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DOE OSTI2020

The Novel Hybrid Ab Initio Model of High-Performance Structural Alloys Design for Fossil Energy Power Plants

The current project developed a novel HT-CALPHAD/DFT approach, which can quickly design new high-performance structural alloys for the application of FE power plants. The PI will mainly take charge of high-throughput DFT simulations and computational thermodynamics of the selected multicomponent alloy systems for the FE power plant applications. At the end of the project, a novel hybrid model based on high throughput CALPHAD/DFT simulations and computational thermodynamics will be developed to provide guidance on how to identify multi-component new high-performance structural alloys with much less computational effort needed. It will address the extensive computation time needed for DFT on the new alloys design. In addition, it will also address the well-known headache of DFT, i.e. how to make the accurate prediction of the high-temperature equilibria. The novel hybrid model the PI proposed will not only be applied to the design of high-performance structural alloys in FE power plants but in many different applications, such as nuclear reactors. This hybrid modeling approach includes four sections: 1) HT-CALPHAD modeling of Al-Co-Cr-Ni-Fe system with FCC and BCC phase. In this section, 3561 non-equiatomic compositions were randomly generated in order to investigate the phase stability of single FCC and BCC phases. Meanwhile, we proposed a data screening procedure to screen out the good candidates within these compositions, considering the temperature range, average density, and melting temperature, etc. 2) Investigation of FCC-Cr lattice stability in Fe-Cr system. We systematically assessed the reliability of FCC-Cr lattice stability derived by DFT and CALPHAD approaches. Meanwhile, the Fe-Cr binary system was chosen as a case study to verify the Cr lattice stability obtained by both approaches. 3) High-throughput DFT modeling on elastic properties of Al-Co-Cr-Ni-Fe systems. We predicted and established the FCC quinary elastic constant database of the Al-Co-Cr-Fe-Ni systems at 0K by using special quasi-random structure (SQS) approach. The predictions will start with pure elements of Al-Co-Cr-Fe-Ni system and will be continued with binaries, ternaries, quaternaries, and finally the quinary compositions. 3) Modeling of temperature-dependent elastic properties in Al-Co-Cr-Ni-Fe systems. In this part, we predict the thermal expansion coefficient and elastic stiffness coefficient as a function of temperature by applying quasiharmonic approximation. With this approach, the elastic properties of HEAs at elevate temperature can be estimated.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2025

FLAMES─Fast, Low-Storage, Accurate, and Memory-Efficient Adaptive Sampling─Approach to Resolve Spatially Dependent Dynamics of Molecular Liquids

Many critical phenomena in soft matter occur at large length scales, necessitating the resolution of their structure and dynamics at low wavenumbers. However, resolving wavenumber-dependent dynamics computationally via molecular dynamics simulations presents significant challenges, as these phenomena span several orders of magnitude in both time and length scales, resulting in high computational costs and memory demands. Here, this work highlights the computational and memory challenges associated with analyzing molecular trajectories in reciprocal space and demonstrates a method to address them. We introduce FLAMESFast, Low-storage, Accurate, and Memory-Efficient adaptive Sampling, which is a direct method for calculation of structure factors, allowing us to select only the required number of wavevectors for binning. We also use wavenumber-dependent time steps to extract dynamics. Our FLAMES approach effectively mitigates computational and memory/storage bottlenecks. We demonstrate the method using simulations of a model system, liquid octane, at various temperatures. Comparisons with experimental data and real space computation show that the FLAMES technique achieves high accuracy in resolving temperature- and spatially dependent dynamics while being significantly more computationally efficient and requiring less memory and storage than methods based on a uniform wavevector grid and fixed temporal spacing.

Chen, Guang [Argonne National Laboratory (ANL), Ar↗

DOE OSTI2022

Complexity Phase Diagram for Interacting and Long-Range Bosonic Hamiltonians

Here, we classify phases of a bosonic lattice model based on the computational complexity of classically simulating the system. We show that the system transitions from being classically simulable to classically hard to simulate as it evolves in time, extending previous results to include on-site number-conserving interactions and long-range hopping. Specifically, we construct a complexity phase diagram with easy and hard “phases” and derive analytic bounds on the location of the phase boundary with respect to the evolution time and the degree of locality. We find that the location of the phase transition is intimately related to upper bounds on the spread of quantum correlations and protocols to transfer quantum information. Remarkably, although the location of the transition point is unchanged by on-site interactions, the nature of the transition point does change. Specifically, we find that there are two kinds of transitions, sharp and coarse, broadly corresponding to interacting and noninteracting bosons, respectively. Our Letter motivates future studies of complexity in many-body systems and its interplay with the associated physical phenomena.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Operating Hardware Impact on the Heat Transfer Properties of Windows

