Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Reduce order modeling”

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 1,261 records · Page 70
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Exotic Phases of a Higgs-Yukawa Model with Reduced Staggered Fermions

We investigate the phase structure of a four dimensional SO(4) invariant lattice Higgs-Yukawa model comprising four reduced staggered fermions interacting with a real scalar field. The fermions belong to the fundamental representation of the symmetry group while the three scalar field components transform in the self-dual representation of SO(4). We explore the phase diagram and find evidence of a continuous transition between a phase where the fermions are massless to one where the fermions acquire mass. This transition is not associated with symmetry breaking and there is no obvious local order parameter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Direct Recycling R&D at the ReCell Center

The expected rapid growth in electric vehicle deployment will inevitably be followed by a corresponding rise in the supply of end-of-life vehicles and their lithium-ion batteries (LIBs). The batteries may be reused, but will eventually be spent and provide a potential domestic resource that can help supply materials for future battery production. However, commercial recycling processes depend on profits from recovery of cobalt, use of which is being reduced in new cathode chemistries. The U.S. Department of Energy, therefore, established the ReCell Center in early 2019 to develop robust LIB recycling technology that would be economical even for batteries that contain no cobalt. The central feature of the technology is recovery of the cathode material with its unique crystalline cathode morphology intact in order to retain its value and functionality. Other materials are recovered as well in order to maximize revenues and minimize waste-handling costs. Analysis and modeling serve to evaluate and compare process options so that we can identify those that will be most economical while still minimizing energy use and environmental impacts. This paper provides background and describes highlights of the center’s first 2 years of operation.

Gaines, Linda (ORCID:0000000237263387)↗
DOE OSTI2021

Modernizing the active neutron collar poison rod correction using simulations to enhance PWR fresh fuel verification

The declared inventory of 235 U in fresh, low enriched uranium, nuclear fuel assemblies is routinely verified by nuclear safeguards inspectorates using the UNCL (Uranium Neutron Collar – Light Water Reactor Fuel) nondestructive assay instrument. The trend in modern fuels is towards higher initial enrichment, which in turn requires a larger number of burnable poison pins with higher Gadolinia concentration to hold down the initial reactivity. UNCL assay error for modern fuel assemblies typically exceeds 10%. The traditional algorithm used to correct the response for burnable poison content needs revision to achieve accuracy comparable to the $\sigma_\text{R}$ of 4.5% expected for poison-free assemblies. Here we review the problem and use a large set of 287 Monte Carlo simulations based on an experimentally benchmarked model corresponding to the 16×16 PWR array used in Brazilian Angra type II and III fuel. Simulated relative responses are used to evaluate the functional form of the poison correction and determine parameters optimal for 16×16 PWR assemblies. This update is conducted using between 4–24 Gadolinia pins ranging 2–11 wt% Gd 2 O 3 with assemblies having mean enrichments ranging 2.5%–5%. Experimental validation of the updated coefficients using seven measurements shows bias is reduced by an order of magnitude and $\sigma_\text{R}$R reduced from 10% to less than 2%. Two updated sets of coefficients are provided, the most accurate of which is directly useable in the existing analysis code (INCC) in use by inspectorate at fuel fabrication facilities.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Correlation-aware binning for small-angle neutron scattering via Gaussian-process inference

Binning in small-angle neutron scattering (SANS) is typically performed empirically, with fixed parameters chosen for convenience rather than statistical optimality. Such practices often fail to balance statistical precision and spatial resolution, leading to inconsistencies across instruments and datasets. Here we establish a correlation-aware framework that determines the optimal bin width from first principles by extending the classical Freedman–Diaconis (FD) rule to account for inter-bin correlations with a Gaussian process. In this formulation, the scattering intensity is treated as a smooth stochastic field whose statistical coherence is described by a covariance matrix. Analytical expressions of errors derived from this model yield closed-form criteria that separate the total deviation into contributions from counting noise, aliasing distortion and curvature-dependent correlation effects. Expressed in reduced variables, the resulting dimensionless error surface reveals a continuous transition from the uncorrelated FD regime to the correlation-dominated limit, providing a unified description of noise suppression and resolution control. Because the formulation depends only on the profile characteristics of scattering intensity I(Q), specifically its average intensity and first- and second-order derivatives, it applies generally to any SANS measurement regardless of sample, instrument or geometry. Experimental validation using small- and ultra-small-angle neutron scattering data confirms the predicted scaling behavior, demonstrating that correlation-aware inference systematically reduces mean-squared error and enables information-efficient reproducible data reduction across materials and instruments.

