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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.

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At least 1,531 records · Page 85
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Nitrogen: A promising doping strategy for high-performance ovonic threshold switching selectors

The Ovonic Threshold Switching (OTS) selector serves as an essential component in the development of three-dimensional high-density memory integration technology. Nevertheless, the state-of-the-art high-performance OTS materials usually contain toxic elements such as arsenic (As), posing significant risks to both environmental and human health. Nitrogen (N), which belongs to the same group as arsenic (As), has emerged as a highly promising alternative for As doping. However, the underlying mechanisms that govern N-based OTS materials have not yet been extensively investigated. In this study, we delve into the effects of N doping on the structural, bonding, and electronic properties of amorphous GeSe (a-GeNSe) by ab initio molecular dynamics simulations to bridge the knowledge gap. Our findings indicate that upon N doping in a-GeSe, the formation of robust Ge-N bonds, along with N-centered tetrahedral and triangular structures, resulting in the sluggish atomic movement that enhances the thermal stability and endurance of a-GeNSe. The OTS characteristics are significantly influenced by the material’s electronic band structure, and thus the relatively slow performance drift can be attributed to the stabilization of mid-gap states, a result of N doping which effectively slows down the aging process of chalcogenide glass. Moreover, the increased mobility gap in a-GeNSe raises the threshold voltage (V th ), making it more compatible with commercially available phase-change memory materials. Furthermore, our findings reveal the extensive impact of the N element on a typical OTS material and offer valuable perspectives for alternative doping strategies that could potentially supplant As practices.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Modulation of thermal conductivity of iron-doped ß-Ga2O3 by helium-ion irradiation

This study examines the impact of helium-ion irradiation on the thermal conductivity of ß-Ga2O3. A laser-based spatial domain thermoreflectance technique is used to investigate thermal conductivity map for both un-irradiated and irradiated ß-Ga2O3, which are then validated against simulation results derived from density functional theory-based phonon transport simulations. Since helium bubble evolution was ob- served at the nanoscale using transmission electron microscopy, the simulation study was carried out on eight distinct helium-induced sites in ß-Ga2O3. Our findings indicate a reduction in thermal conductivity for the irradiated samples. Experimental results show a significant reduction in thermal conductivity in irradiated samples, with de- creases of approximately 25% along the [100] direction and 40% along [001] directions. Phonon transport simulations closely replicate these findings, particularly when helium occupying interstitial sites, predicting reductions of ˜53% along [100] and ˜50% along [001] directions. This work underscores the role of irradiation-induced microstructural changes in the heat transport properties of ß-Ga2O3 which is crucial for its application in sensor devices in extreme environments.

36 - MATERIALS SCIENCE↗
DOE OSTI2025

Magnetic structure evolution of LiFe 1- x Co x PO 4 olivines upon delithiation

We present a comprehensive study of the nuclear and magnetic structures of the mixed olivine solid solution series LiFe 1-x Co x PO 4 as well as their delithiated counterparts, for metal concentrations x = 0.2 - 0.6. Through neutron powder diffraction studies, we find that the LiFe 1-x Co x PO 4 series orders in the magnetic space group Pnma', consistent with their Li(Fe/Co)PO 4 parent structures. After chemical delithiation using peracetic acid, however, the removal of over 30% of the lithium from the lattice results in a transition from an A y -type to an A x -type antiferromagnetic structure. The magnetic space group consistent with A x antiferromagnetism was found to be Pn'm'a'. Interestingly, magnetic susceptibility measurements of both series reveal that delithiation increases the magnetic transition temperature, T N , from 50 K to 115 K. We find through analysis of the diffraction data that the unit cell parameters change linearly as a function of x; consequently, the exchange pathways between the Fe/Co magnetic cations are affected by the delithiation. Here, we discuss how exchange pathways, metal oxidation states, and d-orbital occupation all contribute to the observed magnetic symmetries and trends in T N in both series.

