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At least 541 records · Page 30

Difference equations and integral families for Witten diagrams

We show that tree-level and one-loop Mellin space correlators in anti-de Sitter space obey certain difference equations, which are the direct analog to the differential equations for Feynman loop integrals in the flat space. Finite-difference relations, which we refer to as “summation-by-parts relations”, in parallel with the integration-by-parts relations for Feynman loop integrals, are derived to reduce the integrals to a basis. We illustrate the general methodology by explicitly deriving the difference equations and summation-by-parts relations for various tree-level and one-loop Witten diagrams up to the four-point bubble level.

AdS-CFT Correspondence↗

High-resolution ion mobility based on traveling wave structures for lossless ion manipulation resolves hidden lipid features

Abstract High-resolution ion mobility (resolving power > 200) coupled with mass spectrometry (MS) is a powerful analytical tool for resolving isobars and isomers in complex samples. High-resolution ion mobility is capable of discerning additional structurally distinct features, which are not observed with conventional resolving power ion mobility (IM, resolving power ~ 50) techniques such as traveling wave IM and drift tube ion mobility (DTIM). DTIM in particular is considered to be the “gold standard” IM technique since collision cross section (CCS) values are directly obtained through a first-principles relationship, whereas traveling wave IM techniques require an additional calibration strategy to determine accurate CCS values. In this study, we aim to evaluate the separation capabilities of a traveling wave ion mobility structures for lossless ion manipulation platform integrated with mass spectrometry analysis (SLIM IM-MS) for both lipid isomer standards and complex lipid samples. A cross-platform investigation of seven subclass-specific lipid extracts examined by both DTIM-MS and SLIM IM-MS showed additional features were observed for all lipid extracts when examined under high resolving power IM conditions, with the number of CCS-aligned features that resolve into additional peaks from DTIM-MS to SLIM IM-MS analysis varying between 5 and 50%, depending on the specific lipid sub-class investigated. Lipid CCS values are obtained from SLIM IM ( TW(SLIM) CCS) through a two-step calibration procedure to align these measurements to within 2% average bias to reference values obtained via DTIM ( DT CCS). A total of 225 lipid features from seven lipid extracts are subsequently identified in the high resolving power IM analysis by a combination of accurate mass-to-charge, CCS, retention time, and linear mobility-mass correlations to curate a high-resolution IM lipid structural atlas. These results emphasize the high isomeric complexity present in lipidomic samples and underscore the need for multiple analytical stages of separation operated at high resolution. Graphical abstract

Reardon, Allison R. (ORCID:0000000165830134)↗

Fundamentals on dependence of volume on pressure and temperature

The common wisdom that volume decreases with pressure and increases with temperature is analyzed in terms of Hillert nonequilibrium thermodynamics in the present work. It is shown that the derivative of volume to pressure in a stable system is always negative, i.e., volume decreases with the increase of pressure, when all other natural variables of the system are kept constant. This originates from the stability requirement that the conjugate variables, such as volume and negative pressure, must change in the same direction in a stable system. Consequently, since volume and temperature are not conjugate variables, they do not have to change in the same direction and thus do change in opposite directions in both natural and man-made systems. It is shown that the decrease of volume with the increase of temperature, commonly referred as negative thermal expansion (NTE) in the literature, originates from the statistical competitions of configurations in the system when the volumes of metastable configurations are smaller than that of the ground-state configuration. As a result, it is demonstrated that the zentropy theory can concisely explain and accurately predict NTE based on the density functional theory without fitting parameters.

36 MATERIALS SCIENCE↗

A discontinuous piecewise polynomial generalized moving least squares scheme for robust finite element analysis on arbitrary grids

A variational approach is developed with a meshless discretization to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. Here, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality, which we call discontinuous piecewise polynomial generalized moving least squares (DPP-GMLS). At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework, providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5 x improvement in accuracy and allows for taking an 8 x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method.

