Simple Coalitional Strategy Profiles in Repeated Games

This paper is a version of the discussion paper titled "Simple coalitional strategy profiles"

Studies in vortex motion

This thesis covers four different problems in the understanding of vortex sheets, and these are presented in four chapters.

In Chapter 1, free streamline theory is used to determine the steady solutions of an array of identical, hollow or stagnant core vortices in an inviscid, incompressible fluid. Assuming the array is symmetric to rotation through π radians about an axis through any vortex centre, there are two solutions or no solutions depending on whether A^(1/2)/L is less than or greater than 0.38 where A is the area of the vortex and L is the separation distance. Stability analysis shows that the more deformed shape is unstable to infinitesimal symmetric disturbances which leave the centres of the vortices undisplaced.

Chapter 2 is concerned with the roll-up of vortex sheets in homogeneous fluid. The flow over conventional and ring wings is used to test the method of Fink and Soh (1974). Despite modifications which improve the accuracy of the method, unphysical results occur. A possible explanation for this is that small scales are important and an alternate method based on "Cloud-in-Cell" techniques is introduced. The results show small scale growth and amalgamation into larger structures.

The motion of a buoyant pair of line vortices of opposite circulation is considered in Chapter 3. The density difference between the fluid carried by the vortices and the fluid outside is considered small, so that the Boussinesq approximation may be used. A macroscopic model is developed which shows the formation of a detrainment filament and this is included as a modification to the model. The results agree well with the numerical solution as developed by Hill (1975b) and show that after an initial slowdown, the vortices begin to accelerate downwards.

Chapter 4 reproduces completely a paper that has already been published (Baker, Barker, Bofah and Saffman (1974)) on the effect of "vortex wandering" on the measurement of velocity profiles of the trailing vortices behind a wing.

Space-resolved spectral diagnosis of line-shaped laser-produced magnesium plasmas

Space-resolved spectra of line-shaped laser-produced magnesium plasmas in the normal direction of the target have been obtained using a pinhole crystal spectrograph. These spectra are treated by a spectrum analyzing code for obtaining the true spectra and fine structures of overlapped lines. The spatial distributions of electron temperature and density along the normal direction of the target surface have been obtained with different spectral diagnostic techniques. Especially, the electron density plateaus beyond the critical surface in line-shaped magnesium plasmas have been obtained with a fitting technique applied to the Stark-broadened Ly-alpha wings of hydrogenic ions. The difference of plasma parameters between those obtained by different diagnostic techniques is discussed. Other phenomena, such as plasma satellites, population inversion, etc., which are observed in magnesium plasmas, are also presented.

Challenges in using science-based shoreline setbacks: Examples from South Carolina

Beachfront jurisdictional lines were established by the South Carolina Beachfront Management Act (SC Code §48- 39-250 et seq.) in 1988 to regulate the new construction, repair, or reconstruction of buildings and erosion control structures along the state’s ocean shorelines. Building within the state’s beachfront “setback area” is allowed, but is subject to special regulations. For “standard beaches” (those not influenced by tidal inlets or associated shoals), a baseline is established at the crest of the primary oceanfront sand dune; for “unstabilized inlet zones,” the baseline is drawn at the most landward point of erosion during the past forty years. The parallel setback line is then established landward of the baseline a distance of forty times the long-term average annual erosion rate (not less than twenty feet from the baseline in stable or accreting areas). The positions of the baseline and setback line are updated every 8-10 years using the best available scientific and historical data, including aerial imagery, LiDAR, historical shorelines, beach profiles, and long-term erosion rates. One advantage of science-based setbacks is that, by using actual historical and current shoreline positions and beach profile data, they reflect the general erosion threat to beachfront structures. However, recent experiences with revising the baseline and setback line indicate that significant challenges and management implications also exist. (PDF contains 3 pages)