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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Knowledge management information tool Web analytics - 15182

The Knowledge Management Information Tool (KM-IT) is a web-based [01] system developed to maintain and preserve the Department of Energy's (DOE's) D and D knowledge base. The system was developed by Florida International University's Applied Research Center (FIU-ARC) with the support of the D and D community including the DOE Office of Environmental Management, and with the active collaboration and support of the DOE's Energy Facility Contractors Group (EFCOG). The KM-IT system is a D and D community driven system tailored to serve the technical issues faced by the D and D workforce across the DOE Complex. The D and D KM-IT is an interactive web-based system operational and available for free access at www.dndkm.org. [02] The D and D KM-IT is currently composed of the following tailored D and D modules: Web Crawler, Hotline, Technology, Document Library (including Hanford's and Savannah River Sites' ALARA Center Reports), Specialist Directory, Lessons Learned, Best Practices, Video/Picture Library, Vendors, Collaboration Tools, Training, and Mobile Systems. The Web Crawler dynamically searches through the D and D KM-IT repository as well as the web and displays search results based on the search criteria. The Hotline allows registered users to post questions/problems related to D and D and to receive solutions from a subject-matter specialist. The Technology module serves as repository of D and D technologies and contains technology/ demonstration fact sheets and vendor information. D and D community members can add Lessons Learned, Best Practices, Documents, and Pictures/Videos to the D and D KM-IT repository, after a formal approval process. The Vendor module provides a directory of commercial vendors who provide D and D related technologies, supplies, and services. D and D KM-IT makes excellent use of the knowledge that exists within the D and D community by allowing D and D project managers around the DOE complex to collaborate by sharing innovative ideas, past experiences, and practices and by maintaining a directory of subject matter specialists. The mobile version of the KM-IT can be accessed from m.dndkm.org [03] and currently has six active modules: Vendor, Technology, Picture/Video Library, Hotline, Lessons Learned and Specialist Directory. Web analytics is a key tool being implemented by the D and D KM-IT project team in an effort to enhance the system to better meet users' needs. The D and D KM-IT project team incorporates web analytics as part of its operational elements to analyze information and key data points on how the system is being used. Web analytics is the measurement, collection, analysis and reporting of internet data for the purposes of understanding and optimizing web usage. The use of web analytics retains or attracts D and D community members to access and share knowledge through virtual collaboration on the KM-IT platform. D and D KM-IT web analytics measures details on the overall usage of the system without tracking personal information or specific user behavior: how many users visited the application, how many of those users were unique visitors, how visitors come to the system (i.e., by following a link to the system or by using the web site URL via bookmark or directly typing the address), what keywords were used to perform searches with the search engine, how long the average user stayed on a given screen or on the entire system and what links were clicked on. This information is used to identify which areas of the system are more popular than the others and provides information that can be used to streamline the application for a better user experience. (authors)

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
DOE OSTI2023

Solid-phase sampling device and methods for point-source sampling of polar organic analytes

Sampling devices for sampling an aqueous source (e.g., field testing of ground water) for multiple different analytes are described. Devices include a solid phase extraction component for retention of a wide variety of targeted analytes. Devices include analyte derivatization capability for improved extraction of targeted analytes. Thus, a single device can be utilized to examine a sample source for a wide variety of analytes. Devices also include an isotope dilution capability that can prevent error introduction to the sample analysis and can correct for sample loss and degradation from the point of sampling until analysis as well as correction for incomplete or poor derivatization reactions. The devices can be field-deployable and rechargeable.

Boggess, Andrew J.↗
DOE OSTI2017

Determining appropriate data analytics for transformer health monitoring - 107

Transformers are vital assets for the safe, reliable and cost-effective operation of nuclear power plants. The unexpected failure of a transformer can lead to different consequences ranging from a lack of export capability, with the corresponding economic penalties, to catastrophic failure, with the associated health, safety and economic effects. Condition monitoring techniques examine the health of the transformer periodically, with the aim to identify early indicators of anomalies. However, many transformer failures occur because diagnostic and monitoring models do not identify degraded conditions in time. Therefore, health monitoring is an essential component to transformer life cycle management. Existing tools for transformer health monitoring use traditional dissolved gas analysis based diagnostics techniques. With the advance of prognostics and health management (PHM) applications, we can enhance traditional transformer health monitoring techniques using PHM analytics. The design of an appropriate data analytics system requires a multi-stage design process including: (i) specification of engineering requirements; (ii) characterization of existing data sources and analytics to identify complementary techniques; (iii) development of the functional specification of the analytics suite to formalize its behavior, and finally (iv) deployment, validation, and verification of the functional requirements in the final platform. Accordingly, in this paper we propose a transformer analytics suite which incorporates anomaly detection, diagnostics, and prognostics modules in order to complement existing tools for transformer health monitoring. (authors)

