Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “gaussian processes”

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 1,333 records · Page 74
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

FY2021 Improvements to the New CTH Code Verification & Validation Test Suite

Over the past few years, the CTH multiphysics hydrocode has overhauled its software quality and testing processes, implementing current best practices in software quality and building a robust V&V test suite comprised of traditional hydrocode verification problems, including ASC Tri-Lab Test Suite and Enhanced Tri-Lab Test Suite problems, as well as validation problems for some of CTH’s most frequently used equations of state, materials models, and other key capabilities. Substantial progress towards building this new test suite was made in FY19 and FY20. In FY21, the test suite has been expanded to include verification and validation tests of the Steinberg-Guinan-Lund (ST) viscoplastic model and the Johnson Cook (JFRAC) fracture model. Additionally, two new verification tests were added, covering hydrodynamics and high explosive (HE) modeling capabilities: the Kidder Gaussian density problem and the Escape of HE Products (EHEP) problem from the Tri-Lab Test Suite. This report discusses each of these test problems in detail. Verification test results are compared to analytic solutions. Validation test results are compared to experimental data. Wherever possible, convergence or mesh refinement studies are included. Additionally, while implementing the Kidder verification problem, a bug was identified that affects the use of tables to initialize pressure or density in 1D or 2D calculations. A brief discussion of the bug and its fix is included. CTH demonstrates good performance overall on the new test suite problems. Simulation results showed good agreement with analytic solutions for the Kidder problem, with convergence rates ranging between 1.8 and sub-linear, and relatively good agreement for the EHEP problem, though convergence rates for pressure and density were nearly 0. The ST and JFRAC strain rate loading verification tests show good agreement with analytic solutions. Likewise, CTH simulation results show good agreement with experimental validation data, including Taylor rod impact testing, for the materials tested. Future V&V work will focus on adding 2D and 3D versions of existing verification tests as well as adding validation tests of other frequently used capabilities such as other fracture models.

42 ENGINEERING↗
DOE OSTI2020

Improving qubit readout with hidden Markov models

We demonstrate the application of pattern recognition algorithms via hidden Markov models (HMM) for qubit readout. This scheme provides a state-path trajectory approach capable of detecting qubit-state transitions and makes for a robust classification scheme with higher starting-state assignment fidelity than when compared to a multivariate Gaussian or a support vector machine scheme. Therefore, the method also eliminates the qubit-dependent readout time optimization requirement in current schemes. Using a HMM state discriminator we estimate fidelities reaching the ideal limit. Unsupervised learning gives access to transition matrix, priors, and IQ distributions, providing a toolbox for studying qubit-state dynamics during strong projective readout.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Chaotic Dynamics Driven by Particle-Core Interactions

High-intensity beams in modern linacs are frequently encircled by diffuse halos, which drive sustained particle losses and result in gradual degradation of accelerating structures. In large part, the growth of halos is facilitated by internal space-charge forces within the beams, and detailed characterization of this process constitutes an active area of ongoing research. A partial understanding of dynamics that ensue within space-charge dominated beams is presented by the particle-core interaction paradigm – a mathematical model wherein single particle dynamics, subject to the collective potential of the core, are treated as a proxy for the broader behavior of the beam. In this work, we investigate the conditions for the onset of large-scale chaos within the framework of this model, and demonstrate that the propensity towards stochastic evolution is strongly dependent upon the charge distribution of the beam. In particular, we show that while particle motion within a uniformly charged beam is dominantly regular, rapid deterministic chaos readily arises within space-charge dominated Gaussian beams. Importantly, we find that for sufficiently high values of the beam’s space charge and beam pulsation amplitude, enhanced chaotic mixing between the core and the halo can lead to an enhanced radial diffusion of charged particles. We explain our results from analytic grounds by demonstrating that chaotic motion is driven by the intersection of two principal resonances of the system, and derive the relevant overlap conditions. Additionally, our analysis illuminates a close connection between the mathematical formulation of the particle-core interaction model and the Andoyer family of integrable Hamiltonians

