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3,196 records · Page 49

Thermodynamics of Tritium Trapping by Point Defects at Interfacial Cr-based Phases of the Al Coating

Density functional theory (DFT) simulations have been carried out to evaluate the potential for tritium trapping by metal vacancies in four phases Cr-containing phases (i.e., Cr3Si, Al0.3Cr0.7, Al8Cr5-HT, and Al8Cr5) identified near the interface between the Al coating and 316 stainless steel (316 SS) cladding. In addition, an ab initio thermodynamics approach has been employed to predict the temperature and T2-partial pressure dependence on the thermodynamics of singly tritiated defects. Key results in this work suggest that metal vacancies in the four phases have the potential to favorably trap tritium species, especially Si vacancies in Cr3Si phase. This overall thermodynamic trend can be correlated to the energy cost of having an interstitial tritium in the lattice, which has been calculated to range from 0.17 eV in Al8Cr5-HT to 0.89 eV in Cr3Si. A comparison of the results from this study with previous theoretical works investigating tritium behavior in other Fe-Al phases identified in the aluminide coating, suggests that metal vacancies are generally able to trap tritium in various Fe-Al aluminide phases. Especially, it was found that Si and Al vacancies would be the most efficient to trap for tritium, followed by Cr vacancies, then Fe and Ni vacancies. In the four Cr-based material phases investigated in this work, it is interesting to note that, in the absences of Fe or Ni species, strong interactions between tritium and the metal vacancies are always occurring by the formation of preferential Cr—T bonds (i.e., no Si—T or Al—T bonds were formed).

Sassi, Michel J.

Mass Economy Evaluation for Integrated ECLSS and Propulsion Architecture

As missions in low Earth orbit (LEO) lengthen and extend to deep space, minimizing resupply needs becomes vital for sustaining crewed operations. Traditional life support systems depend on consumables resupplied from Earth, a method that is increasingly impractical for missions beyond LEO, such as lunar outposts or Mars transit. Long-duration missions require more efficient, autonomous systems that can recycle essential resources, particularly water and oxygen, to minimize the frequency and mass of resupply missions. The Environmental Control and Life Support System (ECLSS) is essential to such missions, with the International Space Station (ISS) serving as a testbed for advanced water recovery and partial oxygen recycling via physico-chemical methods. Yet, ECLSS and propulsion subsystems generally operate independently, despite overlapping requirements and potential areas for synergy. For instance, ECLSS byproducts, water, CO 2 , and hydrogen, could be repurposed for propulsion, potentially reducing dedicated propellant mass and increasing overall system efficiency. One promising approach is to develop shared-resource architectures that integrate ECLSS with propulsion systems. This study examines the potential of such integration through the Sabatier CO₂ reduction process, focusing on water management as a key factor in system mass trade-offs. The Sabatier reaction produces water and methane from metabolic CO 2 and electrolytic hydrogen, partially closing the life support loop and providing methane, which could serve as a propellant. This integration could minimize waste, reduce resupply requirements, and enhance mission mass efficiency. A dynamic modeling framework will be used to simulate resource flows over long missions, capturing interactions between life support and propulsion. By comparing integrated versus separate system configurations, the study aims to quantify mass benefits and penalties, informing future habitat designs and trade studies for missions prioritizing autonomy and mass efficiency.

ECLSS

In situ studies on heavy ion irradiation and partial oxidation induced stacking faults and nanograins in tungsten nanolaminates

Understanding the microstructural evolution of tungsten (W) under extreme irradiation environments is critical for its application as a plasma-facing material in future fusion reactors. Heavy ion irradiation study offers expedited damage accumulation and thus allows irradiation tolerance property prediction in a short period of time. In this study we explore in situ Kr ion irradiation of W nanolaminates at 800 °C and uncover a complex interplay of irradiation-induced transformations, including the emergence of stacking faults, nanograin formation, and generation of thickened grain boundaries defined as GB regions with the thickness of up to 15 nm. High-resolution transmission electron microscopy studies reveal the formation of extended planar faults and a metastable hexagonal close-packed (hcp) phase within the body-centered cubic (bcc) matrix. These structural transitions are facilitated by irradiation-induced shear. They are further stabilized by the presence of oxygen, which promotes stacking fault formation and vacancy trapping. Elevated temperatures enhance defect mobility, enabling dynamic recrystallization into ultrafine grains and the thickening of GBs due to defect absorption and impurity segregation. These findings unravel non-equilibrium phase transformation pathways in heavy ion irradiated W and highlight the critical role of impurity-mediated defect dynamics in governing its radiation tolerance properties.

