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Python – a Tool for Percolation Analysis in Triangular Lattice

Authors: Gupta, N.; Nath, M.; Chakraborty, S.; Bandyopadhyay, A.;

Python – a Tool for Percolation Analysis in Triangular Lattice

Abstract

Теорія перколяції, яка запропонована понад 60 років тому для опису поведінки явищ течії в пористому середовищі, в останні роки набула широкого застосування, починаючи від епідеміології, фінансового ринку, грунтознавства, фармацевтичних технологій і закінчуючи структурою композиційних матеріалів. У статті теорія перколяції застосовується до трикутної гратки, а її дослідження було виконано з використанням моделювання Монте-Карло. Для розробки коду використовувалася мова програмування Python. Для цього ми застосували вбудовані бібліотеки Python, такі як NumPy, SciPy, Matplotlib тощо. Алгоритм Хошена-Копельмана використовується для ідентифікації кластера та процедури його нумерації. Цей алгоритм має перевагу над іншими методами, оскільки він потребує менше пам'яті і часу на обчислення. Об'єктом підвищеного інтересу в теорії перколяції є поріг перколяції (pc), який у нашому випадку є рівним 0,5. Ми також охарактеризували перколяцію, знайшовши інші величини, такі як нормована маса кластера (M), ймовірність перколяції (Pp), густина нескінченного кластера (Pα ) і параметр порядку Ω(L). Ми отримали критичні показники з наших даних і виявили, що вони точно відповідають своїм універсальним значенням. Наскільки нам відомо, ми є першою групою, яка повідомила про перколяції в трикутній гратці за допомогою алгоритму Хошена-Копельмана з використанням мови Python. Percolation theory, developed more than 60 years before to describe the behavior of flow phenomena in porous medium, has undergone an extensive area of applications in recent years, ranging from epidemiology, financial market, soil science, pharmaceutical technology to composite material structure. Here in this paper, percolation theory is applied to the triangular lattice and its characterization has been done using MonteCarlo simulation. Python language has been used to develop the code. For this, we have used the inbuilt libraries of Python like NumPy, SciPy, Matplotlib etc. Hoshen-Kopelman (HK) algorithm is used to identify the cluster and its numbering procedure. This algorithm is being preferred over the other methods as it consumes low computer memory and less computation time. The prime point of interest in percolation is known as percolation threshold (pc) which is computed for our case is 0.5. We have also characterized the percolation by finding the other quantities as: normalized mass of cluster (M), percolation probability (Pp), the density of the infinite cluster (Pα) and ordered parameter Ω(L). We have extracted critical exponents from our data and found that they match exactly with their universal values. To the best of our knowledge, we are the first group to report percolation in triangular lattice by means of HK algorithm using Python language.

Keywords

алгоритм Хошена-Копельмана, HK algorithm, моделювання Монте-Карло, percolation threshold, Monte-Carlo simulation, поріг перколяції

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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