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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A dataset of recorded electricity outages by United States county 2014–2022

In this Data Descriptor, we present county-level electricity outage estimates at 15-minute intervals from 2014 to 2022. By 2022 92% of customers in the 50 US States, Washington DC, and Puerto Rico are represented. These data have been produced by the Environment for Analysis of Geo-Located Energy Information (EAGLE-I TM ), a geographic information system and data visualization platform created at Oak Ridge National Laboratory to map the population experiencing electricity outages every 15 minutes at the county level. Although these data do not cover every US customer, they represent the most comprehensive outage information ever compiled for the United States. The rate of coverage increases through time between 2014 and 2022. We present a quantitative Data Quality Index for these data for the years 2018–2022 to demonstrate temporal changes in customer coverage rates by FEMA region and indicators of data collection gaps or other errors.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Land cover change-induced decline in terrestrial gross primary production over the conterminous United States from 2001 to 2016

As one of the most dynamic aspects of global environmental change, land cover change (LCC) has a profound impact on terrestrial carbon sequestration. However, LCC-induced carbon fluxes are still the most uncertain terms in global and regional carbon budgets. Ecosystem gross primary production (GPP) is the total carbon uptake by vegetation through photosynthesis, serving as a major control on ecosystem function and land carbon balance during and after the modification of the land surface. However, accurately capturing LCC-induced GPP changes requires both high-quality land cover data and controlling for variation driven by other environmental factors such as climate. In this study, we comprehensively examined the effects of LCC on annual GPP trends over the conterminous United States (CONUS) from 2001 to 2016 using the USGS National Land Cover Database, a remote sensing-driven ecosystem model, and the Google Earth Engine cloud computing platform. We designed a series of model experiments to identify LCC effects on GPP by controlling climate effects. During the study period, LCC exerted a strong negative effect on total GPP across the CONUS ([-2.2, -1.8] Tg C yr -2 ), while climate had smaller positive effects ([0.17, 0. 92] Tg C yr -2 ). The LCC-induced reduction of GPP was mainly caused by net forest loss ([-1.98, -1.39] Tg C yr -2 ) and urban expansion ([-2.03, -1.92] Tg C yr -2 ), but was partially offset by increases in crop area ([+0.66, +0.79] Tg C yr -2 ). Ensemble simulations from TRENDY did not capture the strong negative LCC influences on GPP, likely due to limitations of the adopted land use/cover data. Overall, our study provides a novel perspective on LCC-induced GPP changes, which could help to improve our understanding of ecosystem function changes and constrain the estimation of land carbon balance in the context of anthropogenic activity and climate change.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Robust global detection of forced changes in mean and extreme precipitation despite observational disagreement on the magnitude of change

Detection and attribution (D&A) of forced precipitation change are challenging due to internal variability, limited spatial, and temporal coverage of observational records and model uncertainty. These factors result in a low signal-to-noise ratio of potential regional and even global trends. Here, we use a statistical method – ridge regression – to create physically interpretable fingerprints for the detection of forced changes in mean and extreme precipitation with a high signal-to-noise ratio. The fingerprints are constructed using Coupled Model Intercomparison Project phase 6 (CMIP6) multi-model output masked to match coverage of three gridded precipitation observational datasets – GHCNDEX, HadEX3, and GPCC – and are then applied to these observational datasets to assess the degree of forced change detectable in the real-world climate in the period 1951–2020. We show that the signature of forced change is detected in all three observational datasets for global metrics of mean and extreme precipitation. Forced changes are still detectable from changes in the spatial patterns of precipitation even if the global mean trend is removed from the data. This shows the detection of forced change in mean and extreme precipitation beyond a global mean trend is robust and increases confidence in the detection method's power as well as in climate models' ability to capture the relevant processes that contribute to large-scale patterns of change. We also find, however, that detectability depends on the observational dataset used. Not only coverage differences but also observational uncertainty contribute to dataset disagreement, exemplified by the times of emergence of forced change from internal variability ranging from 1998 to 2004 among datasets. Furthermore, different choices for the period over which the forced trend is computed result in different levels of agreement between observations and model projections. These sensitivities may explain apparent contradictions in recent studies on whether models under- or overestimate the observed forced increase in mean and extreme precipitation. Lastly, the detection fingerprints are found to rely primarily on the signal in the extratropical Northern Hemisphere, which is at least partly due to observational coverage but potentially also due to the presence of a more robust signal in the Northern Hemisphere in general.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Topological Analysis of Temporal Hypergraphs

