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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.

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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Rationalizing Acidic Oxygen Evolution Reaction over IrO 2 : Essential Role of Hydronium Cation

Abstract The development of active, stable, and more affordable electrocatalysts for acidic oxygen evolution reaction (OER) is of great importance for the practical application of electrolyzers and the advancement of renewable energy conversion technologies. Currently, IrO 2 is the only catalyst with high stability and activity, but a high cost. Further optimization of the catalyst is limited by the lack of understanding of catalytic behaviors at the acid‐IrO 2 interface. Here, in strong interaction with the experiment, we develop an explicit model based on grand‐canonical density function theory (GC‐DFT) calculations to describe acidic OER over IrO 2 . Compared to the explicit models reported previously, hydronium cations (H 3 O + ) are introduced at the electrochemical interface in the current model. As a result, a variation in stable IrO 2 surface configuration under the OER operating condition from previously proposed complete *O‐coverage to a mixture coverage of *OH and *O is revealed, which is well supported by in situ Raman measurements. In addition, the accuracy of predicted overpotential is increased in comparison with the experimentally measured. More importantly, an alteration of the potential limiting step from previously identified *O→*OOH to *OH→*O is observed, which opens new opportunities to advance the IrO 2 ‐based catalysts for acidic OER.

Mou, Tianyou↗
DOE OSTI2024

Rationalizing Acidic Oxygen Evolution Reaction over IrO 2 : Essential Role of Hydronium Cation

The development of active, stable, and more affordable electrocatalysts for acidic oxygen evolution reaction (OER) is of great importance for the practical application of electrolyzers and the advancement of renewable energy conversion technologies. Currently, IrO 2 is the only catalyst with high stability and activity, but a high cost. Further optimization of the catalyst is limited by the lack of understanding of catalytic behaviors at the acid-IrO 2 interface. Here, in strong interaction with the experiment, we develop an explicit model based on grand-canonical density function theory (GC-DFT) calculations to describe acidic OER over IrO 2 . Compared to the explicit models reported previously, hydronium cations (H 3 O + ) are introduced at the electrochemical interface in the current model. As a result, a variation in stable IrO 2 surface configuration under the OER operating condition from previously proposed complete *O-coverage to a mixture coverage of *OH and *O is revealed, which is well supported by in situ Raman measurements. In addition, the accuracy of predicted overpotential is increased in comparison with the experimentally measured. More importantly, in this study, an alteration of the potential limiting step from previously identified *O→*OOH to *OH→*O is observed, which opens new opportunities to advance the IrO 2 -based catalysts for acidic OER.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Cosmology and signals of light pseudo-Dirac dark matter

In this paper, we analyze the cosmological evolution, allowed parameter space, and observational prospects for a dark sector consisting of thermally produced pseudo-Dirac fermions with a small mass splitting, coupled to the Standard Model through a dark photon. This scenario is particularly notable in the context of sub-GeV dark matter, where the mass-off-diagonal leading interaction limits applicability of both CMB energy injection constraints and standard direct detection searches. We present the first general study of the thermal history of pseudo-Dirac DM with splittings from 100 eV to MeV, focusing on the depletion of the heavier “excited” state abundance via scatterings and decays, and on the distinctive signals arising from its small surviving abundance. We analyze CMB energy injection bounds on both DM annihilation and decay, accelerator-based probes, and new line-like direct-detection signals from the excited DM down-scattering on either nuclei or electrons, as well as future search prospects in each channel. We also comment on the relevance of this signal to the few-keV Xenon1T electron excess and on possible diurnal modulation of this signal, and introduce a signal-strength parametrization to facilitate the comparison of future experimental results to theoretical expectations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Continuous and discrete modeling of HIV-1 decline on therapy

