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At least 469 records · Page 26

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DOE OSTI2025

Seismic response of vertical dry storage casks under three-dimensional earthquake motions

Ensuring the long-term seismic safety of dry storage casks (DSCs) is becoming increasingly critical as these systems evolve from temporary to de facto permanent repositories for spent nuclear fuels. Traditional seismic soil–structure interaction (SSI) assessment methods use one-dimensional deconvolution or simplified boundary conditions to model incident waves. Although computationally appealing, simplifying assumptions may alter the seismic risk by neglecting the full complexity of three-dimensional (3D) wave propagation effects. To address this challenge, this paper introduces a novel high-fidelity computational framework that leverages the Domain Reduction Method (DRM) with perfectly matched layers (PML) to accurately transfer complex, 3D seismic wavefields from regional-scale fault-rupture simulations into local-scale finite element models of DSCs. Using broadband, physics-based ground motions from a generic M w 7.0 strike-slip event, both single-cask and multi-cask configurations were investigated under near- and far-field conditions. Emphasis is placed on capturing complex SSI, spatial variability in the ground motion, and nonlinear phenomena such as cask rocking and sliding. Numerical results demonstrate that near-field conditions, where forward directivity and fling-step effects dominate, lead to significantly higher DSC rocking and sliding. Far-field cases, by contrast, generally exhibit modest responses. Incorporating SSI tends to amplify or alter DSC response spectra and introduce response variability, which underscores the need for site-specific evaluations and robust modeling approaches to ensure the seismic integrity of DSCs in interim spent fuel storage installations.

Das, Tonmoy↗

DOE OSTI2023

Stochastic multiscale modeling for quantifying statistical and model errors with application to composite materials

This paper provides a coherent and efficient computational framework for stochastic multiscale analysis of material systems in the presence of parametric uncertainties and modeling errors. Uncertainty in those model parameters that are not deduced as upscaled quantities is attributed to an uncertainty “germ”. While such parameters can appear at any scale, they are predominant at the finest analysis scale. Additional uncertainties stemming from statistical estimation, attributed to lack of data and model error, are associated with each submodel contributing to the multiscale system. Here, a robust and efficient framework based on a generalized extended polynomial chaos expansion (gEPCE) is proposed to simultaneously propagate all these uncertainties in order to provide a probabilistic representation of specific quantities of interest (QoI). We characterize the full probability distribution of the QoI and the uncertainty in the failure probability pertaining to its tails. By combining gEPCE with kernel density estimation (KDE) and directional derivatives, we construct sensitivity measures that connect these statistical metrics of QoI to the various sources of uncertainty to assess their individual and combined impacts. An illustrative problem featuring three-point bending of a composite beam is investigated to demonstrate the presented approach.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Using sensor arrays to decode NO x /NH 3 /C 3 H 8 gas mixtures for automotive exhaust monitoring

In this work, an array of four mixed-potential sensors is employed to identify and quantify gases in complex mixtures of unknown composition which mimic diesel engine exhaust. The sensors use dense metal and metal oxide electrodes with a porous ceramic electrolyte, yttria-stabilized zirconia (YSZ). Since the sensors exhibit cross-specificity toward target gases, we develop a computational model for predicting gas concentrations in the mixtures. Our model is based on fundamental principles of gas-sensor interactions and, furthermore, takes into account the non-linearity of the observed sensor voltage response. Our approach enables accurate predictions of gas concentrations from the voltage output of the sensor array exposed to an extensive set of mixtures involving C 3 H 8 , NH 3 , NO and NO 2 . We find that our predictions remain accurate even if the model is trained using a reduced set of mixtures, or if the number of sensors is decreased to three or two. Finally, our experimental and computational framework can be used to decipher contents of complex gas mixtures of unknown composition in numerous industrial, automotive, and national security settings.