43 PARTICLE ACCELERATORS↗
NASA NTRS2019

An X-Ray Spectroscopic Search For Dark Matter And Unidentified Line Signatures In The Perseus Cluster With Hitomi

The reported detection of a 3.5 keV emission signal in the Perseus cluster core by Bulbulet al. (2014, ApJ, 789, 13) was ruled out at high confidence in analysis conducted by Aharonian et al. (2017, ApJ, 837, L15) of X-ray spectra at 5 eV energy resolution obtained with the Hitomi observatory Soft X-ray Spectrometer (SXS). Using the same data, we search the full 2–12 keV SXS energy band for previously unidentified emission and absorption features. No significant unidentified line emission or absorption is found. Line flux upper limits (1σper resolution element) vary with photon energy and assumed intrinsic width, decreasing from∼100 at 2 keV to<10 photons cm−2s−1sr−1over most of the 5–10 keV energy range for a Gaussian line with Doppler broadening of 640 kms−1. Limits for narrower and broader lines have a similar energy dependence and are systematically smaller and larger, respectively. These line flux limits are used to constrain the decay rate of hypothetical dark matter candidates. For the sterile neutrino decay rate, we place new constraints over the mass range of 4–24 keV with mass resolution better than any previous X-ray analysis. Additionally, the accuracy of relevant thermal spectral models and atomic data are evaluated. The Perseus cluster spectra may be described by a composite of multi-temperature thermal and active galactic nuclei (AGN) power-law continua. Superposed on these, a few line emission signals possibly originating from unmodeled atomic processes (including SiXIV and FeXXV)are marginally detected and tabulated. Comparisons with previous X-ray upper limits and future prospects for dark matter searches using high-energy resolution spectroscopy are discussed.

Takayuki Tamura↗
DOE OSTI2022

Galaxy blending effects in deep imaging cosmic shear probes of cosmology

ABSTRACT Upcoming deep imaging surveys such as the Vera C. Rubin Observatory Legacy Survey of Space and Time will be confronted with challenges that come with increased depth. One of the leading systematic errors in deep surveys is the blending of objects due to higher surface density in the more crowded images; a considerable fraction of the galaxies which we hope to use for cosmology analyses will overlap each other on the observed sky. In order to investigate these challenges, we emulate blending in a mock catalogue consisting of galaxies at a depth equivalent to 1.3 yr of the full 10-yr Rubin Observatory that includes effects due to weak lensing, ground-based seeing, and the uncertainties due to extraction of catalogues from imaging data. The emulated catalogue indicates that approximately 12 per cent of the observed galaxies are ‘unrecognized’ blends that contain two or more objects but are detected as one. Using the positions and shears of half a billion distant galaxies, we compute shear–shear correlation functions after selecting tomographic samples in terms of both spectroscopic and photometric redshift bins. We examine the sensitivity of the cosmological parameter estimation to unrecognized blending employing both jackknife and analytical Gaussian covariance estimators. An ∼0.025 decrease in the derived structure growth parameter S8 = σ8(Ωm/0.3)0.5 is seen due to unrecognized blending in both tomographies with a slight additional bias for the photo-z-based tomography. This bias is greater than the 2σ statistical error in measuring S8.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1987

Personal computer (PC) based image processing applied to fluid mechanics research

A PC based image processing system was employed to determine the instantaneous velocity field of a two-dimensional unsteady flow. The flow was visualized using a suspension of seeding particles in water, and a laser sheet for illumination. With a finite time exposure, the particle motion was captured on a photograph as a pattern of streaks. The streak pattern was digitized and processsed using various imaging operations, including contrast manipulation, noise cleaning, filtering, statistical differencing, and thresholding. Information concerning the velocity was extracted from the enhanced image by measuring the length and orientation of the individual streaks. The fluid velocities deduced from the randomly distributed particle streaks were interpolated to obtain velocities at uniform grid points. For the interpolation a simple convolution technique with an adaptive Gaussian window was used. The results are compared with a numerical prediction by a Navier-Stokes commputation.

