Histogram-based methodology for the determination of the critical point in condensation-evaporation systems

Santos, Gustavo Jorge dos; Linares, Daniel; Ramírez-Pastor, A. J.

doi:10.1088/1742-5468/aa7df2

Cited by 3 publications

(11 citation statements)

References 36 publications

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“…The study developed here is a natural continuation of our previous paper [52], and also contributes to the comprehension of some essential characteristics of the phase transitions occurring in adsorbed monolayer films by means of a very simple model. It is well-known, that the model of a two-dimensional gas of rigid k-mers is the simplest representation of a strongly adsorbed film of linear molecules in submonolayer or monolayer regime.…”

Section: Introductionmentioning

confidence: 70%

“…In addition, bi-dimensional histograms W (H, N) are constructed for each value of μ in every single temperature simulation. The histograms are needed to apply the MCM [52] in order to obtain the temperature of the condensation transition. Under this framework, the fourth order Binder cumulant U L is obtained with the aid of the Histogram Reweighting (HR) technique,…”

Section: Monte Carlo Simulation Schemementioning

confidence: 99%

“…The coverage values for which the maximums of the two peaks occur are the two coexistence points of the phase diagram for that precise temperature. This procedure is described in further detail in [52].…”

Section: Monte Carlo Simulation Schemementioning

confidence: 99%

“…In this line of work, a new methodology based on a combination of the histogram reweighting technique [48][49][50] and on the fourth order Binder cumulant [51] was developed in a recent article from our research group [52]. The technique, which will be called "Maximum Cumulant Method" (MCM), was applied to the study of the phase transition occurring in a system of attractive dimers 2 adsorbed on 2D square lattices.…”

Section: Introductionmentioning

confidence: 99%

“…The method introduced in Ref. [52] proved to be a very useful tool for the research of phase transitions in lattice-gas models. In the present paper, this scheme is applied to the study of the phase behavior of attractive k-mers adsorbed on square lattices in the presence of anisotropy.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Statistical thermodynamics of aligned rigid rods with attractive lateral interactions: Theory and Monte Carlo simulations

Santos

Linares

Ramírez-Pastor

2018

Physica A: Statistical Mechanics and its Applications

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The phase behavior of aligned rigid rods of length k (k-mers) adsorbed on twodimensional square lattices has been studied by Monte Carlo (MC) simulations and histogram reweighting technique. The k-mers, containing k identical units (each one occupying a lattice site) were deposited along one of the directions of the lattice. In addition, attractive lateral interactions were considered. The methodology was applied, particularly, to the study of the critical point of the condensation transition occurring in the system. The process was monitored by following the fourth order Binder cumulant as a function of temperature for different lattice sizes. The results, obtained for k ranging from 2 to 7, show that: (i) the transition coverage exhibits a decreasing behaviour when it is plotted as a function of the k-mer size and (ii) the transition temperature, T c , exhibits a power law dependence on k, T c ∼ k 0,4 , shifting to higher values as k increases. Comparisons with an analytical model based on a generalization of the Bragg-Williams approximation (BWA) were performed in order to support the simulation technique. A significant qualitative agreement was obtained between BWA and MC results.

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Section: Introductionmentioning

confidence: 70%

Section: Monte Carlo Simulation Schemementioning

confidence: 99%

Section: Monte Carlo Simulation Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Statistical thermodynamics of aligned rigid rods with attractive lateral interactions: Theory and Monte Carlo simulations

Santos

Linares

Ramírez-Pastor

2018

Physica A: Statistical Mechanics and its Applications

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Maximum cumulant method for studying condensation-evaporation phase transitions

2018

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In a previous paper [G. J. dos Santos, D. H. Linares, and A. J. Ramirez-Pastor, J. Stat. Mech. ( 2017) 073211] a methodology for the determination of the critical point of the condensation phase transition occurring in monolayers of linear adsorbates (k-mers) was presented. The maximum cumulant method was developed from the phenomenological observation that the fourth-order Binder cumulant and the isotherm inflection point are produced at the same value of chemical potential. In the present work, mathematical arguments are presented to show analytically that the previously mentioned relationship is satisfied by evaporation-condensation systems under the conditions that: (i) the surface coverage distribution function is a bimodal distribution composed of a linear combination of two normalized functions g 1 (θ ) and g 2 (θ ) with zero overlap and mean values θ 1 and θ 2 , respectively; and (ii) g 1 (θ ) and g 2 (θ ) are unimodal distributions that are symmetric with respect to the middle point (θ 1 + θ 2 )/2. In addition, numerical results from Monte Carlo simulations of four different adsorption-desorption systems (linear k-mers on square and triangular lattices, S-shaped k-mers on square lattices and k 2 -mers on square lattices) are presented to check the theoretical results and to provide evidence of the general validity and robustness of the method.

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Fast Generation of Image’s Histogram Using Approximation Technique for Image Processing Algorithms

Appiah¹,

Hayfron-Acquah²

2018

IJIGSP

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The process of generating histogram from a given image is a common practice in the image processing domain. Statistical information that is generated using histograms enables various algorithms to perform a lot of pre-processing task within the field of image processing and computer vision. The statistical subtasks of most algorithms are normally effectively computed when the histogram of the image is known. Information such as mean, median, mode, variance, standard deviation, etc. can easily be computed when the histogram of a given dataset is provided. Image brightness, entropy, contrast enhancement, threshold value estimation and image compression models or algorithms employ histogram to get the work done successfully. The challenge with the generation of the histogram is that, as the size of the image increases, the time expected to traverse all elements in the image also increases. This results in high computational time complexity for algorithms that employs the generation histogram as subtask. Generally the time complexity of histogram algorithms can be estimated as O(N 2) where the height of the image and its width are almost the same. This paper proposes an approximated method for the generation of the histogram that can reduce significantly the time expected to complete a histogram generation and also produce histograms that are acceptable for further processing. The method can theoretically reduce the computational time to a fraction of the time expected by the actual method and still generate outputs of acceptable level for algorithms such as Histogram Equalization (HE) for contrast enhancement and Otsu automatic threshold estimation.

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Histogram-based methodology for the determination of the critical point in condensation-evaporation systems

Cited by 3 publications

References 36 publications

Statistical thermodynamics of aligned rigid rods with attractive lateral interactions: Theory and Monte Carlo simulations

Statistical thermodynamics of aligned rigid rods with attractive lateral interactions: Theory and Monte Carlo simulations

Maximum cumulant method for studying condensation-evaporation phase transitions

Fast Generation of Image’s Histogram Using Approximation Technique for Image Processing Algorithms

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