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NASA NTRS1978

The isotopic composition of galactic cosmic ray lithium, beryllium and boron

The isotopic composition of galactic-cosmic-ray Li, Be, and B has been measured near 100 MeV/nucleon by using the University of Chicago IMP 7 and IMP 8 cosmic-ray telescopes during 1973-1975. The measured abundances allow detailed checks of models of interstellar propagation and solar modulation to be made and conclusions to be drawn concerning the spectral forms at the source and the minimum solar modulation level. For example, comparing these results with local interstellar spectra calculated by using a 'leaky box' model, it is found that if solar modulation is ignored, there is no unique leakage mean free path consistent with all the observations. However, by taking account of a sizable level of residual solar modulation, excellent agreement is obtained between the calculated and measured abundances. Thus, these isotopic abundances confirm the old hypothesis that cosmic-ray Li, Be, and B are produced as secondaries in interstellar space.

Garcia-Munoz, M.↗

NASA NTRS1994

Anomalous HNO3/NO(x) ratio of remote tropospheric air: Conversion of nitric acid to formic acid and NO(x)?

The N oxidation ratio, (HNO3)/(NO(x)), in the free troposphere is measured at approx. 1 to 9 (averaging approx. 5), consistently lower than the values of 15-100 which known theory suggests to be reached rapidly. This discrepancy casts doubt on current models' abilities to predict effects of NO sources on remote (NO), and so also (O3) and (OH). HNO3-to-NO(x) recycling processes involving HCHO in solution are appealing explanations for the ratio. Known chemical theory are illustrated using a Lagrangian box model of the mid-troposphere which simulates characteristic episodes form NO(x) input to HNO3 washout. Ratio and budget constraint equations for No(y) can usefully restrict conceivable explanations of missing chemistry of fast nitrogen cycling; most explanations could be called 'fast-cycles' or 're-NO(x)-ification.' These equations also show how current global models may suggest spuriously good N oxidation ratios and errors in OH. Aerosol or cloud droplets reactions with HCHO may produce (a) formic acid (which needs an appropriate source) and NO(x), or alternatively, (b) hydroxymethyl nitrate (or methyl dinitrate), which might supply a large, variable amount of 'missing NO(y) not currently measurable except by NO(y) instruments.

Chatfield, Robert B.↗

NASA NTRS2007

Aeroelastic Model Structure Computation for Envelope Expansion

Structure detection is a procedure for selecting a subset of candidate terms, from a full model description, that best describes the observed output. This is a necessary procedure to compute an efficient system description which may afford greater insight into the functionality of the system or a simpler controller design. Structure computation as a tool for black-box modelling may be of critical importance in the development of robust, parsimonious models for the flight-test community. Moreover, this approach may lead to efficient strategies for rapid envelope expansion which may save significant development time and costs. In this study, a least absolute shrinkage and selection operator (LASSO) technique is investigated for computing efficient model descriptions of nonlinear aeroelastic systems. The LASSO minimises the residual sum of squares by the addition of an l(sub 1) penalty term on the parameter vector of the traditional 2 minimisation problem. Its use for structure detection is a natural extension of this constrained minimisation approach to pseudolinear regression problems which produces some model parameters that are exactly zero and, therefore, yields a parsimonious system description. Applicability of this technique for model structure computation for the F/A-18 Active Aeroelastic Wing using flight test data is shown for several flight conditions (Mach numbers) by identifying a parsimonious system description with a high percent fit for cross-validated data.

Kukreja, Sunil L.↗

NASA NTRS2007

Aeroelastic Model Structure Computation for Envelope Expansion

Structure detection is a procedure for selecting a subset of candidate terms, from a full model description, that best describes the observed output. This is a necessary procedure to compute an efficient system description which may afford greater insight into the functionality of the system or a simpler controller design. Structure computation as a tool for black-box modeling may be of critical importance in the development of robust, parsimonious models for the flight-test community. Moreover, this approach may lead to efficient strategies for rapid envelope expansion that may save significant development time and costs. In this study, a least absolute shrinkage and selection operator (LASSO) technique is investigated for computing efficient model descriptions of non-linear aeroelastic systems. The LASSO minimises the residual sum of squares with the addition of an l(Sub 1) penalty term on the parameter vector of the traditional l(sub 2) minimisation problem. Its use for structure detection is a natural extension of this constrained minimisation approach to pseudo-linear regression problems which produces some model parameters that are exactly zero and, therefore, yields a parsimonious system description. Applicability of this technique for model structure computation for the F/A-18 (McDonnell Douglas, now The Boeing Company, Chicago, Illinois) Active Aeroelastic Wing project using flight test data is shown for several flight conditions (Mach numbers) by identifying a parsimonious system description with a high percent fit for cross-validated data.

