Search NASA⌕ Search

SEARCH · Search NASA

Results for “atomic data”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 613 records · Page 34

Cryotrapping peroxide in the active site of human mitochondrial manganese superoxide dismutase crystals for neutron diffraction

Structurally identifying the enzymatic intermediates of redox proteins has been elusive due to difficulty in resolving the H atoms involved in catalysis and the susceptibility of ligand complexes to photoreduction from X-rays. Cryotrapping ligands for neutron protein crystallography combines two powerful tools that offer the advantage of directly identifying hydrogen positions in redox-enzyme intermediates without radiolytic perturbation of metal-containing active sites. However, translating cryogenic techniques from X-ray to neutron crystallography is not straightforward due to the large crystal volumes and long data-collection times. Here, methods have been developed to visualize the evasive peroxo complex of manganese superoxide dismutase (MnSOD) so that all atoms, including H atoms, could be visualized. The subsequent cryocooling and ligand-trapping methods resulted in neutron data collection to 2.30 Å resolution. The P 6 1 22 crystal form of MnSOD is challenging because it has some of the largest unit-cell dimensions ( a = b = 77.8, c = 236.8 Å) ever studied using high-resolution cryo-neutron crystallography. The resulting neutron diffraction data permitted the visualization of a dioxygen species bound to the MnSOD active-site metal that was indicative of successful cryotrapping.

59 BASIC BIOLOGICAL SCIENCES↗

Generation IV Benchmarking of TRISO Fuel Performance Models Under Accident Conditions Final Report

The Generation IV International Forum (GIF) is a co-operative international endeavor of fourteen members organized to carry out the research and development needed to establish the feasibility and performance capabilities of the next generation nuclear energy systems. GIF selected six reactor technologies, amongst which is the Very High Temperature Reactor (VHTR) that is primarily dedicated to the cogeneration of electricity and hydrogen. The technical basis for VHTR is the tristructural isotropic (TRISO)-coated particle fuel, the graphite as the core structure, helium coolant, as well as the dedicated core layout and lower power density to removal decay heat in a natural way. At the heart of safety features of the VHTR concept lie the TRISO fuel particles that are designed to keep their structural integrity and retain fission products at temperatures up to 1600°C. As part as the design and future operation of VHTRs, a key aspect is the accurate prediction of fuel performance under irradiation and accident conditions. Modeling and simulation allow prediction of TRISO fuel behavior when subject to neutron flux and in high temperature accident scenarios. The refinement of the fuel performance models and codes is performed by comparison to in-pile and out-of-pile experimental data that reproduce the expected irradiation conditions in high temperature gas-cooled reactors (HTGRs). Historically, the International Atomic Energy Agency (IAEA) developed a benchmark dedicated to the validation of predictive methods for fuel and fission product behavior through the Coordinated Research Program CRP-2 (IAEA, 1997). CRP-2 was later updated to cover fuel fabrication, quality assurance, irradiation performance, safety testing, and spent fuel. The scope of the resulting CRP-6 benchmarks focused on HTGR fuel performance and fission product release (IAEA, 2012). Taking advantage of additional TRISO fuel fabrication, irradiation, and safety testing campaigns, GIF launched a Generation IV Benchmarking of TRISO Fuel Performance Models under Accident Conditions in late 2015. This GIF benchmark is a three-year program steered by Idaho National Laboratory (INL, USA). The other participants include the Japan Atomic Energy Agency (JAEA, Japan) and the Korea Atomic Energy Research Institute (KAERI, Korea). The objectives of the benchmark are to: follow on the IAEA CRP benchmarks, (2) model fission product release under accident conditions, (3) compare results obtained by the fuel performance modeling codes of the benchmark participants, and (4) compare these code predictions to experimental data. Safety tests chosen for modeling include the first and second experiments of the Advanced Gas Reactor program (AGR-1 and AGR-2) and the High Flux Reactor (HFR) EU1bis experiment. This report presents the results obtained by the three research institutions using their respective fuel performance modeling codes. Comparisons of the corresponding fission product release predictions are made with experimental data from AGR-1, AGR-2, and HFR-EU1bis. The benchmark results show good agreements between all participants but also show a general trend of over-prediction of the experimental release data, which is mainly attributed to the use of over-estimated diffusion coefficients.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A data-driven peridynamic continuum model for upscaling molecular dynamics