47 OTHER INSTRUMENTATION↗

DOE OSTI2026

Thermomechanical analysis and modeling of a high-temperature light trapping planar cavity solar receiver

The development of durable particle-based high-temperature solar receivers is critical for advancing concentrating solar-thermal (CST) technologies to enable high-efficiency power generation and industrial process heat. Here, this study presents a computational framework to evaluate the thermomechanical performance of a proposed enclosed light-trapping planar cavity receiver designed for particle-based thermal energy systems. The receiver incorporates absorptive cavities and fluidized particle-bed channels to enhance heat capture and reduce thermal losses. Finite element analysis (FEA) is employed to assess stress, strain, and creep-fatigue behavior under concentrated solar flux using realistic thermal boundary conditions derived from coupled system models and experimental assembly parameters. The analysis investigates the influence of particle-to-wall heat transfer coefficients (HTC) ranging from 800 to 1800 W/m 2 .K on the thermomechanical response of six candidate high-temperature alloys: Alloy 740H, Alloy 282, Alloy 617, 316H, Alloy 230, and 800H. Results show that increasing HTC reduces thermal gradients, leading to lower stresses and strains and extended minimum predicted creep life. While all materials satisfy fatigue life requirements under the investigated conditions, significant differences in creep resistance are observed. Alloy 740H consistently exhibits the longest minimum predicted creep life and the most favorable durability margins, followed by Alloy 282, with the remaining materials showing reduced creep resistance under identical loading. The reported creep lives are conservative lower-bound estimates intended for comparative material evaluation. This framework highlights the critical roles of material selection and geometry optimization in improving mechanical durability and reliability of solar-thermal receivers, forming a foundation for future experimental validation and design optimization.

14 SOLAR ENERGY↗

DOE OSTI2020

Logic-based analysis of gene expression data predicts association between TNF, TGFB1 and EGF pathways in basal-like breast cancer

For breast cancer, clinically important subtypes are well characterized at the molecular level in terms of gene expression profiles. In addition, signaling pathways in breast cancer have been extensively studied as therapeutic targets due to their roles in tumor growth and metastasis. However, it is challenging to put signaling pathways and gene expression profiles together to characterize biological mechanisms of breast cancer subtypes since many signaling events result from post-translational modifications, rather than gene expression differences. We designed a logic-based computational framework to explain the differences in gene expression profiles among breast cancer subtypes using Pathway Logic and transcriptional network information. Pathway Logic is a rewriting-logic-based formal system for modeling biological pathways including post-translational modifications. Our method demonstrated its utility by constructing subtype-specific path from key receptors (TNFR, TGFBR1 and EGFR) to key transcription factor (TF) regulators (RELA, ATF2, SMAD3 and ELK1) and identifying potential association between pathways via TFs in basal-specific paths, which could provide a novel insight on aggressive breast cancer subtypes. Lastly, codes and results are available at http://epigenomics.snu.ac.kr/PL/.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2014

A Human Life-Stage Physiologically Based Pharmacokinetic and Pharmacodynamic Model for Chlorpyrifos: Development and Validation

Sensitivity to chemicals in animals and humans are known to vary with age. Age-related changes in sensitivity to chlorpyrifos have been reported in animal models. A life-stage physiologically based pharmacokinetic and pharmacodynamic (PBPK/PD) model was developed to computationally predict disposition of CPF and its metabolites, chlorpyrifos-oxon (the ultimate toxicant) and 3,5,6-trichloro-2-pyridinol (TCPy), as well as B-esterase inhibition by chlorpyrifos-oxon in humans. In this model, age-dependent body weight was calculated from a generalized Gompertz function, and compartments (liver, brain, fat, blood, diaphragm, rapid, and slow) were scaled based on body weight from polynomial functions on a fractional body weight basis. Blood flows among compartments were calculated as a constant flow per compartment volume. The life-stage PBPK/PD model was calibrated and tested against controlled adult human exposure studies. Model simulations suggest age-dependent pharmacokinetics and response may exist. At oral doses ≥ 0.55 mg/kg of chlorpyrifos (significantly higher than environmental exposure levels), 6 mo old children are predicted to have higher levels of chlorpyrifos-oxon in blood and higher levels of red blood cell cholinesterase inhibition compared to adults from equivalent oral doses of chlorpyrifos. At lower doses that are more relevant to environmental exposures, the model predicts that adults will have slightly higher levels of chlorpyrifos-oxon in blood and greater cholinesterase inhibition. This model provides a computational framework for age-comparative simulations that can be utilized to predict CPF disposition and biological response over various postnatal life-stages.

