Search NASA⌕ Search

SEARCH · Search NASA

Results for “Fractional derivative”

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 217 records · Page 12

Reference Gastrointestinal Absorption Fractions for Radionuclides Ingested in Soil

Oak Ridge National Laboratory is conducting a project for the Environmental Protection Agency (EPA) Office of Superfund Remediation and Technology Innovation involving derivation of cancer risk coefficients for ingestion of radionuclides in soil. EPA provides guidance on quantifying gastrointestinal (GI) absorption of a chemical in a given medium for use in risk evaluations including assessments for Superfund sites. Essentially, a medium-specific GI absorption fraction may be applied if and only if there is sound information to support that value. Otherwise, the applied GI absorption fraction should be the best estimate of fractional absorption of the chemical when ingested in highly soluble form. Based on our review of the literature on GI absorption of elements in soil, we have concluded that for many elements there is convincing evidence of substantially reduced absorption in ingested soil compared with ingestion in readily dissolved form. This report summarizes the reviewed information and proposes a comprehensive set of GI absorption fractions for ingestion of elements in soil. For most elements, the proposed GI absorption fractions are lower than the default absorption fractions recommended by the International Commission on Radiological Protection for radionuclides ingested in highly soluble form, even though considerable conservatism has been incorporated into the proposed soil-specific GI absorption fractions.

59 BASIC BIOLOGICAL SCIENCES↗

Relaxing the constant molar overflow assumption in distillation optimization

Abstract The constant molar overflow (CMO) framework, while useful for shortcut distillation models, assumes that all components have the same latent heats of vaporization. A simple transformation, from molar flows to latent‐heat flows, allows shortcut models to retain the mathematical simplicity of the CMO framework while accounting for different latent heats, resulting in the constant heat transport (CHT) framework for adiabatic distillation columns. Although several past works have already proposed this transformation in the literature, it has not been well utilized in recent times. In this article, we show the utility of this transformation in upgrading various applications such as identifying energy‐efficient multicomponent distillation configurations based on heat duty rather than surrogate vapor flow. The method transforms the diagram to a diagram. Furthermore, we derive new and insightful analytical results in distillation, such as cumulative latent‐heat stage fractions having monotonic profiles within a distillation column under the CHT framework.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

What can we learn from N 2 O isotope data? – Analytics, processes and modelling

The isotopic composition of nitrous oxide (N 2 O) provides useful information for evaluating N 2 O sources and budgets. Due to the co–occurrence of multiple N 2 O transformation pathways, it is, however, challenging to use isotopic information to quantify the contribution of distinct processes across variable spatiotemporal scales. Here, we present an overview of recent progress in N 2 O isotopic studies and provide suggestions for future research, mainly focusing on: analytical techniques; production and consumption processes; and interpretation and modelling approaches. Comparing isotope–ratio mass spectrometry (IRMS) with laser absorption spectroscopy (LAS), we conclude that IRMS is a precise technique for laboratory analysis of N 2 O isotopes, while LAS is more suitable for in situ/inline studies and offers advantages for site–specific analyses. When reviewing the link between the N 2 O isotopic composition and underlying mechanisms/processes, we find that, at the molecular scale, the specific enzymes and mechanisms involved determine isotopic fractionation effects. In contrast, at plot–to–global scales, mixing of N 2 O derived from different processes and their isotopic variability must be considered. We also find that dual isotope plots are effective for semi–quantitative attribution of co–occurring N 2 O production and reduction processes. More recently, process–based N 2 O isotopic models have been developed for natural abundance and 15 N–tracing studies, and have been shown to be effective, particularly for data with adequate temporal resolution. Here, despite the significant progress made over the last decade, there is still great need and potential for future work, including development of analytical techniques, reference materials and inter–laboratory comparisons, further exploration of N 2 O formation and destruction mechanisms, more observations across scales, and design and validation of interpretation and modelling approaches. Synthesizing all these efforts, we are confident that the N 2 O isotope community will continue to advance our understanding of N 2 O transformation processes in all spheres of the Earth, and in turn to gain improved constraints on regional and global budgets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Self-assembled complex micelle phase stability in ABA-type triblock copolymers and related core-shell bottlebrushes