Mathematical models have shed light on the dynamics of HIV- 1 infection in vivo. In this paper, we generalize continuous mathematical models of drug therapy for HIV-1 by Perelson et al. (Science 271:1582–1586, 1996) and Perelson and Nelson (SIAM Rev 41:3–44, 1999) on time scales, i.e., a nonempty closed subset of real numbers in order to derive new discrete models that predict the total concentration of plasma virus as a function of time. Here, one of our main goals is to compare discrete mathematical models with the continuous model in Perelson et al. (1996) where HIV infected patients were given protease inhibitors and sampled frequently thereafter. For the comparison, we use experimental data collected in Perelson et al. (1996) and estimate the parameters such as the virion clearance rate and the rate of loss of infected cells by fitting the total concentration of plasma virus to this data set. Our results show that discrete systems describe the best fit. In the previous models of this study, the efficacy of protease inhibitor is assumed to be perfect. Motivated by Perelson and Nelson (1999), we end the paper with a mathematical model of imperfect protease inhibitor and reverse transcriptase (RT) inhibitor combination therapy of HIV-1 infection on time scales with its stability analysis.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Image processing methods for Rayleigh scattering measurements of diesel spray mixing at high repetition rate

This work describes the diagnostic implementation and image processing methods to quantitatively measure diesel spray mixing injected into a high-pressure, high-temperature environment. We used a high-repetition-rate pulse-burst laser developed in-house, a high-speed CMOS camera, and optimized the optical configuration to capture Rayleigh scattering images of the vaporized fuel jets inside a constant volume chamber. The experimental installation was modified to reduce reflections and flare levels to maximize the images’ signal-to-noise ratios by anti-reflection coatings on windows and surfaces, as well as series of optical baffles. Because of the specificities of the high-speed system, several image processing techniques had to be developed and implemented to provide quantitative fuel concentration measurements. We find that these methods involve various correction procedures such as camera linearity, laser intensity fluctuation, dynamic background flare, as well as beam-steering effects. Image inpainting was also applied to correct the Rayleigh scattering signal from large scatterers (e.g. particulates). The experiments demonstrate that applying planar laser Rayleigh scattering at high repetition rate to quantitatively resolve the mixing of fuel and ambient gases in diesel jets is challenging, but possible. The thorough analysis of the experimental uncertainty and comparisons to past data prove that such measurements can be accurate, whilst providing valuable information about the mixing processes of high-pressure diesel jets.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Spontaneous rearrangement of acetylated xylan on hydrophilic cellulose surfaces

The interaction of xylan, an abundant plant polysaccharide, with cellulose microfibrils is essential for secondary cell wall strength. A deeper understanding of these interactions is crucial both to improve our understanding of plant cell wall architecture and to design alternate strategies to overcome cellulose recalcitrance for the production of biofuels and sustainable biomaterials. Naturally occurring acetate or glucuronic acid substitutions on xylan have been shown to influence xylan-cellulose interactions. In this work, we use unrestrained molecular dynamics simulations to determine the interactions with the (110) hydrophilic face of cellulose fibers of four different xylans. In the absence of cellulose, all xylans, independent of the substitution pattern, adopt a highly flexible threefold helical screw conformation. However, when xylan is spatially close to a cellulose surface 1,2 linked acetyl xylans (2AcX) adopt rigid twofold helical screw conformations. The 2AcX conformations are primarily stabilized by interactions between the acetylated oxygen and the glycosidic linkage with C-O6 of cellulose. In contrast, the glycosidic oxygens and acetyl decorations for 1,3 linked acetyl groups (3AcX) are oriented away from the cellulose surface and the 3AcX xylans maintain threefold helical screw conformations on the cellulose surface. Our results show that evenly spaced chemical functionalization (with acetyl groups) and the position of substitution (1,2) on xylan backbone play key roles in tuning the xylan-cellulose interactions to stabilize the twofold helical screw conformations of xylan on the cellulose surface. A comparison with previous experimental findings further suggests that 1,2 substitutions induce twofold helical screw conformations of xylan on the cellulose surface irrespective of the chemical nature of the substituent, while 1,3 substitutions primarily bind lignin in threefold helical screw conformations rather than cellulose in plant cell walls.