Smith, Jordan N.↗

DOE OSTI2017

Simulating Charge, Spin, and Orbital Ordering: Application to Jahn–Teller Distortions in Layered Transition-Metal Oxides

The degrees of freedom associated with orbital, spin, and charge ordering can signifcantly affect the properties of many crystalline solids, including battery materials, high-temperature superconductors, and naturally occurring minerals. Our research reports on the development of a computational framework to systematically explore the ordering of electronic degrees of freedom and presents results on orbital ordering associated with Jahn–Teller distortions in four layered oxides relevant for Li- and Na-ion batteries: LiNiO 2 , NaNiO 2 , LiMnO 2 , and NaMnO 2 . Our calculations reveal a criterion for the stability of orbital orderings in these layered materials: each oxygen atom must participate in two short and one long transition-metal/oxygen bond. The only orderings that satisfy this stability criterion are row orderings, such as the “zigzag” ordering. The near degeneracy of such row-orderings in LiNiO 2 suggests that boundaries between domains with distinct but symmetrically equivalent Jahn–Teller distortions will be relatively low in energy. Based on this finding, we speculate that a microstructure consisting of nanoscale Jahn–Teller domains could be responsible for the apparent absence of a collective distortion in experiments on LiNiO 2 .

25 ENERGY STORAGE↗

DOE OSTI2019

Assessing Correlations of Perovskite Catalytic Performance with Electronic Structure Descriptors

Electronic structure descriptors are computationally efficient quantities used to construct qualitative correlations for a variety of properties. In particular, the oxygen p-band center has been used to guide material discovery and fundamental understanding of an array of perovskite compounds for use in catalyzing the oxygen reduction and evolution reactions. Yet, an assessment of the effectiveness of the oxygen p-band center at predicting key measures of perovskite catalytic activity has not been made and would be highly beneficial to guide future predictions and codify best practices. In this work, we have used density functional theory at the Perdew–Burke–Ernzerhof (PBE), PBEsol, PBE + U, strongly constrained and appropriately normed functional, and Heyd–Scuseria–Ernzerhof (HSE06) levels to assess the correlations of numerous measures of catalytic performance for a series of technologically relevant perovskite oxides, using the bulk oxygen p-band center as an electronic structure descriptor. We have analyzed correlations of the calculated oxygen p-band center for all considered functionals with the experimentally measured X-ray emission spectroscopy oxygen p-band center and multiple measures of catalytic activity, including high-temperature oxygen reduction surface exchange rates, aqueous oxygen evolution current densities, and binding energies of oxygen evolution intermediate species. Our findings show that the best correlations for all measures of catalytic activity considered here are made with PBE-level calculations, with strong observed linear correlations with the bulk oxygen p-band center (R 2 = 0.81–0.87). This study illustrates that strong linear correlations between numerous important measures of catalytic activity and the oxygen p-band bulk descriptor can be obtained under a consistent computational framework, and these correlations can serve as a guide for future experiments and simulations for development of perovskite and related oxide catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Charge Transport in Solvated Donor–Acceptor Functionalized Peptoids: Molecular Dynamics and Rate Theory

Scalable solar-energy conversion requires photoactive materials that combine the efficiency of natural photosynthetic systems with the stability and processability needed for practical applications. Achieving reliable charge transport in soft, self-assembled organic materials remains challenging, as structural fluctuations and environmental effects strongly influence charge-transfer (CT) rates. Here, we present a broadly applicable computational framework for evaluating CT rates in the condensed phase, combining Fermi’s golden rule rate theory with inputs from all-atom molecular dynamics (MD) simulations and first-principles electronic-structure calculations. The approach does not rely on system-specific parametrization and is applicable to a wide range of soft and disordered materials. We demonstrate the applicability and usefulness of the framework on redox-active peptoids functionalized with iron–porphyrin (Fe–P) complexes, a bioinspired platform with programmable donor–acceptor units and tunable three-dimensional organization. The calculated CT rates exhibit strong sensitivity to molecular conformation, with variations spanning several orders of magnitude. This dependence is shown to arise from the pronounced variation in diabatic electronic coupling with the relative orientations and separations of the Fe–P complexes across the conformational ensemble. The framework provides a consistent route for connecting atomistic structure to CT kinetics in the condensed phase and enables analysis of structure–rate relations in organic semiconducting systems.