97 MATHEMATICS AND COMPUTING↗

Roles of the atmosphere and ocean in the projected north atlantic warming hole

There exists a warming deficit in sea surface temperatures (SST) over the subpolar North Atlantic in response to quadrupled CO 2 , referred to as the projected North Atlantic warming hole (WH). This study employs a partial coupling technique to accurately verify the relative roles of oceanic and atmospheric processes in the formation of the projected WH within an atmosphere-ocean coupled framework. By decomposing the SST anomalies in the subpolar North Atlantic into two components: those induced by atmospheric processes (i.e., the atmosphere-forced component) and those driven by changes in ocean circulation (i.e., the ocean-driven component), we find that the projected WH is primarily driven by changes in ocean circulation, with almost no contribution from atmospheric processes. Specifically, the slowdown of the Atlantic Meridional Overturning Circulation (AMOC) results in a cooling of SST in the WH region due to reduced northward ocean heat transport into this region. This study further quantifies the influence of a positive coupled feedback through surface heat flux (SHF) on the AMOC response under greenhouse gas forcing within this self-consistent framework. It is found that the AMOC slowdown leads to a negative SST anomaly in the subpolar North Atlantic and subsequently a positive ocean-driven SHF anomaly, which in turn further weakens the AMOC. In conclusion, this positive feedback through the SHF contributes about 50% to the total AMOC slowdown in response to quadrupled CO 2 .

54 ENVIRONMENTAL SCIENCES↗

The first ensemble of kilometer-scale simulations of a hydrological year over the third pole

An accurate understanding of the current and future water cycle over the Third Pole is of great societal importance, given the role this region plays as a water tower for densely populated areas downstream. An emerging and promising approach for skillful climate assessments over regions of complex terrain is kilometer-scale climate modeling. As a foundational step towards such simulations over the Third Pole, we present a multi-model and multi-physics ensemble of kilometer-scale regional simulations for the hydrological year of October 2019 to September 2020. The ensemble consists of 13 simulations performed by an international consortium of 10 research groups, configured with a horizontal grid spacing ranging from 2.2 to 4 km covering all of the Third Pole region. These simulations are driven by ERA5 and are part of a Coordinated Regional Climate Downscaling EXperiment Flagship Pilot Study on Convection-Permitting Third Pole. The simulations are compared against available gridded and in-situ observations and remote-sensing data, to assess the performance and spread of the model ensemble compared to the driving reanalysis during the cold and warm seasons. Although ensemble evaluation is hindered by large differences between the gridded precipitation datasets used as a reference over this region, we show that the ensemble improves on many warm-season precipitation metrics compared with ERA5, including most wet-day and hour statistics, and also adds value in the representation of wet spells in both seasons. As such, the ensemble will provide an invaluable resource for future improvements in the process understanding of the hydroclimate of this remote but important region.

54 ENVIRONMENTAL SCIENCES↗

On the relationship between precipitation extreme and local temperature over eastern China based on convection permitting simulations: roles of different moisture processes and precipitation types

The Clausius–Clapeyron (CC) scaling, which indicates a roughly 7% increase in saturated water vapor per 1 °C increase in temperature, can serve as a strong constraint linking the intensity of precipitation extremes and local temperature. However, the relationship between precipitation extreme and local temperature (referred to as the PE-T relationship) does not always follow the CC scaling and is highly dependent on climate regimes. In this study, we investigated the impacts of different moisture processes and precipitation types on the PE-T relationship over eastern China during the summertime based on convection-permitting model simulations. Consistent with observations, the simulated intensity of precipitation extremes increases with temperature at a rate close to CC (double-CC) scaling below (above) 20 °C. When the temperature exceeds 25 °C, precipitation intensity starts to drop. Precipitation extremes are mainly contributed by the stratiform, MCS (i.e., mesoscale convective system) convective, and non-MCS convective precipitation at low (< 20 °C), medium (20–25 °C), and high (> 25 °C) temperatures, respectively, suggesting that the double-CC scaling occurs when convective types become dominant, while the negative scaling at high temperatures is attributed to the reduced horizontal scale of convection. Corresponding to the reduced intensity of precipitation at high temperatures, there are stronger divergence and subsidence in the low-level atmosphere, which is probably caused by the net cooling associated with the enhanced melting and evaporation of falling hydrometeors due to the lower relative humidity in the low-level atmosphere. Overall, our findings contribute to a deeper understanding of the temperature dependence of precipitation extremes in eastern China.

