Condensed Matter Theory

Abstract:

We investigate the hydrodynamic interactions between micro-organisms swimming at low Reynolds number. By considering simple model swimmers, and combining analytic and numerical approaches, we investigate the time-averaged flow field around a swimmer. At short distances the swimmer behaves like a pump. At large distances the velocity field depends on whether the swimming stroke is invariant under a combined time-reversal and parity transformation. We then consider two swimmers and find that the interaction between them consists of two parts: a passive term, independent of the motion of the second swimmer, and an active term resulting from the simultaneous swimming action of both swimmers. The swimmer-swimmer interaction is a complicated function of their relative displacement, orientation, and phase, leading to motion that can be attractive, repulsive, or oscillatory.

Abstract:

As the technological advances lead to miniaturization of mechanical devices, engineers face new challenges that are brought about by the fundamentally different rules that apply at small scales. One of the biggest problems in small machines is the excessive wear of the many surfaces that work in contact with each other, which severely constrains the durability of such machine parts. Here, a force that is caused by the quantum fluctuations of electromagnetic field - known as the lateral Casimir force - is employed to propose a design for a potentially wear-proof rack and pinion with no contact, which can be miniaturized to nano-scale. We demonstrate that both uniform and harmonic lateral motion of the rack can be converted into unidirectional rotation of the pinion. The robustness of the design is studied by exploring the relation between the pinion velocity and the rack velocity in the different domains of the parameter space. The effects of friction and added external load are also examined. © 2007 IOP Publishing Ltd.