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DOE OSTI2026

Feature-Based PMU Event Classification under Variable PMU Participation and Overlapping Events

Danovo Energy Solution's presented its paper named: Feature-Based PMU Event Classification under Variable PMU Participation and Overlapping Events at the 2026 Georgia Tech Fault & Disturbance Analysis Conference. The full paper can be found at OSTI ID# 3169150 Paper Abstract—Phasor Measurement Units (PMUs) stream time synchronized, high-resolution measurements from the grid, enabling data-driven techniques for event detection and classification. Accurate event classification improves grid reliability and stability. Events can be detected by varying numbers of PMUs and exhibit different durations depending on the event type. This variability challenges standard classifiers that require uniform input sizes. Moreover, multiple events may coincide, which increases classification complexity. Standard classifiers assign each instance to the class with the highest predicted probability, whereas overlapping events may exhibit comparable probabilities across multiple classes. In this study, to handle data size variability, we extract a wide range of time–frequency domain features from all available PMUs for each event into a fixed-length vector, facilitating the application of standard machine learning classifiers, including Random Forest, XGBoost, LightGBM, Support Vector Machine, and Multilayer Perceptron. To account for overlapping events, a probabilistic post-processing step is applied. For a given data instance, if multiple predicted class probabilities exceed 30% and the differences between them are less than 10%, the event is assigned to multiple classes. Experiments using real-world PMU data demonstrate that the Random Forest and XGBoost models achieve the highest accuracy, while the proposed post-processing method yields perfect classification performance on external unseen test sets.

Nematirad, Reza [Danova Energy Solutions]↗

DOE OSTI2019

Electron extraction efficiency study for dual-phase xenon dark matter experiments

Dual-phase xenon detectors are widely used in dark matter direct detection experiments, and have demonstrated the highest sensitivities to a variety of dark matter interactions. However, a key component of the dual-phase detector technology—the efficiency of charge extraction from liquid xenon into gas—has not been well characterized. We report a new measurement of the electron extraction efficiency (EEE) in a small xenon detector using two monoenergetic decay features of $^{37}\mathrm{Ar}$. By achieving stable operation at very high voltages, we measured the EEE values at the highest extraction electric field strength reported to date. For the first time, an apparent saturation of the EEE is observed over a large range of electric field; between 7.5 and $10.4\text{ }\text{ }\mathrm{kV}/\mathrm{cm}$ extraction field in the liquid xenon the EEE stays stable at the level of 1% $(\mathrm{kV}/\mathrm{cm}{)}^{{-}1}$. In the context of electron transport models developed for xenon, we discuss how the observed saturation may help calibrate this relative EEE measurement to the absolute EEE values. In addition, we present the implications of this result not only to current and future xenon-based dark matter searches, but also to xenon-based searches for coherent elastic neutrino-nucleus scatters.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2023

Domain Adaptive Graph Neural Networks for Constraining Cosmological Parameters Across Multiple Data Sets

State of the art astronomical simulations have provided datasets which enabled the training of novel deep learning techniques for constraining cosmological parameters. However, differences in subgrid physics implementation and numerical approximations among simulation suites lead to differences in simulated datasets, which pose a hard challenge when trying to generalize across diverse data domains and ultimately when applying models to observational data. Recent work reveals deep learning algorithms are able to extract more information from complex cosmological simulations than summary statistics like power spectra. We introduce Domain Adaptive Graph Neural Networks (DA-GNNs), trained on CAMELS data, inspired by CosmoGraphNet (Villanueva-Domingo et al 2023). By utilizing GNNs, we can capitalize on their capacity to capture both astrophysical and topological features of galaxy distributions. Mixing these capabilities with domain adaptation techniques such as Maximum Mean Discrepancy (MMD), which enable extraction of domain-invariant features, our framework demonstrates enhanced accuracy and robustness. We present experimental results, including the alignment of distributions across domains through data visualization. These findings suggest that DA-GNNs are an efficient way of extracting domain independent cosmological information, a vital step toward robust deep learning for real cosmic survey data.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Ultrasonic Characterization of Lithium Ion Thermal Runaway Conditions for Real-time Ultrasonic Enabled BMS Integration

