1. Collective thermoregulation in bee clusters S. Ocko and L. Mahadevan,  Journal of the Royal Society - Interface  11, 20131033, 2014.
    [View PDF] [Download PDF] Swarming is an essential part of honeybee behaviour. When a fertilized queen leaves the hive she takes a swarm of bees with her to start a new colony. Up to 20000 bees might accompany a newly fertilised queen bee on her quest. These bees usually form a cluster and cling to each other for several days whilst scouts leave to search for a new home to relocate to. The bees, exposed to the outside temperature, are at risk of getting too cold but in their tightly packed cluster they may also become too hot.
  2. Flagellar dynamics of a connected chain of active, polar, Brownian particles R. Chelakkot, A. Gopinath, L. Mahadevan and M.F. Hagan,  Journal of the Royal Society - Interface  11, 20130884, 2014.
    [View PDF] [Download PDF] We show that active, self-propelled particles that are connected together to form a single chain that is anchored at one end can produce the graceful beating motions of flagella. Changing the boundary condition from a clamp to a pivot at the anchor leads to steadily rotating tight coils. Strong noise in the system disrupts the regularity of the oscillations. We use a combination of detailed numerical simulations, mean-field scaling analysis and first passage time theory to characterize the phase diagram as a function of the filament length, passive elasticity, propulsion force and noise. Our study suggests minimal experimental tests for the onset of oscillations in an active polar chain.
  3. How a blister heals J.E. Longley, L. Mahadevan and M.K. Chaudhury  Europhysics Letters , 104, 46002, 2013.
    [View PDF] [Download PDF] We use experiments to study the dynamics of the healing of a blister, a localized bump in a thin elastic layer that is adhered to a soft substrate everywhere except at the bump. We create a blister by gently placing a glass cover slip on a PDMS substrate. The pressure jump across the elastic layer drives fluid flow through micro-channels that form at the interface between the layer and the substrate; these channels coalesce at discrete locations as the blister heals and eventually disappear at a lower critical radius. The spacing of the channel follows a simple scaling law that can be theoretically justified, and the kinetics of healing is rate limited by fluid flow, but with a non-trivial dependence on the substrate thickness that likely arises due to channelization. Our study is relevant to a variety of soft adhesion scenarios.
  4. Biased migration of confined neutrophil-like cells in asymmetric hydraulic environments H.V. Prentice-Mott, C-H Chang, L. Mahadevan, T.J. Mitchison, D. Irimia, and J.V. Shah  Proceedings of the National Academy of Sciences (USA) , 110, 21006-21110, 2013.
    [View PDF] [Download PDF] Cells integrate multiple measurement modalities to navigate their environment. Soluble and substrate-bound chemical gradients and physical cues have all been shown to influence cell orientation and migration. Here we investigate the role of asymmetric hydraulic pressure in directional sensing. Cells confined in microchannels identified and chose a path of lower hydraulic resistance in the absence of chemical cues. In a bifurcating channel with asymmetric hydraulic resistances, this choice was preceded by the elaboration of two leading edges with a faster extension rate along the lower resistance channel. Retraction of the “losing” edge appeared to precipitate a final choice of direction. The pressure differences altering leading edge protrusion rates were small, suggesting weak force generation by leading edges. The response to the physical asymmetry was able to override a dynamically generated chemical cue. Motile cells may use this bias as a result of hydraulic resistance, or “barotaxis,” in concert with chemotaxis to navigate complex environments.
  5. Quantifying cell-generated mechanical forces within living embryonic tissues O. Campàs, T. Mammoto, S. Hasso, R.A. Sperling, D. O’Connell, A.G. Bischof, R. Maas, D.A. Weitz, L. Mahadevan & D.E. Ingber  Nature Methods , 183-189, 2013.
    [View PDF] [Download PDF] Cell-generated mechanical forces play a critical role during tissue morphogenesis and organ formation in the embryo. Little is known about how these forces shape embryonic organs, mainly because it has not been possible to measure cellular forces within developing three-dimensional (3D) tissues in vivo. We present a method to quantify cell-generated mechanical stresses exerted locally within living embryonic tissues, using fluorescent, cell-sized oil microdroplets with defined mechanical properties and coated with adhesion receptor ligands. After a droplet is introduced between cells in a tissue, local stresses are determined from droplet shape deformations, measured using fluorescence microscopy and computerized image analysis. Using this method, we quantified the anisotropic stresses generated by mammary epithelial cells cultured within 3D aggregates, and we confirmed that these stresses (3.4 nN mm−2) are dependent on myosin II activity and are more than twofold larger than stresses generated by cells of embryonic tooth mesenchyme, either within cultured aggregates or in developing whole mouse mandibles.
  6. Elastic platonic shells E.H. Yong, D.R. Nelson, and L. Mahadevan  Physical Review Letters , 111, 177801, 2013.
    [View PDF] [Download PDF] On microscopic scales, the crystallinity of flexible tethered or cross-linked membranes determines their mechanical response. We show that by controlling the type, number, and distribution of defects on a spherical elastic shell, it is possible to direct the morphology of these structures. Our numerical simulations show that by deflating a crystalline shell with defects, we can create elastic shell analogs of the classical platonic solids. These morphologies arise via a sharp buckling transition from the sphere which is strongly hysteretic in loading or unloading. We construct a minimal Landau theory for the transition using quadratic and cubic invariants of the spherical harmonic modes. Our approach suggests methods to engineer shape into soft spherical shells using a frozen defect topology
  7. How ticks get under your skin: insertion mechanics of the feeding apparatus of Ixodes ricinus ticks D. Richter, F-R. Matuschka, A. Spielman, and L. Mahadevan  Proceedings of the Royal Society B,  280, 20131758, 2013.
