Sensitivity to initial conditions in self-organized critical systems

We discuss sensitivity to initial conditions in a model for avalanches in granular media displaying self-organized criticality. We show that damage, due to a small perturbation in initial conditions, does not spread. The damage persists in a statistically time-invariant and scale-free form. We argue that the origin of this behavior is the Abelian nature of the model, which generalizes our results to all Abelian models, including the BTW model and the Manna model. An ensemble average of the damage leads to seemingly time dependent damage spreading. Scaling arguments show that this numerical result is due to the time lag before avalanches reach the initial perturbation.Comment: 4 pages, 4 figures, submitted to Physical Review Letter

Concentrated Poverty Increased in Both Rural and Urban Areas Since 2000, Reversing Declines in the 1990s

In this brief, authors Brian Thiede, Hyojung Kim, and Matthew Valasik discuss changes in poverty levels among U.S. counties using data from the 2000 U.S. Decennial Census and the 2005–2009 and 2011-2015 American Community Surveys. They report that the share of rural counties with high poverty rates (20 percent or more) increased from 20.6 percent in 2000 to 32.5 percent in the aggregate 2011–2015 data, and the share of high-poverty urban counties increased from 6.7 to 15.6 percent. The share of the population living in these high-poverty counties nearly doubled in both rural and urban areas during this period. Substantial increases in concentrated poverty occurred in rural areas both before and after the Great Recession, but increases in urban areas primarily occurred in years during and after the downturn. In rural areas, increases in concentrated poverty were greatest among micropolitan counties with small cities, which had historically been characterized by lower poverty rates than more sparsely populated and isolated areas. Increases in the population exposed to concentrated poverty were greater among the rural non-Hispanic white and black populations than among rural Hispanics. The authors conclude that the overall resurgence of concentrated poverty since 2000 should be of concern to policy makers and other stakeholders since areas with very high poverty rates face many social, economic, and health challenges