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At least 577 records · Page 32

Review–From LiMn 2 O 4 to Partially-Disordered Li 2 MnNiO 4 : The Evolution of Lithiated-Spinel Cathodes for Li-Ion Batteries

This personal narrative relates to the discovery in 1981 of stoichiometric LiM 2 O 4 spinel electrodes (where M = metal cation) for lithium-ion batteries by the Goodenough group at Oxford University, UK, and the subsequent identification and evolution of stable lithiated-spinel Li 2 M 2 O 4 (or LiMO 2 ) cathodes at the Council for Scientific and Industrial Research in South Africa and Argonne National Laboratory (USA). In this work, the competition that occurs between the formation of lithiated-spinel and layered (LiMO 2 ) structures at 400 °C, and recent efforts to design high-capacity, Mn-rich composite cathodes with partial disorder, are discussed. The paper is written in honor of John Goodenough's 100th birthday.

25 ENERGY STORAGE↗

Learning Only on Boundaries: A Physics-Informed Neural Operator for Solving Parametric Partial Differential Equations in Complex Geometries

Recently, deep learning surrogates and neural operators have shown promise in solving partial differential equations (PDEs). However, they often require a large amount of training data and are limited to bounded domains. In this work, we present a novel physics-informed neural operator method to solve parameterized boundary value problems without labeled data. By reformulating the PDEs into boundary integral equations (BIEs), we can train the operator network solely on the boundary of the domain. This approach reduces the number of required sample points from $O(N^d)$ to $O(N^{d-1}$), where $d$ is the domain’s dimension, leading to a significant acceleration of the training process. Additionally, our method can handle unbounded problems, which are unattainable for existing physics-informed neural networks (PINNs) and neural operators. Finally, our numerical experiments show the effectiveness of parameterized complex geometries and unbounded problems.

97 MATHEMATICS AND COMPUTING↗

Measuring Nd(III) Solution Concentration in the Presence of Interfering Er(III) and Cu(II) Ions: A Partial Least Squares Analysis of Ultraviolet–Visible Spectra

Optical spectroscopy is a powerful characterization tool with applications ranging from fundamental studies to real-time process monitoring. However, it can be difficult to apply to complex samples that contain interfering analytes which are common in processing streams. Multivariate (chemometric) analysis has been examined for providing selectivity and accuracy to the analysis of optical spectra and expanding its potential applications. Here we will discuss chemometric modeling with an in-depth comparison to more simplistic analysis approaches and outline how chemometric modeling works while exploring the limits on modeling accuracy. Understanding the limitations of the chemometric model can provide better analytical assessment regarding the accuracy and precision of the analytical result. This will be explored in the context of UV–Vis absorbance of neodymium (Nd 3+ ) in the presence of interferents, erbium (Er 3+ ) and copper (Cu 2+ ) under conditions simulating the liquid–liquid extraction approach used to recycle plutonium (Pu) and uranium (U) in used nuclear fuel worldwide. Finally, the selected chemometric model, partial least squares regression, accurately quantifies Nd 3+ with a low percentage error in the presence of interfering analytes and even under conditions that the training set does not describe.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Partial wet oxidation of dairy manure as a pretreatment process to produce acetic acid ‘a Source Growth of Methanogens’

Wet oxidation can be an effective process for the pretreatment of complex biomass such as lignocellulose. However, studies on the use of wet oxidation for treating solid waste such as dairy manure are limited. The use of partial wet oxidation to convert dairy manure into low molecular weight carboxylic acids as final products were investigated. This work focuses on the performance of the sub-critical wet oxidation treatment of dairy cattle manure as a conversion/pretreatment process to release matter from the lignocellulosic fraction rather than a destructive process. The operating conditions were controlled at the short residence time and optimal temperature in the presence of oxygen under a pressure of 120 psi. The thermal hydrolysis under wet oxidation significantly affected conversion manure slurry into organic acids. The concentration of acetic acid reached 1778 mg L –1 , achieved at 190°C (60 minutes reaction time) as the reaction temperature increased within the range of 150°C–200°C, total organic carbon was reduced and monomers in the process liquids decreased. On the other hand, soluble COD in process liquids increased with an increment in reaction temperature. The results provide insights into technical options to pretreat dairy manure to improve biochemical conversion yield.

