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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

The Pantheon+ Analysis: Evaluating Peculiar Velocity Corrections in Cosmological Analyses with Nearby Type Ia Supernovae

Separating the components of redshift due to expansion and peculiar motion in the nearby universe (z < 0.1) is critical for using Type Ia Supernovae (SNe Ia) to measure the Hubble constant (H 0 ) and the equation-of-state parameter of dark energy (w). Here, we study the two dominant "motions" contributing to nearby peculiar velocities: large-scale, coherent-flow (CF) motions and small-scale motions due to gravitationally associated galaxies deemed to be in a galaxy group. We use a set of 584 low-z SNe from the Pantheon+ sample, and evaluate the efficacy of corrections to these motions by measuring the improvement of SN distance residuals. We study multiple methods for modeling the large and small-scale motions and show that, while group assignments and CF corrections individually contribute to small improvements in Hubble residual scatter, the greatest improvement comes from the combination of the two (relative standard deviation of the Hubble residuals, Rel. SD, improves from 0.167 to 0.157 mag). We find the optimal flow corrections derived from various local density maps significantly reduce Hubble residuals while raising H 0 by ~0.4 km s -1 Mpc -1 as compared to using CMB redshifts, disfavoring the hypothesis that unrecognized local structure could resolve the Hubble tension. We estimate that the systematic uncertainties in cosmological parameters after optimally correcting redshifts are 0.06–0.11 km s -1 Mpc -1 in H 0 and 0.02–0.03 in w which are smaller than the statistical uncertainties for these measurements: 1.5 km s -1 Mpc -1 for H 0 and 0.04 for w.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Glacial fluctuations in tropical Africa during the last glacial termination and implications for tropical climate following the Last Glacial Maximum

The tropics are a dynamic component of the global climate system and exert a profound influence on modern climate variability. Yet the role of the tropics in past climate changes, for example during the last glacial termination, is uncertain. This uncertainty is due in part to the relative paucity of terrestrial temperature records from the tropics, which hinders efforts to understand the mechanisms that influenced deglacial warming and abrupt climate events. Tropical glaciers are sensitive to changes in climate, and mapping and dating past tropical glacial fluctuations provides a valuable record of terrestrial climate changes in the low latitudes. We report a chronology of past glacial extents in the Rwenzori Mountains of Uganda (0.3°N, 29.9°E) based on 51 beryllium-10 ( 10 Be) surface-exposure ages from three separate glacial catchments. Results indicate that Rwenzori glaciers retreated considerably during Heinrich Stadial 1. The rate of net glacial recession slowed between ~15 and 11 ka, although glaciers continued to retreat during this period. Rwenzori glaciers then retreated more rapidly during the early Holocene. The Rwenzori glacial chronology is broadly similar to glacial chronologies reconstructed elsewhere in East Africa and in tropical South America. We suggest that this similarity may reflect coherent, tropics-wide temperature fluctuations during the last deglaciation. We report that the Rwenzori glacial chronology provides crucial information on the global footprint of deglacial warming and abrupt climate events and, thus, the potential mechanisms that influenced tropical climate during the last glacial termination.

58 GEOSCIENCES↗
DOE OSTI2021

Utah FORGE: Seismic Velocity Models, February 2021

This dataset contains a map, showing the Utah FORGE seismic stations, and seismic velocity model data. There are 61 1-D velocity models which are in a compressed TAR file. A paper is referenced at the end of this description which discusses the use of these data in 3D modelling. The paper summary follows: We expand the application of spatial autocorrelation (SPAC) from typical 1-D Vs profiles to quasi-3-D imaging via Bayesian Monte Carlo inversion (BMCI) using a dense nodal array (49 nodes) located at the Utah Frontier Observatory for Research in Geothermal Energy (FORGE) site. Combinations of 4 and 9 geophones in subarrays provide for 36 and 25 1-D Vs profiles, respectively. Profiles with error bars are determined by calculating coherency functions that fit observations in a frequency range of 0.2-5 Hz. Thus, a high-resolution quasi-3-D Vs model from the surface to 2.0 km depth is derived and shows that surface-parallel sedimentary strata deepen to the west, consistent with a 3-D seismic reflection survey. Moreover, the resulting Vs profile is consistent with a Vs profile derived from distributed acoustic sensing (DAS) data located in a borehole at the FORGE site. The quasi-3-D velocity model shows that the base of the basin dips ~22 degrees to the west and topography on the basement interface coincident with the Mag Lee Wash suggests that the bedrock interface is an unconformity. Reference: Zhang, H. and K. L. Pankow (2021). High-resolution Bayesian spatial auto-correlation (SPAC) pseudo-3D Vs model of Utah FORGE site with a dense geophone array, Geophys. Res. Int, https://doi.org/10.1093/gji/ggab049