Cho, Y.-C.↗
DOE OSTI2022

Bayesian operator inference for data-driven reduced-order modeling

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian inverse problem with Gaussian prior and likelihood. The resulting posterior distribution characterizes the operators defining the reduced-order model, hence the predictions subsequently issued by the reduced-order model are endowed with uncertainty. The statistical moments of these predictions are estimated via a Monte Carlo sampling of the posterior distribution. Since the reduced models are fast to solve, this sampling is computationally efficient. Furthermore, the proposed Bayesian framework provides a statistical interpretation of the regularization term that is present in the deterministic operator inference problem, and the empirical Bayes approach of maximum marginal likelihood suggests a selection algorithm for the regularization hyperparameters. The proposed method is demonstrated on two examples: the compressible Euler equations with noise-corrupted observations, and a single-injector combustion process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Electron energy loss spectroscopy database synthesis and automation of core-loss edge recognition by deep-learning neural networks

Abstract The ionization edges encoded in the electron energy loss spectroscopy (EELS) spectra enable advanced material analysis including composition analyses and elemental quantifications. The development of the parallel EELS instrument and fast, sensitive detectors have greatly improved the acquisition speed of EELS spectra. However, the traditional way of core-loss edge recognition is experience based and human labor dependent, which limits the processing speed. So far, the low signal–noise ratio and the low jump ratio of the core-loss edges on the raw EELS spectra have been challenging for the automation of edge recognition. In this work, a convolutional-bidirectional long short-term memory neural network (CNN-BiLSTM) is proposed to automate the detection and elemental identification of core-loss edges from raw spectra. An EELS spectral database is synthesized by using our forward model to assist in the training and validation of the neural network. To make the synthesized spectra resemble the real spectra, we collected a large library of experimentally acquired EELS core edges. In synthesize the training library, the edges are modeled by fitting the multi-Gaussian model to the real edges from experiments, and the noise and instrumental imperfectness are simulated and added. The well-trained CNN-BiLSTM network is tested against both the simulated spectra and real spectra collected from experiments. The high accuracy of the network, 94.9%, proves that, without complicated preprocessing of the raw spectra, the proposed CNN-BiLSTM network achieves the automation of core-loss edge recognition for EELS spectra with high accuracy.

36 MATERIALS SCIENCE↗
NASA NTRS2009

Multi-Modulator for Bandwidth-Efficient Communication

A modulator circuit board has recently been developed to be used in conjunction with a vector modulator to generate any of a large number of modulations for bandwidth-efficient radio transmission of digital data signals at rates than can exceed 100 Mb/s. The modulations include quadrature phaseshift keying (QPSK), offset quadrature phase-shift keying (OQPSK), Gaussian minimum-shift keying (GMSK), and octonary phase-shift keying (8PSK) with square-root raised-cosine pulse shaping. The figure is a greatly simplified block diagram showing the relationship between the modulator board and the rest of the transmitter. The role of the modulator board is to encode the incoming data stream and to shape the resulting pulses, which are fed as inputs to the vector modulator. The combination of encoding and pulse shaping in a given application is chosen to maximize the bandwidth efficiency. The modulator board includes gallium arsenide serial-to-parallel converters at its input end. A complementary metal oxide/semiconductor (CMOS) field-programmable gate array (FPGA) performs the coding and modulation computations and utilizes parallel processing in doing so. The results of the parallel computation are combined and converted to pulse waveforms by use of gallium arsenide parallel-to-serial converters integrated with digital-to-analog converters. Without changing the hardware, one can configure the modulator to produce any of the designed combinations of coding and modulation by loading the appropriate bit configuration file into the FPGA.

