"Dragons" on the landscape: Modeling the abundance of large carnivorous dinosaurs of the Upper Jurassic Morrison Formation (USA) and the Upper Cretaceous Dinosaur Park Formation (Canada).

Counts of the number of skeletal specimens of "adult" megaherbivores and large theropods from the Morrison and Dinosaur Park formations-if not biased by taphonomic artifacts-suggest that the big meat-eaters were more abundant, relative to the number of big plant-eaters, than one would expect on the basis of the relative abundance of large carnivores and herbivores in modern mammalian faunas. Models of megaherbivore population density (number of individuals per square kilometer) that attempt to take into account ecosystem productivity, the size structure of megaherbivore populations, and individual megaherbivore energy requirements, when combined with values of the large theropod/megaherbivore abundance ratio, suggest that large theropods may have been more abundant on the landscape than estimates extrapolated from the population density versus body mass relationship of mammalian carnivores. Models of the meat production of megaherbivore populations and the meat requirements of "adult" large theropods suggest that herbivore productivity would have been insufficient to support the associated number of individuals of "adult" large theropods, unless the herbivore production/biomass ratio was substantially higher, and/or the large theropod meat requirement markedly lower, than expectations based on modern mammals. Alternatively, or in addition to one or both of these other factors, large theropods likely included dinosaurs other than megaherbivores as significant components of their diet.

Oscillatory instability in a reaction front separating fluids of different densities.

Reaction fronts described by the Kuramoto-Sivashinsky (KS) equation can exhibit complex behavior as they separate reacted from unreacted fluids. If the fluid of higher density is above a fluid of lower density, then the Rayleigh-Taylor instability can lead to fluid motion. In the reverse situation, where the lighter fluid is on top, gravitationally driven forces can stabilize a convectionless flat front inhibiting the complex front propagation described by the KS equation. In these cases, a critical density difference is required to provide stability to the flat front. A linear stability analysis shows that the transition from stable to unstable flat fronts can be oscillatory for viscous fluid motion. Once the transition takes place, the fronts exhibit oscillatory convection resulting in oscillations of the shape and speed of the front.

Stability of convective patterns in reaction fronts: a comparison of three models.

Autocatalytic reaction fronts generate density gradients that may lead to convection. Fronts propagating in vertical tubes can be flat, axisymmetric, or nonaxisymmetric, depending on the diameter of the tube. In this paper, we study the transitions to convection as well as the stability of different types of fronts. We analyze the stability of the convective reaction fronts using three different models for front propagation. We use a model based on a reaction-diffusion-advection equation coupled to the Navier-Stokes equations to account for fluid flow. A second model replaces the reaction-diffusion equation with a thin front approximation where the front speed depends on the front curvature. We also introduce a new low-dimensional model based on a finite mode truncation. This model allows a complete analysis of all stable and unstable fronts.