Friction enhancement in concertina locomotion of snakes

Narrow crevices are challenging terrain for most organisms and biomimetic robots. Snakes move through crevices using sequential folding and unfolding of their bodies in the manner of an accordion or concertina. In this combined experimental and theoretical investigation, we elucidate this effective means of moving through channels. We measure the frictional properties of corn snakes, their body kinematics and the transverse forces they apply to channels of varying width and inclination. To climb channels inclined at 60°, we find snakes use a combination of ingenious friction-enhancing techniques, including digging their ventral scales to double their frictional coefficient and pushing channel walls transversely with up to nine times body weight. Theoretical modelling of a one-dimensional n-linked crawler is used to calculate the transverse force factor of safety: we find snakes push up to four times more than required to prevent sliding backwards, presumably trading metabolic energy for an assurance of wall stability.     

An intermittent control model of flexible human gait using a stable manifold of saddle-type unstable limit cycle dynamics

Stability of human gait is the ability to maintain upright posture during walking against external perturbations. It is a complex process determined by a number of cross-related factors, including gait trajectory, joint impedance and neural control strategies. Here, we consider a control strategy that can achieve stable steady-state periodic gait while maintaining joint flexibility with the lowest possible joint impedance. To this end, we carried out a simulation study of a heel-toe footed biped model with hip, knee and ankle joints and a heavy head-arms-trunk element, working in the sagittal plane. For simplicity, the model assumes a periodic desired joint angle trajectory and joint torques generated by a set of feed-forward and proportional-derivative feedback controllers, whereby the joint impedance is parametrized by the feedback gains. We could show that a desired steady-state gait accompanied by the desired joint angle trajectory can be established as a stable limit cycle (LC) for the feedback controller with an appropriate set of large feedback gains. Moreover, as the feedback gains are decreased for lowering the joint stiffness, stability of the LC is lost only in a few dimensions, while leaving the remaining large number of dimensions quite stable: this means that the LC becomes saddle-type, with a low-dimensional unstable manifold and a high-dimensional stable manifold. Remarkably, the unstable manifold remains of low dimensionality even when the feedback gains are decreased far below the instability point. We then developed an intermittent neural feedback controller that is activated only for short periods of time at an optimal phase of each gait stride. We characterized the robustness of this design by showing that it can better stabilize the unstable LC with small feedback gains, leading to a flexible gait, and in particular we demonstrated that such an intermittent controller performs better if it drives the state point to the stable manifold, rather than directly to the LC. The proposed intermittent control strategy might have a high affinity for the inverted pendulum analogy of biped gait, providing a dynamic view of how the step-to-step transition from one pendular stance to the next can be achieved stably in a robust manner by a well-timed neural intervention that exploits the stable modes embedded in the unstable dynamics.     

Periodic travelling waves in cyclic populations: field studies and reaction–diffusion models

Periodic travelling waves have been reported in a number of recent spatio-temporal field studies of populations undergoing multi-year cycles. Mathematical modelling has a major role to play in understanding these results and informing future empirical studies. We review the relevant field data and summarize the statistical methods used to detect periodic waves. We then discuss the mathematical theory of periodic travelling waves in oscillatory reaction-diffusion equations. We describe the notion of a wave family, and various ecologically relevant scenarios in which periodic travelling waves occur. We also discuss wave stability, including recent computational developments. Although we focus on oscillatory reaction-diffusion equations, a brief discussion of other types of model in which periodic travelling waves have been demonstrated is also included. We end by proposing 10 research challenges in this area, five mathematical and five empirical.     

Modelling of attenuation of Lamb waves using Rayleigh damping: Numerical and experimental studies

In this study, the Lamb mode attenuation constants were derived in terms of the attenuation coefficient, group velocity and central frequency of excitation of the Lamb mode, using the Rayleigh damping model. Attenuation of Lamb waves, both fundamental symmetric and anti-symmetric modes, propagating through viscoelastic media (cross-ply glass/epoxy laminate) was modelled using the Finite Element Method. Numerically simulated attenuation of Lamb waves using Lamb mode attenuation constants was found to be in good agreement with the assumed attenuation. Experiments were performed on a quasi-isotropic laminate, employing air-coupled ultrasonic transducers, to measure the attenuation coefficient. Lamb mode attenuation constants, computed using the attenuation coefficient, were used to model the attenuation of the Lamb mode in quasi-isotropic laminates. Numerically simulated amplitude variation was found to be in good agreement with that computed from experiments.     

Metal availability in heavy metal-contaminated open burning and open detonation soil: Assessment using soil enzymes, earthworms, and chemical extractions

The effects of heavy metal contamination on soil enzyme activity and earthworm health (bioaccumulation and condition) were studied in contaminated soils collected from an formerly open burning and open detonation (OBOD) site. Soil extraction methods were also evaluated using CaCl₂ and DTPA solutions as surrogate measures of metal bioavailability and ecotoxicity. Total heavy metal content of the soils ranged from 0.45 to 9.68 mg Cd kg⁻¹, 8.96 to 5103 mg Cu kg⁻¹, 40.21 to 328 mg Pb kg⁻¹, and 56.61 to 10,890 mg Zn kg⁻¹. Elevated metal concentrations are assumed to be primarily responsible for the reduction in enzyme activities and earthworm health indices. We found significant negative relationships between CaCl₂- and DTPA-extractable metal content (Cd, Cu, and Zn) and soil enzyme activity (P < 0.01). Therefore, it could be concluded that soil enzyme activity and metal bioaccumulation by earthworms can be used as an ecological indicator of metal availability. Furthermore, CaCl₂ and DTPA extraction methods are proved as promising, precise, and inexpensive surrogate measures of Cd, Cu, Pb, and Zn bioavailability from heavy metal-contaminated soils.