Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Learning theory”

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 1,513 records · Page 84
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Accurate prediction of global-density-dependent range-separation parameters based on machine learning

In this work, we develop an accurate and efficient XGBoost machine learning model for predicting the global-density-dependent range-separation parameter, ωGDD, for long-range corrected functional (LRC)-ωPBE. This ωGDDML model has been built using a wide range of systems (11 466 complexes, ten different elements, and up to 139 heavy atoms) with fingerprints for the local atomic environment and histograms of distances for the long-range atomic correlation for mapping the quantum mechanical range-separation values. The promising performance on the testing set with 7046 complexes shows a mean absolute error of 0.001 117 a0−1 and only five systems (0.07%) with an absolute error larger than 0.01 a0−1, which indicates the good transferability of our ωGDDML model. In addition, the only required input to obtain ωGDDML is the Cartesian coordinates without electronic structure calculations, thereby enabling rapid predictions. LRC-ωPBE(ωGDDML) is used to predict polarizabilities for a series of oligomers, where polarizabilities are sensitive to the asymptotic density decay and are crucial in a variety of applications, including the calculations of dispersion corrections and refractive index, and surpasses the performance of all other popular density functionals except for the non-tuned LRC-ωPBE. Finally, LRC-ωPBE (ωGDDML) combined with (extended) symmetry-adapted perturbation theory is used in calculating noncovalent interactions to further show that the traditional ab initio system-specific tuning procedure can be bypassed. The present study not only provides an accurate and efficient way to determine the range-separation parameter for LRC-ωPBE but also shows the synergistic benefits of fusing the power of physically inspired density functional LRC-ωPBE and the data-driven ωGDDML model.

Chemistry↗
NASA NTRS1995

The AAMP5/AAMP-FV project

This presentation describes a project, formal verification of the microcode in the AAMP5 microprocessor, conducted to explore how formal techniques for specification and verification could be introduced into an industrial process. Sponsored by the Systems Validation Branch of NASA Langley and by Collins Commercial Avionics, a division of Rockwell International, it was conducted by Collins and the SRI International Computer Science Laboratory. The project consisted of specifying in the PVS language developed by SRI a portion of a Rockwell proprietary microprocessor, the AAMP5, at both the instruction set and register-transfer levels and using the PVS theorem prover to prove the microcode correct for a representative subset of instructions. While this presentation includes a brief technical overview, its emphasis is on the lessons learned in using PVS for an example of this size and the implications for using formal methods in an industrial setting. The central result of this project was to demonstrate the feasibility of formally specifying a commercial microprocessor and the use of mechanical proofs of correctness to verify microcode. This is particularly significant since the AAMP5 was not designed for formal verification, but to provide a more than three fold performance improvement, by pipelining instruction execution, while remaining object code compatible with the earlier AAMP2. As a consequence, the AAMP5 is one of the most complex microprocessors to which formal methods have been applied. Another key result was the discovery of both actual and seeded errors. Two actual microcode errors were discovered and corrected during development of the formal specification, illustrating the value of simply creating a precise specification. Two seeded errors were systematically uncovered while doing correctness proofs. One of these was an actual error that had been discovered after first fabrication but left in the microcode provided to SRI. The other error was designed to be unlikely to be detected by walkthroughs, testing, or simulation. Several other results emerged during the project, including the ease with which practicing engineers became comfortable with PVS, the need for libraries of general purpose theories, the usefulness of formal specification in revealing errors, the natural fit between formal specification and inspections, the difficulty of selecting the best style of specification for a new problem domain, the high level of assurance provided by proofs of correctness, and the need to engineer proof strategies for reuse.

