Spurious Behaviour of Numerically Computed Fluid Flow

We investigate the stability to aliasing errors of numericalschemes for hydrodynamics, taking the viscous Burgers' equationas a model for systems with a term that is quadratic in thevelocity. Considering wavelengths equal to three times the mesh-spacing,and arbitrary mean flow, we are able to demonstrate explicitlyfor common schemes (a) a sufficient criterion for stabilityand (b) blow-up of solutions in a finite time when (a) is violated.Singular behaviour is shown to persist at all wavelengths: studiesof wavelengths up to thirty times mesh-spacing make it clearthat a profile with a single region of strong convergent flowis most conducive to instability. In contrast, spectral (Galerkin)and upwind schemes are shown to be stable for all flows andperiods.     

A METAPHYSIOLOGICAL POPULATION MODEL OF STORAGE IN VARIABLE ENVIRONMENTS

ABSTRACT. We use mechanistic arguments to generalize a hierarchical metaphysiological approach developed by one of us to modeling biological populations (Getz, [1991, 1993]) and extend the approach to include a storage component in the population. We model the growth of single species and consumer-resource interactions, both with and without storage. Our approach unifies modeling storage across trophic levels and is much simpler and more efficient to implement numerically than individual based approaches or population approaches that include integral, delay, or partial differential equation components in the model. Using intake functions (i.e., functional responses) that include the effects of interference competition, we apply the model to a hypothetical herbivore feeding on a resource that fluctuates seasonally and demonstrate the importance of a flow from storage that buffers the population against periods when resources are scarce or absent. We also apply the model to a hypothetical plant population that is driven by fluctuating resources and demonstrate the importance of a translocation flow from storage at the end of a dormant season, corresponding to periods when resources are most scarce. Finally, we couple these two populations for the case where the herbivore feeds exclusively on non-storage biomass, and demonstrate how the population dynamics can be affected by the rates at which buffering and translocation flows transfer from storage to active tissue in the herbivore and plant populations. In particular, for certain buffering and translocation flow rates, 1-year unimodal, 2-year bimodal, and 2-year unimodal cycles can emerge in the same herbivore population.     

Interaction induced Raman light scattering as a probe of the local density structure of binary supercritical solutions

Interaction induced Raman light scattering is presented as a unique tool for the understanding of solvation processes from the solute's point of view in weakly interacting solute-solvent systems. A review of pertinent literature shows that this technique should be useful at least in single-phase binary mixtures such as supercritical solutions. Methane is used here as a probe molecule at 10mol% concentration (as the solute) and 90mol% CO and CO₂ are the solvents. The light scattering results, i.e., the dependence of the anisotropic intensities divided by density (I/d) on the density, are interpreted by use of the Duh-Haymet-Henderson closure (bridge) function of the Ornstein-Zernike integral equation. These data, together, are examined in the context of known supercritical solution thermodynamics and statistical mechanical results. It is shown that the light scattering I/d data versus density yield maxima in both attractive and repulsive solute-solvent systems. The local number density maxima were found near these same densities by the integral equation calculations for both methane + carbon monoxide or carbon dioxide using only Lennard-Jones single-centre parameters as input. The methane + carbon monoxide system is identified as weakly attractive (augmenting), whereas the methane + carbon dioxide system is identified as repulsive (avoidance).