Charge transfer↗

DOE OSTI2018

Predicting the Conformational Variability of Abl Tyrosine Kinase using Molecular Dynamics Simulations and Markov State Models

Understanding protein conformational variability remains a challenge in drug discovery. The issue arises in protein kinases, whose multiple conformational states can affect the binding of small-molecule inhibitors. To overcome this challenge, we propose a comprehensive computational framework based on Markov state models (MSMs). Our framework integrates the information from explicit-solvent molecular dynamics simulations to accurately rank-order the accessible conformational variants of a target protein. We tested the methodology using Abl kinase with a reference and blind-test set. Only half of the Abl conformational variants discovered by our approach are present in the disclosed X-ray structures. We report the approach successfully identified a protein conformational state not previously observed in public structures but evident in a retrospective analysis of Lilly in-house structures: the X-ray structure of Abl with WHI-P154. Using a MSM-derived model, the free energy landscape and kinetic profile of Abl was analyzed in detail highlighting opportunities for targeting the unique metastable states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Modeling Equilibrium Solid–Liquid Interfaces under Effective Constant Chemical Potential Using Machine Learning Interatomic Potentials

The chemical potential (μ) of species in solution is essential for understanding various chemical processes at interfaces. Molecular dynamics (MD) simulations, constrained by fixed compositions, cannot maintain constant chemical potential with reference to a targeted concentration or chemical potential under nonequilibrium or dynamic conditions, as solute species can migrate to the interface and deplete (or enrich) the bulk due to solute-interface interactions. In this study, we introduce a simple and computationally efficient approach named iterative quasi-constant chemical potential molecular dynamics (iqCμMD) simulation, which helps simulate targeted molar concentrations of species in solution. iqCμMD overcomes the limitations of conventional MD by adjusting the number of species in the solution to reach a target bulk concentration (chemical potential), which allows simulation of the interface under the bulk conditions comparable to experiment. We demonstrate our approach using machine learning interatomic potential (MLIP)-based MD simulations of the Na 2 SO 4,aq –graphene interface, and to show the transferability of our approach, we also perform classical force field-based MD simulations of NaCl aq –air and NaCl aq –graphite interfaces, which produce comparable results to previous CμMD simulations. Our results also show that the iqCμMD approach efficiently achieves the desired bulk ion concentration within two iterations, and by utilizing MLIPs, we can achieve converged results using relatively small-scale simulations compared to previous CμMD simulations. By combining iqCμMD with MLIP-driven simulations, solid–liquid interfaces can be modeled under an effective constant chemical potential with DFT-level accuracy. Here, we show that iqCμMD offers a robust and simple computational framework for constant chemical potential simulations, as its only requirement is to be able to converge interfacial simulations with a measurable bulk region.

Chemical structure↗

DOE OSTI2021

Comparative Studies of the Structural and Transport Properties of Molten Salt FLiNaK Using the Machine-Learned Neural Network and Reparametrized Classical Forcefields

Despite surging interest in molten salt reactors and thermal storage systems, knowledge of the physicochemical properties of molten salts are still inadequate due to demanding experiments that require high temperature, impurity control, and corrosion mitigation. Therefore, the ability to predict these properties for molten salts from first-principles computations is urgently needed. Herein, we developed and compared a machine-learned neural network force field (NNFF) and a reparametrized rigid ion model (RIM) for a prototypical molten salt LiF–NaF–KF (FLiNaK). We found that NNFF was able to reproduce both the structural and transport properties of the molten salt with first-principles accuracy and classical-MD computational efficiency. Furthermore, the correlation between the local atomic structures and the dynamics was identified by comparing with RIMs, suggesting the significance of polarization of anions implicitly embedded in the NNFF. Furthermore, this work demonstrated a computational framework that can facilitate the screening of molten salts with different chemical compositions, impurities, and additives, and at different thermodynamic conditions suitable for the next-generation nuclear reactors and thermal energy storage facilities.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Deciphering the Cofilin Oligomers via Intermolecular Disulfide Bond Formation: A Coarse-Grained Molecular Dynamics Approach to Understanding Cofilin’s Regulation on Actin Filaments

