Anchored Peskin filaments evolve by a fractional Laplacian with homogeneous Dirichlet conditions, have circular-arc equilibria for broad elastic energies, and regularize instantly to C^∞.
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In concentric setups the droplet velocity is independent of surface shear viscosity but depends on dilatational viscosity via confinement and viscosity ratio; eccentricity introduces shear-viscosity dependence that consistently enhances droplet motion.
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Anchored Peskin Problem
Anchored Peskin filaments evolve by a fractional Laplacian with homogeneous Dirichlet conditions, have circular-arc equilibria for broad elastic energies, and regularize instantly to C^∞.
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Effects of surface viscosities on the motion of a droplet enclosing a translating particle
In concentric setups the droplet velocity is independent of surface shear viscosity but depends on dilatational viscosity via confinement and viscosity ratio; eccentricity introduces shear-viscosity dependence that consistently enhances droplet motion.