. Our analysis generalizes similar approaches for rupture in capillary thin film hydrodynamics and suggests experimentally verifiable predictions for a new class of singular flows linking elasticity, hydrodynamics, and adhesion
  4. Self-sustained lift and low friction via soft lubrication B. Saintyves, T. Jules, T. Saleza, and L. Mahadevan  Proceedings of the National Academy of Sciences  (USA) 113:21 5847–5849, 2016.
    [View PDF] [Download PDF] Relative motion between soft wet solids arises in a number of applications in natural and artificial settings, and invariably couples elastic deformation fluid flow. We explore this in a minimal setting by considering a fluid-immersed negatively buoyant cylinder moving along a soft inclined wall. Our experiments show that there is an emergent robust steady-state sliding regime of the cylinder with an effective friction that is significantly reduced relative to that of rigid fluid-lubricated contacts. A simple scaling approach that couples the cylinder-induced flow to substrate deformation allows us to explain the elastohydrodynamic lift that underlies the self-sustained lubricated motion of the cylinder, consistent with recent theoretical predictions. Our results suggest an explanation for a range of effects such as reduced wear in animal joints and long-runout landslides, and can be couched as a design principle for low-friction interfaces.
  5. Optimal switching between geocentric and egocentric strategies in navigation O. Peleg and L. Mahadevan  Royal Society Open Science  3: 160128, 2016.
    [View PDF] [Download PDF] Animals use a combination of egocentric navigation driven by the internal integration of environmental cues, interspersed with geocentric course correction and reorientation. These processes are accompanied by uncertainty in sensory acquisition of information, planning and execution. Inspired by observations of dung beetle navigational strategies that show switching between geocentric and egocentric strategies, we consider the question of optimal reorientation rates for the navigation of an agent moving along a preferred direction in the presence of multiple sources of noise. We address this using a model that takes the form of a correlated random walk at short time scales that is punctuated by reorientation events leading to a biased random walks at long time scales. This allows us to identify optimal alternation schemes and characterize their robustness in the context of noisy sensory acquisition as well as performance errors linked with variations in environmental conditions and agent–environment interactions.
  6. Recovery of locomotion after injury in Drosophila melanogaster depends on proprioception A. Isakov, S. M. Buchanan, B. Sullivan, A. Ramachandran, J. K. S. Chapman, E. S. Lu, L. Mahadevan, and B. de Bivort  Journal of Experimental Biology,  219, 1760-1771, 2016.
    [View PDF] [Download PDF] Locomotion is necessary for survival in most animal species. However, injuries to the appendages mediating locomotion are common. We assess the recovery of walking in Drosophila melanogaster following leg amputation. Whereas flies preamputation explore open arenas in a symmetric fashion on average, foreleg amputation induces a strong turning bias away from the side of the amputation. However, we find that unbiased walking behavior returns over time in wild-type flies, while recovery is significantly impaired in proprioceptive mutants. To identify the biomechanical basis of this locomotor impairment and recovery, we then examine individual leg motion (gait) at a fine scale. A minimal mathematical model that links neurodynamics to body mechanics during walking shows that redistributing leg forces between the right and left side enables the observed recovery. Altogether, our study suggests that proprioceptive input from the intact limbs plays a crucial role in the behavioral plasticity associated with locomotor recovery after injury.
  7. Integrative neuromechanics of crawling in D. melanogaster larvae C. Pehlevan, P. Paoletti, L Mahadevan  eLife,  5:e11031,  2016.
    [View PDF] [Download PDF] Locomotion in an organism is a consequence of the coupled interaction between brain, body and environment. Motivated by qualitative observations and quantitative perturbations of crawling in Drosophila melanogaster larvae, we construct a minimal integrative mathematical model for its locomotion. Our model couples the excitation-inhibition circuits in the nervous system to force production in the muscles and body movement in a frictional environment, thence linking neural dynamics to body mechanics via sensory feedback in a heterogeneous environment. Our results explain the basic observed phenomenology of crawling with and without proprioception, and elucidate the stabilizing role that proprioception plays in producing a robust crawling phenotype in the presence of biological perturbations. More generally, our approach allows us to make testable predictions on the effect of changing body-environment interactions on crawling, and serves as a step in the development of hierarchical models linking cellular processes to behavior.
  8. Phototactic guidance of a tissue-engineered soft-robotic ray S-J Park, M. Gazzola, K. S. Park, S. Park, V. Di Santo, E. L. Blevins, J. U. Lind, P. H. Campbell, S. Dauth, A. K. Capulli, F. S. Pasqualini, S. Ahn, A. Cho, H. Yuan, B. M. Maoz, R. Vijaykumar, J-W Choi, K. Deisseroth, G. V. Lauder, L. Mahadevan, K. K. Parker, Science , 353, 158-62, 2016.
    [View PDF] [Download PDF] Inspired by the relatively simple morphological blueprint provided by batoid fish such as stingrays and skates, we created a biohybrid system that enables an artificial animal—a tissue-engineered ray—to swim and phototactically follow a light cue. By patterning dissociated rat cardiomyocytes on an elastomeric body enclosing a microfabricated gold skeleton, we replicated fish morphology at 1=10 scale and captured basic fin deflection patterns of batoid fish. Optogenetics allows for phototactic guidance, steering, and turning maneuvers. Optical stimulation induced sequential muscle activation via serpentinepatterned muscle circuits, leading to coordinated undulatory swimming. The speed and direction of the ray was controlled by modulating light frequency and by independently eliciting right and left fins, allowing the biohybrid machine to maneuver through an obstacle course.
  9. Elastic instability-mediated actuation by a supra-molecular polymer A. Levin, T. C. T. Michaels, L. Adler-Abramovich, T. O. Mason, T. Müller, B. Zhang, L. Mahadevan, E. Gazit, and T. P. J. Knowles.  Nature Physics , 12, 926-30, 2016.