Gray, Andrew↗
DOE OSTI2024

Physics-based reward driven image analysis in microscopy

The rise of electron microscopy has expanded our ability to acquire nanometer and atomically resolved images of complex materials. The resulting vast datasets are typically analyzed by human operators, an intrinsically challenging process due to the multiple possible analysis steps and the corresponding need to build and optimize complex analysis workflows. We present a methodology based on the concept of a Reward Function coupled with Bayesian Optimization, to optimize image analysis workflows dynamically. The Reward Function is engineered to closely align with the experimental objectives and broader context and is quantifiable upon completion of the analysis. Here, cross-section, high-angle annular dark field (HAADF) images of ion-irradiated (Y, Dy)Ba 2 Cu 3 O 7–δ thin-films were used as a model system. The reward functions were formed based on the expected materials density and atomic spacings and used to drive multi-objective optimization of the classical Laplacian-of-Gaussian (LoG) method. These results can be benchmarked against the DCNN segmentation. This optimized LoG* compares favorably against DCNN in the presence of the additional noise. We further extend the reward function approach towards the identification of partially-disordered regions, creating a physics-driven reward function and action space of high-dimensional clustering. We pose that with correct definition, the reward function approach allows real-time optimization of complex analysis workflows at much higher speeds and lower computational costs than classical DCNN-based inference, ensuring the attainment of results that are both precise and aligned with the human-defined objectives.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

FLIT: A Generic Fortran Library based on Interfaces and Templates

This Fortran code consists of multiple modules with a focus on simplifying array operations, image processing, and numerical computation especially for computational geophysics applications. We intend to use this code to demonstrate the application and usefulness of Fortran interface and templates for generic programming, especially for computational geophysics and seismology applications. The code has several notable features. Firstly, it is based on a modularized structure, where each module contains multiple functions but with a focus of functionality. Secondly, it heavily uses interfaces and templates for improving the genericness and convenience of the resulting code, where a same function interface can enclose a group of functions that perform the same functionality but with inputs/output variables of different data types. Thirdly, it includes a variety of generic functions with an emphasis on array operations, such as rotation, flipping, cropping, padding, fast Fourier transform, Gaussian blurring, interpolation, and so on. We name this package FLIP – a generic Fortran Library based on Interfaces and Templates.

Gao, Kai↗
DOE OSTI2022

A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems

Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional O(10 n ), n ≥ 2, stochastic inputs (e.g., forcing terms, boundary conditions, initial conditions) poses tremendous challenges. The “curse of dimensionality” can be addressed with suitable unsupervised learning techniques used as a pre-processing tool to encode inputs onto lower-dimensional subspaces while retaining its structural information and meaningful properties. In this work, we review and investigate thirteen dimension reduction methods including linear and nonlinear, spectral, blind source separation, convex and non-convex methods and utilize the resulting embeddings to construct a mapping to quantities of interest via polynomial chaos expansions (PCE). Here, we refer to the general proposed approach as manifold PCE (m-PCE), where manifold corresponds to the latent space resulting from any of the studied dimension reduction methods. To investigate the capabilities and limitations of these methods we conduct numerical tests for three physics-based systems (treated as black-boxes) having high-dimensional stochastic inputs of varying complexity modeled as both Gaussian and non-Gaussian random fields to investigate the effect of the intrinsic dimensionality of input data. We demonstrate both the advantages and limitations of the unsupervised learning methods and we conclude that a suitable m-PCE model provides a cost-effective approach compared to alternative algorithms proposed in the literature, including recently proposed expensive deep neural network-based surrogates and can be readily applied for high-dimensional UQ in stochastic PDEs.

42 ENGINEERING↗
NASA NTRS1994

Constraints on Neural Mechanisms Underlying the Spatial Integration of Speed Information

We measured human ability to integrate speed information presented simultaneously at multiple locations in the visual field. Observers did a two-interval forced-choice speed discrimination task with n grating patches in each interval at 4' eccentricity from fixation. In the first (integration) paradigm, all gratings in each interval moved at the same speed and observers were asked to pick the interval containing the faster gratings. Speed discrimination improved as the number of gratings in each interval increased. The observed decrease in threshold is not due simply to an increase in the effective area because performance with a single grating two, four, or six times the area of the original grating showed no such improvement. Furthermore, the improvement with n was still observed even when the speeds of the individual gratings in each interval were independent samples from a Gaussian distribution and the grating directions were balanced (i.e. equal numbers of gratings moved to the left and right). These results indicate that the neural mechanisms responsible for the integration of speed information act as if each patch provides an independent sample of speed, independent of grating direction. The results are not consistent with simple summation across space by a directionally selective mechanism with a large receptive field. In the second (search) paradigm, only one of the gratings in an interval moved faster and observers were asked to pick this interval. In this case, thresholds increased with the number of distractor gratings. The decrease in performance with increased n is common in search tasks and is often attributed to a bottleneck in the information that observers can process simultaneously. However, the results in the integration paradigm show that subjects indeed have access to and can use additional information with increasing n, at least up to 4 patches. Finally, simple detection models predict the trends in both the search and integration paradigms without invoking an input bottleneck.