42 ENGINEERING↗
DOE OSTI2023

A projection-based analytical Jacobian framework for chemical kinetics applications

A major challenge in simulating complex combustion systems with detailed chemical kinetic models is the cost of integrating the chemical source terms, often done using stiff ODE solvers that require frequent Jacobian evaluations. Using analytically derived Jacobian matrices instead of divided-difference-based numerical Jacobian approximations can significantly reduce the associated computational cost. However, ambiguities arise in the formulation of analytical Jacobians because the chemical state of the system, or state vector, can be expressed in multiple ways, involving variables that are typically not independent from one another. Here, in this work, the consequences of those ambiguities on practical calculations are characterized in detail, and a generalized, projection-based framework is proposed as a mitigation strategy. Performances are assessed in a series of test cases involving a variety of configurations and numerical solution approaches. Results show that with proper treatment, commonly used analytical Jacobian formulations can be considered as equivalent for practical purposes, thereby alleviating concerns that the state vector chosen to express the governing equations and corresponding analytical Jacobian may significantly impact the accuracy of the simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

The “2T” ion-electron semi-analytic shock solution for code-comparison with xRAGE: A report for FY16

This report documents an effort to generate the semi-analytic "2T" ion-electron shock solution developed in the paper by Masser, Wohlbier, and Lowrie, and the initial attempts to understand how to use this solution as a code-verification tool for one of LANL's ASC codes, xRAGE. Most of the work so far has gone into generating the semi-analytic solution. Considerable effort will go into understanding how to write the xRAGE input deck that both matches the boundary conditions imposed by the solution, and also what physics models must be implemented within the semi-analytic solution itself to match the model assumptions inherit within xRAGE. Therefore, most of this report focuses on deriving the equations for the semi-analytic 1D-planar time-independent "2T" ion-electron shock solution, and is written in a style that is intended to provide clear guidance for anyone writing their own solver.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Analytical Laboratory Presentation at Canadian Nuclear Laboratory

The INL Analytical Research Laboratories and the CNL Analytical Laboratories share many of the same capabilities and expertise while also overlapping significantly in mission. Where there are similarities and differences in the types of samples and analytical procedures between the two facilities, each laboratory can learn much from the other, and establish a technical baseline that may be mutually beneficial. An exchange of knowledge and exposure to the international laboratories benefits both organizations, and it is the purpose of the proposed visits to the two facilities to foster understanding and learning between the respective scientists. Topics of common interest include but are not limited to multi-collector ICP-MS; high resolution gas MS; alpha, beta, and gamma spectrometry; and separations chemistry of nuclear materials. By sharing expertise, the INL and CNL Analytical Laboratories will improve their analyses providing more reliable results and capabilities that are competitive with other world-class facilities.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

NREL's Capabilities in Analytical Sciences Supporting Research and Development (R&D)

NREL researchers perform biomass characterization in dedicated laboratories working with over $5 million in state-of-the-art analytical equipment. A dedicated team of highly skilled analytical chemists have over 100 cumulative years of experience in characterization. They have three specialized laboratories with dedicated sample processing and advanced analytical equipment. Core capabilities include biomass and biochemical characterization and quantification, publicly available laboratory analytical procedures (LAPs), and near-infrared rapid analysis.

analysis↗
DOE OSTI2023

Advanced Analytical Methodologies Enable Feedstock Screening and Correlation to Pyrolysis Yields and Catalytic Upgrading