    [View PDF] [Download PDF] The tick Ixodes ricinus uses its mouthparts to penetrate the skin of its host and to remain attached for about a week, during which time Lyme disease spirochaetes may pass from the tick to the host. To understand how the tick achieves both tasks, penetration and attachment, with the same set of implements, we recorded the insertion events by cinematography, interpreted the mouthparts’ function by scanning electron microscopy and identified their points of articulation by confocal microscopy. Our structural dynamic observations suggest that the process of insertion and attachment occurs via a ratchet-like mechanism with two distinct stages. Initially, the two telescoping chelicerae pierce the skin and, by moving alternately, generate a toehold. Subsequently, a breaststroke-like motion, effected by simultaneous flexure and retraction of both chelicerae, pulls in the barbed hypostome. This combination of a flexible, dynamic mechanical ratchet and a static holdfast thus allows the tick to solve the problem of how to penetrate skin and also remain stuck for long periods of time.
  8. Villification: how the gut gets its villi A. Shyer, T. Tallinen, N. Nerurkar, Z. Wei, E. Kim, D. Kaplan, C. and L. Mahadevan  Science,  342, 212-218, 2013.
    [View PDF] [Download PDF] The villi of the human and chick gut are formed in similarstepwise progressions, wherein the mesenchyme and attached epithelium first fold into longitudinal ridges, then a zigzag pattern, and lastly individual villi. We find that these steps of villification depend on the sequential differentiation of the distinct smooth muscle layers of the gut, which restrict the expansion of the growing endoderm and mesenchyme, generating compressive stresses that lead to their buckling and folding. A quantitative computational model, incorporating measured properties of the developing gut, recapitulates the morphological patterns seen during villification in a variety of species. These results provide a mechanistic understanding of the formation of these elaborations of the lining of the gut, essential for providing sufficient surface area for nutrient absorption.
  9. Digital instability of a confined elastic meniscus J.S. Biggins, B. Saintyves, Z. Wei, E. Bouchard, and L. Mahadevan  Proceedings of the National Academy of Sciences (USA) , 110, 12545-12548, 2013.
    [View PDF] [Download PDF] Thin soft elastic layers serving as joints between relatively rigid bodies may function as sealants, thermal, electrical, or mechanical insulators, bearings, or adhesives. When such a joint is stressed, even though perfect adhesion is maintained, the exposed free meniscus in the thin elastic layer becomes unstable, leading to the formation of spatially periodic digits of air that invade the elastic layer, reminiscent of viscous fingering in a thin fluid layer. However, the elastic instability is reversible and rate-independent, disappearing when the joint is unstressed. We use theory, experiments, and numerical simulations to show that the transition to the digital state is sudden (first-order), the wavelength and amplitude of the fingers are proportional to the thickness of the elastic layer, and the required separation to trigger the instability is inversely proportional to the in-plane dimension of the layer. Our study reveals the energetic origin of this instability and has implications for the strength of polymeric adhesives; it also suggests a method for patterning thin films reversibly with any arrangement of localized fingers in a digital elastic memory, which we confirm experimentally.
  10. A pendulum in a flowing soap film M.M. Bandi, A. Concha, R. Wood, and L. Mahadevan, Physics of Fluids, 25, 041702, 2013.
    [View PDF] [Download PDF] We consider the dynamics of a pendulum made of a rigid ring attached to an elastic filament immersed in a flowing soap film. The system shows an oscillatory instability whose onset is a function of the flow speed, length of the supporting string, the ring mass, and ring radius. We characterize this system and show that there are different regimes where the frequency is dependent or independent of the pendulum length depending on the relative magnitude of the added-mass. Although the system is an infinite-dimensional, we can explain many of our results in terms of a one degree-of-freedom system corresponding to a forced pendulum. Indeed, using the vorticity measured via particle imaging velocimetry allows us to make the model quantitative, and a comparison with our experimental results shows we can capture the basic phenomenology of this system.
  11. Geometric mechanics of periodic pleated origami Z.Y. Wei, Z.V. Guo, L. Dudte, H.Y. Liang, and L. Mahadevan, Physical Review Letters, 110, 215501, 2013 .
    [View PDF] [Download PDF] Origami structures are mechanical metamaterials with properties that arise almost exclusively from the geometry of the constituent folds and the constraint of piecewise isometric deformations. Here we characterize the geometry and planar and nonplanar effective elastic response of a simple periodically folded Miura-ori structure, which is composed of identical unit cells of mountain and valley folds with four-coordinated ridges, defined completely by two angles and two lengths. We show that the in-plane and out-of-plane Poisson’s ratios are equal in magnitude, but opposite in sign, independent of material properties. Furthermore, we show that effective bending stiffness of the unit cell is singular, allowing us to characterize the two-dimensional deformation of a plate in terms of a one-dimensional theory. Finally, we solve the inverse design problem of determining the geometric parameters for the optimal geometric and mechanical response of these extreme structures
  12. Rationally designed complex, hierarchical microarchitectures W.L. Noorduin, A. Grinthal, L. Mahadevan, J. Aizenberg. Science, 340, 832-837.
    [View PDF] [Download PDF] The emergence of complex nano- and microstructures is of fundamental interest, and the ability to program their form has practical ramifications in fields such as optics, catalysis, and electronics. We developed carbonate-silica microstructures in a dynamic reaction-diffusion system that allow us to rationally devise schemes for precisely sculpting a great variety of elementary shapes by diffusion of carbon dioxide (CO2) in a solution of barium chloride and sodium metasilicate. We identify two distinct growth modes and show how continuous and discrete modulations in CO2 concentration, pH, and temperature can be used to deterministically switch between different regimes and create a bouquet of hierarchically assembled multiscale microstructures with unprecedented levels of complexity and precision. These results outline a nanotechnology strategy for “collaborating” with self-assembly processes in real time to build arbitrary tectonic architectures.
  13. Adaptive fluid-infused porous films with tunable transparency and wettability X. Yao, Y. Hu, A. Grinthal, T-S. Wong, L. Mahadevan and J. Aizenberg, Nature Materials, 12, 529-34, 2013 .
