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At least 1,711 records · Page 95

A machine-learning-aided data recovery approach for predicting multi-material thermal behaviors in advanced test reactor capsules

Instrumented experiments conducted at test reactors are essential to the deployment of new advanced reactor systems. Designing new experiments and generating data on specific reactor conditions require significant investments in terms of both time and cost. Finite element analysis software can be used to create high-fidelity models of experiment environments in order to support the actual experiments, but computation time remains a concern in terms of applying outcomes to real-time usage of data (e.g., a digital twin [DT]). Here, the present research proposes a machine-learning (ML) aided approach to making temperature and displacement predictions based on the thickness of the outer gas gap on the experimental capsule used for in-pile demonstration of a novel new thermal conductivity probe in the Advanced Test Reactor (ATR). This capsule consisted of U10Zr fuel, a rodlet, sodium, and inner and outer capsules. Gas gaps existed between the fuel and the rodlet, and between the inner and the outer capsule. The learning data pertained to an experimental capsule's radial distributions of temperature and displacement, as obtained based on Abaqus and the physical features. For the first step of ML sequence, the temperature was predicted using three positional parameters. Next, the displacement was predicted using seven additional parameters. Each physical feature was normalized in order to be both nondimensional and standardized. The temperature and displacement predictions showed good agreement with the simulation results in all cases involving interpolation and extrapolation. Furthermore, data similarity enhancement increased the similarity between the training and the target data, thereby increasing the predictive accuracy of the ML models. In certain extrapolation cases involving limited original ML model accuracy, data similarity enhancement and data recovery was able to somewhat improve this accuracy.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Dynamic recrystallization of a wrought magnesium alloy: Grain size and texture maps and their application for mechanical behavior predictions

Effect of dynamic recrystallization (DRX) on the grain refinement and texture modification was studied by conducting a series of hot compression on AZ31B Mg alloy. Processing-grain size-texture maps were established as a function of temperature, strain rate, strain, and the Zener-Hollomon parameter (Z). Moreover, influence of simultaneous changes in the grain size and texture on tensile yield strength and ductility of the hot-worked Mg alloy was studied using the grain size and texture maps established. The processing-grain size map showed that the DRX grain size decreased with the increase in Z, also revealing various characteristics ranging from a grain growth, grain refinement, to a bimodal distribution of ultrafine grains and partially recrystallized grains. The effect of twinning on the grain refinement was also evident at high Z conditions. The processing-texture map revealed that the initial fiber texture was altered significantly to a shear, off-normal, or extension-twin texture with the increase in Z. The Schmid-factor maps were calculated to identify a dominant deformation mode during a subsequent tensile deformation of the hot-worked samples. Finally, a corresponding Hall-Petch relationship for each dominant deformation mode was used to establish tensile yield-strength maps, which agree well with the measured data.

36 MATERIALS SCIENCE↗

Thermalization & hydrodynamics in Bjorken & Gubser flows

The dynamical scaling behavior of hydrodynamic and non-hydrodynamic moments of the distribution function is studied using third-order Chapman-Enskog hydrodynamics and anisotropic hydrodynamics for systems undergoing Bjorken and Gubser expansions, where exact solutions of the Boltzmann equation in Relaxation Time Approximation (RTA) are available for comparison. While dimensionless quantities like normalized shear, pressure anisotropy and normalized entropy show at late times universal scaling relations with small (large) Knudsen number for Bjorken (Gubser) flows, dimensionful quantities like the entropy per unit rapidity do not. Although the two hydrodynamic approximation schemes describe the exact attractors for normalized shear with high accuracy, their description for the normalized entropy is less precise. We attribute this to non-negligible couplings to non-hydrodynamic modes in the entropy evolution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Cluster Mass Calibration at High Redshift: HST Weak Lensing Analysis of 13 Distant Galaxy Clusters from the South Pole Telescope Sunyaev-Zel’dovich Survey