    [View PDF] [Download PDF] In nature, fast, high-power-density actuation can be achieved through the release of stored elastic energy by exploiting mechanical instabilities in systems including the closure of the Venus flytrap1 and the dispersal of plant or fungal spores2. Here, we use droplet microfluidics to tailor the geometry of a nanoscale self-assembling supra-molecular polymer to create a mechanical instability. We show that this strategy allows the build-up of elastic energy as a result of peptide selfassembly, and its release within milliseconds when the buckled geometry of the nanotube confined within microdroplets becomes unstable with respect to the straight form. These results overcome the inherent limitations of self-assembly for generating large-scale actuation on the sub-second timescale and illuminate the possibilities and performance limits of irreversible actuation by supra-molecular polymers.
  10. On the growth and form of cortical convolutions T. Tallinen, J.Y. Chung, F. Rousseau, N. Girard, J. Lefèvre, and L. Mahadevan,  Nature Physics , 12, 588-93, 2016.
    [DOI] [View PDF] [Download PDF] The rapid growth of the human cortex during development is accompanied by the folding of the brain into a highly convoluted structure1,2,3. Recent studies have focused on the genetic and cellular regulation of cortical growth4,5,6,7,8, but understanding the formation of the gyral and sulcal convolutions also requires consideration of the geometry and physical shaping of the growing brain9,10,11,12,13,14,15. To study this, we use magnetic resonance images to build a 3D-printed layered gel mimic of the developing smooth fetal brain; when immersed in a solvent, the outer layer swells relative to the core, mimicking cortical growth. This relative growth puts the outer layer into mechanical compression and leads to sulci and gyri similar to those in fetal brains. Starting with the same initial geometry, we also build numerical simulations of the brain modelled as a soft tissue with a growing cortex, and show that this also produces the characteristic patterns of convolutions over a realistic developmental course. All together, our results show that although many molecular determinants control the tangential expansion of the cortex, the size, shape, placement and orientation of the folds arise through iterations and variations of an elementary mechanical instability modulated by early fetal brain geometry.
  11. Programming curvature using origami tessellations L.H. Dudte, E. Vouga, T. Tachi and L. Mahadevan,  Nature Materials , 15, 583-88, 2016.
    [View PDF] [Download PDF] Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can be designed to fit target shapes. Here, starting from the simplest periodic origami pattern that yields one-degree-of-freedom collapsible structures—we show that scale-independent elementary geometric constructions and constrained optimization algorithms can be used to determine spatially modulated patterns that yield approximations to given surfaces of constant or varying curvature. Paper models confirm the feasibility of our calculations. We also assess the diculty of realizing these geometric structures by quantifying the energetic barrier that separates the metastable flat and folded states. Moreover, we characterize the trade-o between the accuracy to which the pattern conforms to the target surface, and the eort associated with creating finer folds. Our approach enables the tailoring of origami patterns to drape complex surfaces independent of absolute scale, as well as the quantification of the energetic and material cost of doing so.
  12. Biomimetic 4D printing A. S. Gladman, E. A. Matsumoto, R.G. Nuzzo, L. Mahadevan, and J.A. Lewis,  Nature Materials , 15, 413-19, 2016.
    [View PDF] [Download PDF] Shape-morphing systems can be found in many areas, including smart textiles1 , autonomous robotics2 , biomedical devices3 , drug delivery4 and tissue engineering5 . The natural analogues of such systems are exemplified by nastic plant motions, where a variety of organs such as tendrils, bracts, leaves and flowers respond to environmental stimuli (such as humidity, light or touch) by varying internal turgor, which leads to dynamic conformations governed by the tissue composition and microstructural anisotropy of cell walls6–10. Inspired by these botanical systems, we printed composite hydrogel architectures that are encoded with localized, anisotropic swelling behaviour controlled by the alignment of cellulose fibrils along prescribed four-dimensional printing pathways. When combined with a minimal theoretical framework that allows us to solve the inverse problem of designing the alignment patterns for prescribed target shapes, we can programmably fabricate plant-inspired architectures that change shape on immersion in water, yielding complex three-dimensional morphologies.
  13. Directional memory arises from long-lived cytoskeletal asymmetries in polarized chemotactic cells H.V. Prentice-Mott, Y. Meroz, A. Carlson, M.A. Levine, M.W. Davidson, D. Irimia, G.T. Charras, L. Mahadevan, and J.V. Shah,  Proceedings of the National Academy of Sciences  (USA) 113, 1267-72, 2016.
    [View PDF] [Download PDF] Chemotaxis, the directional migration of cells in a chemical gradient, is robust to fluctuations associated with low chemical concentrations and dynamically changing gradients as well as high saturating chemical concentrations. Although a number of reports have identified cellular behavior consistent with a directional memory that could account for behavior in these complex environments, the quantitative and molecular details of such a memory process remain unknown. Using microfluidics to confine cellular motion to a 1D channel and control chemoattractant exposure, we observed directional memory in chemotactic neutrophil-like cells. We modeled this directional memory as a long-lived intracellular asymmetry that decays slower than observed membrane phospholipid signaling. Measurements of intracellular dynamics revealed that moesin at the cell rear is a longlived element that when inhibited, results in a reduction of memory. Inhibition of ROCK (Rho-associated protein kinase), downstream of RhoA (Ras homolog gene family, member A), stabilized moesin and directional memory while depolymerization of microtubules (MTs) disoriented moesin deposition and also reduced directional memory. Our study reveals that long-lived polarized cytoskeletal structures, specifically moesin, actomyosin, and MTs, provide a directional memory in neutrophil-like cells even as they respond on short time scales to external chemical cues.
  14. Pressure-driven occlusive flow of a confined red blood cell T. Savin, M. M. Bandi and L. Mahadevan,  Soft Matter , 12, 562-573, 2015.
    [View PDF] [Download PDF] When red blood cells (RBCs) move through narrow capillaries in the microcirculation, they deform as they flow. In pathophysiological processes such as sickle cell disease and malaria, RBC motion and flow are severely restricted. To understand this threshold of occlusion, we use a combination of experiment and theory to study the motion of a single swollen RBC through a narrow glass capillary of varying inner diameter. By tracking the movement of the squeezed cell as it is driven by a controlled pressure drop, we measure the RBC velocity as a function of the pressure gradient as well as the local capillary diameter, and find that the effective blood viscosity in this regime increases with both decreasing RBC velocity and tube radius by following a power-law that depends upon the length of the confined cell. Our observations are consistent with a simple elasto-hydrodynamic model and highlight the role of lateral confinement in the occluded pressure-driven slow flow of soft confined objects.