Nonlocal models, including peridynamics, often use integral operators that embed lengthscales in their definition. However, the integrands in these operators are difficult to define from the data that are typically available for a given physical system, such as laboratory mechanical property tests. In contrast, molecular dynamics (MD) does not require these integrands, but it suffers from computational limitations in the length and time scales it can address. To combine the strengths of both methods and to obtain a coarse-grained, homogenized continuum model that efficiently and accurately captures materials’ behavior, we propose a learning framework to extract, from MD data, an optimal Linear Peridynamic Solid (LPS) model as a surrogate for MD displacements. To maximize the accuracy of the learnt model we allow the peridynamic influence function to be partially negative, while preserving the well-posedness of the resulting model. To achieve this, we provide sufficient well-posedness conditions for discretized LPS models with sign-changing influence functions and develop a constrained optimization algorithm that minimizes the equation residual while enforcing such solvability conditions. This framework guarantees that the resulting model is mathematically well-posed, physically consistent, and that it generalizes well to settings that are different from the ones used during training. We illustrate the efficacy of the proposed approach with several numerical tests for single layer graphene. Our two-dimensional tests show the robustness of the proposed algorithm on validation data sets that include thermal noise, different domain shapes and external loadings, and discretizations substantially different from the ones used for training.

homogenization↗

Leveraging Artificial Intelligence to Predict Novel Eutectic Alloys

The goal of this project was to train an artificial neural network (ANN) to predict the fractional composition and melting point of eutectic alloys using fundamental atomic properties as inputs. The fundamental properties considered include atomic number, atomic weight, atomic radius, valence electron concentration, electronegativity, and electron affinity. The project involved several phases, starting with data preparation, where phase diagram data was harvested from the ASM International database. Approximately 1300 binary eutectics were collected and cleaned to ensure relevance and accuracy. A regression model was selected for training, utilizing a rectified linear unit as the activation function. Various model configurations were evaluated for predictive accuracy, with validation techniques employed to ensure robustness. The model demonstrated predictive capabilities above random guessing and was able to achieve up to 11% accuracy under certain conditions. An ablative test identified atomic radius and valence electron concentration as critical inputs for model performance. Incorporating the melting point of atomic constituents improved accuracy significantly, although ultimately the model’s predictive capability still fell short of the 80% target. This report details the methodology, results, and implications of the research, contributing to the understanding of employing artificial intelligence to predict the phase transition behavior of eutectic alloys.

36 MATERIALS SCIENCE↗

Equation of state for He bubbles in W and model of He bubble growth and bursting near W{100} surfaces derived from molecular dynamics simulations

Abstract Molecular dynamics (MD) simulations are performed to derive an equation of state (EOS) for helium (He) bubbles in tungsten (W) and to study the growth of He bubbles under a W(100) surface until they burst. We study the growth as a function of the initial nucleation depth of the bubbles. During growth, successive loop-punching events are observed, accompanied by shifts in the depth of the bubble towards the surface. Subsequently, the MD data are used to derive models that describe the conditions that cause the loop punching and bursting events. Simulations have been performed at 500, 933, 1500, 2000, and 2500 K to fit the parameters in the models. To compute the pressure in the bubble at the loop punching and bursting events from the models, we derive an EOS for He bubbles in tungsten with an accompanying volume model to compute the bubble volume for a given number of vacancies ( $$N_\text {V}$$ N V ), He atoms ( $$N_\text {He}$$ N He ), and temperature ( T ). To derive the bubble EOS, we firstly derive the EOS for a free He gas. The derived free-gas EOS can accurately predict all MD data included in the analysis (which span up to 54 GPa at 2500 K). Subsequently, the bubble EOS is derived based on the free-gas EOS by correcting the gas density to account for the interaction between He and W atoms. The EOS for the bubbles is fitted to data from MD simulations of He bubbles in bulk W that span a wide range of gas density and sizes up to about 3 nm in diameter. The pressure of subsurface bubbles at the loop punching events as calculated using the bubble-EOS and the volume model agrees well with the pressure obtained directly from the MD simulations. In the loop punching model, for bubbles consisting of $$N_\text {V}$$ N V vacancies and $$N_\text {He}$$ N He helium atoms, the $$N_\text {He}/N_\text {V}$$ N He / N V ratio that causes the event, the resulting increase in $$N_\text {V}$$ N V , and the associated shift of the bubble depth are formulated as a function of $$N_\text {V}$$ N V and T . In the bursting model, a bubble must simultaneously reach a certain depth and $$N_\text {He}/N_\text {V}$$ N He / N V ratio in order to burst. The burst depth and $$N_\text {He}/N_\text {V}$$ N He / N V are also modeled as a function of $$N_\text {V}$$ N V and T . The majority of the loop punching events occur at bubble pressures between 20 and 60 GPa, depending on the bubble size and temperature. The larger the bubble and the higher the temperature, the lower the bubble pressure. Furthermore, our results indicate that at a higher temperature, a bubble can burst from a deeper region.