Pyrolysis of lignocellulosic biomass can serve as a powerful pathway for the generation of renewable fuels and industrial products. However, procurement of some biomass may be costly, especially when there is competition for alternative uses. Forestry and agricultural byproducts may serve as valuable pyrolysis feedstocks due to their high availability and low cost. Although waste products may fill demand for affordable pyrolysis feedstocks, they are often high in ash and extractives which contribute to unfavorable changes in pyrolysis vapor composition, as well as end products. The work presented here investigates the correlations between various pine anatomical fractions to understand their effect on pyrolysis oil composition for forest residues. Analytical pyrolysis coupled to direct analysis by molecular beam mass spectrometry (MBMS) provides real-time monitoring of pyrolysis vapor composition, even for compounds that are not amenable to gas chromatography. Statistical analysis of MBMS data from the fast pyrolysis (FP) of clean pine, cambium, twigs and branches, needles, bark, and a forest residue samples revealed that bark and needles made the greatest differences in the vapor composition of forest residues during pyrolysis and were enriched in resin acids, furfural derivatives, and ions that have been previously observed from catalysis corresponding to ash content. These results were also compared to catalytic fast pyrolysis (CFP) using a platinum on titania catalyst, and correlations between FP and CFP products were observed for the anatomical fractions. The forest residues and corresponding anatomical fractions from a stand of 23-year-old pine will be converted by fast pyrolysis in a bench-scale 2-inch fluidized-bed reactor, and statistical correlations between the bench-scale products and analytical-scale pyrolysis vapors will be shown. This work highlights the power of advanced analytical methodologies in determining the contributions of vapor components to catalytic pyrolysis outcomes for mixed feedstocks and demonstrates the use of analytical methodologies to better screen feedstocks prior to pyrolysis.

analytical↗
DOE OSTI2021

Unlocking the secret of lignin-enzyme interactions: Recent advances in developing state-of-the-art analytical techniques

Bioconversion of renewable lignocellulosics to produce liquid fuels and chemicals is one of the most effective ways to solve the problem of fossil resource shortage, energy security, and environmental challenges. Among the many biorefinery pathways, hydrolysis of lignocellulosics to fermentable monosaccharides by cellulase is arguably the most critical step of lignocellulose bioconversion. In the process of enzymatic hydrolysis, the direct physical contact between enzymes and cellulose is an essential prerequisite for the hydrolysis to occur. However, lignin is considered one of the most recalcitrant factors hindering the accessibility of cellulose by binding to cellulase unproductively, which reduces the saccharification rate and yield of sugars. This results in high costs for the saccharification of carbohydrates. The various interactions between enzymes and lignin have been explored from different perspectives in literature, and a basic lignin inhibition mechanism has been proposed. However, the exact interaction between lignin and enzyme as well as the recently reported promotion of some types of lignin on enzymatic hydrolysis is still unclear at the molecular level. Multiple analytical techniques have been developed, and fully unlocking the secret of lignin-enzyme interactions would require a continuous improvement of the currently available analytical techniques. This review summarizes the current commonly used advanced research analytical techniques for investigating the interaction between lignin and enzyme, including quartz crystal microbalance with dissipation (QCM-D), surface plasmon resonance (SPR), attenuated total reflectance-Fourier transform infrared (ATR-FTIR) spectroscopy, atomic force microscopy (AFM), nuclear magnetic resonance (NMR) spectroscopy, fluorescence spectroscopy (FLS), and molecular dynamics (MD) simulations. Interdisciplinary integration of these analytical methods is pursued to provide new insight into the interactions between lignin and enzymes. Finally, this review will serve as a resource for future research seeking to develop new methodologies for a better understanding of the basic mechanism of lignin-enzyme binding during the critical hydrolysis process.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2017

A semi-analytical method for simulating matrix diffusion in numerical transport models

We report a semi-analytical approximation for transient matrix diffusion is developed for use in numerical contaminant transport simulators. This method is an adaptation and extension of the heat conduction method of Vinsome and Westerveld (1980) used to simulate heat losses during thermally enhanced oil recovery. The semi-analytical method is used in place of discretization of the low permeability materials, and it represents the concentration profile in the low permeability materials with a fitting function that is adjusted in each element at each time-step. The resulting matrix diffusion fluxes are added to the numerical model as linear concentration-dependent source/sink terms. Since only the high permeability zones need to be discretized, the numerical formulation is extremely efficient compared to traditional approaches that require discretization of both the high and low permeability zones. The semi-analytical method compares favorably with the analytical solution for transient one-dimensional diffusion with first order decay, with a two-layer aquifer/aquitard solution, with the solution for transport in a fracture with matrix diffusion and decay, and with a fully numerical solution for transport in a thin sand zone bounded by clay with variable decay rates.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

Connecting the dots: Semi-analytical and random walk numerical solutions of the diffusion–reaction equation with stochastic initial conditions

