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NASA NTRS2008

Assessments of Hollow Cathode Wear in the Xenon Ion Propulsion System (XIPs(c)) by Numerical Analyses and Wear Tests

The standard approach presently followed by NASA to qualify electric propulsion for the required mission throughput has been based largely on life tests, which can be costly and time consuming. Revised electric propulsion lifequalification approaches are being formulated that combine analytical and/or computational methods with (shorter-duration) wear tests. As a model case, a wear test is being performed at JPL to assess the lifetime of the discharge hollow cathode in the Xenon Ion Propulsion System (XIPS(c)), a 25-cm ion engine developed by L-3 Communications Electron Technologies, Inc. for commercial applications. Wear and plasma data accumulated throughout this life-assessment program are being used to validate the existing 2-D hollow cathode code OrCa2D. We find that the OrCa2D steady-state solution predicts very well the time-averaged plasma data and the keeper voltage after 5500 hrs of operation in high-power mode. When the wave motion that occurs naturally in these devices is accounted for, based on an estimate of the maximum wave amplitude, the molybdenum-keeper erosion profile observed in the XIPS(c) discharge cathode is also reproduced within a factor of two of the observation. When the same model is applied to predict the erosion of a tantalum keeper we find that erosion is reduced by more than two orders of magnitude compared to the molybdenum keeper due the significantly lower sputtering yield of tantalum. A tantalum keeper would therefore allow keeper lifetimes that greatly exceed the present requirements for deep-space robotic missions considered by NASA. Moreover, such large reduction of the erosion renders the largest uncertainties in the models, which are associated with the wave amplitude estimates and the electron transport model, negligible.

plasma simulations↗

DOE OSTI2026

Numerical Water Tracers in the Atmospheric Component of the Energy Exascale Earth System Model: Implementation and Changes in Moisture Origin

Numerical water tracers are implemented in the Energy Exascale Earth System Model version 2. Simulations performed with the water‐tag‐enabled model for both pre‐industrial and future greenhouse gas concentrations reveal a marked increase in the role of mid‐latitude and southern subtropical regions as exporters of atmospheric moisture—to the extratropical upper troposphere and the tropical free troposphere. For the latter, the northward shift of the Intertropical Convergence Zone increases cross‐hemispheric transport of subtropical water vapor to the Northern Hemisphere. In the polar regions, most of the lower tropospheric moistening instead arises from increases in local evaporation. These findings illustrate the utility of the water tags, underscore critical changes in global hydrologic cycle, and provide insight into atmospheric dynamics under future climate scenarios. For applications when a global grid is desired, we additionally propose a novel statistical reconstruction, based on copula modeling, of the joint distribution of origin of water vapor, which reduces the number of tracers from order $\mathcal{O}\left({n}^{2}\right)$to order $\mathcal{O}(n)$, substantially ameliorating the considerable computational cost of water tracers. This statistical reconstruction is particularly beneficial to the interpretation of the relationship between latitude and longitude of origin of moisture over the tropical oceans and in the lower troposphere over land.

copula modeling↗

DOE OSTI2022

Towards Compact Neural Networks via End-to-End Training: A Bayesian Tensor Approach with Automatic Rank Determination

Post-training model compression can reduce the inference costs of deep neural networks, but uncompressed training still consumes enormous hardware resources and energy. To enable low-energy training on edge devices, it is highly desirable to directly train a compact neural network from scratch with a low memory cost. Low-rank tensor decomposition is an effective approach to reduce the memory and computing costs of large neural networks. However, directly training low-rank tensorized neural networks is a very challenging task because it is hard to determine a proper tensor rank a priori, and the tensor rank controls both model complexity and accuracy. Here, this paper presents a novel end-to-end framework for low-rank tensorized training. We first develop a Bayesian model that supports various low-rank tensor formats (e.g., CANDECOMP/PARAFAC, Tucker, tensor-train, and tensor-train matrix) and reduces neural network parameters with automatic rank determination during training. Then we develop a customized Bayesian solver to train large-scale tensorized neural networks. Our training methods shows orders-of-magnitude parameter reduction and little accuracy loss (or even better accuracy) in the experiments. On a very large deep learning recommendation system with over 4.2 ×10 9 model parameters, our method can reduce the parameter number to 1.6 ×10 5 automatically in the training process (i.e., by 2.6 ×10 4 times) while achieving almost the same accuracy. Code is available at https://github.com/colehawkins/bayesian-tensor-rank-determination.