Despite significant advancements in fenestration technology in the last two decades, the thermal transmittance of fenestration products is still significantly higher than that of walls. This corresponds to 60% of the total energy loss of a modern building envelope through the windows. Hence, further development and improvements of fenestration products are necessary. Increasingly stringent codes and standards for fenestration stimulate industry to work on improved solutions. Thus, it is crucial that assessment techniques are able to account for innovations accurately. The thermal effects of non-continuous hardware in window frames are currently ignored by international rating procedures. A preliminary investigation conducted by our team showed significant performance degradation in two of the three out-opening casement profiles caused by the presence of operating hardware. Frames with the structure made of vinyl and fiberglass consist of many air cavities that are penetrated by operating hardware made of highly conductive materials. In these frames, in order to have an accurate assessment, it may be required to employ three-dimensional modeling due to the convective nature of heat transfer within the cavities. However, in this study, we demonstrate that the three-dimensional (3D) effects of non-continuous hardware can be approximated accurately with simpler two-dimensional (2D) simulations. We then develop a simplified model based on weighted average capable of replacing the time- and computation-intensive 3D simulations with 2D simulations and validate it against market available frames and their corresponding hardware. Validation results show that our approximation technique results in discrepancies lower than 0.05 W/(m2K), or 3% of the total thermal transmittance. Thus, we conclude that simplified 2D simulation models may be used for predicting hardware impact in window frames with reasonable accuracy. As windows and glazing structures are becoming ever better thermally insulated, it is becoming even more important to be able to model the impact of the operating hardware on the total thermal performance in order to design the best windows possible and not let the operating hardware ruin an otherwise well-proven design, which is hence addressed in this study.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2024

Developing Multiphysics, Integrated, High-Fidelity, Massively Parallel Computational Capabilities for Fusion Applications Using MOOSE

As the need for fusion as a clean, sustainable, and abundant energy source grows internationally, so does the need for multiphysics, computational tools to model, study, and predict the complex interactions between plasma, materials, and engineering processes. These tools have a crucial role to play in solving scientific and engineering challenges and accelerating fusion energy deployment. To address these needs, modeling capabilities should enable massively parallel, multiphysics, fully integrated high-fidelity simulations of fusion systems. Additional attributes, such as being open source and modular while maintaining high software quality assurance standards will maximize impact by ensuring accessibility for all and wide acceptance, rapid expansion and development, as well as reliability, efficiency, and robustness. In this paper, we describe how the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework, which has a track record of success in the fission space thanks to the attributes listed above, can be leveraged in the fusion energy field. We highlight key successes of the MOOSE application in the fission space and describe how MOOSE has been and is being applied to fusion applications in the United States---e.g., Tritium Migration Analysis Program, version 8 (TMAP8), MOOSE Fusion Module, Fusion ENergy Integrated multiphys-X (FENIX)---and the United Kingdom---e.g., AURORA, Achlys, Apollo. These efforts aim to establish a suite of tools that can be further extended to accelerate fusion energy deployment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

AI for Science: Report on the Department of Energy (DOE) Town Halls on Artificial Intelligence (AI) for Science

The report documents the DOE Town Halls held during 2019 at Argonne National Laboratory, Oak Ridge National Laboratory, Lawrence Berkeley National Laboratory, and in Washington, DC. From July to October 2019, the Argonne, Oak Ridge, and Berkeley National Laboratories hosted a series of four town hall meetings attended by more than 1,000 U.S. scientists and engineers. The goal of the town hall series was to examine scientific opportunities in the areas of artificial intelligence (AI), Big Data, and high-performance computing (HPC) in the next decade, and to capture the big ideas, grand challenges, and next steps to realizing these opportunities. In this report and in the Department of Energy (DOE) laboratory community, we use the term “AI for Science” to broadly represent the next generation of methods and scientific opportunities in computing, including the development and application of AI methods (e.g., machine learning, deep learning, statistical methods, data analytics, automated control, and related areas) to build models from data and to use these models alone or in conjunction with simulation and scalable computing to advance scientific research. The AI for Science town hall discussions focused on capturing the transformational uses of AI that employ HPC and/or data analysis, leveraging data sets from HPC simulations or instruments and user facilities, and addressing scientific challenges unique to DOE user facilities and the agency’s wide-ranging fundamental and applied science enterprise.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Oxidation Behavior and Property Degradation of Nuclear Graphites

