Integro-difference equations for interacting species and the Neolithic transition

We introduce a set of sequential integro-difference equations to analyze the dynamics of two interacting species. Firstly, we derive the speed of the fronts when a species invades a space previously occupied by a second species, and check its validity by means of numerical random-walk simulations. As an example, we consider the Neolithic transition: the predictions of the model are consistent with the archaeological data for the front speed, provided that the interaction parameter is low enough. Secondly, an equation for the coexistence time between the invasive and the invaded populations is obtained for the first time. It agrees well with the simulations, is consistent with observations of the Neolithic transition, and makes it possible to estimate the value of the interaction parameter between the incoming and the indigenous populations

Oxidation of silicon: further tests for the interfacial silicon emission model

The classical description of Si oxidation given by Deal and Grove has well-known limitations for thin oxides (below 200 Ã). Among the large number of alternative models published so far, the interfacial emission model has shown the greatest ability to fit the experimental oxidation curves. It relies on the assumption that during oxidation Si interstitials are emitted to the oxide to release strain and that the accumulation of these interstitials near the interface reduces the reaction rate there. The resulting set of differential equations makes it possible to model diverse oxidation experiments. In this paper, we have compared its predictions with two sets of experiments: (1) the pressure dependence for subatmospheric oxygen pressure and (2) the enhancement of the oxidation rate after annealing in inert atmosphere. The result is not satisfactory and raises serious doubts about the model’s correctness