Miller, Steven P.↗
NASA NTRS1999

Its a Wind, Its a Wave, Its Two Phenomena in One: Jerry Schubert, Superrotation, and the UV Markings on Venus

In the early 1970's, ground-based astronomers had already discovered that Ultraviolet (UV) cloud markings on Venus reappeared every 4 days. When radar evidence later revealed a 243-day rotation period for the solid planet, planetary scientists were faced with a quandary: Could the Venus atmosphere really move 60 times as fast as the planet below, or were the apparent movements of the UV features just an illusion caused by propagating waves? The former explanation seemed unlikely - a planet that hardly rotates should generate only a very sluggish circulation. The historical impact of Jerry Schubert's moving flame theory was twofold: It was the forerunner of current thermal tide explanations of the cloud-level superrotation, but it was also the first plausible mechanism for explaining a seemingly inconsistent set of observations. In 1974, Mariner 10 acquired UV images of the Venus clouds at unprecedented levels of detail. Although few have noted it, this began the shift of planetary atmospheric research primarily from the domain of astronomy to that of meteorology. Jerry was among the first scientists to apply terrestrial meteorology to the analysis of planetary data. At that time a young UCLA graduate student with plans to do research on mantle convection, but having flunked the solid earth geophysics section of his departmental comprehensive exam, was gently invited by Jerry to switch to atmospheric science. Jerry suggested that the Venus UV features could be revealing both superrotating winds and planetary-scale waves at the same time, and that we could distinguish the two by looking at motions on different spatial scales. This was my first science research lesson - the complexity of real geophysical systems. Over the next couple of years I was inculcated with Jerry's philosophy of a comprehensive, rigorous approach to research, which manifested itself as a scouring of the literature and the UCLA meteorology faculty to learn about every possible type of planetary-scale wave. The resulting identification of large-scale UV features on Venus as the product of Kelvin and Rossby-type wave motions was validated by extensive Pioneer Venus observations a decade later and remains one of the best examples of the use of terrestrial knowledge to understand other planets.

DelGenio, Anthony↗
DOE OSTI2021

Nonintuitive Surface Self-Assembly of Functionalized Molecules on Ag(111)

The fabrication of nanomaterials involves selfordering processes of functional molecules on inorganic surfaces. To obtain specific molecular arrangements, a common strategy is to equip molecules with functional groups. However, focusing on the functional groups alone does not provide a comprehensive picture. Especially at interfaces, processes that govern self-ordering are complex and involve various physical and chemical effects, often leading to unexpected structures, as we showcase here on the example of a homologous series of quinones on Ag(111). Naively, one could expect that such quinones, which all bear the same functionalization, form similar motifs. In salient contrast, our joint theoretical and experimental study shows that profoundly different structures are formed. Using a machine-learning-based structure search algorithm, we find that this is due to a shift of the balance of three antagonizing driving forces: adsorbate-substrate interactions governing adsorption sites, adsorbate-adsorbate interactions favoring close packing, and steric hindrance inhibiting certain otherwise energetically beneficial molecular arrangements. The theoretical structures show excellent agreement with our experimental characterizations of the organic/ inorganic interfaces, both for the unit cell sizes and the orientations of the molecules within. The nonintuitive interplay of similarly important interaction mechanisms will continue to be a challenging aspect for the design of functional interfaces. With a detailed examination of all driving forces, we are, however, still able to devise a design principle for self-assembly of functionalized molecules.

structure prediction↗
DOE OSTI2021

Communication-Avoiding and Memory-Constrained Sparse Matrix-Matrix Multiplication at Extreme Scale

Sparse matrix-matrix multiplication (SpGEMM) is a widely used kernel in various graph, scientific computing and machine learning algorithms. In this paper, we consider SpGEMMs performed on hundreds of thousands of processors generating trillions of nonzeros in the output matrix. Distributed SpGEMM at this extreme scale faces two key challenges: (1) high communication cost and (2) inadequate memory to generate the output. Furthermore, we address these challenges with an integrated communication-avoiding and memory-constrained SpGEMM algorithm that scales to 262,144 cores (more than 1 million hardware threads) and can multiply sparse matrices of any size as long as inputs and a fraction of output fit in the aggregated memory. As we go from 16,384 cores to 262,144 cores on a Cray XC40 supercomputer, the new SpGEMM algorithm runs 10x faster when multiplying large-scale protein-similarity matrices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Artificial intelligence-driven approaches for materials design and discovery

