Simulation Box Research Articles

Intermittent Drip Irrigation Soil Wet Front Prediction Model and Effective Water Storage Analysis

The depth and width of drip infiltration play a critical role in designing effective irrigation strategies. However, existing models primarily focus on continuous irrigation and fail to predict wetting patterns under intermittent drip irrigation. This study developed an infiltration model to estimate soil moisture depth and width under intermittent drip irrigation and identified strategies that enhance effective water storage. Indoor soil box simulations were conducted, with continuous drip irrigation as the control. Results showed that intermittent irrigation increased infiltration width and reduced depth, maximizing water storage efficiency. We recommend adopting an intermittent irrigation system with 1.5 h of irrigation followed by a 0.5 h interval, repeated four times. This system increased effective water storage by up to 16.23% compared to continuous irrigation. The proposed method is suitable for sandy loam farmland in southern Xinjiang and can significantly improve water use efficiency in arid regions.

Alcock–Paczyński effect on void-finding

Under the assumption of statistical isotropy, and in the absence of directional selection effects, a stack of voids is expected to be spherically symmetric, which makes it an excellent object to use for an Alcock–Paczyński (AP) test. This test is commonly carried out using the void-galaxy cross-correlation function (CCF), which has emerged as a competitive probe, especially in combination with the galaxy-galaxy auto-correlation function. Current studies of the AP effect around voids assume that void-centre positions are influenced by the choice of fiducial cosmology in the same way as galaxy positions. We show that this assumption, though prevalent in the literature, is complicated by the response of void-finding algorithms to shifts in tracer positions. Using stretched simulation boxes to emulate the AP effect, we investigate how the void-galaxy CCF changes due to its presence, revealing an additional effect imprinted in the CCF that must be accounted for. The effect originates from the response of void finders to the distorted tracer field – which leads to reduction of the amplitude of the AP signal in the CCF – and thus depends on the specific void-finding algorithm used. We present results for four different void-finding packages, namely REVOLVER, VIDE, voxel, and the spherical void finder in the Pylians3 library, demonstrating how incorrect treatment of the AP effect results in biases in the recovered parameters, regardless of the technique used. Finally, we propose a method to alleviate this issue without resorting to complex and finder-specific modelling of the void-finder response to AP.

Composition and Injection Rate Co-Optimization Method of Supercritical Multicomponent Thermal Fluid Used for Offshore Heavy Oil Thermal Recovery

Supercritical multicomponent thermal fluid injection is a new technology with great potential for offshore heavy oil thermal recovery. In the process of thermal fluid generation, the reaction conditions including temperature, pressure, and the organic mass concentration in the reaction material will significantly affect its composition and injection rate and will further affect the thermal recovery and development quality of heavy oil. However, there is a lack of relevant research on the variation rules and control methods of the composition and injection rate of supercritical multicomponent thermal fluids, resulting in a lack of technical mechanisms for effective optimization. To fill this gap, a reaction molecular dynamics simulation method was used to simulate thermal fluid generation under different temperatures, pressures, and organic mass concentrations. The changes in thermal fluid composition and yield with reaction conditions were studied, and a control model of thermal fluid composition and yield was established. The proportional relationship between the thermal fluid generation scale of an offshore heavy oil platform and the simulated thermal fluid generation scale is analyzed, and a collaborative optimization method of thermal fluid composition and injection rate in field applications is proposed. The results show the following: (1) The higher the mass concentration of organic matter, the higher the content of supercritical carbon dioxide and supercritical nitrogen in thermal fluids, and the lower the content of supercritical water. (2) The higher the temperature and pressure, the higher the thermal fluid yield, and the higher the organic mass concentration, the lower the thermal fluid yield. (3) The component fitting model conforms to the power function relationship, and the coefficient of determination R2 is greater than 0.9; the yield fitting model conforms to the modified inverse linear logarithmic function relationship, the determination coefficient R2 is greater than 0.8, and the fitting degree is high. (4) The ratio between the actual injection rate of thermal fluids in the mine field and the molecular simulated thermal fluid yield is the ratio of organic matter mass in the platform thermal fluid generator and organic matter mass in the simulated box. (5) Based on the composition and yield control model, combined with the simulation of the ratio relationship between yield and injection rate in the field, a collaborative optimization method of thermal fluid composition and injection rate was established. The research results can provide an effective technical method for predicting, controlling, and optimizing the composition and injection rate of supercritical multicomponent thermal fluids.