Cofilin, a key actin-binding protein, orchestrates the dynamics of the actomyosin network through its actin-severing activity and by promoting the recycling of actin monomers. Recent experimental work suggests that cofilin also forms functionally distinct oligomers through thiol post-translational modification (PTM) that encourages actin nucleation and assembly. Despite these advances, the structural conformations of cofilin oligomers that modulate actin activity remain elusive because there are combinatorial ways to oxidize thiols in cysteines to form disulfide bonds rapidly. This study employs molecular dynamics simulations to investigate human cofilin 1 as a case study for exploring cofilin dimers via disulfide bond formation. Using the free energy profiling, our simulations unveil a range of probable cofilin dimer structures not represented in current Protein Data Bank entries. These candidate dimers are characterized by their distinct population distributions and relative free energies. Of particular note is a dimer featuring an interface between cysteines 139 and 147 residues, which demonstrates stable free energy characteristics and intriguingly symmetrical geometry. In contrast, the experimentally proposed dimer structure exhibits a less stable free energy profile. Here, we also evaluate frustration quantification based on the energy landscape theory in the protein-protein interactions at the dimer interfaces. Notably, the 39-39 dimer configuration emerges as a promising candidate for forming cofilin tetramers, as substantiated by frustration analysis. Additionally, docking simulations with actin filaments further evaluate the stability of these cofilin dimer-actin complexes. Our findings thus offer a computational framework for understanding the role of thiol post-translational modification cofilin proteins in regulating oligomerization, and the subsequent cofilin-mediated actin dynamics in the actomyosin network.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Wetting of a Hydrophobic Surface: Far-IR Action Spectroscopy and Dynamics of Microhydrated Naphthalene

The interaction of water and polycyclic aromatic hydrocarbons is of fundamental importance in areas as diverse as materials science and atmospheric and interstellar chemistry. The interplay between hydrogen bonding and dipole–π interactions results in subtle dynamics that are challenging to describe from first principles. Here, we employ far-IR action vibrational spectroscopy with the infrared free-electron laser FELIX to investigate naphthalene with one to three water molecules. We observe diffuse bands associated with intermolecular vibrational modes that serve as direct probes of the loose binding of water to the naphthalene surface. These signatures are poorly reproduced by static DFT or Møller–Plesset computations. Instead, a rationalization is achieved through Born–Oppenheimer Molecular Dynamics simulations, revealing the active mobility of water over the surface, even at low temperatures. Therefore, our work provides direct insights into the wetting interactions associated with shallow potential energy surfaces while simultaneously demonstrating a solid experimental–computational framework for their investigation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Molecular Dynamics Investigation of Oil Wetting on Synthetic Polymer Substrates

Understanding the interaction of polymer surfaces with nonpolar, low surface tension liquids, or whether a substrate is oleophobic versus oleophilic, is critical for applications ranging from antifingerprint coatings to oil–water separation membranes and oil spill remediation. Despite its technological importance, the molecular mechanisms underpinning polymer–oil wetting are not well characterized. Here, we employ molecular dynamics simulations to investigate the behavior of n-hexadecane in contact with chemically distinct polymer surfaces, spanning eight constitutional unit chemistries as well as amorphous and crystalline morphologies. This permits a critical examination of both thermodynamic and dynamic descriptors of oleophobicity, including oil contact angle, dewetting free energy, interfacial diffusivity, and a proposed “ghost probe energy,” which does not require explicit simulation of oil–polymer interactions. We find that the oil contact angle does not reliably distinguish oleophobic behavior across polymer chemistries, whereas other metrics provide clearer and more consistent differentiation. Analysis of the results reveals that polymer–oil wetting behavior is primarily governed by interfacial van der Waals interactions and modulated by surface flexibility and morphology. Collectively, this work establishes a computational framework for characterizing oil wetting and provides additional insight into what molecular-level factors dictate trends in oleophobicity.

