Abstract
We introduce a modeling framework that can be applied to cases of multiple converging fronts during episodes of population expansion and innovation diffusion, referring to two prehistoric case studies known archaeologically (the spread of pottery-making in Europe, and the spread of farming in southern Africa). We model front propagation using Fast Marching methods, drawing on the analogy with crystallization processes to build compoundly-weighted Voronoi diagrams of a spatially partitioned surface in which the zones of influence of each competing spreading process are determined by their respective front initiation times and propagation rates. We analyze the phase space for the general two-source case, and illustrate the potential of this approach by modeling the evolving interface for the archaeological case studies.
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