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Creators/Authors contains: "Shattuck, Mark D."

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  5. Numerous experimental and computational studies show that continuous hopper flows of granular materials obey the Beverloo equation that relates the volume flow rate Q and the orifice width w : Q ∼ ( w / σ avg − k ) β , where σ avg is the average particle diameter, kσ avg is an offset where Q ∼ 0, the power-law scaling exponent β = d − 1/2, and d is the spatial dimension. Recent studies of hopper flows of deformable particles in different background fluids suggest that the particle stiffness and dissipation mechanism can also strongly affect the power-law scaling exponent β . We carry out computational studies of hopper flows of deformable particles with both kinetic friction and background fluid dissipation in two and three dimensions. We show that the exponent β varies continuously with the ratio of the viscous drag to the kinetic friction coefficient, λ = ζ / μ . β = d − 1/2 in the λ → 0 limit and d − 3/2 in the λ → ∞ limit, with a midpoint λ c that depends on the hopper opening angle θ w . We also characterize the spatial structure of the flows and associate changes in spatial structure of the hopper flows to changes in the exponent β . The offset k increases with particle stiffness until k ∼ k max in the hard-particle limit, where k max ∼ 3.5 is larger for λ → ∞ compared to that for λ → 0. Finally, we show that the simulations of hopper flows of deformable particles in the λ → ∞ limit recapitulate the experimental results for quasi-2D hopper flows of oil droplets in water. 
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  6. The spongy mesophyll is a complex, porous tissue found in plant leaves that enables carbon capture and provides mechanical stability. Unlike many other biological tissues, which remain confluent throughout development, the spongy mesophyll must develop from an initially confluent tissue into a tortuous network of cells with a large proportion of intercellular airspace. How the airspace in the spongy mesophyll develops while the tissue remains mechanically stable is unknown. Here, we use computer simulations of deformable polygons to develop a purely mechanical model for the development of the spongy mesophyll tissue. By stipulating that cell wall growth and remodelling occurs only near void space, our computational model is able to recapitulate spongy mesophyll development observed inArabidopsis thalianaleaves. We find that robust generation of pore space in the spongy mesophyll requires a balance of cell growth, adhesion, stiffness and tissue pressure to ensure cell networks become porous yet maintain mechanical stability. The success of this mechanical model of morphogenesis suggests that simple physical principles can coordinate and drive the development of complex plant tissues like the spongy mesophyll.

     
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