    [View PDF] [Download PDF] Materials that adapt dynamically to environmental changes are currently limited to two-state switching of single properties, and only a small number of strategies that may lead to materials with continuously adjustable characteristics have been reported1–3 . Here we introduce adaptive surfaces made of a liquid film supported by a nanoporous elastic substrate. As the substrate deforms, the liquid flows within the pores, causing the smooth and defect-free surface to roughen through a continuous range of topographies. We show that a graded mechanical stimulus can be directly translated into finely tuned, dynamic adjustments of optical transparency and wettability. In particular, we demonstrate simultaneous control of the film’s transparency and its ability to continuously manipulate various low-surface-tension droplets from freesliding to pinned. This strategy should make possible the rational design of tunable, multifunctional adaptive materials for a broad range of applications.
  14. Hydrodynamics of hemostasis in sickle-cell disease S.I.A. Cohen and L. Mahadevan,  Physical Review Letters 110, 138104, 2013.
    [View PDF] [Download PDF] Vaso-occlusion, the stoppage of blood flow in sickle-cell disease, is a complex dynamical process spanning multiple time and length scales. Motivated by recent ex vivo microfluidic measurements of hemostasis using blood from sickle-cell patients, we develop a multiphase model that couples the kinetics and hydrodynamics of a flowing suspension of normal and sickled cells in a fluid. We use the model to derive expressions for the cell velocities and concentrations that quantify the hydrodynamics of hemostasis, and provide simple criteria as well as a phase diagram for occlusion, consistent with our simulations and earlier observations.
  15. Planar morphometry, shear and optimal quasi-conformal mappings G.W. Jones and L. Mahadevan,  Proceedings of the Royal Society (A) , 469, 20120653, 2013.
    [View PDF] [Download PDF] To characterize the diversity of planar shapes in such instances as insect wings and plant leaves, we present a method for the generation of a smooth morphometric mapping between two planar domains which matches a number of homologous points. Our approach tries to balance the competing requirements of a descriptive theory which may not reflect mechanism and a multi-parameter predictive theory that may not be well constrained by experimental data. Specifically, we focus on aspects of shape as characterized by local rotation and shear, quantified using quasi-conformal maps that are defined precisely in terms of these fields. To make our choice optimal, we impose the condition that the maps vary as slowly as possible across the domain, minimizing their integrated squared-gradient. We implement this algorithm numerically using a variational principle that optimizes the coefficients of the quasi-conformal map between the two regions and show results for the recreation of a sample historical grid deformation mapping of D’Arcy Thompson. We also deploy our method to compare a variety of Drosophila wing shapes and show that our approach allows us to recover aspects of phylogeny as marked by morphology
  16. Dissolution-driven convection in a Hele-Shaw cell A.C. Slim, M.M. Bandi, J.C. Miller, and L. Mahadevan,  Physics of Fluids , 25, 024101, 2013.
    [View PDF] [Download PDF] Motivated by convection in the context of geological carbon-dioxide (CO2) storage, we present an experimental study of dissolution-driven convection in a Hele–Shaw cell for Rayleigh numbers R in the range 100 < R < 1700. We use potassium permanganate (KMnO4) in water as an analog for CO2 in brine and infer concentration profiles at high spatial and temporal resolution and accuracy from transmitted light intensity. We describe behavior from first contact up to 65% average saturation and measure several global quantities including dissolution flux, average concentration, amplitude of perturbations away from pure one-dimensional diffusion, and horizontally averaged concentration profiles. We show that the flow evolves successively through distinct regimes starting with a simple one-dimensional diffusional profile. This is followed by linear growth in which fingers are initiated and grow quasiexponentially, independently of one-another. Once the fingers are well-established, a flux-growth regime begins as fresh fluid is brought to the interface and contaminated fluid removed, with the flux growing to a local maximum. During this regime, fingers still propagate independently. However, beyond the flux maximum, fingers begin to interact and zip together from the root down in a merging regime. Several generations of merging occur before only persistent primary fingers remain. Beyond this, the reinitiation regime begins with new fingers created between primary existing ones before merging into them. Through appropriate scaling, we show that the regimes are universal and independent of layer thickness (equivalently R) until the fingers hit the bottom. At this time, progression through these regimes is interrupted and the flow transitions to a saturating regime. In this final regime, the flux gradually decays in a manner well described by a Howard-style phenomenological model.
  17. Swarming, swirling and stasis in sequestered bristle-bots. L. Giomi, N. Hawley-Weld and L. Mahadevan,  Proceedings of the Royal Society (A), (2012),  469, 20120637.
    [View PDF] [Download PDF] The collective ability of organisms to move coherently in space and time is ubiquitous in any group of autonomous agents that can move and sense each other and the environment. Here, we investigate the origin of collective motion and its loss using macroscopic self-propelled bristle-bots, simple automata made from a toothbrush and powered by an onboard cell phone vibrator-motor, that can sense each other through shape-dependent local interactions, and can also sense the environment nonlocally via the effects of confinement and substrate topography. We show that when bristle-bots are confined to a limited arena with a soft boundary, increasing the density drives a transition from a disordered and uncoordinated motion to organized collective motion either as a swirling cluster or a collective dynamical stasis. This transition is regulated by a single parameter, the relative magnitude of spinning and walking in a single automaton. We explain this using quantitative experiments and simulations that emphasize the role of the agent shape, environment and confinement via boundaries. Our study shows how the behavioural repertoire of these physically interacting automatons controlled by one parameter translates into the mechanical intelligence of swarms.
  18. Surface sulci in squeezed soft solids T. Tallinen, J.S. Biggins, and L. Mahadevan,  Physical Review Letters , 110, 024302, 2013.