Kukreja, Sunil L.↗

NASA NTRS1995

Radial energy transport by magnetospheric ULF waves: Effects of magnetic curvature and plasma pressure

The 'radial' transport of energy by internal ULF waves, stimulated by dayside magnetospheric boundary oscillations, is analyzed in the framework of one-fluid magnetohydrodynamics. (the term radial is used here to denote the direction orthogonal to geomagnetic flux surfaces.) The model for the inhomogeneous magnetospheric plasma and background magnetic field is axisymmetric and includes radial and parallel variations in the magnetic field, magnetic curvature, plasma density, and low but finite plasma pressure. The radial mode structure of the coupled fast and intermediate MHD waves is determined by numerical solution of the inhomogeneous wave equation; the parallel mode structure is characterized by a Wentzel-Kramer-Brillouin (WKB) approximation. Ionospheric dissipation is modeled by allowing the parallel wave number to be complex. For boudnary oscillations with frequencies in the range from 10 to 48 mHz, and using a dipole model for the background magnetic field, the combined effects of magnetic curvature and finite plasma pressure are shown to (1) enhance the amplitude of field line resonances by as much as a factor of 2 relative to values obtained in a cold plasma or box-model approximation for the dayside magnetosphere; (2) increase the energy flux delivered to a given resonance by a factor of 2-4; and (3) broaden the spectral width of the resonance by a factor of 2-3. The effects are attributed to the existence of an 'Alfven buoyancy oscillation,' which approaches the usual shear mode Alfven wave at resonance, but unlike the shear Alfven mode, it is dispersive at short perpendicular wavelengths. The form of dispersion is analogous to that of an internal atmospheric gravity wave, with the magnetic tension of the curved background field providing the restoring force and allowing radial propagation of the mode. For nominal dayside parameters, the propagation band of the Alfven buoyancy wave occurs between the location of its (field line) resonance and that of the fast mode cutoff that exists at larger radial distances.

Kouznetsov, Igor↗

DOE OSTI2018

User-Oriented Modeling Tools for Advanced Hybrid and Climate-Appropriate Rooftop Air Conditioners

Hybrid unitary air conditioning systems offer a pathway to substantially reduce energy use and peak electrical demand for cooling, heating, and ventilation in commercial buildings. Hybrid air conditioners incorporate multiple subsystems that are carefully orchestrated to provide climate- and application-specific efficiency advantages. There are a multitude of hybrid system architectures, but common subsystems include: heat recovery ventilation, indirect evaporative cooling, desiccant dehumidification, variable speed fans, modulating dampers, and multi-stage or variable-speed vapor compression cooling. Categorically, hybrid systems can operate in numerous discrete modes. For example: indirect evaporative cooling may operate for periods when the subsystem provides adequate sensible cooling, then vapor compression cooling will be included when more cooling or dehumidification is necessary. Laboratory assessments, field studies, and simulations have demonstrated that hybrid unitary air conditioners could reduce energy use for cooling and ventilation by 30-90% depending on climate and application. Heretofore, it has been challenging - if not impossible - for practitioners to model hybrid air conditioners as part of building energy simulations; and the limitation has severely obstructed broader adoption of technologies in this class. In this project, we developed a new feature for EnergyPlus that enables modeling hybrid unitary air conditioning equipment for building energy simulations. This is a significant advancement for both theory and practice, and confers public benefit by enabling practitioners to evaluate this compelling efficiency technology as a part of building energy simulations. The feature is a black-box model that requires extensive performance data for each hybrid unitary product. In parallel, we also developed new features for the Technology Performance Exchange to enable manufacturers to submit performance data in a standard format that can be used with the hybrid unitary model in EnergyPlus. Additionally, through this project we expanded university educational resources, and university- manufacturing industry collaborations in the field of energy efficiency technology. Over two years, we involved 20 undergraduate students in ambitious research projects focused on modeling complex multi-mode mechanical systems, supported three mechanical engineering bachelor theses, established undergraduate apprenticeships with multiple industry partners, and involved those partners in the process of design, validation, and debugging for the new EnergyPlus feature. The EnergyPlus feature is described and discussed in an academic article, as well as in an engineering reference, and input/output reference documentation for EnergyPlus. The Technology Performance Exchange features are live and publicly accessible, our manufacturer partners are primed to submit initial product information and performance data to the exchange, and the EnergyPlus feature is scheduled for public release in Spring 2018 as a part of EnergyPlus v8.9.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Exploiting Machine Learning in Multiscale Modelling of Materials

