Search NASA⌕ Search

SEARCH · Search NASA

Results for “distributed solutions”

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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

HTGR Multiphysics Application Drivers FY26 Updates

This report summarizes FY26 progress under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program's high-temperature gas-cooled reactor (HTGR) application driver work, covering a wide range of activities such as code validation and multi-physics code assessment. 1) A detailed SAM model of the High-Temperature Engineering Test Reactor (HTTR) was developed using a unique-block grouping approach, with an extended parallel thermal network method to capture block-to-block conduction and radiation heat transfer, and applied to steady-state simulations of the HTTR 30~MW and 9~MW cases. 2) In another activity, SAM's newly implemented multi-component gas flow model was validated against the Natural convection Shutdown heat removal Test Facility (NSTF) argon ingress experiment, correctly capturing the density-driven suppression and thermal recovery of natural circulation observed when argon is introduced into the air-cooled Reactor Cavity Cooling System (RCCS) loop. 3) For the OECD/NEA High Temperature Test Facility (HTTF) benchmark, we co-led the international benchmark activities as well as the OECD/NEA final benchmark report to be released at the end of this year. 4) Finally, the coupled Griffin-SAM modeling capability for pebble-bed HTGRs was advanced by verifying the Griffin neutronics solution against Serpent Monte Carlo for a realistic non-uniform temperature distribution, resolving several deficiencies in the SAM-to-Griffin temperature transfer scheme, and enabling distinct fuel kernel, moderator, and coolant temperatures for cross section feedback. These new features were demonstrated in a PBR load-following transient.

Lee, Alvin↗
DOE OSTI2026

HydroDCM: Hydrological Domain-Conditioned Modulation for Cross-Reservoir Inflow Prediction

Deep learning models have shown promise in reservoir inflow prediction, yet their performance often deteriorates when applied to different reservoirs due to distributional differences, referred to as the domain shift problem. Domain generalization (DG) solutions aim to address this issue by extracting domain-invariant representations that mitigate errors in unseen domains. However, in hydrological settings, each reservoir exhibits unique inflow patterns, while some metadata beyond observations like spatial information exerts indirect but significant influence. This mismatch limits the applicability of conventional DG techniques to many-domain hydrological systems. To overcome these challenges, we propose HydroDCM, a scalable DG framework for cross-reservoir inflow forecasting. Spatial metadata of reservoirs is used to construct pseudo-domain labels that guide adversarial learning of invariant temporal features. During inference, HydroDCM adapts these features through light-weight conditioning layers informed by the target reservoir’s metadata, reconciling DG’s invariance with location-specific adaptation. Experiment results on 30 real-world reservoirs in the Upper Colorado River Basin demonstrate that our method substantially outperforms state-of-the-art DG baselines under many-domain conditions and remains computationally efficient.

Hu, Pengfei [ORNL] (ORCID:0009000367130950)↗
DOE OSTI2024

A bicarbonate-rich liquid condensed phase in non-saturated solutions in the absence of divalent cations

Bicarbonate (HCO 3 - ) and sodium (Na + )-containing solutions contain droplets of a separate, bicarbonate-rich liquid condensed phase (LCP) that have higher concentrations of HCO 3 - relative to the bulk solution in which they reside. The existence and composition of the LCP droplets has been investigated by nanoparticle tracking analysis, nuclear magnetic resonance spectroscopy, refractive index measurements and X-ray pair distribution function analysis. The bicarbonate-rich LCP species is a previously unaccounted-for, ionic phenomenon which occurs even in solutions with solely monovalent cations. Its existence requires re-evaluation of models used to describe and model aqueous solution physicochemistry, especially those used to describe and model carbonate mineral formation.

