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Abstract The generalized Hastings–McLeod solutions to the inhomogeneous Painlevé-II equation arise in multi-critical unitary random matrix ensembles, the chiral two-matrix model for rectangular matrices, non-intersecting squared Bessel paths, and non-intersecting Brownian bridges on the circle. We establish the leading-order asymptotic behavior of the generalized Hastings–McLeod functions as the inhomogeneous parameter approaches infinity using the Deift–Zhou nonlinear steepest-descent method for Riemann–Hilbert problems. This analysis is done in both the pole-free region and pole region. The asymptotic formulae show excellent agreement with numerically computed solutions in both regions. 

Abstract Between the 1780 and 1980s, more than half of the wetlands in the conterminous US were lost. As wetlands have been lost, numerous artificial water features (AWFs), such as stormwater retention ponds, golf course water features, and reservoirs, have been constructed. We contrasted the loss of wetland area and perimeter to the gain of AWF area and perimeter and further explored how this transformation has altered the spatial characteristics of the waterscape. We conducted this analysis in the Tampa Bay Watershed, a large coastal watershed that lost 33% of its wetland area between the 1950s-2007. Trends have been towards fewer, smaller wetlands and more, smaller AWFs. The loss of wetland area far exceeds the gain in AWF area, leading to an overall loss of 23% of the combined wetland and AWF area. However, the loss of wetland perimeter almost equals the gain in AWF perimeter, leading to an overall loss of just 2% of the combined wetland and AWF perimeter. The loss of wetlands and gain of AWFs have predominantly occurred in different geographic locations, with the loss of wetlands predominantly in the headwaters and the gain in AWFs predominantly adjacent to Tampa Bay. Wetlands became further apart, though generally retained their natural distribution, while AWFs became closer to one another and now mirror the more natural wetland distribution. Overall, the physical structure of the waterscape of today is different than in the past, which likely reflects a change in functions performed and related ecological services provided at local and landscape scales.