    [View PDF] [Download PDF] The squeezing of soft solids, the constrained growth of biological tissues, and the swelling of soft elastic solids such as gels can generate large compressive stresses at their surfaces. This causes the otherwise smooth surface of such a solid to become unstable when its stress exceeds a critical value. Previous analyses of the surface instability have assumed two-dimensional plane-strain conditions, but in experiments isotropic stresses often lead to complex three-dimensional sulcification patterns. Here we show how such diverse morphologies arise by numerically modeling the lateral compression of a rigidly clamped elastic layer. For incompressible solids, close to the instability threshold, sulci appear as I-shaped lines aligned orthogonally with their neighbors; at higher compressions they are Y-shaped and prefer a hexagonal arrangement. In contrast, highly compressible solids when squeezed show only one sulcified phase characterized by a hexagonal sulcus network.
  19. The cytoplasm of living cells behaves as a poroelastic material E. Moeendarbary, L. Valon, M. Fritzsche, A.R. Harris, D.A. Moulding, A.J. Thrasher, E. Stride, L. Mahadevan, and G.T. Charras,  Nature Materials , 12, 253-261, 2013.
    [View PDF] [Download PDF] The cytoplasm is the largest part of the cell by volume and hence its rheology sets the rate at which cellular shape changes can occur. Recent experimental evidence suggests that cytoplasmic rheology can be described by a poroelastic model, in which the cytoplasm is treated as a biphasic material consisting of a porous elastic solid meshwork (cytoskeleton, organelles, macromolecules) bathed in an interstitial fluid (cytosol). In this picture, the rate of cellular deformation is limited by the rate at which intracellular water can redistribute within the cytoplasm. However, direct supporting evidence for the model is lacking. Here we directly validate the poroelastic model to explain cellular rheology at short timescales using microindentation tests in conjunction with mechanical, chemical and genetic treatments. Our results show that water redistribution through the solid phase of the cytoplasm (cytoskeleton and macromolecular crowders) plays a fundamental role in setting cellular rheology at short timescales.
  20. Watching paint dry L. Mahadevan, Op-Ed,  The Harvard Undergraduate Research Journal , 5, 64, 2012.
    [View PDF] [Download PDF] “Vulgar and inactive minds confound familiarity with knowledge .... The scientist, who is not content with super!cial views, harasses himself with fruitless curiosity; and still, as he inquires more, perceives only that he knows less...”
  21. And the Ignobel goes to …. Joe Keller,  L. Mahadevan,  SIAM News , Dec. 2012.
    [View PDF] [Download PDF]
  22. Slicing softly with shear E. Reyssat, T. Tallinen, M. Le Merrer, and L. Mahadevan,  Physical Review Letters , 109, 244301, 2012.
    [View PDF] [Download PDF] Experienced chefs know that to make a neat cut in a boiled egg or a piece of cheese, a thin wire, or even a fine piece of thread, can work better than a knife. But even a blunt knife can cut soft solids well if it is rocked back and forth while applying a gentle pressure. Understanding the balance of forces needed to make a clean cut into deformable materials could be important for developing highly efficient techniques in industrial-scale food processing, or new tools for cutting biological tissue for analysis or during surgery. Writing in Physical Review Letters[1], Etienne Reyssat, at Harvard University, and colleagues provide an intriguing analysis of the cutting of soft solids, applying a combination of theory and experiments to pinpoint the role played by shear in facilitating the fracture of a highly deformable material.
  23. Elastic configurations of self-supported oxide membranes for fuel cells K. Kerman, T. Tallinen, S. Ramanathan, L. Mahadevan,  Journal of Power Sources , 222, 359-366, 2012.
    [View PDF] [Download PDF] Ultra-thin oxide films are of interest in energy conversion technologies such as low temperature solid oxide fuel cells and permeation membranes. Understanding their thermo-mechanical stability is an important problem. Edge clamped, self-supported thin film membranes show hierarchical wrinkles; with the largest wavelengths in the center, while smaller ones arise near the clamped boundary; correspondingly the largest strains, with tensile stress comparable to the residual stress, are in the vicinity of the clamped boundary. Our results can be understood by simple scaling arguments and are valid for membranes in the post-buckling regime far from threshold. We confirm the validity of our analysis by quantitative experimental comparison to self-supported, square micro-machined yttria-stabilized zirconia membranes of edge length 160 mm fabricated by lithography. The modeling and experiments combined provide a foundation for designing failure resistant self-supported membranes of interest to energy conversion. We show this by utilizing such membranes to fabricate thin film solid oxide fuel cells and demonstrate power generation utilizing natural gas as fuel at w400 C.
  24. The size, shape, and dynamics of cellular blebs F.Y. Lim, K-H. Chiam, L. Mahadevan,  Europhysics Letters , 100, 28004, 2012.
    [View PDF] [Download PDF] A cellular bleb grows when a portion of the cell membrane detaches from the underlying cortex under the influence of a cytoplasmic pressure. We develop a quantitative model for the growth and dynamics of these objects in a simple two-dimensional setting. In particular, we first find the minimum cytoplasmic pressure and minimum unsupported membrane length for a stationary bleb to nucleate and grow as a function of the membrane-cortex adhesion. We next show how a bleb may travel around the periphery of the cell when the cytoplasmic pressure varies in space and time in a prescribed way and find that the traveling speed is governed by the speed of the pressure change induced by local cortical contraction while the shape of the traveling bleb is governed by the speed of cortical healing. Finally, we relax the assumption that the pressure change is prescribed and couple it hydrodynamically to the cortical contraction and membrane deformation. By quantifying the phase space of bleb formation and dynamics, our framework serves to delineate the range and scope of bleb-associated cell motility.
