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A Nonlocal Continuum Model for Biological Aggregation
We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short-range dispersal. For the case of one spatial dimension, we study theExpand
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Swarming Patterns in a Two-Dimensional Kinematic Model for Biological Groups
TLDR
We construct a continuum model for the motion of biological organisms experiencing social interactions and study its pattern-forming behavior. Expand
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A Primer of Swarm Equilibria
TLDR
We study equilibrium configurations of swarming biological organisms subject to exogenous and pairwise endogenous forces. Expand
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Topological Data Analysis of Biological Aggregation Models
TLDR
We apply tools from topological data analysis to two mathematical models inspired by biological aggregations such as bird flocks, fish schools, and insect swarms. Expand
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Asymptotic Dynamics of Attractive-Repulsive Swarms
TLDR
We classify and predict the asymptotic dynamics of a class of swarming models. Expand
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Flipped Calculus: A Study of Student Performance and Perceptions
Abstract Flipping the classroom refers to moving lectures outside of the classroom to incorporate other activities into a class during its standard meeting time. This pedagogical modality hasExpand
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Gender Representation on Journal Editorial Boards in the Mathematical Sciences
We study gender representation on the editorial boards of 435 journals in the mathematical sciences. Women are known to comprise approximately 15% of tenure-stream faculty positions inExpand
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Nonlocal Aggregation Models: A Primer of Swarm Equilibria
TLDR
We derive a nonlocal partial differential equation describing the evolving population density of a continuum aggregation using the calculus of variations and find exact analytical expressions for the equilibria. Expand
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A model for rolling swarms of locusts
Abstract.We construct an individual-based kinematic model of rolling migratory locust swarms. The model incorporates social interactions, gravity, wind, and the effect of the impenetrable boundaryExpand
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Locust Dynamics: Behavioral Phase Change and Swarming
TLDR
We develop a partial integrodifferential equation model incorporating the interplay between phase change and spatial movement at the individual level in order to predict the dynamics of hopper band formation at the population level. Expand
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