compact neural networks↗

DOE OSTI2013

MODELING OF HIGH SPEED FRICTION STIR SPOT WELDING USING A LAGRANGIAN FINITE ELEMENT APPROACH

Friction stir spot welding (FSSW) has been shown to be capable of joining steels of very high strength, while also being very flexible in terms of controlling the heat of welding and the resulting microstructure of the joint. This makes FSSW a potential alternative to resistance spot welding (RSW) if tool life is sufficiently high, and if machine spindle loads are sufficiently low so that the process can be implemented on an industrial robot. Robots for spot welding can typically sustain vertical loads of about 8kN, but FSSW at tool speeds of less than 3000 rpm cause loads that are too high, in the range of 11-14 kN. Therefore, in the current work tool speeds of 3000 rpm and higher were employed, in order to generate heat more quickly and to reduce welding loads to acceptable levels. The FSSW process was modeled using a finite element approach with the Forge® software package. An updated Lagrangian scheme with explicit time integration was employed to model the flow of the sheet material, subjected to boundary conditions of a rotating tool and a fixed backing plate [3]. The modeling approach can be described as two-dimensional, axisymmetric, but with an aspect of three dimensions in terms of thermal boundary conditions. Material flow was calculated from a velocity field which was two dimensional, but heat generated by friction was computed using a virtual rotational velocity component from the tool surface. An isotropic, viscoplastic Norton-Hoff law was used to model the evolution of material flow stress as a function of strain, strain rate, and temperature. The model predicted welding temperatures and the movement of the joint interface with reasonable accuracy for the welding of a dual phase 980 steel.

Advanced High strength steel↗

DOE OSTI2020

Multiphase Reacting Flow Simulations and Optimization of Commercial-Scale Aerobic Bioreactors

Aerobic bioreactors are widely used in the synthesis of value-added products in pharmaceutical and biotechnology industries, wherein microbial bioreactions aid in the conversion of sugars to macromolecules. These reactors are also being actively investigated as a cost-effective pathway for the production of low-value commodities such as biofuels and animal feed. Reactor scale-up is one of the important challenges when designing these systems. Gas and liquid phase transport, mass-transfer, and mixing physics at large length scales can significantly affect microbial conversion rates, particularly when the microbial reaction requires a narrow set of conditions. These phenomena are difficult to study in small-scale bench-top reactors that are typically well-mixed. Predictive computational fluid dynamics (CFD) based simulations can therefore aid in the design and optimization of these reactors. This work presents multiphase Euler-Euler CFD simulations of commercial-scale (~ 500 m3) aerobic bioreactors. Our mathematical model treats the gas and liquid as interpenetrating phases. This approach reduces the computational complexity of tracking individual gas bubbles that are several orders of magnitude smaller than reactor dimensions. We solve the Reynolds averaged Navier-Stokes (RANS) multiphase equations that account for phase and chemical species transport, interphase mass and momentum transfer and uses a phenomenological model for oxygen uptake by microbes. We use a customized solver derived from open-source CFD toolbox, OpenFOAM, to perform these simulations, which has been validated against small-scale reactors in our previous work. This work examines the performance of three different reactor designs, viz. bubble column reactor, airlift reactor with an internal draft tube, and a stirred-tank reactor with Rushton impellers. Reactor oxygen mass-transfer coefficient, gas hold-up, and oxygen distribution are critically analyzed among reactors, and sensitivity studies pertaining to gas flow rates and reactor geometry will be presented.