  25. Macroscopic magnetic frustration P. Mellado, A. Concha, L. Mahadevan,  Physical Review Letters , 109, 257203, 2012.
    [View PDF] [Download PDF] A cellular bleb grows when a portion of the cell membrane detaches from the underlying cortex under the influence of a cytoplasmic pressure. We develop a quantitative model for the growth and dynamics of these objects in a simple two-dimensional setting. In particular, we first find the minimum cytoplasmic pressure and minimum unsupported membrane length for a stationary bleb to nucleate and grow as a function of the membrane-cortex adhesion. We next show how a bleb may travel around the periphery of the cell when the cytoplasmic pressure varies in space and time in a prescribed way and find that the traveling speed is governed by the speed of the pressure change induced by local cortical contraction while the shape of the traveling bleb is governed by the speed of cortical healing. Finally, we relax the assumption that the pressure change is prescribed and couple it hydrodynamically to the cortical contraction and membrane deformation. By quantifying the phase space of bleb formation and dynamics, our framework serves to delineate the range and scope of bleb-associated cell motility.
  26. Geometric mechanics of curved crease origami M.A. Dias, L.H. Dudte, L. Mahadevan, C.D. Santangelo,  Physical Review Letters , 109, 114301, 2012.
    [View PDF] [Download PDF] Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical frustration. We quantify this shape in terms of the radius of the circle, the dihedral angle of the fold, and the mechanical properties of the sheet of paper and the fold itself. When the sheet is isometrically deformed everywhere except along the fold itself, stiff folds result in creases with constant curvature and oscillatory torsion. However, relatively softer folds inherit the broken symmetry of the buckled shape with oscillatory curvature and torsion. Our asymptotic analysis of the isometrically deformed state is corroborated by numerical simulations that allow us to generalize our analysis to study structures with multiple curved creases.
  27. Strategies for cell shape control in the tip-growing cells O. Campas, E. Rojas, J. Dumais, and L. Mahadevan,  American Journal of Botany  99(9):1577–1582, 2012.
    [View PDF] [Download PDF] Despite the large diversity in biological cell morphology, the processes that specify and control cell shape are not yet fully understood. Here we study the shape of tip-growing, walled cells, which have evolved a polar mode of cell morphogenesis leading to characteristic fi lamentous cell morphologies that extend only apically.
  28. How the cucumber tendril coils and overwinds S.J. Gerbode, J.R. Puzey, A.G. McCormick, L. Mahadevan,  Science  337, 1087, 2012.
    [View PDF] [Download PDF] The helical coiling of plant tendrils has fascinated scientists for centuries, yet the underlying mechanism remains elusive. Moreover, despite Darwin’s widely accepted interpretation of coiled tendrils as soft springs, their mechanical behavior remains unknown. Our experiments on cucumber tendrils demonstrate that tendril coiling occurs via asymmetric contraction of an internal fiber ribbon of specialized cells. Under tension, both extracted fiber ribbons and old tendrils exhibit twistless overwinding rather than unwinding, with an initially soft response followed by strong strain-stiffening at large extensions. We explain this behavior using physical models of prestrained rubber strips, geometric arguments, and mathematical models of elastic filaments. Collectively, our study illuminates the origin of tendril coiling, quantifies Darwin’s original proposal, and suggests designs for biomimetic twistless springs with tunable mechanical responses.
  29. Physical basis for the adaptive flexibility of bacillus spore coats O. Sahin, E-H Yong, A. Driks and L. Mahadevan,  Journal of the Royal Society - Interface,  9, 3156-3160, 2012.
    [View PDF] [Download PDF] Bacillus spores are highly resistant dormant cells formed in response to starvation. The spore is surrounded by a structurally complex protein shell, the coat, which protects the genetic material. In spite of its dormancy, once nutrient is available (or an appropriate physical stimulus is provided) the spore is able to resume metabolic activity and return to vegetative growth, a process requiring the coat to be shed. Spores dynamically expand and contract in response to humidity, demanding that the coat be flexible. Despite the coat’s critical biological functions, essentially nothing is known about the design principles that allow the coat to be tough but also flexible and, when metabolic activity resumes, to be efficiently shed. Here, we investigated the hypothesis that these apparently incompatible characteristics derive from an adaptive mechanical response of the coat. We generated a mechanical model predicting the emergence and dynamics of the folding patterns uniformly seen in Bacillus spore coats. According to this model, spores carefully harness mechanical instabilities to fold into a wrinkled pattern during sporulation. Owing to the inherent nonlinearity in their formation, these wrinkles persist during dormancy and allow the spore to accommodate changes in volume without compromising structural and biochemical integrity. This characteristic of the spore and its coat may inspire design of adaptive materials.
  30. Deformation and capillary self-repair of carbon nanotube brushes V. Pushparaj, L. Mahadevan, S. Sreekala, L. Ci, R. Nalamasu, P.M. Ajayan.  Carbon , 50, 5618-5630, 2012.
    [View PDF] [Download PDF] Brushes with nanoscale bristles, such as nanotube arrays held together by van der Waals forces, have applications as compliant electrical switches, probes and micro-scale cleaning tools. Repeated use exposes the brushes to contact and impact at high strains resulting in the bristles undergoing exfoliation, deformation and damage. We show that the damages incurred can be nearly recovered by capillary evaporation of solvents from the free standing aligned nanotube brushes.
  31. Discovering communities through friendship G. Morrison, L. Mahadevan.  PLoS ONE  7(7): e38704. 2012.
    [View PDF] [Download PDF] We introduce a new method for detecting communities of arbitrary size in an undirected weighted network. Our approach is based on tracing the path of closest-friendship between nodes in the network using the recently proposed Generalized Erdo¨s Numbers. This method does not require the choice of any arbitrary parameters or null models, and does not suffer from a system-size resolution limit. Our closest-friend community detection is able to accurately reconstruct the true network structure for a large number of real world and artificial benchmarks, and can be adapted to study the multi-level structure of hierarchical communities as well. We also use the closeness between nodes to develop a degree of robustness for each node, which can assess how robustly that node is assigned to its community. To test the efficacy of these methods, we deploy them on a variety of well known benchmarks, a hierarchal structured artificial benchmark with a known community and robustness structure, as well as real-world networks of coauthorships between the faculty at a major university and the network of citations of articles published in Physical Review. In all cases, microcommunities, hierarchy of the communities, and variable node robustness are all observed, providing insights into the structure of the network.