Wazeer, Adil [Purdue University]

Intrinsically Conductive {pi}‑d Conjugated Layers with Co–N4 Active Sites for Efficient Nitrate Electrocatalysis and Zinc-Nitrate Batteries

Electrochemical synthesis of ammonia from nitrate has been extensively investigated as a potential alternative to the energy-intensive Haber-Bosch process. This approach not only operates under ambient conditions but also simultaneously removes nitrate contaminants while producing ammonia as a value-added product. However, the ongoing quest lies in designing an efficient electrocatalyst that achieves a high ammonia yield rate, high selectivity, and long-term stability. Herein, we report the outstanding performance of a Co–N4 coordinated π-d layered Co3(HITP)2 (HITP = 2,3,6,7,10,11-hexaiminotriphenylene) in nitrate electrocatalysis. The unique combination of abundant Co–N4 active sites and superior electrical conductivity enables significant electrocatalytic activity, delivering a maximum ammonia yield rate of 56.8 mg cm–2 h–1 at −0.8 V vs RHE and a Faradaic efficiency of ∼91% at −0.4 V vs RHE. Mechanistic analysis reveals that alkaline conditions accelerate water dissociation to generate adsorbed hydrogen intermediates (H*), which are utilized by Co–N4 sites to drive the stepwise hydrogenation of nitrate to ammonia while suppressing competing hydrogen evolution reaction (HER) pathways. Furthermore, integration of this catalyst into a zinc-nitrate battery resulted in a maximum power density of 5.3 mW cm–2 and an open-circuit potential of ∼1.45 V. These results highlight the potential of π-d conjugated Co–N4 materials as an efficient catalyst for both environmental remediation and energy conversion.

Namvar, shahrirar

Adventures in Research: A History of Ames Research Center, 1940-1965

The present document, which I have called a history-though it certainly was not written for historians-was prepared for and at the request of the NASA Ames Research Center which, in sponsoring the project, acted with the encouragement of NASA Headquarters. It is an account of the establishment, evolutionary development, and activities of the Ames Research Center covering a period characterized by unprecedented scientific and technological revolution. The writing of this book about the Ames Research Center was undertaken with considerable pleasure by one who for many years was employed by the Center’s parent organization NASA and, before that, NACA; who had closely followed the Center’s growth from the beginning; and who was personally acquainted with, and who held in some affection, the members of its founding staff. These facts are given to alert readers to the presence of bias and the inaccuracies stemming therefrom. It should be emphasized that this work is a history only of the Ames Research Center. It is not a history of the U.S. Government, of NACA or NASA, of other research centers, of the military services, of industry, or of world events. Information on these peripheral subjects is introduced merely to provide the reader with a generalized feeling for the local and world environment in which the formation and subsequent activities of the Ames Research Center took place. The background material provided is notably incomplete and in some instances reveals the bias of the NACA/NASA community at the time the events took place. Frequently, also, it reflects the personalized viewpoint of the author who was a close observer of many of these events.

NASA Center History Series

Multi-Ion Complexes and Competition from Bulky BArF – Anions for Chloride Binding in Ion Pairing Conditions

Cationic charges have long been used to enhance anion binding. Embedding charge introduces strong ion pairing for target anions but also for off-target ions, ultimately generating a mixture of multi-ion species that are hard to identify and quantify. While many sidestep this problem using polar solvents and weakly coordinating ions, these approaches exclude a substantial cross-section of conditions found in applications spanning recognition, assembly, separations, templation, and catalysis. To confront this complexity, we study the binding of an anion to a cationic receptor featuring low shape complementarity in a low-polarity solvent to maximize ionic interactions. We prepared the receptor as a salt of the weakly coordinating tetrakis­[3,5-bis­(trifluoromethyl)­phenyl]­borate (BArF – ) anion and studied the binding of small chloride (Cl – ) and medium-sized iodide (I – ) anions. Surprisingly, the use of the bulky BArF – anion does not suppress ion pairing interactions, with 65% of the receptor being paired at 0.5 mM in dichloromethane. We observe multi-ion receptor-Cl – complexes (2:1, 1:1, 1:2), reinforcing the complexity that emerges when working in low-polarity media. Here, we reveal the dependence of affinity on anion charge density and size and that bulky BArF – counteranions compete for chloride binding. These studies reveal the noninnocence of BArF – anions and strategies to quantify multi-ion species.