54 ENVIRONMENTAL SCIENCES↗

A minor respiratory process with major global implications: is atmospheric methane oxidation in tree stems driven by stem respiration rather than microbial methanotrophy?

Tree stem surfaces are widely recognized as sites of carbon dioxide (CO₂) efflux and oxygen (O₂) influx, reflecting the dynamics of aerobic respiration of photosynthate substrates, such as sugars, delivered via the phloem. Stems are also largely considered passive conduits for methane (CH₄) produced in anoxic soils via microbial methanogenesis, where CH₄ is thought to be transported upward through the transpiration stream and/or diffusion and emitted through stem surfaces and the canopy. However, recent observations from dynamic stem chambers suggest that stems may also act as active sinks for atmospheric CH₄. Despite these findings, the extent and drivers of stem CH₄ consumption remain poorly characterized across biomes, species, and environmental gradients, and its quantitative relationship to stem respiration has not been established. Moreover, previous studies captured only snapshot fluxes, leaving diurnal patterns of CH₄ exchange uncharacterized. Here, we address these limitations by combining real-time measurements of stem CH₄ and O₂ uptake under ambient conditions in a California cherry tree, using a dynamic stem gas exchange system with three chambers receiving a continuous flow of ambient air and automated chamber and reference air sampling every 10 min. Our results confirm that stems of upland trees can actively consume both atmospheric CH₄ and O₂, but with decreasing temperature sensitivity as daily temperatures increase. Early mornings were marked by rapid influxes of both gases, followed by declining uptake as temperatures rose further. Methane uptake was tightly coupled with O₂ influx and represented a minor (0.012% ± 0.002%) fraction of stem respiratory activity, as determined by concurrent O₂ uptake. These findings suggest that while atmospheric CH₄ oxidation is a minor respiratory process in stems, it is strongly linked with stem physiological activity. This challenges the current assumption that terrestrial CH₄ uptake is driven solely by microbial methanotrophy and raises the possibility that living stem tissues may contribute to CH₄ oxidation through an as-yet-unidentified plant-based mechanism.

Atmospheric greenhouse gases↗

Stress Dependency of Brittle Creep in Granite: Insights into Source Mechanisms and Parameters

Creep in rocks refers to the gradual deformation of rock material over time under the influence of constant stress. Characterizing these deformations is of great importance for engineering design, geotechnical assessment, mining operations, geological studies, and understanding natural hazards. While laboratory experiments and a variety of numerical approaches have offered explanations for microcrack interaction and damage accumulation under the three stages of creep (primary, secondary and tertiary) in conventional creep experiments, the micromechanisms of the fractures produced in brittle creep and its dependency on the applied stress have not been explored in detail. The present study focused on investigating the fracturing mechanisms that occur during creep-induced fracturing at different stress levels and estimation of the source parameters and energy budget components. A series of uniaxial compression creep experiments have been conducted at different stress level ratios (70%, 75%, 80% and 85%), to the unconfined compressive strength (UCS) of double-flawed Barre granite specimen. Creep measurements were complemented with the Acoustic Emission (AE) measurements. The creep-induced fractures were classified into double-couple (DC), compensated linear vector dipole (CLVD) and isotropic (ISO) components using the AE moment tensor decomposition technique. The results show that non-double-couple sources dominated during creep at all the specified stress levels; however, their proportions decreased as the stress level was increased. The source parameters estimation indicated a significant increase in the magnitude of the events and the radiated seismic energy with increasing levels of stress and a slight increase in the evaluated source radius and stress drop with increasing stress levels. Furthermore, this study contributes to the existing knowledge of creep-induced fracturing by providing insights into the fracturing mechanisms and the radiated seismic energy produced, which can be helpful for the development of improved models and strategies for rock engineering and geoscience applications.

