Search NASA⌕ Search

SEARCH · Search NASA

Results for “Analytic linearization”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 289 records · Page 16

Self‐Propelling Macroscale Sheets Powered by Enzyme Pumps

Nanoscale enzymes anchored to surfaces act as chemical pumps by converting chemical energy released from enzymatic reactions into spontaneous fluid flow that propels entrained nano‐ and microparticles. Enzymatic pumps are biocompatible, highly selective, and display unique substrate specificity. Utilizing these pumps to trigger self‐propelled motion on the macroscale has, however, constituted a significant challenge and thus prevented their adaptation in macroscopic fluidic devices and soft robotics. Using experiments and simulations, we herein show that enzymatic pumps can drive centimeter‐scale polymer sheets along directed linear paths and rotational trajectories. In these studies, the sheets are confined to the air/water interface. With the addition of appropriate substrate, the asymmetric enzymatic coating on the sheets induces chemically driven, buoyancy flows that controllably propel the sheet's motion on the air/water interface. The directionality and speed of the motion can be tailored by changing the pattern of the enzymatic coating, type of enzyme, and nature and concentration of the substrate. This work highlights the utility of biocompatible enzymes for generating motion in macroscale fluidic devices and robotics and indicates their potential utility for in vivo applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Catalytic resonance theory for parametric uncertainty of programmable catalysis

Microkinetic models are useful tools for screening catalytic materials; however, errors in their input parameters can lead to significant uncertainty in model predictions of catalyst performance. Here, in this work, we investigate the impact of linear scaling and Brønsted-Evans-Polanyi relation parametric uncertainty on microkinetic predictions of programmable-catalyst performance. Two case studies are considered: a generic A-to-B prototype reaction and the oxygen evolution reaction (OER). The results show that error-unaware models can accurately predict trends and, for the prototype reaction, values of optimal waveform parameters. The specific model parameters driving output uncertainty are identified via variance-based global sensitivity analysis. However, predictions of dynamic rate enhancement can decrease when uncertainty is propagated into the models. In both cases, we identify operating conditions where the programmable catalyst achieves a rate enhancement of at least one order of magnitude despite parametric uncertainty in the model, supporting programmable catalysis as a viable strategy for exceeding the Sabatier limit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Tests of the DFT Ladder for the Fulminic Acid Challenge

Properties of the historically pivotal fulminic acid (HCNO) molecule have been computed with a panoply of 473 density functionals of all varieties, providing a snapshot of the performance of contemporary density functional theory (DFT) for a challenging chemical system. Exhaustive tabulations and statistical analyses have been carried out for geometric parameters, vibrational frequencies, barriers to linearity, and the HCN–O dissociation energy. As the DFT ladder is climbed, confusion rather than consensus ensues regarding the details of the distinctive, extremely flat H–C–N bending potential of fulminic acid and whether the equilibrium structure is linear or bent. While high-ranking DFT functionals produce the smallest errors for the HCN + O( 3 P) → HCNO reaction energy, lower rungs emerge as the best performers for many of the bond distances and harmonic vibrational frequencies. This research shows that the current DFT zoo of approximations does not constitute a transparent ladder of increasingly accurate methods that consistently converges on definitive predictions for various properties of HCNO. Additional analyses are performed on the side effects of popular dispersion corrections on the covalently bonded properties and thermochemistry of HCNO.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Interaction between dissolution and precipitation during olivine carbonation: Implications for CO 2 mineralization