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

The Upgrade of the SNS Extraction Kicker Power Supplies for the Proton Power Upgrade

The Proton Power Upgrade (PPU) project at the Spallation Neutron Source (SNS) aims to enhance the linear accelerator's power output from 1.4 to 2.8 megawatts. A critical focus lies on upgrading the Extraction Kicker Power Supplies to handle the amplified beam power. The existing capacitor charging power supplies lacked the capability to charge the Blumlein-type Pulse Forming Network (PFN) to the required 40 kV at a repetition rate of 60 Hz. To address this limitation, an initial solution involving the use of a resonant charging circuit was proposed. However, a challenge arose with a self-firing issue in the thyristor switch, which proved unsolvable within the given timeframe. Facing a critical decision point in the project, an alternative approach was explored: integrating a supplementary power supply to enhance the overall power capacity. This solution was tested and ultimately chosen as the path forward. To accommodate the additional power supply, the power distribution system had to undergo upgrades. Throughout this endeavor, a comprehensive examination of the system took place, with meticulous identification of key components. This paper delves into the technical challenges encountered during the process and the corresponding solutions that were implemented.

Tan, Yugang [ORNL] (ORCID:0000000155968252)↗
DOE OSTI2024

Fabrication of model ultrafiltration membranes with uniform, high aspect ratio pores

Here, in this manuscript, we report the facile fabrication of large-area model membranes with highly uniform and high aspect ratio pores with diameters <20 nm. These membranes are useful for fundamental investigations of separation by size exclusion in the ultrafiltration regime, where species to be separated from solution have dimensions of 1–100 nm. Such investigations require membranes with narrow pores and high aspect ratios such that the Hagen–Poiseuille equation is followed, enabling well-known models such as the hindered transport model to be evaluated and other affecting factors to be ignored. We demonstrate that the sub-20 nm pores in the membrane are of sufficiently high aspect ratio such that water flux through the membrane is consistent with the Hagen–Poiseuille equation. The fabrication relies on self-assembling block copolymers to form uniform, densely packed patterns with sub-20 nm resolution, sequential infiltration synthesis to convert the block copolymer in situ into a mask with adequate contrast to etch pores with an aspect ratio >5, and low-resolution photolithography to transfer the pattern over a large area into a silicon nitride membrane. Model membranes with narrow pore-size distribution fabricated in this way provide the means to investigate parameters that impact size-selective ultrafiltration separations such as the relationships between solute or particle size and pore size, their distributions, and rejection profiles, and, therefore, test the validity or limits of separation models.

Chen, Wen↗
DOE OSTI2024

Optimizing and Exploring Untapped Micro-Hydro Hybrid Systems: a Multi-Objective Approach for Crystal Lake as a Large-Scale Energy Storage Solution

Increasing electricity demand and concerns about climate change and fossil fuel consumption have highlighted the importance of renewable energy resources and storage systems. This paper proposes a method for exploring untapped pumped hydro storage potentials to accommodate intermittent renewable energy generation profiles. Hourly measured data from 2022 in Benzie County, Michigan, United States, were gathered for system sizing and a thorough, realistic analysis. By employing the multi-objective grey wolf optimization algorithm, we formulated optimal sizing and energy-management strategies for three different scenarios. Unlike similar studies, the 3rd with triple objective functions (OFs) scenario aims to maximize both reliability and ecological OFs while minimizing the cost OF. It has shown promising results with multiple solutions, considering economic, environmental, and reliability factors. A case study conducted in Crystal Lake, Michigan, revealed that although Crystal Lake would function only as a micro-hydro power facility, it is a promising and huge storage unit with a substantial storage capacity of around 14.9734GWh. The system investigated is significant in the USA due to its rapid deployment capabilities, minimal construction requirements, and ease of integration with the distribution grid. The fuzzy logic method was employed to identify the best non-dominant solution among the other solutions. Furthermore, these outcomes include a notably low levelized cost of energy at 0.046147$/kWh, a robust index of reliability of 99.705%, and a significant reduction in CO₂ emissions amounting to 7.9142×10 3 tons/year, when considering the triple OFs. The paper’s methodology provides valuable insights for regions aiming to utilize renewable energy from untapped storage sources.

