Hydrodynamics and direction change of tumbling bacteria

The bacterium Escherichia coli (E. coli) swims in viscous fluids by rotating several helical flagellar filaments, which are gathered in a bundle behind the cell during ‘runs’ wherein the cell moves steadily forward. In between runs, the cell undergoes quick ‘tumble’ events, during which at least one flagellum reverses its rotation direction and separates from the bundle, resulting in erratic motion in place and a random reorientation of the cell. Alternating between runs and tumbles allows cells to sample space by stochastically changing their propulsion direction after each tumble. The change of direction during a tumble is not uniformly distributed but is skewed towards smaller angles with an average of about 62°–68°, as first measured by Berg and Brown (1972). Here we develop a theoretical approach to model the angular distribution of swimming E. coli cells during tumbles. We first use past experimental imaging results to construct a kinematic description of the dynamics of the flagellar filaments during a tumble. We then employ low-Reynolds number hydrodynamics to compute the consequences of the kinematic model on the force and torque balance of the cell and to deduce the overall change in orientation. The results of our model are in good agreement with experimental observations. We find that the main change of direction occurs during the ‘bundling’ part of the process wherein, at the end of a tumble, the dispersed flagellar filaments are brought back together in the helical bundle, which we confirm using a simplified forced-sphere model.

Active turbulence in a gas of self-assembled spinners

Colloidal particles subject to an external periodic forcing exhibit complex collective behavior and self-assembled patterns. A dispersion of magnetic microparticles confined at the air–liquid interface and energized by a uniform uniaxial alternating magnetic field exhibits dynamic arrays of self-assembled spinners rotating in either direction. Here, we report on experimental and simulation studies of active turbulence and transport in a gas of self-assembled spinners. We show that the spinners, emerging as a result of spontaneous symmetry breaking of clock/counterclockwise rotation of self-assembled particle chains, generate vigorous vortical flows at the interface. An ensemble of spinners exhibits chaotic dynamics due to self-generated advection flows. The same-chirality spinners (clockwise or counterclockwise) show a tendency to aggregate and form dynamic clusters. Emergent self-induced interface currents promote active diffusion that could be tuned by the parameters of the external excitation field. Furthermore, the erratic motion of spinners at the interface generates chaotic fluid flow reminiscent of 2D turbulence. Our work provides insight into fundamental aspects of collective transport in active spinner materials and yields rules for particle manipulation at the microscale.

Choreographic Arrhythmias

Aberrations in the constancy and duration of movement challenge the determination of bodies and things within and beyond dance. In fact, 19th-century anthropological studies on animism and recent cognitive science experiments on timescale bias demonstrate that the agency of erratic motion is difficult to apprehend. From irregular and unexpected movements in dance to the variable tempos of cell motility, this paper considers how arrhythmic choreography recalibrates the agency of matter, objects, bodies and environments.

A Preliminary Study on the Use of Haptic Feedback to Assist Users with Impaired Arm Coordination During Mouse Interactions

Physical movement impairments caused by central nervous system dysfunction or by muscle spasms generated from other neurological damage or dysfunction can often make it difficult or impossible for affected individuals to interact with computer generated environments using the conventional mouse interfaces. This work investigates the use of a 2 dimensional haptic device as an assistive robotic aid to minimize the effects of the pathological absence of motor control on the upper limb in impaired users while using a mouse interface. The haptic system used in this research is a two degree of freedom (DOF) Pantograph planar device. To detect the intended user motion, the device is equipped with force sensing allowing the monitoring of the user applied loads. Impedance based techniques are used to develop a “clumsy” motion suppression control system. The erratic motion suppression techniques and the experimental system setup are evaluated in two dimensional tracking tasks using a human subject with failure of the gross coordination of the upper limb muscle movements resulting from a disorder called ‘Muscle Ataxia’. The results presented demonstrate the ability of the system to improve the tracking performance of the impaired user while interacting with a simple computer generated 2D space.

Adaptive Nonlinear Control of SMA-Based Bending Micro Actuator

Shape Memory Alloys (SMAs) have several attractive features that make them potentially useful concepts as bending micro actuators. SMA linear actuators are among those producing the highest strains and highest forces available, and when employed in a bending mode, their deflection capability is enhanced even more leading to potential new applications. This paper addresses the basic design concept for a bi-material actuator modeled as an initially curved composite beam with one active layer, the SMA material, and one conventional elastic layer. This device must be accurately controlled to achieve an optimal range of motion and to serve in many new applications so we have designed a nonlinear and adaptive control scheme based on Lypaunove stability theory to prevent erratic motion and even component separation and partial buckling. In addition, this control scheme is able to achieve high precision tracking without the need for detailed system parameters. Simulation is conducted which confirm the effectiveness of the proposed method.

A Conjectured Solder Fatigue Law Based on Nonlinear Dynamics

A discipline of nonlinear dynamics (Chaos Theory), not traditionally used in the study of solder, is applied here in developing a conjectured general form for fatigue based on creep. Solder joint data are analyzed which demonstrates two strain-rate regimes. In the literature, this is recognized as related to the two modes of grain boundary and matrix creep. In this paper, the behavior is treated as a “bifurcation” and a quadratic normal form identified which addresses qualitative features of the observed data. The resulting mathematical model is transformed into a quadratic map (difference equation) which is a classic paradigm for chaotic motion. This model addresses not only the two distinct rate regimes but also an unstable intermediate range of erratic motion which is observed in the data. Correlation between solder fatigue behavior and onset of model instability regarding effects of solder dwell (model relaxation) and solder grain size (assumed to be associated with model time increment) has been discussed in previous work. This has motivated examination of the classic Coffin-Manson (C.M.) low cycle fatigue law for elastic, plastic deformation in terms of appropriate quadratic maps. The result is a “curve-fit” representation of the C.M. forms in terms of map parameters. In particular, a simple relationship appears to exist between the “universal slopes” of the C.M. law and the “universal” Feigenbaum constant δ = 4.66920..., so called because it is associated with a wide class of maps which includes the quadratic as a special case. With this approach, a conjectured form of solder fatigue law under creep deformation is generated. General properties of the resulting form are discussed and compared with some of the fatigue models currently in use.