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The authors employ three numerical methods to explore the motion of low Reynolds number swimmers, modeling the hydrodynamic interactions by means of the Oseen tensor approximation, lattice Boltzmann simulations, and multiparticle collision dynamics. By applying the methods to a three bead linear swimmer, for which exact results are known, the authors are able to compare and assess the effectiveness of the different approaches. They then propose a new class of low Reynolds number swimmers, generalized three bead swimmers that can change both the length of their arms and the angle between them. Hence they suggest a design for a microstructure capable of moving in three dimensions. They discuss multiple bead, linear microstructures and show that they are highly efficient swimmers. They then turn to consider the swimming motion of elastic filaments. Using multiparticle collision dynamics the authors show that a driven filament behaves in a qualitatively similar way to the micron-scale swimming device recently demonstrated by Dreyfus et al. [Nature (London) 437, 862 (2005)]. [ABSTRACT FROM AUTHOR]

The problem of gravitational fluctuations confined inside a finite cutoff at radius \(r=r_c\) outside the horizon in a general class of black hole geometries is considered. Consistent boundary conditions at both the cutoff surface and the horizon are found and the resulting modes analyzed. For general cutoff \(r_c\) the dispersion relation is shown at long wavelengths to be that of a linearized Navier-Stokes fluid living on the cutoff surface. A cutoff-dependent line-integral formula for the diffusion constant \(D(r_c)\) is derived. The dependence on \(r_c\) is interpreted as renormalization group (RG) flow in the fluid. Taking the cutoff to infinity in an asymptotically AdS context, the formula for \(D(\infty)\) reproduces as a special case well-known results derived using AdS/CFT. Taking the cutoff to the horizon, the effective speed of sound goes to infinity, the fluid becomes incompressible and the Navier-Stokes dispersion relation becomes exact. The resulting universal formula for the diffusion constant \(D(horizon)\) reproduces old results from the membrane paradigm. Hence the old membrane paradigm results and new AdS/CFT results are related by RG flow. RG flow-invariance of the viscosity to entropy ratio \(\frac{\eta} {s}\) is shown to follow from the first law of thermodynamics together with isentropy of radial evolution in classical gravity. The ratio is expected to run when quantum gravitational corrections are included., Physics