1,2 Ac↗
DOE OSTI2022

Well-Balanced Second-Order Convex Limiting Technique for Solving the Serre–Green–Naghdi Equations

In this article, we introduce a numerical method for approximating the dispersive Serre–Green–Naghdi equations with topography using continuous finite elements. The method is an extension of the hyperbolic relaxation technique introduced in Guermond et al. (J Comput Phys 450:110809, 2022). It is explicit, second-order accurate in space, third-order accurate in time, and is invariant-domain preserving. It is also well balanced and parameter free. Special attention is given to the convex limiting technique when physical source terms are added in the equations. The method is verified with academic benchmarks and validated by comparison with laboratory experimental data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Systematically derived thermodynamic properties for alkane oxidation

Key combustion properties, such as ignition delay time, show strong sensitivity to the thermochemistry of the main species in the standard radical oxidation pathway at low temperatures (600-1000K). Significant uncertainties persist in current estimates of thermodynamic properties, particularly for the larger species of relevance to common practical fuels. In this article, we use advanced computational schemes to evaluate thermodynamic properties for the fuel, fuel radical, peroxy, hydroperoxy-alkyl radical, and hydroperoxide species for a set of 17 fuels containing up to 9 carbon atoms, and with various degrees of branching in the alkane backbone. The procedure, termed STAR-1D, combines conformer sampling to find the minimum geometry, B2PLYP-D3/cc-pVTZ harmonic frequency evaluations, and omega B97X-D/cc-pVTZ one-dimensional torsional mapping. It includes two physically-based scaling routines: a frequency-dependent scaling to B2PLYP-D3/cc-pVTZ anharmonic frequencies and a scaling of one-dimensional omega B97X-D/ccpVTZ torsional profiles to reproduce the product of the B2PLYP-D3/cc-pVTZ frequencies in the harmonic limit. Substantive comparisons with existing experimental databases, together with careful examinations of key theoretical assumptions, are used to explore the accuracy of the predictions. These computationally intensive explorations of 195 species were facilitated by automated thermochemistry software. Further, high accuracy 0 K heats of formation from a separate study are used with the STAR-1D computations to generate NASA polynomial representations. In addition to their intrinsic value, the present results also provide a reliable database for the optimization of group additivity or machine learning schemes for scaling to larger combustion systems. Towards this end a complementary extensive conformational analysis is carried out for the medium sized species and the thermodynamic properties of the lowest energy hydrogen-bonded and non-hydrogen bonded conformers are contrasted for larger hydroperoxy-alkyl radical species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

The solubility of La hydroxide and stability of La 3+ and La hydroxyl complexes at acidic to mildly acidic pH from 25 to 250 °C

The mobility of rare earth elements (REE) in natural hydrothermal systems can be assessed using geochemical modeling, which requires reliable thermodynamic data of relevant aqueous species. In this study, we evaluate the controls of pH and temperature on La speciation and the role of hydroxyl complexes in REE transport at hydrothermal conditions. Batch-type hydrothermal solubility experiments were conducted using synthetic La hydroxide powders equilibrated in perchloric acid-based aqueous solutions at temperatures between 150 and 250 °C and starting pH of 2 to 5. The La hydroxide solubility is retrograde with temperature and displays a strong pH dependence with a decrease in La concentrations from acidic to mildly acidic pH spanning between 3 and 5 orders of magnitude (e.g. log La molality of –2.5 to –7.2 at 250 °C). Thermodynamic optimizations using GEMSFITS allow to retrieve the standard partial molal Gibbs energies for the La 3+ aqua ion and the formation constants for the La hydroxyl species (i.e., LaOH 2+ , La(OH) 2 + , La(OH) 3 0 ) between 25 and 250 °C. A comparison between the experimentally derived thermodynamic properties with the calculated values from the Helgeson-Kirkham-Flowers equation of state parameters indicates an increased divergence with temperature. Discrepancies in standard partial molal Gibbs energies range between ~ 1 – 12 kJ/mol and result in a predicted La hydroxide solubility differing by up to 3 orders of magnitude at 250 °C. Speciation calculations indicate a higher stability of La 3+ and LaOH 2+ over the other La hydroxyl species in the studied pH range of 3.4 to 6. Here, the optimized thermodynamic properties for La aqueous species have important implications for modeling the solubility of REE minerals such as monazite and the mobility of REE in hydrothermal systems.