  32. Banding, excitability and chaos in active nematic suspensions L. Giomi, L Mahadevan, B. Chakraborty and M. F. Hagan.  Nonlinearity  25, 2245–2269, 2012.
    [View PDF] [Download PDF] Motivated by the observation of highly unstable flowing states in suspensions of microtubules and kinesin, we analyse a model of mutually propelled filaments suspended in a solvent. The system undergoes a mean-field isotropic–nematic transition for large enough filament concentrations when the nematic order parameter is allowed to vary in space and time. We analyse the model in two contexts: a quasi-one-dimensional channel with no-slip walls and a two-dimensional box with periodic boundaries. Using stability analysis and numerical calculations we show that the interplay between non-uniform nematic order, activity, and flow results in a variety of complex scenarios that include spontaneous banded laminar flow, relaxation oscillations and chaos
  33. Scale and nature of sulcification patterns E. Hohlfeld and L. Mahadevan,  Physical Review Letters , 109, 025701, 2012.
    [View PDF] [Download PDF] Sulci are surface folds commonly seen in strained soft elastomers and form via a strongly subcritical, yet scale-free, instability. Treating the threshold for nonlinear instability as a nonlinear critical point, we explain the nature of sulcus patterns in terms of the scale and translation symmetries which are broken by the formation of an isolated, small sulcus. Our perturbative theory and simulations show that sulcus formation in a thick, compressed slab can arise either as a supercritical or as a weakly subcritical bifurcation relative to this nonlinear critical point, depending on the boundary conditions. An infinite number of competing, equilibrium patterns simultaneously emerge at this critical point, but the one selected has the lowest energy. We give a simple, physical explanation for the formation of these sulcification patterns using an analogy to a solid-solid phase transition with a finite energy of transformation.
  34. Flow induced channelization in a porous medium A. Mahadevan, A.V. Orpe, A. Kudrolli, and L. Mahadevan,  Europhysics Letters , 98, 58003, 2012.
    [View PDF] [Download PDF] Flow through a saturated, granular, porous medium can lead to internal erosion, preferential flow enhancement, and the formation of channels within the bulk of the medium. We examine this phenomenon using a combination of experimental observations, continuum theory and numerical simulations in a minimal setting. Our experiments are carried out by forcing water through a Hele-Shaw cell packed with bidisperse grains. When the local flow-induced stress exceeds a critical threshold, the smaller grains are dislodged and transported. This changes the porosity of the medium, thence, the local hydraulic conductivity, and leads to the development of erosional channels. Erosion is ultimately arrested due to the drop in the mean pressure gradient, while most of the flow occurs through the channels. We describe this using a minimal multiphase description of erosion where the volume fraction of the fluid, mobile, and immobile, grains change in space and time. Numerical solutions of the resulting initial boundary value problem yield results for the dynamics and morphology that are in qualitative agreement with our experiments. In addition to providing a basis for channelization in porous media, our study highlights how heterogeneity in porous media may arise from flow as a function of the erosion threshold.
  35. How things get stuck: kinetics, elastohydrodynamics, and soft adhesion M. Mani, A. Gopinath, and L. Mahadevan,  Physical Review Letters , 108, 226104, 2012.
    [View PDF] [Download PDF] We consider the sticking of a fluid-immersed colloidal particle with a substrate coated by polymeric tethers, a model for soft, wet adhesion in many natural and artificial systems. Our theory accounts for the kinetics of binding, the elasticity of the tethers, and the hydrodynamics of fluid drainage between the colloid and the substrate, characterized by three dimensionless parameters: the ratio of the viscous drainage time to the kinetics of binding, the ratio of elastic to thermal energies, and the size of the particle relative to the height of the polymer brush. For typical experimental parameters and discrete families of tethers, we find that adhesion proceeds via punctuated steps, where rapid transitions to increasingly bound states are separated by slow aging transients, consistent with recent observations. Our results also suggest that the bound particle is susceptible to fluctuation-driven instabilities parallel to the substrate.
  36. Geometric control of rippling in supported polymer nanolines V.R. Tirumala, C.M. Stafford, L.E. Ocola, J.F. Douglas, and L. Mahadevan,  Nanoletters , 12, 1516-1521, 2012.
    [View PDF] [Download PDF] We study the swelling behavior of finlike polymer line gratings supported on a rigid substrate and show that the edge-supported polymer laminae undergo a rippling instability with a well-defined ripple wavelength λ transverse to the plane of the solid supporting substrate and a ripple amplitude that monotonically decreases from its maximum at the free-edge. These ripple patterns develop due to inhomogeneous compressive strains that arise from the geometric constraints that progressively suppress swelling near the supporting substrate where the laminae are clamped. By experimentally examining the influence of swelling strain and pattern geometry on the observed rippling instability, we find that the ripple wavelength λ scales with line width w for sufficiently long gratings, which is consistent with a simple theory. These trends were validated for polymer nanoline test patterns having w between (50 to 250) nm and a height-to-width aspect-ratio in the range 0.5 to 5. Our results suggest that line geometry, rather than material properties, governs the onset of rippling and suggest simple rules for their control.
  37. A method for tensile tests of biological tissues at the mesoscale T. Savin, A. E. Shyer, and L. Mahadevan,  Journal of Applied Physics  111, 074704, 2012.
    [View PDF] [Download PDF] We describe a new technique for determining the tensile properties of biological tissues at the mesoscale. The procedure uses a calibrated magnetic interaction between a steel bead attached to the sample and a permanent magnet to apply a uniaxial tensile force, along with a simple video assay to monitor the sample extension and thus the strain. Our method fills a significant gap in the accessible range of both forces and strains and is useful for forces in the micro and milliNewton range, and displacements in the range of hundreds of microns with strains of up to 200%. We give two examples of the mechanical characterization of tissues using our technique, employing it to characterize the elastic modulus of tubular and membraneous embryonic tissues from the chick.