Large-scale carbonation of olivine is considered a promising approach for in situ mineral carbonation, offering a permanent and stable method for CO 2 storage. A critical aspect of this process is understanding how dissolution and precipitation interact, as this could drive fracturing and enhance further reactions. In this study, we conducted carbonation experiments on olivine using CO 2 -saturated aqueous solutions of NaHCO 3 and NaCl. Two experimental setups were used: one representing an open geochemical system and the other a closed system, corresponding to reaction-limited and flow-limited scenarios, respectively. Further, post-reaction textural analysis using scanning electron microscopy (SEM) revealed surface coatings of reaction products in the closed system, while etch pits and etch channels were prevalent in the open system. Although no direct evidence of reaction-driven fracturing was observed, etch pits and etch channels may serve as initiation points for subcritical crack formation and growth, potentially maintaining permeability and exposing new unreacted surfaces. Using linear elastic fracture mechanics (LEFM) model, we estimate that microcracks could propagate under a pressure of 0.1 GPa if reaction products accumulate within the etch pits. Our findings offer new insights into the mechanisms governing olivine carbonation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mechanically Accelerated Depolymerization of Entangled Linear Polymer Melts

Mechanical forces can enhance the chemical depolymerization of synthetic polymers when shear flow accelerates chain scission. To quantify the extent of mechanically-accelerated scission, the effect of simple shear flow (duration and strength) with low Weissenberg and Deborah numbers was investigated by considering the impact of applied work in both simple shear and shear dominated mixed flows. Hydrogenated polyisoprene was chosen as a model linear, entangled system. The conditions (strain amplitude, frequency, and shearing time) necessary to increase chain scission were assessed in the rubbery melt. Shear flow accelerated chain scission at higher temperatures, suggesting an activated process. Isothermal scission versus work curves were superposed by applying shift factors a T,S , whose Arrhenius-like temperature dependence gave an apparent activation energy for chain scission of ~ 110 kJ/mol, which is likely a combination of the activation energy of viscosity and bond energy. This work provides a base for quantifying the impact of shear on depolymerization of polymer melts and highlight the connection between viscous dissipation and scission chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Uncovering the binding nature of thiocyanate in contact ion pairs with lithium ions

Ion pair formation is a fundamental molecular process that occurs in a wide variety of systems, including electrolytes, biological systems, and materials. In solution, the thiocyanate (SCN–) anion interacts with cations to form contact ion pairs (CIPs). Due to its ambidentate nature, thiocyanate can bind through either its sulfur or nitrogen atoms, depending on the solvent. This study focuses on the binding nature of thiocyanate with lithium ions as a function of the solvents using FTIR, 2D infrared spectroscopy (2DIR) spectroscopies, and theoretical calculations. The study reveals that the SCN– binding mode (S or N end) in CIPs can be identified through 2DIR spectroscopy but not by linear IR spectroscopy. Linear IR spectroscopy shows that the CN stretch frequencies are too close to one another to separate N- and S-bound CIPs. Moreover, the IR spectrum shows that the S–C stretch presents different frequencies for the salt in different solvents, but it is related to the anion speciation rather than to its binding mode. A similar trend is observed for the anion bend. 2DIR spectra show different dynamics for N-bound and S-bound thiocyanate. In particular, the frequency–frequency correlation function (FFCF) dynamics extracted from the 2DIR spectra have a single picosecond exponential decay for N-bound thiocyanate and a biexponential decay for S-bound thiocyanate, consistent with the binding mode of the anion. Lastly, it is also observed that the binding mode also affects the line shape parameters, probably due to the different molecular mechanisms of the FFCF for N- and S-bound CIPs.

25 ENERGY STORAGE↗

Continuous Evolution of Eu 2+ /Eu 3+ Mixed Valency Driven by Pressure and Temperature

Continuous mixed valency involving Eu 2+ and Eu 3+ in Eu 4 Bi 6 Se 13 can be induced under applied pressure or at reduced temperatures. The monoclinic structure of Eu 4 Bi 6 Se 13 , crystallizing in the P2 1 /m space group (No. 11), features linear chains of Eu atoms aligned along the b-axis. Magnetic susceptibility measurements, conducted both parallel and perpendicular to the b-axis and analyzed using Curie–Weiss theory, alongside high-pressure partial fluorescence yield (PFY) data from X-ray absorption spectroscopy (XAS), indicate the material’s propensity to adopt a mixed-valent state. Within this state, the trivalent Eu 3+ configuration becomes increasingly favored as the pressure rises or the temperature decreases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Dynamic density functional theory of polymers with salt in electric fields

