Inspired by observations of beads packed on a thin string in such systems as sea-grapes and dental plaque, we study the random sequential adsorption of spheres on a cylinder. We determine the asymptotic fractional coverage of the cylinder as a function of the sole parameter in the problem, the ratio of the sphere radius to the cylinder radius (for a very long cylinder) using a combination of analysis and numerical simulations. Examining the asymptotic structures, we find weak chiral ordering on sufficiently small spatial scales. Experiments involving colloidal microspheres that can attach irreversibly to a silica wire via electrostatic forces or DNA hybridization allow us to verify our predictions for the asymptotic coverage.
Localized deformation patterns are a common motif in morphogenesis and are increasingly finding applications in materials science and engineering, in such instances as mechanical memories. Here, we describe the emergence of spatially localized deformations in a minimal mechanical system by exploring the impact of growth and shear on the conformation of a semi-flexible filament connected to a pliable shearable substrate. We combine numerical simulations of a discrete rod model with theoretical analysis of the differential equations recovered in the continuum limit to quantify (in the form of scaling laws) how geometry, mechanics and growth act together to give rise to such localized structures in this system. We find that spatially localized deformations along the filament emerge for intermediate shear modulus and increasing growth. Finally, we use experiments on a 3D-printed multi-material model system to demonstrate that external control of the amount of shear and growth may be used to regulate the spatial extent of the localized strain texture.
Kirigami tessellations, regular planar patterns formed by partially cutting flat, thin sheets, allow compact shapes to morph into open structures with rich geometries and unusual material properties. However, geometric and topological constraints make the design of such structures challenging. Here we pose and solve the inverse problem of determining the number, size and orientation of cuts that enables the deployment of a closed, compact regular kirigami tessellation to conform approximately to any prescribed target shape in two or three dimensions. We first identify the constraints on the lengths and angles of generalized kirigami tessellations that guarantee that their reconfigured face geometries can be contracted from a non-trivial deployed shape to a compact, non-overlapping planar cut pattern. We then encode these conditions into a flexible constrained optimization framework to obtain generalized kirigami patterns derived from various periodic tesselations of the plane that can be deployed into a wide variety of prescribed shapes. A simple mechanical analysis of the resulting structure allows us to determine and control the stability of the deployed state and control the deployment path. Finally, we fabricate physical models that deploy in two and three dimensions to validate this inverse design approach. Altogether, our approach, combining geometry, topology and optimization, highlights the potential for generalized kirigami tessellations as building blocks for shape-morphing mechanical metamaterials.
Moving along a straight path is a surprisingly difficult task. This is because, with each ensuing step, noise is generated in the motor and sensory systems, causing the animal to deviate from its intended route. When relying solely on internal sensory information to correct for this noise, the directional error generated with each stride accumulates, ultimately leading to a curved path. In contrast, external compass cues effectively allow the animal to correct for errors in its bearing. Here, we studied straight-line orientation in two different sized dung beetles. This allowed us to characterize and model the size of the directional error generated with each step, in the absence of external visual compass cues (motor error) as well as in the presence of these cues (compass and motor errors). In addition, we model how dung beetles balance the influence of internal and external orientation cues as they orient along straight paths under the open sky. We conclude that the directional error that unavoidably accumulates as the beetle travels is inversely proportional to the step size of the insect, and that both beetle species weigh the two sources of directional information in a similar fashion.
Evolution of avian egg shape: underlying mechanisms and the importance of taxonomic scale C. Sheard, D. Akkaynak, EH Yong, L. Mahadevan & J. A. Tobias, IBIS 161 (4) 15 July 2019.
Deep-reinforcement learning for gliding and perching G. Novati, L. Mahadevan, P. Koumoutsakos, arXiv
Tumbling of a falling card Mahadevan, L. Comptes Rendus de l’Academie des Sciences, Paris, Series II , 323, 729-736, 1996.
We describe a number of different phenomena seen
in the free-surface flow inside a partially filled circular cylinder
which is rotated about its horizontal axis of symmetry. At low
angular velocities the flow settles into a steady two-dimensional flow with a front where the coating film coalesces with
the pool at the bottom of the cylinder. This mode becomes
unstable at higher angular velocities, initially to a sloshing
mode on the rising side of the coating film and then to an axial
instability on the front. The undulations that appear on the
front grow into large-amplitude stationary patterns with
cusp-like features for some parameter values. At still higher
angular velocities and volume fractions, a number of different
inertial instabilities and patterns appear. We present a phase
diagram of the various transitions and characterize some of the
more prominent instabilities and patterns in detail, along with
some possible mechanisms for the observed behaviour.
The shape of a Möbius band Mahadevan, L., and J.B. Keller, Proceedings of the Royal Society of London, Series A , 1440, 149-162, 1993.
When a thin sheet of a flexible material such as paper is fed from a horizontal spool towards
a rough horizontal plane below it, the sheet folds on itself in a regular manner. We model
this phenomenon as a free boundary problem for a nonlinearly elastic sheet, taking into
account the stiffness and weight of the sheet and the height of the spool above the plane.
By using a continuation scheme we solve the problem numerically and follow the evolution
of one period of the fold for various values of the parameters. The results are found to
agree well with observations of the folding of paper sheets.