In this work we study the topological properties of temporal hypergraphs. Hypergraphs provide a higher dimensional generalization of a graph that is capable of capturing multi-way connections. As such, they have become an integral part of network science. A common use of hypergraphs is to model events as hyperedges in which the event can involve many elements as nodes. This provides a more complete picture of the event in comparison to the standard dyadic connection limitation of a graph. However, a common attribution to events is temporal information as an interval for when the event occurred. Consequently, a temporal hypergraph is born which accurately captures both the temporal information of events as well as their multi-way connections. Common tools for studying these temporal hypergraphs typically use summary statistics of snapshots from a sliding window procedure to capture changes in the underlying dynamics. However, these do not provide insight into how the changing structure of the hypergraph evolves and which components of the temporal hypergraph persist and are influential to the underlying system. To alleviate this need we leverage zigzag persistence from the field of Topological Data Analysis (TDA) to study the change in topological structure of time-evolving hypergraphs. We apply our pipeline to both a cyber security and social network dataset and show how the topological structure of their temporal hypergraphs change and can be used to understand the underlying dynamics.

hypergraphs, topological data analysis, zigzag per↗
DOE OSTI2024

Artifacts in the Aerosol Size Distribution Measured by the Ultra-High-Sensitivity Aerosol Spectrometer (UHSAS)

The ultra-high-sensitivity aerosol spectrometer (UHSAS) (Droplet Measurement Technologies, Longmont, Colorado) is an optical particle size spectrometer that determines aerosol size distributions in the diameter range from 60 to 1000 nm in 100 logarithmically spaced diameter bins1 by measuring the amount of light scattered by individual aerosol particles from a 1054-nm laser. Recently, it was noticed that aerosol size distributions determined by the UHSAS from all U.S. Department of Energy Atmospheric Radiation Measurement (ARM) user facility sites exhibited modes at diameters greater than ~500 nm (Figure 1, blue arrows). These modes were not present in size distributions determined by another aerosol spectrometer that was co-located with the UHSAS, the Grimm 11D optical particle counter (OPC) (GRIMM Aerosol Technik Ainring GmbH & Co. KG, Germany), which sizes particles into 31 linearly spaced diameters bins from 253 to 35,150 nm using a 683-nm wavelength laser. Additionally, abrupt changes in aerosol particle number concentration with changing particle diameter are seen in UHSAS data at several diameters (Figure 1, red arrows). The purpose of this report is to explain the origin of the modes and the abrupt changes in aerosol size distributions observed by the UHSAS and why they are absent in the data from the Grimm OPC.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Examining polymer‐protein biophysical interactions with small‐angle x‐ray scattering and quartz crystal microbalance with dissipation

Abstract Polymer‐protein hybrids can be deployed to improve protein solubility and stability in denaturing environments. While previous work used robotics and active machine learning to inform new designs, further biophysical information is required to ascertain structure–function behavior. Here, we show the value of tandem small‐angle x‐ray scattering (SAXS) and quartz crystal microbalance with dissipation (QCMD) experiments to reveal detailed polymer‐protein interactions with horseradish peroxidase (HRP) as a test case. Of particular interest was the process of polymer‐protein complex formation under thermal stress whereby SAXS monitors formation in solution while QCMD follows these dynamics at an interface. The radius of gyration ( R g ) of the protein as measured by SAXS does not change significantly in the presence of polymer under denaturing conditions, but thickness and dissipation changes were observed in QCMD data. SAXS data with and without thermal stress were utilized to create bead models of the potential complexes and denatured enzyme, and each model fit provided insight into the degree of interactions. Additionally, QCMD data demonstrated that HRP deforms by spreading upon surface adsorption at low concentration as shown by longer adsorption times and smaller frequency shifts. In contrast, thermally stressed and highly inactive HRP had faster adsorption kinetics. The combination of SAXS and QCMD serves as a framework for biophysical characterization of interactions between proteins and polymers which could be useful in designing polymer‐protein hybrids.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

The cosmology of ultralight scalar dark matter coupled to right-handed neutrinos

We consider ultralight scalar dark matter that couples to right-handed neutrinos. Due to the high density of neutrinos in the early universe, the background neutrino density dominates the dynamics of the scalar field, and qualitatively alters the field’s cosmological evolution. This effect has not been included in previous literature, and changes the interpretation of cosmological data and its interplay with laboratory experiments. To illustrate these points a simplified model of a 1 + 1 setup with a single scalar field is analyzed.