Verghese, Preeti↗
NASA NTRS1994

Constraints on Neural Mechanisms Underlying the Spatial Integration of Speed Information

We measured human ability to integrate speed information presented simultaneously at multiple locations in the visual field. Observers did a two-interval forced-choice speed discrimination task with n grating patches in each interval at 4deg eccentricity from fixation. In the first (integration) paradigm, all gratings in each interval moved at the same speed and observers were asked to pick the interval containing the faster gratings. Speed discrimination improved as the number of gratings in each interval increased. The observed decrease in threshold is not due simply to an increase in the effective area because performance with a single grating two, four, or six times the area of the original grating showed no such improvement. Furthermore, the improvement with n was still observed even when the speeds of the individual gratings in each interval were independent samples from a Gaussian distribution and the grating directions were balanced (i.e. equal numbers of gratings moved to the left and right). These results indicate that the neural mechanisms responsible for the integration of speed information act as if each patch provides an independent sample of speed, independent of grating direction. The results are not consistent with simple summation across space by a directionally selective mechanism with a large receptive field. in the second (search) paradigm, only one of the gratings in an interval moved faster and observers were asked to pick this interval. In this case, thresholds increased with the number of distractor gratings. The decrease in performance with increased n is common in search tasks and is often attributed to a bottleneck in the information that observers can process simultaneously. However, the results in the integration paradigm show that subjects indeed have access to and can use additional information with increasing n, at least up to 4 patches. Finally, simple detection models predict the trends in both the search and integration paradigms without invoking an input bottleneck.

Verghese, Preeti↗
DOE OSTI2021

Quantum kinetics of anomalous and nonlinear Hall effects in topological semimetals

Highlights: • Linear and photogalvanic anomalous Hall responses are systematically derived. • Extrinsic mechanisms of AHE include Gaussian, diffractive, hybrid skew scattering. • Diagrammatic calculations are matched to semiclassical picture of AHE. • The Pancharatnam phase of multifold fermions determines the skew scattering amplitude. • Photon-induced interband scattering are accompanied by coordinate shifts. We present a systematic microscopic derivation of the semiclassical Boltzmann equation for band structures with the finite Berry curvature based on Keldysh technique of nonequilibrium systems. In the analysis, an AC electrical driving field is kept up to quadratic order, and both cases of small and large frequencies corresponding to intra- and interband transitions are considered. In particular, this formulation is suitable for the study of nonlinear Hall effect and photogalvanic phenomena. The role of impurity scattering is carefully addressed. Specifically, in addition to previously studied side-jump and skew-scattering processes, quantum interference diffractive contributions are now explicitly incorporated within the developed framework. This theory is applied to multifold fermions in topological semimetals, for which the generic formula for the skew scattering rate from the Pancharatnam phase is obtained along with the corresponding anomalous Hall conductivity.

36 MATERIALS SCIENCE↗
NASA NTRS2004

Characterizing Oscillatory Bursts in Single-Trial EEG Data

Oscillatory bursts in numerous bands ranging from low (theta) to high frequencies (e.g., gamma) undoubtedly play an important role in cortical dynamics. Largely because of the inadequacy of existing analytic techniques. however, oscillatory bursts and their role in cortical processing remains poorly understood. To study oscillatory bursts effectively one must be able to isolate them and characterize them in the single trial. We describe a series of straightforward analysis techniques that produce useful indices of burst characteristics. First, stimulus-evoked responses are estimated using Differentially Variable Component Analysis (dVCA), and are subtracted from the single-trial. The single-trial characteristics of the evoked responses are stored to identify possible correlations with burst activity. Time-frequency (T-F), or wavelet, analyses are then applied to the single trial residuals. While T-F plots have been used in recent studies to identify and isolate bursts, we go further by fitting each burst in the T-F plot with a two-dimensional Gaussian. This provides a set of burst characteristics, such as, center time. burst duration, center frequency. frequency dispersion. and amplitude, all of which contribute to the accurate characterization of the individual burst. The burst phase can also be estimated. Burst characteristics can be quantified with several standard techniques (e.g.. histogramming and clustering), as well as Bayesian techniques (e.g., blocking) to allow a more parametric description analysis of the characteristics of oscillatory bursts, and the relationships of specific parameters to cortical excitability and stimulus integration.