We report the synthesis and temperature-dependent morphologies of a series of polylactide--poly (-decalactone)--polylactide (LDL) triblock copolymers with M n = 16.0 – 18.1 kg / mol and volume fractions f L = 0.27 – 0.31 and associated core-shell bottlebrush (csBB) polymers, which derive from enchaining LDL triblocks through a polymerizable midchain functionality. While the LDL triblocks form micellar Frank-Kasper A15 and phases due to the conformational asymmetry of this monomer pair, the csBB morphologies sensitively depend on the backbone degree of polymerization ( N bb ). At low N bb values, micellar Frank-Kasper phases with the brush backbone situated in the matrix domain are stable, albeit with a modest reduction in the mean interfacial curvature evidenced by a to A15 order-to-order transition. However, larger N bb values drive csBBs to form hexagonally packed cylinders phases. This N bb -dependent phase behavior is rationalized in terms of a star-to-bottlebrush transition. At low N bb values, the csBBs are akin to star polymers with pointlike junctions that can support complex micelle packings. As N bb increases, the csBBs adopt cylindrical molecular geometries with extended backbones situated in the matrix domain that prefer hexagonally packed cylinders morphologies. Published by the American Physical Society 2024

Materials Science↗

A modified Susceptible-Infected-Recovered model for observed under-reported incidence data

Fitting Susceptible-Infected-Recovered (SIR) models to incidence data is problematic when not all infected individuals are reported. Assuming an underlying SIR model with general but known distribution for the time to recovery, this paper derives the implied differential-integral equations for observed incidence data when a fixed fraction of newly infected individuals are not observed. The parameters of the resulting system of differential equations are identifiable. Using these differential equations, we develop a stochastic model for the conditional distribution of current disease incidence given the entire past history of reported cases. We estimate the model parameters using Bayesian Markov Chain Monte-Carlo sampling of the posterior distribution. We use our model to estimate the transmission rate and fraction of asymptomatic individuals for the current Coronavirus 2019 outbreak in eight American Countries: the United States of America, Brazil, Mexico, Argentina, Chile, Colombia, Peru, and Panama, from January 2020 to May 2021. Our analysis reveals that the fraction of reported cases varies across all countries. For example, the reported incidence fraction for the United States of America varies from 0.3 to 0.6, while for Brazil it varies from 0.2 to 0.4.

60 APPLIED LIFE SCIENCES↗

Stellar Radial Velocities in the Old Open Cluster M67 (NGC 2682). II. The Spectroscopic Binary Population

We present and analyze 120 spectroscopic binary and triple cluster members of the old (4 Gyr) open cluster M67 (NGC 2682). As a cornerstone of stellar astrophysics, M67 is a key cluster in the WIYN Open Cluster Study (WOCS); radial-velocity (RV) observations of M67 are ongoing and extend back over 45 yr, incorporating data from seven different telescopes, and allowing us to detect binaries with orbital periods ≲10{sup 4} days. Our sample contains 1296 stars (604 cluster members) with magnitudes of 10 ≤ V ≤ 16.5 (about 1.3–0.7 M {sub ⊙}), from the giants down to ∼4 mag below the main-sequence turnoff, and extends in radius to 30′ (7.4 pc at a distance of 850 pc, or ∼7 core radii). This paper focuses primarily on the main-sequence binaries, but orbital solutions are also presented for red giants, yellow giants, and sub-subgiants. Out to our period detection limit and within our magnitude and spatial domain, we find a global main-sequence incompleteness-corrected binary fraction of 34% ± 3%, which rises to 70% ± 17% in the cluster center. We derive a tidal circularization period of P{sub circ}=11.0{sub −1.0}{sup +1.1} days. We also analyze the incompleteness-corrected distributions of binary orbital elements and masses. The period distribution rises toward longer periods. The eccentricity distribution, beyond P {sub circ}, is consistent with a uniform distribution. The mass-ratio distribution is also consistent with a uniform distribution. Overall, these M67 binaries are closely consistent with similar binaries in the galactic field, as well as with the old (7 Gyr) open cluster NGC 188. WOCS. 83.