Antiferromagnet↗
DOE OSTI2022

Stabilization of glucose-6-phosphate dehydrogenase oligomers enhances catalytic activity and stability of clinical variants

Glucose-6-phosphate dehydrogenase (G6PD) deficiency is a genetic trait that can cause hemolytic anemia. To date, over 150 nonsynonymous mutations have been identified in G6PD, with pathogenic mutations clustering near the dimer and/or tetramer interface and the allosteric NADP + -binding site. Recently, our lab identified a small molecule that activates G6PD variants by stabilizing the allosteric NADP + and dimer complex, suggesting therapeutics that target these regions may improve structural defects. Here, we elucidated the connection between allosteric NADP + binding, oligomerization, and pathogenicity to determine whether oligomer stabilization can be used as a therapeutic strategy for G6PD deficiency (G6PD def ). We first solved the crystal structure for G6PD K403Q , a mutant that mimics the physiological acetylation of wild-type G6PD in erythrocytes and demonstrated that loss of allosteric NADP + binding induces conformational changes in the dimer. These structural changes prevent tetramerization, are unique to Class I variants (the most severe form of G6PD def ), and cause the deactivation and destabilization of G6PD. We also introduced nonnative cysteines at the oligomer interfaces and found that the tetramer complex is more catalytically active and stable than the dimer. Furthermore, stabilizing the dimer and tetramer improved protein stability in clinical variants, regardless of clinical classification, with tetramerization also improving the activity of G6PD K403Q and Class I variants. These findings were validated using enzyme activity and thermostability assays, analytical size-exclusion chromatography (SEC), and SEC coupled with small-angle X-ray scattering (SEC-SAXS). Taken together, our findings suggest a potential therapeutic strategy for G6PD def and provide a foundation for future drug discovery efforts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Molecular simulation of lignin-related aromatic compound permeation through gram-negative bacterial outer membranes

Lignin, an abundant aromatic heteropolymer in secondary plant cell walls, is the single largest source of renewable aromatics in the biosphere. Leveraging this resource for renewable bioproducts through targeted microbial action depends on lignin fragment uptake by microbial hosts and subsequent enzymatic action to obtain the desired product. Recent computational work has emphasized that bacterial inner membranes are permeable to many aromatic compounds expected from lignin depolymerization processes. In this study, we expand on these findings through simulations for 42 lignin-related compounds across a gram-negative bacterial outer membrane model. Unbiased simulation trajectories indicate that spontaneous crossing for the full outer membrane is relatively rare at molecular simulation timescales, primarily due to preferential membrane partitioning and slow diffusion within the lipopolysaccharide layer within the outer membrane. Membrane partitioning and permeability coefficients were determined through replica exchange umbrella sampling simulations to overcome sampling limitations. We find that the glycosylated lipopolysaccharides found in the outer membrane increase the permeation barrier to many lignin-related compounds, particularly the most hydrophobic compounds. However, the effect is relatively modest; at industrially relevant concentrations, uncharged lignin-related compounds will readily diffuse across the outer membrane without the need for specific porins. Together, our results provide insight into the permeability of the bacterial outer membrane for assessing lignin fragment uptake and the future production of renewable bioproducts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Novel Z-DNA binding domains in giant viruses

Z-nucleic acid structures play vital roles in cellular processes and have implications in innate immunity due to their recognition by Zα domains containing proteins (Z-DNA/Z-RNA binding proteins, ZBPs). Although Zα domains have been identified in six proteins, including viral E3L, ORF112, and I73R, as well as, cellular ADAR1, ZBP1, and PKZ, their prevalence across living organisms remains largely unexplored. In this study, we introduce a computational approach to predict Zα domains, leading to the revelation of previously unidentified Zα domain-containing proteins in eukaryotic organisms, including non-metazoan species. Our findings encompass the discovery of new ZBPs in previously unexplored giant viruses, members of the Nucleocytoviricota phylum. Through experimental validation, we confirm the Zα functionality of select proteins, establishing their capability to induce the B-to-Z conversion. Additionally, we identify Zα-like domains within bacterial proteins. While these domains share certain features with Zα domains, they lack the ability to bind to Z-nucleic acids or facilitate the B-to-Z DNA conversion. Our findings significantly expand the ZBP family across a wide spectrum of organisms and raise intriguing questions about the evolutionary origins of Zα-containing proteins. Moreover, our study offers fresh perspectives on the functional significance of Zα domains in virus sensing and innate immunity and opens avenues for exploring hitherto undiscovered functions of ZBPs.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