The demand for energy storage is growing, and lithium-ion batteries are a promising technology to meet this need due to their high power/energy density, high round-trip efficiency, rapid response time, and portability. However, recent catastrophic events caused by thermal runaway have slowed their adoption, highlighting the need for an early warning system for battery failure. In this work, ultrasound is used to detect physical changes in 950 mAh batteries by identifying material property changes independent of voltage and current. [Ultrasound signal features (e.g., time of flight, maximum frequency component) were extracted as the batteries were cycled and subjected to both constant current and constant voltage overcharge and were used to develop two metrics identifying failure: a warning to detect the start of overcharge and an emergency stop (E-stop) to immediately take the battery out of service. The identification method involved locating magnitude differences of several ultrasound features compared to baseline operation considering different currents and temperatures, and the warning/stopping metrics were consistent across all experiments. For an average overcharge time of 140 minutes, the average warning was issued 124 minutes before the failure and the average E-stop was triggered 94 minutes before failure. As a test of using ultrasound for early warning detection, a battery was forced into overcharge and returned to normal cycling conditions based on the previously determined warning metric. Both the voltage profile and the ultrasound measurements returned to their baseline behavior, indicating that ultrasonic detection can not only identify battery failure before a catastrophic event, but can also provide early enough warnings such that overcharges can be detected and corrected quickly enough so the battery does not need to be decommissioned.]

25 ENERGY STORAGE↗

DOE OSTI2019

Mobile Ion Concentration Measurement and Open-Access Band Diagram Simulation Platform for Halide Perovskite Solar Cells

We propose two approaches to compute the band diagram of highly efficient perovskite solar cells, both based on the migration of a single-mobile ion (halide vacancies). The first is a full analytical approach to quickly calculate the main features of the perovskite band diagram and easily extract the mobile vacancy concentration from experimental data. The second approach is an online-open-access platform that can be used by anyone to accurately simulate their own band diagram. We combine the first approach with current transient measurements to extract the mobile ion concentration for six different perovskite compositions - including perovskite solar cells with power conversion efficiencies exceeding 19%. For the devices measured herein, we obtain ion concentrations in the range 7 x 10 16 -5 x 10 17 cm -3 . We use the second approach to quantitatively discuss the implications of the mobile ion concentrations we measured in terms of device performance and stability.

14 SOLAR ENERGY↗

DOE OSTI2019

Emerging Design Principles for Enhanced Solar Energy Utilization with Singlet Fission

Singlet fission (SF), the generation of two triplet excitons per the absorption of one photon, is a promising strategy for increasing the efficiency of solar cells beyond the theoretical Shockley-Queisser limit of 34%. Upon photon absorption by a SF molecule, the initially created singlet excited state (S1) interacts with a neighboring chromophore and is first transformed into a triplet pair (TT), which can be subsequently separated into independent triplet excitons (2T1). These independent triplet excitons can be harvested through triplet charge extraction or triplet energy transfer to an acceptor. Research on SF systems has revealed rates and efficiencies of triplet formation and triplet pair decorrelation that are strongly dependent on interchromophore coupling, which is dictated by molecular structure and the resulting geometrical arrangement of chromophores adopted in covalent (e.g., dimers) and noncovalent (e.g., films and crystals) systems. Incorporation of SF materials into realistic device architectures introduces a host of new challenges to consider regarding the efficient extraction of triplets generated through SF. In this Feature Article, we review our work that has led to some degree of understanding and control of inter- and intramolecular SF rates placed in the context of solar energy harvesting architectures, including dye-sensitized solar cells, conjugated polymer films, and ligand-exchanged quantum dots. We emphasize the importance of understanding and manipulating interactions between SF molecules with each other and with the charge or energy collectors across an interface in order to strike a kinetic balance that leads to efficient utilization of triplet excitons.