Recent developments in efficient machine learning algorithms have spurred significant interest in the materials community. The inherently complex and multiscale problems in Materials Science and Engineering pose a formidable challenge. The present scenario of machine learning research in Materials Science has a clear lacunae, where efficient algorithms are being developed as a separate endeavour, while such methods are being applied as ‘black-box’ models by others. The present article aims to discuss pertinent issues related to the development and application of machine learning algorithms for various aspects of multiscale materials modelling. The authors present an overview of machine learning of equivariant properties, machine learning-aided statistical mechanics, the incorporation of ab initio approaches in multiscale models of materials processing and application of machine learning in uncertainty quantification. In addition to the above, the applicability of Bayesian approach for multiscale modelling will be discussed. Critical issues related to the multiscale materials modelling are also discussed.

42 ENGINEERING↗

DOE OSTI2018

Constraining nucleation, condensation, and chemistry in oxidation flow reactors using size-distribution measurements and aerosol microphysical modeling

Oxidation flow reactors (OFRs) allow the concentration of a given atmospheric oxidant to be increased beyond ambient levels in order to study secondary organic aerosol (SOA) formation and aging over varying periods of equivalent aging by that oxidant. Previous studies have used these reactors to determine the bulk OA mass and chemical evolution. To our knowledge, no OFR study has focused on the interpretation of the evolving aerosol size distributions. In this study, we use size-distribution measurements of the OFR and an aerosol microphysics model to learn about size-dependent processes in the OFR. Specifically, we use OFR exposures between 0.09 and 0.9 equivalent days of OH aging from the 2011 BEACHON-RoMBAS and GoAmazon2014/5 field campaigns. We use simulations in the TOMAS (TwO-Moment Aerosol Sectional) microphysics box model to constrain the following parameters in the OFR: (1) the rate constant of gas-phase functionalization reactions of organic compounds with OH, (2) the rate constant of gas-phase fragmentation reactions of organic compounds with OH, (3) the reactive uptake coefficient for heterogeneous fragmentation reactions with OH, (4) the nucleation rate constants for three different nucleation schemes, and (5) an effective accommodation coefficient that accounts for possible particle diffusion limitations of particles larger than 60 nm in diameter. We find the best model-to-measurement agreement when the accommodation coefficient of the larger particles ( D p > 60 nm) was 0.1 or lower (with an accommodation coefficient of 1 for smaller particles), which suggests a diffusion limitation in the larger particles. When using these low accommodation-coefficient values, the model agrees with measurements when using a published H 2 SO 4 -organics nucleation mechanism and previously published values of rate constants for gas-phase oxidation reactions. Further, gas-phase fragmentation was found to have a significant impact upon the size distribution, and including fragmentation was necessary for accurately simulating the distributions in the OFR. The model was insensitive to the value of the reactive uptake coefficient on these aging timescales. Monoterpenes and isoprene could explain 24 %–95 % of the observed change in total volume of aerosol in the OFR, with ambient semivolatile and intermediate-volatility organic compounds (S/IVOCs) appearing to explain the remainder of the change in total volume. These results provide support to the mass-based findings of previous OFR studies, give insight to important size-distribution dynamics in the OFR, and enable the design of future OFR studies focused on new particle formation and/or microphysical processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2020

On the Role of Trend and Variability of Hydroxyl Radical (OH) in the Global Methane Budget