36 MATERIALS SCIENCE↗

Illustrated formalisms for total scattering data: a guide for new practitioners

The total scattering method is the simultaneous study of both the real- and reciprocal-space representations of diffraction data. While conventional Bragg-scattering analysis (employing methods such as Rietveld refinement) provides insight into the average structure of the material, pair distribution function (PDF) analysis allows for a more focused study of the local atomic arrangement of a material. Generically speaking, a PDF is generated by Fourier transforming the total measured reciprocal-space diffraction data (Bragg and diffuse) into a real-space representation. However, the details of the transformation employed and, by consequence, the resultant appearance and weighting of the real-space representation of the system can vary between different research communities. As the worldwide total scattering community continues to grow, these subtle differences in nomenclature and data representation have led to conflicting and confusing descriptions of how the PDF is defined and calculated. This paper provides a consistent derivation of many of these different forms of the PDF and the transformations required to bridge between them. Some general considerations and advice for total scattering practitioners in selecting and defining the appropriate choice of PDF in their own research are presented. This contribution aims to benefit people starting in the field or trying to compare their results with those of other researchers.

36 MATERIALS SCIENCE↗

Machine Learning Atom Probe Tomography Tool For Automatic And Fast Clustering

The software uses a YOLO11 segmentation model trained on synthetic data to analyze APT datasets. The workflow operates as follows: 1. Data Slicing: The APT dataset is divided into multiple 2D cross-sections of a specified thickness. 2. Segmentation: The model identifies point-dense regions within each 2D slice. 3. 3D Reconstruction: Detected regions (masks) from all slices are combined and reconstructed back into the original 3D space, forming clusters. The integration with HPC resources enables the software to process large-scale APT datasets efficiently. This combination of automation and scalability reduces manual intervention, improves reproducibility, and accelerates the clustering workflow.

Tang, Yalei [Idaho National Laboratory (INL), Idah↗

Complete collision data set for electrons scattering on molecular hydrogen and its isotopologues: I. Fully vibrationally-resolved electronic excitation of H 2 $X^1Σ^+_g)$

Here, we present a comprehensive set of vibrationally-resolved cross sections for electron-impact electronic excitation of molecular hydrogen suitable for implementation in collisional-radiative models. The adiabatic-nuclei molecular convergent close-coupling method is used to calculate cross sections for excitation of all bound vibrational levels and dissociative excitation of the B 1 Σ u + , C 1 Π u , E F 1 Σ g + , B ′ 1 Σ u + , G K 1 Σ g + , I 1 Π g , J 1 Δ g , D 1 Π u , H 1 Σ g + , b 3 Σ u + , c 3 Π u , a 3 Σ g + , e 3 Σ u + , d 3 Π u , h 3 Σ g + , g 3 Σ g + , i 3 Π g , and j 3 Δ g electronic states from all –14 bound vibrational levels of the ground electronic ($\text{X}$ $^1&#x3A3^+_g$) state. The data set consists of cross sections from threshold to 500 eV for over 5000 transitions, representing all possible electronic and vibrational transitions between the state and the –3 singlet and triplet states (where refers to the united-atoms-limit principle quantum number). The cross sections are presented in graphical form and provided as both numerical values and analytic fit functions in supplementary data files.