We study a system with bimolecular irreversible kinetic reaction A+B→∅ where the underlying transport of reactants is governed by diffusion, and the local reaction term is given by the law of mass action. We consider the case where the initial concentrations are given in terms of an average and a white noise perturbation. Our goal is to solve the diffusion–reaction equation which governs the system, and we tackle it with both analytical and numerical approaches. To obtain an analytical solution, we develop the equations of moments and solve them approximately. To obtain a numerical solution, we develop a grid-less Monte Carlo particle tracking approach, where diffusion is modeled by a random walk of the particles, and reaction is modeled by annihilation of particles. The probability of annihilation is derived analytically from the particles' co-location probability. We rigorously derive the relationship between the initial number of particles in the system and the amplitude of white noise represented by that number. This enables us to compare the particle simulations and the approximate analytical solution and offer an explanation of the late time discrepancies. - Graphical abstract:.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

The evaluation of an analytical protocol for the determination of substances in waste for hazard classification

Highlights: • Knowledge of wastes in substances will be necessary to assess HP1–HP15 hazard properties. • A new analytical protocol is proposed for this and tested by two service laboratories on 32 samples. • Sixty-three percentage of the samples have a satisfactory analytical balance between 90% and 110%. • Eighty-four percentage of the samples were classified identically (Seveso Directive) for their hazardousness by the two laboratories. • The method, in progress, is being normalized in France and is be proposed to CEN. - Abstract: The classification of waste as hazardous could soon be assessed in Europe using largely the hazard properties of its constituents, according to the the Classification, Labelling and Packaging (CLP) regulation. Comprehensive knowledge of the component constituents of a given waste will therefore be necessary. An analytical protocol for determining waste composition is proposed, which includes using inductively coupled plasma (ICP) screening methods to identify major elements and gas chromatography/mass spectrometry (GC–MS) screening techniques to measure organic compounds. The method includes a gross or indicator measure of ‘pools’ of higher molecular weight organic substances that are taken to be less bioactive and less hazardous, and of unresolved ‘mass’ during the chromatography of volatile and semi-volatile compounds. The concentration of some elements and specific compounds that are linked to specific hazard properties and are subject to specific regulation (examples include: heavy metals, chromium(VI), cyanides, organo-halogens, and PCBs) are determined by classical quantitative analysis. To check the consistency of the analysis, the sum of the concentrations (including unresolved ‘pools’) should give a mass balance between 90% and 110%. Thirty-two laboratory samples comprising different industrial wastes (liquids and solids) were tested by two routine service laboratories, to give circa 7000 parameter results. Despite discrepancies in some parameters, a satisfactory sum of estimated or measured concentrations (analytical balance) of 90% was reached for 20 samples (63% of the overall total) during this first test exercise, with identified reasons for most of the unsatisfactory results. Regular use of this protocol (which is now included in the French legislation) has enabled service laboratories to reach a 90% mass balance for nearly all the solid samples tested, and most of liquid samples (difficulties were caused in some samples from polymers in solution and vegetable oil). The protocol is submitted to French and European normalization bodies (AFNOR and CEN) and further improvements are awaited.

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

How machine learning can extend electroanalytical measurements beyond analytical interpretation

Electroanalytical measurements are routinely used to estimate material properties exhibiting current and voltage signatures. Analysis of such measurements relies on analytical expressions of material properties to describe the experiments. The need for analytical expressions limits the experiments that can be used to measure properties as well as the properties that can be estimated from a given experiment. Such analytical relations are essentially solutions of the physics-based differential equations (with properties as coefficients) describing the material behavior under certain specific conditions. In recent years, a new machine learning-based approach has been gaining popularity wherein the differential equations are numerically solved to interpret the electroanalytical experiments in terms of corresponding material properties. Since the physics-based differential equations are solved, one can additionally estimate underlying fields, e.g., concentration profile, using such an approach. To exemplify the characteristics of such a machine learning assisted interpretation of electroanalytical measurements, we use data from the Hebb–Wagner test on a magnesium spinel intercalation host. In conclusion, as compared to the traditional analytical expression-based interpretation, the emerging approach decreases experimental efforts to characterize relevant material properties as well as provides field information that was previously inaccessible.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Molecular properties of excited electronic state: Formalism, implementation, and applications of analytical second energy derivatives within the framework of the time-dependent density functional theory/molecular mechanics

