MATHEMATICAL MODELS OF DIFFUSION WITHIN A BONE BED

The issue of diffusion often enters the analysis of paleoecological abundance and diversity data from bone beds containing dermal and dental elements from amphibians, chondrichthyans, acanthodians, placoderms, or osteichthyans. We are in the initial stages of collecting various mathematical models for this diffusion, using various models from physics for inspiration. The simplest diffusion model is the classical theory of Einstein and Smoluchowski, used to analyze Brownian motion. Variations of this classical theory include anisotropic diffusion coefficients (a tensor theory), as well as inhomogeniety in the diffusion and/or drift velocity. Studies of particle diffusion in thermonuclear plasma confinement devices have led to models of far greater complexity. Each level of complexity adds more unknown parameters, and hence a drastic decrease in the prospects of a model that can be tested by analyzing samples taken from the bonebed. Our search is therefore for a bonebed with the following properties:

1. The mathematical model must contain only a few unknown parameters.

2. The bonebed should be either sufficiently large, or be associated with a sufficiently large number on nearly identical bonebeds. This will permit inferences from a sample to be tested on larger sample for statistical significance.

3. There should be maximum understanding and minimal controversy concerning both the original ecosystem, as well as the subsequent geological processes associated with the bonebed.