09 BIOMASS FUELS↗

DOE OSTI2023

Gas-Liquid Flow Modeling for Renewable Fuels Production

Aerobic/anaerobic and gas fermentation pathways have emerged as promising new technologies for the generation of renewable fuels/chemicals from biomass derived sugars, and mixtures of greenhouse/energy rich gas streams (CO2/CH4/H2/CO) via microbial action. Example pathways include sugars-to-ethanol conversion, biomethanation (CO2/H2 to CH4), biogas upgrading, CO fermentation and wet-waste conversion. Gas and liquid phase transport, mass-transfer, and mixing physics at large length scales can significantly affect microbial conversion rates, particularly when the microbial reaction requires a narrow set of conditions. These phenomena are difficult to study in small-scale bench-top reactors that are typically well-mixed. Predictive computational fluid dynamics (CFD) based simulations can therefore aid in the scale-up, design and optimization of these reactors. This work presents multiphase Euler-Euler CFD simulations of at-scale (~500 m3) bioreactors. Our mathematical model treats the gas and liquid as interpenetrating phases. This approach reduces the computational complexity of tracking individual gas bubbles that are several orders of magnitude smaller than reactor dimensions. We solve the Reynolds averaged Navier-Stokes (RANS) multiphase equations that account for phase and chemical species transport, interphase mass and momentum transfer and uses a phenomenological model for gas uptake by microbes. We use a customized solver derived from open-source CFD toolbox, OpenFOAM [1], to perform these simulations, which has been validated against small-scale reactors in our previous work [2]. There is currently a knowledge-gap regarding bubble-size distributions when using gas mixtures with vastly different properties, which can have a significant impact overall mass-transfer. For example, hydrogen bubbles are more buoyant compared to other relatively heavier gases (CO2/CH4/CO), resulting in a large distribution of residence times and bubble sizes. This work therefore develops a deeper understanding of bubble dynamics and interphase mass transfer in such heterogenous gas mixtures through well-resolved computational models. We use a population balance model (PBM) for bubble-size-distribution modeling that is validated against small-scale experiments in our solver with an uncertainty quantification study for bubble coalescence and break-up model parameters. Results pertaining to multiple simulations of gas-fermentation reactors are presented where gas mixtures with varying compositions of CO2/CH4/CO/H2 are imposed at the sparger boundaries. The spatio-temporal variations in bubble-size distribution and mass transfer coefficient are analyzed for varying superficial velocities and gas-compositions for varying sizes of bubble-column and airlift reactors. This work will also examine the performance of different reactor designs, viz. bubble column reactor, airlift reactor with an internal draft tube, and a stirred-tank reactor with Rushton impellers. Reactor mass-transfer coefficient, gas hold-up, and dissolved gas distribution are critically analyzed among reactors, and sensitivity studies pertaining to gas flow rates and reactor geometry will be presented. [1] Weller, H., Tabor, G., Jasak, H. and Fureby, C., A tensorial approach to computational continuum mechanics using object-oriented techniques, Computers in physics, 12, 6, 620--631, 1998. [2] Rahimi, M., Sitaraman, H., Humbird, D. and Stickel, J., Computational fluid dynamics study of full-scale aerobic bioreactors: Evaluation of gas-liquid mass transfer, oxygen uptake, and dynamic oxygen distribution, Chemical Engineering Research and Design, 139: 283-295.

BIOMASS FUELS↗

DOE OSTI2021

Effect of Urban Heat Island and Global Warming Countermeasures on Heat Release and Carbon Dioxide Emissions from a Detached House

Urban air temperature rises induced by the urban heat island (UHIE) effect or by global warming (GW) can be beneficial in winter but detrimental in summer. The SCIENCE-Outdoor model was used to simulate changes to sensible heat release and CO 2 emissions from buildings yielded by four UHIE countermeasures and five GW countermeasures. This model can evaluate the thermal condition of building envelope surfaces, both inside and outside. The results showed that water-consuming UHIE countermeasures such as evaporative space cooling and roof water showering provided positive effects (decreasing sensible heat release and CO 2 emissions related to space conditioning) in summer. Additionally, they had no negative (unwanted cooling) effects in winter since they can be turned off in the heating season. Roof greening can provide the greatest space- conditioning CO 2 emissions reductions among four UHIE countermeasures, and it reduces the amount of heat release slightly in the heating season. Since the effect on reducing carbon dioxide (CO 2 ) emissions by UHIE countermeasures is not very significant, it is desirable to introduce GW countermeasures in order to reduce CO 2 emissions. The significance of this study is that it constructed the new simulation model SCIENCE-Outdoor and applied it to show the influence of countermeasures upon both heat release and CO 2 emissions.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Rheo-Structural Spectroscopy: Fingerprinting the In Situ Response of Fluids to Arbitrary Flow Fields

