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. 2021 May 17;11:10456. doi: 10.1038/s41598-021-89953-3

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© The Author(s) 2021

Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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The highest singular DMD eigenvector, $D^{(1)}$ , obtained for: (a) $S t = 1.0$ mono-disperse system, (b) a bi-disperse mixture of $S t = {1, 2}$ with 7:3 ratio of initial particle concentrations. The horizontal lines correspond to the caustic wavefronts, and the number of such fronts indicate the different Stokes number particles. Also notice that the wavefronts corresponding to $S t = 1.0$ appear around the same values of y in both (a,b), indicating that the positions of DMD wavefronts are not perturbed by the presence of particles with different Stokes numbers. The figures were created using Matlab 2020a, https://www.mathworks.com/products/matlab.html.