Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Spatial dependence”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A Perspective on the Milky Way Bulge Bar as Seen from the Neutron-capture Elements Cerium and Neodymium with APOGEE

Abstract This study probes the chemical abundances of the neutron-capture elements cerium and neodymium in the inner Milky Way from an analysis of a sample of ∼2000 stars in the Galactic bulge bar spatially contained within ∣X Gal ∣ < 5 kpc, ∣Y Gal ∣ < 3.5 kpc, and ∣Z Gal ∣ < 1 kpc, and spanning metallicities between −2.0 ≲ [Fe/H] ≲ +0.5. We classify the sample stars into low- or high-[Mg/Fe] populations and find that, in general, values of [Ce/Fe] and [Nd/Fe] increase as the metallicity decreases for the low- and high-[Mg/Fe] populations. Ce abundances show a more complex variation across the metallicity range of our bulge-bar sample when compared to Nd, with ther-process dominating the production of neutron-capture elements in the high-[Mg/Fe] population ([Ce/Nd] < 0.0). We find a spatial chemical dependence of Ce and Nd abundances for our sample of bulge-bar stars, with low- and high-[Mg/Fe] populations displaying a distinct abundance distribution. In the region close to the center of the MW, the low-[Mg/Fe] population is dominated by stars with low [Ce/Fe], [Ce/Mg], [Nd/Mg], [Nd/Fe], and [Ce/Nd] ratios. The low [Ce/Nd] ratio indicates a significant contribution in this central region fromr-process yields for the low-[Mg/Fe] population. The chemical pattern of the most metal-poor stars in our sample suggests an early chemical enrichment of the bulge dominated by yields from core-collapse supernovae andr-process astrophysical sites, such as magnetorotational supernovae.

Astronomy & Astrophysics↗
DOE OSTI2023

Modeling Wind-Hydrogen System and Analyzing Curtailment

Low-cost green hydrogen can be achieved by integrating utility-scale wind farms to an electrolyzer. The power produced by a wind farm depends on spatial and temporal changes in the wind, and this variability can affect the electrolyzer's performance. This study examines the trade-offs between two electrolyzer configurations: a large centralized electrolyzer connected to the wind farm versus several smaller distributed electrolyzers connected directly to each wind turbine. The results show that a centralized configuration generates more hydrogen because turbines that are waked and produce less power are compensated but other un-waked turbines.

electrolyzer↗
DOE OSTI2024

Cosmic topology. Part IIa. Eigenmodes, correlation matrices, and detectability of orientable Euclidean manifolds

Abstract If the Universe has non-trivial spatial topology, observables depend on both the parameters of the spatial manifold and the position and orientation of the observer. In infinite Euclidean space, most cosmological observables arise from the amplitudes of Fourier modes of primordial scalar curvature perturbations. Topological boundary conditions replace the full set of Fourier modes with specific linear combinations of selected Fourier modes as the eigenmodes of the scalar Laplacian. We present formulas for eigenmodes in orientable Euclidean manifolds with the topologiesE 1 –E 6 ,E 11 ,E 12 ,E 16 , andE 18 that encompass the full range of manifold parameters and observer positions, generalizing previous treatments. Under the assumption that the amplitudes of primordial scalar curvature eigenmodes are independent random variables, for each topology we obtain the correlation matrices of Fourier-mode amplitudes (of scalar fields linearly related to the scalar curvature) and the correlation matrices of spherical-harmonic coefficients of such fields sampled on a sphere, such as the temperature of the cosmic microwave background (CMB). We evaluate the detectability of these correlations given the cosmic variance of the observed CMB sky. We find that topologies where the distance to our nearest clone is less than about 1.2 times the diameter of the last scattering surface of the CMB give a correlation signal that is larger than cosmic variance noise in the CMB. This implies that if cosmic topology is the explanation of large-angle anomalies in the CMB, then the distance to our nearest clone is not much larger than the diameter of the last scattering surface. We argue that the topological information is likely to be better preserved in three-dimensional data, such as will eventually be available from large-scale structure surveys.