Tung, Chi-Huan [ORNL] (ORCID:0000000221972074)↗
DOE OSTI2025

Two-Dimensional Silk Crystal Films as Matrix Layer for High-Performance Microelectronics

This study explores a bio-inspired approach for memristive devices by combining Keggin-type polyoxometalates (POMs)-[SiW 12 O 40 ] 4 (POM-T) and [PW 12 O 40 ] 3 (POM-P), with silk fibroin (SF) to create 2D SF–POM layers on highly ordered pyrolytic graphite (HOPG) as resistive switching layers for memristors. We propose that the ordered SF layer template 0D POMs facilitate the formation of conductive filaments, thereby enhancing the variability of the manufactured memristors. AFM analysis revealed that both SF and SF–POM layers shared similar morphologies, while SF–POM–T formed larger aggregates, likely due to the stronger acidity of POM-T, which probably caused SF to aggregate and alter its secondary structure. Scanning Kelvin probe microscopy (SKPM) revealed that POMs reduced the contact potential difference of HOPG, resulting in lower work functions. Compared to an SF device, the SF–POM–P device showed improved memristive behavior, with a larger current gap and good repeatability over multiple sweeps; whereas the SF–POM–T device did not exhibit memristor activity, likely due to acidity-induced disruption of the SF template’s order and CF formation. More importantly, SF–POM–P devices also demonstrated programmable memristive states. Finally, combining simulation-driven memristor modeling, we showcase a co-design workflow for advancing bioinspired memristors through new materials design, synthesis, and device modeling and development.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Quantum simulations of hadron dynamics in the Schwinger model using 112 qubits

Hadron wave packets are prepared and time evolved in the Schwinger model using 112 qubits of IBM’s 133-qubit Heron quantum computer ibm_torino. The initialization of the hadron wave packet is performed in two steps. First, the vacuum is prepared across the whole lattice using the recently developed SC-ADAPT-VQE algorithm and workflow. SC-ADAPT-VQE is then extended to the preparation of localized states, and used to establish a hadron wave packet on top of the vacuum. This is done by adaptively constructing low-depth circuits that maximize the overlap with an adiabatically prepared hadron wave packet. Due to the localized nature of the wavepacket, these circuits can be determined on a sequence of small lattices using classical computers, and then robustly scaled to prepare wave packets on large lattices for simulations using quantum computers. Time evolution is implemented with a second-order Trotterization. To reduce both the required qubit connectivity and circuit depth, an approximate quasilocal interaction is introduced. This approximation is made possible by the emergence of confinement at long distances, and converges exponentially with increasing distance of the interactions. Using multiple error-mitigation strategies, up to 14 Trotter steps of time evolution are performed, employing 13,858 two-qubit gates (with a CNOT depth of 370). The propagation of hadrons is clearly identified, with results that compare favorably with Matrix Product State simulations. Finally, prospects for a near-term quantum advantage in simulations of hadron scattering are discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

AI-accelerated protein-ligand docking for SARS-CoV-2 is 100-fold faster with no significant change in detection