58 GEOSCIENCES↗
DOE OSTI2021

Modeling of crystallization fouling on a horizontal-tube falling-film evaporator for thermal desalination

Scale formation within horizontal-tube falling-film evaporators is an important issue for thermal desalination, because of the deterioration of heat transfer performance and added maintenance costs. Predicting the fouling process is crucial for desalination plant design, operation, and maintenance. In this paper, a model is developed to predict the crystallization fouling process during seawater falling-film flow over a horizontal tube bundle. The scaling is estimated based on deposition theory, with couple heat transfer including the in-tube steam condensation, conduction through the tube wall and the scale layer, and falling-film evaporation. The spatial and temporal variations of temperature, heat transfer coefficient, and scale thickness are predicted, and the effects of variations in process parameters of steam, feed seawater, and tube properties on the scale thickness, evaporation rate, and heat transfer coefficient for falling-film evaporation are analyzed. Comparisons to existing experimental data show the scaling layer thickness falls in the general range of reported measurements, with a slight overestimation due to neglecting the delay of scaling onset under real conditions. The scale layer thickness increases dramatically as the in-tube steam pressure is increased or the seawater flow rate is decreased. In general, the scaling layer becomes thicker on the lower tubes in the tube bundle, due to the heat and mass transfer of the falling film. The effect of tube material on scaling appears mainly dependent on thermal conductivity; thus, using polymer rather than a stainless steel tube decreases scaling and evaporation rate 96% and 88%, respectively. Finally, this work has potential to guide thermal desalination plant design, material selection, and operating parameter optimization.

42 ENGINEERING↗
DOE OSTI2021

Energy based fracture initiation criterion for strain-crystallizing rubber-like materials with pre-existing cracks

Fracture prediction is indispensable for polymers, like rubbers, which have a broad range of applications mainly due to their high extensibility. The phenomenon known as strain-induced crystallization further contributes to the fracture toughness of certain rubbers. Here in this study, a criterion based on internal bond energy, incorporating the effects of crystallization, is proposed to predict fracture initiation in rubber-like materials with pre-existing cracks. First, a multi-scale mechanical model is developed for characterizing the behavior of rubber when subjected to both uniaxial and biaxial deformation states. At the microscale, both the amorphous and crystalline chain segments are modeled as elastic in order to consider the energy contribution by the molecular bond distortions. This internal energy is considered along with the entropic and crystalline free energy for each chain. In the chain model, the effects of loading condition and the relative orientation of a chain on its crystallinity are taken into account. At the macroscopic scale, an existing crystallinity distribution function is adapted and a mixed finite element formulation with an augmented Lagrangian multiplier is utilized to impose the incompressibility constraint. A non-affine maximal advance path constraint based homogenization model is utilized for bridging the two scales. Its potential to account for anisotropy in the stretched network compels the model to be preferable due to its physical significance, for the purpose of fracture modeling. The rigidity of the crystallites is accounted for by proposing a crystallite distortion energy in addition to the critical bond dissociation energy, for fracture initiation to occur. The model is validated by comparison with existing experimental results for both crystallizing and non-crystallizing rubbers. In addition to its potential to predict the material behavior when subjected to uniaxial and biaxial loading, the capability of the model to quantitatively estimate the effect of crystallization on fracture initiation is also verified.

36 MATERIALS SCIENCE↗
DOE OSTI2022

A review of computational methods for studying oscillating water columns – the Navier-Stokes based equation approach

This review evaluates the state-of-the-practice numerical tools used to predict the performance of Oscillating Water Column (OWC). The OWC is a widely studied Wave Energy Converter that provides a reliable form of renewable form of electricity that can potentially meet global energy needs. However, the fluid-flow phenomena affecting its hydrodynamic performance are not fully understood. While there has been the successful full-scale deployment of OWCs, various computational methods are being explored to optimize this technology. Potential flow theory is commonly used to evaluate the efficiency of OWCs; however, this assumption tends to over-predict the hydrodynamic performance. Recently, numerical studies using a diverse set of commercial, open-source, or in-house Computational Fluid Dynamics (CFD) using Reynolds Averaged Navier Stokes (RANS) and Large-Eddy Simulation codes show a better comparison to available experimental results but are computationally expensive. ANSYS Fluent was found to be the most widely used CFD code applied to the study of the OWCs, with a high degree of accuracy in terms of experimental validation of numerical results.

