How simple grazing rules can lead to persistent boundaries in vegetation communities.

Natural landscape boundaries between vegetation communities are dynamically influenced by the selective grazing of herbivores. Here we show how this may be an emergent property of very simple animal decisions, without the need for any sophisticated choice rules etc., using a model based on biased diffusion. Animal grazing intensity is coupled with plant competition, resulting in reaction-diffusion dynamics, from which stable boundaries spontaneously emerge. In the model, animals affect their resources by both consumption and trampling. It is assumed that forage consists of two heterogeneously distributed competing resource species, one that is preferred (grass) over the other (heather) by the animals. The solutions to the resulting system of differential equations for three cases a) optimal foraging, b) random walk foraging and c) taxis-diffusion are presented. Optimal and random foraging gave unrealistic results, but taxis-diffusion accorded well with field observations. Persistent boundaries between patches of near-monoculture vegetation were predicted, with these boundaries drifting in response to overall grazing pressure (grass advancing with increased grazing and vice versa). The reaction-taxis-diffusion model provides the first mathematical explanation for such vegetation mosaic dynamics and the parameters of the model are open to experimental testing.

Breaking the boundaries: Geographical approaches to integrating 200 years of the Census

The census and similar sources of data have been published for two centuries so the information that they contain should provide an unparalleled insight into the changing population of Britain over this time period. To date, however, the seemingly trivial problem of changes in boundaries has seriously hampered the use of these sources as they make it impossible to create long run time series of spatially detailed data. The paper reviews methodologies that attempt to resolve this problem by using geographical information systems and areal inter-polation to allow the reallocation of data from one set of administrative units onto another. This makes it possible to examine change over time for a standard geography and thus it becomes possible to unlock the spatial detail and the temporal depth that are held in the census and in related sources.

Correlated electron-ion dynamics with open boundaries: formalism

We extend a new formalism, which allows correlated electron-ion dynamics to be applied to the problem of open boundary conditions. We implement this at the first moment level (allowing heating of ions by electrons) and observe the expected cooling in the classical part of the ionic kinetic energy and current-induced heating in the quantum contribution. The formalism for open boundaries should be easily extended to higher moments of the correlated electron-ion fluctuations.

Structural and chemical embrittlement of grain boundaries by impurities: A general theory and first-principles calculations for copper

First-principles calculations of the Sigma 5(310)[001] symmetric tilt grain boundary in Cu with Bi, Na, and Ag substitutional impurities provide evidence that in the phenomenon of Bi embrittlement of Cu grain boundaries electronic effects do not play a major role; on the contrary, the embrittlement is mostly a structural or "size" effect. Na is predicted to be nearly as good an embrittler as Bi, whereas Ag does not embrittle the boundary in agreement with experiment. While we reject the prevailing view that "electronic" effects (i.e., charge transfer) are responsible for embrittlement, we do not exclude the role of chemistry. However, numerical results show a striking equivalence between the alkali metal Na and the semimetal Bi, small differences being accounted for by their contrasting "size" and "softness" (defined here). In order to separate structural and chemical effects unambiguously if not uniquely, we model the embrittlement process by taking the system of grain boundary and free surfaces through a sequence of precisely defined gedanken processes; each of these representing a putative mechanism. We thereby identify three mechanisms of embrittlement by substitutional impurities, two of which survive in the case of embrittlement or cohesion enhancement by interstitials. Two of the three are purely structural and the third contains both structural and chemical elements that by their very nature cannot be further unraveled. We are able to take the systems we study through each of these stages by explicit computer simulations and assess the contribution of each to the net reduction in intergranular cohesion. The conclusion we reach is that embrittlement by both Bi and Na is almost exclusively structural in origin; that is, the embrittlement is a size effect.