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Abstract |
In this talk, we will introduced two tools that can be used
together to study simulated combustion dynamics. The first tool
is persistent homology, a dimension reduction technique that
encodes the relationship of critical points of a scalar field
(local minima, maxima, and saddle points) into the Euclidean
plane. The output of this `topological transformation' is called
a persistence diagram, and the space of all persistence diagrams
is a metric space. The second tool we use are diffusion maps,
which are used to map point clouds in high-dimensional metric
spaces to lower-dimensional representations that preserve local
distance relations. Specifically, we will show how persistent
homology and diffusion maps can be used together to study the
topological characteristics of dynamics related to certain numerical
quantities, e.g. enstrophy and higher-order statistics. |