15 GEOTHERMAL ENERGY↗
DOE OSTI2022

Engineering infinite-range SU($\textit{n}$) interactions with spin-orbit-coupled fermions in an optical lattice

Here, we study multilevel fermions in an optical lattice described by the Hubbard model with on-site SU($\textit{n}$) -symmetric interactions. We show that in an appropriate parameter regime this system can be mapped onto a spin model with all-to-all SU($\textit{n}$)-symmetric couplings. Raman pulses that address internal spin states modify the atomic dispersion relation and induce spin-orbit coupling, which can act as a synthetic inhomogeneous magnetic field that competes with the SU($\textit{n}$) exchange interactions. We investigate the mean-field dynamical phase diagram of the resulting model as a function of $\textit{n}$ and different initial configurations that are accessible with Raman pulses. Consistent with previous studies for $\textit{n}$ = 2 , we find that for some initial states the spin model exhibits two distinct dynamical phases that obey simple scaling relations with $\textit{n}$. Moreover, for $\textit{n}$ > 2 we find that dynamical behavior can be highly sensitive to initial intraspin coherences. Our predictions are readily testable in current experiments with ultracold alkaline-earth-metal(-like) atoms.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Phase diagram and spectroscopic signatures of a supersolid in the quantum ising magnet K 2 Co(SeO 3 ) 2

Supersolid phases are quantum-entangled states of matter exhibiting the dual characteristics of superfluidity and solidity. Theory predicts that hard-core bosons on a triangular lattice can form such phases at half filling and near complete filling. Leveraging an exact mapping between bosons and spin-$\frac{1}{2}$ degrees of freedom, here we show that these phases are realized in the triangular-lattice antiferromagnet K 2 Co(SeO 3 ) 2 . At zero field, neutron diffraction reveals the development of quasi-two-dimensional $\sqrt3$ x $\sqrt3$ magnetic order with Z 3 translational symmetry breaking (solidity), though with reduced amplitude indicating strong quantum fluctuations. These fluctuations manifest as equidistant bands of continuum neutron scattering, where the lowest-energy mode is gapless at K ($\frac{1}{3}$ $\frac{1}{3}$), consistent with broken U(1) spin rotational symmetry (superfluidity). For c-axis-oriented magnetic fields near saturation, we find a second phase consistent with a high-field supersolid. These two supersolids are separated by a pronounced 1/3 magnetization plateau phase that supports coherent spin waves, from which we determine the underlying spin Hamiltonian.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Martensitic Transformation in Fe x Mn 80-x Co 10 Cr 10 High-Entropy Alloy

High-entropy alloys and even medium-entropy alloys are an intriguing class of materials in that structure and property relations can be controlled via alloying and chemical disorder over wide ranges in the composition space. Employing density-functional theory combined with the coherent-potential approximation to average over all chemical configurations, we tune free energies between face-centered-cubic and hexagonal-close-packed phases in Fe x Mn 80 - x Co 10 Cr 10 systems. Within Fe-Mn-based alloys, we show that the martensitic transformation and chemical short-range order directly correlate with the face-centered-cubic and hexagonal-close-packed energy difference and stacking-fault energies, which are in quantitative agreement with recent observation of two phase region (face-centered cubic and hexagonal closed pack) in a polycrystalline high-entropy alloy sample at x = 40 at.%. Our predictions are further confirmed by single-crystal measurements on a x = 40 at.% using transmission-electron microscopy, selective-area diffraction, and electron-backscattered-diffraction mapping. The results herein offer an understanding of transformation-induced or twinning-induced plasticity in this class of high-entropy alloys and a design guide for controlling the physics at the electronic level.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Hourglass-type bulk Ni 3 d band and Ce 4 f Kondo resonance states in the potential topological Kondo semimetal CeNiSn via angle-resolved photoemission spectroscopy

