Explore the vast range of titles available.

Muscle is a complex, hierarchically organized, soft contractile engine. To understand the limits on the rate of contraction and muscle energetics, we construct a coarse-grained multiscale model that describes muscle as an active sponge. Our analysis of existing experiments across species and muscle types highlights the importance of spatially heterogeneous strains and local volumetric deformations. Our minimal theoretical model shows how contractions induce intracellular fluid flow and power active hydraulic oscillations, yielding the limits of ultrafast muscular contractions. We further demonstrate that the viscoelastic response of muscle is naturally non-reciprocal—or odd—owing to its active and anisotropic nature. This enables an alternate mode of muscular power generation from periodic cycles in spatial strain alone, contrasting with previous descriptions based on temporal cycles. Our work suggests a revised view of muscle dynamics that emphasizes the multiscale spatiotemporal origins of soft hydraulic power, with potential implications for physiology, biomechanics and locomotion. A multiscale model of muscle as a fluid-filled sponge suggests that hydraulics limits rapid contractions and that the mechanical response of muscle is non-reciprocal.

Nonlinear inertial flows usually influence the motion of swimming organisms, but most studies focus on the tractable case of swimmers too small to feel such effects. A mechanistic principle now unifies the varied dynamics of macroscopic swimmers. 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 ∼ Sw α , 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.

We consider the motion of a fluid-immersed negatively buoyant particle in the vicinity of a thin compressible elastic wall, a situation that arises in a variety of technological and natural settings. We use scaling arguments to establish different regimes of sliding, and complement these estimates using thin-film lubrication dynamics to determine an asymptotic theory for the sedimentation, sliding and spinning motions of a cylinder. The resulting theory takes the form of three coupled nonlinear singular-differential equations. Numerical integration of the resulting equations confirms our scaling relations and further yields a range of unexpected behaviours. Despite the low-Reynolds-number feature of the flow, we demonstrate that the particle can spontaneously oscillate when sliding, can generate lift via a Magnus-like effect, can undergo a spin-induced reversal effect and also shows an unusual sedimentation singularity. Our description also allows us to address a sedimentation–sliding transition that can lead to the particle coasting over very long distances, similar to certain geophysical phenomena. Finally, we show that a small modification of our theory allows us to generalize the results to account for additional effects such as wall poroelasticity.

A 3D-printed fetal brain undergoes constrained expansion to reproduce the shape of the human cerebral cortex. The soft gels of the model swell in solvent, mimicking cortical growth and revealing the mechanical origin of the brain’s folded geometry. The rapid growth of the human cortex during development is accompanied by the folding of the brain into a highly convoluted structure 1 , 2 , 3 . Recent studies have focused on the genetic and cellular regulation of cortical growth 4 , 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 brain 9 , 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.

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

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 difficulty of realizing these geometric structures by quantifying the energetic barrier that separates the metastable flat and folded states. Moreover, we characterize the trade-off between the accuracy to which the pattern conforms to the target surface, and the effort 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. Elementary geometric constructions and constrained optimization algorithms can be used to fit origami tessellations to any curved surface.

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

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.

Inspired by the differential-growth-driven morphogenesis of leaves, flowers, and other tissues, there is increasing interest in artificial analogs of these shape-shifting thin sheets made of active materials that respond to environmental stimuli such as heat, light, and humidity. But how can we determine the growth patterns to achieve a given shape from another shape? We solve this geometric inverse problem of determining the growth factors and directions (the metric tensors) for a given isotropic elastic bilayer to grow into a target shape by posing and solving an elastic energy minimization problem. A mathematical equivalence between bilayers and curved monolayers simplifies the inverse problem considerably by providing algebraic expressions for the growth metric tensors in terms of those of the final shape. This approach also allows us to prove that we can grow any target surface from any reference surface using orthotropically growing bilayers. We demonstrate this by numerically simulating the growth of a flat sheet into a face, a cylindrical sheet into a flower, and a flat sheet into a complex canyon-like structure.

Materials that respond mechanically to external chemical stimuli have applications in biomedical devices, adaptive architectural systems, robotics and energy harvesting 1 , 2 , 3 , 4 , 5 . Inspired by biological systems, stimuli-responsive materials have been created that can oscillate 2 , transport fluid 3 , provide homeostasis 4 and undergo complex changes in shape 5 . However, the effectiveness of synthetic stimuli-responsive materials in generating work is limited when compared with mechanical actuators 6 . Here, we show that the mechanical response of Bacillus spores to water gradients exhibits an energy density of more than 10 MJ m −3 , which is two orders of magnitude higher than synthetic water-responsive materials 7 , 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 actuators 9 , 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. Bacillus spores can be used to assemble water-responsive materials with high energy densities and to create energy-harvesting devices that can generate electrical power from an evaporating body of water.