Ion pairing

The Relevance of the VIPER Mission to NASA’s Artemis Human Exploration of the Moon

NASA has ambitious plans to send astronaut crews to the south polar region of the Moon and explore this lunar terrain with humans for the first time through a series of Artemis missions. Artemis will provide economic benefits, drive technological advancement, and inspire the next generation of explorers. Simultaneously, Artemis presents a unique opportunity for humans to conduct high-priority planetary science in situ in the south polar region of the Moon. Prior to human exploration, landed robotic precursor investigations can provide valuable information to reduce risk and maximize discovery and productivity of subsequent crewed missions. NASA’s Volatiles Investigating Polar Exploration Rover (VIPER) is a robotic mission designed to explore and characterize the lunar south polar region prior to crewed Artemis landed missions. VIPER is designed to explore multiple thermal regimes to characterize the lunar polar environment and regolith properties, and to explore for surface and subsurface ices. Each of these objectives are key for both scientific investigation and to detect and assess volatile deposits to support in situ resource utilization (ISRU) and a sustained human presence on the Moon. VIPER would also operate with a real-time mission operations architecture with relevance and feed-forward to Artemis crewed operations on the lunar surface. VIPER would provide key information regarding the lunar environment, scientific exploration, technologies, and real-time operations to optimize the valuable surface exploration time of Artemis crew members while simultaneously reducing risk to crew and increasing health and human safety on the lunar surface.

Jennifer L Heldmann

Analytical Model for Steady Flow through a Finite Channel with One Porous Wall with Arbitrary Variable Suction or Injection

This paper presents an exact solution of two-dimensional laminar flow through a finite length channel with one porous wall. It improves upon previous solutions by (1) satisfying the no-slip boundary condition at the channel dead end, (2) adding a turbulent term to the porous wall boundary condition, (3) allowing for arbitrary variable suction or injection across the porous wall, and (4) model validation against new cryogenic liquid hydrogen and oxygen experimental data. Of particular interest in the current work is the modeling of cryogenic propellant flow through a porous liquid acquisition device (LAD) screen and channel inside a propellant tank. First, a detailed review of the literature is presented for previously attempted solutions to channel flow with one porous wall. Next, the governing equations, boundary conditions, and model assumptions are used to derive the analytical flow solution and present general model results for pressure and velocity fields within the channel. Then, the model solution is compared with horizontal LAD channel flow data in liquid oxygen as well as vertical LAD channel flow data in an inverted outflow configuration in liquid hydrogen. Model results are used to update the static cryogenic bubble point pressure model with a dynamic bubble point term which factors in enhanced convection and cooling at the screen during propellant outflow. Convective heat transfer at the LAD screen during outflow is also quantified by comparing model and data. The new analytical flow solution with the dynamic bubble point model is shown to compare well with available cryogenic experimental data

Navier Stokes Equations

Activation dynamics of a water-soluble human mu-opioid receptor

The mu-opioid receptor (MOR), a class A G protein-coupled receptor mediates opioid analgesia and remains a central target for pain therapeutics. While crystal structures of MOR exist, they provide limited insight into the receptor’s dynamic conformational landscape underlying function. Here, we engineered a thermostable water-soluble MOR variant (wsMOR) that retains native-like ligand-binding and activation dynamics. This variant enables high-yield production and detailed solution-phase structural studies that are challenging with membrane-embedded MOR, providing a valuable tool for studying receptor activation and aqueous-phase drug screening. Using a combined computational and experimental approach, we performed long-timescale all-atom molecular dynamics simulations together with neutron scattering and single-molecule FRET, revealing a structurally stable receptor with a diverse ensemble of conformations at different temporal resolutions. In the ligand-free state, wsMOR displayed high conformational flexibility, which decreased upon agonist binding, particularly in transmembrane helix 6, a hallmark of G protein-coupled receptor activation. Positive allosteric modulation and G protein binding further stabilized active-like states. These findings highlight wsMOR’s conformational plasticity across picosecond to millisecond timescales and provide a foundation for structure-guided development of next-generation opioid ligands with improved efficacy and safety.

