Zone design of specific sizes using adaptive additively weighted Voronoi diagrams

Territory or zone design processes entail partitioning a geographic space, organized as a set of areal units, into different regions or zones according to a specific set of criteria that are dependent on the application context. In most cases, the aim is to create zones of approximately equal sizes (zones with equal numbers of inhabitants, same average sales, etc.). However, some of the new applications that have emerged, particularly in the context of sustainable development policies, are aimed at defining zones of a predetermined, though not necessarily similar, size. In addition, the zones should be built around a given set of seeds. This type of partitioning has not been sufficiently researched; therefore, there are no known approaches for automated zone delimitation. This study proposes a new method based on a discrete version of the adaptive additively weighted Voronoi diagram that makes it possible to partition a two-dimensional space into zones of specific sizes, taking both the position and the weight of each seed into account. The method consists of repeatedly solving a traditional additively weighted Voronoi diagram, so that each seed's weight is updated at every iteration. The zones are geographically connected using a metric based on the shortest path. Tests conducted on the extensive farming system of three municipalities in Castile-La Mancha (Spain) have established that the proposed heuristic procedure is valid for solving this type of partitioning problem. Nevertheless, these tests confirmed that the given seed position determines the spatial configuration the method must solve and this may have a great impact on the resulting partition.     

A geochemical approach to distinguishing competing tectono-magmatic processes preserved in small eruptive centres

Small eruptive centres (SECs) representing short-lived, isolated eruptions are effective samples of mantle heterogeneity over a given area, as they are generally of basaltic composition and show evidence of little magmatic processing. This is particularly powerful in volcanic arcs where the original melting process generating stratovolcanoes is often obscured by additions from the down-going slab (fluids and sediments) and the overlying crust. The Pucón area of southern Chile contains active and dormant stratovolcanoes, Holocene, basaltic SECs and an arc-scale strike-slip fault (the Liquiñe Ofqui Fault System: LOFS). The SECs show unexpected compositional heterogeneity considering their spatial proximity. We present a detailed study of these SECs combining whole rock major and trace element concentrations, U-Th isotopes and olivine-hosted melt inclusion major element and volatile contents to highlight the complex inter-relations in this small but active area. We show that heterogeneity preserved at individual SECs relates to different processes: some start in the melting region with the input of slab-derived fluids, whilst others occur later in a centre’s magmatic history with the influence of crustal contamination prior to olivine crystallisation. These signals are deduced through the combination of the different geochemical tools used in this study. We show that there is no correlation between composition and distance from the arc front, whilst the local tectonic regime has an effect on melt composition: SECs aligned along the LOFS have either equilibrium U-Th ratios or small Th-excesses instead of the large—fluid influenced—U-excesses displayed by SECs situated away from this feature. One of the SECs is modelled as being generated from fluid-enriched depleted mantle, a source which it may share with the stratovolcano Villarrica, whilst another SEC with abundant evidence of crustal contamination may share its plumbing system with its neighbouring stratovolcano Quetrupillán, showing that polygenetic–monogenetic connections are unpredictable. Such marked preservation of individual magmatic histories highlights the isolation of individual melting events even in complex and highly volcanically active areas.     

Computation of X-Ray Blazar Light Curves Using RHD Simulations

We present the results of a two-dimensional relativistic hydrodynamic simulation of collisions of dense shells of matter moving within a uniform jet. The non-thermal synchrotron radiation produced by the relativistic electrons injected at shocks is computed following their temporal and spatial evolution. We test different parameterizations of the shock acceleration process and compute the corresponding X-ray light curves. A time lag between hard and soft X-ray radiation is found. The collision has an efficiency of few times 10^?3 in converting kinetic energy into radiation.