The electronic structure of CeNiSn, which is a potential topological Kondo insulator and a Dirac nodal-loop semimetal, has been investigated by employing temperature (T) dependent angle-resolved photoemission spectroscopy (ARPES). The Fermi surfaces (FSs) and the band structures of CeNiSn for three orthogonal crystallographic planes are measured, in which both the very dispersive bands and the flat bands are observed, having mainly the Ni 3d character and the Ce 4f character, respectively. The measured FSs and ARPES bands agree reasonably well with the density functional theory (DFT) calculations. The Fermi-edge (E F ) photon energy (hν) map along k b (=k (010) ) shows that the metallic E F -crossing states on the (010) surface have the three-dimensional character, suggesting that the observed E F -crossing metallic states do not correspond to the topological surface states of the two-dimensional character. On the other hand, albeit weak, the features of the hourglass-type bulk band crossings are observed along SXS, with the energies and the slopes being similar to those predicted by the DFT calculations, supporting the Dirac semimetallic nature of CeNiSn. In T-dependent ARPES, the Ce 4f Kondo resonance states are clearly revealed at low T, which become much suppressed above ~80 K. This feature is consistent with the Kondo temperature of CeNiSn, estimated from its ρ(T) data. This work demonstrates the importance of the coherent Kondo states in determining the topological properties of CeNiSn.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

A robust aerosol impact on clouds along the subtropical to tropical transition

Marine clouds undergo a transition from subtropical stratocumulus (Sc) to shallow cumulus (Cu) and eventually to deep convective (DC) systems as air masses advect from the subtropics towards the deep tropics. How aerosols modulate this Lagrangian cloud evolution remains largely uncertain. Here we use both 5 years of satellite observations mapped along 8 d Lagrangian trajectories and complementary large-eddy simulations from 9 initiation locations across the Northeast Pacific, Southeast Pacific, and Southeast Atlantic. This Lagrangian framework allows us to quantify the aerosol effect and its co-variability with meteorological conditions on cloud microphysics, macrophysics, and top-of-atmosphere radiation through the full Sc-Cu-DC transition. We show that increasing aerosol concentrations leads to deeper and more reflective clouds throughout this cloud transition. Examining the thermodynamic evolution along the trajectory indicates a well-known trend: enhanced moistening near the boundary-layer top and lower free troposphere under polluted conditions, suggesting that part of the co-variability between aerosol and meteorological conditions may be internally driven. The agreement between model simulations and satellite data alongside the multi-basin coherence of the results indicates that aerosols systematically amplify cloud depth and reflectivity during the subtropical–to–tropical cloud transition.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Impact of dynamics, entanglement and Markovian noise on the fidelity of few-qubit digital quantum simulation

Quantum algorithms have been proposed to accelerate the simulation of the chaotic dynamical systems that are ubiquitous in the physics of plasmas. Quantum computers without error correction might even use noise to their advantage to calculate the Lyapunov exponent by measuring the Loschmidt echo fidelity decay rate. For the first time, digital Hamiltonian simulations of the quantum sawtooth map, performed on the IBM-Q quantum hardware platform, show that the fidelity decay rate of a digital quantum simulation increases during the transition from dynamical localization to chaotic diffusion in the map. The observed error per CNOT gate increases by $1.5{\times }$ as the dynamics varies from localized to diffusive, while only changing the phases of virtual RZ gates and keeping the overall gate count constant. A gate-based Lindblad noise model that captures the effective change in relaxation and dephasing errors during gate operation qualitatively explains the effect of dynamics on fidelity as being due to the localization and entanglement of the states created. Specifically, highly delocalized states that are entangled with random phases show an increased sensitivity to dephasing and, on average, a similar sensitivity to relaxation as localized states. In contrast, delocalized unentangled states show an increased sensitivity to dephasing but a lower sensitivity to relaxation. This gate-based Lindblad model is shown to be a useful benchmarking tool by estimating the effective Lindblad coherence times during CNOT gates and finding a consistent $2\unicode{x2013}3{\times }$ shorter $T_2$ time than reported for idle qubits. Thus, the interplay of the dynamics of a simulation with the noise processes that are active can strongly influence the overall fidelity decay rate.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Single-shot in-line x-ray phase-contrast imaging of void-shockwave interactions in fusion energy materials