E, Agyemang [University of Tennessee Knoxville]

Multiscale and multidimensional modeling of particle acceleration and transport in solar flares

Multi-messenger, multi-viewpoint, and time-resolved observations of solar flares are now providing unprecedented constraints on particle acceleration sites, energy conversion, and energy transport. The interpretation of current observations, including microwave imaging spectroscopy from EOVSA, hard x-ray (HXR) imaging from Solar Orbiter/STIX, gamma-ray diagnostics from Fermi, and in situ measurements from Parker Solar Probe and Solar Orbiter, collectively demands modeling frameworks that go beyond traditional spatially unresolved, one-zone models or single-mechanism descriptions. This review surveys multiscale and multidimensional modeling approaches, including kinetic, magnetohydrodynamic (MHD), and macroscopic particle models, that are being developed to meet the need. Kinetic simulations reveal that three-dimensional (3D) effects, including field-line chaos and self-generated turbulence, are essential for sustained power-law particle acceleration. MHD simulations now capture flux-rope eruptions, plasmoid-unstable current sheets, and turbulent flare regions in realistic magnetic topologies. Macroscopic models coupling MHD with energetic-particle models produce spatially resolved electron distributions and synthetic HXR and microwave emissions for direct comparison with observations. Despite these advances, outstanding challenges remain in bridging kinetic and global scales, improving MHD simulations and macroscopic particle models, and achieving quantitative model-observation closure.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Uranus Orbiter and Probe: Mission Challenges and Concept Updates Since the Origins, Worlds, and Life Decadal Survey

Origins, Worlds, and Life: Planetary Science and Astrobiology in the Next Decade identified a Uranus Orbiter and Probe as the highest-priority strategic mission for the decade 2023–2032, as it enables broad cross-disciplinary science in the largely unexplored Uranian system. The mission architecture evaluated by the Decadal Survey was a singular proof of concept demonstrating that a moderately instrumented mission could deliver Decadal-priority science with a reduced cost and risk posture by leveraging existing technologies to the maximum extent possible. With revised assumptions since the Decadal, we have explored a large trade space including launch vehicles, propulsion options, cruise trajectories, available power sources, viable concept of operations, and science data return for later launch dates without a Jupiter gravity assist. The most repeatable trajectory solutions employ either a commercially derived solar electric propulsion (SEP) transfer stage or the availability of a more capable launch vehicle under development, such as the SpaceX Starship. Orbit insertion has been moved farther from Uranus to acknowledge the remaining uncertainty in Uranian ring structure. A streamlined, SEP-adaptable, orbiter design was developed using two Next Gen Radioisotope Thermoelectric Generators, and the probe design was matured, reducing the entry gravitational acceleration, and assuming the largest Decadal-recommended payload to provide margin for future instrument selections. With this updated design, we also constructed a detailed concept of operations for three representative science cases, returning 13–15 Gbit of science data and spacecraft telemetry per ∼34 day orbit.

Amy A Simon

Ranger Spacecraft

The thermal-control philosophy of the spacecraft currently under development by the Jet Propulsion Laboratory is design by passive means to maintain all components within the tolerances specified by cognizant engineers. Due to the complexity of the configurations, calculations are) of necessity, fairly generalized and final design is based upon tests in an environmental chamber. The Ranger series spacecraft is designed with a basic structure which is common to all models, with additional hardware to suit the individual mission. This basic structure of Rangers A-1 and A-2 is seen as the hexagonal instrument section, the erectable solar panels, the movable antenna, and the omniantenna. The Ranger A-1 and A-2 configuration is for engineering tests and space-exploration, with the scientific instrumentation isolation requirement dictating the spread-out design. The spacecraft stands 12 feet high, weighs 700 to 800 pounds, and has an internal power of 150 watts. Rangers A-3, A-4, and A-5 are designed to rough land a capsule on the moon. For these, a capsule and retrorocket replace the scientific instruments, occupying the space inside the tower structure. The spacecraft must survive many environments. Chronologically they are: 1) Folded configuration inside an aerodynamic shroud on the pad. 2) Thermal flux from shroud aerodynamically heated during boost phase. 3) Coasting up to 30 minutes attached to Agena stage after booster and shroud are separated. 4) Agena stage burning. 5) Coasting and tumbling after separation from Agena until it passes from earth's shadow. 6) Upon reaching sunlight, panels open and begin sun acquisition. 7) Antenna seeks earth after spacecraft locks onto sun. 8) Space phase- "steady state" with vehicle's vertical axis locked on sun, communicating with earth. The philosophy is to design for the sun-acquired mode, making allowances for the transient conditions.