Here we present a dynamic density functional theory for modeling the effects of applied electric fields on the local structure of polymers with added salt (polymer electrolytes). Time-dependent equations for the local electrostatic potential and volume fractions of polymer, cation, and anion of added salt are developed using the principles of linear irreversible thermodynamics. For such a development, a field theoretic description of the free energy of polymer melts doped with salts is used, which captures the effects of local variations in the dielectric function. Connections of the dynamic density functional theory with experiments are established by relating the three phenomenological Onsager’s transport coefficients of the theory to the mutual diffusion of electrolyte, ionic conductivity, and transference number of one of the ions. The theory is connected with a statistical mechanical model developed by Bearman and Kirkwood [J. Chem. Phys. 28, 136 (1958)] after relating the three transport coefficients to friction coefficients. The steady-state limit of the dynamic density functional theory is used to understand the effects of dielectric inhomogeneity on the phase separation in polymer electrolytes. The theory developed here provides not only a way to connect with experiments but also to develop multi-scale models for studying connections between local structure and ion transport in polymer electrolytes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Precise Synthesis of Complex Si–Si Molecular Frameworks

In this Perspective, we highlight the emergence of target-oriented syntheses of complex molecules composed of Si–Si (oligosilanes) rather than C–C bonds. Saturated oligosilanes structurally resemble alkanes with respect to a tetrahedral geometry, a preference for a staggered conformation in linear chains, the ability to form stable small rings, and tetrahedral stereochemistry at asymmetrically functionalized Si centers. There are also critical differences, for example, differences in multiple bonding and the ability to form penta- and hexacoordinated structures, that mean that chemical reactivity and, in particular, rules for stereoselective synthesis do not cleanly translate from carbon to silicon. This Perspective will discuss recent achievements in the precise, controlled synthesis of complex molecules comprised mainly of Si–Si bonds and highlight the mechanistic insights enabling increased molecular complexity. New tools, such as electrochemical and catalytic reactions, will be discussed as well as the problem of controlling relative configuration in molecules containing multiple stereogenic-at-silicon centers. Furthermore, these synthetic achievements facilitate the discovery of new properties, including insight into light absorption, conformation, and mechanical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Identification of Carbonyl Species on Palladium Supported on Ceria in Complex Microenvironments

Herein, we present a systematic comparison between Pd carbonyl (Pd-CO) species, specifically over Pd/CeO 2 based catalysts, observed during isothermal adsorption and in several prototypical catalytic reactions to identify and understand CO adsorption on palladium-ceria based catalysts. Pd-CO is observed via DRIFTS to probe the gas-solid conditions, while ATR-IR is used to probe the affinity of Pd-CO under more complex solvated gas-solid-liquid conditions to discern the influence of the microenvironments for carbonyl adsorption. Here, we explore the presence of Pd-CO under several reactive environments, including CO adsorption, CO 2 + H 2 , CO + H 2 , CH 4 + CO 2 and CO under gas-solid-liquid media, highlighting reactions with notable Pd-CO formation. The differences between palladium carbonyls and carbonate species show that carbonyl species are much more affected via a shifting of the peak position than carbonates, which remain static irrespective of the immediate chemical environment. By following the rate of CO accumulation via K-M mode DRIFTS, we observe migration from linear, 2095 cm -1 , to bridge site, 1978 cm -1 , as a function of time under a static CO atmosphere. With the use of DFT, we discerned changes in Pd-carbonyl stretches due to both coverage effects of CO under simulated reaction conditions and temperature effects. Regardless of whether CO is formed as an intermediate or a reactant, the competitive adsorption of *H and *CO affects the binding strength of *CO at all temperatures, with low temperature favoring atop binding and high temperature favoring the more stable FCC Pd-CO site.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

MAGIC: M arching Cubes Isosurface Uncertainty Visualization for G auss i an Uncertain Data With Spatial C orrelation