Materials design is an important component of modern science and technology, yet traditional approaches rely heavily on trial and error and can be inefficient. Computational techniques, enhanced by modern artificial intelligence, have reshaped the landscape of designing new materials. Among these approaches, inverse design has shown great promise in designing materials that meet specific property requirements. Here, in this Review, we present key computational advances in materials design over the past few decades. We follow the evolution of relevant materials design techniques, from high-throughput forward machine learning methods and evolutionary algorithms, to advanced artificial intelligence strategies such as reinforcement learning and deep generative models. We highlight the paradigm shift from conventional screening approaches to inverse generation driven by deep generative models. Finally, we discuss current challenges and future perspectives of materials inverse design. This Review may serve as a brief guide to the approaches, progress and outlook of designing future functional materials with technological relevance.

computational methods↗
DOE OSTI2025

Certifying almost all quantum states with few single-qubit measurements

Certifying that an n -qubit state synthesized in the laboratory is close to a given target state is a fundamental task in quantum information science. However, existing rigorous protocols applicable to general target states have potentially prohibitive resource requirements in the form of either deep quantum circuits or exponentially many single-qubit measurements. Here we prove that almost all n -qubit target states, including those with exponential circuit complexity, can be certified from only O ( n 2 ) single-qubit measurements. Given access to the target state’s amplitudes, our protocol requires only O ( n 3 ) classical computation. This result is established by a technique that relates certification to the mixing time of a random walk. Our protocol has applications for benchmarking quantum systems, for optimizing quantum circuits to generate a desired target state and for learning and verifying neural networks, tensor networks and various other representations of quantum states using only single-qubit measurements. We show that such verified representations can be used to efficiently predict highly non-local properties of a synthesized state that would otherwise require an exponential number of measurements on the state. We demonstrate these applications in numerical experiments with up to 120 qubits and observe an advantage over existing methods such as cross-entropy benchmarking.

information theory and computation↗
DOE OSTI2023

Hybrid physics-based and machine learning tools for materials assessment

In this work, we develop novel physics-based and machine learning computational techniques to predict fundamental properties of metallic systems that affect radiation damage behavior in reactor structural materials. Oftentimes, atomistic predictions of engineering alloys simplify chemical compositions to a single element to reduce computational cost and complexity, introducing large sources of uncertainty and potentially missing important behavior. In addition, engineering alloys such as SS 316 are particularly challenging to simulate with first principles methods because of the additional degrees of freedom introduced by magnetic natures of the constituent elements, and very little data of this type exists within the literature. These novel methods aim to improve the qualitative prediction of radiation damage in engineering alloys by more accurately simulating their compositions, both by accelerating the computations and by developing novel analyses.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS2007

The Business Case for Automated Software Engineering

Adoption of advanced automated SE (ASE) tools would be more favored if a business case could be made that these tools are more valuable than alternate methods. In theory, software prediction models can be used to make that case. In practice, this is complicated by the 'local tuning' problem. Normally. predictors for software effort and defects and threat use local data to tune their predictions. Such local tuning data is often unavailable. This paper shows that assessing the relative merits of different SE methods need not require precise local tunings. STAR 1 is a simulated annealer plus a Bayesian post-processor that explores the space of possible local tunings within software prediction models. STAR 1 ranks project decisions by their effects on effort and defects and threats. In experiments with NASA systems. STARI found one project where ASE were essential for minimizing effort/ defect/ threats; and another project were ASE tools were merely optional.

model evaluation↗
DOE OSTI2023

Department of Energy’s Atmospheric System Research (ASR) Program’s Workshop on the Future of Atmospheric Large Eddy Simulation (LES): Workshop Report