09 BIOMASS FUELS↗

X-ray computed tomography using partially coherent Fresnel diffraction with application to an optical fiber

A reconstruction algorithm for partially coherent x-ray computed tomography (XCT) including Fresnel diffraction is developed and applied to an optical fiber. The algorithm is applicable to a high-resolution tube-based laboratory-scale x-ray tomography instrument. The computing time is only a few times longer than the projective counterpart. The algorithm is used to reconstruct, with projections and diffraction, a tilt series acquired at the micrometer scale of a graded-index optical fiber using maximum likelihood and a Bayesian method based on the work of Bouman and Sauer. The inclusion of Fresnel diffraction removes some reconstruction artifacts and use of a Bayesian prior probability distribution removes others, resulting in a substantially more accurate reconstruction.

Levine, Zachary H. (ORCID:000000029928276X)↗

A multiresolution adaptive wavelet method for nonlinear partial differential equations

We report the multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to solve partial differential equations (PDEs) with features evolving on a wide range of spatial and temporal scales. To meet these challenges, we present a multiresolution wavelet algorithm to solve PDEs with significant data compression and explicit error control. We discretize in space by projecting fields and spatial derivative operators onto wavelet basis functions. We provide error estimates for the wavelet representation of fields and their derivatives. Then, our estimates are used to construct a sparse multiresolution discretization which guarantees the prescribed accuracy. Additionally, we embed a predictor-corrector procedure within the temporal integration to dynamically adapt the computational grid and maintain the accuracy of the solution of the PDE as it evolves. We present examples to highlight the accuracy and adaptivity of our approach.

97 MATHEMATICS AND COMPUTING↗

Characterization of Partial Charge Collection Induced by Neutron Damage in High-Purity Germanium Detectors

This paper investigates the correlation of damage induced by neutron interactions and degradation in the spectra of HPGe detectors. As neutrons kinetically interact with germanium crystals, they create interstitial and vacancy defects within the lattice. These defects then interfere with the charge migration of electron-hole pairs and reduce resolution in the observed energy spectrum. The partial charge collection produces observable spectral changes by increasing the peak width and reducing resolution (full width half maximum). A detailed characterization using various check sources was performed before and after iterations of neutron exposure in order to observe the effects of the neutron damage. An additional set of measurements was performed along with characterizations to show the detector’s response at discrete locations on the HPGe crystal. This was done to observe how the spectrum changes when the gamma rays are isolated to regions of various thicknesses of germanium. In order to impart damage, the detector was placed inside a californium shuffler with the face of the detector against the guide tube for the 252 Cf source. For irradiation of the HPGe, the source was then positioned in front of the face of the detector using the stepper motor of the shuffler. The neutron exposure time intervals were recorded and increased based on the initial damage observed. An MCNP simulation was performed to estimate the amount of interactions that occurred in the germanium crystal to ensure enough damage had occurred. Studying the effects that neutron damage imparts on a bullet-type HPGe detector can help provide necessary data to estimate total neutron exposure limits, reduce the likelihood of decisions made on suspect data, and aid in diagnostics of a damaged detector.

36 MATERIALS SCIENCE↗

Characterization of Partially Observed Epidemics - Application to COVID-19

This report documents a statistical method for the "real-time" characterization of partially observed epidemics. Observations consist of daily counts of symptomatic patients, diagnosed with the disease. Characterization, in this context, refers to estimation of epidemiological parameters that can be used to provide short-term forecasts of the ongoing epidemic, as well as to provide gross information for the time-dependent infection rate. The characterization problem is formulated as a Bayesian inverse problem, and is predicated on a model for the distribution of the incubation period. The model parameters are estimated as distributions using a Markov Chain Monte Carlo (MCMC) method, thus quantifying the uncertainty in the estimates. The method is applied to the COVID-19 pandemic of 2020, using data at the country, provincial (e.g., states) and regional (e.g. county) levels. The epidemiological model includes a stochastic component due to uncertainties in the incubation period. This model-form uncertainty is accommodated by a pseudo-marginal Metropolis-Hastings MCMC sampler, which produces posterior distributions that reflect this uncertainty. We approximate the discrepancy between the data and the epidemiological model using Gaussian and negative binomial error models; the latter was motivated by the over-dispersed count data. For small daily counts we find the performance of the calibrated models to be similar for the two error models. For large daily counts the negative-binomial approximation is numerically unstable unlike the Gaussian error model. Application of the model at the country level (for the United States, Germany, Italy, etc.) generally provided accurate forecasts, as the data consisted of large counts which suppressed the day-to-day variations in the observations. Further, the bulk of the data is sourced over the duration before the relaxation of the curbs on population mixing, and is not confounded by any discernible country-wide second wave of infections. At the state-level, where reporting was poor or which evinced few infections (e.g., New Mexico), the variance in the data posed some, though not insurmountable, difficulties, and forecasts were able to capture the data with large uncertainty bounds. The method was found to be sufficiently sensitive to discern the flattening of the infection and epidemic curve due to shelter-in-place orders after around 90% quantile for the incubation distribution (about 10 days for COVID-19). The proposed model was also used at a regional level to compare the forecasts for the central and north-west regions of New Mexico. Modeling the data for these regions illustrated different disease spread dynamics captured by the model. While in the central region the daily counts peaked in the late April, in the north-west region the ramp-up continued for approximately three more weeks.

