Pairwise interactions in inertially-driven one-dimensional microfluidic crystals

In microfluidic devices, inertia drives particles to focus on a finite number of inertial focusing streamlines. Particles on the same streamline interact to form one-dimensional microfluidic crystals (or "particle trains"). Here we develop an asymptotic theory to describe the pairwise interactions underlying the formation of a 1D crystal. Surprisingly, we show that particles assemble into stable equilibria, analogous to the motion of a damped spring. Although previously it has been assumed that particle spacings scale with particle diameters, we show that the equilibrium spacing of particles depends on the distance between the inertial focusing streamline and the nearest channel wall, and therefore can be controlled by tuning the particle radius.Comment: 15 pages, 9 figure

Homogeneous Interpretable Approximations to Heterogeneous SIR Models

The SIR-compartment model is among the simplest models that describe the spread of a disease through a population. The model makes the unrealistic assumption that the population through which the disease is spreading is well-mixed. Although real populations have heterogeneities in contacts not represented in the SIR model, it nevertheless well fits real US state Covid-19 case data. Here we demonstrate mathematically how closely the simple continuous SIR model approximates a model which includes heterogeneous contacts, and provide insight onto how one can interpret parameters gleaned from regression in the context of heterogeneous dynamics

Summoning the wind: Hydrodynamic cooperation of forcibly ejected fungal spores

The forcibly launched spores of the crop pathogen \emph{Sclerotinia sclerotiorum} must eject through many centimeters of nearly still air to reach the flowers of the plants that the fungus infects. Because of their microscopic size, individually ejected spores are quickly brought to rest by drag. In the accompanying fluid dynamics video we show experimental and numerical simulations that demonstrate how, by coordinating the nearly simultaneous ejection of hundreds of thousands of spores,\emph{Sclerotinia} and other species of apothecial fungus are able to sculpt a flow of air that carries spores across the boundary layer and around intervening obstacles. Many spores are sacrificed to create this flow of air. Although high speed imaging of spore launch in a wild isolate of the dung fungus \emph{Ascobolus} shows that the synchronization of spore ejections is self-organized, which could lead to spores delaying their ejection to avoid being sacrificed, simulations and asymptotic analysis show that, close the fruit body, ejected spores form a sheet-like jet that advances across the fruit body as more spores are ejected. By ejecting on the arrival of the sheet spores maximize \emph{both} their range and their contribution to the cooperative wind.Comment: Submission to the DFD 2009 Gallery of Fluid Motio