  15. Joseph B. Keller (1923–2016) A Whittemore, G Papanicolau, D Cohen, L Mahadevan, B Matkowsky,  Notices of the American Mathematical Society  64, 606-615.
    [View PDF] [Download PDF] Joseph Bishop Keller was an applied mathematician of world renown, whose research interests spanned a wide range of topics, including wave propagation, semi-classical mechanics, geophysical fluid dynamics, operations research, finance, biomechanics, epidemiology, biostatistics, and the mathematics of sports. His work combined a love of physics, mathematics, and natural phenomena with an irrepressible curiosity to pursue explanations of practical and often playful enigmas.
  16. The Monge–Ampère constraint: Matching of isometries, density and regularity, and elastic theories of shallow shells
    M. Lewicka, L. Mahadevan, M. R. Pakzad,  Ann. I. H. Poincare - AN , 2015. 
    [View PDF] [Download PDF] The main analytical ingredients of the first part of this paper are two independent results: a theorem on approximation of W2,2 solutions of the Monge–Ampère equation by smooth solutions, and a theorem on the matching (in other words, continuation) of second order isometries to exact isometric embeddings of 2d surface in R3. In the second part, we rigorously derive the -limit of 3-dimensional nonlinear elastic energy of a shallow shell of thickness h, where the depth of the shell scales like hα and the applied forces scale like hα+2, in the limit when h → 0. We offer a full analysis of the problem in the parameter range α ∈ (1/2, 1). We also complete the analysis in some specific cases for the full range α ∈ (0, 1), applying the results of the first part of the paper. © 2015 Elsevier Masson SAS. All rights reserved.
  17. Elastohydrodynamics and kinetics of protein patterning in the immunological synapse
    A. Carlson, L. Mahadevan,  PLoS Comput Biol  11(12): e1004481, 2015. 
    [View PDF] [Download PDF] We propose a minimal mathematical model for the physical basis of membrane protein patterning in the immunological synapse (IS), which encompass membrane mechanics, protein binding kinetics and motion, and fluid flow in the synaptic cleft. Our theory leads to simple predictions for the spatial and temporal scales of protein cluster formation, growth and arrest as a function of membrane stiffness, rigidity and kinetics of the adhesive proteins, and the fluid flow in the synaptic cleft. Numerical simulations complement these scaling laws by quantifying the nucleation, growth and stabilization of proteins domains on the size of the cell. Direct comparison with experiment shows that passive elastohydrodynamics and kinetics of protein binding in the synaptic cleft can describe the short-time formation and organization of protein clusters, without evoking any active processes in the cytoskeleton. Despite the apparent complexity of the process, our analysis shows that just two dimensionless parameters characterize the spatial and temporal evolution of the protein pattern: a ratio of membrane elasticity to protein stiffness, and the ratio of a hydrodynamic time scale for fluid flow relative to the protein binding rate. A simple phase diagram encompasses the variety of patterns that can arise
  18. Elastic cheerios effect: Self-assembly of cylinders on a soft solid
    A. Chakrabarti, L. Ryan, M. K. Chaudhury and L. Mahadevan,  Europhysics Letters , 112, 54001, 2015. 
    [View PDF] [Download PDF] A rigid cylinder placed on a soft gel deforms its surface. When multiple cylinders are placed on the surface, they interact with each other via the topography of the deformed gel which serves as an energy landscape; as they move, the landscape changes which in turn changes their interaction. We use a combination of experiments, simple scaling estimates and numerical simulations to study the self-assembly of cylinders in this elastic analog of the “Cheerios Effect”, which describes capillary interactions on a fluid interface. Our results show that the effective two-body interaction can be well described by an exponential attraction potential as a result of which the dynamics also show an exponential behavior with respect to the separation distance. When many cylinders are placed on the gel, the cylinders cluster together if they are not too far apart; otherwise their motion gets elastically arrested.
  19. Dynamics of evaporative colloidal patterning
    C. N. Kaplan, N. Wu, S. Mandre, J.Aizenberg, and L. Mahadevan,  Physics of Fluids  27, 092105, 2015. 
    [DOI] [View PDF] [Download PDF] Drying suspensions often leave behind complex patterns of particulates, as might be seen in the coffee stains on a table. Here, we consider the dynamics of periodic band or uniform solid film formation on a vertical plate suspended partially in a drying colloidal solution. Direct observations allow us to visualize the dynamics of band and film deposition, where both are made of multiple layers of close packed particles. We further see that there is a transition between banding and filming when the colloidal concentration is varied. A minimal theory of the liquid meniscus motion along the plate reveals the dynamics of the banding and its transition to the filming as a function of the ratio of deposition and evaporation rates. We also provide a complementary multiphase model of colloids dissolved in the liquid, which couples the inhomogeneous evaporation at the evolving meniscus to the fluid and particulate flows and the transition from a dilute suspension to a porous plug. This allows us to determine the concentration dependence of the bandwidth and the deposition rate. Together, our findings allow for the control of drying-induced patterning as a function of the colloidal concentration and evaporation rate.
  20. Evaporation-driven ring and film deposition from colloidal droplets
    C. N. Kaplan and L. Mahadevan,  J. Fluid Mech . 781, R2 , 2015. 
    [DOI] [View PDF] [Download PDF] Evaporating suspensions of colloidal particles lead to the formation of a variety of patterns, ranging from a left-over ring of a dried coffee drop to uniformly distributed solid pigments left behind wet paint. To characterize the transition between rings and uniform deposits, we investigate the dynamics of a drying droplet via a multiphase model of colloidal particles in a solvent. Our theory couples the inhomogeneous evaporation at the evolving droplet interface to the dynamics inside the drop. This includes the liquid flow, local variations of the particle concentration leading to a cross-over between dilute and dense suspensions, and the resulting propagation of the deposition front. A dimensionless parameter combining the capillary number and the droplet aspect ratio captures the formation conditions of different pattern types while correctly accounting for the transition from Stokes flow to Darcy flow at high solute concentrations.
