Hypoconstrained Jammed Packings of Nonspherical Hard Particles: Ellipses and Ellipsoids

Continuing on recent computational and experimental work on jammed packings of hard ellipsoids [Donev et al., Science, vol. 303, 990-993] we consider jamming in packings of smooth strictly convex nonspherical hard particles. We explain why the isocounting conjecture, which states that for large disordered jammed packings the average contact number per particle is twice the number of degrees of freedom per particle (\bar{Z}=2d_{f}), does not apply to nonspherical particles. We develop first- and second-order conditions for jamming, and demonstrate that packings of nonspherical particles can be jammed even though they are hypoconstrained (\bar{Z}<2d_{f}). We apply an algorithm using these conditions to computer-generated hypoconstrained ellipsoid and ellipse packings and demonstrate that our algorithm does produce jammed packings, even close to the sphere point. We also consider packings that are nearly jammed and draw connections to packings of deformable (but stiff) particles. Finally, we consider the jamming conditions for nearly spherical particles and explain quantitatively the behavior we observe in the vicinity of the sphere point.Comment: 33 pages, third revisio

Mass Preferences on Shared Representation and the Composition of Legislative Districts

Abstract Scholars of redistricting often discuss &quot;communities of interest&quot; as a guideline for drawing districts, but scholarship offers little guidance on how citizens construe communities and interests in the context of representation. In this article, we seek to better understand how citizens&apos; perceptions of people and places affect preferences regarding representation. Using an original survey conducted in 15 Massachusetts communities, we explore whether citizens have meaningful preferences about the communities with whom they share the same representative. To the extent they do, we test whether these preferences are driven by geographic considerations or other factors such as partisanship, race, and socioeconomic status. Our findings not only offer the opportunity to refine the concept of &quot;communities of interest&quot; to account for voter preferences but also more broadly speak to the literature on the increasingly political nature of residential preferences and their impact on political attitudes, participation, and voting behavior