16 TIDAL AND WAVE POWER↗
DOE OSTI2024

Direct numerical simulations of three-component Rayleigh–Taylor mixing and an improved model for multicomponent reacting mixtures

We present direct numerical simulations of a three-layer Rayleigh–Taylor instability (RTI) problem with a configuration based on the experiments of Suchandra & Ranjan ( J. Fluid Mech. , vol. 974, 2023, A35) and Jacobs & Dalziel ( J. Fluid Mech. , vol. 542, 2005, pp. 251–279). The problem consists of a layer of light fluid between two layers of heavy fluid with an Atwood number of 0.3. These simulations are first validated through comparison with available experimental data. The validated simulations are then utilized to analyse statistics in this three-component flow. First, length scales are examined utilizing spectra and two-point spatial correlations of velocity and species concentration fluctuations. Next, joint probability density functions (p.d.f.s) of species concentration are compared against several model p.d.f.s representing generalizations of the bivariate beta distribution. Notably, the joint p.d.f.s do not appear to be accurately described by a Dirichlet distribution, indicating the marginal distributions do not conform to a beta distribution. Finally, similarity of the present configuration to three-component mixing found in inertial confinement fusion (ICF) applications is exploited to develop and validate an improved model for the impact of multicomponent mixing on thermonuclear (TN) reaction rates. A single time instant from the present simulations is chosen for a TN burn calculation under the hypothetical assumption of ICF materials and temperatures. Total TN output from this second calculation is then compared against the prediction of the improved model. The new model is found to accurately predict TN reaction rates in both premixed and non-premixed configurations.

42 ENGINEERING↗
DOE OSTI2020

Identifying the Molecular Edge Termination of Exfoliated Hexagonal Boron Nitride Nanosheets with Solid-State NMR Spectroscopy and Plane-Wave DFT Calculations

Hexagonal boron nitride nanosheets (h-BNNS), the isoelectronic analog to graphene, have received interest over the past decade due to their high thermal oxidative resistance, high bandgap, catalytic activity, and low cost. The functional groups that terminate boron and nitrogen zigzag and/or armchair edges directly affect their chemical, physical, and electronic properties. However, an understanding of the molecular edge termination present in h-BNNS is lacking. Here, high-resolution magic-angle spinning (MAS) solid-state NMR (SSNMR) spectroscopy, and plane-wave density-functional theory (DFT) calculations are used to determine the molecular edge termination in exfoliated h-BNNS. 1 H → 11 B cross-polarization MAS (CPMAS) SSNMR spectra of h-BNNS revealed multiple hydroxyl/oxygen coordinated boron edge sites that were not detectable in direct excitation experiments. A dynamic nuclear polarization (DNP)-enhanced 1 H → 15 N CPMAS spectrum of h-BNNS displayed four distinct 15 N resonances while a 2D 1 H{ 14 N} dipolar-HMQC spectrum acquired with fast MAS revealed three distinct 14 N environments. Plane-wave DFT calculations were used to construct model edge structures and predict the corresponding 11 B, 14 N and 15 N SSNMR spectra. Comparison of the experimental and predicted SSNMR spectra confirms that zigzag and armchair edges with both amine and boron hydroxide/oxide termination are present. The detailed characterization of h-BNNS molecular edge termination will prove useful for many material science applications. The techniques outlined here should also be applicable to understand the molecular edge terminations in other 2D materials

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Vibrational Spectroscopy of Hexahalo Complexes