Cosmology of Theories BSM↗
DOE OSTI2025

60 years of science in ICF: from conception to scientific breakeven on the National Ignition Facility

The recent achievements of a burning plasma, fusion ignition, and scientific energy gain with deuterium-tritium (DT) fuel at Lawrence Livermore National Laboratory’s National Ignition Facility (NIF) represents a major milestone in the development of inertial confinement fusion (ICF) and all of fusion research. In these experiments, fuel pressures well in excess of hundreds of GBars were achieved in the compressed fuel, and robust alpha heating of the fuel, far in excess of the energy provided by the implosion, were demonstrated for the first time. These achievements occurred 60 years after the inception of ICF and the first laser demonstration, and were made possible by more than five decades of research at laser facilities around the world. Advances in laser technology both in wavelength and precision, motivated by improved understanding of laser-plasma interaction physics and the demands of targets; improvements in target fabrication inspired by the need to control and minimize hydrodynamic instabilities in the implosion; and multi-dimensional simulations and diagnostics have been critical to this achievement. This paper will summarize the scientific and technical advances, the surprises, and the challenges that had to be overcome to achieve these goals.

fusion↗
DOE OSTI2022

Tuning the fluid wetting dynamics on gold microstructures using photoactive compounds

This work demonstrates how photoactive compounds can be used to tune the surface chemistry, surface free energy, and the wetting velocity of fluids on Spiropyran functionalized surfaces with different surface microstructures. Evidence of this photowetting effect is based on data showing: (1) the cyclic changes in the static, advancing, and receding contact angles $\theta$ CA for multiple UV$\rightleftarrows$vis photoswitching cycles with both smooth and microstructured surfaces and (2) the changes in the fluid wicking velocity (via UV$\rightleftarrows$vis photoswitching) on different Spiropyran functionalized hemiwicking surfaces. X-ray photoelectron spectroscopy is used to determine the efficiency of photoswitching caused by the quality of the Spiropyran functionalization. Reversible photoisomerization of Spiropyran generates a gradient in surface free energy, resulting in a similar change in contact angle ($\theta$ CA ) in the photoswitchable surfaces. In conclusion, by incorporating these changes into the Owens-Wendt and Van Oss surface energy models, the energy of smooth Au surfaces can also be predicted for both UV and visible light irradiations, where reversible contact angle variations of $\Delta$$\theta$ CA ≈ 5–10° are achieved with both water and water-ethanol mixtures due to the conversion of SP to merocyanine, which corresponds to a total free energy change of ~13% on the photoswitchable surface.

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

A multi-length-scale investigation of the applicability of ductility laws for annealed and work-hardened copper

Small-scale mechanical testing provides unique advantages over conventional testing in investigating the mechanical response of nuclear materials. While small-scale testing enables accelerated materials research, it raises the question of comparability to large-scale properties for engineering design considerations. Among different mechanical properties for structural design considerations such as yield and ultimate tensile stress, ductility is of critical importance with respect to structural component health. The effectiveness of using small-scale mechanical testing for probing these mechanical properties is dictated by understanding how the mechanical responses translate from the microscale to the engineering scale. Therefore, a better understanding of size scaling effects via gathering and analysis of experimental data is required to bridge length-scales. Further, this work builds upon previous reports to provide statistical data on how mechanical response changes as the size of the specimens are reduced from conventional sizes. One hundred twenty mesoscale tensile coupons of oxygen-free high thermal conductivity (OFHC) copper in work-hardened and annealed state have been manufactured using micro-wire electrical discharge machining (EDM) and tested under uniaxial tension. The mesoscale specimens have dimensions dictated by pre-selected geometric ratios (i.e., gauge section length over the square root of the cross-section area) with gauge length dimensions of 3 mm (or less) and sub-millimeter gauge widths and thicknesses. The mesoscale responses were compared to bulkscale properties to reveal the effect of specimen size on the mechanical response as a function of grain size and material state for a single phase face-centered cubic metal.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Cell dark current–voltage from non-calibrated module electroluminescence image analysis

Here, we present a fast, accurate, and reliable method of obtaining cell dark current–voltage (I–V) curves from module electroluminescence (EL) images without requiring calibration or correction. For a pristine module, EL-derived dark I–V are compared to directly probed data for a variety of changing imaging parameters: camera sensor, lens, filter, aperture width, exposure time (level of sensor saturation), number of images used, and various combinations of these. Pristine modules and those experiencing different modes and degrees of degradation are examined. A recent study of modules using five different cell technologies demonstrates the practicality of our “EL sweep” technique for performance and degradation studies.

