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Biological invasions often have outsized consequences for the invaded ecosystem and represent an interesting challenge to model mathematically. Landscape heterogeneity, non-local or time-dependent spreading mechanisms, coarse data, and air or water flow transport are but a few of the complications that can greatly affect our understanding of small organism movement – a critical component of […] |
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In water-limited regions, competition for water resources results in the formation of vegetation patterns; on sloped terrain, one finds that the vegetation typically aligns in stripes or arcs. The dynamics of these patterns can be modeled by reaction-diffusion PDEs describing the interplay of vegetation and water resources, where sloped terrain is modeled through advection terms […] |
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