Peristaltic transport of Prandtl hybrid nanofluid (MWCNTs-SWCNTs/engine oil) in non-uniform ducts: Exploring electro-osmosis and Joule heating effects through Keller box simulations

Peristaltic transport of Prandtl hybrid nanofluid (MWCNTs-SWCNTs/engine oil) in non-uniform ducts: Exploring electro-osmosis and Joule heating effects through Keller box simulations

PIC simulation of a nonoscillatory perturbation on a subcritical fast magnetosonic shock wave

Abstract We use a two-dimensional particle-in-cell (PIC) simulation to study the propagation of subcritical fast magnetosonic shocks in electron-nitrogen plasma and their stability against an initial deformation. A slab of dense plasma launches two planar blast waves into a surrounding ambient plasma, which is permeated by a magnetic field that points out of the simulation box and is spatially uniform at the start of the simulation. One shock propagates into a spatially uniform ambient plasma. This reference shock has a Mach number of 1.75, and the heating of ions only along the shock normal compresses the ions that cross the shock to twice the upstream density. Drift instabilities lead to rapidly growing electron-cyclotron harmonic waves ahead of the location where the shock's density overshoot peaks, and to slowly growing lower-hybrid waves with a longer wavelength behind it. The second shock wave enters a perturbation layer that deforms it into a sine shape. Once the shock leaves the perturbation layer, the deformation is weakly damped and non-oscillatory, and the shock remains stable. Even without an external perturbation, and for the plasma parameters considered here, drift instabilities will cause ripples in the shock wave. These instabilities lead to a spatially and temporally varying compression of the plasma that crosses the shock.

Runtime integration of machine learning and simulation for business processes: Time and decision mining predictions

Recent research in Computer Science has investigated the use of Deep Learning (DL) techniques to complement outcomes or decisions within a Discrete Event Simulation (DES) model. The main idea of this combination is to maintain a white box simulation model complement it with information provided by DL models to overcome the unrealistic or oversimplified assumptions of traditional DESs. State-of-the-art techniques in BPM combine Deep Learning and Discrete Event Simulation in a post-integration fashion: first an entire simulation is performed, and then a DL model is used to add waiting times and processing times to the events produced by the simulation model.In this paper, we aim at taking a step further by introducing Rims (Runtime Integration of Machine Learning and Simulation). Instead of complementing the outcome of a complete simulation with the results of predictions a posteriori, Rims provides a tight integration of the predictions of the DL model at runtime during the simulation. This runtime-integration enables us to fully exploit the specific predictions while respecting simulation execution, thus enhancing the performance of the overall system both w.r.t. the single techniques (Business Process Simulation and DL) separately and the post-integration approach. In particular, the runtime integration ensures the accuracy of intercase features for time prediction, such as the number of ongoing traces at a given time, by calculating them during directly the simulation, where all traces are executed in parallel. Additionally, it allows for the incorporation of online queue information in the DL model and enables the integration of other predictive models into the simulator to enhance decision point management within the process model. These enhancements improve the performance of Rims in accurately simulating the real process in terms of control flow, as well as in terms of time and congestion dimensions. Especially in process scenarios with significant congestion – when a limited availability of resources leads to significant event queues for their allocation – the ability of Rims to use queue features to predict waiting times allows it to surpass the state-of-the-art. We evaluated our approach with real-world and synthetic event logs, using various metrics to assess the simulation model’s quality in terms of control-flow, time, and congestion dimensions.

Dynamic Evolution of Local Atomic Environments in a Cu66Zr34 Bulk Metallic Glass

This study presents a molecular dynamics (MD) investigation of the evolution of local atomic environments (LAEs) in a Cu66Zr34 bulk metallic glass (BMG), both at rest and under constant shear deformation. LAEs were characterized using Voronoi polyhedra analysis. Even in the absence of external load, LAEs frequently transformed into one another due to short-ranged atomic position fluctuations. However, as expected, each transition from one polyhedra to another was balanced by the reverse transition, thereby preserving the proportions of the different polyhedra. Cu-centered icosahedral LAEs were observed to preferentially transform into and from <1,0,9,3,0>, <0,1,10,2,0>, and <0,2,8,2,0> LAEs. Upon applying pure shear, the simulation box was first deformed in one direction up to a strain of 25% and then in the opposite direction to the same strain level. Shear deformation induced large nonaffine atomic displacements in the directions parallel to the shear, which were concentrated in specific regions of the BMG, forming band-like regions. From the onset, shear deformation led to the destabilization of Cu-centered icosahedral LAEs, as indicated by more frequent transitions to and from other polyhedra. Unlike other Cu-centered LAEs, icosahedra were also found to be more sensitive to yielding. The destruction of Cu-centered icosahedra was primarily a result of net transformations into <1,0,9,3,0> and <0,2,8,2,0> LAEs in the BMG subjected to pure shear, with a minor contribution of transformations involving the <0,1,10,2,0> polyhedra.