Astronomy & Astrophysics↗
DOE OSTI2024

Spatially Resolved Near Field Spectroscopy of Vibrational Polaritons at the Small N Limit

Vibrational polaritons, which have been primarily studied in Fabry–Pérot cavities with a large number of molecules (N ~ 10 6 –10 10 ) coupled to the resonator mode, exhibit various experimentally observed effects on chemical reactions. However, the exact mechanism is elusively understood from the theoretical side, as the large number of molecules involved in an experimental strong coupling condition cannot be represented completely in simulations. This discrepancy between theory and experiment arises from computational descriptions of polariton systems typically being limited to only a few molecules, thus failing to represent the experimental conditions adequately. To address this mismatch, we used surface phonon polariton (SPhP) resonators as an alternative platform for vibrational strong coupling. SPhPs exhibit strong electromagnetic confinement on the surface and thus allow for coupling to a small number of molecules. As a result, this platform can enhance nonlinearity and slow down relaxation to the dark modes. In this study, we fabricated a pillar-shaped quartz resonator and then coated it with a thin layer of cobalt phthalocyanine (CoPc). By employing scattering-type scanning near-field optical microscopy (s-SNOM), we spatially investigated the dependency of vibrational strong coupling on the spatially varying electromagnetic field strength and demonstrated strong coupling with 38,000 molecules only–reaching to the small N limit. Through s-SNOM analysis, we found that strong coupling was observed primarily on the edge of the quartz pillar and the apex of the s-SNOM tip, where the maximum field enhancement occurs. In contrast, a weak resonance signal and lack of coupling were observed closer to the center of the pillar. This work demonstrates the importance of spatially resolved polariton systems in nanophotonic platforms and lays a foundation to explore polariton chemistry and chemical dynamics at the small N limit–one step closer to reconcile with high-level quantum calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Ultrafast formation of domain walls of a charge density wave in SmTe 3

We study ultrafast x-ray diffraction on the charge density wave (CDW) of SmTe 3 using an x-ray free-electron laser. The high momentum and time resolution afforded by the x-ray laser enabled capturing fine wave-vector and time-dependent features of the CDW that originate from fast (in time) and sharp (in real space) variations of the CDW lattice distortion, which we attribute to an inversion of the order parameter. These domain inversions occur near the surface and are caused by the short penetration depth of the near-infrared pump with the wavelength centered at 800 nm, resulting in CDW domain walls perpendicular to the sample surface. These domain walls break the CDW long-range order on the scale of the x-ray probe depth, controlled experimentally by the x-ray incidence angle and suppress the diffraction intensity of the CDW for times much longer than the ~1–ps recovery of the electronic gap observed in time and angle-resolved photoemission spectroscopy. We model the spatial and temporal dependences of the order parameter using a simple Ginzburg-Landau model with all the parameters obtained from the published literature. We find reasonable agreement between the calculated and the measured diffraction across the momentum, time, fluence, and incidence angle dependence without adjusting any parameters. In conclusion, we reconstruct the spatial and temporal dependences of the lattice order parameter and find that at long times, depending on the pump fluence, multiple domain walls remain at distances of a few nanometers from the surface.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Urbanization effects on the spatial patterns of spring vegetation phenology depend on the climatic background

Cities have been considered ideal surrogates for evaluating ecological responses to climate warming. Although research has revealed that the urban heat island effect is not the only determinant that drives the rural-urban difference in spring phenology, limited attempts further explore the effect of complex interactions between urbanization and climates on the start of the season (SOS). Here, we employed the percentage of impervious surface area as an indicator of urbanization levels, incorporating the urban heat island (UHI) effect and climates to decipher the multiple effects on the temporal shift in SOS. Our results suggest that urbanization, the UHI effect, and climates jointly drive the phenological timing in cities. Further, the SOS is highly linearly correlated with urbanization levels and UHI effects (p<0.001) in the zones with warm and humid climates, whereas relatively warmer, cooler, or arid climates break down the linearity. Geographically, the SOS is north-south symmetrical for the rural-urban ecosystem at the national scale, which initiates at the mid-latitudes (around 30 °N, 67.58 DOY ± 2.23 days) first and then towards the low (around 20 °N, 105.25 DOY ± 1.31 days) and high-latitudes (45 °N, 123.01 DOY ± 1.45 days). Chilling accumulation and spring temperature jointly contribute to this phenomenon. As the UHI effect is similar to the projected global warming in the future, understanding the phenological responses to urbanization in various climates is insightful for evaluating the impact of future warming on plants' phenological behavior in the global ecosystem.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