We present an HST/Advanced Camera for Surveys (ACS) weak gravitational lensing analysis of 13 massive high-redshift (z(median) = 0.88) galaxy clusters discovered in the South Pole Telescope (SPT) Sunyaev-Zel'dovich Survey. This study is part of a larger campaign that aims to robustly calibrate mass-observable scaling relations over a wide range in redshift to enable improved cosmological constraints from the SPT cluster sample. We introduce new strategies to ensure that systematics in the lensing analysis do not degrade constraints on cluster scaling relations significantly. First, we efficiently remove cluster members from the source sample by selecting very blue galaxies in V - I colour. Our estimate of the source redshift distribution is based on Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) data, where we carefully mimic the source selection criteria of the cluster fields. We apply a statistical correction for systematic photometric redshift errors as derived from Hubble Ultra Deep Field data and verified through spatial cross-correlations. We account for the impact of lensing magnification on the source redshift distribution, finding that this is particularly relevant for shallower surveys. Finally, we account for biases in the mass modelling caused by miscentring and uncertainties in the concentration-mass relation using simulations. In combination with temperature estimates from Chandra we constrain the normalization of the mass-temperature scaling relation ln (E(z) M-500c/10(14)M(circle dot)) = A + 1.5ln (kT/7.2 keV) to A = 1.81(-0.14)(+0.24)(stat.)+/- 0.09(sys.), consistent with self-similar redshift evolution when compared to lower redshift samples. Additionally, the lensing data constrain the average concentration of the clusters to c(200c) = 5.6(-1.8)(+3.7).

cosmology: observations↗

Temporal and angular variations of 3D core-collapse supernova emissions and their physical correlations

Abstract We provide the time series and angular distributions of the neutrino and gravitational wave emissions of 11 state-of-the-art 3D non-rotating core-collapse supernova models and explore correlations between these signatures and the real-time dynamics of the shock and the proto-neutron star (PNS) core. The neutrino emissions are roughly isotropic on average, with instantaneous excursions about the mean inferred luminosity of as much as ±20 per cent. The deviation from isotropy is least for the ‘νμ’-type neutrinos and the lowest mass progenitors. Instantaneous temporal luminosity variations along a given direction for exploding models average ∼2–4 per cent, but can be as high as ∼10 per cent. For non-exploding models, they can achieve ∼25 per cent. The temporal variations in the neutrino emissions correlate with the temporal and angular variations in the mass accretion rate. We witness the lepton-number emission self-sustained asymmetry (LESA) phenomenon in all our models and find that the vector direction of the LESA dipole and that of the inner Ye distribution are highly correlated. For our entire set of 3D models, we find strong connections between the cumulative neutrino energy losses, the radius of the proto-neutron star, and the f-mode frequency of the gravitational wave emissions. When physically normalized, the progenitor-to-progenitor variation in any of these quantities is no more than ∼10 per cent. Moreover, the reduced f-mode frequency is independent of time after bounce to better than ∼10 per cent. Therefore, simultaneous measurement of gravitational waves and neutrinos from a given supernova event can be used synergistically to extract real physical quantities of the supernova core.

79 ASTRONOMY AND ASTROPHYSICS↗

Short-Term Global Horizontal Irradiance Forecasting Based on Sky Imaging and Pattern Recognition

Accurate short-term forecasting is crucial for solar integration in the power grid. In this paper, a classification forecasting framework based on pattern recognition is developed for 1-hour-ahead global horizontal irradiance (GHI) forecasting. Three sets of models in the forecasting framework are trained by the data partitioned from the preprocessing analysis. The first two sets of models forecast GHI for the first four daylight hours of each day. Then the GHI values in the remaining hours are forecasted by an optimal machine learning model determined based on a weather pattern classification model in the third model set. The weather pattern is determined by a support vector machine (SVM) classifier. The developed framework is validated by the GHI and sky imaging data from the National Renewable Energy Laboratory (NREL). Results show that the developed short-term forecasting framework outperforms the persistence benchmark by 16% in terms of the normalized mean absolute error and 25% in terms of the normalized root mean square error.

14 SOLAR ENERGY↗

Flow instabilities in non-uniformly heated helium jet arrays used for divertor PFCs

