Efficient sliding locomotion of three-link bodies with inertia.

Many previous studies of sliding locomotion have assumed that body inertia is negligible. Here we optimize the kinematics of a three-link body for efficient locomotion and include among the kinematic parameters the temporal period of locomotion, or equivalently, the body inertia. The optimal inertia is nonnegligible when the coefficient of friction for sliding transverse to the body axis is small.

Efficient sliding locomotion of three-link bodies.

We study the efficiency of sliding locomotion for three-link bodies with prescribed joint angle motions. The bodies move with no inertia, under dry (Coulomb) friction that is anisotropic (different in the directions normal and tangent to the links) and directional (different in the forward and backward tangent directions). Friction coefficient space can be partitioned into several regions, each with distinct types of efficient kinematics.

Intermittent sliding locomotion of a two-link body.

We study the possibility of efficient intermittent locomotion for two-link bodies that slide by changing their interlink angle periodically in time. We find that the anisotropy ratio of the sliding friction coefficients is a key parameter, while solutions have a simple scaling dependence on the friction coefficients' magnitudes. With very anisotropic friction, efficient motions involve coasting in low-drag states, with rapid and asymmetric power and recovery strokes.

Efficient sliding locomotion with isotropic friction.

Snakes' bodies are covered in scales that make it easier to slide in some directions than in others. This frictional anisotropy allows for sliding locomotion with an undulatory gait, one of the most common for snakes. Isotropic friction is a simpler situation (that arises with snake robots, for example) but is less understood.

Author Correction: Intracellular localization of nanoparticle dimers by chirality reversal.

The original version of this Article contained an error in the spelling of the author Joong Hwan Bahng, which was incorrectly given as Joong Hwan Banhg. This has been corrected in both the PDF and HTML versions of the Article.

Dynamics and locomotion of flexible foils in a frictional environment.

Over the past few decades, oscillating flexible foils have been used to study the physics of organismal propulsion in different fluid environments. Here, we extend this work to a study of flexible foils in a frictional environment. When the foil is oscillated by heaving at one end but is not free to locomote, the dynamics change from periodic to non-periodic and chaotic as the heaving amplitude increases or the bending rigidity decreases.

Intracellular localization of nanoparticle dimers by chirality reversal.

The intra- and extracellular positioning of plasmonic nanoparticles (NPs) can dramatically alter their curative/diagnostic abilities and medical outcomes. However, the inability of common spectroscopic identifiers to register the events of transmembrane transport denies their intracellular vs. extracellular localization even for cell cultures.

Optimizing snake locomotion on an inclined plane.

We develop a model to study the locomotion of snakes on inclined planes. We determine numerically which snake motions are optimal for two retrograde traveling-wave body shapes, triangular and sinusoidal waves, across a wide range of frictional parameters and incline angles. In the regime of large transverse friction coefficients, we find power-law scalings for the optimal wave amplitudes and corresponding costs of locomotion.

Functional morphology of the fin rays of teleost fishes.

Ray-finned fishes are notable for having flexible fins that allow for the control of fluid forces. A number of studies have addressed the muscular control, kinematics, and hydrodynamics of flexible fins, but little work has investigated just how flexible ray-finned fish fin rays are, and how flexibility affects their response to environmental perturbations. Analysis of pectoral fin rays of bluegill sunfish showed that the more proximal portion of the fin ray is unsegmented while the distal 60% of the fin ray is segmented.

Optimization of two- and three-link snakelike locomotion.

We analyze two- and three-link planar snakelike locomotion and optimize the motion for efficiency. The locomoting system consists of two or three identical inextensible links connected via hinge joints, and the angles between the links are actuated as prescribed periodic functions of time. An essential feature of snake locomotion is frictional anisotropy: The forward, backward, and transverse coefficients of friction differ.

Using computational and mechanical models to study animal locomotion.

Recent advances in computational methods have made realistic large-scale simulations of animal locomotion possible. This has resulted in numerous mathematical and computational studies of animal movement through fluids and over substrates with the purpose of better understanding organisms' performance and improving the design of vehicles moving through air and water and on land. This work has also motivated the development of improved numerical methods and modeling techniques for animal locomotion that is characterized by the interactions of fluids, substrates, and structures.

Passive robotic models of propulsion by the bodies and caudal fins of fish.