STFM: Accurate Spatio-Temporal Fusion Model for Weather Forecasting

Meteorological prediction is crucial for various sectors, including agriculture, navigation, daily life, disaster prevention, and scientific research. However, traditional numerical weather prediction (NWP) models are constrained by their high computational resource requirements, while the accuracy of deep learning models remains suboptimal. In response to these challenges, we propose a novel deep learning-based model, the Spatiotemporal Fusion Model (STFM), designed to enhance the accuracy of meteorological predictions. Our model leverages Fifth-Generation ECMWF Reanalysis (ERA5) data and introduces two key components: a spatiotemporal encoder module and a spatiotemporal fusion module. The spatiotemporal encoder integrates the strengths of convolutional neural networks (CNNs) and recurrent neural networks (RNNs), effectively capturing both spatial and temporal dependencies. Meanwhile, the spatiotemporal fusion module employs a dual attention mechanism, decomposing spatial attention into global static attention and channel dynamic attention. This approach ensures comprehensive extraction of spatial features from meteorological data. The combination of these modules significantly improves prediction performance. Experimental results demonstrate that STFM excels in extracting spatiotemporal features from reanalysis data, yielding predictions that closely align with observed values. In comparative studies, STFM outperformed other models, achieving a 7% improvement in ground and high-altitude temperature predictions, a 5% enhancement in the prediction of the u/v components of 10 m wind speed, and an increase in the accuracy of potential height and relative humidity predictions by 3% and 1%, respectively. This enhanced performance highlights STFM’s potential to advance the accuracy and reliability of meteorological forecasting.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Angular Momentum Variation of the Milky Way Thick Disk: The Dependence of Chemical Abundance and Evidence of the Inside-out Formation Scenario

We investigate the angular momentum of mono-abundance populations (MAPs) of the Milky Way thick disk by using a sample of 26,076 giant stars taken from APOGEE Data Release (DR) 17 and Gaia early DR3. The vertical and perpendicular angular momentum components, L Z and L P , of the MAPs in narrow bins have significant variations across the [α/M]–[M/H] plane. L Z and L P systematically change with [M/H] and [α/M] and can be alternatively quantified by the chemical gradients: d[M/H]/dL Z = 1.2 × 10 -3 dex kpc -1 km -1 s, d[M/H]/dL P = -5.0 × 10 -3 dec kpc -1 km -1 s, and d[α/M]/dL Z = -3.0 × 10 -4 dex kpc -1 km -1 s, d[α/M]/dL P = 1.2 × 10 -3 dec kpc -1 km -1 s. These correlations can also be explained as the chemical dependence of the spatial distribution shape of the MAPs. We also exhibit the corresponding age dependence of the angular momentum components. Under the assumption that the guiding radius (R g ) is proportional to L Z , this provides direct observational evidence of the inside-out structure formation scenario of the thick disk, with dR g /dAge = -1.9 kpc Gyr -1 . The progressive changes in the disk thickness can be explained by the upside-down formation or/and the consequent kinematical heating.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Spatial organization of FcγR and TLR2/1 on phagosome membranes differentially regulates their synergistic and inhibitory receptor crosstalk

Abstract Many innate immune receptors function collaboratively to detect and elicit immune responses to pathogens, but the physical mechanisms that govern the interaction and signaling crosstalk between the receptors are unclear. In this study, we report that the signaling crosstalk between Fc gamma receptor (FcγR) and Toll-like receptor (TLR)2/1 can be overall synergistic or inhibitory depending on the spatial proximity between the receptor pair on phagosome membranes. Using a geometric manipulation strategy, we physically altered the spatial distribution of FcγR and TLR2 on single phagosomes. We demonstrate that the signaling synergy between FcγR and TLR2/1 depends on the proximity of the receptors and decreases as spatial separation between them increases. However, the inhibitory effect from FcγRIIb on TLR2-dependent signaling is always present and independent of receptor proximity. The overall cell responses are an integration from these two mechanisms. This study presents quantitative evidence that the nanoscale proximity between FcγR and TLR2 functions as a key regulatory mechanism in their signaling crosstalk.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Temperature dependence of resistivity of carbon micro/nanostructures: Microscale spatial distribution with mixed metallic and semiconductive behaviors