Recent breakthroughs in nuclear fusion, specifically the report of reactions exceeding scientific breakeven at the National Ignition Facility (NIF), highlight the potential of inertial fusion energy (IFE) as a sustainable and virtually limitless energy source. However, further progress in IFE requires characterization of defects in ablator materials and how they affect fuel capsule compression. Voids within the ablator can degrade energy yield, but their impact on the density distribution has primarily been studied through simulations, with limited high-resolution experimental validation. To address this, we used the x-ray free-electron laser (XFEL) at the matter in extreme conditions (MECs) instrument at the Linac coherent light source (LCLS) to capture 2D x-ray phase-contrast (XPC) images of a void-bearing sample with a composition similar to inertial confinement fusion (ICF) ablators. By driving a compressive shockwave through the sample using MEC's long-pulse laser system, we analyzed how voids influence shockwave propagation and density distribution during compression. To quantify this impact, we extracted phase information using two phase retrieval algorithms. First, we applied the contrast transfer function (CTF) method, paired with Tikhonov regularization and a fast optimization approach to generate an initial phase estimate. We then refined the result using a projected gradient descent (PGD) method that works directly with the sample's refractive index. Comparing these results with radiation adaptive grid Eulerian (xRAGE) radiation hydrodynamic simulations enables identification of model validation needs or improvements. By calculating phase maps in situ, it becomes possible to reconstruct areal density maps, improving understanding of laser-capsule interactions and advancing IFE research.

Hodge, D. S. [Colorado State Univ., Fort Collins, ↗
DOE OSTI2021

Controlling $H_{3}^{+}$ Formation From Ethane Using Shaped Ultrafast Laser Pulses

An adaptive learning algorithm coupled with 3D momentum-based feedback is used to identify intense laser pulse shapes that control $H_{3}^{+}$ formation from ethane. Specifically, we controlled the ratio of D 2 H + to $D_{3}^{+}$ produced from the D 3 C-CH 3 isotopologue of ethane, which selects between trihydrogen cations formed from atoms on one or both sides of ethane. We are able to modify the D 2 H + :$D_{3}^{+}$ ratio by a factor of up to three. In addition, two-dimensional scans of linear chirp and third-order dispersion are conducted for a few fourth-order dispersion values while the D 2 H + and $D_{3}^{+}$ production rates are monitored. The optimized pulse is observed to influence the yield, kinetic energy release, and angular distribution of the D 2 H + ions while the $D_{3}^{+}$ ion dynamics remain relatively stable. We subsequently conducted COLTRIMS experiments on C 2 D 6 to complement the velocity map imaging data obtained during the control experiments and measured the branching ratio of two-body double ionization. Two-body $D_{3}^{+}$ + $C_{2}D_{3}^{+}$ is the dominant final channel containing $D_{3}^{+}$ ions, although the three-body D + $D_{3}^{+}$ + $C_{2}D_{2}^{+}$ final state is also observed.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Dark Energy Survey Year 6 Results: improved mitigation of spatially varying observational systematics with masking