A conserved chaperone protein is required for the formation of a noncanonical type VI secretion system spike tip complex

Type VI secretion systems (T6SSs) are dynamic protein nanomachines found in Gram-negative bacteria that deliver toxic effector proteins into target cells in a contact-dependent manner. Prior to secretion, many T6SS effector proteins require chaperones and/or accessory proteins for proper loading onto the structural components of the T6SS apparatus. However, despite their established importance, the precise molecular function of several T6SS accessory protein families remains unclear. In this study, we set out to characterize the DUF2169 family of T6SS accessory proteins. Using gene co-occurrence analyses, we find that DUF2169-encoding genes strictly co-occur with genes encoding T6SS spike complexes formed by valine-glycine repeat protein G (VgrG) and DUF4150 domains. Although structurally similar to Pro-Ala-Ala-Arg (PAAR) domains, “PAAR-like” DUF4150 domains lack PAAR motifs and instead contain a conserved PIPY motif, leading us to designate them PIPY domains. Next, we present both genetic and biochemical evidence that PIPY domains require a cognate DUF2169 protein to form a functional T6SS spike complex with VgrG. This contrasts with canonical PAAR proteins, which bind VgrG on their own to form functional spike complexes. By solving the first crystal structure of a DUF2169 protein, we show that this T6SS accessory protein adopts a novel protein fold. Furthermore, biophysical and structural modeling data suggest that DUF2169 contains a dynamic loop that physically interacts with a hydrophobic patch on the surface of its cognate PIPY domain. Based on these findings, we propose a model whereby DUF2169 proteins function as molecular chaperones that maintain VgrG–PIPY spike complexes in a secretion-competent state prior to their export by the T6SS apparatus.

DUF2169↗
DOE OSTI2025

ER stress and viral defense: Advances and future perspectives on plant unfolded protein response in pathogenesis

Viral infections pose significant threats to crop productivity and agricultural sustainability. The frequency and severity of these infections are increasing, and pathogens are evolving rapidly under the influence of climate change. This underscores the importance of exploring the fundamental mechanisms by which plants defend themselves against dynamic viral threats. One such mechanism is the unfolded protein response (UPR), which is activated when the protein folding demand exceeds the capacity of the endoplasmic reticulum, particularly under adverse environmental conditions. While the key regulators of the UPR in response to viral infections have been identified, our understanding of how they modulate the UPR to suppress plant viral infections at the molecular and genetic levels is still in its infancy. Recent findings have shown that, in response to plant viral infections, the UPR swiftly reprograms transcriptional changes to support cellular, metabolic, and physiological processes associated with cell viability. However, the underlying mechanisms and functional outcomes of these changes remain largely unexplored. Here, we highlight recent advances in plant UPR research and summarize key findings related to viral infection–induced UPR, focusing on the balance between prosurvival and prodeath strategies. We also discuss the potential of systems-level approaches to uncover the full extent of the functional link between the UPR and plant responses to viral infections.

ER stress↗
DOE OSTI2025

Surface intermediates identified using IR spectroscopy during the catalytic oxidation of C 2 H 6 on IrO 2 (1 1 0) at near-ambient pressures