On the capabilities of k-ART over MD for the study of the kinetics of small point defect clusters in α-Fe

Molecular Dynamics simulations, while contributing to the understanding of the mechanisms of diffusion and interactions of point defects and their clusters, are inherently limited in their temporal scope (few nanoseconds). This constraint becomes particularly evident when studying the dynamics of vacancies at low temperatures, where their jump frequency is exceedingly low, posing challenges for accurate reproduction. Additionally, the size of the simulation box imposes constraints, influencing the representation of the system and potentially affecting the accuracy of results. A relatively new kinetic activation-relaxation technique (k-ART) efficiently resolves the limitations of MD simulations, such as computation time and system dimensionality, without the need for a priori knowledge of the simulated system. This technique enables simulations lasting up to several seconds and encompassing systems with higher dimensions. In this paper we check the validity of k-ART to reproduce accurately the migration mechanisms and energies of point defects and small clusters, previously obtained by MD and validated experimentally. We point out the advantages and difficulties of using AKMC with k-ART.

Box replication effects in weak lensing light-cone construction

Abstract Weak gravitational lensing simulations serve as indispensable tools for obtaining precise cosmological constraints. In particular, it is crucial to address the systematic uncertainties in theoretical predictions, given the rapid increase in galaxy numbers and the reduction in observational noise. Both on-the-fly and post-processing methods for constructing lensing light-cones encounter limitations due to the finite simulated volume, necessitating the replication of the simulation box to encompass the volume to high redshifts. To address this issue, our primary focus lies on investigating and quantifying the impact of box replication on the convergence power spectrum and higher-order moments of lensing fields. Subsequently, a univariate model is utilized to estimate the amplitude parameter A by fitting four statistics measured from partial-sky light-cones along specific angles, to the averaged result from random directions. The investigation demonstrates that the systematic bias stemming from the box replication phenomenon falls within the bounds of statistical errors for the majority of cases. However, caution should be exercised when considering high-order statistics on a small sky coverage (≲ 25 deg2). For this case, we have developed a code that facilitates the identification of optimal viewing angles for the light-cone construction. This code has been made publicly accessible https://github.com/czymh/losf.

Viscosity of Asphalt Binder through Equilibrium and Non-Equilibrium Molecular Dynamics Simulations

Viscosity is a curial indicator for evaluating asphalt performance, representing its ability to resist deformation under external forces. The Green–Kubo integral in equilibrium molecular dynamics simulations and the Muller-Plathe algorithm in reverse non-equilibrium molecular dynamics simulations were used to calculate the asphalt viscosity. Meanwhile, the key parameters of both methods were rationalized. The results show that in equilibrium calculations, using a 1/t weighting for the viscosity integral curve results in a well-fitted curve that closely matches the original data. The isotropy of the asphalt model improves for atomic counts exceeding 260,000, rendering viscosity calculations more reasonable. When the viscosity did not converge, it increased linearly with the number of atoms. In non-equilibrium calculations, the number of region divisions had almost no effect on the viscosity value. A momentum exchange period of 20 timesteps exhibits a favorable linear trend in velocity gradients, and an ideal momentum exchange period was found to be between 10 and 20 timesteps. As the model size increased, the linear relationship with the shear rate became more pronounced, and the isotropy of the asphalt system improved. Using an orthogonal simulation box with a side length of 75 Å effectively meets the computational requirements.