14 SOLAR ENERGY↗
DOE OSTI2023

Mapping the Spatial Footprint of Sea Breeze Winds in the Southeastern United States

Abstract Sea breeze winds are observed at various locations worldwide, but the spatially continuous mapping of sea breeze winds is rare. We have developed a scheme to map the areas of the southeastern United States (SEUS) coast influenced by sea breeze winds using a range of surface re‐analysis data to identify their occurrence. Changes in wind direction and dew point temperature are both used to detect a potential sea breeze signature, which is then confirmed by cumuliform clouds seen in satellite images or coastal fronts shown as cohesive lines in radar reflectivity images. Filters are employed to remove onshore winds not induced by the temperature difference between land and sea. From March to September 2019, this scheme identified 134 days with sea breeze occurrence somewhere in the SEUS, a frequency of 63 percent. The number of sea breezes increased from March to July and then decreased to September. Deep inland propagation of sea breezes during this period left footprints in a band parallel to the coastline up to about 220 km inland, after which the sea breeze winds quickly diminished. Comparisons show that the findings using the scheme are consistent with site observations, theoretical estimates, and idealized and semi‐idealized numerical model simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

A Greening Future Elevates Flash Drought Risk in Northern Mid‐to‐High Latitudes

Flash droughts have become a growing concern, as they can emerge rapidly and increase the risk of crop failure. Although past studies have investigated the meteorological drivers and future changes of flash drought, why flash drought is more frequent over humid and vegetated regions remains underexplored. This study delves further into the mechanism by which vegetation regulates flash drought and its future change using observations from multiple data sets and large ensemble simulations from three Earth system models. On an interannual timescale, both observations and simulations show robust increases in flash drought frequency and a higher flash-to-sub-seasonal drought ratio during spring or antecedent conditions with dense vegetation, supporting the important role of vegetation in flash drought occurrence, especially in the northern mid-to-high latitudes. In the latter regions, the large ensemble simulations show robust increases in flash drought (e.g., 67% and 46% increases in Eastern U.S. and North Asia in 2050–2100 relative to 1950–2000 under the high emission scenario), where the growing season is lengthening. Although greening might suggest reduced drought stress, it drives precipitation-soil moisture-evapotranspiration decoupling by increasing evapotranspiration partitioning to transpiration. As transpiration can access deep soil water through the plant root system, its increased portion can weaken the constraints of concurrent precipitation on evapotranspiration, thus accelerating soil moisture depletion under high evaporative demand, driving a slow-to-rapid drought transition. How vegetation regulates flash drought by regulating surface moisture budget is supported by observations and simulations. Although warming supports early planting, agriculture may increasingly be threatened by surging flash drought risk.

Drought↗
DOE OSTI2025

Extreme flood return levels in a U.S. mid-Atlantic estuary using 40-year fluvial-coastal model simulations

Using an integrated watershed-coastal modeling framework, we conducted long-term historical simulations (1980-2019) of fluvial and coastal flooding in the Delaware Bay and River, a vulnerable estuarine system in the U.S., at high spatial resolutions. By applying process-based models, we generated physically consistent and spatially detailed estimates of estuarine, riverine, and surge-driven extreme water level compared to previous studies that used field data only. We then evaluated changes in the magnitude of flood events using the 40-year simulations and detrended Floodwater Depth values with stationary extreme value analysis. Our detailed assessment of spatial-varying extreme values revealed how different flood-generation mechanisms can dominate various zones in the estuary. The datasets produced through this work will be valuable for long-term flood hazard mitigation planning in coastal communities in the Delaware Bay and River region. Additionally, this work will serve as a benchmark for other coastal flood hazard modeling communities worldwide, aiding them in systematically modeling long-term and continuous extreme flood events.

Coastal and Riverine Flooding↗
DOE OSTI2025

A comprehensive approach for elucidating the interplay between 4f n +1 and 4f n 5d 1 configurations in Ln 2+ complexes

Lanthanides (Ln) are typically found in the +3 oxidation state. However, in recent decades, their chemistry has been expanded to include the less stable +2 oxidation state across the entire series except promethium (Pm), facilitated by the coordination of ligands such as trimethylsilylcyclopentadienyl, C 5 H 4 SiMe 3 (Cp'). The [LnCp' 3 ] complexes have been the workhorse for the synthesis and theoretical study of the fundamental aspects of divalent lanthanide chemistry, where experimental and computational evidence have suggested the existence of different ground state (GS) configurations, 4f n+1 or 4f n 5d 1 , depending on the specific metal. Standard reduction potentials and 4f n+1 to 4f n 5d 1 promotion energies have been two factors usually considered to rationalize the occurrence of these variable GS configurations, however the driving force behind this phenomenon is still not clear. In this work we present a comprehensive theoretical approach to shed light on this matter using the [LnCp 3 ] - model systems. We begin by calculating 4f n+1 to 4f n 5d 1 promotion energies and successfully correlate them with existing experimental data. Furthermore, we analyze how changes in the GS charge distribution between the Ln ions, LnCp 3 and the reduced [LnCp 3 ] - complexes (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) correlate with experimental trends in redox potentials and the calculated promotion energies. For this purpose, a comprehensive theoretical work that includes relativistic ligand field density functional theory (LFDFT) and relativistic ab initio wavefunction methods was performed. This study will help the rational design of suitable environments to tune the different GS configurations as well as modulating the spectroscopic properties of new Ln 2+ complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Planck 2018 results. VI. Cosmological parameters