74 ATOMIC AND MOLECULAR PHYSICS↗

Competing ionization and dissociation in the H 2 gerade system

A numerically solvable two-dimensional (2D) model, employed by the authors to study the dissociative recombination of H$^+_2$ in the ungerade symmetry, is extended to describe the collision process in the gerade symmetry of H$_2$. In this symmetry, the ionization and dissociation processes are driven primarily by the direct, curve-crossing mechanism. The model is represented by a set of three coupled electronic channels in 2D, in the space of $\textit{s, p, d}$ partial waves of the colliding electron. In this work, we demonstrate that the Born-Oppenheimer properties of the H$_2$ molecule in the relevant range of internuclear distances can be described by such a model. The molecular rotational degrees of freedom are accounted for by the rotational frame transformation. The numerical solution of the model is discussed, and the resulting rovibrationally inelastic and dissociative recombination cross sections are compared with the available data.

74 ATOMIC AND MOLECULAR PHYSICS↗

Electron-impact excitation data for W 2+ in support of tungsten spectroscopy and re-deposition measurements for magnetically-confined plasmas

Abstract To better understand plasma wall interactions involving tungsten, accurate atomic structure and electron-impact driven collisional processes for near-neutral ion stages of tungsten are required. Complementing existing work on neutral and singly ionised tungsten, atomic structure and collisional calculations for W 2+ electron-impact excitation have been completed. These excitation calculations are an important component of S/XB coefficients for near-neutral charge states, which may be used to spectroscopically infer re-deposition of tungsten at the plasma-solid boundary of fusion relevant devices. With W 2+ in particular having emission lines that can be observed at ultraviolet (UV) wavelengths, while higher charge states of tungsten are unlikely to have lines possible to observe outside of the vacuum UV range. The atomic structure was generated using the General-purpose Relativistic Atomic Structure Package (GRASP 0 ), implementing the Multi-configuration Dirac Fock approach. This structure was the basis for a subsequent Dirac R -matrix electron-impact excitation calculation to provide Maxwellian averaged rate coefficients. A synthetic spectrum was generated from this data using a collisional-radiative model to predict the strongest W III spectral lines and these lines were compared to emission from the Compact Toroidal Hybrid (CTH) plasma device. Several of the strongest W III lines are observed in CTH and agree well with the modelled line wavelengths and intensities, a table of these lines is provided that could be observed in other devices.

McCann, M. (ORCID:0000000215321240)↗

A multimodal large language model for materials science

Understanding and predicting the properties of inorganic materials is crucial for accelerating advancements in materials science and driving applications in energy, electronics and beyond. Integrating material structure data with language-based information through multimodal large language models (LLMs) offers great potential to support these efforts by enhancing human–artificial intelligence interaction. However, a key challenge lies in integrating atomic structures at full resolution into LLMs. In this work, we introduce MatterChat, a versatile structure-aware multimodal LLM that unifies material structural data and textual inputs into a single cohesive model. MatterChat uses a bridging module to effectively align a pretrained universal machine learning interatomic potential with a pretrained LLM, reducing training costs and enhancing flexibility. Our results demonstrate that MatterChat greatly improves performance in material property prediction and human–artificial intelligence interaction, surpassing general-purpose LLMs such as GPT-4. We also demonstrate its usefulness in applications such as more advanced scientific reasoning and step-by-step material synthesis.

Tang, Yingheng [Lawrence Berkeley National Laborat↗

Predicting the propensity for thermally activated β events in metallic glasses via interpretable machine learning

Abstract The elementary excitations in metallic glasses (MGs), i.e., β processes that involve hopping between nearby sub-basins, underlie many unusual properties of the amorphous alloys. A high-efficacy prediction of the propensity for those activated processes from solely the atomic positions, however, has remained a daunting challenge. Recently, employing well-designed site environment descriptors and machine learning (ML), notable progress has been made in predicting the propensity for stress-activated β processes (i.e., shear transformations) from the static structure. However, the complex tensorial stress field and direction-dependent activation could induce non-trivial noises in the data, limiting the accuracy of the structure-property mapping learned. Here, we focus on the thermally activated elementary excitations and generate high-quality data in several Cu-Zr MGs, allowing quantitative mapping of the potential energy landscape. After fingerprinting the atomic environment with short- and medium-range interstice distribution, ML can identify the atoms with strong resistance or high compliance to thermal activation, at a high accuracy over ML models for stress-driven activation events. Interestingly, a quantitative “between-task” transferring test reveals that our learnt model can also generalize to predict the propensity of shear transformation. Our dataset is potentially useful for benchmarking future ML models on structure-property relationships in MGs.