Protein-ligand docking is a computational method for identifying drug leads. The method is capable of narrowing a vast library of compounds down to a tractable size for downstream simulation or experimental testing and is widely used in drug discovery. While there has been progress in accelerating scoring of compounds with artificial intelligence, few works have bridged these successes back to the virtual screening community in terms of utility and forward-looking development. We demonstrate the power of high-speed ML models by scoring 1 billion molecules in under a day (50 k predictions per GPU seconds). We showcase a workflow for docking utilizing surrogate AI-based models as a pre-filter to a standard docking workflow. Our workflow is ten times faster at screening a library of compounds than the standard technique, with an error rate less than 0.01% of detecting the underlying best scoring 0.1% of compounds. Our analysis of the speedup explains that another order of magnitude speedup must come from model accuracy rather than computing speed. In order to drive another order of magnitude of acceleration, we share a benchmark dataset consisting of 200 million 3D complex structures and 2D structure scores across a consistent set of 13 million “in-stock” molecules over 15 receptors, or binding sites, across the SARS-CoV-2 proteome. We believe this is strong evidence for the community to begin focusing on improving the accuracy of surrogate models to improve the ability to screen massive compound libraries 100 × or even 1000 × faster than current techniques and reduce missing top hits. The technique outlined aims to be a fast drop-in replacement for docking for screening billion-scale molecular libraries.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Toward more accurate adiabatic connection approach for multireference wavefunctions

A multiconfigurational adiabatic connection (AC) formalism is an attractive approach to compute the dynamic correlation within the complete active space self-consistent field and density matrix renormalization group (DMRG) models. Practical realizations of AC have been based on two approximations: (i) fixing one- and two-electron reduced density matrices (1- and 2-RDMs) at the zero-coupling constant limit and (ii) extended random phase approximation (ERPA). This work investigates the effect of removing the “fixed-RDM” approximation in AC. The analysis is carried out for two electronic Hamiltonian partitionings: the group product function- and the Dyall Hamiltonians. Exact reference AC integrands are generated from the DMRG full configuration interaction solver. Two AC models are investigated, employing either exact 1- and 2-RDMs or their second-order expansions in the coupling constant in the ERPA equations. Calculations for model molecules indicate that lifting the fixed-RDM approximation is a viable way toward improving the accuracy of existing AC approximations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Time–connectivity superposition and the gel/glass duality of weak colloidal gels

Colloidal gels result from the aggregation of Brownian particles suspended in a solvent. Gelation is induced by attractive interactions between individual particles that drive the formation of clusters, which in turn aggregate to form a space-spanning structure. We study this process in aluminosilicate colloidal gels through time-resolved structural and mechanical spectroscopy. Using the time–connectivity superposition principle a series of rapidly acquired linear viscoelastic spectra, measured throughout the gelation process by applying an exponential chirp protocol, are rescaled onto a universal master curve that spans over eight orders of magnitude in reduced frequency. This analysis reveals that the underlying relaxation time spectrum of the colloidal gel is symmetric in time with power-law tails characterized by a single exponent that is set at the gel point. The microstructural mechanical network has a dual character; at short length scales and fast times it appears glassy, whereas at longer times and larger scales it is gel-like. These results can be captured by a simple three-parameter constitutive model and demonstrate that the microstructure of a mature colloidal gel bears the residual skeleton of the original sample-spanning network that is created at the gel point. Our conclusions are confirmed by applying the same technique to another well-known colloidal gel system composed of attractive silica nanoparticles. The results illustrate the power of the time–connectivity superposition principle for this class of soft glassy materials and provide a compact description for the dichotomous viscoelastic nature of weak colloidal gels.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Accurate shear estimation with fourth-order moments

ABSTRACT As imaging surveys progress in exploring the large-scale structure of the Universe through the use of weak gravitational lensing, achieving sub-per cent accuracy in estimating shape distortions caused by lensing, or shear, is imperative for precision cosmology. In this paper, we extend the Fourier power function shapelets (FPFS) shear estimator using fourth-order shapelet moments and combine it with the original second-order shear estimator to reduce galaxy shape noise. We calibrate this novel shear estimator analytically to a sub-per cent level-accuracy using the AnaCal framework. This higher order shear estimator is tested with realistic image simulations, and after analytical correction for the detection/selection bias and noise bias, the multiplicative shear bias $|m|$ is below $3\times 10^{-3}$ (99.7 per cent confidence interval) for both isolated and blended galaxies. Once combined with the second-order FPFS shear estimator, the shape noise is reduced by $\sim 35~{{\ \rm per\ cent}}$ for isolated galaxies in simulations with Hyper Suprime-Cam and Vera C. Rubin Observatory Legacy Survey of Space and Time observational conditions. However, for blended galaxies, the effective number density does not significantly improve with the combination of the two estimators. Based on these results, we recommend exploration of how this framework can further reduce the systematic uncertainties in shear due to point spread function leakage and modelling error, and potentially provide improved precision in shear inference in high-resolution space-based images.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Suppression of Deflecting Forces in Planar-Symmetric Dielectric Wakefield Accelerating Structures with Elliptical Bunches