Large-eddy simulation (LES) is used as a tool to understand physical processes such as turbulence, aerosols, clouds, precipitation, radiation, the interactions among all these, and their interactions with the underlying surface. Over the next 10 years, LES will drive fundamental progress in open scientific questions in these areas as LES is increasingly used to gain understanding of complex interacting physical processes involving atmospheric turbulence. This growth will be driven both by scientific demand and the expansion of computational resources needed to conduct LES, and the form that the growth takes will largely be determined by how computational resources are leveraged for scientific gain. In particular, we suggest that computational resources are likely to be leveraged in two separate but not necessarily distinct ways. On one hand, growth in computational resources will allow LES to be made more routine, that is, performed more frequently, while on the other hand, the computational expense (measured in total floating point operations) afforded to individual LES will expand dramatically, allowing simulations to increase in both domain size and resolution as well as physical detail. Current U.S. Department of Energy (DOE) projects such as LES ARM Symbiotic Simulation and Observation Activity (LASSO) are leading the way in conducting routine LES, building large, public databases that are accessible for data science, sensitivity studies, and training for machine learning. LES will also become more routine as it becomes more accessible for individual researchers to address their scientific questions of interest. Scientific questions addressed by LES over the next 10 years are likely to include cloud organization and aggregation; aerosol cloud interactions and atmospheric chemistry (including geo-engineering); urban-scale LES; atmospheric extreme events, ranging from small-scale severe weather to wildfires; and ocean-wave-atmosphere interactions. Further LES-related research will likely grow significantly in areas related to societal impact studies of air quality and extreme weather events, applications to renewable energy forecasting and resource assessment, and aid in decision-making processes. The growth in the use of LES in atmospheric science research will drive the need for better physical process representations (e.g., cloud aerosol microphysics, radiation, and atmospheric chemistry) at the scales resolved by LES. To date, many of the process representations used by LES have been taken directly from coarser-resolution models. Promising methods for LES process representations include superdroplet and quadrature methods for microphysics, 3D approaches for radiation, and better representation of chemistry and aerosol processes. At LES resolution, land-atmosphere interactions for complex terrains, land cover/types, biogeochemistry, and plant canopy models are needed as an improvement beyond traditional and widely used Monin-Obuhkov similarity theory.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Multi-scale, Multi-disciplinary, and Multi-agent Explainable AI with Koopman-Undergirded Learning, Prediction, and Analysis (M3EA KULPA) (Project Closeout Report)

The goal of this project was to develop and use domain-aware machine learning formulations, based on the Koopman Operator (KO), for modelling multi-scale, multi-disciplinary (e.g., multi-physics), and/or multi-agent systems. The project developed these formulations for the following cases: • Systems with dynamics at two separate time scales, • Systems with a bi-level hierarchical control structure, • Systems with bi-level hierarchical control and dynamics at two separate time scales (the lower level controls operating at the faster time scale), and • Systems with n separate but interacting agents/disciplines (with/without control, respectively); the controls for each agent could include bi-level hierarchical control and dynamics at two separate time scales as described above. The project then defined a set of dynamical systems consisting of different nonlinear oscillators that could be used to test these different formulations and then subsequently learned the KO models for those systems. With the KO models, we were able to do the following: • Quantify system stability, including both long-term and transient behavior, • Quantify the effects of feedbacks between the different time scales and agents/disciplines in terms of those feedbacks’ effects on system stability, • Replace a standard Proportional-Integral (PI) control in the hierarchical control structure with a KO-based Linear-Quadratic Regular (LQR), a form of optimal control, • Calculate optimal supervisory control policies a) with and without time scale separated dynamics at the lower level control levels and b) with both PI and KO-based LQR lower level control policies, and • Calculate dynamic Nash equilibria for multi-agent systems where each agent makes its own control decisions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Greedy emulators for nuclear two-body scattering

Applications of reduced basis method emulators are increasing in low-energy nuclear physics because they enable fast and accurate sampling of high-fidelity calculations, enabling robust uncertainty quantification. Here, in this paper, we develop, implement, and test two model-driven emulators based on the (Petrov-)Galerkin projection using the prototypical test case of two-body scattering with the Minnesota potential and a more realistic local chiral potential. The high-fidelity scattering equations are solved with the matrix Numerov method, a reformulation of the popular Numerov recurrence relation for solving special second-order differential equations as a linear system of coupled equations. A novel error estimator based on reduced-space residuals is applied to an active learning approach (a greedy algorithm) to choosing training samples (“snapshots”) for the emulator and contrasted with a proper orthogonal decomposition (POD) approach. Both approaches allow for computationally efficient offline-online decompositions, but the greedy approach requires many fewer snapshot calculations. These developments set the groundwork for emulating scattering observables based on chiral nucleon-nucleon and three-nucleon interactions and optical models, where computational speed-ups are necessary for Bayesian uncertainty quantification. Our emulators and error estimators are widely applicable to linear systems.