13 HYDRO ENERGY↗
DOE OSTI2025

Quantifying dispersity in size and shape of nanoparticles from small-angle scattering data using machine learning based CREASE

Here, we use machine learning (ML) enhanced computational reverse engineering analysis of scattering experiments (CREASE) to interpret small-angle X-ray scattering (SAXS) data obtained from a system of nanoparticles without a priori knowledge of their exact shapes (e.g. spheres or ellipsoids), sizes (0.5–50 nm) and distributions. The SAXS measurements yielded three categories of scattering profiles exhibiting 'strong', 'weak' and 'no' features. Diminishing features (e.g. broadening or disappearing peaks) in scattering profiles have always been attributed to the presence of significant dispersity in the system. Such featureless SAXS data are not suitable for traditional analysis using analytical models. If one were to fit a relevant analytical model (e.g. the lmfit analytical model for polydisperse spheres) to these 'weak' and 'no' SAXS profiles from our nanoparticle systems, one would obtain non-unique interpretations of the data. Relying on electron microscopy to identify the distributions of nanoparticle shapes and sizes is also unfeasible, especially in high-throughput synthesis and characterization loops. In such situations, to identify the distributions of particle sizes and shapes that could be present in the sample, one must rely on methods like ML-CREASE to interpret the data quickly and output all relevant interpretations about the structure present in the system. The ML-CREASE optimization loop takes the experimental scattering profile as input and outputs multiple candidate solutions whose computed scattering profiles match the SAXS profile input. The ML-CREASE method outputs distributions of relevant structural features, such as the volume fraction of the nanoparticles in the system and the mean and standard deviation of the particle size and aspect ratio, assuming a type of distribution (e.g. normal, log-normal) for size and aspect ratio. We find that, for the SAXS profiles analyzed here, accounting for the shape dispersity along with size dispersity of the nanoparticles using ML-CREASE improved the match between the computed scattering profiles and input experimental profiles.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Computationally efficient and error aware surrogate construction for numerical solutions of subsurface flow through porous media

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O ( n log n ) instead of the typical O ( n 3 ) rate in the number of samples n used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Finally, although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

High-order limiting methods using maximum principle bounds derived from the Boltzmann equation I: Euler equations

The use of limiting methods for high-order numerical approximations of hyperbolic conservation laws generally requires defining an admissible region/bounds for the solution. In this work, we present a novel approach for computing solution bounds and limiting for the Euler equations through the kinetic representation provided by the Boltzmann equation, which allows for extending limiters designed for linear advection directly to the Euler equations. Given an arbitrary set of solution values to compute bounds over (e.g., numerical stencil) and a desired linear advection limiter, the proposed approach yields an analytic expression for the admissible region of particle distribution function values, which may be numerically integrated to yield a set of bounds for the density, momentum, and total energy. Further, these solution bounds are shown to preserve positivity of density/pressure/internal energy and, when paired with a limiting technique, can robustly resolve strong discontinuities while recovering high-order accuracy in smooth regions without any ad hoc corrections (e.g., relaxing the bounds). This approach is demonstrated in the context of an explicit unstructured high-order discontinuous Galerkin/flux reconstruction scheme for a variety of difficult problems in gas dynamics, including cases with extreme shocks and shock-vortex interactions. Furthermore, this work presents a foundation for limiting techniques for more complex macroscopic governing equations that can be derived from an underlying kinetic representation for which admissible solution bounds are not well-understood.

