🍩 Database of Original & Non-Theoretical Uses of Topology

(found 2 matches in 0.000873s)

  1. Characterizing Fluid Dynamical Systems Using Euler Characteristic Surface and Euler Metric (2023)

    A. Roy, R. A. I. Haque, A. J. Mitra, S. Tarafdar, T. Dutta
    Abstract Euler characteristic ( χ ), a topological invariant, helps to understand the topology of a network or complex. We demonstrate that the multi-scale topological information of dynamically evolving fluid flow systems can be crystallized into their Euler characteristic surfaces χ s ( r , t ). Furthermore, we demonstrate the Euler Metric (EM), introduced by the authors, can be utilized to identify the stability regime of a given flow pattern, besides distinguishing between different flow systems. The potential of the Euler characteristic surface and the Euler metric have been demonstrated first on analyzing a simulated deterministic dynamical system before being applied to analyze experimental flow patterns that develop in micrometer sized drying droplets.

  2. Euler Characteristic Surfaces: A Stable Multiscale Topological Summary of Time Series Data (2024)

    Anamika Roy, Atish J. Mitra, Tapati Dutta
    Abstract We present Euler Characteristic Surfaces as a multiscale spatiotemporal topological summary of time series data encapsulating the topology of the system at different time instants and length scales. Euler Characteristic Surfaces with an appropriate metric is used to quantify stability and locate critical changes in a dynamical system with respect to variations in a parameter, while being substantially computationally cheaper than available alternate methods such as persistent homology. The stability of the construction is demonstrated by a quantitative comparison bound with persistent homology, and a quantitative stability bound under small changes in time is established. The proposed construction is used to analyze two different kinds of simulated disordered flow situations.