  38. Balancing on tightropes and slacklines P. Paoletti and L. Mahadevan,  Journal of the Royal Society - Interface , 9, 2097-2108, 2012.
    [View PDF] [Download PDF] Balancing on a tightrope or a slackline is an example of a neuromechanical task where the whole body both drives and responds to the dynamics of the external environment, often on multiple timescales. Motivated by a range of neurophysiological observations, here we formulate a minimal model for this system and use optimal control theory to design a strategy for maintaining an upright position. Our analysis of the open and closed-loop dynamics shows the existence of an optimal rope sag where balancing requires minimal effort, consistent with qualitative observations and suggestive of strategies for optimizing balancing performance while standing and walking. Our consideration of the effects of nonlinearities, potential parameter coupling and delays on the overall performance shows that although these factors change the results quantitatively, the existence of an optimal strategy persists.
  39. Skating on a film of air: drops impacting on a surface J. M. Kolinski, S. M. Rubinstein, S. Mandre, M. P. Brenner, D. A. Weitz, and L. Mahadevan,  Physical Review Letters , 108, 074503, 2012.
    [View PDF] [Download PDF] The commonly accepted description of drops impacting on a surface typically ignores the essential role of the air that is trapped between the impacting drop and the surface. Here we describe a new imaging modality that is sensitive to the behavior right at the surface. We show that a very thin film of air, only a few tens of nanometers thick, remains trapped between the falling drop and the surface as the drop spreads. The thin film of air serves to lubricate the drop enabling the fluid to skate on the air film laterally outward at surprisingly high velocities, consistent with theoretical predictions. Eventually this thin film of air breaks down as the fluid wets the surface via a spinodal-like mechanism. Our results show that the dynamics of impacting drops are much more complex than previously thought, with a rich array of unexpected phenomena that require rethinking classic paradigms
  40. Twisting graphene nanoribbons into carbon nanotubes O.O. Kit, T. Tallinen, L. Mahadevan, J. Timonen, P. Koskinen,  Physical Review B , 85, 085428, 2012.
    [View PDF] [Download PDF] Although carbon nanotubes consist of honeycomb carbon, they have never been fabricated from graphene directly. Here, it is shown by quantum molecular-dynamics simulations and classical continuum-elasticity modeling, that graphene nanoribbons can, indeed, be transformed into carbon nanotubes by means of twisting. The chiralities of the tubes thus fabricated can be not only predicted but also externally controlled. This twisting route is an opportunity for nanofabrication, and is easily generalizable to ribbons made of other planar nanomaterials.
  41. A biophysical indicator of vaso-occlusive risk in sickle cell disease D.K. Wood, A. Soriano, L. Mahadevan, J.M. Higgins, S.N. Bhatia,  Science Translational Medicin e, 4:123, 123ra26, 2012.
    [View PDF] [Download PDF] The search for predictive indicators of disease has largely focused on molecular markers. However, biophysical markers, which can integrate multiple pathways, may provide a more global picture of pathophysiology. Sickle cell disease affects millions of people worldwide and has been studied intensely at the molecular, cellular, tissue, and organismal level for a century, but there are still few, if any, markers quantifying the severity of this disease. Because the complications of sickle cell disease are largely due to vaso-occlusive events, we hypothesized that a physical metric characterizing the vaso-occlusive process could serve as an indicator of disease severity. Here, we use a microfluidic device to characterize the dynamics of “jamming,” or vaso-occlusion, in physiologically relevant conditions, by measuring a biophysical parameter that quantifies the rate of change of the resistance to flow after a sudden deoxygenation event. Our studies show that this single biophysical parameter could be used to distinguish patients with poor outcomes from those with good outcomes, unlike existing laboratory tests. This biophysical indicator could therefore be used to guide the timing of clinical interventions, to monitor the progression of the disease, and to measure the efficacy of drugs, transfusion, and novel small molecules in an ex vivo setting.
  42. Actin network growth under load O. Campàs, L. Mahadevan, and J-F. Joanny,  Biophysical Journal , 102, 1049-1058, 2012.
    [View PDF] [Download PDF] Many processes in eukaryotic cells, including the crawling motion of the whole cell, rely on the growth of branched actin networks from surfaces. In addition to their well-known role in generating propulsive forces, actin networks can also sustain substantial pulling loads thanks to their persistent attachment to the surface from which they grow. The simultaneous network elongation and surface attachment inevitably generate a force that opposes network growth. Here, we study the local dynamics of a growing actin network, accounting for simultaneous network elongation and surface attachment, and show that there exist several dynamical regimes that depend on both network elasticity and the kinetic parameters of actin polymerization. We characterize this in terms of a phase diagram and provide a connection between mesoscopic theories and the microscopic dynamics of an actin network at a surface. Our framework predicts the onset of instabilities that lead to the local detachment of the network and translate to oscillatory behavior and waves, as observed in many cellular phenomena and in vitro systems involving actin network growth, such as the saltatory dynamics of actin-propelled oil drops.
  43. Minimal surfaces bounded by elastic lines L. Giomi and L. Mahadevan, Proceedings of the Royal Society of London (A) , 468, 1851-1864, 2012.
    [View PDF] [Download PDF] In mathematics, the classical Plateau problem consists of finding the surface of least area that spans a given rigid boundary curve. A physical realization of the problem is obtained by dipping a stiff wire frame of some given shape in soapy water and then removing it; the shape of the spanning soap film is a solution to the Plateau problem. But what happens if a soap film spans a loop of inextensible but flexible wire? We consider this simple query that couples Plateau’s problem to Euler’s Elastica: a special class of twist-free curves of given length that minimize their total squared curvature energy. The natural marriage of two of the oldest geometrical problems linking physics and mathematics leads to a quest for the shape of a minimal surface bounded by an elastic line: the Euler–Plateau problem. We use a combination of simple physical experiments with soap films that span soft filaments and asymptotic analysis combined with numerical simulations to explore some of the richness of the shapes that result. Our study raises questions of intrinsic interest in geometry and its natural links to a range of disciplines, including materials science, polymer physics, architecture and even art.