Knuth, K. H.↗
DOE OSTI2023

A new approach for simulating inhomogeneous chemical kinetics

Abstract In this paper, inhomogeneous chemical kinetics are simulated by describing the concentrations of interacting chemical species by a linear expansion of basis functions in such a manner that the coupled reaction and diffusion processes are propagated through time efficiently by tailor-made numerical methods. The approach is illustrated through modelling $$\alpha$$ α - and $$\gamma$$ γ -radiolysis in thin layers of water and at their solid interfaces from the start of the chemical phase until equilibrium was established. The method’s efficiency is such that hundreds of such systems can be modelled in a few hours using a single core of a typical laptop, allowing the investigation of the effects of the underlying parameter space. Illustrative calculations showing the effects of changing dose-rate and water-layer thickness are presented. Other simulations are presented which show the approach’s capability to solve problems with spherical symmetry (an approximation to an isolated radiolytic spur), where the hollowing out of an initial Gaussian distribution is observed, in line with previous calculations. These illustrative simulations show the generality and the computational efficiency of this approach to solving reaction-diffusion problems. Furthermore, these example simulations illustrate the method’s suitability for simulating solid-fluid interfaces, which have received a lot of experimental attention in contrast to the lack of computational studies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

TurboRVB: A many-body toolkit for ab initio electronic simulations by quantum Monte Carlo

TurboRVB is a computational package for ab initio Quantum Monte Carlo (QMC) simulations of both molecular and bulk electronic systems. The code implements two types of well established QMC algorithms: Variational Monte Carlo (VMC) and diffusion Monte Carlo in its robust and efficient lattice regularized variant. A key feature of the code is the possibility of using strongly correlated many-body wave functions (WFs), capable of describing several materials with very high accuracy, even when standard mean-field approaches [e.g., density functional theory (DFT)] fail. The electronic WF is obtained by applying a Jastrow factor, which takes into account dynamical correlations, to the most general mean-field ground state, written either as an antisymmetrized geminal power with spin-singlet pairing or as a Pfaffian, including both singlet and triplet correlations. This WF can be viewed as an efficient implementation of the so-called resonating valence bond (RVB) Ansatz, first proposed by Pauling and Anderson in quantum chemistry [L. Pauling, The Nature of the Chemical Bond (Cornell University Press, 1960)] and condensed matter physics [P.W. Anderson, Mat. Res. Bull 8, 153 (1973)], respectively. The RVB Ansatz implemented in TurboRVB has a large variational freedom, including the Jastrow correlated Slater determinant as its simplest, but nontrivial case. Moreover, it has the remarkable advantage of remaining with an affordable computational cost, proportional to the one spent for the evaluation of a single Slater determinant. Therefore, its application to large systems is computationally feasible. The WF is expanded in a localized basis set. Several basis set functions are implemented, such as Gaussian, Slater, and mixed types, with no restriction on the choice of their contraction. The code implements the adjoint algorithmic differentiation that enables a very efficient evaluation of energy derivatives, comprising the ionic forces. Thus, one can perform structural optimizations and molecular dynamics in the canonical NVT ensemble at the VMC level. For the electronic part, a full WF optimization (Jastrow and antisymmetric parts together) is made possible, thanks to state-of-the-art stochastic algorithms for energy minimization. In the optimization procedure, the first guess can be obtained at the mean-field level by a built-in DFT driver. The code was efficiently parallelized by using a hybrid MPI-OpenMP protocol, which is also an ideal environment for exploiting the computational power of modern Graphics Processing Unit accelerators.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