In this study, due to a lack of prototypical experimental data, little is known about the off-normal behavior of recently proposed divertor jet cooling concepts. This article describes a computational fluid dynamics (CFD) study on two jet array designs to investigate their susceptibility to parallel flow instabilities induced by non-uniform heating and large increases in the helium outlet temperature. The study compared a single 25-jet helium-cooled modular divertor (HEMJ) thimble and a micro-jet array with 116 jets. Both have pure tungsten armor and a total mass flow rate of 10 g/s at a 600 °C inlet temperature. We investigated flow perturbations caused by a 30 MW/m 2 off-normal heat flux applied over a 25 mm 2 area in addition to the nominal 5 MW/m 2 applied over a 75 mm 2 portion of the face. The micro-jet array exhibited lower temperatures and a more uniform surface temperature distribution than the HEMJ thimble. We also investigated the response of a manifolded nine-finger HEMJ assembly using the nominal heat flux and a 274 mm 2 heated area. For the 30 MW/m2 case, the micro-jet array absorbed 750 W in the helium with a maximum armor surface temperature of 1280 °C and a fluid/solid interface temperature of 801 °C. The HEMJ absorbed 750 W with a maximum armor surface temperature of 1411 °C and a fluid/solid interface temperature of 844 °C. For comparison, both the single HEMJ finger and the micro-jet array used 5-mm-thick tungsten armor. The ratio of maximum to average temperature and variations in the local heat transfer coefficient were lower for the micro-jet array compared to the HEMJ device. Although high heat flux testing is required to validate the results obtained in these simulations, the results provide important guidance in jet design and manifolding to increase heat removal while providing more even temperature distribution and minimizing non-uniformity in the gas flow and thermal stresses at the armor joint.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Introduction to Special Section: Machine Learning for Image-based Geologic Interpretation

Image-based geological interpretation has been a labor-intensive and time-consuming process because it requires well-trained geoscientists to identify geological structures, features, and textures from various types of images. These images include scanning electron microscopic images, optical microscopic images, optical photos, resistivity images, seismic volumes, remote-sensing images, etc. With fast-evolving machine learning (ML) technology and computing power in recent decades, computers can achieve nearhuman-level to super-human-level performance with scalable high efficiency in the computer vision field. These technological revolutions facilitated image-based geological interpretation in petroleum exploration and production. For example, a fault picking method applied to 3-D seismic volume data using deep learning can achieve superior performance in comparison to conventional auto-picking methods. In addition, under the new normal of low oil prices, the petroleum industry seeks cost-effective strategies such as automating traditionally labor-intensive processes. Nevertheless, the potential of applying ML to geological image interpretation is still facing a few key challenges including data scarcity, data distribution, poor data and/or label quality, data leakage, learning algorithms, model architecture, training methodologies, testing and evaluation metrics, hyper-parameters optimization, model drift, production deployment, and the like.

58 GEOSCIENCES↗

Preliminary Thermal-Hydraulic Analysis of the UTA–2 Subcritical Linear Accelerator–Driven System

The National Nuclear Security Administration’s mission includes establishing a reliable supply of 99 Mo without highly enriched uranium. Oak Ridge National Laboratory (ORNL) supports this objective through collaborative research and development with industrial partners. Niowave Inc., a current partner, is currently designing a subcritical linear accelerator-driven system (ADS) and preparing for the US Nuclear Regulatory Commission’s licensing process. Niowave’s system has the potential to efficiently supply medical radioisotopes. The technology includes a superconducting electron accelerator and a pile of both natural and low-enriched uranium (LEU) targets. The process fissions uranium and many valuable isotopes can then be extracted from the targets. Niowave is currently iterating through conceptual and detailed design processes for several system sizes. This report discusses UTA–2, which is at the demonstration stage. UTA–2 will validate numerical modeling results with experimental measurements before progressing to the detailed design of UTA–3, the commercial-sized ADS. The thermal-hydraulic behavior of the UTA–2 core design was numerically investigated using STAR-CCM+, as described in this report. STAR-CCM+, a state-of-the-art computational fluid dynamics (CFD) software that was commercially developed by Siemens, has an extensive user base and a set of validation studies. It is also compliant with the American Society of Mechanical Engineers’ Nuclear Quality Assurance 1 standard. Three cases are investigated in this report. Case 1 quantified the temperature field within the UTA–2 assembly and water tank using only conduction as the method of thermal energy transport. This simplified approach was overly conservative and yielded wetted cladding temperatures above the coolant saturation temperature. In this case, the maximum temperature of the wetted cladding surface of the highest power rod exceeded the saturation temperature of water by 63.8°C. Because of the overly conservative approach taken in Case 1 and its negative subcooled margin, buoyancy-driven natural circulation flow physics were implemented in Case 2. Adding coolant motion significantly distributed the thermal energy of the system through convective heat transfer. This relatively small amount of convective heat transfer significantly reduced system temperatures and increased the subcooled margin from –63.8 to 61.3°C. This margin confirmed that no boiling was expected during normal operation of UTA–2 at 230 W. Case 3 had no additional physics models but considered an overpower event during which the power of each LEU and natural uranium rod was at its respective peak values. This resulted in a study with the total assembly power equal to 176% of the nominal power of 230 W considered in Cases 1 and 2. The resulting natural circulation flows were slightly enhanced. The subcooled margin decreased slightly to 46.3°C, which is still a significant margin to local boiling of the water within the tank. This margin confirmed that no boiling was expected during an abnormal operation of UTA–2 at 406 W.

