Euler characteristic (χ), a topological invariant, helps to understand the topology of a network ... more 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.
Crack formation and its possible prevention or remedy is an important branch of material science,... more Crack formation and its possible prevention or remedy is an important branch of material science, closely related to study of granular materials and soft matter physics. This work reports a study on cracking behaviour in composites of bentonite and Laponite® in varying proportions. Both components are clays of the montmorillonite group. Our experiments demonstrate that for the particular composition - Laponite® : bentonite ∼1:1, cracks are totally absent. If either component exceeds the other, cracks develop. This is demonstrated over a range of film thickness. Scanning Electron Microscope (SEM) images of the films at different compositions indicate that at this particular ratio, the much smaller particles of Laponite®, pack into the spaces between the bentonite platelets perfectly, to form a defect-free smooth film.
In this paper, we propose a mathematical picture of flow in a drying multiphase droplet. The syst... more In this paper, we propose a mathematical picture of flow in a drying multiphase droplet. The system studied consists of a suspension of microscopic polystyrene beads in water. The time development of the drying process is described by defining the “Euler characteristic surface,” which provides a multiscale topological map of this dynamical system. A novel method is adopted to analyze the images extracted from experimental video sequences. Experimental image data are converted to binary data through appropriate Gaussian filters and optimal thresholding and analyzed using the Euler characteristic determined on a hexagonal lattice. In order to do a multiscale analysis of the extracted image, we introduce the concept of Euler characteristic at a specific scale r > 0. This multiscale time evolution of the connectivity information on aggregates of polysterene beads in water is summarized in a Euler characteristic surface and, subsequently, in a Euler characteristic level curve plot. We...
Euler characteristic (χ), a topological invariant, helps to understand the topology of a network ... more 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.
Crack formation and its possible prevention or remedy is an important branch of material science,... more Crack formation and its possible prevention or remedy is an important branch of material science, closely related to study of granular materials and soft matter physics. This work reports a study on cracking behaviour in composites of bentonite and Laponite® in varying proportions. Both components are clays of the montmorillonite group. Our experiments demonstrate that for the particular composition - Laponite® : bentonite ∼1:1, cracks are totally absent. If either component exceeds the other, cracks develop. This is demonstrated over a range of film thickness. Scanning Electron Microscope (SEM) images of the films at different compositions indicate that at this particular ratio, the much smaller particles of Laponite®, pack into the spaces between the bentonite platelets perfectly, to form a defect-free smooth film.
In this paper, we propose a mathematical picture of flow in a drying multiphase droplet. The syst... more In this paper, we propose a mathematical picture of flow in a drying multiphase droplet. The system studied consists of a suspension of microscopic polystyrene beads in water. The time development of the drying process is described by defining the “Euler characteristic surface,” which provides a multiscale topological map of this dynamical system. A novel method is adopted to analyze the images extracted from experimental video sequences. Experimental image data are converted to binary data through appropriate Gaussian filters and optimal thresholding and analyzed using the Euler characteristic determined on a hexagonal lattice. In order to do a multiscale analysis of the extracted image, we introduce the concept of Euler characteristic at a specific scale r > 0. This multiscale time evolution of the connectivity information on aggregates of polysterene beads in water is summarized in a Euler characteristic surface and, subsequently, in a Euler characteristic level curve plot. We...
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