58 GEOSCIENCES↗

A scalable and autoclavable oxygen nanosensor platform for metabolic monitoring of Saccharomyces cerevisiae in a bioreactor and other in situ systems

Polymer-encapsulated dye nanoparticle sensors are a valuable approach to achieving in situ analyte measurements with luminescence; however, typical emulsion-based nanosensors are poorly suited for large-scale biological samples due to limitations of synthesis scalability and stability. Branched polyethylenimine (PEI) is a versatile polymer scaffold ideal for constructing nanoparticles with various covalently conjugated moieties due to their high density of reactive primary amines, high water solubility, and biological stability. In this work, we used branched polyethylenimine as a scaffold-based approach for making a stable and scalable ratiometric oxygen sensor. Pt (II) tetracarboxyporphine was used as an oxygen-sensing dye and coumarin 343 as a reference dye, all covalently linked to the PEI scaffold producing a product that could withstand sterilization procedures and easily be scaled. To minimize toxicity from the PEI scaffold, we conjugated it with 2000 MW PEG. The applicability of the sensors was demonstrated in a 200 mL Saccharomyces cerevisiae yeast culture, using orthogonal luminescent and electrochemical oxygen measurements to validate sensor response and measure the metabolic activity of the yeast in our culture. Further, this approach was able to match the sensitivity of our electrochemical measurements while improving upon drawbacks of other luminescent methods of oxygen detection, demonstrating effective monitoring for at least 20 h. Our scaffold-based approach is a modular and easily translatable technology that could be useful in various biotechnological applications.

59 BASIC BIOLOGICAL SCIENCES↗

The DECOVALEX international collaboration on modeling of coupled subsurface processes and its contribution to confidence building in radioactive waste disposal

Abstract The long-lived radiotoxicity of the high-level radioactive waste generated by nuclear power plants requires safe isolation from the biosphere for many hundreds of thousands of years. An international consensus has emerged that such isolation can best be provided by disposal in mined geologic repositories, a strategy that today is pursued by most countries dealing with radioactive waste. However, the need to predict the performance of such repositories over very long time periods generates large uncertainties that have to be accounted for in safety assessments. The findings from such safety assessments need to be conveyed to all stakeholders in a clear way, such that public confidence in geologic disposal solutions can be achieved. It is suggested here that close international collaboration on the technical aspects of geologic waste disposal has helped, and will continue to help, building trust and increasing confidence. This paper discusses a particular international collaboration initiative referred to as DECOVALEX, which brings together multiple teams and disciplines to collectively tackle complex experimental and modeling challenges related to geologic disposal. By describing how DECOVALEX works and by providing joint research examples, a case is made that such international collaboration contributes to knowledge transfer and confidence building in radioactive waste disposal science.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Review: Pre-Darcy flows in low-permeability porous media

The widely used Darcy’s law specifies a linear relation between the Darcy velocity of fluid flow and the pressure gradient that drives the flow. However, studies have shown that Darcy velocity can exhibit a nonlinear dependence on the pressure gradient in low-permeability porous media such as clay and shale when the pressure gradient is adequately low. This phenomenon is referred to as low-velocity non-Darcian flow or pre-Darcy flow. This paper provides a comprehensive review of the theories, experimental data, and modeling methods for pre-Darcy flow in low-permeability porous media. The review begins by outlining the fundamental mechanisms underlying pre-Darcy flow that regulate the unique characteristics such as nonlinear dependence of the Darcy velocity on the pressure gradient and its relevance to fluid–rock interactions. The review then proceeds to present a thorough compilation of experimental investigations performed in various low-permeability geomaterials including tight sandstones, shales, and clays. Next, empirical and theoretical models and simulation methods that have been developed to fit and interpret experimental data are reviewed. Finally, the review underscores the challenges encountered in conducting and interpreting pre-Darcy flow experiments and suggests future research directions. By analyzing previous experimental investigations, this review aims to offer a valuable resource for researchers and practitioners seeking to enhance their understanding of fluid dynamics in low-permeability geomaterials. This provides insights into the application of pre-Darcy flow in numerous natural and engineered processes such as shale oil and gas recovery, contaminant transport in low-permeability aquifers, and geological disposal of nuclear waste.

