Continuous Characterization of the Planform Geometry and Curvature of Meandering Rivers

The complex feedback between process and form that governs planform migration of meandering rivers is still incompletely understood. Current theoretical models aimed at predicting planform migration relate the rate of meander migration at a particular location to the channel curvature at and upstream of that location. However, these models are still incapable of reproducing complex forms of bend development, such as compound loops. Evaluation of such models requires a representation of planform curvature better than that provided by traditional methods where the curvature is calculated from directional change between the successive digitized points—an approach that provides a discrete representation of curvature dependent on the density of the digitized points used to characterize the channel planform. This article presents and evaluates a methodology that provides a continuous functional representation of the planform geometry and curvature of meandering rivers. The method involves the fitting of splines, specifically parametric cubic splines (PCSs), to discrete digitization data of the channel centerline (CL) and the arc-length parameterization of the resulting composite curve. The arc-length parameterized PCS-interpolated curve is then used to compute analytically the channel CL location and curvature for any value of the streamwise axis. Evaluation of the method involves examination of the effects of digitization interval size and digitization error on the characterization of the planform geometry and curvature using PCS fitting. The derivation of curvature values from continuous planform function for any location and any spatial interval overcomes the reliance either on average bend curvature values or on discrete curvature values based on digitized points.     

The Comparative Cost of Privatized Public School Transportation in Tennessee

This paper provides evidence from an empirical test of service contracting versus bureaucratic production of school bus transportation. Actual contracted cost of school bus service is compared to the estimate of in-house cost for providing the same service in 19 Tennessee public school systems. In-house cost is estimated from a two-output, two-input translog cost function regressed on 91 school systems. Contracted cost is found to be lower than in-house cost in 15 of the 19 contract systems. The potential savings equals 27% of average contract cost for these 15 systems. In the other 4 contract systems, actual cost exceeds the estimated in-house cost by 21% of their average contract cost.     

Dueling Decisions

In a government of divided powers, the respective roles of the president and Congress in determining American foreign policy often are disputed. Rival Supreme Court decisions on this matter, U.S. v. Curtiss-Wright Export Corporation (1936), and Youngstown Sheet and Tube Co. v. Sawyer (1952), were resurrected and argued with renewed vigor following the Iran-contra affair. Despite attempts by the defenders of each decision to discredit or reinterpret the rival case, both decisions stand as reasonable, if incompatible, interpretations of constitutional meaning.