Characterizing surface intermediates during catalysis is essential for developing mechanistic models of catalytic reactions and for identifying rate-controlling steps. Here, in this work, we used polarization-dependent reflection absorption infrared spectroscopy (PD-RAIRS) to investigate surface intermediates that form on IrO 2 (1 1 0) during the catalytic oxidation of C 2 H 6 at pressures near 0.5 Torr. Our results show that adsorbed CO and HCO 2 are the only intermediates detectable with PD-RAIRS across a wide range of temperatures and reactant compositions during complete C 2 H 6 oxidation, giving rise to dominant peaks at about 2093 and 1310 cm −1 , respectively. These assignments were corroborated by RAIRS measurements following CO and HCOOH adsorption in ultrahigh vacuum, RAIRS with C 2 H 6 – 18 O 2 mixtures during catalysis and vibrational frequencies and IR intensities computed using density functional theory. We find that increasing the C 2 H 6 mole fraction in the reaction mixture raises the CO surface coverage relative to HCO 2 , correlating with increasing catalytic oxidation rates. The formation of CO and HCO 2 surface species at temperatures well below catalytic ignition indicates that the overall rate of C 2 H 6 oxidation on IrO 2 (1 1 0) is governed by steps late in the reaction sequence, such as H 2 O formation, CO oxidation and HCO 2 dehydrogenation. These findings provide key insight into the mechanism of alkane oxidation on IrO 2 (1 1 0) and valuable input for first-principles microkinetic modeling.

Pope, Connor [Univ. of Florida, Gainesville, FL (U↗
DOE OSTI2022

Electrically regenerated ion-exchange technology: Leveraging faradaic reactions and assessing the effect of co-ion sorption

Capacitive deionization (CDI) technologies have the potential to become cost-competitive alternatives to reverse osmosis for the treatment of brackish waters. In this study, we describe our findings on the effect of co-ion sorption and faradaic side reactions on our ion exchange resin functionalized desalination electrodes which passively capture salt and reject it upon charging. This system, which we previously reported on and refer to as electrically regenerated ion exchange (ERI), avoids the use of expensive ion exchange membranes in an effort to save costs. Surprisingly, we find that, compared to a reference CDI system, ERI electrodes capture salt most effectively at low applied voltages (0.5 mg/cm 3 at 0.8 V). Both CDI and ERI systems also seem to suffer from co-ion sorption effects which negatively impact salt adsorption. However, Faradaic side reactions at higher voltages (1 V and 1.2 V) which we track via pH measurements, serve as a detriment to CDI but seem to facilitate the functionality of ERI.

42 ENGINEERING↗
DOE OSTI2024

Unveiling mesoscopic structures in distorted lamellar phases through deep learning-based small angle neutron scattering analysis

Hypothesis: The formation of distorted lamellar phases, distinguished by their arrangement of crumpled, stacked layers, is frequently accompanied by the disruption of long-range order, leading to the formation of interconnected network structures commonly observed in the sponge phase. Nevertheless, traditional scattering functions grounded in deterministic modeling fall short of fully representing these intricate structural characteristics. Our hypothesis posits that a deep learning method, in conjunction with the generalized leveled wave approach used for describing structural features of distorted lamellar phases, can quantitatively unveil the inherent spatial correlations within these phases. Experiments and Simulations: This report outlines a novel strategy that integrates convolutional neural networks and variational autoencoders, supported by stochastically generated density fluctuations, into a regression analysis framework for extracting structural features of distorted lamellar phases from small angle neutron scattering data. To evaluate the efficacy of our proposed approach, we conducted computational accuracy assessments and applied it to the analysis of experimentally measured small angle neutron scattering spectra of AOT surfactant solutions, a frequently studied lamellar system. Findings: The findings unambiguously demonstrate that deep learning provides a dependable and quantitative approach for investigating the morphology of wide variations of distorted lamellar phases. It is adaptable for deciphering structures from the lamellar to sponge phase including intermediate structures exhibiting fused topological features. In conclusion, this research highlights the effectiveness of deep learning methods in tackling complex issues in the field of soft matter structural analysis and beyond.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Physicochemical control of solvation and molecular assembly of charged amphiphilic oligomers at air-aqueous interfaces