58 GEOSCIENCES↗

Proximal Galerkin: A Structure-Preserving Finite Element Method for Pointwise Bound Constraints

The proximal Galerkin finite element method is a high-order, low iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of pointwise bound constraints in infinite-dimensional function spaces. This paper introduces the proximal Galerkin method and applies it to solve free boundary problems, enforce discrete maximum principles, and develop a scalable, mesh-independent algorithm for optimal design with pointwise bound constraints. This paper also introduces the latent variable proximal point (LVPP) algorithm, from which the proximal Galerkin method derives. When analyzing the classical obstacle problem, we discover that the underlying variational inequality can be replaced by a sequence of second-order partial differential equations (PDEs) that are readily discretized and solved with, e.g., the proximal Galerkin method. Throughout this work, we arrive at several contributions that may be of independent interest. These include (1) a semilinear PDE we refer to as the entropic Poisson equation; (2) an algebraic/geometric connection between high-order positivity-preserving discretizations and certain infinite-dimensional Lie groups; and (3) a gradient-based, bound-preserving algorithm for two-field, density-based topology optimization. The complete proximal Galerkin methodology combines ideas from nonlinear programming, functional analysis, tropical algebra, and differential geometry and can potentially lead to new synergies among these areas as well as within variational and numerical analysis. Open-source implementations of our methods accompany this work to facilitate reproduction and broader adoption.

97 MATHEMATICS AND COMPUTING↗

Adaptive anomaly detection for identifying attacks in cyber-physical systems: A systematic literature review

Modern cyberattacks in cyber-physical systems (CPS) rapidly evolve and cannot be deterred effectively with most current methods, which focus on characterizing past threats. Adaptive anomaly detection (AAD) is among the most promising techniques to detect evolving cyberattacks, with an emphasis on fast data processing and model adaptation. AAD has been researched extensively; however, to the best of our knowledge, our work is the first systematic literature review (SLR) on current research in this field. We present a comprehensive SLR, gathering 397 relevant papers and systematically analyzing 65 of them (47 research and 18 survey papers) on AAD in CPS from 2013 to November 2023. We introduce a novel taxonomy considering attack types, CPS application, learning paradigm, data management, and algorithms. Our findings show that most studies addressed either model adaptation or data processing, but rarely both simultaneously. This indicates a research gap in fully adaptive solutions. We also categorize algorithms, datasets, and attack characteristics, and summarize strengths and weaknesses across the literature. Our review provides a structured and accessible reference for researchers and practitioners, offering insights into key trends and highlighting limitations in current approaches. Finally, we outline several future research directions, including the need for integrated real-time processing and adaptive learning, explainability, and uncertainty quantification in AAD for CPS.

Adaptation↗

Revisiting a Drag Partition Model For Canopy-Like Roughness Elements

Turbulent flows over a large surface area (S) covered by n obstacles experience an overall drag due to the presence of the ground and the protruding obstacles into the flow. The drag partition between the roughness obstacles and the ground is analyzed using an analytical model proposed by Raupach (Boundary-Layer Meteorol 60:375-395, 1992) and is hereafter referred to as R92. The R92 is based on the premise that the wake behind an isolated roughness element can be described by a shelter area A and a shelter volume V. The individual sizes of A and V without any interference from other obstacles can be determined from scaling analysis for the spread of wakes. To upscale from an individual roughness element to n/S elements where wakes may interact, R92 adopted a background stress re-normalizing instead of reducing A or V with each element addition. This work demonstrates that R92’s approach results in a linear background stress reduction in A and V only when the ratio of n/S is small, due to a low probability of wake interactions. This probabilistic nature suggests that up-scaling from individual to multiple roughness elements can be re-formulated using stochastic averaging methods proposed here. The two approaches are shown to recover R92 under plausible conditions. An alternative scaling for the shelter volume is also proposed here using thermodynamic arguments of work and dissipation though the final outcome remains similar to R92. Comparisons between R92 and available data spanning more than two decades after R92 on blocks and vegetation-like roughness elements confirm the practical utility of R92. The agreement between R92 and this updated databases of experiments and simulations confirm the potential use of R92 in large-scale models provided that the relevant parameters accommodate certain features of the roughness element type (cube versus vegetation-like) and, to a lesser extent, their configuration throughout S. Last, a comparison between R92 and models based on first-order closure principles with constant mixing length suggests that R92 can outperform such models when evaluated across a wide range of roughness densities.