47 OTHER INSTRUMENTATION↗

Star-spots and magnetism: testing the activity paradigm in the Pleiades and M67

We measure star-spot filling fractions for 240 stars in the Pleiades and M67 open star clusters using APOGEE high-resolution H-band spectra. For this work, we developed a modified spectroscopic pipeline which solves for star-spot filling fraction and star-spot temperature contrast. We exclude binary stars, finding that the large majority of binaries in these clusters (80 per cent) can be identified from Gaia DR3 and APOGEE criteria – important for field star applications. Our data agree well with independent activity proxies, indicating that this technique recovers real star-spot signals. In the Pleiades, filling fractions saturate at a mean level of 0.248 ± 0.005 for active stars with a decline at slower rotation; we present fitting functions as a function of Rossby number. In M67, we recover low mean filling fractions of 0.030 ± 0.008 and 0.003 ± 0.002 for main sequence GK stars and evolved red giants, respectively, confirming that the technique does not produce spurious spot signals in inactive stars. Star-spots also modify the derived spectroscopic effective temperatures and convective overturn time-scales. Effective temperatures for active stars are offset from inactive ones by −109 ± 11 K, in agreement with the Pecaut & Mamajek empirical scale. Star-spot filling fractions at the level measured in active stars changes their inferred overturn time-scale, which biases the derived threshold for saturation. Finally, we identify a population of stars statistically discrepant from mean activity–Rossby relations and present evidence that these are genuine departures from a Rossby scaling. Our technique is applicable to the full APOGEE catalogue, with broad applications to stellar, galactic, and exoplanetary astrophysics.

79 ASTRONOMY AND ASTROPHYSICS↗

Phase Formation in Nuclear Fallout

An understanding of the physical and chemical process occurring in a nuclear explosion enables predictions of the effects of nuclear weapons, including characteristics of radioactive fallout resulting from the explosion. Near-surface nuclear explosions are of particular interest due to the potential for significant amounts of environmental material to interact with and alter the physical and chemical behavior of the fireball. Such interactions have the potential to affect the distribution of radioactive species in the fireball and subsequently become incorporated into fallout through a process known as radiochemical fractionation. Studying variations in fallout formed in different historical testing environments allows us to understand the influence of local environments on fallout formation processes. In particular, constraining variations in thermal evolution and redox conditions during the evolution of the fireball can be useful to understanding how sensitive fallout radiochemical fractionation may be to the local explosion environment. However, untangling these conditions in complex, multicomponent fallout is a challenge. Here we present one method of constraining and interpreting fallout formation conditions by relating computationally derived phase stability predictions to observations in historic fallout. Development of such approaches will help improve physics-based models of fallout formation and radiochemical fractionation in complex, near surface nuclear detonations.

36 MATERIALS SCIENCE↗

Lignin valorization reshapes sustainable biomass refining

As the largest natural reservoir of aromatics, lignin offers significant potential for bioproduct manufacturing through advances in valorization technologies. However, the intrinsically complex structures of lignin pose significant challenges for its fractionization and downstream valorization. Overcoming challenges in lignin chemistry modification is crucial for achieving effective lignin valorization and establishing sustainable biorefinery industries. This review explores the potential of tailoring lignin reactivity to enable functional bioproduct manufacturing thereby contributing to profitable biorefining. The intrinsic characteristics of lignin are first summarized, highlighting their roles in both fractionization and valorization. The latest progress in lignin fractionation is then presented, emphasizing their potential to tailor lignin chemistry, reactivity, and processibility. Furthermore, advancements in lignin valorization are covered, recognizing that tailored lignin reactivity is key to defining bioproduct functionality. By examining these chemical mechanisms, this review sheds on the structure-function relationships between lignin and its derived products. To address the dilemma of lignin valorization and biorefineries, a promising synergistic biorefinery is proposed. This involves redesigning biomass fractionation strategies, tailoring lignin chemistry, and upgrading both carbohydrate and lignin streams across the entire biorefinery chain—from feedstock to application. Altogether, a deeper understanding of tailored lignin chemistry is crucial for decoding the reaction mechanisms in biomass processing. A synergistic biorefinery could harness lignin's intrinsic properties to improve product functionality and address key challenges, paving the way for cost-effective, sustainable biorefinery solutions.