Decadal trends and interannual variations in the hydroxyl radical (OH), while poorly constrained at present, are critical for understanding the observed evolution of atmospheric methane (CH4). Through analyzing the OH fields simulated by the model ensemble of the Chemistry-Climate Model Initiative (CCMI), we find (1) the negative OH anomalies during the El Niño years mainly corresponding to the enhanced carbon monoxide (CO) emissions from biomass burning and (2) a positive OH trend during 1980-2010 dominated by the elevated primary production and the reduced loss of OH due to decreasing CO after 2000. Both two-box model inversions and variational 4D inversions suggest that ignoring the negative anomaly of OH during the El Niño years leads to a large overestimation of the increase in global CH4 emissions by up to10±3Tg yr-1to match the observed CH4 increase over these years. Not accounting for the increasing OH trends given by the CCMI models leads to an underestimation of the CH4 emission increase by 23±9Tg yr-1from 1986 to 2010. The variational inversion estimated CH4 emissions show that the tropical regions contribute most to the uncertainties related to OH. This study highlights the significant impact of climate and chemical feedbacks related to OH on the top-down estimates of the global CH4 budget.

Hydroxyl radical (OH)↗

NASA NTRS1991

Ion pickup, scattering, and stochastic acceleration in the cometary environment of P/Giacobini-Zinner

Observations and theory related to the scattering and acceleration of cometary pickup ions are reviewed with emphasis on Comet P/Giacobini-Zinner. A comparison of the regions upstream and downstream of the bow shock is made to assess the relative merits of each as a site for stochastic acceleration of ions above the pickup energy through interaction with low-frequency MHD waves. In the far upstream region the data are most consistent with a model where pickup ions generate a low level of MHD waves but remain relatively scatter-free. In the downstream region intense magnetic fluctuations gives rise to rapid isotropization of the ions and a second-order stochastic acceleration. The properties of the MHD power spectrum are related to the energetic ion spectrum in the framework of a leaky box model where the bulk of the acceleration occurs downstream of the shock throughout the cometosheath. Good agreement of the observations with theory is evident for both P/Giacobini-Zinner and P/Halley.

Barbosa, D. D.↗

NASA NTRS1988

Stellar nucleosynthesis and chemical evolution of the solar neighborhood

Current theoretical models of nucleosynthesis (N) in stars are reviewed, with an emphasis on their implications for Galactic chemical evolution. Topics addressed include the Galactic population II red giants and early N; N in the big bang; star formation, stellar evolution, and the ejection of thermonuclearly evolved debris; the chemical evolution of an idealized disk galaxy; analytical solutions for a closed-box model with continuous infall; and nuclear burning processes and yields. Consideration is given to shell N in massive stars, N related to degenerate cores, and the types of observational data used to constrain N models. Extensive diagrams, graphs, and tables of numerical data are provided.

Clayton, Donald D.↗

NASA NTRS1987

Origin and propagation of galactic cosmic rays

The study of systematic trends in elemental abundances is important for unfolding the nuclear and/or atomic effects that should govern the shaping of source abundances and in constraining the parameters of cosmic ray acceleration models. In principle, much can be learned about the large-scale distributions of cosmic rays in the galaxy from all-sky gamma ray surveys such as COS-B and SAS-2. Because of the uncertainties in the matter distribution which come from the inability to measure the abundance of molecular hydrogen, the results are somewhat controversial. The leaky-box model accounts for a surprising amount of the data on heavy nuclei. However, a growing body of data indicates that the simple picture may have to be abandoned in favor of more complex models which contain additional parameters. Future experiments on the Spacelab and space station will hopefully be made of the spectra of individual nuclei at high energy. Antiprotons must be studied in the background free environment above the atmosphere with much higher reliability and presion to obtain spectral information.