36 MATERIALS SCIENCE↗

The ENDF/B Nuclear Data Library and Its Impact on Reactor Simulations

The ENDF/B library, which is developed, maintained, and distributed by the Cross Section Evaluation Working Group, is the main source of nuclear data for analyses and computational simulations in nuclear applications, like different nuclear reactors concepts, radiation shielding, medical applications, astrophysics, etc. The library is constantly being improved and updated, with each release bringing an optimal representation of nuclear interactions as they are understood in their time. The most recent release, ENDF/B-VIII.1, represents a significant improvement in terms of the performance and consistency of the measured differential data relative to previous versions, as it combines the most recent experimental differential data and advanced theoretical nuclear models. As one of the many highlights, ENDF/B-VIII.1 restores a high-burnup depletion performance, comparable to ENDF/B-VII.1, that had been degraded in ENDF/B-VIII.0, while further improving the performance in criticality benchmarks, such as those in the Mosteller’s suite. Additionally noteworthy is the improved performance of ENDF/B-VIII.1 in radiation shielding and thick-target leakage spectrum integral experiments, which are also important for fusion and reactor applications. In this work we present in a very summarized way the main updates implemented in the ENDF/B-VIII.1 release and its main impacts, and also begin to delineate the path forward as to what to expect in the future for the next ENDF/B release, which, based on the timeline of the past few releases, is estimated to happen around 5 years from now. We emphasize that the ENDF/B-VIII.1 release was the product of an enormous collaborative effort among many authors and that for a complete detailed picture, the reader is strongly encouraged to refer to the article accompanying the release, which is currently in the publication process, but available as preprint [G. P. A. Nobre et al. arXiv Preprint arXiv: 2511.03564 (2025)].

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Forming mechanism of equilibrium and non-equilibrium metallurgical phases in dissimilar aluminum/steel (Al–Fe) joints

Abstract Forming metallurgical phases has a critical impact on the performance of dissimilar materials joints. Here, we shed light on the forming mechanism of equilibrium and non-equilibrium intermetallic compounds (IMCs) in dissimilar aluminum/steel joints with respect to processing history (e.g., the pressure and temperature profiles) and chemical composition, where the knowledge of free energy and atomic diffusion in the Al–Fe system was taken from first-principles phonon calculations and data available in the literature. We found that the metastable and ductile (judged by the presently predicted elastic constants) Al 6 Fe is a pressure ( P ) favored IMC observed in processes involving high pressures. The MoSi 2 -type Al 2 Fe is brittle and a strong P -favored IMC observed at high pressures. The stable, brittle η-Al 5 Fe 2 is the most observed IMC (followed by θ-Al 13 Fe 4 ) in almost all processes, such as fusion/solid-state welding and additive manufacturing (AM), since η-Al 5 Fe 2 is temperature-favored, possessing high thermodynamic driving force of formation and the fastest atomic diffusivity among all Al–Fe IMCs. Notably, the ductile AlFe 3 , the less ductile AlFe, and most of the other IMCs can be formed during AM, making AM a superior process to achieve desired IMCs in dissimilar materials. In addition, the unknown configurations of Al 2 Fe and Al 5 Fe 2 were also examined by machine learning based datamining together with first-principles verifications and structure predictions. All the IMCs that are not P- favored can be identified using the conventional equilibrium phase diagram and the Scheil-Gulliver non-equilibrium simulations.