Revisiting evolution of domain walls and their gravitational radiation with CosmoLattice

Employing the publicly available 𝒞osmoℒattice code, we conduct numerical simulations of a domain wall network and the resulting gravitational waves (GWs) in a radiation-dominated Universe in the Z2-symmetric scalar field model. In particular, the domain wall evolution is investigated in detail both before and after reaching the scaling regime, using the combination of numerical and theoretical methods. We demonstrate that the total area of closed walls is negligible compared to that of a single long wall stretching throughout the simulation box. Therefore, the closed walls are unlikely to have a significant impact on the overall network evolution. This is in contrast with the case of cosmic strings, where formation of loops is crucial for maintaining the system in the scaling regime. To obtain the GW spectrum, we develop a technique that separates physical effects from numerical artefacts arising due to finite box size and non-zero lattice spacing. Our results on the GW spectrum agree well with refs. [29,30], which use different codes. Notably, we observe a peak at the Hubble scale, an exponential falloff at scales shorter than the wall width, and a plateau/bump at intermediate scales. We also study sensitivity of obtained results on the choice of initial conditions. We find that different types of initial conditions lead to qualitatively similar domain wall evolution in the scaling regime, but with important variations translating into different intensities of GWs.

Neural force functional for non-equilibrium many-body colloidal systems

Abstract We combine power functional theory and machine learning to study non-equilibrium overdamped many-body systems of colloidal particles at the level of one-body fields. We first sample in steady state the one-body fields relevant for the dynamics from computer simulations of Brownian particles under the influence of randomly generated external fields. A neural network is then trained with this data to represent locally in space the formally exact functional mapping from the one-body density and velocity profiles to the one-body internal force field. The trained network is used to analyse the non-equilibrium superadiabatic force field and the transport coefficients such as shear and bulk viscosities. Due to the local learning approach, the network can be applied to systems much larger than the original simulation box in which the one-body fields are sampled. Complemented with the exact non-equilibrium one-body force balance equation and a continuity equation, the network yields viable predictions of the dynamics in time-dependent situations. Even though training is based on steady states only, the predicted dynamics is in good agreement with simulation results. A neural dynamical density functional theory can be straightforwardly implemented as a limiting case in which the internal force field is that of an equilibrium system. The framework is general and directly applicable to other many-body systems of interacting particles following Brownian dynamics.

Magnetically Driven Turbulence in the Inner Regions of Protoplanetary Disks

Given the important role turbulence plays in the settling and growth of dust grains in protoplanetary disks, it is crucial that we determine whether these disks are turbulent and to what extent. Protoplanetary disks are weakly ionized near the midplane, which has led to a paradigm in which largely laminar magnetic field structures prevail deeper in the disk, with angular momentum being transported via magnetically launched winds. Yet, there has been little exploration of the precise behavior of the gas within the bulk of the disk. We carry out 3D, local shearing box simulations that include all three low-ionization effects (ohmic diffusion, ambipolar diffusion, and the Hall effect) to probe the nature of magnetically driven gas dynamics 1–30 au from the central star. We find that gas turbulence can persist with a generous yet physically motivated ionization prescription (order unity Elsässer numbers). The gas velocity fluctuations range from 0.03 to 0.09 of the sound speed c s at the disk midplane to ∼c s near the disk surface, and are dependent on the initial magnetic field strength. However, the turbulent velocities do not appear to be strongly dependent on the field polarity, and thus appear to be insensitive to the Hall effect. The midplane turbulence has the potential to drive dust grains to collision velocities exceeding their fragmentation limit, and likely reduces the efficacy of particle clumping in the midplane, though it remains to be seen if this level of turbulence persists in disks with lower ionization levels.

A statistical analysis of the first stages of freezing and melting of Lennard-Jones particles: Number and size distributions of transient nuclei.

The freezing/melting transition is at the heart of many natural and industrial processes. In the classical picture, the transition proceeds via the nucleation of the new phase, which has to overcome a barrier associated with the free energy cost of the growing nucleus. The total nucleation rate is also influenced by a kinetic factor, which somehow depends on the number of attempts to create a nucleus, that translates into a significant density of proto-nuclei in the system. These transient tiny nuclei are not accessible to experiments, but they can be observed in molecular simulations, and their number and size distributions can be acquired and analyzed. The number distributions are carefully characterized as a function of the system size, showing the expected behavior, with limited spurious effects due to the finite simulation box. It is also shown that the proto-nuclei do exist even in the stable phase, in agreement with the fact that the (unfavorable) volume contribution to their free energy is negligible in the first stages of nucleation. Moreover, the number and size distributions evolve continuously between the stable and the metastable phases, in particular when crossing the coexistence temperature. The size distributions associated with any nucleus and with the largest one have also been calculated, and their relationship recently established for bubbles in a liquid [Puibasset, J. Chem. Phys. 157, 191102 (2022)] has been shown to apply here. This is an important relation for free energy barrier calculations with biased molecular simulations.

