“Islands in Sea” and “Lakes in Mainland” phases and related transitions simulated on a square lattice

Khatun, Tajkera; Dutta, Tapati; Tarafdar, Sujata

doi:10.1140/epjb/e2017-80365-3

Cited by 5 publications

(21 citation statements)

References 6 publications

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“…Furthermore, we used the method of finite size scaling to estimate the actual percolation thresholds p c for different values of q. We know that |p eff (L) − p c | ∝ L − 1 ν where ν is a percolation critical exponent which has a standard value of 4 3 for dimension d = 2 lattices. According to the universality principle the value of the critical exponents are independent of local details [1] as they describe the system in the limit where the correlation length diverges.…”

Section: Variation Of Spanning Cluster Percolation Threshold With Diamentioning

confidence: 99%

“…and thus are very useful in image characterization to match shapes, recognize objects, image database retrieval and other image processing and computer vision applications. Analysis of images of real systems like soil crack patterns [3,4], fast reading of car number plates [5] and automatic signature matching [6] have been facilitated through use of Euler numbers. In diagnostic imaging, analysis of patterns with proper thresholding, is extremely important to identify irregularities indicating possible medical conditions.…”

Section: Introductionmentioning

confidence: 99%

“…In diagnostic imaging, analysis of patterns with proper thresholding, is extremely important to identify irregularities indicating possible medical conditions. Here again the Euler number plays an important role [7,8] Recently the Euler number and its variation with site occupation probability on a square lattice, has been discussed by Khatun et al [4]. Black (B) unit squares are randomly dropped, with probability p onto a lattice initially filled Figure 1: Possible diagonal connections in a 2 × 2 square lattice having two diagonally opposite black pixels (squares) and two diagonally opposite white pixels which orthogonally neighbour them.…”

Section: Introductionmentioning

confidence: 99%

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Euler Number and Percolation Threshold on a Square Lattice With Diagonal Connection Probability and Revisiting the Island-Mainland Transition

Dutta

Sen

Khatun³

et al. 2019

Front. Phys.

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We report some novel properties of a square lattice filled with white sites, randomly occupied by black sites (with probability p). We consider connections up to second nearest neighbours, according to the following rule. Edgesharing sites, i.e. nearest neighbours of similar type are always considered to belong to the same cluster. A pair of black corner-sharing sites, i.e. second nearest neighbours may form a 'cross-connection' with a pair of white corner-sharing sites. In this case assigning connected status to both pairs simultaneously, makes the system quasi-three dimensional, with intertwined black and white clusters. The two-dimensional character of the system is preserved by considering the black diagonal pair to be connected with a probability q, in which case the crossing white pair of sites are deemed disjoint. If the black pair is disjoint, the white pair is considered connected. In this scenario we investigate (i) the variation of the Euler number χ(p) [= N B (p) − N W (p)] versus p graph for varying q, (ii) variation of the site percolation threshold with q and (iii) size distribution of the black clusters for varying p, when q = 0.5. Here N B is the number of black clusters and N W is the number of white clusters, at a certain probability p. We also discuss the earlier proposed 'Island-Mainland' transition (Khatun, T., Dutta, T. & Tarafdar, S. Eur. Phys. J. B (2017) 90: 213) and show mathematically that the proposed transition is not, in fact, a critical phase transition and does not survive finite size scaling. It is also explained mathematically why clusters of size 1 are always the most numerous. arXiv:1904.05748v1 [cond-mat.stat-mech]

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Section: Variation Of Spanning Cluster Percolation Threshold With Diamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Euler Number and Percolation Threshold on a Square Lattice With Diagonal Connection Probability and Revisiting the Island-Mainland Transition

Dutta

Sen

Khatun³

et al. 2019

Front. Phys.

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“…A simple Monte Carlo algorithm for evaporation and pattern formation has been developed by Dutta Choudhury et al to reproduce the formation of faceted salt crystals and dendritic aggregates in drying droplets of aqueous gelatin containing NaCl [142]. The pattern formation can be correlated to the topological concept of the Euler number [220].…”

Section: D Models Of Mass Transfermentioning

confidence: 99%

“…Both nonequilibrium growth and presence of impurities may produce dendritic shape of crystals [259]; these effects can be reproduced in a simple model [260]. The semiempirical Monte Carlo approach by Dutta Choudhury et al [142] qualitatively reproduces the crossover in faceted and dendritic crystal growth and shows the relevance of statistical methods in this problem through the Euler number [220].…”

Section: Crystal Growthmentioning

confidence: 99%

Droplet Drying Patterns on Solid Substrates: From Hydrophilic to Superhydrophobic Contact to Levitating Drops

Tarafdar

Tarasevich

Choudhury

et al. 2018

Advances in Condensed Matter Physics

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This review is devoted to the simple process of drying a multicomponent droplet of a complex fluid which may contain salt or other inclusions. These processes provide a fascinating subject for study. The explanation of the rich variety of patterns formed is not only an academic challenge but also a problem of practical importance, as applications are growing in medical diagnosis and improvement of coating/printing technology. The fundamental scientific problem is the study of the mechanism of microand nanoparticle self-organization in open systems. The specific fundamental problems to be solved, related to this system, are the investigation of the mass transfer processes, the formation and evolution of phase fronts, and the identification of mechanisms of pattern formation. The drops of liquid containing dissolved substances and suspended particles are assumed to be drying on a horizontal solid insoluble smooth substrate. The chemical composition and macroscopic properties of the complex fluid, the concentration and nature of the salt, the surface energy of the substrate, and the interaction between the fluid and substrate which determines the wetting all affect the final morphology of the dried film. The range of our study encompasses the fully wetting case with zero contact angle between the fluid and substrate to the case where the drop is levitated in space, so there is no contact with a substrate and angle of contact can be considered as 180 ∘ .

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Understanding flow features in drying droplets via Euler characteristic surfaces—A topological tool

et al. 2020

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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 introduce a metric between Euler characteristic surfaces as a possible similarity measure between two flow situations. The constructions proposed by us are used to interpret flow patterns (and their stability) generated on the upper surface of the drying droplet interface. The philosophy behind the topological tools developed in this work is to produce low-dimensional signatures of dynamical systems, which may be used to efficiently summarize and distinguish topological information in various types of flow situations.

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“Islands in Sea” and “Lakes in Mainland” phases and related transitions simulated on a square lattice

Cited by 5 publications

References 6 publications

Euler Number and Percolation Threshold on a Square Lattice With Diagonal Connection Probability and Revisiting the Island-Mainland Transition

Euler Number and Percolation Threshold on a Square Lattice With Diagonal Connection Probability and Revisiting the Island-Mainland Transition

Droplet Drying Patterns on Solid Substrates: From Hydrophilic to Superhydrophobic Contact to Levitating Drops

Understanding flow features in drying droplets via Euler characteristic surfaces—A topological tool

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