Bayesian methods↗
DOE OSTI2022

Estimating the randomness of quantum circuit ensembles up to 50 qubits

Random quantum circuits have been utilized in the contexts of quantum supremacy demonstrations, variational quantum algorithms for chemistry and machine learning, and blackhole information. The ability of random circuits to approximate any random unitaries has consequences on their complexity, expressibility, and trainability. To study this property of random circuits, we develop numerical protocols for estimating the frame potential, the distance between a given ensemble and the exact randomness. Our tensor-network-based algorithm has polynomial complexity for shallow circuits and is high-performing using CPU and GPU parallelism. We study 1. local and parallel random circuits to verify the linear growth in complexity as stated by the Brown–Susskind conjecture, and; 2. hardware-efficient ansätze to shed light on its expressibility and the barren plateau problem in the context of variational algorithms. Our work shows that large-scale tensor network simulations could provide important hints toward open problems in quantum information science.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Transferable dispersion-aware machine learning interatomic potentials for multilayer transition metal dichalcogenide heterostructures

Stacking atomically thin transition metal dichalcogenides (TMDs) into heterostructures enables exploration of exotic quantum phases, particularly through twist-angle-controlled moiré superlattices. These structures exhibit novel electronic and optical behaviors driven by atomic-scale structural reconstruction. However, studying such systems with DFT is computationally demanding due to their large unit cells and van der Waals (vdW) interactions between layers. To address this, we develop a transferable neural network potential (NNP) that includes long-range vdW corrections up to 12Å with minimal overhead. Trained on vdW-corrected DFT data for Mo- and W-based TMDs with S, Se, and Te, the NNP accurately models monolayers, bilayers, heterostructures, and their interaction with h-BN substrates. It reproduces equilibrium structures, energy landscapes, phonon dispersions, and matches experimental atomic reconstructions in twisted WS2 and MoS2/WSe2 systems. We demonstrate that our NNP achieves DFT-level accuracy and high computational efficiency, enabling large-scale simulations of TMD-based moiré superlattices both with and without substrates.

materials for energy and catalysis↗
DOE OSTI2022

Neural network acceleration of large-scale structure theory calculations

Here, we make use of neural networks to accelerate the calculation of power spectra required for the analysis of galaxy clustering and weak gravitational lensing data. For modern perturbation theory codes, evaluation time for a single cosmology and redshift can take on the order of two seconds. In combination with the comparable time required to compute linear predictions using a Boltzmann solver, these calculations are the bottleneck for many contemporary large-scale structure analyses. Here, we construct neural network-based surrogate models for Lagrangian perturbation theory (LPT) predictions of matter power spectra, real and redshift space galaxy power spectra, and galaxy-matter cross power spectra that attain ~ 0.1% (at one sigma) accuracy over a broad range of scales in a ωCDM parameter space. The neural network surrogates can be evaluated in approximately one millisecond, a factor of 1000 times faster than the full Boltzmann code and LPT computations. In a simulated full-shape redshift space galaxy power spectrum analysis, we demonstrate that the posteriors obtained using our surrogates are accurate compared to those obtained using the full LPT model. We make our surrogate models public at https://github.com/sfschen/EmulateLSS, so that others may take advantage of the speed gains they provide to enable rapid iteration on analysis settings, something that is essential in complex contemporary large-scale structure analyses.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2019

High-Performance Computing Optimization for Aladyn – Adaptive Neural Network Molecular Dynamics Mini-Application