Cesarsky, Catherine J.↗

DOE OSTI2017

MODAL TRACKING of A Structural Device: A Subspace Identification Approach

Mechanical devices operating in an environment contaminated by noise, uncertainties, and extraneous disturbances lead to low signal-to-noise-ratios creating an extremely challenging processing problem. To detect/classify a device subsystem from noisy data, it is necessary to identify unique signatures or particular features. An obvious feature would be resonant (modal) frequencies emitted during its normal operation. In this report, we discuss a model-based approach to incorporate these physical features into a dynamic structure that can be used for such an identification. The approach we take after pre-processing the raw vibration data and removing any extraneous disturbances is to obtain a representation of the structurally unknown device along with its subsystems that capture these salient features. One approach is to recognize that unique modal frequencies (sinusoidal lines) appear in the estimated power spectrum that are solely characteristic of the device under investigation. Therefore, the objective of this effort is based on constructing a black box model of the device that captures these physical features that can be exploited to “diagnose” whether or not the particular device subsystem (track/detect/classify) is operating normally from noisy vibrational data. Here we discuss the application of a modern system identification approach based on stochastic subspace realization techniques capable of both (1) identifying the underlying black-box structure thereby enabling the extraction of structural modes that can be used for analysis and modal tracking as well as (2) indicators of condition and possible changes from normal operation.

42 ENGINEERING↗

DOE OSTI2018

Photo-tautomerization of acetaldehyde as a photochemical source of formic acid in the troposphere

Organic acids play a key role in the troposphere, contributing to atmospheric aqueous-phase chemistry, aerosol formation, and precipitation acidity. Atmospheric models currently account for less than half the observed, globally averaged formic acid loading. Here we report that acetaldehyde photo-tautomerizes to vinyl alcohol under atmospherically relevant pressures of nitrogen, in the actinic wavelength range, λ = 300–330 nm, with measured quantum yields of 2–25%. Recent theoretical kinetics studies show hydroxyl-initiated oxidation of vinyl alcohol produces formic acid. Adding these pathways to an atmospheric chemistry box model (Master Chemical Mechanism) demonstrates increased formic acid concentrations by a factor of ~1.7 in the polluted troposphere and a factor of ~3 under pristine conditions. Incorporating this mechanism into the GEOS-Chem 3D global chemical transport model reveals an estimated 7% contribution to worldwide formic acid production, with up to 60% of the total modeled formic acid production over oceans arising from photo-tautomerization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2023

An Observation-Based, Reduced-Form Model for Oxidation in the Remote Marine Troposphere

The hydroxyl radical (OH) fuels atmospheric chemical cycling as the main sink for methane and a driver of the formation and loss of many air pollutants, but direct OH observations are sparse. We develop and evaluate an observation-based proxy for short term, spatial variations in OH (Proxy OH ) in the remote marine troposphere using unprecedented and comprehensive measurements from the NASA Atmospheric Tomography (ATom) airborne campaign. Proxy OH is a reduced form of the OH steady-state equation representing the dominant OH production and loss pathways in the remote marine troposphere, according to box model simulations of OH constrained with ATom observations. Proxy OH comprises only eight variables that are generally observed by routine ground- or satellite-based instruments. ProxyOH scales linearly with in situ [OH] spatial variations along the ATom flight tracks (median r 2 = 0.90, interquartile range = 0.80 – 0.94 across 2 km altitude by 20° latitudinal regions). We deconstruct spatial variations in Proxy OH as a first-order approximation of the sensitivity of OH variations to individual terms. Two terms modulate within-region Proxy OH variations—water vapor (H 2 O) and, to a lesser extent, nitric oxide (NO). This implies that a limited set of observations could offer a novel avenue for observation-based mapping of OH spatial variations over much of the remote marine troposphere. Both H 2 O and NO are expected to change with climate, while NO also varies strongly with human activities. We also illustrate the utility of Proxy OH as a process-based approach for evaluating inter-model differences in remote marine tropospheric OH.

Colleen B. Baublitz↗

NASA NTRS2016

Non-OH Chemistry in Oxidation Flow Reactors for the Study of Atmospheric Chemistry Systematically Examined by Modeling

