Spatial Decay Bounds for the Brinkman Fluid Equations in Double-Diffusive Convection

In this paper, we consider the Brinkman equations pipe flow, which includes the salinity and the temperature. Assuming that the fluid satisfies nonlinear boundary conditions at the finite end of the cylinder, using the symmetry of differential inequalities and the energy analysis methods, we establish the exponential decay estimates for homogeneous Brinkman equations. That is to prove that the solutions of the equation decay exponentially with the distance from the finite end of the cylinder. To make the estimate of decay explicit, the bound for the total energy is also derived.

Geomorphological patterns of remotely sensed methane hot spots in the Mackenzie Delta, Canada

We studied geomorphological controls on methane (CH4) hotspots in the Mackenzie Delta region in northern Canada using airborne imaging spectroscopy collected as part of the Arctic Boreal Vulnerability Experiment (ABoVE). Methane emissions hotspots were retrieved at ~25 m2 spatial resolution from a ~10,000 km2 AVIRIS-NG survey of the Mackenzie Delta acquired 31 July – 3 August 2017. Separating the region into the permafrost plateau and the lowland delta, we refined the domain wide power law of CH4 enhancements detected as a function of distance to standing water in different ecoregions. We further studied the spatial decay of the distance to water relationship as a function of land cover across the Delta. We show that geomorphology exerts a strong control on the spatial patterns of emissions at regional to sub-regional scales: compared to methane hotspots detected in the upland, we find that methane hotspots detected in the lowland have a more gradual power law curve indicating a weaker spatial decay with respect to distance from water. Spatial decay of CH4 hotspots in uplands is more than 2.5 times stronger than in lowlands, which is due to differences in topography and geomorphological influence on hydrology. We demonstrate that while the observed spatial distributions of CH4 follow expected trends in lowlands and uplands, these quantitatively complement knowledge from conventional wetland and freshwater CH4 mapping and modelling.

The impact of scale on spatial connections: an exploratory analysis

Quantifying the intensity of spatial connections has been a crucial topic in many research fields, such as urban transportation, migration, and trade. Researchers have proposed various models, such as the gravity model and the radiation model, to quantify the magnitude of spatial connections. Traditionally, modeling the connections (relatedness) between spatial entities is limited to the physical space, but with the rapid growth of information technologies, the scope of spatial connections extends to the virtual space. However, one topic that has not been fully studied is how spatial scale may impact spatial connections in the virtual space and how this influence can be reflected in spatial decay models. In this study, we used two types of datasets (mass media and social media data) to explore the impact of scale on fitting the distance decay coefficient. The results confirmed that spatial scale can impact the magnitude of spatial decay effects in datasets with different characteristics.

The Influence of Voids in the Vibrations of Bodies with Dipolar Structure

In our study we analyse the vibration of a right cylinder which consists of an elastic material with dipolar structure and has pores. One end of this cylinder is subjected to an excitation, harmonically in time. The other end of the cylinder and its lateral surface are free of loads. We prove that the presence of the voids does not affect the spatial decay of effects away from the excited end, if the harmonic excitation level is below a predetermined threshold.

Ethnic Violence Across Space

Spatial analyses focus to a large extent on the ‘bright side of proximity’, namely voluntary (positive-sum) interactions such as, e.g., in trade and innovation. In contrast, the violent ‘dark side of proximity’ has often been overlooked. To address this gap, we study the role of spatial proximity in ethnic conflict, developing a structural model of spatial violence in which ethnic groups recruit fighters strategically across space. The spatial decay of violence determines the equilibrium placement of fighters and drives specific spatial patterns of conflict. The structural parameters of the model are estimated using fine-grained data on ethnic groups and violence from 24 ethnically divided countries. We find that in more than half of these, spatial decay is substantial: half of all ethnic violence dissipates after 350km. Violence is asymmetric, is higher near ethnic borders and typically originates from outside a location. Counterfactual estimates suggest that setting up barriers would reduce violence but pacifying groups suffering from grievances would often be more effective.