Wakefield based accelerators capable of accelerating gradients two orders of magnitude higher than present accelerators offer a path to compact high energy physics instruments and light sources. However, for high gradient accelerators, beam instabilities driven by commensurately high transverse wakefields limit beam quality. It has been previously theoretically shown that transverse wakefields can be reduced by elliptically shaping the transverse sizes of beams in dielectric structures with planar symmetry. We report here experimental measurements that demonstrate reduced transverse wakefields for elliptical beams in planar symmetric structures which are consistent with theoretical models. Furthermore, these results may enable the design of gigavolt-per-meter gradient wakefield based accelerators that produce and stably accelerate high quality beams.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Module-OT: A Hardware Security Module for Operational Technology

Increased penetration levels of renewable energy and other types of distributed energy resources (DERs) on the modern electric grid-combined with technological advancements for electric system monitoring and control-introduce new cyberattack vectors and increase the cyberattack surface of energy systems. According to the IEEE Std. 1547-2018, DERs must use Modbus, Distributed Network Protocol 3 (DNP3), or Smart Energy Profile 2.0 (SEP2) as their communication protocol. Previous research identified several vulnerabilities and security breaches in each one of these communication protocols; despite this, existing standards for DERs do not recommend cybersecurity measures. In order to reduce vulnerabilities in power distribution systems, this paper presents a novel open-source hardware security module that improves both information and operational security to better protect data and communications on the distribution grid. The security hardware is called “module for operational technology,” or simply Module-OT, and it has been validated and tested in an emulated distribution system application. Module-OT is integrated within a communication system in the transport layer of the Open Systems Interconnection (OSI) model. It improves system security through encryption, authentication, authorization, certificate management, and user access control. The main advancement of Module-OT is the addition of hardware cryptographic acceleration that improves the overall communication performance in terms of end-to-end latency.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Scalable Risk Assessment of Rare Events in Power Systems With Uncertain Wind Generation and Loads

Risk assessment of rare events has become increasingly important in power system planning and operation with the increasing integration of renewable energy and the presence of system uncertainties. However, quantifying the risk posed by rare events via the traditional method, i.e., Monte Carlo sampling (MCS), incurs substantial computational expense stemming from the vast ensemble of power flow simulations. To accelerate the assessment, this paper proposes a Deep Neural Network (DNN)-kernelized vector-valued Gaussian Process (VVGP) approach with excellent computational efficiency while maintaining high accuracy. Consequently, serving as a surrogate model for the power flow solver, the DNN-kernelized VVGP enables significantly faster but accurate risk assessment compared to the power flow solver. The developed surrogate model evaluates low-order N - k events that contain more than 90% instances by adeptly capturing the topological features while the high-order N - k events are assessed via a power flow solver, thereby striking a balance between computational efficiency and uncertainty quantification accuracy. Moreover, the model incorporates a Support Vector Machine (SVM) classifier to resample concerning low-probability tail events to counteract the biases potentially introduced during the DNN-kernelized VVGP evaluations. Simulations conducted on the modified IEEE 24-bus, 118-bus, and European 1354-bus systems demonstrate that the proposed method maintains the accuracy benchmark set by MCS while significantly reducing computational demands in large-scale power systems as compared to other state-of-the-art methods.

