Hessian geometry and the holomorphic anomaly

We present a geometrical framework which incorporates higher derivative corrections to the action of N = 2 vector multiplets in terms of an enlarged scalar manifold which includes a complex deformation parameter. This enlarged space carries a deformed version of special Kahler geometry which we characterise. The holomorphic anomaly equation arises in this framework from the integrability condition for the existence of a Hesse potential.Comment: 43 pages. Revised version: minimal changes. Final version, accepted for publication by JHE

Shallow Surveying in Hazardous Waters

Of order one importance to any study of nearshore processes is knowledge of the bathymetry in shallow water. This is true for studies on open coast sandy beaches where surf zone dynamics drive the system, inlet environments where bathymetric evolution can rapidly change navigation channels, and in more benign, lower-energy coastal environments that evolve slowly over 10’s to 100’s of years. Difficulties in obtaining shallow bathymetry where depth-limited wave breaking occurs, submerged hazards are present, or other harsh environments has led to the development of survey systems on highly maneuverable personal watercraft (Beach, et al., 1994; Cote, 1999; Dugan, et al., 1999; MacMahan, 2001). In this work we discuss shallow water surveying from the Coastal Bathymetry Survey System (CBASS), a Yamaha Waverunner equipped with differential GPS, single-beam 192 KHz acoustic echo-sounder, and onboard navigation system. Data obtained with the CBASS in three regions will be discussed, including an energetic surf zone located in southern California during the 2003 Nearshore Canyon Experiment (NCEX), on Lake Erie in 2002 (and compared with historical surveys dating back 150 years), and around Piscataqua River Inlet, NH, in 2007. Estimated accuracy (for sandy bottoms) in water depths ranging 1–10 m are 0.07-0.10 m in the vertical, and on the order of 0.1-1 m horizontally depending on water depth and bottom slope. The high maneuverability of the personal watercraft makes very shallow water bathymetric surveys possible with acoustic altimeters, particularly in regions where airborne remote sensing systems fail (owing to water clarity issues) or where repeated high resolution surveys are required (e.g., where an erodible bottom is rapidly evolving)