As photometric surveys reach unprecedented statistical precision, systematic uncertainties increasingly dominate large-scale structure probes relying on galaxy number density. Defining the final survey footprint is critical, as it excludes regions affected by artefacts or suboptimal observing conditions. For galaxy clustering, spatially varying observational systematics, such as seeing, are a leading source of bias. Template maps of contaminants are used to derive spatially dependent corrections, but extreme values may fall outside the applicability range of mitigation methods, compromising correction reliability. The complexity and accuracy of systematics modelling depend on footprint conservativeness, with aggressive masking enabling simpler, robust mitigation. We present a unified approach to define the DES Year 6 joint footprint, integrating observational systematics templates and artefact indicators that degrade mitigation performance. This removes extreme values from an initial seed footprint, leading to the final joint footprint. By evaluating the DES Year 6 lens sample MagLim++ plus plus on this footprint, we enhance the Iterative Systematics Decontamination (ISD) method, detecting non-linear systematic contamination and improving correction accuracy. While the mask's impact on clustering is less significant than systematics decontamination, it remains non-negligible, comparable to statistical uncertainties in certain w(theta) scales and redshift bins. Supporting coherent analyses of galaxy clustering and cosmic shear, the final footprint spans 4031.04 deg2, setting the basis for DES Year 6 1x2pt, 2x2pt, and 3x2pt analyses. This work highlights how targeted masking strategies optimise the balance between statistical power and systematic control in Stage-III and -IV surveys.

Rodríguez-Monroy, M. [Madrid, IFT; IJCLab, Orsay]↗
DOE OSTI2024

A MUSE source-blind survey for emission from the circumgalactic medium

The recent detection of optical emission lines from the circumgalactic medium (CGM) in combined, large samples of low-redshift, normal galaxy spectra hints at the potential to map the cool (∼10 4 kelvin) CGM in individual, representative galaxies. Using archival data from a forefront instrument (MUSE) on the VLT, we present a source-blind, wide-redshift-range (z∼ 0 to 5) narrowband imaging survey for CGM emission. Our detected, resolved emission line sources are cataloged and include a 30-kiloparsec-wide Hα source likely tracing the CGM of a low-mass galaxy (stellar mass ∼ 10 8.78±0.42 solar mass) atz= 0.1723, a 60-kiloparsec-wide Ly α structure associated with a galaxy atz= 3.9076, and a 130-kiloparsec (∼r vir )–wide [O II] feature revealing an interaction between a galaxy pair atz= 1.2480. The Hα velocity field for the low-mass galaxy suggests that the CGM is more chaotic or turbulent than the galaxy disk, while that for the interacting galaxies shows large-scale (∼50 kiloparsec) coherent motions.

Science & Technology - Other Topics↗
DOE OSTI2022

dlppi2 (b1)

The Doppler lidar (DL) is an active remote-sensing instrument that provides range- and time-resolved measurements of the line-of-sight component of air velocity (i.e., radial velocity) and attenuated aerosol backscatter. The DL operates in the near-infrared and is sensitive to backscatter from atmospheric aerosol, which are assumed to be ideal tracers of atmospheric wind fields. The DL works by transmitting short pulses of infrared laser light into the atmosphere. Atmospheric aerosols scatter a small fraction of that light energy back to the transceiver, where it is collected and recorded as a time-resolved signal. From the delay between the outgoing pulse and the backscattered signal, the instrument infers the distance to the scattering volume. Coherent detection is used to measure the Doppler frequency shift of the backscatter signal. This is accomplished by mixing the backscatter signal with a reference laser beam (i.e., local oscillator) of known frequency. The onboard signal processor then determines the Doppler frequency shift from the spectrum of the mixed signal. The Doppler frequency shift and thus the radial air velocity is determined from the peak of the Doppler spectrum. The attenuated backscatter is determined from the energy content of the Doppler spectra. The DL provides accurate measurements of radial velocity in regions of the atmosphere where aerosol concentrations are high enough to ensure good signal-to-noise ratio. Thus, valid data are usually limited to the atmospheric boundary layer where aerosol is ubiquitous. Valid measurements can also be obtained in elevated aerosol layers or in optically thin clouds above the boundary layer. Most of the ARM DLs have full upper-hemispheric scanning capability, enabling 3D mapping of turbulent flows in the atmospheric boundary layer. With the scanner pointed vertically, the DL provides height- and time-resolved measurements of vertical velocity.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