59 BASIC BIOLOGICAL SCIENCES↗

Bound Constrained Partial DifferentialEquation Inverse Problem Solution by theSemi-Smooth Newton Method

We present the mathematical derivation, software implementation details, and computational results for a semi-smooth Newton method applied to two inverse problems governed by partial differential equations with bound constraints. The two problems share mathematical structural similarities to density-based topology optimization problems. The semi-smooth Newton method provides a mesh independent solution computation for the two test problems. A key step is that the complementarity part of the necessary optimality conditions are reformulated with the use of a complementarity functionφsuch that the complementarity conditions are satisfied if and only if a zero of a nonsmooth function has been obtained. The modular finite element package MFEM is utilized for the software implementation. In addition we constructed a matrix-free Operator to enable the use of efficient Krylov subspace IterativeSolver of MFEM for the solution of our two target problems.

97 MATHEMATICS AND COMPUTING↗

Development, Implementation, and Verification of Partially-Ionized Collisional Multifluid Plasma Models in Drekar

We consider the development of multifluid models for partially ionized multispecies plasmas. The models are composed of a standard set of five-moment fluid equations for each species plus a description of electromagnetics. The most general model considered utilizes a full set of fluid equations for each charge state of each atomic species, plus a set of fluid equations for electrons. The fluid equations are coupled through source terms describing electromagnetic coupling, ionization, recombination, charge exchange, and elastic scattering collisions in the low-density coronal limit. The form of each of these source terms is described in detail, and references for required rate coefficients are identified for a diverse range of atomic species. Initial efforts have been made to extend these models to incorporate some higher-density collisional effects, including ionization potential depression and three- body recombination. Some reductions of the general multifluid model are considered. First, a reduced multifluid model is derived which averages over all of the charge states (including neutrals) of each atomic species in the general multifluid model. The resulting model maintains full consistency with the general multifluid model from which it is derived by leveraging a quasi-steady-state collisional ionization equilibrium assumption to recover the ionization fractions required to make use of the general collision models. Further reductions are briefly considered to derive certain components of a single-fluid magnetohydrodynamics (MHD) model. In this case, a generalized Ohm's law is obtained, and the standard MHD resistivity is expressed in terms of the collisional models used in the general multifluid model. A number of numerical considerations required to obtain robust implementations of these multifluid models are discussed. First, an algebraic flux correction (AFC) stabilization approach for a continuous Galerkin finite element discretization of the multifluid system is described in which the characteristic speeds used in the stabilization of the fluid systems are synchronized across all species in the model. It is demonstrated that this synchronization is crucial in order to obtain a robust discretization of the multifluid system. Additionally, several different formulations are considered for describing the electromagnetics portion of the multifluid system using nodal continuous Galerkin finite element discretizations. The formulations considered include a parabolic divergence cleaning method and an implicit projection method for the traditional curl formulation of Maxwell's equations, a purely- hyperbolic potential-based formulation of Maxwell's equations, and a mixed hyperbolic-elliptic potential-based formulation of Maxwell's equations. Some advantages and disadvantages of each formulation are explored to compare solution robustness and the ease of use of each formulation. Numerical results are presented to demonstrate the accuracy and robustness of various components of our implementation. Analytic solutions for a spatially homogeneous damped plasma oscillation are derived in order to verify the implementation of the source terms for electromagnetic coupling and elastic collisions between fluid species. Ionization balance as a function of electron temperature is evaluated for several atomic species of interest by comparing to steady-state calculations using various sets of ionization and recombination rate coefficients. Several test problems in one and two spatial dimensions are used to demonstrate the accuracy and robustness of the discretization and stabilization approach for the fluid components of the multifluid system. This includes standard test problems for electrostatic and electromagnetic shock tubes in the two-fluid and ideal shock-MHD limits, a cylindrical diocotron instability, and the GEM challenge magnetic reconnection problem. A one-dimensional simplified prototype of an argon gas puff configuration as deployed on Sandia's Z-machine is used as a demonstration to exercise the full range of capabilities associated with the general multifluid model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The battle of clean and dirty qubits in the era of partial error correction