  44. Soft catenaries K. Kamrin and L. Mahadevan,  Journal of Fluid Mechanics  691, 165-177, 2012.
    [View PDF] [Download PDF]
  45. The branch with the furthest reach Z. Wei, S. Mandre and L. Mahadevan,  Europhysics Letters , 97, 14005, 2012.
    [View PDF] [Download PDF] How should a given amount of material be moulded into a cantilevered beam clamped at one end, so that it will have the furthest horizontal reach? Here, we formulate and solve this variational problem for the optimal variation of the cross-section area of a heavy cantilevered beam with a given volume V , Young’s modulus E, and density ρ, subject to gravity g. We find that the cross-sectional area should vary according a universal profile that is independent of material parameters, with both the length and maximum reach-out distance of the branch that scale as (EV /ρg) 1/4 , with a universal self-similar shape at the tip with the area of cross-section a ∼ s 3 , s being the distance from the tip, consistent with earlier observations of tree branches, but with a different local interpretation than given before. A simple experimental realization of our optimal beam shows that our result compares favorably with that of our observations. Our results for the optimal design of slender structures with the longest reach are valid for cross-sections of arbitrary shape that can be solid or hollow and thus relevant for a range of natural and engineered systems.
  46. The Foppl-von Karman equations for plates with incompatible strains M. Lewicka, L. Mahadevan, and M. Pakzad,  Proceedings of the Royal Society, Lond. (A) , 467, 402-426, 2011.
    [View PDF] [Download PDF] We provide a derivation of the Föppl-von Kármán equations for the shape of and stresses in an elastic plate with incompatible or residual strains. These might arise from a range of causes: inhomogeneous growth, plastic deformation, swelling or shrinkage driven by solvent absorption. Our analysis gives rigorous bounds on the convergence of the threedimensional equations of elasticity to the low-dimensional description embodied in the plate-like description of laminae and thus justifies a recent formulation of the problem to the shape of growing leaves. It also formalizes a procedure that can be used to derive other low-dimensional descriptions of active materials with complex non-Euclidean geometries
  47. Hydrodynamics of writing with ink J. Kim, M-W. Moon, K-R. Lee, L. Mahadevan, and H-Y. Kim, Physical Review Letters,  107, 264502, 2011. 
    [View PDF] [Download PDF]
  48. Evolution of spur-length diversity in Aquilegia petals is achieved solely through cell-shape anisotropy J. R. Puzey, S.J. Gerbode, S.A. Hodges, E.M. Kramer and L. Mahadevan,  Proceedings of the Royal Society (B) , 279, 1640-1645, 2011.
    [View PDF] [Download PDF] The role of petal spurs and specialized pollinator interactions has been studied since Darwin. Aquilegia petal spurs exhibit striking size and shape diversity, correlated with specialized pollinators ranging from bees to hawkmoths in a textbook example of adaptive radiation. Despite the evolutionary significance of spur length, remarkably little is known about Aquilegia spur morphogenesis and its evolution. Using experimental measurements, both at tissue and cellular levels, combined with numerical modelling, we have investigated the relative roles of cell divisions and cell shape in determining the morphology of the Aquilegia petal spur. Contrary to decades-old hypotheses implicating a discrete meristematic zone as the driver of spur growth, we find that Aquilegia petal spurs develop via anisotropic cell expansion. Furthermore, changes in cell anisotropy account for 99 per cent of the spur-length variation in the genus, suggesting that the true evolutionary innovation underlying the rapid radiation of Aquilegia was the mechanism of tuning cell shape.
  49. Forced tearing of ductile and brittle thin sheets T. Tallinen and L. Mahadevan,  Physical Review Letters , 107, 245502, 2011.
    [View PDF] [Download PDF] Tearing a thin sheet by forcing a rigid object through it leads to complex crack morphologies; a single oscillatory crack arises when a tool is driven laterally through a brittle sheet, while two diverging cracks and a series of concertinalike folds forms when a tool is forced laterally through a ductile sheet. On the other hand, forcing an object perpendicularly through the sheet leads to radial petallike tears in both ductile and brittle materials. To understand these different regimes we use a combination of experiments, simulations, and simple theories. In particular, we describe the transition from brittle oscillatory tearing via a single crack to ductile concertina tearing with two tears by deriving laws that describe the crack paths and wavelength of the concertina folds and provide a simple phase diagram for the morphologies in terms of the material properties of the sheet and the relative size of the tool.
  50. A simple model for nanofiber formation by rotary jet-spinning P. Mellado, H.A. McIlwee, M.R. Badrossamay, J.A. Goss, L. Mahadevan, and K.K. Parker,  Applied Physics Letters ., 99, 203107, 2011.
    [View PDF] [Download PDF] Nanofibers are microstructured materials that span a broad range of applications from tissue engineering scaffolds to polymer transistors. An efficient method of nanofiber production is rotary jet-spinning (RJS), consisting of a perforated reservoir rotating at high speeds along its axis of symmetry, which propels a liquid, polymeric jet out of the reservoir orifice that stretches, dries, and eventually solidifies to form nanoscale fibers. We report a minimal scaling framework complemented by a semi-analytic and numerical approach to characterize the regimes of nanofiber production, leading to a theoretical model for the fiber radius consistent with experimental observations. In addition to providing a mechanism for the formation of nanofibers, our study yields a phase diagram for the design of continuous nanofibers as a function of process parameters with implications for the morphological quality of fibers.
1 … 4 5 6 7 8 9