This report provides a description and performance evaluation of the optimization techniques for high performance computing (HPC) implementation of the open source Computational Materials mini-application Aladyn (https://github.com/nasa/aladyn). Aladyn is a basic molecular dynamics code written in FORTRAN 2003, which is designed to demonstrate the use of adaptive neural networks (ANNs) in atomistic simulations. The role of ANNs is to efficiently reproduce the very complex energy landscape resulting from the atomic interactions in materials with the accuracy of the more expensive quantum mechanics-based calculations. The ANN is trained on a large set of atomic structures calculated using the density functional theory (DFT) method. While achieving orders of magnitude faster computational performance than DFT, the ANN-based approach was still very computationally demanding compared to the conventional approach of using empirically fitted energy functions. After its initial development, Aladyn was evaluated and optimized by experts at the NASA Advanced Supercomputing (NAS) division to exploit modern supercomputer architectures. The code has been optimized for execution on multicore central processing units (CPUs), including Intel® Skylake microarchitecture, and on graphic accelerators, such as Nvidia® V100 graphic processing units (GPUs), using Open Multi-Processing (OpenMP) and Open Accelerators (OpenACC) programming interfaces. The optimization achieved a speedup of 4.7 times the baseline version on CPU performance and an additional 2.4 times on CPU+GPU performance. Atomistic computer simulations are a fundamental tool in materials research to model material properties form physics-based first principles. Atomic interaction, governed by Quantum Mechanics (QM) require sophisticated and highly computationally demanding mathematical models to calculate [1]. Classical methods use approximate functional forms, empirically fitted through a set of variable parameters to emulate atomic energies as direct functions of atomic coordinates [2]. While empirical potentials are computationally much simpler, allowing simulations of large-scale systems of up to a trillion (1012) atoms [3], they are substantially less accurate compared to quantum calculations and applicable only to very specific atomic configurations or predefined crystallographic phases. A recently suggested approach is to use heuristic machine learning methods [4], such as those based on Adaptive Neural Networks (ANNs) to predict atomic energies, after being trained on a sufficiently large database of QM-calculated structures [5,6]. This approach reduces significantly the computational complexity, allowing for simulations of orders of magnitude larger systems compared to QM-based methods without compromising accuracy. Still, compared to classical methods using empirical energy functions, ANN methods remain two- to three orders of magnitude more computationally demanding. Hence, the computational cost of simulations, together with the need for extensive training of ANNs, still makes the practical implementation of ANN-based methods quite challenging. The purpose of the Aladyn mini-application software [7], available as open source at https://github.com/nasa/aladyn, is to be a testbed for exploring possible optimization strategies to develop highly scalable parallel algorithms for ANN-based atomistic simulations. Aladyn is aimed at utilizing the architecture of the high-end modern highperformance computing (HPC) hardware based on multicore central processing units (CPUs) equipped with graphic processing unit (GPU) accelerators. Specifically, the goal is to optimize the performance on a single HPC compute node, before implementing scaling to multi-node parallelization using message passing interface (MPI). At the same time, the open source code of Aladyn can serve as a training model for students and professors in academia.

Yamakov, Vesselin I.↗
DOE OSTI2023

The Symmetry Energy: Current Status of Ab Initio Predictions vs. Empirical Constraints

Infinite nuclear matter is a suitable laboratory to learn about nuclear forces in many-body systems. In particular, modern theoretical predictions of neutron-rich matter are timely because of recent and planned experiments aimed at constraining the equation of state of isospin-asymmetric matter. For these reasons, we have taken a broad look at the equation of state of neutron-rich matter and the closely related symmetry energy, which is the focal point of this article. Its density dependence is of paramount importance for a number of nuclear and astrophysical systems, ranging from neutron skins to the structure of neutron stars. We review and discuss ab initio predictions in relation to recent empirical constraints. We emphasize and demonstrate that free-space nucleon–nucleon data pose stringent constraints on the density dependence of the neutron matter equation of state, which essentially determines the slope of the symmetry energy at saturation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Phase Diagram of a Deep Potential Water Model

Using the Deep Potential methodology, we construct a model that reproduces accurately the potential energy surface of the SCAN approximation of density functional theory for water, from low temperature and pressure to about 2400 K and 50 GPa, excluding the vapor stability region. The computational efficiency of the model makes it possible to predict its phase diagram using molecular dynamics. Satisfactory overall agreement with experimental results is obtained. Here, the fluid phases, molecular and ionic, and all the stable ice polymorphs, ordered and disordered, are predicted correctly, with the exception of ice III and XV that are stable in experiments, but metastable in the model. The evolution of the atomic dynamics upon heating, as ice VII transforms first into ice VII" and then into an ionic fluid, reveals that molecular dissociation and breaking of the ice rules coexist with strong covalent fluctuations, explaining why only partial ionization was inferred in experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