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

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

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

The archetypal instability of a structure is associated with the eponymous Euler beam, modeled as an inextensible curve which exhibits a supercritical bifurcation at a critical compressive load. In contrast, a soft compressible beam is capable of a subcritical instability, a problem that is far less studied, even though it is increasingly relevant in the context of soft materials and structures. Here, we study the stability of a soft extensible elastic beam on an elastic foundation under the action of a compressive axial force, using the Lyapunov-Schmidt reduction method which we corroborate with numerical calculations. Our calculated bifurcation diagram differs from those associated with the classical Euler-Bernoulli beam, and shows two critical loads, , for each buckling mode . The beam undergoes a supercritical pitchfork bifurcation at for all and slenderness. Due to the elastic foundation, the lower order modes at exhibit subcritical pitchfork bifurcations, and perhaps surprisingly, the first supercritical pitchfork bifurcation point occurs at a higher critical load. The presence of the foundation makes it harder to buckle the elastic beam, but when it does so, it tends to buckle into a more undulated shape. Overall, we find that an elastic support can lead to a myraid of buckled shapes for the classical elastica and one can tune the substrate stiffness to control desired buckled modes -- an experimentally testable prediction.

The dynamics of many macromolecular machines are characterized by chemically mediated structural changes that achieve large-scale functional deployment through local rearrangements of constitutive protein subunits. Motivated by recent high-resolution structural microscopy of a particular class of such machines, contractile injection systems (CISs), we construct a coarse-grained semianalytical model that recapitulates the geometry and bistability of CISs in terms of a minimal set of measurable physical parameters. We use this model to predict the size, shape, and speed of a dynamical actuation front that underlies contraction. Scaling laws for the velocity and physical extension of the contraction front are consistent with our numerical simulations and may be generally applicable to related systems.

Self-organized branching structures can emerge spontaneously as interfacial instabilities in both simple and complex fluids, driven by the interplay between bulk material rheology, boundary constraints, and interfacial forcing. In our experiments, injecting dye between a source and a sink in a Hele-Shaw cell filled with a yield-stress fluid reveals an abrupt transition in morphologies as a function of injection rate. Slow injection leads to a direct path connecting the source to the sink, while fast injection leads to a rapid branching morphology that eventually converges to the sink. This shift from an exploitative (direct) to an exploratory (branched) strategy resembles search strategies in living systems; however, here it emerges in a simple physical system from a combination of global constraints (fluid conservation) and a switch-like local material response. We show that the amount of fluid needed to achieve breakthrough is minimal at the transition, and that there is a trade-off between speed and accuracy in these arborization patterns. Altogether, our study provides an embodied paradigm for fluidic computation driven by a combination of local material response (body) and global boundary conditions (environment).