Deciphering the Impact of Cyclization and Lysine Charges on Antimicrobial Peptides Using Molecular Dynamics Simulations and Density Functional Theory

AbstractThis study utilized molecular dynamics simulations (MD) to explore the impact of cyclization and lysine charges on antimicrobial peptides (AMPs) across eight simulation boxes designed with water and water‐sodium dodecyl sulfate (SDS) micelles. Cyclic AMPs with positively charged lysine residues (c‐AMP+) displayed increased stability in both environments compared to linear AMPs (l‐AMP+), with removal of positive charges notably destabilizing the linear form in water‐SDS. Findings revealed enhanced mobility due to cyclization and charged lysine residues, further boosted by SDS presence. Notably, lysine residues exhibited a stronger affinity for SDS than tryptophan and phenylalanine, especially lysine number 5. Analysis extended to peptide backbone conformation and electronic features, showing cyclization's greater impact on psi and phi angles over charge presence, with linear AMPs displaying lower reactivity than cyclic counterparts. This research underscores the significance of cyclization and lysine charges in AMP behavior, suggesting the potential of c‐AMP+ for further development owing to their improved stability, mobility, and membrane interactions.

Effect of Solid Electrolyte Interphase Heterogeneity on the Lithium Deposition Dynamic: A Phase-Field Approach

Lithium dendrites formation is an inherent drawback in the development of all solid-state lithium batteries technology. These issues remain unsolved due to the multiple and competing troubleshooting during lithium plating and stripping. The inhomogeneous mechanical and chemical properties of the Solid Electrolyte Interphase (SEI) [1] lead to uneven current distribution and unsmooth lithium plating and stripping [2,3,4]. A fine understanding of the relationship between the SEI composition and the dynamic of dendrite growth under polarization is not well established. All computational studies are based on homogeneous SEI on the top of the lithium electrode [5, 6]. The local deformation of the SEI under polarization may lead to several mechanical defect such as cracking and therefore a dendrite nucleation. To link the crack dynamic to the current density, we developed a novel multiphase-field approach in order to probe the first instants of the dendrite formation. Indicative variables are used in order to define dynamics phases of lithium electrode (in black on the figure), electrolyte (green) and two SEI domains (blue and red) and their interaction. This method allows to consider the SEI as a multi-domains object, where each region has its own (chemical, mechanical and ion transport) properties. Our results show that a smaller current density result in homogeneous deposition (top row on the figure), where a high current leads to a fracture of the SEI and a dendrite growth (bottom row). We highlighted the influence of SEI properties such as the thickness, the ratio between SEI domains or the surface tension on the deposition dynamic.On the left of the figure, the simulation box constituted of lithium (in black color) in contact with a solid electrolyte interphase constituted of a dense (blue) and porous (red) SEI, and electrolyte (green). The dynamic evolution of lithium and SEI, under low and high current density 0.12 and 12 mA/cm² are reported on top and bottom figures respectively.

Effects of Carbon-Based Modified Materials on Soil Water and Fertilizer Retention and Pollution Control in Rice Root Zone

To seek an appropriate stabilization and remediation scheme for cadmium (Cd) and arsenic (As) pollution in farmland, a typical polluted soil sample was selected from a mining area in Southwest China for a soil box simulation experiment. Biochar (BC), a modified type of biochar made from rice husk with different mass ratios of ferric chloride and rice husk, was set up (the mass ratio of ferric chloride to rice husk was 1:9 (defined as LFB), 3:7 (defined as MFB), and 5:5 (defined as HFB) and the control group (BL)) to explore the effects of soil water and fertilizer loss, the bioavailability of Cd and As, and the bioenrichment effects of plant organs during the growth period of rice. The results showed that the porous structure and large specific surface area of biochar effectively regulated soil aggregate composition and improved soil water holding capacity. Compared to the BL treatment, soil water storage under the four carbon-based material control modes increased from 8.98% to 14.52%. Biochar has a strong ion exchangeability and can absorb soil ammonium, nitrogen, and phosphoric acid groups, effectively inhibiting the loss of soil fertilizer. Biochar improves soil pH and reduces the specific gravity of exchangeable Cd. In addition, the oxygen-containing functional groups in biochar can react with metals in a complex manner. The diethylenetriaminepentaacetic acid (DTPA) concentrations of Cd in soils treated with BC, LFB, MFB, and HFB were 79.69%, 72.92%, 64.58%, and 69.27% lower, respectively, than those treated with BL. In contrast, the Fe3+ in ferric chloride combines with As after hydrolysis and oxidation to form amorphous ferric arsenate precipitates or insoluble secondary minerals. Therefore, the curing effect of the modified biochar on As was more potent than that of applied biochar alone. In conclusion, ferric chloride-modified biochar can effectively inhibit the effects of water and fertilizer loss in farmland soil and realize cross-medium long-term inhibition and control of combined Cd and As pollution.

