Characterizing fluid dynamical systems using Euler characteristic surface and Euler metric

Author:

Roy A.123ORCID,Haque R. A. I.23ORCID,Mitra A. J.4ORCID,Tarafdar S.2,Dutta T.23ORCID

Affiliation:

1. Physics Department, Charuchandra College 1 , Kolkata 700029, India

2. Condensed Matter Physics Research Centre, Jadavpur University 2 , Kolkata 700032, India

3. Physics Department, St. Xavier's College 3 , Kolkata 700016, India

4. Mathematical Sciences, Montana Tech 4 , Butte, Montana 59701, USA

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 χs(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.

Funder

University Grants Commission

Publisher

AIP Publishing

Subject

Condensed Matter Physics,Fluid Flow and Transfer Processes,Mechanics of Materials,Computational Mechanics,Mechanical Engineering

Reference26 articles.

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2. Persistent Homology for Random Fields and Complexes,2010

3. R. J. Adler , K.Bartz, S. C.Kou, and A.Monod, “ Estimating thresholding levels for random fields via Euler characteristics,” arXiv:1704.08562 (2017).

4. Minkowski functionals used in the morphological analysis of cosmic microwave background anisotropy maps;Mon. Not. R. Astron. Soc.,1998

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