When error correction becomes possible it will be necessary to dedicate a large number of physical qubits to each logical qubit. Error correction allows for deeper circuits to be run, but each additional physical qubit can potentially contribute an exponential increase in computational space, so there is a trade-off between using qubits for error correction or using them as noisy qubits. In this work, we look at the effects of using noisy qubits in conjunction with noiseless qubits (an idealized model for error-corrected qubits), which we call the “clean and dirty” setup. We employ analytical models and numerical simulations to characterize this setup. Numerically we show the appearance of Noise-Induced Barren Plateaus (NIBPs), i.e., an exponential concentration of observables caused by noise, in an Ising model Hamiltonian variational ansatz circuit. We observe this even if only a single qubit is noisy and given a deep enough circuit, suggesting that NIBPs cannot be fully overcome simply by error-correcting a subset of the qubits. On the positive side, we find that for every noiseless qubit in the circuit, there is an exponential suppression in the concentration of gradient observables, showing the benefit of partial error correction. Finally, our analytical models corroborate these findings by showing that observables concentrate with a scaling in the exponent related to the ratio of dirty-to-total qubits.

97 MATHEMATICS AND COMPUTING↗

Non-Intrusive Parallel-in-Time Solvers for Partial Differential Equations (Final Report)

Many time-dependent problems and simulations are often modeled using Partial Differential Equations. Traditional modeling approaches that use sequential time-stepping are reaching a bottleneck in optimizing efficiency. The Center of Applied Science and Computing at Lawrence Livermore National Laboratory extensively works on parallelizing these algorithms to leverage the increasing computational power from the growing number of processors in computer hardware. In particular, they aim to design non-intrusive algorithms that can generalize to a variety of problems and sizes without requiring additional information from or modifications on the original problems. Multigrid Reduction in Time (MGRIT) is a parallel-in-time algorithm that is designed to be non-intrusive. This project focuses on increasing the efficiency of MGRIT by approximating the coarse-grid operator using machine learning approaches as a means to find the most non-intrusive, or general, solution.

97 MATHEMATICS AND COMPUTING↗

Application of Partial Least Squares Approaches to Pyroprocessing ER Data

Multivariate approaches show promise for application to process monitoring for safeguards of pyroprocessing. Past MPACT work explored the application of Principal Component Analysis (PCA) to detect off-normal conditions in pyroprocessing electrorefiner (ER) data from in the Hot Fuel Examination Facility (HFEF) at Idaho National Laboratory (INL) known as the Scalable Pyrochemical Recycling testbed (SPyRe) ER. PCA, however, does not consider the output variables. In FY24, multivariate analysis was extended from PCA to Partial Least Squares (PLS) analysis. PLS maximizes the variance between both the input signals and output variables. In the case of this work, PLS was applied in two different manners: Predictive PLS and Discriminant PLS. Predictive PLS maximizes the covariance between the process variables of the ER and the measured U concentration from in-situ voltammetry. Discriminant PLS maximizes the covariance between the process variables and a set of training process “states” such as known off-normal conditions. By projecting into the latent variable space in PLS, the process variables can be regressed onto the outputs and predictions can be made for new data sets. In this work, by applying predictive PLS, a penalized non-linear PLS approach was able to make predictions of concentration based on test and training data and detect when operations were off-normal. However, the predictive PLS does not classify the signals to which off-normal operations are attributable. Discriminant PLS can be used to classify off-normal operations but is inadequate to properly classify specific off-normal classes like power supply faults when the Discriminant PLS model is only specifically trained to detect that off-normal class. When all faults are trained against the observation data, all three operational classes are accurately classified and distinguished. Thus, future application of latent variable techniques should not select any given method, but should use a mixture of PCA, Predictive PLS, and Discriminant PLS.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

PRIME - A Software Toolkit for the Characterization of Partially Observed Epidemics in a Bayesian Framework

PRIME is a modeling framework designed for the “real-time’” characterization and forecasting of partially observed epidemics. Characterization is the estimation of infection spread parameters using daily counts of symptomatic patients. The method is designed to help guide medical resource allocation in the early epoch of the outbreak. The estimation problem is posed as one of Bayesian inference and solved using a Markov Chain Monte Carlo technique. The framework can accommodate multiple epidemic waves and can help identify different disease dynamics at the regional, state, and country levels. We include examples using publicly available COVID-19 data.