The objectives of this project were to develop new sample environments, measurement methodologies and associated modeling tools for characterizing the structural response to arbitrarily complex processing flows using small angle scattering, and to apply these new tools for understanding the fundamental physics governing the structuring of anisotropic particulate and polymeric materials under flow histories and conditions relevant to industrial processing flows. The research resulted in the development and implementation of a new sample environment, the fluidic four roll mill (FFoRM), for in situ small angle neutron and X-ray scattering (SANS/SAXS) measurements. These measurements are capable of generating large data sets that “fingerprint” how a complex fluid responds to a wide range of flow histories involving time variations in deformation type and rate. New modeling tools were developed to extract detailed microstructural information from such data sets, including orientation distribution functions and interparticle correlation functions, as well as reduced-order parametric descriptors of these high-dimensional functions that can be used to readily map, visualize and interpret a fluid’s structural response to its flow history. These new tools were applied to a range of model materials involving elongated particle suspensions in order to provide new insights into the physics of how flow couples with orientational and structural order in complex flows, particularly under non-dilute conditions for which no accurate theories currently exist. Using these investigations, we elucidated a number of new insights into the fundamental phenomena driving such process-structure-property relationships. These findings provide guidance for the further development of rheological models, and ultimately can inform the rational and model-based design of flow processes to achieve optimized orientational ordering that is key to the properties and function of a wide range of energy-relevant materials.

36 MATERIALS SCIENCE↗

NASA NTRS1993

Predicting Failure Behaviors Of Thermoset Polymers

Useful predictions made from measurements on test-tube quantities. Mathematical model for viscoelastic failure behavior of epoxy or other thermoset polymer reduces considerably time and expense necessary to evaluate new polymer. One quickly obtains first-order estimates of viscoelastic properties, and decides more easily whether material rejected or good candidate for more thorough evaluation. Only properties required by model are equilibrium pressure vs. volume vs. temperature (PVT) response and linear viscoelastic shear and bulk moduli.

Bowles, Kenneth J.↗

NASA NTRS1987

A model-free method for mass spectrometer response correction

A new method for correction of mass spectrometer output signals is described. Response-time distortion is reduced independently of any model of mass spectrometer behavior. The delay of the system is found first from the cross-correlation function of a step change and its response. A two-sided time-domain digital correction filter (deconvolution filter) is generated next from the same step response data using a regression procedure. Other data are corrected using the filter and delay. The mean squared error between a step response and a step is reduced considerably more after the use of a deconvolution filter than after the application of a second-order model correction. O2 consumption and CO2 production values calculated from data corrupted by a simulated dynamic process return to near the uncorrupted values after correction. Although a clean step response or the ensemble average of several responses contaminated with noise is needed for the generation of the filter, random noise of magnitude not above 0.5 percent added to the response to be corrected does not impair the correction severely.

Shykoff, Barbara E.↗

DOE OSTI2017

Improving the FLORIS wind plant model for compatibility with gradient-based optimization

The FLORIS (FLOw Redirection and Induction in Steady-state) model, a parametric wind turbine wake model that predicts steady-state wake characteristics based on wind turbine position and yaw angle, was developed for optimization of control settings and turbine locations. This article provides details on changes made to the FLORIS model to make the model more suitable for gradient-based optimization. Changes to the FLORIS model were made to remove discontinuities and add curvature to regions of non-physical zero gradient. Exact gradients for the FLORIS model were obtained using algorithmic differentiation. A set of three case studies demonstrate that using exact gradients with gradient-based optimization reduces the number of function calls by several orders of magnitude. The case studies also show that adding curvature improves convergence behavior, allowing gradient-based optimization algorithms used with the FLORIS model to more reliably find better solutions to wind farm optimization problems.