The temperature coefficient of resistivity (θ T ) of carbon-based materials is a critical property that directly determines their electrical response upon thermal impulses. It could have metal- (positive) or semiconductor-like (negative) behavior, depending on the combined temperature dependence of electron density and electron scattering. Its distribution in space is very difficult to measure and is rarely studied. Here, for the first time, we report that carbon-based micro/nanoscale structures have a strong non-uniform spatial distribution of θ T . This distribution is probed by measuring the transient electro-thermal response of the material under extremely localized step laser heating and scanning, which magnifies the local θ T effect in the measured transient voltage evolution. For carbon microfibers (CMFs), after electrical current annealing, θ T varies from negative to positive from the sample end to the center with a magnitude change of >130% over <1 mm. This θ T sign change is confirmed by directly testing smaller segments from different regions of an annealed CMF. For micro-thick carbon nanotube bundles, θ T is found to have a relative change of >125% within a length of ~2 mm, uncovering strong metallic to semiconductive behavior change in space. In conclusion, our θ T scanning technique can be readily extended to nm-thick samples with μm scanning resolution to explore the distribution of θ T and provide a deep insight into the local electron conduction.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Using aircraft measurements to characterize subgrid-scale variability of aerosol properties near the Atmospheric Radiation Measurement Southern Great Plains site

Abstract. Complex distributions of aerosol properties evolve in space and time as a function of emissions, new particle formation, coagulation, condensational growth, chemical transformation, phase changes, turbulent mixing and transport, removal processes, and ambient meteorological conditions. The ability of chemical transport models to represent the multi-scale processes affecting the life cycle of aerosols depends on their spatial resolution since aerosol properties are assumed to be constant within a grid cell. Subgrid-scale-dependent processes that affect aerosol populations could have a significant impact on the formation of particles, their growth to cloud condensation nuclei (CCN) sizes, aerosol–cloud interactions, dry deposition and rainout and hence their burdens, lifetimes, and radiative forcing. To address this issue, we characterize subgrid-scale variability in terms of measured aerosol number, size, composition, hygroscopicity, and CCN concentrations made by repeated aircraft flight paths over the Atmospheric Radiation Measurement (ARM) program's Southern Great Plains (SGP) site during the Holistic Interactions of Shallow Clouds, Aerosols and Land Ecosystem (HI-SCALE) campaign. Subgrid variability is quantified in terms of both normalized frequency distributions and percentage difference percentiles using grid spacings of 3, 9, 27, and 81 km that represent those typically used by cloud-system-resolving models as well as the current and next-generation climate models. Even though the SGP site is a rural location, surprisingly large horizontal gradients in aerosol properties were frequently observed. For example, 90 % of the 3, 9, and 27 km cell mean organic matter concentrations differed from the 81 km cell around the SGP site by as much as ∼ 46 %, large spatial variability in aerosol number concentrations and size distributions were found during new particle formation events, and consequently 90 % of the 3, 9, and 27 km cell mean CCN number concentrations differed from the 81 km cell mean by as much as ∼ 38 %. The spatial variability varied seasonally for some aerosol properties, with some having larger spatial variability during the spring and others having larger variability during the late summer. While measurements at a single surface site cannot reflect the surrounding variability of aerosol properties at a given time, aircraft measurements that are averaged within an 81 km cell were found to be similar to many, but not all, aerosol properties measured at the ground SGP site. This analysis suggests that it is reasonable to directly compare most ground SGP site aerosol measurements with coarse global climate model predictions. In addition, the variability quantified by the aircraft can be used as an uncertainty range when comparing the surface point measurements with model predictions that use coarse grid spacings.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Characterizing vertical upper ocean temperature structures in the European Arctic through unsupervised machine learning

In-situ observations of subsurface ocean temperatures are, in many regions, inconsistently distributed in time and space. These spatio-temporal inconsistencies in the observational network lead to difficulties in utilizing those observations effectively for ocean model evaluation or understanding larger-scale ocean characteristics. Model accuracy of subsurface ocean characteristics is especially important within regions that contain complex ocean structures. One such region is the European Arctic which not only contains several types of water masses with unique characteristics, but also wintertime sea ice coverage and complex bathymetry. This study presents an unsupervised neural networking technique that can be used in combination with traditional ocean model evaluation techniques to provide additional information on the accuracy of modeled vertical ocean temperature profiles. Self-organizing maps is an unsupervised machine learning technique that we apply to approximately twenty thousand Argo and CTD temperature profiles from 2012 to 2020 in the European Arctic to categorize the observed vertical ocean temperature structures in the top 150 m. The observed ocean profile categories, or neurons, defined by the self-organizing map show strong spatial and temporal dependencies. We then use the neuron weights, or the learned temperature profile structure of each neuron, to validate the spatial and temporal variability of modeled vertical temperature structures. This analysis gives us new insights about the model’s capabilities to reproduce specific vertical structures of the top-most ocean layer within different regions and seasons. Mapping modeled ocean temperature profiles onto the neuron-space of the observationally-defined self organized map highlights the potential of this method to advance our understanding of model deficiencies in that region.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Bayesian Physics Informed Spatio-Temporal Network for Streamflow Data Imputation

