Floppy swimming: Viscous locomotion of actuated elastica

Actuating periodically an elastic filament in a viscous liquid generally breaks the constraints of Purcell's scallop theorem, resulting in the generation of a net propulsive force. This observation suggests a method to design simple swimming devices - which we call "elastic swimmers" - where the actuation mechanism is embedded in a solid body and the resulting swimmer is free to move. In this paper, we study theoretically the kinematics of elastic swimming. After discussing the basic physical picture of the phenomenon and the expected scaling relationships, we derive analytically the elastic swimming velocities in the limit of small actuation amplitude. The emphasis is on the coupling between the two unknowns of the problems - namely the shape of the elastic filament and the swimming kinematics - which have to be solved simultaneously. We then compute the performance of the resulting swimming device, and its dependance on geometry. The optimal actuation frequency and body shapes are derived and a discussion of filament shapes and internal torques is presented. Swimming using multiple elastic filaments is discussed, and simple strategies are presented which result in straight swimming trajectories. Finally, we compare the performance of elastic swimming with that of swimming microorganisms.Comment: 23 pages, 6 figure

Experimental Investigations of Elastic Tail Propulsion at Low Reynolds Number

A simple way to generate propulsion at low Reynolds number is to periodically oscillate a passive flexible filament. Here we present a macroscopic experimental investigation of such a propulsive mechanism. A robotic swimmer is constructed and both tail shape and propulsive force are measured. Filament characteristics and the actuation are varied and resulting data are quantitatively compared with existing linear and nonlinear theories

Synchronization of active mechanical oscillators by an inertial load

Motivated by the operation of myogenic (self-oscillatory) insect flight muscle, we study a model consisting of a large number of identical oscillatory contractile elements joined in a chain, whose end is attached to a damped mass-spring oscillator. When the inertial load is small, the serial coupling favors an antisynchronous state in which the extension of one oscillator is compensated by the contraction of another, in order to preserve the total length. However, a sufficiently massive load can sychronize the oscillators and can even induce oscillation in situations where isolated elements would be stable. The system has a complex phase diagram displaying quiescent, synchronous and antisynchrononous phases, as well as an unsual asynchronous phase in which the total length of the chain oscillates at a different frequency from the individual active elements.Comment: 5 pages, 4 figures, To appear in Phys. Rev. Let

Complement and cytokine response in acute Thrombotic Thrombocytopenic Purpura

Complement dysregulation is key in the pathogenesis of atypical Haemolytic Uraemic Syndrome (aHUS), but no clear role for complement has been identified in Thrombotic Thrombocytopenic Purpura (TTP). We aimed to assess complement activation and cytokine response in acute antibody-mediated TTP. Complement C3a and C5a and cytokines (interleukin (IL)-2, IL-4, IL-6, IL-10, tumour necrosis factor, interferon-γ and IL-17a) were measured in 20 acute TTP patients and 49 remission cases. Anti-ADAMTS13 immunoglobulin G (IgG) subtypes were measured in acute patients in order to study the association with complement activation. In acute TTP, median C3a and C5a were significantly elevated compared to remission, C3a 63·9 ng/ml vs. 38·2 ng/ml (P < 0·001) and C5a 16·4 ng/ml vs. 9·29 ng/ml (P < 0·001), respectively. Median IL-6 and IL-10 levels were significantly higher in the acute vs. remission groups, IL-6: 8 pg/ml vs. 2 pg/ml (P = 0·003), IL-10: 6 pg/ml vs. 2 pg/ml (P < 0·001). C3a levels correlated with both anti-ADAMTS13 IgG (rs  = 0·604, P = 0·017) and IL-10 (rs  = 0·692, P = 0·006). No anti-ADAMTS13 IgG subtype was associated with higher complement activation, but patients with the highest C3a levels had 3 or 4 IgG subtypes present. These results suggest complement anaphylatoxin levels are higher in acute TTP cases than in remission, and the complement response seen acutely may relate to anti-ADAMTS13 IgG antibody and IL-10 levels

Seasonal variation in breast cancer diagnosis in Singapore

This study investigates seasonality in the diagnosis of 3219 female breast carcinoma cases reported between 1995–8 in Singapore. There is little evidence of marked seasonal variation. Angular regression suggested that observed differences in peak diagnosis with respect to menopausal status, tumour size, ER and PR status may be chance. © 2001 Cancer Research Campaign http://www.bjcancer.co

Nonlinear instability in flagellar dynamics: a notel modulation mechanism in sperm migration

Throughout biology, cells and organisms use flagella and cilia to propel fluid and achieve motility. The beating of these organelles, and the corresponding ability to sense, respond to and modulate this beat is central to many processes in health and disease. While the mechanics of flagellum–fluid interaction has been the subject of extensive mathematical studies, these models have been restricted to being geometrically linear or weakly nonlinear, despite the high curvatures observed physiologically. We study the effect of geometrical nonlinearity, focusing on the spermatozoon flagellum. For a wide range of physiologically relevant parameters, the nonlinear model predicts that flagellar compression by the internal forces initiates an effective buckling behaviour, leading to a symmetry-breaking bifurcation that causes profound and complicated changes in the waveform and swimming trajectory, as well as the breakdown of the linear theory. The emergent waveform also induces curved swimming in an otherwise symmetric system, with the swimming trajectory being sensitive to head shape—no signalling or asymmetric forces are required. We conclude that nonlinear models are essential in understanding the flagellar waveform in migratory human sperm; these models will also be invaluable in understanding motile flagella and cilia in other systems

The role of body rotation in bacterial flagellar bundling

In bacterial chemotaxis, E. coli cells drift up chemical gradients by a series of runs and tumbles. Runs are periods of directed swimming, and tumbles are abrupt changes in swimming direction. Near the beginning of each run, the rotating helical flagellar filaments which propel the cell form a bundle. Using resistive-force theory, we show that the counter-rotation of the cell body necessary for torque balance is sufficient to wrap the filaments into a bundle, even in the absence of the swirling flows produced by each individual filament

Beating patterns of filaments in viscoelastic fluids

Many swimming microorganisms, such as bacteria and sperm, use flexible flagella to move through viscoelastic media in their natural environments. In this paper we address the effects a viscoelastic fluid has on the motion and beating patterns of elastic filaments. We treat both a passive filament which is actuated at one end, and an active filament with bending forces arising from internal motors distributed along its length. We describe how viscoelasticity modifies the hydrodynamic forces exerted on the filaments, and how these modified forces affect the beating patterns. We show how high viscosity of purely viscous or viscoelastic solutions can lead to the experimentally observed beating patterns of sperm flagella, in which motion is concentrated at the distal end of the flagella

Self-organized Beating and Swimming of Internally Driven Filaments

We study a simple two-dimensional model for motion of an elastic filament subject to internally generated stresses and show that wave-like propagating shapes which can propel the filament can be induced by a self-organized mechanism via a dynamic instability. The resulting patterns of motion do not depend on the microscopic mechanism of the instability but only of the filament rigidity and hydrodynamic friction. Our results suggest that simplified systems, consisting only of molecular motors and filaments could be able to show beating motion and self-propulsion.Comment: 8 pages, 2 figures, REVTe