Validation of a novel, low-fidelity virtual reality simulator and an artificial intelligence assessment approach for peg transfer laparoscopic training

Simulators are widely used in medical education, but objective and automatic assessment is not feasible with low-fidelity simulators, which can be solved with artificial intelligence (AI) and virtual reality (VR) solutions. The effectiveness of a custom-made VR simulator and an AI-based evaluator of a laparoscopic peg transfer exercise was investigated. Sixty medical students were involved in a single-blinded randomised controlled study to compare the VR simulator with the traditional box trainer. A total of 240 peg transfer exercises from the Fundamentals of Laparoscopic Surgery programme were analysed. The experts and AI-based software used the same criteria for evaluation. The algorithm detected pitfalls and measured exercise duration. Skill improvement showed no significant difference between the VR and control groups. The AI-based evaluator exhibited 95% agreement with the manual assessment. The average difference between the exercise durations measured by the two evaluation methods was 2.61 s. The duration of the algorithmic assessment was 59.47 s faster than the manual assessment. The VR simulator was an effective alternative practice compared with the training box simulator. The AI-based evaluation produced similar results compared with the manual assessment, and it could significantly reduce the evaluation time. AI and VR could improve the effectiveness of basic laparoscopic training.

Mass transfer at vapor-liquid interfaces of H2O + CO2 mixtures studied by molecular dynamics simulation

Abstract In many industrial applications as well as in nature, the mass transfer of CO2 at vapor-liquid interfaces in aqueous systems plays an important role. In this work, this process was studied on the atomistic level using non-equilibrium molecular dynamics simulations. In a first step, a molecular model of the system water + CO2 was developed that represents both bulk and interfacial equilibrium properties well. This system is characterized by a very large adsorption and enrichment of CO2 at the vapor-liquid interface. Then, non-equilibrium mass transfer simulations were carried out using a method that was developed recently: CO2 is inserted into the vapor phase of a simulation box which contains a liquid slab. Surprising effects are observed at the interface such as a net repulsion of CO2 particles from the interface and a complex time dependence of the amount of CO2 adsorbed at the interface.

Adsorption Mechanism and Characteristic Temperatures of the Monolayer Adsorption of CO2 on Graphite: The Role of Graphene Dimensions.

Although simulation results for gaseous adsorption on a surface of infinite extent, modeled with periodic conditions at the boundaries of the simulation box, agree with experimental data at high temperatures, simulated isotherms at temperatures below the triple point temperature show unphysical substeps because of the compromise of interactions within the box and interactions between the box and its mirror image boxes. This has been alleviated with surfaces of finite dimensions (Loi, Q. K.; Colloids Surf., A 2021, 622, 126690 and Castaño Plaza, O.; Langmuir 2023, 39 (21), 7456-7468) to account for free boundaries at the adsorbate patch on the surface, and the critical parameter of this model substrate is the size of the finite surface. If it is too small, the adsorbate patch does not model the physical reality; however, if it is too large, the computation time is excessive, making the simulation impractical. In this study, we used carbon dioxide/graphite as the model system to explore the effects of finite dimensions on the description of experimental data of Terlain, A.; Larher, Y. Surf. Sci. 1983, 125 (1), 304-311, especially for temperatures below the bulk triple point temperature. With the appropriate choice of graphene size, we derived the 2D triple point and 2D critical point temperatures of the monolayer, and most importantly, for temperatures below the 2D critical point temperature, the adsorption mechanism for the formation of the monolayer is due to the interplay between the boundary growth process and the vacancy filling. The extent of this interplay is found to depend on the fractional coverage of the surface.