# Biomechanics

### Stiffness of the human foot and evolution of the transverse arch

Biomechanics Foot EvolutionThe stiff human foot enables an efficient push-off when walking or running, and was critical for the evolution of bipedalism. The uniquely arched morphology of the human midfoot is thought to stiffen it, whereas other primates have flat feet that bend severely in the midfoot. However, the relationship between midfoot geometry and stiffness remains debated in foot biomechanics, podiatry and palaeontology. These debates centre on the medial longitudinal arch and have not considered whether stiffness is affected by the second, transverse tarsal arch of the human foot.

### Dynamics and stability of running on rough terrains

Biomechanics RunningStability of running on rough terrain depends on the propagation of perturbations due to the ground. We consider stability within the sagittal plane and model the dynamics of running as a two-dimensional body with alternating aerial and stance phases. Stance is modelled as a passive, impulsive collision followed by an active, impulsive push-off that compensates for collisional losses. Such a runner has infinitely many strategies to maintain periodic gaits on flat ground.

### Controllable biomimetic birdsong

Biomechanics BirdsongBirdsong is the product of the controlled generation of sound embodied in a neuromotor system. From a biophysical perspective, a natural question is that of the difficulty of producing birdsong. To address this, we built a biomimetic syrinx consisting of a stretched simple rubber tube through which air is blown, subject to localized mechanical squeezing with a linear actuator. A large static tension on the tube and small dynamic variations in the localized squeezing allow us to control transitions between three states: a quiescent state, a periodic state and a solitary wave state.

### Curvature-induced stiffening of fish fin

Biomechanics Fish finsHow fish modulate their fin stiffness during locomotive manoeuvres remains unknown. We show that changing the fin’s curvature modulates its stiffness. Modelling the fin as bendable bony rays held together by a membrane, we deduce that fin curvature is manifested as a misalignment of the principal bending axes between neighbouring rays. An external force causes neighbouring rays to bend and splay apart, and thus stretches the membrane. This coupling between bending the rays and stretching the membrane underlies the increase in stiffness.

### Linear stability analysis for monami in a submerged seagrass bed

Fluid Mechanics Biomechanics EnvironmentThe onset of monami – the synchronous waving of seagrass beds driven by a steady flow – is modelled as a linear instability of the flow. Unlike previous works, our model considers the drag exerted by the grass in establishing the steady flow profile, and in damping out perturbations to it. We find two distinct modes of instability, which we label modes 1 and 2. Mode 1 is closely related to Kelvin–Helmholtz instability modified by vegetation drag, whereas mode 2 is unrelated to Kelvin–Helmholtz instability and arises from an interaction between the flow in the vegetated and unvegetated layers.

### The branch with the furthest reach

Biomechanics OptimizationHow 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 generalized theory of viscous and inviscid flutter

Fluid Mechanics Biomechanics Geophysics Fluid-structure interaction FlutterWe present a unified theory of flutter in inviscid and viscous flows interacting with flexible structures based on the phenomenon of 1 : 1 resonance. We show this by treating four extreme cases corresponding to viscous and inviscid flows in confined and unconfined flows. To see the common mechanism clearly, we consider the limit when the frequencies of the first few elastic modes are closely clustered and small relative to the convective fluid time scale.

### A simple model illustrating the role of turbulence on phytoplankton blooms

Biomechanics Fluid MechanicsThe problem of the vertical distribution of phytoplankton is considered in the presence of gravitational settling, turbulent mixing, population growth due to cell division and a constant rate of loss due to predation and natural death. Nutrients are assumed to be plentiful so that the production rate depends only on the light available for photosynthesis. The non-linear saturation of plankton growth is modeled by allowing the attenuation rate of light to be a linear function of the plankton density.