42 ENGINEERING↗
DOE OSTI2025

Optimization problems governed by systems of PDEs with uncertainties

This paper reviews current theoretical and numerical approaches to optimization problems governed by partial differential equations (PDEs) that depend on random variables or random fields. Such problems arise in many engineering, science, economics and societal decision-making tasks. This paper focuses on problems in which the governing PDEs are parametrized by the random variables/fields, and the decisions are made at the beginning and are not revised once uncertainty is revealed. Examples of such problems are presented to motivate the topic of this paper, and to illustrate the impact of different ways to model uncertainty in the formulations of the optimization problem and their impact on the solution. A linear–quadratic elliptic optimal control problem is used to provide a detailed discussion of the set-up for the risk-neutral optimization problem formulation, study the existence and characterization of its solution, and survey numerical methods for computing it. Different ways to model uncertainty in the PDE-constrained optimization problem are surveyed in an abstract setting, including risk measures, distributionally robust optimization formulations, probabilistic functions and chance constraints, and stochastic orders. Furthermore, approximation-based optimization approaches and stochastic methods for the solution of the large-scale PDE-constrained optimization problems under uncertainty are described. Some possible future research directions are outlined.

Heinkenschloss, Matthias [Rice Univ., Houston, TX ↗
DOE OSTI2025

Distributed Coordination of Demand-side Flexible Resources in Microgrid with All-Time Feasibility

The prevalence of distributed renewable generators motivates microgrid operators to exploit demand-side flexible resources (DFRs). Due to their dispersed nature, distributed DFR coordination has been a vibrant research area, while there are several issues awaiting to be addressed. On one hand, DFR power is internally coupled through power flow, while DFR usually cannot access grid information. On the other hand, in time-restricted scenarios, solution feasibility cannot be guaranteed by conventional dual-based algorithms. To fill these gaps, we propose a distributed DFR coordination framework with all-time feasibility. The proposed framework accounts for the distinct access of microgrid entities to grid information. A distributed and all-time feasible algorithm is proposed for optimal DFR coordination, which allows DFRs to make local decisions without violating constraints throughout iterations. The effectiveness of the proposed algorithm is demonstrated through case studies. The impact of peer-to-peer communication links on algorithm convergence is also investigated, which emphasizes the balance between communication investment and algorithm performance.

Li, Hongyi [Iowa State Univ., Ames, IA (United Sta↗
DOE OSTI2025

Reorganization of Water at Aqueous Aluminum Chloride (AlCl 3 ) Interfaces: Vibrational Sum Frequency Generation and Molecular Dynamics Simulations

AlCl 3 hydration states and complexation are not well understood both in solutions and at the air–aqueous interface despite their potential significance in natural waters and their industrial and energy-related applications. Here, we investigated Al 3+ and Cl – ion behaviors in an AlCl 3 aqueous bulk solution and at the air–aqueous interface using interface-selective vibrational sum frequency generation (SFG), Raman and infrared spectroscopies, molecular dynamics (MD) simulation, as well as molecular-informed reduced modeling. Our reduced modeling reveals relatively long-range effects for Al 3+ as compared to monovalent ions such as Na + indicating that the interfacial depth of trivalent ions can be significantly larger than that of monovalent ions at the air–water interface. MD simulations reveal interfacial stratification and multiple layering of the ions. Compression of the Al 3+ and Cl – distributions with increasing concentrations from 0.5 to 2.5 m is also observed in the subsurface regions. Significant SSP- and PPP-polarized SFG OH spectral intensity increases are observed from 0.5 to 1.5 m and 0.5 to 2.5 m, respectively, indicative of interfacial depth increases and a change in average orientation above 1.5 m. Extensive evaluation of SFG spectra, Fresnel-corrected using several approaches, shows the same trends. The nonmonotonic trend points to a changing structure in surface and subsurface water orientation and hydrogen bonding environment generally consistent with the MD simulation of stratification and water orientation changes. Furthermore, solvent-shared ion pairing is implicated with MD simulation radial distribution analysis and consistent with infrared spectral identification of the hexaaqua aluminum ion in the solution phase. Spectral evidence of a strong Al 3+ hydration shell and the acidic behavior of the Al 3+ ions is obvious in the Raman and infrared spectra of the bulk solution. In conclusion, we show that the MD dipole potential is directly related to the MD second-order susceptibility of the interface, χ SFG–MD (2) , both of which correlate up to ∼35 Å with the spectral observations of increasing and then saturating intensities, suggesting that both ion stratification and interfacial depth determine the water orientations at an air–water interface of 1-3 electrolyte solutions.

