Curvature-induced stiffening of a fish fin

How 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. Using analysis of a 3D reconstruction of a Mackerel (Scomber japonicus) pectoral fin, we calculate the range of stiffnesses this fin is expected to span by changing curvature. The 3D reconstruction shows that, even in its geometrically flat state, a functional curvature is embedded within the fin microstructure owing to the morphology of individual rays. Since the ability of a propulsive surface to transmit force to the surrounding fluid is limited by its stiffness, the fin curvature controls the coupling between the fish and its surrounding fluid. Thereby, our results provide mechanical underpinnings and morphological predictions for the hypothesis that the spanned range of fin stiffnesses correlates with the behaviour and the ecological niche of the fish

Multifractal burst in the spatio-temporal dynamics of jerky flow

The collective behavior of dislocations in jerky flow is studied in Al-Mg polycrystalline samples subjected to constant strain rate tests. Complementary dynamical, statistical and multifractal analyses are carried out on the stress-time series recorded during jerky flow to characterize the distinct spatio-temporal dynamical regimes. It is shown that the hopping type B and the propagating type A bands correspond to chaotic and self-organized critical states respectively. The crossover between these types of bands is identified by a large spread in the multifractal spectrum. These results are interpreted on the basis of competing scales and mechanisms.Comment: 4 pages, 6 figures To be published in Phys. Rev. Lett. (2001

A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio

Force-Field Compensation in a Manual Tracking Task

This study addresses force/movement control in a dynamic “hybrid” task: the master sub-task is continuous manual tracking of a target moving along an eight-shaped Lissajous figure, with the tracking error as the primary performance index; the slave sub-task is compensation of a disturbing curl viscous field, compatibly with the primary performance index. The two sub-tasks are correlated because the lateral force the subject must exert on the eight-shape must be proportional to the longitudinal movement speed in order to perform a good tracking. The results confirm that visuo-manual tracking is characterized by an intermittent control mechanism, in agreement with previous work; the novel finding is that the overall control patterns are not altered by the presence of a large deviating force field, if compared with the undisturbed condition. It is also found that the control of interaction-forces is achieved by a combination of arm stiffness properties and direct force control, as suggested by the systematic lateral deviation of the trajectories from the nominal path and the comparison between perturbed trials and catch trials. The coordination of the two sub-tasks is quickly learnt after the activation of the deviating force field and is achieved by a combination of force and the stiffness components (about 80% vs. 20%), which is a function of the implicit accuracy of the tracking task

A Re-examination of the Portevin-Le Chatelier Effect in Alloy 718 in Connection with Oxidation-Assisted Intergranular Cracking

In Alloy 718, a sharp transition exists in the fracture path changing from an intergranular brittle mode to a transgranular ductile mode which is associated with a transition of flow behavior from smooth in the dynamic strain aging regime to a serrated one in the Portevin-Le Chatelier (PLC) regime. In order to better understand both deformation and rupture behavior, PLC phenomenon in a precipitation-hardened nickel-base superalloy was carefully investigated in a wide range of temperatures [573 K to 973 K (300°C to 700°C)] and strain rates (109^-5 to 3.2910^-2 s^-1 ). Distinction was made between two PLC domains characterized by different evolutions of the critical strain to the onset of the first serration namely normal and inverse behavior. The apparent activation energies associated with both domains were determined using different methods. Results showed that normal and inverse behavior domains are related to dynamic interaction of dislocations with, respectively, interstitial and substitutional solutes atoms. This analysis confirms that normal PLC regime may be associated to the diffusion of carbon atoms, whereas the substitutional species involves in the inverse regime is discussed with an emphasis on the role of Nb and Mo

Slower Visuomotor Corrections with Unchanged Latency are Consistent with Optimal Adaptation to Increased Endogenous Noise in the Elderly