17 WIND ENERGY↗
DOE OSTI2022

Emergent ferroelectricity in subnanometer binary oxide films on silicon

The critical size limit of voltage-switchable electric dipoles has extensive implications for energy-efficient electronics, underlying the importance of ferroelectric order stabilized at reduced dimensionality. Here, we report on the thickness-dependent antiferroelectric-to-ferroelectric phase transition in zirconium dioxide (ZrO 2 ) thin films on silicon. The emergent ferroelectricity and hysteretic polarization switching in ultrathin ZrO 2 , conventionally a paraelectric material, notably persists down to a film thickness of 5 angstroms, the fluorite-structure unit-cell size. This approach to exploit three-dimensional centrosymmetric materials deposited down to the two-dimensional thickness limit, particularly within this model fluorite-structure system that possesses unconventional ferroelectric size effects, offers substantial promise for electronics, demonstrated by proof-of-principle atomic-scale nonvolatile ferroelectric memory on silicon. Additionally, it is also indicative of hidden electronic phenomena that are achievable across a wide class of simple binary materials.

42 ENGINEERING↗
DOE OSTI2022

Potential for Transactive Energy to Improve the Provisioning of Grid Services from Batteries

This study assessed the degree to which transactive energy systems could help reduce or remove barriers to the deployment of battery energy storage, and realize the full potential of battery resources to supply needed services to the grid and fairly compensate various types of battery owners. To enable this assessment, typical battery deployments were characterized, along with energy markets, Federal Energy Regulatory Commission Order rulings and implementations, grid services, and current deployment barriers. Finally, this study analyzed the value that accrues to batteries supplying today’s grid services as a function of the participation models associated with three primary types of battery ownership: merchant-owned transmission-connected batteries; utility-owned distribution-connected batteries; and customer-owned behind-the-meter batteries. This provided both quantitative and qualitative assessments comparing opportunities for battery storage in business-as-usual and transactive energy scenarios.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

thornado-transport: Anderson- and GPU-accelerated nonlinear solvers for neutrino-matter coupling

Algorithms for neutrino-matter coupling in core-collapse supernovae (CCSNe) are investigated in the context of a spectral two-moment model, which is discretized in space with the discontinuous Galerkin method, integrated in time with implicit-explicit (IMEX) methods, and implemented in the toolkit for high-order neutrino-radiation hydrodynamics (thornado). The model considers electron neutrinos and antineutrinos and tabulated opacities from Bruenn (1985), which includes neutrino-electron scattering and pair processes. The nonlinear system arising from implicit time discretization of the equations governing neutrino-matter coupling is iterated to convergence using Anderson-accelerated fixed-point methods, which avoid formation of Jacobians and inversion of dense linear systems. Numerical experiments show that, for a given tolerance, a nested iteration scheme which aims to reduce opacity evaluations can lower the computational cost. Our initial port to GPUs, using both OpenMP and OpenACC, shows an overall speedup of up to ~ 100× when compared to results using a single CPU core. These results indicate that the algorithms implemented in thornado are well-suited to GPU acceleration.

Laiu, Paul↗
DOE OSTI2022

MODELING AND PARAMETRIC STUDY OF END-GAS AUTOIGNITION TO ALLOW THE REALIZATION OF ULTRA-LOW EMISSIONS, HIGH-EFFICIENCY HEAVY-DUTY SPARK-IGNITED NATURAL GAS ENGINES