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

Integration and validation of some modules for modelling of high-speed chemically reactive flows in two-phase gas-droplet mixtures

Three modules are integrated into the built-in OpenFOAM rhoCentralFoam solver towards accurate and efficient modelling of high-speed chemically reactive flows in two-phase gas-droplet mixtures within the OpenFOAM 10.0 framework. The first module is the mixture-averaged diffusion model. The second module is the built-in OpenFOAM Lagrangian solver coupled with optimised droplet drag coefficient and convective heat transfer coefficient sub-models. The last module is a sparse stiff chemistry solver based on dynamic adaptive hybrid integration (AHI-S). The optimised droplet sub-models are first verified in correct implementation for subsequent simulations in this work. Further, they show good accuracy against experimental and analytical data in the modelling of ammonia droplet acceleration and cooling in the flowing and/or low-temperature air. The accuracy and efficiency gains related to the mixture-averaged diffusion model and the AHI-S chemistry solver are examined by simulating 1-D detonation propagation in ammonia droplet-free/laden ammoniaoxygen mixtures. Numerical results of detonation propagation speed, gaseous temperature, density, and species distributions around the induction zone show good agreement with experimental data and analytical solutions. Compared to the built-in OpenFOAM diffusion model, the mixture-averaged diffusion model provides different numerical predictions of pulsating instabilities in detonation propagation. It shows better accuracy in depicting the detonation structure within the droplet-free section attributed to improved multi-component diffusion modelling. Compared to the built-in OpenFOAM solver EulerImplicit (backward Euler), the AHI-S chemistry solver reduces the computational cost by around 50%. It achieves satisfactory accuracy in calculating detonation propagation speed within the droplet-free section with the optimal efficiency when the safety factor, β, equals 0.5.

42 ENGINEERING↗
DOE OSTI2024

In Situ Monitoring the Nucleation and Growth of Nanoscale CaCO 3 at the Oil–Water Interface

Interfaces can actively control the nucleation kinetics, orientations, and polymorphs of calcium carbonate (CaCO 3 ). Prior studies have revealed that CaCO 3 formation can be affected by the interplay between chemical functional moieties on solid–liquid or air–liquid interfaces as well as CaCO 3 ’s precursors and facets. Yet little is known about the roles of a liquid–liquid interface, specifically an oil–liquid interface, in directing CaCO 3 mineralization which are common in natural and engineered systems. Here, in this study, by using in situ X-ray scattering techniques to locate a meniscus formed between water and a representative oil, isooctane, we successfully monitored CaCO 3 formation at the pliable isooctane–water interface and systematically investigated the pivotal roles of the interface in the formation of CaCO 3 (i.e., particle size, its spatial distribution with respect to the interface, and its mineral phase). Different from bulk solution, ∼5 nm CaCO 3 nanoparticles form at the isooctane–water interface. They stably exist for a long time (36 h), which can result from interface-stabilized dehydrated prenucleation clusters of CaCO 3 . There is a clear tendency for enhanced amounts and faster crystallization of CaCO 3 at locations closer to isooctane, which is attributed to a higher pH and an easier dehydration environment created by the interface and oil. Our study provides insights into CaCO 3 nucleation at an oil–water interface, which can deepen our understanding of pliable interfaces interacting with CaCO 3 and benefit mineral scaling control during energy-related subsurface operation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Embedded EPICS server for PowerPMAC motion controllers

An embedded server layer of Experimental Physics and Industrial Control System (EPICS) for PowerPMAC motion controllers has been developed and deployed at two undulator beamlines of the National Institute of General Medical Sciences and the National Cancer Institute (GM/CA) Structural Biology Facility at the Advanced Photon Source (APS). This compact, open source solution makes the power and versatility of PowerPMAC motion controls directly accessible to distributed EPICS clients. At GM/CA the system controls about 200 servo and stepper motors — both encoded and unencoded — and multiple digital and analog I/O accessories. The server stack comprises two sublayers: a lower-level driver and database that communicates directly with PowerPMAC, and a facility-specific soft sublayer built on top. The paper describes installing EPICS on PowerPMAC, the implementation of both layers and client examples, including on-the-fly scanning.