07 ISOTOPE AND RADIATION SOURCES↗

Vexcel Imaging's Suitability for Automatic Verification

Accurate, independently verified geospatial data is essential for automated calibration, validation, and operational decision-making. This study evaluated the positional accuracy of Vexcel Imaging™’s UltraCam® Osprey imagery (7.5 cm GSD) using globally distributed Continuously Operating Reference Stations (CORS) as independent control. Despite manufacturer claims of 15 cm horizontal accuracy, residual errors were consistently one to two orders of magnitude larger, with no subset of imagery meeting precision thresholds. These discrepancies cannot be explained by normal photogrammetric or environmental factors and raise concerns about the reliability of the imagery for high-precision tasks. The results demonstrate that Vexcel imagery, in its current form, is unsuitable for workflows requiring rigorous spatial accuracy or automated verification. At the same time, the reproducible validation framework developed in this study establishes a scalable method for assessing commercial imagery, ensuring that future products can be independently and objectively verified before operational adoption.

47 OTHER INSTRUMENTATION↗

Intensive aerosol properties of boreal and regional biomass burning aerosol at Mt. Bachelor Observatory: larger and black carbon (BC)-dominant particles transported from Siberian wildfires

We characterize the aerosol physical and optical properties of 13 transported biomass burning (BB) events. BB events included long-range influence from fires in Alaskan and Siberian boreal forests transported to Mt. Bachelor Observatory (MBO) in the free troposphere (FT) over 8–14+ d and regional wildfires in northern California and southwestern Oregon transported to MBO in the boundary layer (BL) over 10 h to 3 d. Intensive aerosol optical properties and normalized enhancement ratios for BB events were derived from measured aerosol light scattering coefficients (σ scat ), aerosol light-absorbing coefficients (σ abs ), fine particulate matter (PM 1 ), and carbon monoxide (CO) measurements made from July to September 2019, with particle size distribution collected from August to September. The observations showed that the Siberian BB events had a lower scattering Ångström exponent (SAE), a higher mass scattering efficiency (MSE; Δσ scat /ΔPM 1 ), and a bimodal aerosol size distribution with a higher geometric mean diameter (D g ). We hypothesize that the larger particles and associated scattering properties were due to the transport of fine dust alongside smoke in addition to contributions from condensation of secondary aerosol, coagulation of smaller particles, and aqueous-phase processing during transport. Alaskan and Siberian boreal forest BB plumes were transported long distances in the FT and characterized by lower absorption Ångström exponent (AAE) values indicative of black carbon (BC) dominance in the radiative budget. Significantly elevated AAE values were only observed for BB events with <1 d transport, which suggests strong production of brown carbon (BrC) in these plumes but limited radiative forcing impacts outside of the immediate region.

54 ENVIRONMENTAL SCIENCES↗

The Acceleration of Charged Particles at a Spherical Shock Moving through an Irregular Magnetic Field

We investigate the physics of charged-particle acceleration at spherical shocks moving into a uniform plasma containing a turbulent magnetic field with a uniform mean. This has applications to particle acceleration at astrophysical shocks, most notably, to supernovae blast waves. We numerically integrate the equations of motion of a large number of test protons moving under the influence of electric and magnetic fields determined from a kinematically defined plasma flow associated with a radially propagating blast wave. Distribution functions are determined from the positions and velocities of the protons. The unshocked plasma contains a magnetic field with a uniform mean and an irregular component having a Kolmogorov-like power spectrum. The field inside the blast wave is determined from Maxwell’s equations. The angle between the average magnetic field and unit normal to the shock varies with position along its surface. It is quasi-perpendicular to the unit normal near the sphere’s equator, and quasi-parallel to it near the poles. We find that the highest intensities of particles, accelerated by the shock, are at the poles of the blast wave. The particles “collect” at the poles as they approximately adhere to magnetic field lines that move poleward from their initial encounter with the shock at the equator, as the shock expands. The field lines at the poles have been connected to the shock the longest. We also find that the highest-energy protons are initially accelerated near the equator or near the quasi-perpendicular portion of the shock, where the acceleration is more rapid.

