No abstract

Inspired by recent observations on active self-organized critical (SOC) systems, we designed an active pile (or ant pile) model with two ingredients: beyond-threshold toppling and under-threshold active motions. By including the latter component, we were able to replace the typical power-law distribution for geometric observables with a stretched exponential fat-tailed distribution, where the exponent and decay rate are dependent on the activity’s strength (ζ). This observation helped us to uncover a hidden connection between active SOC systems and α-stable Levy systems. We demonstrate that one can partially sweep α-stable Levy distributions by changing ζ. The system undergoes a crossover towards Bak–Tang–Weisenfeld (BTW) sandpiles with a power-law behavior (SOC fixed point) below a crossover point ζ<ζ*≈0.1.

We present a non-perturbative mesh-free spectral method for the axisymmetric scenario of a radially highly deformed sphere in Stokes flow. Spectra of harmonic and biharmonic Stokes flow modes are used to provide a general algebraic spectral solution to axisymmetric Stokes flow. A solution for the flow field around a sphere with prescribed surface velocity field is presented, and is used to obtain the velocity field around a deformed sphere. The method is demonstrated on two problems: hydrodynamic radii of radially deformed spheres for a range of strength and angular dependence of the deformation, with results in good agreement with the boundary element method; and self-phoretic velocity of spheroids with surface flux of the driving field in a source/sink or source/inert configuration.