EPICS↗
DOE OSTI2026

Partially Ionized Plasma Physics and Technological Applications

Partially ionized plasma physics has attracted increased attention recently due to numerous technological applications made possible by the increased sophistication of computer modelling, the depth of the theoretical analysis, and the technological applications to a vast field of manufacturing for computer components. Partially ionized plasma is characterized by a significant presence of neutral particles in contrast to the fully ionized plasma. The theoretical analysis is based upon solutions of the kinetic Boltzmann equation, yielding the non-Maxwellian electron energy distribution function (EEDF), thereby emphasizing the difference with a fully ionized plasma. The impact of the effect on discharges in inert and molecular gases is described in detail, yielding the complex nonlinear phenomena resulting in plasma selforganization. A few examples of such phenomena are given, including the non-monotonic EEDFs in the discharge afterglow in a mixture of argon with the molecular gas NF3; the explosive generation of cold electron populations in capacitive discharges, hysteresis of EEDF in inductively coupled plasmas. Recently, highly advanced computer codes were developed in order to address the outstanding challenges in plasma technology. These developments are briefly described in general terms.

non-Maxwellian electron energy distribution functi↗
DOE OSTI2024

Self-Assembling Microgrids for Resilient Distribution Systems of the Future: Implementation in a Commercial DERMS Platform

Microgrids have long provided resilience to critical facilities such as hospitals and military installations, and they are now increasingly being looked at as a building block for future grids to support the energy resilience needs of the grid of the future. State-of-the-art technologies, such as blackstart algorithms using renewable distributed energy resources (DERs) to effectively and seamlessly form microgrids, have been produced by national labs over the years. Their adoption by the utility industry would be critical to reap the most benefits toward energy and climate resilience, and the pathway is via commercialization of these self-assembling microgrid algorithms by integrating them in a commercial product platform. This project brings a national labs team (LLNL, LANL) together with a vendor (Smarter Grid Solutions) to perform proof-of-concept integration of the algorithms into the vendor’s commercial Distributed Energy Resources Management System (DERMS). The project provides a strong pathway to commercialization of the algorithms thereby promoting adoption of resilient microgrid technology by utilities to offer resilience benefits to all customers and especially to disadvantaged and underserved communities.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Toward a quantitative description of solvation structure: a framework for differential solution scattering measurements

Appreciating that the role of the solute–solvent and other outer-sphere interactions is essential for understanding chemistry and chemical dynamics in solution, experimental approaches are needed to address the structural consequences of these interactions, complementing condensed-matter simulations and coarse-grained theories. High-energy X-ray scattering (HEXS) combined with pair distribution function analysis presents the opportunity to probe these structures directly and to develop quantitative, atomistic models of molecular systems in situ in the solution phase. However, at concentrations relevant to solution-phase chemistry, the total scattering signal is dominated by the bulk solvent, prompting researchers to adopt a differential approach to eliminate this unwanted background. Though similar approaches are well established in quantitative structural studies of macromolecules in solution by small- and wide-angle X-ray scattering (SAXS/WAXS), analogous studies in the HEXS regime—where sub-ångström spatial resolution is achieved—remain underdeveloped, in part due to the lack of a rigorous theoretical description of the experiment. To address this, herein we develop a framework for differential solution scattering experiments conducted at high energies, which includes concepts of the solvent-excluded volume introduced to describe SAXS/WAXS data, as well as concepts from the time-resolved X-ray scattering community. Our theory is supported by numerical simulations and experiment and paves the way for establishing quantitative methods to determine the atomic structures of small molecules in solution with resolution approaching that of crystallography.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