1,377 research outputs found
Nonlocal Aggregation Models: A Primer of Swarm Equilibria
Biological aggregations such as fish schools, bird flocks, bacterial colonies, and insect swarms have characteristic morphologies governed by the group members\u27 intrinsic social interactions with each other and by their interactions with the external environment. Starting from a simple discrete model treating individual organisms as point particles, we derive a nonlocal partial differential equation describing the evolving population density of a continuum aggregation. To study equilibria and their stability, we use tools from the calculus of variations. In one spatial dimension, and for several choices of social forces, external forces, and domains, we find exact analytical expressions for the equilibria. These solutions agree closely with numerical simulations of the underlying discrete model. The analytical solutions provide a sampling of the wide variety of equilibrium configurations possible within our general swarm modeling framework, and include features such as spatial localization with compact support, mass concentrations, and discontinuous density jumps at the edge of the group. We apply our methods to a model of locust swarms, which in nature are observed to consist of a concentrated population on the ground separated from an airborne group. Our model can reproduce this configuration; in this case quasi-two-dimensionality of the locust swarm plays a critical role
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Neoarchean Arc Magmatism, Subsequent Collisional Orogenesis, and Paleoproterozoic Disruption within the Western Churchill Province: Implications for the Growth and Modification of Lower Continental Crust
The growth and modification of continental lithosphere are fundamental geologic processes that have had a profound effect on Earth’s evolution. The lower continental crust can play a myriad of roles pertaining to these processes depending on the strength, age, temperature, and composition of the rocks present. However, the lower continental crust is impossible to sample in-situ, and thus observations of modern lower continental crust are limited to seismic studies and xenolith studies, which provide mere snap shots of the lower crust. High pressure granulite terranes provide 4 dimensional, and spatially resolvable, analogues of lower continental crust. The Athabasca granulite terrane (AGT), along the eastern margin of the Rae subprovince of the western Churchill Province, is underlain by \u3e20,000 km2 of high pressure granulite, and is arguably to be the largest intact exposure of lower continental crust in the North America. Work presented herein provides a detailed temporal and tectonic framework for interpreting rocks of the AGT, and evaluates rocks ca. 400 km along strike to test for spatial consistency. Results suggest that the Paleoproterozoic involved the juxtaposition of various lithotectonic blocks along major ductile shear zones that vary in metamorphic conditions, timing and kinematics. Sinistral kinematics within the Cora Lake shear zone within the AGT, for instance, are explained by accretion of the Lynn-Lake and La Ronge arcs along the southern periphery of the Churchill Province at ca. 1.88 Ga at the waning phases of granulite-facies conditions. Ca. 1.9 Ga deformation involved upright folding, and the development of a regionally extensive dextral transpressive fabrics, and appears to be spatially related to the Chipman dike swarm. This event may have been driven by accretionary and collisional tectonics between the Slave and western Churchill Province. IN-SIMS micro zircon geochronology suggests a ca. 2.1 Ga emplacement age for the Chipman dikes, and may be indicative of an incipient rift, which was the locust for ca. 1.9 Ga reactivation. Preceding these events was a major crustal thickening event that occurred immediately after widespread arc-like magmatism interpreted to represent early subduction and subsequent collisional orogenisis. Rocks along strike, 400 km to the northeast of the AGT, share a similar Neoarchean history, and dike swarm, but contain little evidence of regionally extensive Paleoproterozoic granulite-facies reactivation. The reasoning for this is unknown at current, but perhaps it is due to an increasing distance from the bounding Paleoproterozoic orogens. These data provide a four dimensional framework to evaluate changes in lower crustal properties and behavior for greater than 600 my
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