  21. Elastohydrodynamics of a sliding, spinning and sedimenting cylinder near a soft wall T. Salez and L. Mahadevan,  J. Fluid Mech . 779, 181-196 2015.
    [View PDF] [Download PDF]
  22. Termite mounds harness diurnal temperature oscillations for ventilation
    H. King, S. Ocko, and L. Mahadevan,  Proceedings of the National Academy of Sciences  112, 37, 11589–11593, 2015. 
    [View PDF] [Download PDF] Many species of millimetric fungus-harvesting termites collectively build uninhabited, massive mound structures enclosing a network of broad tunnels that protrude from the ground meters above their subterranean nests. It is widely accepted that the purpose of these mounds is to give the colony a controlled microclimate in which to raise fungus and brood by managing heat, humidity, and respiratory gas exchange. Although different hypotheses such as steady and fluctuating external wind and internal metabolic heating have been proposed for ventilating the mound, the absence of direct in situ measurement of internal air flows has precluded a definitive mechanism for this critical physiological function. By measuring diurnal variations in flow through the surface conduits of the mounds of the species Odontotermes obesus, we show that a simple combination of geometry, heterogeneous thermal mass, and porosity allows the mounds to use diurnal ambient temperature oscillations for ventilation. In particular, the thin outer flutelike conduits heat up rapidly during the day relative to the deeper chimneys, pushing air up the flutes and down the chimney in a closed convection cell, with the converse situation at night. These cyclic flows in the mound flush out CO2 from the nest and ventilate the colony, in an unusual example of deriving useful work from thermal oscillations.
  23. Optimal control of plates using incompatible strains G.W. Jones and L. Mahadevan,  Nonlinearity  28, 3153–3174, 2015.
    [View PDF] [Download PDF] A flat plate will bend into a curved shell if it experiences an inhomogeneous growth field or if constrained appropriately at a boundary. While the forward problem associated with this process is well studied, the inverse problem of designing the boundary conditions or growth fields to achieve a particular shape is much less understood. We use ideas from variational optimization theory to formulate a well posed version of this inverse problem to determine the optimal growth field or boundary condition that will give rise to an arbitrary target shape, optimizing for both closeness to the target shape and for smoothness of the growth field. We solve the resulting system of PDE numerically using finite element methods with examples for both the fully non-symmetric case as well as for simplified one-dimensional and axisymmetric geometries. We also show that the system can also be solved semi-analytically by positing an ansatz for the deformation and growth fields in a circular disk with given thickness profile, leading to paraboloidal, cylindrical and saddle-shaped target shapes, and show how a soft mode can arise from a non-axisymmetric deformation of a structure with axisymmetric material properties.
  24. The organization and control of an evolving interdependent population D.C. Vural, A. Isakov, L. Mahadevan,  J. R. Soc. Interface  12: 20150044, 2015.
    [View PDF] [Download PDF] Starting with Darwin, biologists have asked how populations evolve from a low fitness state that is evolutionarily stable to a high fitness state that is not. Specifically of interest is the emergence of cooperation and multicellularity where the fitness of individuals often appears in conflict with that of the population. Theories of social evolution and evolutionary game theory have produced a number of fruitful results employing two-state two-body frameworks. In this study, we depart from this tradition and instead consider a multi-player, multi-state evolutionary game, in which the fitness of an agent is determined by its relationship to an arbitrary number of other agents. We show that populations organize themselves in one of four distinct phases of interdependence depending on one parameter, selection strength. Some of these phases involve the formation of specialized large-scale structures. We then describe how the evolution of independence can be manipulated through various external perturbations.
  25. Protein mediated membrane adhesion A. Carlson and L. Mahadevan,  Physics of Fluids  27, 051901, 2015.
    [View PDF] [Download PDF] Adhesion in the context of mechanical attachment, signaling, and movement in cellular dynamics is mediated by the kinetic interactions between membraneembedded proteins in an aqueous environment. Here, we present a minimal theoretical framework for the dynamics of membrane adhesion that accounts for the kinetics of protein binding, the elastic deformation of the membrane, and the hydrodynamics of squeeze flow in the membrane gap. We analyze the resulting equations using scaling estimates to characterize the spatiotemporal features of the adhesive patterning and corroborate them using numerical simulations. In addition to characterizing aspects of cellular dynamics, our results might also be applicable to a range of phenomena in physical chemistry and materials science where flow, deformation, and kinetics are coupled to each other in slender geometries.
  26. Fluid-driven fingering instability of a confined elastic meniscus J.S. Biggins, Z. Wei and L. Mahadevan,  Europhysics Letters , 110, 34001, 2015.
    [View PDF] [Download PDF] When a fluid is pumped into a cavity in a confined elastic layer, at a critical pressure, destabilizing fingers of fluid invade the elastic solid along its meniscus (Saintyves B. et al., Phys. Rev. Lett., 111 (2013) 047801). These fingers occur without fracture or loss of adhesion and are reversible, disappearing when the pressure is decreased. We develop an asymptotic theory of pressurized highly elastic layers trapped between rigid bodies in both rectilinear and circular geometries, with predictions for the critical fluid pressure for fingering, and the finger wavelength. Our results are in good agreement with recent experimental observations of this elastic interfacial instability in a radial geometry. Our theory also shows that, perhaps surprisingly, this lateral-pressure–driven instability is analogous to a transverse-displacement–driven instability of the elastic layer. We verify these predictions by using non-linear finite-element simulations on the two systems which show that in both cases the fingering transition is first order (sudden) and hence has a region of bistability.
  27. Bending gradients: how the intestinal stem cell gets its home A. Shyer, T. Huycke, C-H Lee, L. Mahadevan, and C.,  Cell  , 161, 569-80, 201, 2015.
    [View PDF] [Download PDF] In animal embryos, morphogen gradients determine tissue patterning and morphogenesis. Shyer et al. provide evidence that, during vertebrate gut formation, tissue folding generates graded activity of signals required for subsequent steps of gut growth and differentiation, thereby revealing an intriguing link between tissue morphogenesis and morphogen gradient formation.
  28. Feedback-nduced phase transitions in active heterogeneous conductors S.A. Ocko and L. Mahadevan,  Physical Review Letters  114, 134501, 2015.