Reliable reconstruction of incomplete streamflow records is critical for improving hydrological forecasting, flood preparedness, and water resource management. However, large observational gaps and uncertainties in governing physical parameters limit the accuracy of traditional statistical and machinelearning imputation frameworks. To address these challenges, we develop a Bayesian Physics-Informed Spatio-Temporal Network (BPI-STNet) that jointly captures spatial and temporal dependencies while enforcing hydrologic consistency through embedded physical constraints. The framework integrates a GraphSAGE-LSTM architecture to model spatial connectivity across gauges and temporal flow dynamics, coupled with a Bayesian update mechanism to estimate uncertain parameters in a simplified water-balance framework. Unlike conventional physics-informed networks that rely on sampling-based posterior estimation, BPI-STNet derives an analytic solution to the inverse problem, allowing closed-form Bayesian updates of uncertain parameters Λ={α,β,k} using Gaussian priors and likelihoods. Applied to daily observations from the Susquehanna River Basin (1980-2022), BPI-STNet achieves substantial improvements over a purely data-driven RGNN baseline, which reduced RMSE by 23 % and MAE by 9 %, and achieving an average NSE values up to 0.96. The results demonstrate that coupling Bayesian inference with physics-informed learning yields physically consistent, uncertainty-aware reconstructions that preserve the temporal persistence and statistical distribution of observed flows. The proposed framework establishes a generalizable paradigm for data-sparse hydrologic systems where both data fidelity and physical interpretability are essential.

Krishnan Kutty Ambika, Anukesh [ORNL] (ORCID:00000↗
DOE OSTI2023

Quantifying Pore Morphology in Spray-Formed Tantalum Using X-ray Micro-computed Tomography

In order to establish quantitative process–structure–property relationships in thermal spray coatings, a robust framework for defining (micro)structural characteristics is needed. Here, we present a quantitative characterization of the three-dimensional morphology of porosity in spray-formed tantalum samples based on high-resolution X-ray micro-computed tomography. Using synchrotron facilities, we acquired dozens of high-resolution scans, enabling a statistically meaningful comparison across multiple samples, different regions within samples, and spray processes. We quantify the spatial distribution, size, and topology of porous inclusions, with a significant focus on variability across samples and different spray processes (plasma and cold sprayed), as well as sensitivity to image segmentation and resolution. Based on a typical segmentation, we report porosities ranging from 0.9 to 1.7 pct for all samples tested, with significant sensitivity due to image segmentation resulting in estimates as low as 0.6 pct and as high as 4.8 pct. For the complex pore space morphology observed in these materials, we argue that a conventional analysis based on identifying individual pores is not well suited, and propose an alternative approach based on morphological metrics with a rich history in porous media literature, such as spatial correlations, local pore thickness, and scale-dependent sub-sampling. Spatial correlations indicate anisotropic splat structures, but only mildly anisotropic pores. Various measures of pore size show a wide distribution of sizes, ranging from sub-micron to 10-micron length scales. Scale-dependent variations in porosity suggest that representative volumes of several hundred microns are required for convergence of morphological metrics, with larger volumes for cold-spray materials. This work provides a robust quantitative basis for describing three-dimensional pore structure in thermal spray coatings.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Quantifying albedo susceptibility biases in shallow clouds