09 BIOMASS FUELS↗

Chemical abundances in Seyfert galaxies – Ⅸ. Helium abundance estimates

For the first time, the helium abundance relative to hydrogen (He/H), which relied on direct measurements of the electron temperature, has been derived in the narrow line regions (NLRs) from a local sample of Seyfert 2 nuclei. In view of this, optical emission line intensities [3000 < λ(Å) < 7000] of 65 local Seyfert 2 nuclei (z < 0.2), taken from Sloan Digital Sky Survey Data Release 15 and additional compilation from the literature, were considered. Here we used photoionization model grid to derive an Ionization Correction Factor (ICF) for the neutral helium. The application of this ICF indicates that the NLRs of Seyfert 2 present a neutral helium fraction of ~50 percent in relation to the total helium abundance. We find that Seyfert 2 nuclei present helium abundance ranging from 0.60 to 2.50 times the solar value, while ~85 percent of the sample present oversolar abundance values. The derived (He/H)–(O/H) abundance relation from the Seyfert 2 is stepper than that of star-forming regions (SFs) and this difference could be due to excess of helium injected into the interstellar medium by the winds of Wolf–Rayet stars. From a regression to zero metallicity, by using Seyfert 2 estimates combined with SFs estimates, we obtained a primordial helium mass fraction Y p = 0.2441 ± 0.0037, a value in good agreement with the one inferred from the temperature fluctuations of the cosmic microwave background by the Planck Collaboration, i.e. $Y_{p}^{Planck}$ =0.2471 ± 0.0003.

79 ASTRONOMY AND ASTROPHYSICS↗

Chemical composition, coordination, and stability of Ca–organic associations in the presence of dissolving calcite

Environmental biotic and abiotic factors and soil physical, mineralogical, and chemical properties control the chemical composition of soil organic matter (SOM). Particularly, soil mineralogy and the presence of multivalent cations affect SOM labile fraction composition, stability, and environmental persistence. The persistence of SOM in aridic or limestone deposit derived soils, i.e., calcareous soils, has been partially attributed to SOM stabilization through adsorption or inclusion into the calcite mineral structure. Recently, however, it was shown that Ca(aq) released during calcite dissolution formed aqueous Ca–organic associations with OM components, which were unbound to mineral surface sites. This study investigates the structure, composition, and coordination of these associations by characterizing lyophilized Ca–organic containing solutions with spectromicroscopy [Scanning Transmission X-ray Microscopy (STXM)] and with a nanoimaging chemical probe [Infrared scattering-Scanning Nearfield Optical Microscopy (IR s-SNOM)]. Chemical stability of Ca–organic associations is furthermore determined with pyrolysis mass spectrometry analysis. The results demonstrate that Ca–organic associations are formed in the presence of dissolving calcite and OM components relevant to soil chemistry, i.e., lignin and amino acids. This study further reveals a spatial homogeneity of solution-derived (bi) carbonate in Ca–organic associations indicating for the first time that an inorganic anion, such as (bi)carbonate, may be part of these associations. Most likely, Ca ions are bound to both the (bi)carbonate and the organic components. These Ca (bi)carbonate–organic associations seem to have greater chemical stability than the pristine organic mixtures and, possibly, a higher environmental stability and reduced mineralization rate.

54 ENVIRONMENTAL SCIENCES↗

Fine-scale vegetation composition and structure shape spatiotemporal variation in surface albedo across a low Arctic tundra landscape