14 SOLAR ENERGY↗

DOE OSTI2026

Polarization Control via Artificial Optical Nonlinearity in Dielectric Metasurfaces

Nonlinear optical phenomena are generally governed by geometry in matter systems, as they depend on the spatial arrangement of atoms within materials or molecules. Metasurfaces, through precisely designed geometries on a subwavelength scale, allow the optical response of a material to be tailored far beyond its natural properties. Therefore, metasurfaces are highly appealing for enabling the engineering of nonlinear optical interactions. Current studies of nonlinear metasurfaces predominantly focus on the phase control of the generated light. Nonetheless, investigating the tensorial nature of the nonlinearity of metasurfaces and its effect on the polarization of the generated light is critical to fully unlocking a range of applications, such as nonlinear vector beam generation and nonlinear polarization imaging. Here, we study the artificial optical nonlinearity of a dielectric metasurface originating from its meta-atom symmetry and describe the third-order nonlinear behavior by considering the polarization degree of freedom. We establish an effective nonlinear medium model that serves as a design toolbox for developing amorphous silicon-based geometric metasurfaces with customizable features for third-harmonic generation. We further extract quantitative values of the artificial nonlinear susceptibility tensor elements related to the investigated nonlinear process and geometry. The implemented functional devices demonstrate the versatility of dielectric metasurfaces in shaping the emitted light in terms of amplitude, phase, and polarization for the precise engineering of advanced nonlinear architectures targeting applications in nonlinear imaging and complex light generation.

Diffraction↗

DOE OSTI2023

Fracture-matrix fluid exchange in oil-bearing unconventional mudstones

The poromechanical properties of unconventional reservoir materials are in large part dictated by their mineralogy. Since these properties govern the response to stress experienced during hydraulic fracturing, fluid production, and fluid injection, they play a central role in the formation of microcracks or bedding delaminations which ultimately dominate mass transport. In this work we study access to the porosity of end member unconventional reservoir materials, where the end members are predominantly dictated by carbonate content. Access to the porosity is quantified using state of the art 3D x-ray computed tomography coupled with physics informed data analytics. Xenon gas, which attenuates x-rays, provides a spatiotemporal map of access to the porosity. The accessible porosity is quantified over a range of net confining stress relevant to the manmade disturbances listed above. These experiments demonstrate that heavily carbonated mudstones are nearly impermeable at the core (~ cm) scale, while carbonate free analogues afford better access to the microstructure. Consistent with previous qualitative 2D radiographs, access to the interior of the clastic mudstones is first observed along planar microcracks, followed by slow penetration into the surrounding matrix. Physics informed data analytics of the 3D tomography measurements presented here show that these microcracks do not permit uniform access to the adjacent rock matrix. In addition, variation of the effective pressure elucidates the mechanisms that govern fracture/matrix fluid exchange. Under conditions consistent with hydrocarbon production fluid accumulates in the immediate vicinity of the nearest microcrack. While there is clear evidence that, as intended, part of this accumulation is from the more distant matrix, fluid is also squeezed out of the microcrack. The fluid build-up at the microcrack indicates that migration out of the rock is hindered by the coupled poroelastic response of the microcrack and adjacent rock matrix. We show that these mechanisms ultimately account for the meager oil recovery factors realized in practice. These insights have implications for making reservoir scale predictions based on core scale observations, and provide a basis for devising new asset development techniques to access more porosity, and enhance fluid extraction. Finally, these findings shed light on key features and mechanisms that govern shale storage capacity, with relevance to other important industrial processes, such as geologic CO 2 storage.

58 GEOSCIENCES↗

DOE OSTI2023

DeepAstroUDA: semi-supervised universal domain adaptation for cross-survey galaxy morphology classification and anomaly detection

Abstract Artificial intelligence methods show great promise in increasing the quality and speed of work with large astronomical datasets, but the high complexity of these methods leads to the extraction of dataset-specific, non-robust features. Therefore, such methods do not generalize well across multiple datasets. We present a universal domain adaptation method, DeepAstroUDA , as an approach to overcome this challenge. This algorithm performs semi-supervised domain adaptation (DA) and can be applied to datasets with different data distributions and class overlaps. Non-overlapping classes can be present in any of the two datasets (the labeled source domain, or the unlabeled target domain), and the method can even be used in the presence of unknown classes. We apply our method to three examples of galaxy morphology classification tasks of different complexities (three-class and ten-class problems), with anomaly detection: (1) datasets created after different numbers of observing years from a single survey (Legacy Survey of Space and Time mock data of one and ten years of observations); (2) data from different surveys (Sloan Digital Sky Survey (SDSS) and DECaLS); and (3) data from observing fields with different depths within one survey (wide field and Stripe 82 deep field of SDSS). For the first time, we demonstrate the successful use of DA between very discrepant observational datasets. DeepAstroUDA is capable of bridging the gap between two astronomical surveys, increasing classification accuracy in both domains (up to 40 % on the unlabeled data), and making model performance consistent across datasets. Furthermore, our method also performs well as an anomaly detection algorithm and successfully clusters unknown class samples even in the unlabeled target dataset.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Anatomy of cosmic tidal reconstruction

