Purcell magneto-elastic swimmer controlled by an external magnetic field

International audienceThis paper focuses on the mechanism of propulsion of a Purcell swimmer whose segments are magnetized and react to an external magnetic field applied into the fluid. By an asymptotic analysis, we prove that it is possible to steer the swimmer along a chosen direction when the control functions are prescribed as an oscillating field. Moreover, we discuss what are the main obstructions to overcome in order to get classical controllability result for this system

Curved fluid membranes behave laterally as an effective viscoelastic medium

The lateral mobility of membrane inclusions is essential in biological processes involving membrane-bound macromolecules, which often take place in highly curved geometries such as membrane tubes or small organelles. Probe mobility is assisted by the lateral fluidity, which is thought to be purely viscous for lipid bilayers and synthetic systems such as polymersomes. In previous theoretical studies, the hydrodynamical mobility is estimated assuming a fixed membrane geometry. However, fluid membranes are very flexible out-of-plane. By accounting for the deformability of the membrane and in the presence of curvature, we show that the lateral motion of an inclusion produces a normal force, which results in a nonuniform membrane deformation. Such a deformation mobilizes the bending elasticity, produces extra lateral viscous and elastic forces, and results in an effective lateral viscoelastic behavior. The coupling between lateral and out-of-plane mechanics is mediated by the interfacial hydrodynamics and curvature. We analyze the frequency and curvature dependent rheology of flexible fluid membranes, and interpret it with a simple four-element model, which provides a background for microrheological experiments. Two key technical aspects of the present work are a new formulation for the interfacial hydrodynamics, and the linearization of the governing equations around a cylindrical geometry

Lower Extremity Passive Range of Motion in Community-Ambulating Stroke Survivors

Background: Physical therapists may prescribe stretching exercises for individuals with stroke to improve joint integrity and to reduce the risk of secondary musculoskeletal impairment. While deficits in passive range of motion (PROM) exist in stroke survivors with severe hemiparesis and spasticity, the extent to which impaired lower extremity PROM occurs in community-ambulating stroke survivors remains unclear. This study compared lower extremity PROM in able-bodied individuals and independent community-ambulatory stroke survivors with residual stroke-related neuromuscular impairments. Our hypothesis was that the stroke group would show decreased lower extremity PROM in the paretic but not the nonparetic side and that decreased PROM would be associated with increased muscle stiffness and decreased muscle length. Methods: Individuals with chronic poststroke hemiparesis who reported the ability to ambulate independently in the community (n = 17) and age-matched control subjects (n = 15) participated. PROM during slow (5 degrees/sec) hip extension, hip flexion, and ankle dorsiflexion was examined bilaterally using a dynamometer that measured joint position and torque. The maximum angular position of the joint (ANGmax), torque required to achieve ANGmax (Tmax), and mean joint stiffness (K) were measured. Comparisons were made between able-bodied and paretic and able-bodied and nonparetic limbs. Results: Contrary to our expectations, between-group differences in ANGmax were observed only during hip extension in which ANGmax was greater bilaterally in people post-stroke compared to control subjects (P ≤ 0.05; stroke = 13 degrees, able-bodied = −1 degree). Tmax, but not K, was also significantly higher during passive hip extension in paretic and nonparetic limbs compared to control limbs (P ≤ 0.05; stroke = 40 Nm, able-bodied = 29 Nm). Compared to the control group, Tmax was increased during hip flexion in the paretic and nonparetic limbs of post-stroke subjects (P ≤ 0.05, stroke = 25 Nm, able-bodied = 18 Nm). K in the nonparetic leg was also increased during hip flexion (P ≤ 0.05, nonparetic = 0.52 Nm/degree, able-bodied = 0.37 Nm/degree.) Conclusion: This study demonstrates that community-ambulating stroke survivors with residual neuromuscular impairments do not have decreased lower extremity PROM caused by increased muscle stiffness or decreased muscle length. In fact, the population of stroke survivors examined here appears to have more hip extension PROM than age-matched able-bodied individuals. The clinical implications of these data are important and suggest that lower extremity PROM may not interfere with mobility in community-ambulating stroke survivors. Hence, physical therapists may choose to recommend activities other than stretching exercises for stroke survivors who are or will become independent community ambulators

Mechanics of axisymmetric sheets of interlocking and slidable rods

In this work, we study the mechanics of metamaterial sheets inspired by the pellicle of Euglenids. They are composed of interlocking elastic rods which can freely slide along their edges. We characterize the kinematics and the mechanics of these structures using the special Cosserat theory of rods and by assuming axisymmetric deformations of the tubular assembly. Through an asymptotic expansion, we investigate both structures that comprise a discrete number of rods and the limit case of a sheet composed by infinitely many rods. We apply our theoretical framework to investigate the stability of these structures in the presence of an axial load. Through a linear analysis, we compute the critical buckling force for both the discrete and the continuous case. For the latter, we also perform a numerical post-buckling analysis, studying the non-linear evolution of the bifurcation through finite elements simulations

Shear thickening in densely packed suspensions of spheres and rods confined to few layers

We investigate confined shear thickening suspensions for which the sample thickness is comparable to the particle dimensions. Rheometry measurements are presented for densely packed suspensions of spheres and rods with aspect ratios 6 and 9. By varying the suspension thickness in the direction of the shear gradient at constant shear rate, we find pronounced oscillations in the stress. These oscillations become stronger as the gap size is decreased, and the stress is minimized when the sample thickness becomes commensurate with an integer number of particle layers. Despite this confinement-induced effect, viscosity curves show shear thickening that retains bulk behavior down to samples as thin as two particle diameters for spheres, below which the suspension is jammed. Rods exhibit similar behavior commensurate with the particle width, but they show additional effects when the thickness is reduced below about a particle length as they are forced to align; the stress increases for decreasing gap size at fixed shear rate while the shear thickening regime gradually transitions to a Newtonian scaling regime. This weakening of shear thickening as an ordered configuration is approached contrasts with the strengthening of shear thickening when the packing fraction is increased in the disordered bulk limit, despite the fact that both types of confinement eventually lead to jamming.Comment: 21 pages, 14 figures. submitted to the Journal of Rheolog

Uniaxial and biaxial soft deformations of nematic elastomers

We give a geometric interpretation of the soft elastic deformation modes of nematic elastomers, with explicit examples, for both uniaxial and biaxial nematic order. We show the importance of body rotations in this non-classical elasticity and how the invariance under rotations of the reference and target states gives soft elasticity (the Golubovic and Lubensky theorem). The role of rotations makes the Polar Decomposition Theorem vital for decomposing general deformations into body rotations and symmetric strains. The role of the square roots of tensors is discussed in this context and that of finding explicit forms for soft deformations (the approach of Olmsted).Comment: 10 pages, 10 figures, RevTex, AmsTe

The Formation and Coarsening of the Concertina Pattern

The concertina is a magnetization pattern in elongated thin-film elements of a soft material. It is a ubiquitous domain pattern that occurs in the process of magnetization reversal in direction of the long axis of the small element. Van den Berg argued that this pattern grows out of the flux closure domains as the external field is reduced. Based on experimental observations and theory, we argue that in sufficiently elongated thin-film elements, the concertina pattern rather bifurcates from an oscillatory buckling mode. Using a reduced model derived by asymptotic analysis and investigated by numerical simulation, we quantitatively predict the average period of the concertina pattern and qualitatively predict its hysteresis. In particular, we argue that the experimentally observed coarsening of the concertina pattern is due to secondary bifurcations related to an Eckhaus instability. We also link the concertina pattern to the magnetization ripple and discuss the effect of a weak (crystalline or induced) anisotropy