Foams, Fluctuations and Fractals

Nair S, Anpuj (2023) Foams, Fluctuations and Fractals. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS dissertation of Anpuj Nair S (18MS110)) Thesis_18MS110.pdf - Submitted Version Restricted to Repository staff only Download (9MB)

Abstract

This master’s thesis mainly focuses on various experiments on bubble rafts, some computational modelling and simulations of fractals. First, we look at some image analysis algorithms we developed, like the Detection Algorithms for detecting the bubbles and the voids. The main problem in this thesis is the Kinetic Roughening of the Bubble Raft Interface as it evolves, undergoing drainage, ruptures and rearrangements. The scaling exponents of the width function were obtained to be close to the Kardar-Parisi-Zhang (KPZ) exponents after Multi-fractal Detrended Fluctuation Analysis (MFDFA). Then, we study the KPZ model with a variant of the Totally Asymmetric Simple Exclusion Process simulation and do the same MFDFA analysis to test the validity of our methods. We also describe some other experiments that are still a work in progress. Overall, this thesis provides a comprehensive examination of the KPZ-like dynamics of bubble rafts by combining experimental and computational approaches, and it offers a better understanding of the underlying mechanisms. The fractals part of the thesis mainly deals with the Apollonian Packing and Random Apollonian Packing (RAP) simulations. We estimate the fractal dimension from 2 different power laws and see the Log-Normal Radius Distribution of the RAP. Then, we introduced a 1D version of the RAP, where we also observed some non-trivial boundary effects and saw similar behaviour in the 2D RAP.

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