Abstract 21-cm intensity surveys aim to map neutral hydrogen atoms in the universe through hyper-fine emission. Unfortunately, long-wavelength (low-wavenumber) radial modes are highly contaminated by smooth astrophysical foregrounds that are six orders of magnitude brighter than the cosmological signal. This contamination also leaks into higher radial and angular wavenumber modes and forms a foreground wedge. Cosmic tidal reconstruction aims to extract the large-scale signal from anisotropic features in the local small-scale power spectrum through non-linear tidal interactions; losing small-scale modes to foreground wedge will impair its performance. In this paper, we review tidal interaction theory and estimator construction, and derive the theoretical expressions for the reconstructed spectra. We show the reconstruction is robust against peculiar velocities. Removing low line-of-sight k modes, we demonstrate cross-correlation coefficient r is greater than 0.7 on large scales (k ≲ 0.1 h Mpc−1) even with a cut-off value $k^c_{\Vert }=0.1$h Mpc−1. Discarding wedge modes yields 0.3 ≲ r ≲ 0.5 and completely removes the dependency on $k^c_{\Vert }$. Our theoretical predictions agree with these numerical simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Three-dimensional super line-localization in low signal-to-noise microscope images via prior-apprised unsupervised learning (PAUL)

Biological processes such as processive enzyme turnover and intracellular cargo tracking involve the dynamic motion of a small "article" along a curvilinear biopolymer track. To understand these processes that occur across multiple length and time scales, one must acquire both the trajectory of the particle and the position of the track along which it moves, possibly by combining high-resolution single-particle tracking with conventional microscopy. Yet, usually there is a significant resolution mismatch between these modalities: while the tracked particle is localized with a precision of 10 nm, the image of the surroundings is limited by optical difraction, with 200 nm lateral and 500 nm axial resolutions. Compared to the particle's trajectory, the surrounding curvilinear structure appears as a blurred and noisy image. This disparity in the spatial resolutions of the particle trajectory and the surrounding curvilinear structure image makes data reconstruction, as well as interpretation, particularly challenging. Analysis is further complicated when the curvilinear structures are oriented arbitrarily in 3D space. Here, we present a prior-apprised unsupervised learning (PAUL) approach to extract information from 3D images where the underlying features resemble a curved line such as a filament or microtubule. This three-stage framework starts with a Hessian-based feature enhancement, which is followed by feature registration, where local line segments are detected on repetitively sampled subimage tiles. In the final stage, statistical learning, segments are clustered based on their geometric relationships. Principal curves are then approximated from each segment group via statistical tools including principal component analysis, bootstrap and kernel transformation. This procedure is characterized on simulated images, where sub-voxel medium deviations from true curves have been achieved. The 3D PAUL approach has also been implemented for successful line localization in experimental 3D images of gold nanowires obtained using a multifocal microscope. Lastly, this work not only bridges the resolution gap between two microscopy modalities, but also allows us to conduct 3D super line-localization imaging experiments, without using super-resolution techniques.

42 ENGINEERING↗

DOE OSTI2023

Influence of extreme fracture flow channels on the thermal performance of open-loop geothermal systems at commercial scale