17 WIND ENERGY↗

DOE OSTI2024

UEDGE modeling of plasma detachment of CFETR with ITER ‐like divertor geometry by external impurity seeding

Abstract Efficient handling of high heat flux on the plasma‐facing components, particularly the divertor targets, poses a significant challenge for the Chinese Fusion Engineering Testing Reactor (CFETR) with fusion power of Gigawatt. This work investigates the divertor plasma detachment of CFETR with a standard ITER‐like divertor geometry by neon (Ne) or argon (Ar) impurity seeding using UEDGE code. The cross‐field drifts terms are switched off, and fluid neutral models and a “fixed‐fraction” impurity model are applied to enable efficient simulations for the study of CFETR detachment. In order to reduce the heat load on the divertor targets below the acceptable level (<10 MW/m 2 ), the impurity fraction ( f ), pumping speed ( S ), and upstream density are varied to identify the suitable operations window during Ne seeding. The effects of Ne and Ar impurities on the plasma detachment are compared. It is found that with the power across the core‐edge interface P SOL = 200 MW and separatrix density of 2.8 10 19 , Ne impurity fraction ≥1.7%, and Ar impurity fraction ≥0.24% can achieve the partial detachment. Achieving similar total radiation power (˜148 MW), the Ne fraction is 2.3% and the Ar fraction is 0.24%. Moreover, the simulation results indicate that Ar exhibits better power radiation efficiency and core compatibility compared with Ne.

Zhang, M. Z.↗

DOE OSTI2022

Effect of bacterial cell addition on Fe(III) reduction and soil organic matter transformation in a farmland soil

The coupled biogeochemical processes of Fe(III) reduction and organic matter transformation profoundly impact terrestrial carbon cycling. However, little is known about the microbial role in soil organic matter (SOM) transformation during Fe(III) bio-reduction. Here we investigated the bio-reduction behavior of a black farmland soil and corresponding SOM transformation under circumneutral and anoxic conditions. A model dissimilatory Fe reducing bacterium, Geobacter sulfurreducens, was added in either live or dead form in order to enhance Fe(III) reduction in soil and to evaluate the accompanying transformation of SOM. The progress of Fe reduction was monitored and SOM transformation was characterized by various spectroscopy methods. Results showed that addition of either dead or live G. sulfurreducens cells increased the Fe(III) reduction rate and extent. Without cell addition, SOM transformation was insignificant within 13 days of incubation, only with some consumption of aliphatic/protein compounds, apparently due to their higher bio-degradability. Addition of dead or live cells resulted in more drastic SOM transformation, but through different mechanisms. With dead cell amendment, cell necromass and debris stimulated the activity of indigenous soil microbes by serving as extra carbon/energy sources. During Fe(III) reduction, the aliphatic/protein compounds were preferentially consumed by indigenous microbial communities, similar to the treatment without cell addition but with a greater extent of consumption. In comparison, addition of live G. sulfurreducens cells stimulated degradation of less bioavailable compounds, including more saturated and higher molecular weight SOM. It is possible that fast depletion of labile SOM by live G. sulfurreducens cells favored utilization of less bioavailable molecules (such as those with more aromatic structures) by the originally dormant species in native microbial community, suggesting an active role of live Fe(III)-reducing bacteria in affecting SOM transformation. In addition, fast assimilation of microbial related carbon, such as aromatic proteins and microbial byproducts, into SOM pools was also observed. Overall, our results suggest that addition of Fe(III)-reducing bacteria to a native soil can enhance Fe(III) reduction and accelerate the turnover of SOM through various mechanisms. The study provides new insights into coupled Fe(III) reduction and SOM transformation, as well as the “priming effect” of SOM using microbial cells as substrate.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Reduced-order autodifferentiable ensemble Kalman filters

This paper introduces a computational framework to reconstruct and forecast a partially observed state that evolves according to an unknown or expensive-to-simulate dynamical system. Our reduced-order autodifferentiable ensemble Kalman filters (ROAD-EnKFs) learn a latent low-dimensional surrogate model for the dynamics and a decoder that maps from the latent space to the state space. The learned dynamics and decoder are then used within an EnKF to reconstruct and forecast the state. Numerical experiments show that if the state dynamics exhibit a hidden low-dimensional structure, ROAD-EnKFs achieve higher accuracy at lower computational cost compared to existing methods. If such structure is not expressed in the latent state dynamics, ROAD-EnKFs achieve similar accuracy at lower cost, making them a promising approach for surrogate state reconstruction and forecasting.