Here, in this paper, we study the propagation of data uncertainty through the marching cubes algorithm for isosurface visualization for correlated uncertain data. Consideration of correlation has been shown paramount for avoiding errors in uncertainty quantification and visualization in multiple prior studies. Although the problem of isosurface uncertainty with spatial data correlation has been previously addressed, there are two major limitations to prior treatments. First, there are no analytical formulations for uncertainty quantification of isosurfaces when the data uncertainty is characterized by a Gaussian distribution with spatial correlation. Second, as a consequence of the lack of analytical formulations,existing techniques resort to a Monte Carlo sampling approach, which is expensive and difficult to integrate into visualization tools. To address these limitations, we present a closed-form framework to efficiently derive uncertainty in marching cubes level-sets for Gaussian uncertain data with spatial correlation (MAGIC). To derive closed-form solutions, we leverage the Hinkley's derivation on the ratio of Gaussian distributions. With our analytical framework, we achieve a significant speed-up and enhanced accuracy of uncertainty quantification over classical Monte Carlo methods. We further accelerate our analytical solutions using many-core processors to achieve speed-ups up to 585× and integrability with production visualization tools for broader impact. We demonstrate the effectiveness of our correlation-aware uncertainty framework through experiments on meteorology, urban flow, and astrophysics simulation datasets.

Gaussian↗

Linear Free Energy Relationships Associated with Hydride Transfer From [(6,6'-R 2 -bpy)Re(CO) 3 H]: A Cautionary Tale in Identifying Hydrogen Bonding Effects in the Secondary Coordination Sphere

Here, six rhenium hydride complexes, [(6,6'-R 2 -bpy)Re(CO) 3 H] (bpy = 2,2'-bipyridine, R = OEt, OMe, NHMe, Me, F, Br), were synthesized. These complexes insert CO 2 to form rhenium formate complexes of the type [(6,6'-R 2 -bpy)Re(CO) 3 {OC(O)H}]. All the rhenium formate species were characterized using X-ray crystallography, which revealed that the bpy ligand is not coplanar with the metal coordination plane containing the two nitrogen donors of the bpy ligand but tilted. A solid-state structure of [(6,6'-Me 2 -bpy)Re(CO) 3 H] determined using MicroED also featured a tilted bpy ligand. The kinetics of CO 2 insertion into complexes of the type [(6,6'-R 2 -bpy)Re(CO) 3 H] were measured experimentally and the thermodynamic hydricities of [(6,6'-R 2 -bpy)Re(CO) 3 H] species were determined using theoretical calculations. A Brønsted plot constructed using the experimentally determined rate constants for CO 2 insertion and the calculated thermodynamic hydricities for [(6,6'-R 2 -bpy)Re(CO) 3 H] revealed a linear free energy relationship (LFER) between thermodynamic and kinetic hydricity. This LFER is different to the previously determined relationship for CO 2 insertion into complexes of the type [(4,4'-R 2 -bpy)Re(CO) 3 H]. At a given thermodynamic hydricity, CO 2 insertion is faster for complexes containing a 6,6'-substituted bpy ligand. This is likely in part due to the tilting observed for systems with 6,6'-substituted bpy ligands. Notably, the 6,6'-(NHMe) 2 -bpy ligand could in principle stabilize the transition state for CO 2 insertion via hydrogen bonding. This work shows that if only the rate of CO 2 insertion into [(6,6'-(NHMe) 2 -bpy)Re(CO) 3 H] is compared to [(4,4'-R 2 -bpy)Re(CO) 3 H] systems, the increase in rate could be easily attributed to hydrogen bonding, but in fact all 6,6'-substituted systems lead to faster than expected rates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Binding the Power of Cycloaddition and Cross-Coupling in a Single Mechanism: An Unexpected Bending Journey to Radical Chemistry of Butadiynyl with Conjugated Dienes