Considerable progress in understanding the dynamics of fish locomotion has been made through studies of live fishes and by analyzing locomotor kinematics, muscle activity, and fluid dynamics. Studies of live fishes are limited, however, in their ability to control for parameters such as length, flexural stiffness, and kinematics. Keeping one of these factors constant while altering others in a repeatable manner is typically not possible, and it is difficult to make critical measurements such as locomotor forces and torques on live, freely-swimming fishes.

Interfacing mathematics and biology: a discussion on training, research, collaboration, and funding.

This article summarizes the discussion at a workshop on "Working at the Interface of Mathematics and Biology" at the 2012 Annual Meeting of the Society for Integrative and Comparative Biology. The goal of this workshop was to foster an ongoing discussion by the community on how to effectively train students from the biological, physical, engineering, and mathematical sciences to work at the intersection of these fields. One major point of discussion centered on how to be a successful interdisciplinary researcher in terms of where to publish, how to successfully write grants, and how to navigate evaluations for tenure and promotion.

Effects of shape and stroke parameters on the propulsion performance of an axisymmetric swimmer.

In nature, there exists a special group of aquatic animals which have an axisymmetric body and whose primary swimming mechanism is to use periodic body contractions to generate vortex rings in the surrounding fluid. Using jellyfish medusae as an example, this study develops a mathematical model of body kinematics of an axisymmetric swimmer and uses a computational approach to investigate the induced vortex wakes. Wake characteristics are identified for swimmers using jet propulsion and rowing, two mechanisms identified in previous studies of medusan propulsion.

Edge effects determine the direction of bilayer bending.

We elucidate the reason for preferential bending along the long edge in thin rectangular bilayers in which one of the layers is isotropically strained. While this preference has been observed previously, the physical basis for this preference has not been understood. We find that the bending direction is determined by the existence of doubly curved regions at the curled edges, which lower the energy.

Coordination of multiple appendages in drag-based swimming.

Krill are aquatic crustaceans that engage in long distance migrations, either vertically in the water column or horizontally for 10 km (over 200,000 body lengths) per day. Hence efficient locomotory performance is crucial for their survival. We study the swimming kinematics of krill using a combination of experiment and analysis.

Foldable structures and the natural design of pollen grains.

Upon release from the anther, pollen grains of angiosperm flowers are exposed to a dry environment and dehydrate. To survive this process, pollen grains possess a variety of physiological and structural adaptations. Perhaps the most striking of these adaptations is the ability of the pollen wall to fold onto itself to prevent further desiccation.

Collapse and folding of pressurized rings in two dimensions.

Hydrostatically pressurized circular rings confined to two dimensions (or cylinders constrained to have only z -independent deformations) undergo Euler-type buckling when the outside pressure exceeds a critical value. We perform a stability analysis of rings with arclength-dependent bending moduli and determine how weakened bending modulus segments affect the buckling critical pressure. Rings with a fourfold symmetric modulation are particularly susceptible to collapse.

Packings of a charged line on a sphere.

We find equilibrium configurations of open and closed lines of charge on a sphere, and track them with respect to varying sphere radius. Closed lines transition from a circle to a spiral-like shape through two low-wave-number bifurcations-"baseball seam" and "twist"-which minimize Coulomb energy. The spiral shape is the unique stable equilibrium of the closed line.

Flapping states of a flag in an inviscid fluid: bistability and the transition to chaos.

We investigate the "flapping flag" instability through a model for an inextensible flexible sheet in an inviscid 2D flow with a free vortex sheet. We solve the fully-nonlinear dynamics numerically and find a transition from a power spectrum dominated by discrete frequencies to an apparently continuous spectrum of frequencies. We compute the linear stability domain which agrees with previous approximate models in scaling but differs by large multiplicative factors.

How bumps on whale flippers delay stall: an aerodynamic model.

Wind tunnel experiments have shown that bumps on the leading edge of model humpback whale flippers cause them to "stall" (i.e., lose lift dramatically) more gradually and at a higher angle of attack.

Self-assembly of flat sheets into closed surfaces.

A recent experiment [Boncheva Proc. Natl. Acad.

The mechanics of active fin-shape control in ray-finned fishes.

We study the mechanical properties of fin rays, which are a fundamental component of fish fin structure. We derive a linear elasticity model that predicts the shape of fin rays, given the input muscle actuation and external loading. We then test the model using experiments that measure (i) the ray deflection for a given actuation at the muscular interface, and (ii) the force-displacement response under conditions of actuation and non-actuation.