SpeckleNN: a unified embedding for real-time speckle pattern classification in X-ray single-particle imaging with limited labeled examples

With X-ray free-electron lasers (XFELs), it is possible to determine the three-dimensional structure of noncrystalline nanoscale particles using X-ray single-particle imaging (SPI) techniques at room temperature. Classifying SPI scattering patterns, or `speckles', to extract single-hits that are needed for real-time vetoing and three-dimensional reconstruction poses a challenge for high-data-rate facilities like the European XFEL and LCLS-II-HE. Here, we introduce SpeckleNN, a unified embedding model for real-time speckle pattern classification with limited labeled examples that can scale linearly with dataset size. Trained with twin neural networks, SpeckleNN maps speckle patterns to a unified embedding vector space, where similarity is measured by Euclidean distance. We highlight its few-shot classification capability on new never-seen samples and its robust performance despite having only tens of labels per classification category even in the presence of substantial missing detector areas. Without the need for excessive manual labeling or even a full detector image, our classification method offers a great solution for real-time high-throughput SPI experiments.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Hierarchical Phased-Array Antennas Coupled to Al KIDs: A Scalable Architecture for Multi-band Millimeter/Submillimeter Focal Planes

We present the optical characterization of two-scale hierarchical phased-array antenna kinetic inductance detectors (KIDs) for millimeter/submillimeter wavelengths. Our KIDs have a lumped-element architecture with parallel plate capacitors and aluminum inductors. The incoming light is received with a hierarchical phased array of slot dipole antennas, split into 4 frequency bands (between 125 GHz and 365 GHz) with on-chip lumped-element band-pass filters, and routed to different KIDs using microstriplines. Individual pixels detect light for the 3 higher-frequency bands (190–365 GHz), and the signals from four individual pixels are coherently summed to create a larger pixel detecting light for the lowest frequency band (125–175 GHz). The spectral response of the band-pass filters was measured using Fourier transform spectroscopy (FTS), the far-field beam pattern of the phased-array antennas was obtained using an infrared source mounted on a 2-axis translating stage, and the optical efficiency of the KIDs was characterized by observing loads at 294 K and 77 K. We report on the results of these three measurements.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Site-specific generation of excited state wavepackets with high-intensity attosecond x rays

High-intensity attosecond x rays can produce coherent superpositions of valence-excited states through two-photon Raman transitions. The broad-bandwidth, high-field nature of the pulses results in a multitude of accessible excited states. Multiconfigurational quantum chemistry with the time-dependent Schrödinger equation is used to examine population transfer dynamics in stimulated x-ray Raman scattering of the nitric oxide oxygen and nitrogen K-edges. Two pulse schemes initiate wavepackets of different characters and demonstrate how chemical differences between core-excitation pathways affect the dynamics. The population transfer to valence-excited states is found to be sensitive to the electronic structure and pulse conditions, highlighting complexities attributed to the Rabi frequency. The orthogonally polarized two- color-pulse setup has increased selectivity while facilitating longer, less intense pulses than the one-pulse setup. Population transfer in the 1s → Rydberg region is more effective but less selective at the nitrogen K-edge; the selectivity is reduced by double core-excited states. Result interpretation is aided by resonant inelastic x-ray scattering maps.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Spatial Mapping of Valence Excited-State Landscapes Using Time-Resolved Shake-Down Spectroscopy

Time-resolved X-ray photoelectron spectroscopy (XPS) is used to track the photodissociation dynamics of 2-iodothiophene following 262 nm excitation. The transient XPS features include both direct ionization of the initially populated excited states and pronounced satellite peaks arising from shake-down processes. While the direct ionization signals exhibit only minimal energy shifts during C−I bond cleavage, the shake-down transitions undergo a substantial, 5 eV, shift over the reaction coordinate. By correlating these shifts with simulated C−I bond lengths, a direct structural mapping is established that reveals the exceptional sensitivity of shake-down channels to molecular geometry. These results demonstrate that shake-down transitions provide a new and powerful probe of ultrafast structural dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