Abstract Adequate stewardship of geothermal resources requires accurate forecasting of long-term thermal performance. In enhanced geothermal systems and other fracture-dominated reservoirs, predictive models commonly assume constant-aperture fractures, although spatial variations in aperture can greatly affect reservoir permeability, fluid flow distribution, and heat transport. Whereas previous authors have investigated the effects of theoretical random aperture distributions on thermal performance, here we further explore the influence of permeability heterogeneity considering field-constrained aperture distributions from a meso-scale field site in northern New York, USA. Using numerical models of coupled fluid flow and heat transport, we conduct thermal–hydraulic simulations for a hypothetical reservoir consisting of a relatively impervious porous matrix and a single, horizontal fracture. Our results indicate that in highly channelized fields, most well design configurations and operating conditions result in extreme rates of thermal drawdown (e.g., 50% drop in production well temperatures in under 2 years). However, some other scenarios that account for the risks of short-circuiting can potentially enhance heat extraction when mass flow rate is not excessively high, and the direction of geothermal extraction is not aligned with the most permeable features in the reservoir. Through a parametric approach, we illustrate that well separation distance and relative positioning play a major role in the long-term performance of highly channelized fields, and both can be used to help mitigate premature thermal breakthrough.

Rangel-Jurado, Nicolás↗

DOE OSTI2017

Molecular and ultrastructural studies of a fibrillar collagen from octocoral (Cnidaria)

ABSTRACT We report here the biochemical, molecular and ultrastructural features of a unique organization of fibrillar collagen extracted from the octocoral Sarcophyton ehrenbergi. Collagen, the most abundant protein in the animal kingdom, is often defined as a structural component of extracellular matrices in metazoans. In the present study, collagen fibers were extracted from the mesenteries of S. ehrenbergi polyps. These fibers are organized as filaments and further compacted as coiled fibers. The fibers are uniquely long, reaching an unprecedented length of tens of centimeters. The diameter of these fibers is 9±0.37 μm. The amino acid content of these fibers was identified using chromatography and revealed close similarity in content to mammalian type I and II collagens. The ultrastructural organization of the fibers was characterized by means of high-resolution microscopy and X-ray diffraction. The fibers are composed of fibrils and fibril bundles in the range of 15 to 35 nm. These data indicate a fibrillar collagen possessing structural aspects of both types I and II collagen, a highly interesting and newly described form of fibrillar collagen organization.

Orgel, Joseph P. R. O.↗

DOE OSTI2020

Development of Gamma Background Radiation Digital Twin with Machine Learning Algorithms: Application of Unsupervised Machine Learning to Detection of Anomalies and Nuisances in Gamma Background Radiation Environmental Screening Data

Environmental screening of gamma radiation consists of detecting weak nuisance and anomaly signal in the presence of strong and highly varying background. In a typical scenario, a mobile detector-spectrometer continuously measures gamma radiation spectra in short, e.g., one-second, signal acquisition intervals. The measurement data is a 2D matrix, where one dimension is gamma ray energy, and the other dimension is the number of measurements or total time. In principle, gamma radiation sources can be detected and identified from the measured data by their unique spectral lines. Detecting sources from data measured in a search scenario is difficult due to the highly varying background because of naturally occurring radioactive material (NORM), and low signal-to-noise ratio (S/N) of spectral signal measured during one-second acquisition intervals. The objective of this work is to explore unsupervised machine learning (ML) algorithms for development of a digital twin of gamma radiation background, and for detection and identification of weak nuisances and anomalies events in the presence of highly fluctuating background. In one segment of work, we developed a gamma background estimation model using a Longshort term memory (LSTM) network for one-step CPS time series prediction. The LSTM model was validated with two data sets of measurements from two independent NaI detectors positioned on a mobile platform. The data sets contained background radiation only and no orphan isotope sources. The LSTM model was constructed and tested using data from one of the detectors. Performance of the LSTM model was validate through one-step prediction of CPS time series of another NaI detector without re-training. This approach allows to create a digital twin for nuclear background estimation. Using LSTM, it could be possible to detect a source through subtraction of the estimated counts from the measured background. In another segment of work, we investigated detection of gamma emitting sources in the presence of complex background using unsupervised machine learning. Spectral lines of isotopes are difficult to observe in one-second measurements. Averaging over the entire measurement campaign data set reveals spectral lines of most common background isotopes. Spectral lines of orphan sources, which might appear only in a few measurements during the campaign, will be washed out if averaging is performed over the entire measurement data set. The approach we have explored consists of extracting one-second measurements containing weak spectral features through data clustering. Averaging one-second spectra in a cluster should reveal the presence of anomaly sources. We created two ML models using K-means clustering and Neural Network Self-organizing Map (SOM). Performance of these ML models was benchmarked using search data. One data set contained 137 Cs source, and another dataset contained 131 I source.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Detection of Anomalies in Gamma Background Radiation Data with K-Means and Self-Organizing Map Clustering Algorithms (Consortium on Nuclear Security Technologies (CONNECT) Q1 Report)