    [View PDF] [Download PDF] An active conducting medium is one where the resistance (conductance) of the medium is modified by the current (flow) and in turn modifies the flow, so that the classical linear laws relating current and resistance, e.g., Ohm’s law or Darcy’s law, are modified over time as the system itself evolves. We consider a minimal model for this feedback coupling in terms of two parameters that characterize the way in which addition or removal of matter follows a simple local (or nonlocal) feedback rule corresponding to either flow-seeking or flow-avoiding behavior. Using numerical simulations and a continuum mean field theory, we show that flow-avoiding feedback causes an initially uniform system to become strongly heterogeneous via a tunneling (channel-building) phase separation; flow-seeking feedback leads to an immuring (wallbuilding) phase separation. Our results provide a qualitative explanation for the patterning of active conducting media in natural systems, while suggesting ways to realize complex architectures using simple rules in engineered systems.
  29. Gait and speed selection in slender inertial swimmers M. Gazzolaa, M. Argentina and L. Mahadevan,  Proceedings of the National Academy of Sciences  112, 13, 2015.
    [View PDF] [Download PDF] Inertial swimmers use flexural movements to push water and generate thrust. We quantify this dynamical process for a slender body in a fluid by accounting for passive elasticity and hydrodynamics and active muscular force generation and proprioception. Our coupled elastohydrodynamic model takes the form of a nonlinear eigenvalue problem for the swimming speed and locomotion gait. The solution of this problem shows that swimmers use quantized resonant interactions with the fluid environment to enhance speed and efficiency. Thus, a fish is like an optimized diode that converts a prescribed alternating transverse motion to forward motion. Our results also allow for a broad comparative view of swimming locomotion and provide a mechanistic basis for the empirical relation linking the swimmer’s speed U, length L, and tail beat frequency f, given by U=L ∼ f [Bainbridge R (1958) J Exp Biol 35:109–133]. Furthermore, we show that a simple form of proprioceptive sensory feedback, wherein local muscle activation is function of body curvature, suffices to drive elastic instabilities associated with thrust production and leads to a spontaneous swimming gait without the need for a central pattern generator. Taken together, our results provide a simple mechanistic view of swimming consistent with natural observations and suggest ways to engineer artificial swimmers for optimal performance.
  30. A geometric model for the periodic undulation of a confined adhesive crack Z. Wei and L. Mahadevan,  Soft Matter , 12, 1778-82 , 2015.
    [View PDF] [Download PDF] Inspired by experiments on the instability of confined interfacial cracks, we construct a minimal mathematical model based on symmetry arguments that can reproduce the form of the crack front in a confined domain. We show that the model can be interpreted in terms of the buckling and postbuckling response of a compressed elastica with a nonuniform bending stiffness that is adhered to a linearly elastic substrate. The model has three parameters that allow us to capture the primary wavelength associated with the onset of an undulatory instability of a straight crack front, as well as the finger amplitudes and finger widths in the nonlinear development of the instability. We determine these parameters using an optimization procedure that minimizes the square error between the computed profile and experimental observations. The results of this procedure yield numerical solutions that agree well with the finger profiles experimentally observed in films of different thicknesses. Our approach shows the efficacy of simple models based on symmetry in explaining interfacial instabilities governed by different physical mechanisms.
  31. Solid friction between soft filaments A. Ward, F. Hilitski, W. Schwenger, D. Welch, A.W.C. Lau, V. Vitelli, L. Mahadevan and Z. Dogic,  Nature Materials , 2015.
    [View PDF] [Download PDF] Any macroscopic deformation of a filamentous bundle is necessarily accompanied by local sliding and/or stretching of the constituent filaments1,2. Yet the nature of the sliding friction between two aligned filaments interacting through multiple contacts remains largely unexplored. Here, by directly measuring the sliding forces between two bundled F-actin filaments, we show that these frictional forces are unexpectedly large, scale logarithmically with sliding velocity as in solid-like friction, and exhibit complex dependence on the filaments’ overlap length. We also show that a reduction of the frictional force by orders of magnitude, associated with a transition from solid-like friction to Stokes’s drag, can be induced by coating F-actin with polymeric brushes. Furthermore, we observe similar transitions in filamentous microtubules and bacterial flagella. Our findings demonstrate how altering a filament’s elasticity, structure and interactions can be used to engineer interfilament friction and thus tune the properties of fibrous composite materials.
  32. Oscillation of the velvet worm slime jet by passive hydrodynamic instability A. Concha, P. Mellado, B. Morera-Brenes, C.S. Costa, L. Mahadevan and J. Monge-Najera,  Nature Communications  6, 6292, 2015.
    [View PDF] [Download PDF] The rapid squirt of a proteinaceous slime jet endows velvet worms (Onychophora) with a unique mechanism for defence from predators and for capturing prey by entangling them in a disordered web that immobilizes their target. However, to date, neither qualitative nor quantitative descriptions have been provided for this unique adaptation. Here we investigate the fast oscillatory motion of the oral papillae and the exiting liquid jet that oscillates with frequencies fB30–60 Hz. Using anatomical images, high-speed videography, theoretical analysis and a physical simulacrum, we show that this fast oscillatory motion is the result of an elastohydrodynamic instability driven by the interplay between the elasticity of oral papillae and the fast unsteady flow during squirting. Our results demonstrate how passive strategies can be cleverly harnessed by organisms, while suggesting future oscillating microfluidic devices, as well as novel ways for micro and nanofibre production using bioinspired strategies.
  33. Elastocapillary coalescence of plates and pillars Z. Wei, T. M. Schneider, J. Kim, H.-Y. Kim, J. Aizenberg and L. Mahadevan,  Proceedings of the Royal Society (A)  471,20140593, 2015.
