Standard Embeddings of Smooth Schubert Varieties in Rational Homogeneous Manifolds of Picard Number 1

Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomogeneous smooth Schubert varieties in symplectic Grassmannians and in the 20-dimensional $F_4$-homogeneous manifold associated to a short simple root.Comment: 22 page

A model study of hydrodynamic and water quality characteristics of the Rappahannock Estuary, Virginia

A laterally integrated, two-dimensional, real-time model, consisting of linked hydrodynamic and water quality models, is developed and applied to the Rappahannock Estuary, Virginia. The hydrodynamic model, based on the principles of conservation of volume, momentum and mass, predicts surface elevation, current velocity and salinity. The water quality model, based on the conservation of mass alone, predicts eight parameters; dissolved oxygen (DO), chlorophyll \u27a\u27, carbonaceous biochemical oxygen demand (CBOD), organic nitrogen, ammonia nitrogen, nitrite-nitrate nitrogen, organic phosphorus and inorganic phosphorus. The model equations were solved using a two time level, finite difference scheme. The hydrodynamic model was calibrated and verified using field data collected in 1987 and 1990, and was used to study hydrodynamic processes. A reverse longitudinal salinity gradient, that has been frequently observed in the Rappahannock, was explained in terms of bottom topography and vertical mixing. This argument was further supported by the salinity data from 1981-1990 slackwater surveys. The often confusing usage of the phrase limit of salt intrusion in place of limit of gravitational circulation was clarified. The water quality model was calibrated and verified using the field data from 1990 surveys, and was used to study water quality conditions. Hypoxia, even anoxia, persists during summer in the bottom water of the lower portion of the Rappahannock. Sensitivity analysis showed that the bottom water ends up being hypoxic regardless of DO and CBOD in the incoming bay water, and hypoxia can be relieved more by eliminating CBOD than by increasing DO in the incoming bay water. An increase in either residual velocity or vertical mixing can relieve the hypoxic condition. Water column respiration, including CBOD decay, nitrification and algal respiration, is as important as sediment oxygen demand, and the CBOD decay is the most important in the water column. High chlorophyll concentrations in the lower portion of tidal freshwater have been observed frequently in many estuaries. Sensitivity analysis indicated that the high chlorophyll in the Rappahannock cannot be maintained without an external input of nutrients. A hypothesis was proposed to account for the nutrient source and the downriver limit of high chlorophyll concentrations

Water Quality Conditions in the Tidal Rappahannock River: Longitudinal and Dome Surveys in 1993

Previous field surveys and modeling studies (Kuo et al. 1991; Park et al. 1993) indicated the presence of three different water quality regimes in the tidal Rappahannock River (Fig. 1), a western shore tributary of Chesapeake Bay: : Region I - hypoxic conditions during summer in the bottom water between km 0-55 : Region II - high chlorophyll concentration between km 80-147 : Region III - waste water discharges from sewage treatment plants To study the differences among these 3 reaches of the river, two types of field surveys were conducted during the summer of 1993: 1) longitudinal surveys in Region III and 2) benthic flux surveys using domes in Region I and II. This data report describes these field surveys and presents the data collected from them, consisting of two parts: Part I for longitudinal surveys and Part II for dome surveys. The analysis of the data will be presented in another special report