We analyzed age-related changes in motor response in a visuomotor compensatory tracking task. Subjects used a manipulandum to attempt to keep a displayed cursor at the center of a screen despite random perturbations to its location. Cross-correlation analysis of the perturbation and the subject response showed no age-related increase in latency until the onset of response to the perturbation, but substantial slowing of the response itself. Results are consistent with age-related deterioration in the ratio of signal to noise in visuomotor response. The task is such that it is tractable to use Bayesian and quadratic optimality assumptions to construct a model for behavior. This model assumes that behavior resembles an optimal controller subject to noise, and parametrizes response in terms of latency, willingness to expend effort, noise intensity, and noise bandwidth. The model is consistent with the data for all young (n = 12, age 20–30) and most elderly (n = 12, age 65–92) subjects. The model reproduces the latency result from the cross-correlation method. When presented with increased noise, the computational model reproduces the experimentally observed age-related slowing and the observed lack of increased latency. The model provides a precise way to quantitatively formulate the long-standing hypothesis that age-related slowing is an adaptation to increased noise

Stiffness of the human foot and evolution of the transverse arch

The stiff human foot enables an efficient push-off when walking or running, and was critical for the evolution of bipedalism(1-6). The uniquely arched morphology of the human midfoot is thought to stiffen it(5-9), whereas other primates have flat feet that bend severely in the midfoot(7,10,11). However, the relationship between midfoot geometry and stiffness remains debated in foot biomechanics(12,13), podiatry(14,15) and palaeontology(4-6). These debates centre on the medial longitudinal arch(5,6) and have not considered whether stiffness is affected by the second, transverse tarsal arch of the human foot(16). Here we show that the transverse tarsal arch, acting through the inter-metatarsal tissues, is responsible for more than 40% of the longitudinal stiffness of the foot. The underlying principle resembles a floppy currency note that stiffens considerably when it curls transversally. We derive a dimensionless curvature parameter that governs the stiffness contribution of the transverse tarsal arch, demonstrate its predictive power using mechanical models of the foot and find its skeletal correlate in hominin feet. In the foot, the material properties of the inter-metatarsal tissues and the mobility of the metatarsals may additionally influence the longitudinal stiffness of the foot and thus the curvature-stiffness relationship of the transverse tarsal arch. By analysing fossils, we track the evolution of the curvature parameter among extinct hominins and show that a human-like transverse arch was a key step in the evolution of human bipedalism that predates the genus Homo by at least 1.5 million years. This renewed understanding of the foot may improve the clinical treatment of flatfoot disorders, the design of robotic feet and the study of foot function in locomotion

Atomic Species Associated with the Portevin–Le Chatelier Effect in Superalloy 718 Studied by Mechanical Spectroscopy

In many Ni-based superalloys, dynamic strain aging (DSA) generates an inhomogeneous plastic deformation resulting in jerky flow known as the Portevin--Le Chatelier (PLC) effect. This phenomenon has a deleterious effect on the mechanical properties and, at high temperature, is related to the diffusion of substitutional solute atoms toward the core of dislocations. However, the question about the nature of the atomic species responsible for the PLC effect at high temperature still remains open. The goal of the present work is to answer this important question; to this purpose, three different 718-type and a 625 superalloy were studied through a nonconventional approach by mechanical spectroscopy. The internal friction (IF) spectra of all the studied alloys show a relaxation peak P718 (at 885 K for 0.1 Hz) in the same temperature range, 700 K to 950 K, as the observed PLC effect. The activation parameters of this relaxation peak have been measured, Ea(P718){\thinspace}={\thinspace}2.68{\thinspace}{\textpm}{\thinspace}0.05 eV, $\tau$0{\thinspace}={\thinspace}2{\textperiodcentered}10-15 {\textpm} 1 s as well as its broadening factor $\beta${\thinspace}={\thinspace}1.1. Experiments on different alloys and the dependence of the relaxation strength on the amount of Mo attribute this relaxation to the stress-induced reorientation of Mo-Mo dipoles due to the short distance diffusion of one Mo atom by exchange with a vacancy. Then, it is concluded that Mo is the atomic species responsible for the high-temperature PLC effect in 718 superallo

Stiffness and work contributions of the windlass in human feet

The 9.5th international symposium on Adaptive Motion of Animals and Machines. Ottawa，Canada (Virtual Platform). 2021-06-22/25. Adaptive Motion of Animals and Machines Organizing Committee