97 MATHEMATICS AND COMPUTING↗

High-precision quantum algorithms for partial differential equations

Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for linear ordinary differential equations are well established, the best previous quantum algorithms for linear partial differential equations (PDEs) have complexity poly(1/ϵ), where ϵ is the error tolerance. By developing quantum algorithms based on adaptive-order finite difference methods and spectral methods, we improve the complexity of quantum algorithms for linear PDEs to be poly(d,log(1/ϵ)), where d is the spatial dimension. Our algorithms apply high-precision quantum linear system algorithms to systems whose condition numbers and approximation errors we bound. We develop a finite difference algorithm for the Poisson equation and a spectral algorithm for more general second-order elliptic equations.

97 MATHEMATICS AND COMPUTING↗

The battle of clean and dirty qubits in the era of partial error correction

When error correction becomes possible it will be necessary to dedicate a large number of physical qubits to each logical qubit. Error correction allows for deeper circuits to be run, but each additional physical qubit can potentially contribute an exponential increase in computational space, so there is a trade-off between using qubits for error correction or using them as noisy qubits. In this work we look at the effects of using noisy qubits in conjunction with noiseless qubits (an idealized model for error-corrected qubits), which we call the "clean and dirty" setup. We employ analytical models and numerical simulations to characterize this setup. Numerically we show the appearance of Noise-Induced Barren Plateaus (NIBPs), i.e., an exponential concentration of observables caused by noise, in an Ising model Hamiltonian variational ansatz circuit. We observe this even if only a single qubit is noisy and given a deep enough circuit, suggesting that NIBPs cannot be fully overcome simply by error-correcting a subset of the qubits. On the positive side, we find that for every noiseless qubit in the circuit, there is an exponential suppression in concentration of gradient observables, showing the benefit of partial error correction. Finally, our analytical models corroborate these findings by showing that observables concentrate with a scaling in the exponent related to the ratio of dirty-to-total qubits.

97 MATHEMATICS AND COMPUTING↗

Lowering the computational barrier: Partially Bayesian neural networks for transparency in medical imaging AI

Deep Neural Networks (DNNs) can provide clinicians with fast and accurate predictions that are highly valuable for high-stakes medical decision-making, such as in brain tumor segmentation and treatment planning. However, these models largely lack transparency about the uncertainty in their predictions, potentially giving clinicians a false sense of reliability that may lead to grave consequences in patient care. Growing calls for Transparent and Responsible AI have promoted Uncertainty Quantification (UQ) to capture and communicate uncertainty in a systematic and principled manner. However, traditional Bayesian UQ methods remain prohibitively costly for large, million-dimensional tumor segmentation DNNs such as the U-Net. In this work, we discuss a computationally-efficient UQ approach via the partially Bayesian neural networks (pBNN). In pBNN, only a single layer, strategically selected based on gradient-based sensitivity analysis, is targeted for Bayesian inference. We illustrate the effectiveness of pBNN in capturing the full uncertainty for a 7.8-million parameter U-Net. We also demonstrate how practitioners and model developers can use the pBNN's predictions to better understand the model's capabilities and behavior.

97 MATHEMATICS AND COMPUTING↗

Evaluation of partial volume correction and analysis of longitudinal [ 18 F]GTP1 tau PET imaging in Alzheimer's disease using linear mixed-effects models

Purpose: We evaluated the impact of partial volume correction (PVC) methods on the quantification of longitudinal [ 18 F]GTP1 tau positron-emission tomography (PET) in Alzheimer's disease and the suitability of describing the tau pathology burden temporal trajectories using linear mixed-effects models (LMEM). Methods: We applied van Cittert iterative deconvolution (VC), 2-compartment, and 3-compartment, and the geometric transfer matrix plus region-based voxelwise methods to data acquired in an Alzheimer's disease natural history study over 18 months at a single imaging site. We determined the optimal PVC method by comparing the standardized uptake value ratio change (%ΔSUVR) between diagnostic and tau burden–level groups and the longitudinal repeatability derived from the LMEM. The performance of LMEM analysis for calculating %ΔSUVR was evaluated in a natural history study and in a multisite clinical trial of semorinemab in prodromal to mild Alzheimer's disease by comparing results to traditional per-visit estimates. Results: The VC, 2-compartment, and 3-compartment PVC methods had similar performance, whereas region-based voxelwise overcorrected regions with a higher tau burden. The lowest within-subject variability and acceptable group separation scores were observed without PVC. The LMEM-derived %ΔSUVR values were similar to the per-visit estimates with lower variability. Conclusion: The results indicate that the tested PVC methods do not offer a clear advantage or improvement over non-PVC images for the quantification of longitudinal [ 18 F]GTP1 PET data. LMEM offers a robust framework for the longitudinal tau PET quantification with low longitudinal test–retest variability. Clinical trial registration: NCT02640092 and NCT03289143.

60 APPLIED LIFE SCIENCES↗