The unprecedented rate of warming in the Arctic is driving changes in the structure and composition of tundra vegetation. Increases in deciduous tall shrub cover, height, and density are of particular concern, as these changes alter local surface albedo in ways that could amplify effects on the regional surface energy budget (SEB). Despite this importance, significant uncertainties remain in understanding the interplay between fine-scale vegetation patterns and emergent albedo dynamics across space and time. Here, we address these uncertainties by (1) quantifying spatiotemporal variation in surface shortwave albedo and (2) determining the relative influence of fine-scale vegetation composition, structure, and environmental conditions on albedo across a representative low-Arctic tundra landscape on Alaska’s Seward Peninsula. To do this, we synthesized multi-scale, multi-platform remote sensing observations, including a novel Landsat-derived albedo time series, a fine-scale map of Arctic plant functional type (PFT) fractional cover, and airborne LiDAR estimates of canopy height and topography. We show that there are substantial reductions in winter albedo for pixels dominated by tall, woody PFTs (28.13%) relative to pixels dominated by non-woody vegetation, but almost no change in summer albedo (3% increase). Further, we identified a unimodal trend in the relationship between canopy height and the timing of the springtime transition from high (snowy) to low (leafy) albedo (peak at 5.5 m), possibly because of competing ‘snow-fence’ and ‘protrusion’ snow-shrub interactions. To explore the primary drivers of albedo, we constructed a random forest model and found that canopy height and the fractional cover of woody PFTs were as- or more important predictors of winter albedo than topographic features. These findings provide strong evidence for the impacts of local vegetation characteristics on regional surface albedo, highlighting the need for better quantification of snow-shrub interactions to accurately predict the Arctic’s SEB under future environmental change.

Arctic↗

The Determination of the Spatial Distribution of Indigenous Lipid Biomarkers in an Immature Jurassic Sediment Using Time-of-Flight–Secondary Ion Mass Spectrometry

The ability to detect and map lipids, including potential lipid biomarkers, within a sedimentary matrix using mass spectrometry (MS) imaging may be critical to determine whether potential lipids detected in samples returned from Mars are indigenous to Mars or are contaminants. Here, we use gas chromatography–mass spectrometry (GC-MS) and time-of-flight–secondary ion mass spectrometry (ToF-SIMS) datasets collected from an organic-rich, thermally immature Jurassic geologic sample to constrain MS imaging analysis of indigenous lipid biomarkers in geologic samples. GC-MS data show that the extractable fractions are dominated by C 27 –C 30 steranes and sterenes as well as isorenieratene derivatives. ToF-SIMS spectra from organic matter-rich laminae contain a strong, spatially restricted signal for ions m/z 370.3, m/z 372.3, and m/z 386.3, which we assign to C 27 sterenes, cholestane (C 27 ), and 4- or 24-methyl steranes (C 28 ), respectively, as well as characteristic fragment ions of isorenieratene derivatives, including m/z 133.1, m/z 171.1, and m/z 237.1. We observed individual steroid spatial heterogeneity at the scale of 10's to 100's of microns. The fine-scale heterogeneity observed implies that indigenous lipid biomarkers concentrated within specific regions may be detectable via ToF-SIMS in samples with even low amounts of organic carbon, including in samples returned from Mars.

59 BASIC BIOLOGICAL SCIENCES↗

Determination of Total, Organic, and Inorganic Carbon in Biological Cultures and Liquid Fraction Process Samples

This procedure describes a method for analyzing dissolved and suspended total carbon, in organic and inorganic form in biological cultures, in the presence or absence of cells, and liquid fraction conversion process samples. This method calculates total organic carbon by subtraction of inorganic carbon, derived from sample acidification, from total dissolved carbon by combustion at 680°C with detection of derived gaseous CO 2 by a non-dispersive infrared (NDIR) sensor. The inclusion of details on a process step of heat treating biologically active samples before analysis can potentially halt biological activity, preserving carbon stores and allowing for accurate quantification of the carbon content at the time of sample collection.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

3 He Separation from US Liquid Natural Gas-Derived 4 He (Final Report)

This final report summarizes the technical and economic feasibility study conducted by Interlune, Lisbon Group, and Pacific Northwest National Laboratory on separating 3 He from 4 He derived from liquid natural gas (LNG) using magnetocaloric liquefaction (MCL), superleak heat-flush, and fractional distillation techniques. The project aims to address the growing shortage of 3 He, a critical resource for quantum computing and national security, by exploring a new domestic source, the bulk helium supply.