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2020

ARES. III. Unveiling the Two Faces of KELT-7 b with HST WFC3

We present the analysis of the hot-Jupiter KELT-7 b using transmission and emission spectroscopy from the Hubble Space Telescope, both taken with the Wide Field Camera 3. Our study uncovers a rich transmission spectrum that is consistent with a cloud-free atmosphere and suggests the presence of H{sub 2}O and H{sup −}. In contrast, the extracted emission spectrum does not contain strong absorption features and, although it is not consistent with a simple blackbody, it can be explained by a varying temperature–pressure profile, collision induced absorption, and H{sup −}. KELT-7 b had also been studied with other space-based instruments and we explore the effects of introducing these additional data sets. Further observations with Hubble, or the next generation of space-based telescopes, are needed to allow for the optical opacity source in transmission to be confirmed and for molecular features to be disentangled in emission.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2018

A Copula-Based Conditional Probabilistic Forecast Model for Wind Power Ramps

Efficient management of wind ramping characteristics can significantly reduce wind integration costs for balancing authorities. By considering the stochastic dependence of wind power ramp (WPR) features, this paper develops a conditional probabilistic wind power ramp forecast (cp-WPRF) model based on Copula theory. The WPRs dataset is constructed by extracting ramps from a large dataset of historical wind power. Each WPR feature (e.g., rate, magnitude, duration, and start-time) is separately forecasted by considering the coupling effects among different ramp features. To accurately model the marginal distributions with a copula, a Gaussian mixture model (GMM) is adopted to characterize the WPR uncertainty and features. The Canonical Maximum Likelihood (CML) method is used to estimate parameters of the multivariable copula. The optimal copula model is chosen based on the Bayesian information criterion (BIC) from each copula family. Finally, the best conditions based cp-WPRF model is determined by predictive interval (PI) based evaluation metrics. Numerical simulations on publicly available wind power data show that the developed copula-based cp-WPRF model can predict WPRs with a high level of reliability and sharpness.

17 WIND ENERGY↗

DOE OSTI2024

Speciation and Organic Phase Structure in Nitric Acid Extraction with Trioctylamine

Understanding chemical speciation and intermolecular interactions in multicomponent liquids is essential to understanding their phase and chemical equilibria, which underpin chemical separation processes, including solvent extraction. Here we report on the extraction of nitric acid from its aqueous solutions into organic solutions of trioctylamine (TOA) in toluene, investigated with spectroscopic, X-ray scattering, and computational tools to understand molecular speciation in the organic phase and its relationship with the nanoscale structure of the organic phase. Trends in acid and water extraction clearly show two and three regimes, respectively, indicating different stoichiometric relationships, but speciation of HNO 3 , water, and amine in these regimes is not apparent. 1 H NMR of the organic phase shows that there are at least two distinct acidic protons in the organic phase while ATR-FTIR results show that the organic phase with excess acid extraction is a mixture of trioctylammonium-nitrate ion pairs (TOAHNO 3 ), and undissociated HNO 3 molecules. Comparison with DFT-computed IR spectra show that the chain-like configurations of TOAHNO 3 HNO 3 H 2 O are favored over TOAHNO 3 H 2 OHNO 3 , i.e., direct interaction between the nitrate and HNO 3 molecules is more favored compared to a water-mediated interaction. SAXS of the organic phases were modeled as sums of Ornstein-Zernike (O-Z) scattering and a prepeak feature in the higher Q region that corresponds to extractant packing. The extraction of undissociated HNO 3 by the ion pairs leads to an increased X-ray scattering contrast in the organic phase without any significant change in the correlation length. These results show that the organic phase nanostructure is more sensitive to the concentration of TOAHNO 3 and is relatively unaffected by excess acid extraction. Finally, these findings will enable a molecular understanding of the mechanisms behind metal extraction from acidic media with basic extractants.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