Mahadevan, L., Ryu, W.S. & Samuel, A.D.T. Tumbling cards. Physics of Fluids 11, 1, 1-3 (1999). Publisher's VersionAbstract
When a stiff rectangular card is dropped in still air with its long axis horizontal, it often settles into a regular mode of motion; while revolving around its long axis it descends along a path that is inclined to the vertical at a nearly constant angle. We show experimentally that the tumbling frequency Omega of a card of length \(l\), width \(w\) and thickness \(d (l≫w≫d)(l≫w≫d)\) scales as Omega ~ d1/2w-1, consistent with a simple dimensional argument that balances the drag against gravity.
Mahadevan, L., Ryu, W.S. & Samuel, A.D.T. Fluid ‘rope trick’ investigated . Nature 392, 140, (1998). Publisher's VersionAbstract
Buckling instabilities can arise from competition between axial compression and bending in slender objects. These are not restricted to solids, but also occur with fluids with free surfaces1,4, in geophysics5 and in materials processing6. Here we consider a classic demonstration of fluid buckling7.
Samuel, A.D.T. & Berg, H.C. Statistical kinetics of the bacterial flagellar motor. Physical Review E 55, 6, 7801-7804 (1997). Publisher's VersionAbstract
The statistical behavior of the bacterial flagellar motor matches that of a Poisson stepper that takes at least 400 steps per revolution. Using this fact, we study the effect of motor stochastics on experiments in which fluorescent motors, initially synchronized by polarization photobleaching, become uncorrelated.
Stone, H.A. & Samuel, A.D.T. Propulsion of Microorganisms by Surface Distortions. Physical Review Letters 77, 19, 4102-4104 (1996). Publisher's VersionAbstract
Swimming strategies of microorganisms must conform to the principles of self-propulsion at low Reynolds numbers. Here we relate the translational and rotational speeds to the surface motions of a swimmer and, for spheres, make evident novel constraints on mechanisms for propulsion. The results are applied to a cyanobacterium, an organism whose motile mechanism is unknown, by considering incompressible streaming of the cell surface and oscillatory, tangential surface deformations. Finally, swimming efficiency using tangential motions is related to the surface velocities and a bound on the efficiency is obtained.
Samuel, A.D. & Berg, H.C. Torque-generating units of the bacterial flagellar motor step independently. Biophysical Journal 71, 2, 918-923 (1996). Publisher's VersionAbstract
Measurements of the variance in rotation period of tethered cells as a function of mean rotation rate have shown that the flagellar motor of Escherichia coli is a stepping motor. Here, by measurement of the variance in rotation period as a function of the number of active torque-generating units, it is shown that each unit steps independently.
Ehlers, K.M., Samuel, A.D., Berg, H.C. & Montgomery, R. Do cyanobacteria swim using traveling surface waves?. Proceedings of the National Academy of Sciences 93, 16, 8340–8343 (1996). Publisher's VersionAbstract
Bacteria that swim without the benefit of flagella might do so by generating longitudinal or transverse surface waves. For example, swimming speeds of order 25 microns/s are expected for a spherical cell propagating longitudinal waves of 0.2 micron length, 0.02 micron amplitude, and 160 microns/s speed. This problem was solved earlier by mathematicians who were interested in the locomotion of ciliates and who considered the undulations of the envelope swept out by ciliary tips. A new solution is given for spheres propagating sinusoidal waveforms rather than Legendre polynomials. The earlier work is reviewed and possible experimental tests are suggested.
Samuel, A.D. & Berg, H.C. Fluctuation analysis of rotational speeds of the bacterial flagellar motor. Proceedings of the National Academy of Sciences 92, 8, 3502–3506 (1995). Publisher's VersionAbstract
We measured the dependence of the variance in the rotation rate of tethered cells of Escherichia coli on the mean rotation rate over a regime in which the motor generates constant torque. This dependence was compared with that of broken motors. In either case, motor torque was augmented with externally applied torque. We show that, in contrast to broken motors, functioning motors in this regime do not freely rotationally diffuse and that the variance measurements are consistent with the predicted values of a stepping mechanism with exponentially distributed waiting times (a Poisson stepper) that steps approximately 400 times per revolution.