The evaluation of radiative forcing associated with aerosol–cloud interactions remains a significant source of uncertainty in future climate projections. The problem is confounded by the fact that aerosol particles influence clouds locally and that averaging to larger spatial and/or temporal scales carries biases that depend on the heterogeneity and spatial correlation of the interacting fields and the nonlinearity of the responses. Mimicking commonly applied satellite data analyses for calculation of albedo susceptibility S o , we quantify S o aggregation biases using an ensemble of 127 large eddy simulations of marine stratocumulus. We explore the cloud field properties that control this spatial aggregation bias and quantify the bias for a large range of shallow stratocumulus cloud conditions manifesting a variety of morphologies and ranges of cloud fractions. We show that S o spatial aggregation biases can be on the order of hundreds of percent, depending on the methodology. Key uncertainties emanate from the typically applied adiabatic drop concentration N d retrieval, the correlation between aerosol and cloud fields, and the extent to which averaging reduces the variance in cloud albedo A c and N d . So biases are more often positive than negative and are highly correlated with biases in the liquid water path adjustment. Temporal aggregation biases are shown to offset spatial aggregation biases. Both spatial and temporal biases have significant implications for observationally based assessments of aerosol indirect effects and our inferences of underlying aerosol–cloud–radiation effects.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Imaging Carrier Dynamics and Transport in Hybrid Perovskites with Transient Absorption Microscopy

In this review, the recent progress in using transient absorption microscopy to image charge transport and dynamics in semiconducting hybrid organic–inorganic perovskites is discussed. The basic principles, instrumentation, and resolution of transient absorption microscopy are outlined. With temporal resolution as high as 10 fs, sub-diffraction-limit spatial resolution, and excited-state structural resolution, these experiments have provided crucial details on charge transport mechanisms that have been previously obscured in conventional ultrafast spectroscopy measurements. Morphology-dependent mapping unveils spatial heterogeneity in carrier recombination and cooling dynamics. By spatially separating the pump and probe beams, carrier transport across grain boundaries has been directly visualized. Further, femtosecond temporal resolution allows for the examination of nonequilibrium transport directly, revealing extraordinarily long-range hot carrier migration. The application of transient absorption microscopy is not limited to hybrid perovskites but can also be useful for other polycrystalline materials in which morphology plays an important role in carrier transport.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Tensor factorization for elucidating mechanisms of piezoresponse relaxation via dynamic Piezoresponse Force Spectroscopy

Spatially resolved time and voltage-dependent polarization dynamics in PbTiO 3 thin films is explored using dynamic piezoresponse force microscopy (D-PFM) in conjunction with interferometric displacement sensing. This approach gives rise to 4D data sets containing information on bias-dependent relaxation dynamics at each spatial location without long-range electrostatic artifacts. To interpret these data sets in the absence of defined physical models, we employ a non-negative tensor factorization method which clearly presents the data as a product of simple behaviors allowing for direct physics interpretation. Correspondingly, we perform phase-field modeling finding the existence of ‘hard’ and ‘soft’ domain wall edges. This approach can be extended to other multidimensional spectroscopies for which even exploratory data analysis leads to unsatisfactory results due to many components in the decomposition.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Theory and modeling of molecular modes in the NMR relaxation of fluids

Traditional theories of the nuclear magnetic resonance (NMR) autocorrelation function for intra-molecular dipole pairs assume a single-exponential decay, yet the calculated autocorrelation of realistic systems displays a rich, multi-exponential behavior, resulting in anomalous NMR relaxation dispersion (i.e., frequency dependence). We develop an approach to model and interpret the multi-exponential intra-molecular autocorrelation using simple, physical models within a rigorous statistical mechanical development that encompasses both rotational diffusion and translational diffusion in the same framework. Here, we recast the problem of evaluating the autocorrelation in terms of averaging over a diffusion propagator whose evolution is described by a Fokker–Planck equation. The time-independent part admits an eigenfunction expansion, allowing us to write the propagator as a sum over modes. Each mode has a spatial part that depends on the specified eigenfunction and a temporal part that depends on the corresponding eigenvalue (i.e., correlation time) with a simple, exponential decay. The spatial part is a probability distribution of the dipole pair, analogous to the stationary states of a quantum harmonic oscillator. Drawing inspiration from the idea of inherent structures in liquids, we interpret each of the spatial contributions as a specific molecular mode. These modes can be used to model and predict the NMR dipole–dipole relaxation dispersion of fluids by incorporating phenomena on the molecular level. We validate our statistical mechanical description of the distribution in molecular modes with molecular dynamics simulations interpreted without any relaxation models or adjustable parameters: the most important poles in the Padé–Laplace transform of the simulated autocorrelation agree with the eigenvalues predicted by the theory

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