07 ISOTOPE AND RADIATION SOURCES↗

Building Fraction and Mean Height for Los Angeles (2010 and 2020) at 30 m Resolution

This dataset provides 30 m resolution spatial layers of building fraction and mean building height for the Los Angeles metropolitan region for 2010 and 2020. Derived from the Model America version 2 building dataset, it represents the distribution of total building footprint area and average building height across the metropolitan region, offering a consistent geospatial resource for urban analysis. The dataset is intended to support applications in urban climate studies, land-use assessment, city-scale modeling, and planning by enabling comparison of urban form characteristics over time. Additional dataset details including data processing details are provided in the Readme document (README_LA_BF_MeanHeight_2010_2020 1.txt).

geospatial↗

Bayesian Characterization of Main-sequence Binaries in the Old Open Cluster NGC 188

The binary fractions of open and globular clusters yield powerful constraints on their dynamical state and evolutionary history. We apply publicly available Bayesian analysis tools to a UBV RIJHK {sub S} photometric catalog of the open cluster NGC 188 to detect and characterize photometric binaries along the cluster main sequence. This technique has the advantage of self-consistently handling photometric errors, missing data in various bandpasses, and star-by-star prior constraints on cluster membership. Simulations are used to verify uncertainties and quantify selection biases in our analysis, illustrating that among binaries with mass ratios >0.5, we recover the binary fraction to better than 7% in the mean, with no significant dependence on binary fraction and a mild dependence on assumed mass-ratio distribution. Using our photometric catalog, we recover the majority (65% ± 11%) of spectroscopically identified main-sequence binaries, including eight of the nine with spectroscopically measured mass ratios. Accounting for incompleteness and systematics, we derive a mass-ratio distribution that rises toward lower mass ratios (within our q > 0.5 analysis domain). We observe a raw binary fraction for solar-type main-sequence stars with mass ratios q > 0.5 of 42% ± 4%, independent of the assumed mass-ratio distribution to within its uncertainties, consistent with literature values for old open clusters but significantly higher than the field solar-type binary fraction. We confirm that the binaries identified by our method are more concentrated than single stars, in agreement with previous studies, and we demonstrate that the binary nature of those candidates that remain unidentified spectroscopically is strongly supported by photometry from Gaia DR2.

79 ASTRONOMY AND ASTROPHYSICS↗

Gallium isotopic constraints for the origin of the Earth-Moon system

Comparatively heavy isotopic compositions of moderately volatile elements (MVE) in lunar rocks have been advocated to reflect the loss of light isotopes during devolatilization processes from the Moon. In this study we present new gallium (Ga) isotope data for lunar highland rocks, with a focus on the Ferroan Anorthosite Suite (FAS). These are commonly thought to be direct crystallization products from the late lunar magma ocean (LMO) and should contain the majority of the Ga inventory of the Moon. As such, FAS rocks are crucial for identifying the processes that drove Ga isotope fractionation as well as for inferring the Ga isotopic composition of the bulk Moon. Our data reveal that FAS samples have a range in δ 71 Ga from -0.27 to 0.22‰ and are generally isotopically light in Ga compared to other lunar lithologies, but straddle values typical of terrestrial rocks. Although Ga is defined as an MVE, these Ga isotope variations do not correspond with concentrations of more volatile elements, indicating that Ga isotope variations in the FAS are not primarily controlled by devolatilization processes. Instead, the Ga isotopic compositions of bulk FAS rocks broadly correlate with the composition of plagioclase, with the calcium content of plagioclase decreasing as Ga becomes isotopically heavier. This suggests that fractionation of Ga isotopes in FAS rocks was caused by the preferential incorporation of isotopically light Ga into plagioclase during the later solidification stages of the LMO. The progressive crystallization and extraction of plagioclase forces the residual melt towards increasingly heavier Ga isotope ratios, corroborating similar conclusions derived from correlations between δ 71 and Eu* in the mare basalt suite. Using Ga isotope partitioning calculations, we demonstrate that an isotope fractionation coefficient between plagioclase and coexisting melt of -0.3 to -0.4‰ could explain the observed range of δ 71 values in FAS, mare basalt suite rocks, and KREEP. These calculations allow for a first order estimate of the Ga isotopic composition of the bulk silicate Moon prior to plagioclase fractionation and suggest it was close to the composition of the bulk silicate Earth. This would imply that the Moon did not lose a substantial fraction of its Ga inventory during accretion, consistent with new constraints from Rb-Sr isotope systematics that indicate the Moon's volatile deficit was primarily inherited from Theia. In conjunction with the overlap in non-mass-dependent isotope ratios, these collective observations could be reconciled if Theia and the proto-Earth formed in similar regions of the inner Solar System that were already volatile-depleted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