    [View PDF] [Download PDF] When a fluid-immersed array of supported plates or pillars is dried, evaporation leads to the formation of menisci on the tips of the plates or pillars that bring them together to form complex patterns. Building on prior experimental observations, we use a combination of theory and computation to understand the nature of this instability and its evolution in both the two- and three-dimensional setting of the problem. For the case of plates, we explicitly derive the interaction torques based on the relevant physical parameters associated with pillar deformation, contact-line pinning/depinning and fluid volume changes. A Bloch-wave analysis for our periodic mechanical system captures the window of volumes where the two-plate eigenvalue characterizes the onset of the coalescence instability. We then study the evolution of these binary clusters and their eventual elastic arrest using numerical simulations that account for evaporative dynamics coupled to capillary coalescence. This explains both the formation of hierarchical clusters and the sensitive dependence of the final structures on initial perturbations, as seen in our experiments. We then generalize our analysis to treat the problem of pillar collapse in three dimensions, where the fluid domain is completely connected and the interface is a minimal surface with the uniform mean curvature. Our theory and simulations capture the salient features of experimental observations in a range of different situations and may thus be useful in controlling the ensuing patterns.
  34. Exactly isochoric deformations of soft solids John S. Biggins, Z. Wei and L. Mahadevan,  Europhysics Letters  108, 64001, 2014.
    [View PDF] [Download PDF] Many materials of contemporary interest, such as gels, biological tissues and elastomers, are easily deformed but essentially incompressible. Traditional linear theory of elasticity implements incompressibility only to first order and thus permits some volume changes, which become problematically large even at very small strains. Using a mixed coordinate transformation originally due to Gauss, we enforce the constraint of isochoric deformations exactly to develop a linear theory with perfect volume conservation that remains valid until strains become geometrically large. We demonstrate the utility of this approach by calculating the response of an infinite soft isochoric solid to a point force that leads to a nonlinear generalization of the Kelvin solution. Our approach naturally generalizes to a range of problems involving deformations of soft solids and interfaces in two-dimensional and axisymmetric geometries, which we exemplify by determining the solution to a distributed load that mimics muscular contraction within the bulk of a soft solid.
  35. Neuromimetic Circuits with Synaptic Devices Based on Strongly Correlated Electron Systems Sieu D. Ha, Jian Shi, Yasmine Meroz, L. Mahadevan, and Shriram Ramanathan,  Physical Review Applied 2 , 064003, 2014.
    [DOI] [View PDF] [Download PDF] Many materials of contemporary interest, such as gels, biological tissues and elastomers, are easily deformed but essentially incompressible. Traditional linear theory of elasticity implements incompressibility only to first order and thus permits some volume changes, which become problematically large even at very small strains. Using a mixed coordinate transformation originally due to Gauss, we enforce the constraint of isochoric deformations exactly to develop a linear theory with perfect volume conservation that remains valid until strains become geometrically large. We demonstrate the utility of this approach by calculating the response of an infinite soft isochoric solid to a point force that leads to a nonlinear generalization of the Kelvin solution. Our approach naturally generalizes to a range of problems involving deformations of soft solids and interfaces in two-dimensional and axisymmetric geometries, which we exemplify by determining the solution to a distributed load that mimics muscular contraction within the bulk of a soft solid.
  36. Drops can bounce from perfectly hydrophilic surfaces J. M. Kolinski, L. Mahadevan and S. M. Rubinstein,  Europhysics Letters  108, 24001, 2014.
    [DOI] [View PDF] [Download PDF] Drops are well known to rebound from superhydrophobic surfaces and from liquid surfaces. Here, we show that drops can also rebound from a superhydrophilic solid surface such as an atomically smooth mica sheet. However, the coefficient of restitution CR associated with this process is significantly lower than that associated with rebound from superhydrophobic surfaces. A direct imaging method allows us to characterize the dynamics of the deformation of the drop in entering the vicinity of the surface. We find that drop bouncing occurs without the drop ever touching the solid and there is a nanometer-scale film of air that separates the liquid and solid, suggesting that shear in the air film is the dominant source of dissipation during rebound. Furthermore, we see that any discrete nanometer-height defects on an otherwise hydrophilic surface, such as treated glass, completely inhibits the bouncing of the drop, causing the liquid to wet the surface. Our study adds a new facet to the dynamics of droplet impact by emphasizing that the thin film of air can play a role not just in the context of splashing but also bouncing, while highlighting the role of rare surface defects in inhibiting this response.
  37. Evaporative microclimate driven hygrometers and hygromotors J.Y. Chung, H. King and L. Mahadevan,  Europhysics Letters  107, 64002, 2014.
    [View PDF] [Download PDF] A strip of paper placed on a hand spontaneously curls upwards. This simple observation illustrates the ability of a relatively homogeneous hygroscopic structural material, paper, to sense and respond to the microclimate near a non-equilibrium system, a moist evaporative boundary layer. We quantify this interaction using a simple experiment and show that it can be understood in terms of a minimal model. A small modification of this paper hygrometer that makes one or another surface partly hydrophobic using a crayon or tape allows us to create a hygro-oscillator or a hygromotor that converts transverse moisture gradients into lateral oscillations or directed motion. Our study shows how treating paper as a responsive structural material allows us to extract information and work from a microclimatic boundary layer, transforming a messenger to a machine.
  38. Scaling macroscopic aquatic locomotion M. Gazzola, M. Argentina and L. Mahadevan,  Nature Physics , 10, 758-61, 2014.
    [ONLINE ARTICLE] [View PDF] [Download PDF] Inertial aquatic swimmers that use undulatory gaits range in length L from a few millimetres to 30 metres, across a wide array of biological taxa. Using elementary hydrodynamic arguments, we uncover a unifying mechanistic principle characterizing their locomotion by deriving a scaling relation that links swimming speed U to body kinematics (tail beat amplitude A and frequency ω) and fluid properties (kinematic viscosity ν). This principle can be simply couched as the power law Re ∼ Swα, where Re = UL/ν ≫ 1 and Sw = ω AL/ν, with α = 4/3 for laminar flows, and α = 1 for turbulent flows. Existing data from over 1,000 measurements on fish, amphibians, larvae, reptiles, mammals and birds, as well as direct numerical simulations are consistent with our scaling. We interpret our results as the consequence of the convergence of aquatic gaits to the performance limits imposed by hydrodynamics.
  39. Gyrification from constrained cortical expansion T. Tallinen, J.Y. Chung, J.S. Biggins, and L. Mahadevan,  Proceedings of the National Academy of Sciences (USA) , 111, 35:12667-12672, 2014.