79 ASTRONOMY AND ASTROPHYSICS↗

SU-F-T-592: A Delivery QA-Free Approach for Adaptive Therapy of Prostate Cancer with Static Intensity Modulated Radiotherapy

Purpose: Clinical implementations of adaptive radiotherapy (ART) are limited mainly by the requirement of delivery QA (DQA) prior to the treatment. Small segment size and small segment MU are two dominant factors causing failures of DQA. The aim of this project is to explore the feasibility of ART treatment without DQA by using a partial optimization approach. Methods: A retrospective simulation study was performed on two prostate cancer patients treated with SMLC-IMRT. The prescription was 180cGx25 fractions with daily CT-on-rail imaging for target alignment. For each patient, seven daily CTs were selected randomly across treatment course. The contours were deformablely transferred from the simulation CT onto the daily CTs and modified appropriately. For each selected treatment, dose distributions from original beams were calculated on the daily treatment CTs (DCT plan). An ART plan was also created by optimizing the segmental MU only, while the segment shapes were preserved and the minimum MU constraint was respected. The overlaps, between PTV and the rectum, between PTV and the bladder, were normalized by the PTV volume. This ratio was used to characterize the difficulty of organs-at-risk (OAR) sparing. Results: Comparing to the original plan, PTV coverage was compromised significantly in DCT plans (82% ± 7%) while all ART plans preserved PTV coverage. ART plans showed similar OAR sparing as the original plan, such as V40Gy=11.2cc (ART) vs 11.4cc (original) for the rectum and D10cc=4580cGy vs 4605cGy for the bladder. The sparing of the rectum/bladder depends on overlap ratios. The sparing in ART was either similar or improved when overlap ratios in treatment CTs were smaller than those in original plan. Conclusion: A partial optimization method is developed that may make the real-time ART feasible on selected patients. Future research is warranted to quantify the applicability of the proposed method.

60 APPLIED LIFE SCIENCES↗

SU-F-T-81: Treating Nose Skin Using Energy and Intensity Modulated Electron Beams with Monte Carlo Based Dose Calculation

Purpose: Treating nose skin with an electron beam is of a substantial challenge due to uneven nose surfaces and tissue heterogeneity, and consequently could have a great uncertainty of dose accuracy on the target. This work explored the method using Monte Carlo (MC)-based energy and intensity modulated electron radiotherapy (MERT), which would be delivered with a photon MLC in a standard medical linac (Artiste). Methods: The traditional treatment on the nose skin involves the usage of a bolus, often with a single energy electron beam. This work avoided using the bolus, and utilized mixed energies of electron beams. An in-house developed Monte Carlo (MC)-based dose calculation/optimization planning system was employed for treatment planning. Phase space data (6, 9, 12 and 15 MeV) were used as an input source for MC dose calculations for the linac. To reduce the scatter-caused penumbra, a short SSD (61 cm) was used. A clinical case of the nose skin, which was previously treated with a single 9 MeV electron beam, was replanned with the MERT method. The resultant dose distributions were compared with the plan previously clinically used. The dose volume histogram of the MERT plan is calculated to examine the coverage of the planning target volume (PTV) and critical structure doses. Results: The target coverage and conformality in the MERT plan are improved as compared to the conventional plan. The MERT can provide more sufficient target coverage and less normal tissue dose underneath the nose skin. Conclusion: Compared to the conventional treatment technique, using MERT for the nose skin treatment has shown the dosimetric advantages in the PTV coverage and conformality. In addition, this technique eliminates the necessity of the cutout and bolus, which makes the treatment more efficient and accurate.