Halogenated inorganic complexes A x [MHal y ] (A = alkali metal or alkaline earth, M = transition or main group metal, x = 1–3, and y = 2–9) are an archetypal class of compounds that provide entry points to large areas of inorganic and physical chemistry. All of the hexahalo complexes adopt an octahedral, O h , symmetry (or nearly so). Consequently, one of the bending modes is forbidden in both the infrared and Raman spectra. In the solid state, many of the complexes crystallize in the cubic space group Fm3̅m, which preserves the octahedral symmetry. Even for those that are not cubic, the octahedral symmetry of the [MHal 6 ] n- ion is largely retained and, to a good approximation, so are the selection rules. In the present work, we show that by using the additional information provided by neutron vibrational spectroscopy, in combination with conventional optical spectroscopies, we can generate complete and unambiguous assignments for all the modes. Comparison of the experimental and calculated transition energies for the systems where periodic-density functional theory was possible (i.e., those for which the crystal structure is known) shows that the agreement is almost quantitative. We also provide a linear relationship that enables the prediction of the forbidden mode.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Comparing the Expense and Accuracy of Methods to Simulate Atomic Vibrations in Rubrene

Atomic vibrations can inform about materials properties from hole transport in organic semiconductors to correlated disorder in metal–organic frameworks. Currently, there are several methods for predicting these vibrations using simulations, but the accuracy–efficiency tradeoffs have not been examined in depth. In this work, rubrene is used as a model system to predict atomic vibrational properties using six different simulation methods: density functional theory, density functional tight binding, density functional tight binding with a Chebyshev polynomial-based correction, a trained machine learning model, a pretrained machine learning model called ANI-1, and a classical forcefield model. The accuracy of each method is evaluated by comparison to the experimental inelastic neutron scattering spectrum. All methods discussed here show some accuracy across a wide energy region, though the Chebyshev-corrected tight-binding method showed the optimal combination of high accuracy with low expense. We then offer broad simulation guidelines to yield efficient, accurate results for inelastic neutron scattering spectrum prediction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Route to Chemical Accuracy for Computational Uranium Thermochemistry

Benchmark spinor-based relativistic coupled-cluster calculations for the ionization energies of the uranium atom, the uranium monoxide molecule (UO), and the uranium dioxide molecule (UO 2 ) and for the bond dissociation energies of UO and UO 2 are reported. The accuracy of these calculations in the treatments of relativistic, electron correlation, and basis-set effects is analyzed. Furthermore, the intrinsic convergence of the computed results and the favorable comparison with the experimental values demonstrate the unique applicability of the spinor representation of quantum-chemical methods to open-shell uranium-containing atomic and molecular species with uranium oxidation states ranging from U(0) to U(V).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Ultrafast X-ray Spectroscopy of Intersystem Crossing in Hexafluoroacetylacetone: Chromophore Photophysics and Spectral Changes in the Face of Electron-Withdrawing Groups

Intersystem crossings between singlet and triplet states represent a crucial relaxation pathway in photochemical processes. Herein, we probe the intersystem crossing in hexafluoro-acetylacetone with ultrafast X-ray transient absorption spectroscopy at the carbon K-edge. In this study, we observe the excited state dynamics following excitation with 266 nm UV light to the 1 ππ* (S 2 ) state with element and site-specificity using a broadband soft X-ray pulse produced by high harmonic generation. These results are compared to X-ray spectra computed from orbital optimized density functional theory methods. It is found that the electron-withdrawing fluorine atoms decongest the X-ray absorption spectrum by enhancing separation between features originating from different carbon atoms. This facilitates the elucidation of structural and electronic dynamics at the chromophore. The evolution of the core-to-valence resonances at the carbon K-edge reveals an ultrafast population transfer between the 1 nπ* (S 1 ) and 3 ππ* (T 1 ) states on a 1.6 ± 0.4 ps time scale, which is similar to the 1.5 ps time scale earlier observed for acetylacetone [ J. Am. Chem. Soc. 2017, 139, 16576—16583, DOI: 10.1021/jacs.7b07532]. It therefore appears that terminal fluorination has little influence on the intersystem crossing rate of the acetylacetone chromophore. In addition, the significant role of hydrogen-bond opened and twisted rotational isomers is elucidated in the excited state dynamics by comparison of the experimental transient X-ray spectra with theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