    [View PDF] [Download PDF] The exterior of the mammalian brain—the cerebral cortex—has a conserved layered structure whose thickness varies little across species. However, selection pressures over evolutionary time scales have led to cortices that have a large surface area to volume ratio in some organisms, with the result that the brain is strongly convoluted into sulci and gyri. Here we show that the gyrification can arise as a nonlinear consequence of a simple mechanical instability driven by tangential expansion of the gray matter constrained by the white matter. A physical mimic of the process using a layered swelling gel captures the essence of the mechanism, and numerical simulations of the brain treated as a soft solid lead to the formation of cusped sulci and smooth gyri similar to those in the brain. The resulting gyrification patterns are a function of relative cortical expansion and relative thickness (compared with brain size), and are consistent with observations of a wide range of brains, ranging from smooth to highly convoluted. Furthermore, this dependence on two simple geometric parameters that characterize the brain also allows us to qualitatively explain how variations in these parameters lead to anatomical anomalies in such situations as polymicrogyria, pachygyria, and lissencephalia
  40. The dynamics of sperm cooperation in a competitive environment H.S. Fisher, L. Giomi, H.E. Hoekstra and L. Mahadevan,  Proceedings of the Royal Society (B) , 281, 20140296, 2014.
    [View PDF] [Download PDF] Sperm cooperation has evolved in a variety of taxa and is often considered a response to sperm competition, yet the benefit of this form of collective movement remains unclear. Here, we use fine-scale imaging and a minimal mathematical model to study sperm aggregation in the rodent genus Peromyscus. We demonstrate that as the number of sperm cells in an aggregate increase, the group moves with more persistent linearity but without increasing speed. This benefit, however, is offset in larger aggregates as the geometry of the group forces sperm to swim against one another. The result is a nonmonotonic relationship between aggregate size and average velocity with both a theoretically predicted and empirically observed optimum of six to seven sperm per aggregate. To understand the role of sexual selection in driving these sperm group dynamics, we compared two sister-species with divergent mating systems. We find that sperm of Peromyscus maniculatus (highly promiscuous), which have evolved under intense competition, form optimal-sized aggregates more often than sperm of Peromyscus polionotus (strictly monogamous), which lack competition. Our combined mathematical and experimental study of coordinated sperm movement reveals the importance of geometry, motion and group size on sperm velocity and suggests how these physical variables interact with evolutionary selective pressures to regulate cooperation in competitive environments.
  41. A proprioceptive neuromechanical theory of crawling P. Paoletti and L. Mahadevan,  Proceedings of the Royal Society (B) , 281, 20141092, 2014.
    [View PDF] [Download PDF] The locomotion of many soft-bodied animals is driven by the propagation of rhythmic waves of contraction and extension along the body. These waves are classically attributed to globally synchronized periodic patterns in the nervous system embodied in a central pattern generator (CPG). However, in many primitive organisms such as earthworms and insect larvae, the evidence for a CPG is weak, or even non-existent. We propose a neuromechanical model for rhythmically coordinated crawling that obviates the need for a CPG, by locally coupling the local neuro-muscular dynamics in the body to the mechanics of the body as it interacts frictionally with the substrate. We analyse our model using a combination of analytical and numerical methods to determine the parameter regimes where coordinated crawling is possible and compare our results with experimental data. Our theory naturally suggests mechanisms for how these movements might arise in developing organisms and how they are maintained in adults, and also suggests a robust design principle for engineered motility in soft systems.
  42. Continuum dynamics of elastocapillary coalescence and arrest Z. Wei and L. Mahadevan,  Europhysics Letters  106, 14002, 2014.
    [View PDF] [Download PDF] The surface-tension–driven coalescence of wet hair, nano-pillars and supported lamellae immersed in an evaporating liquid is eventually arrested elastically. To characterize this at a continuum level, we start from a discrete microscopic model of the process and derive a mesoscopic theory that couples the inhomogeneous dynamics of drying to the capillary forcing and elastic bending of the lamellae. Numerical simulations of the resulting partial differential equation capture the primary unstable mode seen in experiments, and the dynamic coalescence of the lamellae into dimers and quadrimers. Our theory also predicts the elastic arrest of the pattern or the separation of lamellar bundles into their constituents as a function of the amount of liquid left at the end of the process.
  43. Density-gradient-free microfluidic centrifugation for analytical and preparative separation of nanoparticles P. Arosio, T. Müller, L. Mahadevan, and T.P.J. Knowles,  Nano Letters , 14, 2365-71, 2014.
    [View PDF] [Download PDF] Sedimentation and centrifugation techniques are widely applied for the separation of biomolecules and colloids but require the presence of controlled density gradients for stable operation. Here we present an approach for separating nanoparticles in free solution without gradients. We use microfluidics to generate a convective flow perpendicular to the sedimentation direction. We show that the hydrodynamic Rayleigh−Taylor-like instability, which, in traditional methods, requires the presence of a density gradient, can be suppressed by the Poiseuille flow in the microchannel. We illustrate the power of this approach by demonstrating the separation of mixtures of particles on the nanometer scale, orders of magnitude smaller than the micrometer-sized objects separated by conventional inertial microfluidic approaches. This technique exhibits a series of favorable features including short analysis time, small sample volume, limited dilution of the analyte, limited interactions with surfaces as well as the possibility to tune easily the separation range by adjusting the geometry of the system. These features highlight the potential of gradient-free microfluidic centrifugation as an attractive route toward a broad range of nanoscale applications
  44. Models for elastic shells with incompatible strains M. Lewicka, L. Mahadevan and M.R. Pakzad,  Proceedings of the Royal Society (A) , 470, 20130604, 2014.
    [View PDF] [Download PDF] The three-dimensional shapes of thin lamina, such as leaves, flowers, feathers, wings, etc., are driven by the differential strain induced by the relative growth. The growth takes place through variations in the Riemannian metric given on the thin sheet as a function of location in the central plane and also across its thickness. The shape is then a consequence of elastic energy minimization on the frustrated geometrical object. Here, we provide a rigorous derivation of the asymptotic theories for shapes of residually strained thin lamina with non-trivial curvatures, i.e. growing elastic shells in both the weakly and strongly curved regimes, generalizing earlier results for the growth of nominally flat plates. The different theories are distinguished by the scaling of the mid-surface curvature relative to the inverse thickness and growth strain, and also allow us to generalize the classical Föppl–von Kármán energy to theories of prestrained shallow shells.
