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Full-Text Articles in Applied Mathematics
Topological Data Analysis Of Biological Aggregation Models, Chad M. Topaz, Lori Ziegelmeier, Tom Halverson
Topological Data Analysis Of Biological Aggregation Models, Chad M. Topaz, Lori Ziegelmeier, Tom Halverson
Chad M. Topaz
We apply tools from topological data analysis to two mathematical models inspired by biological aggregations such as bird flocks, fish schools, and insect swarms. Our data consists of numerical simulation output from the models of Vicsek and D'Orsogna. These models are dynamical systems describing the movement of agents who interact via alignment, attraction, and/or repulsion. Each simulation time frame is a point cloud in position-velocity space. We analyze the topological structure of these point clouds, interpreting the persistent homology by calculating the first few Betti numbers. These Betti numbers count connected components, topological circles, and trapped volumes present in the …
Nonlinear Waves And Solitons On Contours And Closed Surfaces, Andrei Ludu
Nonlinear Waves And Solitons On Contours And Closed Surfaces, Andrei Ludu
Andrei Ludu
No abstract provided.