Oxidation flow reactors (OFRs) using low-pressure Hg lamp emission at 185 and 254 nm produce OH radicals efficiently and are widely used in atmospheric chemistry and other fields. However, knowledge of detailed OFR chemistry is limited, allowing speculation in the literature about whether some non-OH reactants, including several not relevant for tropospheric chemistry, may play an important role in these OFRs. These non-OH reactants are UV radiation, O(1D), O(3P), and O3. In this study, we investigate the relative importance of other reactants to OH for the fate of reactant species in OFR under a wide range of conditions via box modeling. The relative importance of non-OH species is less sensitive to UV light intensity than to relative humidity (RH) and external OH reactivity (OHRext), as both non-OH reactants and OH scale roughly proportional to UV intensity. We show that for field studies in forested regions and also the urban area of Los Angeles, reactants of atmospheric interest are predominantly consumed by OH. We find that O(1D), O(3P), and O3 have relative contributions to VOC consumption that are similar or lower than in the troposphere. The impact of O atoms can be neglected under most conditions in both OFR and troposphere. Under pathological OFR conditions of low RH and/or high OHRext, the importance of non-OH reactants is enhanced because OH is suppressed. Some biogenics can have substantial destructions by O3, and photolysis at non-tropospheric wavelengths (185 and 254 nm) may also play a significant role in the degradation of some aromatics under pathological conditions. Working under low O2 with the OFR185 mode allows OH to completely dominate over O3 reactions even for the biogenic species most reactive with O3. Non-tropospheric VOC photolysis may have been a problem in some laboratory and source studies, but can be avoided or lessened in future studies by diluting source emissions and working at lower precursor concentrations in lab studies, and by humidification. SOA photolysis is shown to be insignificant for most functional groups, except for nitrates and especially aromatics, which may be photolyzed at high UV flux settings. Our work further establishes the OFR's usefulness as a tool to study atmospheric chemistry and enables better experiment design and interpretation, as well as improved future reactor design.

Peng, Zhe↗

NASA NTRS2016

Non-OH Chemistry in Oxidation Flow Reactors for the Study of Atmospheric Chemistry Systematically Examined by Modeling

Peng, Zhe↗

DOE OSTI2016

Non-OH chemistry in oxidation flow reactors for the study of atmospheric chemistry systematically examined by modeling

Abstract. Oxidation flow reactors (OFRs) using low-pressure Hg lamp emission at 185 and 254 nm produce OH radicals efficiently and are widely used in atmospheric chemistry and other fields. However, knowledge of detailed OFR chemistry is limited, allowing speculation in the literature about whether some non-OH reactants, including several not relevant for tropospheric chemistry, may play an important role in these OFRs. These non-OH reactants are UV radiation, O(1D), O(3P), and O3. In this study, we investigate the relative importance of other reactants to OH for the fate of reactant species in OFR under a wide range of conditions via box modeling. The relative importance of non-OH species is less sensitive to UV light intensity than to water vapor mixing ratio (H2O) and external OH reactivity (OHRext), as both non-OH reactants and OH scale roughly proportionally to UV intensity. We show that for field studies in forested regions and also the urban area of Los Angeles, reactants of atmospheric interest are predominantly consumed by OH. We find that O(1D), O(3P), and O3 have relative contributions to volatile organic compound (VOC) consumption that are similar or lower than in the troposphere. The impact of O atoms can be neglected under most conditions in both OFR and troposphere. We define “riskier OFR conditions” as those with either low H2O (< 0.1 %) or high OHRext ( ≥ 100 s−1 in OFR185 and > 200 s−1 in OFR254). We strongly suggest avoiding such conditions as the importance of non-OH reactants can be substantial for the most sensitive species, although OH may still dominate under some riskier conditions, depending on the species present. Photolysis at non-tropospheric wavelengths (185 and 254 nm) may play a significant (> 20 %) role in the degradation of some aromatics, as well as some oxidation intermediates, under riskier reactor conditions, if the quantum yields are high. Under riskier conditions, some biogenics can have substantial destructions by O3, similarly to the troposphere. Working under low O2 (volume mixing ratio of 0.002) with the OFR185 mode allows OH to completely dominate over O3 reactions even for the biogenic species most reactive with O3. Non-tropospheric VOC photolysis may have been a problem in some laboratory and source studies, but can be avoided or lessened in future studies by diluting source emissions and working at lower precursor concentrations in laboratory studies and by humidification. Photolysis of secondary organic aerosol (SOA) samples is estimated to be significant (> 20 %) under the upper limit assumption of unity quantum yield at medium (1 × 1013 and 1.5 × 1015 photons cm−2 s−1 at 185 and 254 nm, respectively) or higher UV flux settings. The need for quantum yield measurements of both VOC and SOA photolysis is highlighted in this study. The results of this study allow improved OFR operation and experimental design and also inform the design of future reactors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