T. O. Thostesen

Machine learning the electric field response of condensed phase systems using perturbed neural network potentials

Abstract The interaction of condensed phase systems with external electric fields is of major importance in a myriad of processes in nature and technology, ranging from the field-directed motion of cells (galvanotaxis), to geochemistry and the formation of ice phases on planets, to field-directed chemical catalysis and energy storage and conversion systems including supercapacitors, batteries and solar cells. Molecular simulation in the presence of electric fields would give important atomistic insight into these processes but applications of the most accurate methods such as ab-initio molecular dynamics (AIMD) are limited in scope by their computational expense. Here we introduce Perturbed Neural Network Potential Molecular Dynamics (PNNP MD) to push back the accessible time and length scales of such simulations. We demonstrate that important dielectric properties of liquid water including the field-induced relaxation dynamics, the dielectric constant and the field-dependent IR spectrum can be machine learned up to surprisingly high field strengths of about 0.2 V Å −1 without loss in accuracy when compared to ab-initio molecular dynamics. This is remarkable because, in contrast to most previous approaches, the two neural networks on which PNNP MD is based are exclusively trained on molecular configurations sampled from zero-field MD simulations, demonstrating that the networks not only interpolate but also reliably extrapolate the field response. PNNP MD is based on rigorous theory yet it is simple, general, modular, and systematically improvable allowing us to obtain atomistic insight into the interaction of a wide range of condensed phase systems with external electric fields.

Science & Technology - Other Topics

Carbon in GaN as a nonradiative recombination center

Trap-assisted nonradiative recombination has been shown to limit the efficiency of optoelectronic devices. While substitutional carbon (⁠C N ) has been suggested to be a nonradiative recombination center in GaN devices, a complete recombination cycle including the two charge-state transition levels has not been previously described. In this work, we investigate the trap-assisted recombination process due to C N in GaN, including multiphonon emission, radiative recombination, trap-assisted Auger–Meitner (TAAM) recombination as well as thermal emission of holes. Our study shows the key role of TAAM processes at the high carrier densities relevant for devices. We also reveal the carrier-density regimes where thermal emission and radiative recombination are expected to play an observable role. Our results highlight that carbon concentrations exceeding ~10 17 cm −3 can have a noticeable impact on device efficiency, not just in GaN active layers but also in InGaN and AlGaN. Furthermore, our comprehensive formalism not only offers detailed results for carbon but also provides a general framework for assessing the multiple processes that participate in trap-assisted recombination in semiconductors.

36 MATERIALS SCIENCE

High-resolution modeling of indoor radon exposure with uncertainty quantification in Utah

Indoor radon accounts for 37% of population-level exposure to ionizing radiation in the United States. However, radon metrics are typically reported at coarse spatial scales, potentially obscuring meaningful local variation. We developed a high-resolution modeling framework to estimate indoor radon concentrations across Utah while explicitly quantifying predictive uncertainty. A total of 19,497 residential radon measurements collected between 2006 and 2017 were combined with environmental and housing characteristics and analyzed using a geospatial neural network that accommodates spatial dependence and nonlinear associations. Predictions were generated on a uniform hexagonal grid at 0.73 km2 resolution (H3 level 8). Out-of-sample predictions aggregated to the H3 level 8 grid showed good agreement with observed concentrations (Pearson r=0.64), while household-level predictions exhibited more moderate agreement (r=0.45). The model produced well-calibrated uncertainty estimates, with 24.1% of held-out observations exceeding the predicted 75th-percentile threshold. Maps of predicted radon concentrations and the probability of exceeding the U.S. EPA action level of 148 Bq/m3 (4 pCi/L) revealed substantial fine-scale spatial heterogeneity that was not apparent in conventional coarse-resolution summaries, with greater local variability observed in densely monitored urban counties than in sparsely sampled regions. High-resolution radon models that explicitly quantify uncertainty provide a useful framework for characterizing the spatial distribution of indoor radon and identifying areas of elevated exceedance risk. These findings highlight the value of fine-scale monitoring data and uncertainty-aware modeling approaches for radon exposure assessment, environmental risk characterization, and radon-related health research.

