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 the nanoscale. 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. It is shown that the device can hold up extremely high velocities, unlike what the general perception of the Casimir force as a weak interaction might suggest.
We study the influence of a wall on the dynamics of a low-Reynolds-number three-sphere swimmer. A far swimmer whose arm makes an angle theta with the horizon experiences the wall presence as an angle-dependent quadrupole force proportional to (a/L)(2)(L/z)(2)cos theta, where a, L, and z are the radius of spheres, the arm length, and the swimmer distance to the wall, respectively. The wall-induced translational velocity of swimmer is perpendicular to the arms. A far swimmer prefers to orient its arms parallel to the plate. This state is stable. Remarkably, the parallel state is unstable when the swimmer is close to the wall. In this regime, the velocity of swimmer decreases as (z/L)(2). Numerical solution of the equations of motion for arbitrary initial z/L and theta reveals four different phases of locomotion.
We study light transport in a honeycomb structure as the simplest two-dimensional model foam. We apply geometrical optics to set up a persistent random walk for the photons. For three special injection angles of 30 degrees, 60 degrees, and 90 degrees relative to a hexagon's edge, we are able to demonstrate by analytical means the diffusive behavior of the photons and to derive their diffusion constants in terms of intensity reflectance, edge length, and velocity of light. Numerical simulations reveal an interesting dependence of the diffusion constant on the injection angle in contrast to the usual assumption that in the diffusive limit the photon has no memory for its initial conditions. Furthermore, for injection angles close to 30 degrees, the diffusion constant does not converge to the value at 30 degrees. We explain this observation in terms of a two-state model.
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