Hypothesis : Understanding the rules that control the assembly of nanostructured soft materials at interfaces is central to many applications. We hypothesize that electrolytes can be used to alter the hydration shell of amphiphilic oligomers at the air-aqueous interface of Langmuir films, thereby providing a means to control the formation of emergent nanostructures. Experiments : Three representative salts – (NaF, NaCl, NaSCN) were studied for mediating the self-assembly of oligodimethylsiloxane methylimidazolium (ODMS-MIM + ) amphiphiles in Langmuir films. The effects of the different salts on the nanostructure assembly of these films were probed using vibrational sum frequency generation (SFG) spectroscopy and Langmuir trough techniques. Experimental data were supported by atomistic molecular dynamic simulations. Findings : Langmuir trough surface pressure – area isotherms suggested a surprising effect on oligomer assembly, whereby the presence of anions affects the stability of the interfacial layer irrespective of their surface propensities. In contrast, SFG results implied a strong anion effect that parallels the surface activity of anions. These seemingly contradictory trends are explained by anion driven tail dehydration resulting in increasingly heterogeneous systems with entangled ODMS tails and appreciable anion penetration into the complex interfacial layer comprised of headgroups, tails, and interfacial water molecules. These findings provide physical and chemical insight for tuning a wide range of interfacial assemblies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Vibrational sum frequency generation spectroscopy reveals the inertness of chromium oxide (001) surfaces

Nanoengineered metal oxides such as Cr(III)-oxide (chromia) films have diverse potential applications in corrosion inhibition, remediation, energy generation, catalysis, data storage, and biological and environmental systems. Concerns about material degradation or oxidation to toxic chromate necessitate an understanding of chromia/aqueous interfaces, beginning with their hydroxylation and hydration behavior. Vibrational sum-frequency generation spectroscopy (vSFG) provides specific molecular-level information about water at the oxide/aqueous junction with high surface selectivity. To overcome the strong absorber problem typical of certain metal oxides in the UV–visible range during nonlinear optical studies, we employed molecular beam epitaxy to deposit transparent, epitaxial nanofilms of Cr 2 O 3 with (001) crystalline orientation on sapphire (Al 2 O 3 (001)) substrates, as confirmed by atomic force microscopy and X-ray diffraction. vSFG spectra of the air and water interfaces of the Cr 2 O 3 (001) films reveal hydroxyl features corresponding to both dissociated and molecular water on the surface. In contrast to the dangling hydroxyls found on the bare Al 2 O 3 (001) substrate, the hydroxyl groups on the deposited Cr 2 O 3 (001) nanofilm do not readily undergo isotopic H/D exchange when exposed to varying forms of D 2 O under ambient conditions. When considering the chemistries of the corresponding trivalent cations in aqueous solution, the finding is at variance with their similar acidities and proton exchange dynamics but consistent with markedly slower inner-sphere water ligand exchange of hexaquo Cr 3+ . This finding challenges the idea that proton and water exchange at the water/Cr₂O₃(001) interface are solely correlated, driven by the strength of metal-bridging oxygen bonds and surface hydroxyl distribution, without direct causation.

Boamah-Agyemang, Mavis D. [Pacific Northwest Natio↗
DOE OSTI2022

An economic analysis of the role of materials, system engineering, and performance in electrochemical carbon dioxide conversion to formate

The development of technologies that utilize carbon dioxide is important to mitigating climate change. The electrochemical reduction of carbon dioxide is one technology that can utilize greenhouse gasses that would be otherwise be emitted to the atmosphere by producing chemicals and fuels from carbon dioxide and electricity. Significant progress has been made in the experimental performance of carbon dioxide reduction systems with novel catalyst designs, new materials, and systems engineering; however, no work has linked such changes in stack design and materials to capital costs for the stack itself. In this study, we present an analysis that accounts for and analyzes the impacts of alternative materials and system architectures on manufactured costs of carbon dioxide reduction stacks, thus providing a framework to understand exactly how these advances impact the at-scale capital costs of these systems. Specifically, we consider the impact that the addition of a catholyte buffer layer has on an electrolyzer reducing carbon dioxide to formate, finding that the cost of manufacturing this part only increases stack costs by about $30/m 2 at high manufacturing rates, while previous work finds that this part improves system performance. This work shows that the links between system performance, materials, and costs are nonlinear, and that achieving low-cost scalability requires optimization of not just performance parameters but also the use of low-cost and highly scalable materials. These results bridge experimental and techno-economic analysis of processes for carbon dioxide reduction, informing researchers by providing a quantifiable estimate of the impact of advances in electrochemical carbon dioxide reduction technology on manufactured stack capital costs.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2020

