FoCM 2014 conference

Workshop A1 - Computational Dynamics

December 12, 17:30 ~ 17:55 - Room B21

Analyzing the dynamics of pattern formation in the space of persistence diagrams

Miroslav Kramar

Rutgers University, USA   -

Persistence diagrams are a relatively new topological tool for describing and quantifying complicated patterns in a simple but meaningful way. We will demonstrate this technique on patterns appearing in Rayleigh-Benard convection. This procedure allows us to transform experimental or numerical data from  experiment or simulation into a point cloud in the space of persistence diagrams. There are a variety of metrics that can be imposed on the space of persistence diagrams. By choosing different metrics one can interrogate the pattern locally or globally, which provides deeper  insight into the dynamics of the process of pattern formation. Because the quantification is being done in the space of persistence diagrams this technique allows us to compare directly numerical simulations with experimental data.

Joint work with Konstantin Miscahikow (Rutgers, USA), Rachel Levanger (Rutgers, USA), Shaun Harker (Rutgers, USA)., Michael Schatz (Georgia Tech, USA), Jeffrey Tithof (Georgia Tech, USA), Balachandra Suri (Georgia Tech, USA), Mark Paul (Virginia Tech, USA) and Mu Xu (Virginia Tech, USA).

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