Mathematics↗

DOE OSTI2014

TH-A-18C-07: Noise Suppression in Material Decomposition for Dual-Energy CT

Purpose: A general problem of dual-energy CT (DECT) is that the decomposition is sensitive to noise in the two sets of dual-energy projection data, resulting in severely degraded qualities of decomposed images. We have previously proposed an iterative denoising method for DECT. Using a linear decomposition function, the method does not gain the full benefits of DECT on beam-hardening correction. In this work, we expand the framework of our iterative method to include non-linear decomposition models for noise suppression in DECT. Methods: We first obtain decomposed projections, which are free of beam-hardening artifacts, using a lookup table pre-measured on a calibration phantom. First-pass material images with high noise are reconstructed from the decomposed projections using standard filter-backprojection reconstruction. Noise on the decomposed images is then suppressed by an iterative method, which is formulated in the form of least-square estimation with smoothness regularization. Based on the design principles of a best linear unbiased estimator, we include the inverse of the estimated variance-covariance matrix of the decomposed images as the penalty weight in the least-square term. Analytical formulae are derived to compute the variance-covariance matrix from the measured decomposition lookup table. Results: We have evaluated the proposed method via phantom studies. Using non-linear decomposition, our method effectively suppresses the streaking artifacts of beam-hardening and obtains more uniform images than our previous approach based on a linear model. The proposed method reduces the average noise standard deviation of two basis materials by one order of magnitude without sacrificing the spatial resolution. Conclusion: We propose a general framework of iterative denoising for material decomposition of DECT. Preliminary phantom studies have shown the proposed method improves the image uniformity and reduces noise level without resolution loss. In the future, we will perform more phantom studies to further validate the performance of the purposed method. This work is supported by a Varian MRA grant.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2015

Web-Based Computational Model Builder for Nuclear Energy Advanced Modeling & Simulation (Phase I Final Report)

Today, the importance of nuclear power in the US is a geopolitical matter as much as it is an economic one. This is due to the notion that increasing the use of nuclear power reduces the US's reliance on imported oil and gas. In order to design future systems and continue operational improvements at existing US plants, advanced modeling and simulation of nuclear power reactors is crucial. A variety of challenges exist to using advanced modeling and simulation in practice, especially for the nuclear energy community and other organizations with fewer computational resources and limited expertise. There is an increasing need of access to highly capable compute, data, and software resources from network systems, which are becoming more administratively restricted from access through installation of traditional client-server applications. The nuclear energy community is not capable of maintaining exponential growth of computing capability and data storage coupled with the necessary end-to-end network bandwidth improvements. Applications that provide higher fidelity with increased physics and decreased assumptions, by their very nature, require more and more computational resources. We believe Web-based, Cloud-enabled, end-to-end simulation software for nuclear energy advanced modeling and simulation to be the solution to these challenges.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Progress Towards an Investigation of the MiniBooNE Low Energy Excess Using Neutral-Current Delta-Like Single Photons in MicroBooNE with Wire-Cell 3D Reconstruction Algorithms

This note presents progress towards a Neutral-Current (NC) Delta-like single photon search in MicroBooNE using Wire-Cell 3D reconstruction and pattern recognition algorithms. This analysis will help address the question of the MiniBooNE Low Energy Excess (LEE) [1]. The selections are similar to the previously published Pandora-based single photon selections [2] in many ways, but here we use independent reconstruction and selection tools and examine a larger phase space (including charged pions and multiple protons). In the future, we will significantly reduce systematic uncertainties via the use of constraining sideband observations in order to statistically test specific models of the MiniBooNE LEE.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Progress towards an investigation of the MiniBooNE Low Energy Excess using neutral-current Delta-like single photons in MicroBooNE with Wire-Cell 3D reconstruction algorithms

This note presents progress towards a Neutral-Current (NC) Delta-like single photon search in MicroBooNE using Wire-Cell 3D reconstruction and pattern recognition algorithms. This analysis will help address the question of the MiniBooNE Low Energy Excess (LEE). The selections are similar to the previously published Pandora-based single photon selections in many ways, but here we use independent reconstruction and selection tools and examine a larger phase space (including charged pions and multiple protons). In the future, we will significantly reduce systematic uncertainties via the use of constraining sideband observations in order to statistically test specific models of the MiniBooNE LEE.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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