What if an experiment could combine the power of cycloaddition and cross-coupling with the in situ formation of an aromatic molecule in a single collision? Crossed molecular beam experiments augmented with electronic structure and statistical calculations provided compelling evidence on a novel radical route involving 1,3-butadiynyl (HCCCC; X 2 Σ + ) radicals synthesizing (substituted) arylacetylenes in the gas phase upon reactions with 1,3-butadiene (CH 2 CHCHCH 2 ; X 1 Ag) and 2-methyl-1,3-butadiene (isoprene; CH 2 C(CH 3 )CHCH 2 ; X 1 A'). Furthermore, this elegant mechanism de facto merges two previously disconnected concepts of cross-coupling and cycloaddition–aromatization in a single collision event via the formation of two new C(sp 2 )–C(sp 2 ) bonds and bending the 180° moiety of the linear 1,3-butadiynyl radical out of the ordinary by 60° to 120°. In addition to its importance to fundamental organic chemistry, this unconventional mechanism links two previously separated routes of gas-phase molecular mass growth processes of polyacetylenes and polycyclic aromatic hydrocarbons (PAHs), respectively, in low-temperature environments such as in cold molecular clouds like the Taurus Molecular Cloud (TMC-1) and in hydrocarbon-rich atmospheres of planets and their moons such as Titan, what revises the established understanding of low-temperature molecular mass growth processes in the Universe.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Shallow Rate-Redox Potential Scaling in Aqueous Molecular Oxygen Reduction Electrocatalysis Across a Family of Iron Macrocycles

Rate-overpotential scaling relationships have been employed widely to understand trends in oxygen reduction reaction (ORR) electrocatalysis by dissolved metal macrocycles in organic electrolytes. Similar scaling relationships remain unknown for surface-adsorbed ORR electrocatalysts in the acidic aqueous environments germane to proton-exchange membrane (PEM) fuel cells. Herein, we examine ORR catalysis in aqueous perchloric acid media for a structurally diverse array of iron macrocycle complexes adsorbed on Vulcan carbon black. The macrocycles encompass Fe– N 4 , Fe–N 2 N' 2 and Fe–N x C 4-x motifs bearing pyrrolic, pyridinic, and N-heterocyclic carbene (NHC) moieties in the primary ligation sphere, giving rise to a 670 mV range in Fe(III/II) redox potentials, E Fe(III/II) . Experimental Tafel data in the micropolarization regime were extrapolated to the E Fe(III/II) to furnish estimated per-site-normalized current density (j per-site ) values that span ~4.6 orders of magnitude across the family of compounds. Despite the structural diversity of this family of compounds, extrapolated j per-site values correlate with the Fe(III/II) redox potentials in a roughly log-linear fashion with a shallow scaling factor of approximately 145 mV/decade. Further, these findings highlight that negative shifts in E Fe(III/II) lead to diminishing returns in catalytic rate promotion and suggest that changes to the primary ligating environment in a macrocycle are insufficient to break fundamental rate-potential scaling relationships in aqueous ORR catalysis. Together these studies motivate the further development of higher-potential iron complexes that employ motifs beyond the equatorial ligation plane to enhance ORR catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Coupling of Nondegenerate Topological Modes in Nitrogen Core-Doped Graphene Nanoribbons

Nitrogen core-doping of graphene nanoribbons (GNRs) allows trigonal planar carbon atoms along the backbone of GNRs to be substituted by higher-valency nitrogen atoms. The excess valence electrons are injected into the π-orbital system of the GNR, thereby changing not only its electronic occupation but also its topological properties. We have observed this topological change by synthesizing dilute nitrogen core-doped armchair GNRs with a width of five atoms (N 2 -5-AGNRs). The incorporation of pairs of trigonal planar nitrogen atoms results in the emergence of topological boundary states at the interface between doped and undoped segments of the GNR. These topological boundary states are offset in energy by approximately ΔE = 300 meV relative to the topological end states at the termini of finite 5-AGNRs. Scanning tunneling microscopy (STM) and spectroscopy (STS) reveal that for finite GNRs the two types of topological states can interact through a linear combination of orbitals, resulting in a pair of asymmetric hybridized states. This behavior is captured by an effective Hamiltonian of nondegenerate diatomic molecules, where the analogous interatomic hybridization interaction strength is tuned by the distance between GNR topological modes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Galactic echoes

