Kinetic Intersections as a Source of Information on Rate Coefficients

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Optimal control of spatial-dynamic processes: The case of biological invasions

This study examines the spatial nature of optimal bioinvasion control. We develop and parameterize a spatially explicit two-dimensional model of species spread that allows for differential control across space and time, and we solve for optimal control strategies. We find that the qualitative nature of optimal strategies depend in interesting ways on aspects of landscape and invasion geometry. For example, we show that reducing the extent of exposed invasion edge, through spread, removal, or strategically employing landscape features, can be an optimal strategy because it reduces long-term containment costs. We also show that optimal invasion control is spatially and temporally “forward-looking” in the sense that strategies should be targeted to slow the spread of an invasion in the direction of greatest potential long-term damages. These and other novel findings contribute to the largely nonspatial literature on optimally controlling invasions and to understanding control of spatial-dynamic processes in general.invasive species, spatial-dynamic processes, spatial spread, reaction-diffusion, management, cellular automaton, eradication, containment, spatial control, integer programming, Environmental Economics and Policy, Land Economics/Use, Resource /Energy Economics and Policy, Q, Q1, Q2, Q5,

Optimal transport in competition with reaction: the Hellinger-Kantorovich distance and geodesic curves

We discuss a new notion of distance on the space of finite and nonnegative measures which can be seen as a generalization of the well-known Kantorovich-Wasserstein distance. The new distance is based on a dynamical formulation given by an Onsager operator that is the sum of a Wasserstein diffusion part and an additional reaction part describing the generation and absorption of mass. We present a full characterization of the distance and its properties. In fact the distance can be equivalently described by an optimal transport problem on the cone space over the underlying metric space. We give a construction of geodesic curves and discuss their properties