Engine knock and misfire are barriers to pathways leading to high-efficiency Spark-Ignited (SI) Natural Gas (NG) engines. The general tendency to knock is highly dependent on engine operating conditions and the fuel reactivity. The problem is further complicated by the low emission limits and the wide range of chemical reactivity in pipeline-quality natural gas. Depending on the region and the source of the natural gas, its reactivity, described by its Methane Number (MN), which is analogous to the Octane Number for liquid SI fuels, can span from 65 to 95. In order to realize diesel-like efficiencies, SI NG engines must be designed to operate at high Brake Mean Effective Pressures (BMEP), near or beyond knock limits, over a wide range of fuel reactivity. This requires a deep understanding of the combustion-engine interactions pertaining to flame propagation and End-Gas Autoignition (EGAI), i.e., the autoignition of the unburned gas (end gas) ahead of the flame front. However, EGAI, if controlled, provides an opportunity to increase SI NG engine efficiency by increasing the combustion rate and the total fraction of burned fuel, mitigating the effects of the slow flame speeds characteristic of natural gas fuels, which generally reduce BMEP and increase unburned hydrocarbon emissions. For this reason, to realize diesel-like efficiencies and ultra-low emissions on SI NG engines, this work proposes the study of the main parameters influencing the modeling and prediction of NG EGAI to allow for its control. In this work, a novel EGAI detection and onset determination method was developed to reliably quantify EGAI for data analysis and engine control. The new method allowed the prediction of EGAI on SI NG engines without the need to use engine- and operating-condition-dependent thresholds and reduced the error in quantifying the fraction of the total energy released by the EGAI event by up to 40%pts. One- and three-dimensional engine models were then developed to study the engine/fuel interactions that lead to NG EGAI and its performance benefits. These models, although having decent agreement with experimental data, showed the need to account for NOx chemistry when predicting NG EGAI due to a consistently later prediction of the EGAI onset (~1.65 crank-angle degrees) and thus, a new reduced chemical mechanism for real NG fuels was developed containing NOx chemistry. The new reduced mechanism improved the EGAI onset prediction agreement to within ±0.5 crank-angle degrees and decreased simulation time during combustion by nearly 50% when using the further reduced AREIS50NOx chemical mechanism. These models were then used to study the role of NG composition on EGAI, evaluate the engine/fuel interactions leading to NG EGAI, and perform engine optimization while leveraging EGAI to increase thermal efficiency. Piston design optimization combined with a Controlled EGAI (C-EGAI) combustion mode allowed a Heavy-Duty (HD) SI NG engine to operate at diesel-like efficiencies, i.e., Brake Thermal Efficiency (BTE) ≥44%. Experimental and modeling data analysis revealed that earlier and faster heat release increases combustion efficiency by an average of 1%pts, increases work transferred to the piston resulting in a decrease in exhaust losses by 50% depending on the engine operating condition while slightly increasing heat losses. Finally, the simulation results revealed an opportunity to further enhance the BTE (up to 50%) by enabling C-EGAI combustion at leaner conditions, λ=1.4-1.6.

Bestel, Diego Bernardi↗
DOE OSTI2021

Structural and Kinetic Characterization of Hyperthermophilic NADH-Dependent Persulfide Reductase from Archaeoglobus fulgidus

NADH-dependent persulfide reductase (Npsr) has been proposed to facilitate dissimilatory sulfur respiration by reducing persulfide or sulfane sulfur-containing substrates to H2S. The presence of this gene in the sulfate and thiosulfate-reducing Archaeoglobus fulgidus DSM 4304 and other hyperthermophilic Archaeoglobales appears anomalous, as A. fulgidus is unable to respire S0 and grow in the presence of elemental sulfur. To assess the role of Npsr in the sulfur metabolism of A. fulgidus DSM 4304, the Npsr from A. fulgidus was characterized. AfNpsr is specific for persulfide and polysulfide as substrates in the oxidative half-reaction, exhibiting k cat / K m on the order of 104 M-1 s-1, which is similar to the kinetic parameters observed for hyperthermophilic CoA persulfide reductases. In contrast to the bacterial Npsr, AfNpsr exhibits low disulfide reductase activity with DTNB; however, similar to the bacterial enzymes, it does not show detectable activity with CoA-disulfide, oxidized glutathione, or cystine. The 3.1 Å X-ray structure of AfNpsr reveals access to the tightly bound catalytic CoA, and the active site Cys 42 is restricted by a flexible loop (residues 60-66) that is not seen in the bacterial homologs from Shewanella loihica PV-4 and Bacillus anthracis. Unlike the bacterial enzymes, AfNpsr exhibits NADH oxidase activity and also shows no detectable activity with NADPH. Models suggest steric and electrostatic repulsions of the NADPH 2 ′ -phosphate account for the strong preference for NADH. The presence of Npsr in the nonsulfur-reducing A. fulgidus suggests that the enzyme may offer some protection against S0 or serve in another metabolic role that has yet to be identified.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