60 APPLIED LIFE SCIENCES↗

Robust optimization of intensity modulated proton therapy

Purpose: Intensity modulated proton therapy (IMPT) is highly sensitive to range uncertainties and uncertainties caused by setup variation. The conventional inverse treatment planning of IMPT optimized based on the planning target volume (PTV) is not often sufficient to ensure robustness of treatment plans. In this paper, a method that takes the uncertainties into account during plan optimization is used to mitigate the influence of uncertainties in IMPT. Methods: The authors use the so-called ''worst-case robust optimization'' to render IMPT plans robust in the face of uncertainties. For each iteration, nine different dose distributions are computed--one each for {+-} setup uncertainties along anteroposterior (A-P), lateral (R-L) and superior-inferior (S-I) directions, for {+-} range uncertainty, and the nominal dose distribution. The worst-case dose distribution is obtained by assigning the lowest dose among the nine doses to each voxel in the clinical target volume (CTV) and the highest dose to each voxel outside the CTV. Conceptually, the use of worst-case dose distribution is similar to the dose distribution achieved based on the use of PTV in traditional planning. The objective function value for a given iteration is computed using this worst-case dose distribution. The objective function used has been extended to further constrain the target dose inhomogeneity. Results: The worst-case robust optimization method is applied to a lung case, a skull base case, and a prostate case. Compared with IMPT plans optimized using conventional methods based on the PTV, our method yields plans that are considerably less sensitive to range and setup uncertainties. An interesting finding of the work presented here is that, in addition to reducing sensitivity to uncertainties, robust optimization also leads to improved optimality of treatment plans compared to the PTV-based optimization. This is reflected in reduction in plan scores and in the lower normal tissue doses for the same coverage of the target volume when subjected to uncertainties. Conclusions: The authors find that the worst-case robust optimization provides robust target coverage without sacrificing, and possibly even improving, the sparing of normal tissues. Our results demonstrate the importance of robust optimization. The authors assert that all IMPT plans should be robustly optimized.

61 RADIATION PROTECTION AND DOSIMETRY↗

Effects of Particle Diameter and Coke Layer Thickness on Solid Flow and Stress Distribution in BF by 3D Discrete Element Method

In order to reduce ironmaking-related CO{sub 2} emissions, hydrogen-enriched blast furnace (BF) operation is currently under development. In hydrogen-enriched BF operation, coke layer thickness can be decreased to reduce CO{sub 2} emissions. However, BFs operating with thin coke layers may experience instability or discontinuous phenomena such as particle slip and gas channeling problems, so it is important to optimize the particle diameter and coke layer thickness for optimal BF operation. In this study, the effects of particle diameter and coke layer thickness on the solid flow and stress distribution in a BF were analyzed using a three-dimensional discrete element method. Furthermore, the effects of particle diameter and coke layer thickness on the burden layer stabilities, particle velocities, and particle stress distributions have been investigated. The results show that decreasing the coke layer thickness caused instability owing to the mixing of the coke and ore layers in the BF-cohesive zone and slight increases in both the average particle velocities and the average normal particle stress magnitudes. In addition, the average particle velocities and average normal particle stresses were higher for the smaller particles than for the larger ones during the simulations.

36 MATERIALS SCIENCE↗

Graphene: A partially ordered non-periodic solid

Molecular dynamics simulations were performed to study the structural features of graphene over a wide range of temperatures from 50 to 4000 K using the PPBE-G potential [D. Wei, Y. Song, and F. Wang, J. Chem. Phys. 134, 184704 (2011)]. This potential was developed by force matching the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional and has been validated previously to provide accurate potential energy surface for graphene at temperatures as high as 3000 K. Simulations with the PPBE‑G potential are the best available approximation to a direct Car-Parrinello Molecular Dynamics study of graphene. One advantage of the PBE-G potential is to allow large simulation boxes to be modeled efficiently so that properties showing strong finite size effects can be studied. Our simulation box contains more than 600 000 C atoms and is one of the largest graphene boxes ever modeled. With the PPBE-G potential, the thermal-expansion coefficient is negative up to 4000 K. With a large box and an accurate potential, the critical exponent for the scaling properties associated with the normal-normal and height-height correlation functions was confirmed to be 0.85. This exponent remains constant up to 4000 K suggesting graphene to be in the deeply cooled regime even close to the experimental melting temperature. The reduced peak heights in the radial distribution function of graphene show an inverse power law dependence to distance, which indicates that a macroscopic graphene sheet will lose long-range crystalline order as predicted by the Mermin-Wagner instability. Although graphene loses long-range translational order, it retains long range orientational order as indicated by its orientational correlation function; graphene is thus partially ordered but not periodic.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