Non-local model for surface tension in fluid-fluid simulations

We propose a non-local model for surface tension obtained in the form of an integral of a molecular-force-like function with support 3.5e added to the Navier-Stokes momentum conservation equation. We demonstrate analytically and numerically that with the non-local model interfaces with a radius of curvature larger than the support length behave macroscopically and microscopically, otherwise. For static droplets, the pressure difference Pe,in - Pe,out satisfies the Young-Laplace law for droplet radius greater than 3.5e and other- wise deviates from the Young-Laplace law. The latter indicates that the surface tension in the proposed model decreases with decreasing radius of curvature, which agrees with molecular dynamics and experimental studies of nanodroplets. Using the non-local model we perform numerical simulations of droplets under dynamic conditions, including a rising droplet, a droplet in shear flow, and two colliding droplets in shear flow, and compare results with a standard Navier-Stokes model subject to the Young-Laplace boundary condition at the fluid-fluid interface implemented via the Conservative Level Set (CLS) method. We find good agreement with existing numerical methods and analytical results for a rising macroscopic droplet and a droplet in a shear flow. For colliding droplets in shear flow, the non- local model converges (with respect to the grid size) to the correct behavior, including sliding, coalescence, and merging and breaking of two droplets depending on the capillary number. In contrast, we find that the results of the CLS model are highly grid-size dependent.

Howard, Amanda A.↗
DOE OSTI2020

An analysis of the spatio-temporal resolution of the immersed boundary method with direct forcing

The immersed boundary method (IBM) with direct forcing is very popular in the simulation of rigid particulate flows. In the IBM, an interaction force is introduced at the interface between fluid and particle in order to approximate the no-slip boundary condition. The interaction force is calculated through dividing the velocity difference (or error) between fluid and particle at the interface by the time step. Here, a dynamic equation for the velocity difference is derived. Additionally, analyses on the dynamic equation provide a few new findings: (i) The interaction force is the solution of a least-squares error problem, with the direct implication that the Lagrangian marker distribution has no effect on the large scale flow structure once the distribution of Lagrangian markers become saturated along the interface (i.e., each marker remains properly correlated with all its neighbors); (ii) The Lagrangian volume-weight is a relaxation factor to control how fast the velocity error decays to the ideal value of zero; (iii) The optimal choice of the Lagrangian volume-weight is the largest value permissible by a stability condition. A comprehensive convergence analysis with regard to the spatial and temporal resolution is presented for the velocity error and also for the shear-stress and surface pressure. In three simple canonical problems, it is analytically and numerically shown that the IBM results converge to the theoretical solutions obtained with precise imposition of no-slip and no-penetration boundary conditions. It is observed that it is not necessary to match the Lagrangian marker volume-weight to that of the local Eulerian cell volume and in fact this matching leads to lower than optimal computational efficiency. However, it is found that extremely high Eulerian grid resolution and small time step have to be used to obtain high precision simulation results. Especially, the time step should be inversely proportional to the particle Reynolds number for low Reynolds number flows. For high frequency oscillation problems, the grid size needs to be reduced by a factor of the square root of the frequency, and the time step to be reduced by a factor of the frequency. The theoretical findings here can be used to alleviate the technical difficulties in simulating non-spherical particles by not requiring the Lagrangian marker distribution to match the Eulerian grids and also in the implementation of IBM on non-uniform Eulerian grids. The present work also provides simple practical guidance on the choice of temporal and spatial resolution so as to control the simulation error a priori.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Noise and error analysis and optimization in particle-based kinetic plasma simulations