In this paper, we present cosmological parameter results from the final full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction. Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to significant gains in the precision of other correlated parameters. Improved modelling of the small-scale polarization leads to more robust constraints on many parameters, with residual modelling uncertainties estimated to affect them only at the 0.5 σ level. We find good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted “base ΛCDM” in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density Ω c h 2 = 0.120 ± 0.001, baryon density Ω b h 2 = 0.0224 ± 0.0001, scalar spectral index n s = 0.965 ± 0.004, and optical depth τ = 0.054 ± 0.007 (in this abstract we quote 68% confidence regions on measured parameters and 95% on upper limits). The angular acoustic scale is measured to 0.03% precision, with 100 θ * = 1.0411 ± 0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: Hubble constant H 0 = (67.4 ± 0.5) km s –1 Mpc –1 ; matter density parameter Ω m = 0.315 ± 0.007; and matter fluctuation amplitude σ 8 = 0.811 ± 0.006. We find no compelling evidence for extensions to the base-ΛCDM model. Combining with baryon acoustic oscillation (BAO) measurements (and considering single-parameter extensions) we constrain the effective extra relativistic degrees of freedom to be N eff = 2.99 ± 0.17, in agreement with the Standard Model prediction N eff = 3.046, and find that the neutrino mass is tightly constrained to Σ m ν < 0.12 eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base ΛCDM at over 2 σ , which pulls some parameters that affect the lensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, Ω K = 0.001 ± 0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w 0 = –1.03 ± 0.03, consistent with a cosmological constant. We find no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r 0.002 < 0.06. Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations. The Planck base-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey’s combined-probe results including galaxy clustering (which prefers lower fluctuation amplitudes or matter density parameters), and in significant, 3.6 σ , tension with local measurements of the Hubble constant (which prefer a higher value). Simple model extensions that can partially resolve these tensions are not favoured by the Planck data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Intermediate scattering functions of a rigid body monoclonal antibody protein in solution studied by dissipative particle dynamic simulation

In the past decade, there was increased research interest in studying internal motions of flexible proteins in solution using Neutron Spin Echo (NSE) as NSE can simultaneously probe the dynamics at the length and time scales comparable to protein domain motions. However, the collective intermediate scattering function (ISF) measured by NSE has the contributions from translational, rotational, and internal motions, which are rather complicated to be separated. Widely used NSE theories to interpret experimental data usually assume that the translational and rotational motions of a rigid particle are decoupled and independent to each other. To evaluate the accuracy of this approximation for monoclonal antibody (mAb) proteins in solution, dissipative particle dynamic computer simulation is used here to simulate a rigid-body mAb for up to about 200 ns. The total ISF together with the ISFs due to only the translational and rotational motions as well as their corresponding effective diffusion coefficients is calculated. The aforementioned approximation introduces appreciable errors to the calculated effective diffusion coefficients and the ISFs. For the effective diffusion coefficient, the error introduced by this approximation can be as large as about 10% even though the overall agreement is considered reasonable. Thus, we need to be cautious when interpreting the data with a small signal change. In addition, the accuracy of the calculated ISFs due to the finite computer simulation time is also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Early-stage dynamics of chloride ion–pumping rhodopsin revealed by a femtosecond X-ray laser

Chloride ion–pumping rhodopsin (ClR) in some marine bacteria utilizes light energy to actively transport Cl – into cells. How the ClR initiates the transport is elusive. Here, we show the dynamics of ion transport observed with time-resolved serial femtosecond (fs) crystallography using the Linac Coherent Light Source. X-ray pulses captured structural changes in ClR upon flash illumination with a 550 nm fs-pumping laser. High-resolution structures for five time points (dark to 100 ps after flashing) reveal complex and coordinated dynamics comprising retinal isomerization, water molecule rearrangement, and conformational changes of various residues. Combining data from time-resolved spectroscopy experiments and molecular dynamics simulations, this study reveals that the chloride ion close to the Schiff base undergoes a dissociation–diffusion process upon light-triggered retinal isomerization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