Gaia has revealed a variety of substructures in the phase space of stars in the Solar neighbourhood, including the vertical ‘Snail’ $(z, v_z)$ in space. Such substructures are often interpreted as the incompletely phase-mixed response of the disc stars to a single perturbation, such as an impulsive encounter with a satellite galaxy. In this paper, we consider the possibility that such structures contain manifestations of phase-space echoes. First established in plasma physics in the 1960s, echoes arise when a collisionless system is perturbed twice: the macroscopic responses to both perturbations mix to small scales in phase space, whereupon they couple non-linearly, producing a third macroscopic ‘echo’ response without the need for a third perturbation. We derive the galactic analogue of the plasma echo theory using angle-action variables and apply it to a one-dimensional model of vertical motion in the Milky Way. We verify the predicted echo behaviour using idealized test particle simulations, both with and without the inclusion of diffusion through orbital scattering off molecular clouds. While we conclude that the Gaia Snail itself is unlikely a (pure) echo effect, the basic physics we uncover is sufficiently generic that we expect phase-space echoes to be common in disc galaxies.

Galaxy: evolution↗

Fermi’s Golden Rule Rate Expression for Transitions Due to Nonadiabatic Derivative Couplings in the Adiabatic Basis

Starting from a general molecular Hamiltonian expressed in the basis of adiabatic electronic and nuclear position states, where a compact and complete expression for the nonadiabatic derivative coupling (NDC) Hamiltonian term is obtained, we provide a general analysis of the Fermi’s golden rule (FGR) rate expression for nonadiabatic transitions between adiabatic states. We then consider a quasi-adiabatic approximation that uses crude adiabatic states and NDC couplings, both evaluated at the minimum potential energy configuration of the initial adiabatic state, for the definition of the zeroth and first-order terms of the Hamiltonian. Although the application of this approximation is rather limited, it allows deriving a general FGR rate expression without further approximation while accounting for non-Condon contribution to the FGR rate arising from momentum operators of NDC terms and its coupling with vibronic displacements. For a generic and widely used model where all nuclear degrees of freedom and environmental effects are represented as linearly coupled harmonic oscillators, we derive a closed-form FGR rate expression that requires only Fourier transform. The resulting rate expression includes quadratic contributions of NDC terms and their couplings to Franck–Condon modes, which require evaluation of two additional bath spectral densities in addition to the conventional one that appears in a typical FGR rate theory based on the Condon approximation. Model calculations for the case where nuclear vibrations consist of both a sharp high-frequency mode and an Ohmic bath spectral density illustrate new features and implications of the rate expression. We then apply our theoretical expression to the nonradiative decay from the first excited singlet state of azulene, which illustrates the utility and implications of our theoretical results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantum Time Dynamics Mediated by the Yang–Baxter Equation and Artificial Neural Networks

Quantum computing shows great potential, but errors pose a significant challenge. This study explores new strategies for mitigating quantum errors using artificial neural networks (ANNs) and the Yang–Baxter equation (YBE). Unlike traditional error mitigation methods, which are computationally intensive, we investigate artificial error mitigation. We developed a novel method that combines ANNs for noise mitigation combined with the YBE to generate noisy data. This approach effectively reduces noise in quantum simulations, enhancing the accuracy of the results. The YBE rigorously preserves quantum correlations and symmetries in spin chain simulations in certain classes of integrable lattice models, enabling effective compression of quantum circuits while retaining linear scalability with the number of qubits. This compression facilitates both full and partial implementations, allowing the generation of noisy quantum data on hardware alongside noiseless simulations using classical platforms. By introducing controlled noise through the YBE, we enhance the data set for error mitigation. We train an ANN model on partial data from quantum simulations, demonstrating its effectiveness in mitigating errors in time-evolving quantum states, providing a scalable framework to enhance quantum computation fidelity, particularly in noisy intermediate-scale quantum (NISQ) systems. We demonstrate the efficacy of this approach by performing quantum time dynamics simulations using the Heisenberg XY Hamiltonian on real quantum devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