36 MATERIALS SCIENCE↗

Short and medium range structure in elastic deformation of metallic and covalent glasses

Here, we present a concise methodology to analyze structural response to the applied stress in amorphous solids, including metallic glasses (MG), glassy selenium, silica and polycarbonate, using high energy x-ray diffraction and atomic pair distribution function (PDF) analysis. To assess the structural anisotropy induced by applied axial stress, diffraction data were expanded into spherical harmonics. Using Bessel transformation, components of the structure function were converted into isotropic and anisotropic PDFs. The PDFs were compared to the expected model behavior for ideal elastic deformation to separate homogeneous affine strain from local non-affine strains. In metallic glass the range of non-affine deformation is limited to the nearest neighbor shell, suggesting local strain relaxation under stress that occurs even in the elastic regime. Beyond the second atomic shell strain is uniform. However, in glassy silica, polycarbonate and selenium strong local bonding inhibits local displacements and strain in short range order is accommodated by rotation of local units. Interestingly, beyond a molecular unit, deformation in covalent systems is similar to MG, and response of the medium range order scales with the macroscopic stress.

glassy structure↗

Efficient machine learning interatomic potentials robust for liquid and multiple solid polymorphs of NaF and KF

Achieving atomic-level understanding of crystallization of molten salts is of importance to a wide range of technological applications. Recent work [Fan et al., Proc. Natl. Acad. Sci. USA 122, e2425702122 (2025)] revealed that crystal nucleation in molten LiF salt is a multistage process according to the molecular-dynamics (MD) simulations based on an atomic cluster expansion (ACE) machine-learning interatomic potential (MLIP). In order to understand the influence of increasing cation size on nucleation pathways and nucleation rates of molten fluoride salts, here we develop two new ACE MLIPs for NaF and KF. The two ACE MLIPs feature DFT-SCAN-level accuracy for liquid and multiple solid polymorphs over a wide temperature (0–2000 K) and pressure (0–100 GPa) range, and also reproduce well a number of experimental data for solid and liquid equilibrium properties. The efficiency of the two ACE MLIPs enable million-atom-scale or microsecond-scale MD simulations. The two general-purpose ACE MLIPs are expected to be useful for atomistic simulations for different purposes, in addition to studying crystallization of molten NaF and KF salts.

Crystal melting↗

Materials Fingerprinting Classification

Significant progress in many classes of materials could be made with the availability of experimentally-derived large datasets composed of atomic identities and three-dimensional coordinates. Methods for visualizing the local atomic structure, such as atom probe tomography (APT), which routinely generate datasets comprised of millions of atoms, are an important step in realizing this goal. However, state-of-the-art APT instruments generate noisy and sparse datasets that provide information about elemental type, but obscure atomic structures, thus limiting their subsequent value for materials discovery. The application of a materials fingerprinting process, a machine learning algorithm coupled with topological data analysis, provides an avenue by which here-to-fore unprecedented structural information can be extracted from an APT dataset. As a proof of concept, the material fingerprint is applied to high-entropy alloy APT datasets containing body-centered cubic (BCC) and face-centered cubic (FCC) crystal structures. A local atomic configuration centered on an arbitrary atom is assigned a topological descriptor, with which it can be characterized as a BCC or FCC lattice with near perfect accuracy, despite the inherent noise in the dataset. Finally, this successful identification of a fingerprint is a crucial first step in the development of algorithms which can extract more nuanced information, such as chemical ordering, from existing datasets of complex materials.

36 MATERIALS SCIENCE↗

“Third-body” collision parameters for hydrocarbons, alcohols, and hydroperoxides and an effective internal rotor approach for estimating them

Collision rate constants and third-body collision efficiencies are calculated for more than 300 alkanes, alcohols, and hydroperoxides, for the bath gases He, Ar, H 2 , and N 2 , and from 300 to 2000 K. The data set includes highly branched species and species with as many as 16 nonhydrogen atoms N , and it is analyzed to develop strategies for estimating collision properties more generally. Simple analytic formulas describing the Lennard-Jones collision parameters $σ$ and $ε$ are obtained for each of the three classes of systems as a function of N . Trends in the collision efficiency range parameter $α$ = $\langle$Δ E d $\rangle$ are more complicated, and a method is developed and validated for estimating $α$ based on the numbers and types of internal rotors and oxygen-containing groups. Specifically, the approach maps the expected value of $α$ for a branched alkane, alcohol, or hydroperoxide onto those for the corresponding normal (linear) series via an effective number of nonhydrogen atoms N eff . The prescription for N eff is based on counting internal rotor types and is shown to be insensitive to temperature and fairly insensitive to the identity of the bath gas. Together, these strategies allow for the ready estimation of the collision parameters $σ$, $ε$, and $α$ so long as results for the associated linear series are available.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