Wu, Yunhan [ORNL] (ORCID:0000000178842994)

Robustness of inertial fusion energy relevant implosions to low-mode asymmetries

Inertial confinement fusion implosions for power production need to be robust. Degradation sources need to be understood and considered for an economic power plant. In this work, the impact of low-mode asymmetries on yield is studied using 2D radiation hydrodynamics simulations for inertial fusion energy relevant implosions. First, a high-gain indirectly driven capsule design is developed. This design is subsequently degraded with low-mode drive asymmetries. The results show that yield is constant with increasing amounts of asymmetry until a cliff is reached where the yield quickly drops below ignition. Robustness arises because the degraded hotspot still has enough time to get to ignition before capsule decompression. This robustness occurs even though the asymmetry couples less energy to the hotspot and causes decompression to occur sooner. The robustness is linked to the generalized Lawson parameter, χ⁠. The value of χ steadily decreases with increasing asymmetry. Once χ is close to one, the hotspot is no longer able to ignite before the capsule decompresses. A simple piston model is used to predict where the robustness cliff is for any design. The trade-off between yield and robustness is also demonstrated.

Physics - Plasma physics

Advanced Materials for the Lunar Surface: Multiscale Computational Design of Refractory Alloys and Carbides

Emerging operational environments, such as the lunar surface, present novel challenges for NASA and drive the need for advanced materials in applications like fission surface power systems. To address these demands, computational materials science is rapidly evolving to augment or replace costly and hazardous empirical testing. Although materials selection at NASA remains predominantly experimentally driven, advanced simulation methodologies are being steadily integrated into the engineering lifecycle. This work details the application of multiscale simulation techniques—including first-principles calculations, CALPHAD, dislocation dynamics, and molecular dynamics—at NASA's Ames Research Center to evaluate advanced materials for extreme environments. First, we present contributions to the Space Nuclear Propulsion Project. Be-cause propellant channel coatings in nuclear thermal rockets must withstand high-pressure, high-temperature hydro-gen, optimizing these materials is critical. First-principles calculations were employed to establish a rigorous quantitative and qualitative understanding of the behavior of the refractory carbides ZrC, NbC, and their mixtures in high-enthalpy hydrogen environments. This necessitated the generation of high-fidelity thermodynamic models for both stoichiometric and carbon-depleted carbides, both with and without the presence of hydrogen. Furthermore, we highlight efforts under the Refractory Alloy Additive Manufacturing Build Optimization (RAAMBO) project, where existing and novel alloy compositions were assessed for additive manufacturing printability and subsequent performance in applications such as heat pipes and rocket nozzle extensions. This was accomplished through a comprehensive multiscale simulation framework that bridged the gap from the nanometer to the millimeter scale. Across both initiatives, rigorous validation against empirical data was prioritized. By systematically employing a verified and validated computational frame-work, we demonstrate how simulation effectively supports multidisciplinary engineering efforts, builds project-wide confidence, and drives critical materials development.

computational materials

Two-dimensional non-equilibrium melting of charged colloids

Thermodynamic two-dimensional melting has been extensively studied in experiments and simulations, and is well predicted by theory. For systems in equilibrium, this transition is well described by the Kosterlitz–Thouless–Halperin–Nelson–Young theory, where melting is directly linked to the unbinding of topological defects. For driven, non-equilibrium melting and other non-equilibrium phase transitions, the picture is less clear. Here, in this work, we study the two-dimensional melting of a crystal of charged colloids. By randomly replacing some charged colloids with magnetic colloids, we can melt our system by rotating a fraction of the particles to create non-equilibrium, hydrodynamic random flows and local stresses. We can also melt it thermally by changing the particle number density. We find that an effective temperature approach cannot explain the results of our driven system. Rather, in both experiments and simulations, we observe that plotting the hexatic order parameter and the hexatic correlation’s exponent versus the density of disclinations and dislocations, respectively, yields universal curves. This implies that in our systems, two-dimensional melting depends directly on the density of topological defects and is independent of whether thermal or non-equilibrium forces generate them.

critical phenomena