In this paper we analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We begin by describing kernel density estimation for continuous values of the spatial variable x, expressing the kernel in a form in which its shape and width are represented separately. The covariance matrix of the noise in the density is computed, first for uniform true density. The bandwidth of the covariance matrix C(x,y) is related to the width of the kernel. A feature that stands out is the presence of constant negative terms in the elements of the covariance matrix both on and off-diagonal. These negative correlations are related to the fact that the total number of particles is fixed at each time step; they also lead to the property ∫C(x,y)dy = 0. We investigate the effect of these negative correlations on the electric field computed by Gauss's law, finding that the noise in the electric field is related to a process called the Ornstein-Uhlenbeck bridge, leading to a covariance matrix of the electric field with variance significantly reduced relative to that of a Brownian process. For non-constant density, p(x), still with continuous x, we analyze the total error in the density estimation and discuss it in terms of bias-variance optimization (BVO). For some characteristic length l, determined by the density and its second derivative, and kernel width h, having too few particles within h leads to too much variance; for h that is large relative to l, there is too much smoothing of the density. The optimum between these two limits is found by BVO. For kernels of the same width, it is shown that this optimum (minimum) is weakly sensitive to the kernel shape. Next, we repeat the analysis for x discretized on a grid. In this case the charge deposition rule is determined by a particle shape. An important property to be respected in the discrete system is the exact preservation of total charge on the grid; this property is necessary to ensure that the electric field is equal at both ends, consistent with periodic boundary conditions. We find that if the particle shapes satisfy a partition of unity property, the particle charge deposited on the grid is conserved exactly. Further, if the particle shape is expressed as the convolution of a kernel with another kernel that satisfies the partition of unity, then the particle shape obeys the partition of unity. This property holds for kernels of arbitrary width, including widths that are not integer multiples of the grid spacing. Furthermore, we show results relaxing the approximations used to do BVO optimization analytically, by doing numerical computations of the total error as a function of the kernel width, on a grid in x. The comparison between numerical and analytical results shows good agreement over a range of particle shapes. We discuss the practical implications of our results, including the criteria for design and implementation of computationally efficient particle shapes that take advantage of the developed theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Explicit physics-informed neural networks for nonlinear closure: The case of transport in tissues

In upscaling methods, closures for nonlinear problems present a well-known challenge. While a number of theoretical methods have been proposed for handling such closures, nonlinearities still remain a significant obstacle for many problems. In this work, we use a combination of formal upscaling and data-driven machine learning for explicitly closing a nonlinear transport and reaction process in multiscale tissues. The classical effectiveness factor model is used to formulate the macroscale reaction kinetics. We train a multilayer perceptron network using training data generated by direct numerical simulations over microscale examples. Once trained, the network is used in an algorithm for numerically solving the upscaled (coarse-grained) differential equation describing mass transport and reaction in two example tissues. The network is described as being explicit in the sense that the network is trained using macroscale concentrations and gradients of concentration as components of the feature space rather than incorporating them as part of a constraint in the optimization process. Network training and solutions to the macroscale transport equations were computed for two different tissues. The two tissue types (brain and liver) exhibit markedly different geometrical complexity and spatial scale (cell size and sample size). The upscaled solutions for the average concentration are compared with numerical solutions derived from the microscale concentration fields by a posteriori averaging. There are three outcomes of this work of particular note. 1) Our overall approach results in an upscaled nonlinear PDE. The PDE is closed using a neural network, and our approach results in the definition of the classical effectiveness factor for effecting closure. 2) We identify particular source terms for the closure problem that are important for representing the structure of the closure. These source terms involve macroscale concentrations and their gradients. We adopt these source terms to use as explicit features in the learning algorithm. We find the trained networks that include the macroscale source terms generate models that are able to predict the correction factor with increased fidelity over those that do not. 3) We find that the trained network exhibits good generalizability, and it is able to predict the effectiveness factor with high fidelity for realistically-structured tissues despite the significantly different scale and geometrical complexity of the two example tissue types. This latter result emphasizes our purposeful connection between conventional averaging methods with the use of machine learning for closure; this contrasts with some machine learning methods for upscaling where the exact form of the macroscale equation remains unknown.

97 MATHEMATICS AND COMPUTING↗