canopy turbulence↗

Convergence analysis for a nonlocal gradient descent method via directional Gaussian smoothing

We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is proposed to define the nonlocal gradient (also referred to as the DGS gradient). The method was first proposed in [Zhang et al., Enabling long-range exploration in minimization of multimodal functions, UAI 2021], in which multiple numerical experiments showed that replacing the traditional local gradient with the DGS gradient can help the optimizers escape local minima more easily and significantly improve their performance. However, a rigorous theory for the efficiency of the method on nonconvex landscape is lacking. In this work, we investigate the scenario where the objective function is composed of a convex function, perturbed by deterministic oscillating noise. We provide a convergence theory under which the iterates exponentially converge to a tightened neighborhood of the solution, whose size is characterized by the noise wavelength. Here, we also establish a correlation between the optimal values of the Gaussian smoothing radius and the noise wavelength, thus justifying the advantage of using moderate or large smoothing radii with the method. Furthermore, if the noise level decays to zero when approaching the global minimum, we prove that DGS-based optimization converges to the exact global minimum with linear rates, similarly to standard gradient-based methods in optimizing convex functions. Several numerical experiments are provided to confirm our theory and illustrate the superiority of the approach over those based on the local gradient.

Tran, Hoang [Oak Ridge National Laboratory (ORNL),↗

What drives embodied carbon policy? A global perspective on adoption

Abstract Embodied carbon refers to the greenhouse gas emission associated with the lifecycle of buildings. Embodied carbon policies are critical for addressing the environmental impact of construction materials and advancing climate goals. Despite their importance, the adoption of embodied carbon policies has been limited globally, influenced by economic, environmental, institutional, and trade factors. This study employs structural equation modeling to analyze 37 countries, testing ten hypotheses across four categorical factors. The base model reveals the significant influence of environmental vulnerability and institutional frameworks on policy adoption, while robustness models confirm the critical role of trade dependencies and economic competitiveness in shaping national embodied carbon strategies. Findings underscore that countries with high climate vulnerability and strong institutional support are more likely to adopt embodied carbon policies. Conversely, trade-reliant nations face challenges balancing competitiveness and sustainability. Policy implications suggest the need for international collaboration to align trade policies with carbon reduction goals, targeted support for vulnerable nations, and the integration of embodied carbon considerations into existing climate frameworks. These results offer a roadmap for policymakers to design more effective and equitable embodied carbon policies, fostering global progress toward sustainable construction and decarbonization.

Hu, Ming (ORCID:0000000325831161)↗

Quantifying Uncertainties in Heat Capacity Measurements of Molten Salts Determined Using Differential Scanning Calorimetry

Uncertainty in specific heat capacity values of a molten salt determined by using differential scanning calorimetry (DSC) was assessed based on the precision of replicate measurements of heat flows used in the calculation and effects of corrections that are commonly made to heat flow measurements. The ratio method of determining heat capacity was applied using the results of replicate heat flow measurements made with two empty cells, a sapphire reference material, and three samples of a doped NaCl-UCl 3 salt mixture. Replicate measurements with empty cells were used to quantify the effects of system instabilities and sensitivities on the measured heat flows of sapphire and salt. The combined effects of uncertainties in individual heat flow measurements made with blank cells using this system were quantified to be 2.6 μV based on isothermal holds before and after the scan, with cell placement adding the greatest uncertainty. This value was used as the tolerance for accepting background-corrected heat flows measured with sapphire and salt to calculate the specific heat capacity. The acceptable heat flows measured for sapphire and salt over the temperature range of 540 to 725 °C resulted in calculated specific heat capacity values ranging from 0.53 to 0.91 J g −1 K −1 with an overall average value of 0.70 J g −1 K −1 and an uncertainty of 0.22 J g −1 K −1 at the 99 % confidence level. The combined uncertainty in the specific heat capacity masked detection of any effect of temperature or salt composition that occurred.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