  45. Lift-off instability during the impact of a drop on a solid surface J.M. Kolinski, L. Mahadevan, and S.M. Rubinstein,  Physical Review Letters  112, 1334501, 2014.
    [View PDF] [Download PDF] We directly measure the rapid spreading dynamics succeeding the impact of a droplet of fluid on a solid, dry surface. Upon impact, the air separating the liquid from the solid surface fails to drain and wetting is delayed as the liquid rapidly spreads outwards over a nanometer thin film of air. We show that the approach of the spreading liquid front toward the surface is unstable and the spreading front lifts off away from the surface. Lift-off ensues well before the liquid contacts the surface, in contrast with prevailing paradigm where lift-off of the liquid is contingent on solid-liquid contact and the formation of a viscous boundary layer. Here we investigate the dynamics of liquid spreading over a thin film of air and its lift-off away from the surface over a large range of fluid viscosities and find that the lift-off instability is dependent on viscosity and occurs at a time that scales with the viscosity to the power of one half.
  46. Aging in complex interdependency networks D.C. Vural, G. Morrison, and L. Mahadevan,  Physical Review E  89, 022811, 2014.
    [View PDF] [Download PDF] Although species longevity is subject to a diverse range of evolutionary forces, the mortality curves of a wide variety of organisms are rather similar. Here we argue that qualitative and quantitative features of aging can be reproduced by a simple model based on the interdependence of fault-prone agents on one other. In addition to fitting our theory to the empiric mortality curves of six very different organisms, we establish the dependence of lifetime and aging rate on initial conditions, damage and repair rate, and system size. We compare the size distributions of disease and death and see that they have qualitatively different properties. We show that aging patterns are independent of the details of interdependence network structure, which suggests that aging is a many-body effect, and that the qualitative and quantitative features of aging are not sensitively dependent on the details of dependency structure or its formation.
  47. Dynamics of a nanodroplet under a transmission electron microscope F.Y. Leong, U.M. Mirsaidov, P. Matsudaira, and L. Mahadevan,  Physics of Fluids  26, 012003, 2014.
    [View PDF] [Download PDF] We investigate the cyclical stick-slip motion of water nanodroplets on a hydrophilic substrate viewed with and stimulated by a transmission electron microscope. Using a continuum long wave theory, we show how the electrostatic stress imposed by nonuniform charge distribution causes a pinned convex drop to deform into a toroidal shape, with the shape characterized by the competition between the electrostatic stress and the surface tension of the drop, as well as the charge density distribution which follows a Poisson equation. A horizontal gradient in the charge density creates a lateral driving force, which when sufficiently large, overcomes the pinning induced by surface heterogeneities in the substrate disjoining pressure, causing the drop to slide on the substrate via a cyclical stick-slip motion. Our model predicts steplike dynamics in drop displacement and surface area jumps, qualitatively consistent with experimental observations.
  48. Statistical mechanics and shape transitions in microscopic plates E.H. Yong and L. Mahadevan,  Physical Review Letters  112, 048101, 2014.
    [View PDF] [Download PDF] Unlike macroscopic multistable mechanical systems such as snap bracelets or elastic shells that must be physically manipulated into various conformations, microscopic systems can undergo spontaneous conformation switching between multistable states due to thermal fluctuations. Here we investigate the statistical mechanics of shape transitions in small elastic elliptical plates and shells driven by noise. By assuming that the effects of edges are small, which we justify exactly for plates and shells with a lenticular section, we decompose the shapes into a few geometric modes whose dynamics are easy to follow. We use Monte Carlo simulations to characterize the shape transitions between conformational minimal as a function of noise strength, and corroborate our results using a Fokker-Planck formalism to study the stationary distribution and the mean first passage time problem. Our results are applicable to objects such as graphene flakes or protein β sheets, where fluctuations, geometry, and finite size effects are important.
  49. Intermittent locomotion as an optimal control strategy P. Paoletti and L. Mahadevan,  Proceedings of the Royal Society (A) , 470, 20130535, 2014.
    [View PDF] [Download PDF] Birds, fish and other animals routinely use unsteady effects to save energy by alternating between phases of active propulsion and passive coasting. Here, we construct a minimal model for such behaviour that can be couched as an optimal control problem via an analogy to travelling with a rechargeable battery. An analytical solution of the optimal control problem proves that intermittent locomotion has lower energy requirements relative to steady-state strategies. Additional realistic hypotheses, such as the assumption that metabolic cost at a given power should be minimal (the fixed gear hypothesis), a nonlinear dependence of the energy storage rate on propulsion and/or a preferred average speed, allow us to generalize the model and demonstrate the flexibility of intermittent locomotion with implications for biological and artificial systems.
  50. Bacillus spores as building blocks for stimuli-responsive materials and nanogenerators X. Chen, L. Mahadevan, A. Driks and O. Sahin,  Nature Nanotechnology , 9, 137-141, 2014.
    [View PDF] [Download PDF] Materials that respond mechanically to external chemical stimuli have applications in biomedical devices, adaptive architectural systems, robotics and energy harvesting1–5. Inspired by biological systems, stimuli-responsive materials have been created that can oscillate2, transport fluid3, provide homeostasis4 and undergo complex changes in shape5. However, the effectiveness of synthetic stimuli-responsive materials in generating work is limited when compared with mechanical actuators6. Here, we show that the mechanical response of Bacillus spores to water gradients exhibits an energy density of more than 10 MJ m23 , which is two orders of magnitude higher than synthetic water-responsive materials7,8. We also identified mutations that can approximately double the energy density of the spores and found that they can self-assemble into dense, submicrometre-thick monolayers on substrates such as silicon microcantilevers and elastomer sheets, creating bio-hybrid hygromorph actuators9,10. To illustrate the potential applications of the spores, we used them to build an energy-harvesting device that can remotely generate electrical power from an evaporating body of water
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