ISOMETRY OF EGG SIZE IN A TEXAS POPULATION OF THE TURTLE STERNOTHERUS ODORATUS THAT EXHIBITS A NEARLY FIXED CLUTCH SIZE

In evaluating optimal egg-size theory and the effects of anatomical constraints on egg size in turtles, pivotal questions concern the significance of the relationship of egg size to female body size and whether the relationship is isometric or hypoallometric. In a central Texas population of the kinosternid turtle Sternotherus odoratus in which clutch size of a sample of turtles was nearly fixed (seven of eight females had two eggs while the largest female had three eggs), there was an isometric increase in egg width with body size among the females with two-egg clutches and significantly reduced egg width in the largest female’s three-egg clutch. Allometric analyses of populations that exhibit little variation in clutch size, as well as analysis of modal clutch sizes in populations with more variable clutch sizes, both have the potential to further illuminate the competing demands of increasing egg size vs. increasing clutch size as females grow larger, enabling them to optimize their reproductive output as it increases with body size

Richardson Varieties and Equivariant K-Theory

We generalize Standard Monomial Theory (SMT) to intersections of Schubert varieties and opposite Schubert varieties; such varieties are called Richardson varieties. The aim of this article is to get closer to a geometric interpretation of the standard monomial theory. Our methods show that in order to develop a SMT for a certain class of subvarieties in G/B (which includes G/B), it suffices to have the following three ingredients, a basis for the space of sections of an effective line bundle on G/B, compatibility of such a basis with the varieties in the class, certain quadratic relations in the monomials in the basis elements. An important tool will be the construction of nice filtrations of the vanishing ideal of the boundary of the varieties above. This provides a direct connection to the equivariant K-theory, where the combinatorially defined notion of standardness gets a geometric interpretation.Comment: 38 page

A three-dimensional lattice gas model for amphiphilic fluid dynamics

We describe a three-dimensional hydrodynamic lattice-gas model of amphiphilic fluids. This model of the non-equilibrium properties of oil-water-surfactant systems, which is a non-trivial extension of an earlier two-dimensional realisation due to Boghosian, Coveney and Emerton [Boghosian, Coveney, and Emerton 1996, Proc. Roy. Soc. A 452, 1221-1250], can be studied effectively only when it is implemented using high-performance computing and visualisation techniques. We describe essential aspects of the model's theoretical basis and computer implementation, and report on the phenomenological properties of the model which confirm that it correctly captures binary oil-water and surfactant-water behaviour, as well as the complex phase behaviour of ternary amphiphilic fluids.Comment: 34 pages, 13 figures, high resolution figures available on reques

Visualizing the Geology of Lake Trout Spawning Sites: Northern Lake Michigan

Geologists and biologists are working together to understand the links between lake floor geology (composition and shape) and the distribution of lake trout throughout their life cycle. Lake floor geology is one of the main factors determining where lake trout spawn, feed, and hide. In support of ongoing research to study Lake Michigan trout habitats, the U.S. Geological Survey in cooperation with the U.S. Army Corps of Engineers mapped the morphology of principle lake trout spawning sites. Using the Army Corps of Engineer\u27s SHOALS airborne lidar (Light Detection and Ranging) system we mapped six regions in Northern Lake Michigan in order to identify ideal spawning regions composed of shallow, clean, gravel/cobble substrate, adjacent to deeper water. Lidar mapping systems, which use laser pulses to measure water depths from an airplane, are now available to map the nearshore lake morphology at meter-scale detail. Maps generated from the bathymetric data are used to define regions with smooth homogeneous substrate, regions with higher relief, and mixed regions with both smooth and rough relief. This morphologic information combined with sediment samples and direct bottom observations enable geologists to map areas with rougher relief composed of rock outcrop, boulders, and cobbles, as well as smooth regions covered with sand or mud. This information helps biologists, fishery managers, and ecologists visualize the lake floor in significant detail which promotes better fishery management, species protection, and habitat identification. These maps present the maps and discuss the geology of the six lake trout spawning sites mapped by the lidar system. Where the mapping approached land, aerial photography of the land is combined with the bathymetric data to help visualize the scale of the offshore features. Map and perspective views of Boulder Reef, Hog Island Reef, and Little Traverse Bay are shown on sheet 1, whereas map and perspective views of Trout and High Island Shoal, Gull Island Reef, and Dahlia Shoal are shown on sheet 2. Additional information, bathymetric data, imagery, and metadata are available online athttp://geopubs.wr.usgs.gov/open-file/of03-120/