lipids↗

DOE OSTI2022

Te/CdTe and Al/CdTe Interfacial Energy Band Alignment by Atomistic Modeling

A synergistic approach that incorporates first-principles atomistic modeling with numerical device simulations is used to systematically evaluate the role of heterointerfaces within metal-chalcogenide-based photovoltaic technologies. Two interfaces involving either a tellurium back contact or aluminum back electrode combined with a cadmium telluride absorber layer within cadmium-telluride-based thin-film solar cells are investigated on an atomic scale to determine the mechanisms contributing to variations in device performance. Electronic structures and predicted charge transport behavior with respect to cadmium and tellurium termination of the absorber layer are studied along the polar oriented CdTe{111} facets. The computational methodology reveals a noticeable contrast between the Schottky barrier forming Al/CdTe interface versus the Type I Te/CdTe heterojunction. Greater band bending features are exhibited by the cadmium termination as opposed to the tellurium termination for each interface case. Subsequent device modeling suggests that 3.6% higher photovoltaic conversion efficiency is achievable for the cadmium termination relative to the tellurium termination of the Te/CdTe interface. Based strictly on an idealistic representation, both interface models show the importance of atomic-scale interfacial properties for cadmium telluride solar cell device performance with their bulk properties being validated in comparison to published experimental data. Here, the synergistic approach offers a suitable method to analyze solar cell interfaces through a predictive computational framework for the engineering and optimization of metal-chalcogenide-based thin-film photovoltaic technologies.

Green’s function↗

DOE OSTI2026

Regio- and Stereoselective Lactone Polymerization: Divergent Effect of Catalyst Modification and Monomer Structure

Selective ring-opening polymerization (ROP) of chiral lactones enables access to biodegradable polyesters with precisely controlled microstructures. Here, combined DFT modeling and experimental validation elucidate how fine-tuning of enantiopure SalBinam aluminum catalysts (through introduction of bromine atoms and tert-butyl groups, respectively, in ortho- and para-positions) modulates regio- and stereocontrol in the ROP of methyl glycolide (MeG) and lactide (LA). Computations reveal that regioselectivity in MeG polymerization arises mainly from steric repulsion, with a small contribution from weak stabilizing C-H···Br interactions that favor ring-opening at the glycolic site, consistent with the experimentally enhanced regioselectivity for (R)-MeG. In contrast, the same steric congestion at the ligand’s ortho positions destabilizes the key transition states in rac-LA polymerization, reducing the calculated stereoselectivity. Experiments confirm the predicted loss of stereocontrol, yielding nearly atactic PLA under standard conditions. Extension of the computational framework to rac-MeG polymerization promoted by racemic catalyst identified a low-barrier, stepwise polymer chain exchange pathway that rationalizes the experimentally observed syndiotacticity of poly(lactic-co-glycolic acid).

DFT calculations↗

DOE OSTI2020

Finite-Temperature Structures of Supported Subnanometer Catalysts Inferred via Statistical Learning and Genetic Algorithm-Based Optimization

Single-atom catalysts (SACs) minimize noble metal utilization and can alter the activity and selectivity of supported metal nanoparticles. However, the morphology of active centers, including single atoms and subnanometer clusters of a few atoms, remains elusive due to experimental challenges. The computational cost to describe numerous cluster shapes and sizes makes direct first-principles calculations impractical. We present a computational framework to enable structure determination for single-atom and subnanometer cluster catalysts. As a case study, we obtained the low energy structures of Pd n (n = 1-21) clusters supported on CeO 2 (111), which are critical components of automobile three-way catalysts. Trained on density functional theory data, a three-dimensional cluster expansion is established using statistical learning to describe the Hamiltonian and predict energies of supported Pdn clusters of any structure. Low energy stable and metastable structures are identified using a Metropolis Monte Carlo-based genetic algorithm in the canonical ensemble at 300 K. We observe that supported single atoms sinter to form bilayer clusters and large cluster isomers share similarities in both shape and energy, and elucidate the significance of the support and microstructure on cluster stability. We discovered a simple surrogate structure-energy model, where the energy per atom scales with the square root of the average first coordination number, which can be used to estimate energies and compare the stability of clusters. Our framework, applicable to any metal/support system, fills an important methodological gap to predict the stability of supported metal catalysts in the subnanometer regime.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