This work extends our previous works [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011); J. Liu and W. Z. Liang, J. Chem. Phys. 135, 184111 (2011)] on analytical excited-state energy Hessian within the framework of time-dependent density functional theory (TDDFT) to couple with molecular mechanics (MM). The formalism, implementation, and applications of analytical first and second energy derivatives of TDDFT/MM excited state with respect to the nuclear and electric perturbations are presented. Their performances are demonstrated by the calculations of adiabatic excitation energies, and excited-state geometries, harmonic vibrational frequencies, and infrared intensities for a number of benchmark systems. The consistent results with the full quantum mechanical method and other hybrid theoretical methods indicate the reliability of the current numerical implementation of developed algorithms. The computational accuracy and efficiency of the current analytical approach are also checked and the computational efficient strategies are suggested to speed up the calculations of complex systems with many MM degrees of freedom. Finally, we apply the current analytical approach in TDDFT/MM to a realistic system, a red fluorescent protein chromophore together with part of its nearby protein matrix. The calculated results indicate that the rearrangement of the hydrogen bond interactions between the chromophore and the protein matrix is responsible for the large Stokes shift.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

The use of nanomaterials for mass spectrometry can be uplifting for analyte detection

Surface-Assisted Laser Desorption Ionization (SALDI) involves desorbing and ionizing analyte molecules from a nanoporous substrate by laser irradiation for detection in a mass spectrometer. In this work experiments were designed to better understand the mechanisms governing desorption and ionization for Desorption Ionization On Silicon (DIOS), a variant of SALDI which uses porous silicon (pSi) as a substrate. Experiments are also reported for other nanoporous semiconducting materials (WO{sub 3}, TiO{sub 2}) which exhibit very similar behaviors; specifically, that both protonated analyte ions and analyte radical cations can be generated with relative intensities that depend on the position of the incident laser focus relative to substrate surface. While thermal desorption appears to be important, preliminary evidence suggests that the ionization mechanism leading to protonated analytes involves in part electrons and holes formed when photoexciting the substrate above its electronic band gap, and the presence of defect states within the band gap. Radical cation formation appears to be driven in part by electron transfer due to the large electron affinity of each substrate used in this work.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Analytic derivative couplings for spin-flip configuration interaction singles and spin-flip time-dependent density functional theory

We revisit the calculation of analytic derivative couplings for configuration interaction singles (CIS), and derive and implement these couplings for its spin-flip variant for the first time. Our algorithm is closely related to the CIS analytic energy gradient algorithm and should be straightforward to implement in any quantum chemistry code that has CIS analytic energy gradients. The additional cost of evaluating the derivative couplings is small in comparison to the cost of evaluating the gradients for the two electronic states in question. Incorporation of an exchange-correlation term provides an ad hoc extension of this formalism to time-dependent density functional theory within the Tamm-Dancoff approximation, without the need to invoke quadratic response theory or evaluate third derivatives of the exchange-correlation functional. Application to several different conical intersections in ethylene demonstrates that minimum-energy crossing points along conical seams can be located at substantially reduced cost when analytic derivative couplings are employed, as compared to use of a branching-plane updating algorithm that does not require these couplings. Application to H{sub 3} near its D{sub 3h} geometry demonstrates that correct topology is obtained in the vicinity of a conical intersection involving a degenerate ground state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Derivation of general analytic gradient expressions for density-fitted post-Hartree-Fock methods: An efficient implementation for the density-fitted second-order Møller–Plesset perturbation theory

General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller–Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele, Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Noble gas encapsulation into carbon nanotubes: Predictions from analytical model and DFT studies

The energetics for the interaction of the noble gas atoms with the carbon nanotubes (CNTs) are investigated using an analytical model and density functional theory calculations. Encapsulation of the noble gas atoms, He, Ne, Ar, Kr, and Xe into CNTs of various chiralities is studied in detail using an analytical model, developed earlier by Hill and co-workers. The constrained motion of the noble gas atoms along the axes of the CNTs as well as the off-axis motion are discussed. Analyses of the forces, interaction energies, acceptance and suction energies for the encapsulation enable us to predict the optimal CNTs that can encapsulate each of the noble gas atoms. We find that CNTs of radii 2.98 − 4.20 Å (chiral indices, (5,4), (6,4), (9,1), (6,6), and (9,3)) can efficiently encapsulate the He, Ne, Ar, Kr, and Xe atoms, respectively. Endohedral adsorption of all the noble gas atoms is preferred over exohedral adsorption on various CNTs. The results obtained using the analytical model are subsequently compared with the calculations performed with the dispersion-including density functional theory at the M06 − 2X level using a triple-zeta basis set and good qualitative agreement is found. The analytical model is however found to be computationally cheap as the equations can be numerically programmed and the results obtained in comparatively very less time.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