During its multidecade operation in the core of nuclear reactors, graphite components are subjected to aggressive and continuous exposure to a high field of ionizing and neutron irradiation, high temperature, and various types of present and postulated chemical attacks. High density, high crystallinity polygranular synthetic graphite is unique among other materials for its extraordinary capacity of resisting and adapting to the aggression inflicted by high temperature, high energy neutron bombardment and ionizing gamma radiation. But, as a carbonaceous material, even though of very high purity, graphite is reactive towards common oxidizing agents: oxygen, carbon dioxide, water. Safe operation of HTGRs relies, among other aspects, on engineered safeguard systems for efficient and continuous protection of graphite components against oxidation. Graphite oxidation behavior was, and continues to be, an important direction of theoretical and experimental research, engineering analyses, models and simulations, and design and safety regulations. The avalanche of publications, reports, experimental data, computer codes, and regulatory documents related to oxidation behavior of nuclear graphite is now accelerating to new levels, prompted by the increased interest for nuclear energy as a clean, carbon-free energy source. Even though public’s perception of nuclear energy advantages may still be influenced by the memories of past accidents of nuclear reactors from generations II and III, the community of informed scientists and engineers, regulators and statemen knows that generation IV of nuclear reactors is designed at very high safety standards, doubled by great advances of scientific knowledge and technological progress. One of routes of these recent advances is directed at better understanding of graphite oxidation behavior, its relationship with graphite manufacturing and microstructural properties, along with the effects of various environmental factors and process variables. Together, the recent progress in manufacturing, properties characterization, and modeling of intricated physical and chemical processes that concur to the oxidation behavior led to development of powerful simulation codes able to analyze various scenarios of normal operation and hypothetical off-normal events, and thus to clearly specify the allowable parameters envelopes for the designers, constructors, and operators of current and future modular HTGRs. This review begins with an introduction on manufacturing methods, structure, and properties of nuclear graphite, including basic requirements that this specialty graphite type must satisfy for nuclear use. It continues with a chapter on environmental effects on nuclear graphite, where emphasis is placed less on irradiation and much more on oxidation phenomena, their safety implications, and the basic traits of chronic and acute oxidation by air (oxygen) and water (humidity, steam). Particular attention is placed on the three graphite grades of interest for this document (IG-110, NBG-18, PCEA). A chapter on properties degradation induced by oxidation follows, with focus on density, dimensional, and mechanical properties changes. The next chapter is intended as a brief review of various approaches used for modeling of graphite oxidation behavior. It summarizes the progress of oxidation models, from the early attempts to complex computational approaches interfaced with specialized computer codes designed for nuclear reactor simulations. Last, a list is presented of knowledge gaps where more research is needed. A short summary concludes the review.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Nowcasting Earthquakes With Stochastic Simulations: Information Entropy of Earthquake Catalogs

Earthquake nowcasting has been proposed as a means of tracking the change in large earthquake potential in a seismically active area. The method was developed using observable seismic data, in which probabilities of future large earthquakes can be computed using Receiver Operating Characteristic methods. Furthermore, analysis of the Shannon information content of the earthquake catalogs has been used to show that there is information contained in the catalogs, and that it can vary in time. So an important question remains, where does the information originate? In this paper, we examine this question using stochastic simulations of earthquake catalogs. Our catalog simulations are computed using an Earthquake Rescaled Aftershock Seismicity (“ERAS”) stochastic model. This model is similar in many ways to other stochastic seismicity simulations, but has the advantage that the model has only 2 free parameters to be set, one for the aftershock (Omori-Utsu) time decay, and one for the aftershock spatial migration away from the epicenter. Generating a simulation catalog and fitting the two parameters to the observed catalog such as California takes only a few minutes of wall clock time. While clustering can arise from random, Poisson statistics, we show that significant information in the simulation catalogs arises from the “non-Poisson” power-law aftershock clustering, implying that the practice of de-clustering observed catalogs may remove information that would otherwise be useful in forecasting and nowcasting. We also show that the nowcasting method provides similar results with the ERAS model as it does with observed seismicity.

58 GEOSCIENCES↗

DOE OSTI2020

A geospatial model for the analysis of time-dependent land subsidence induced by reservoir depletion

Land subsidence due to fluid depletion is an outcome of physical processes operating across a wide range of time and length scales. Although geomechanical models are crucial to simulate reservoir compaction and predict its long-term fate, their use across large regions often bears prohibitive computational costs. To overcome this obstacle, this paper proposes a simplified modelling framework consisting of (i) a near-field numerical solver simulating the coupling between fluid flow and rock deformation with reference to a simplified one-dimensional geometry and (ii) a far-field geospatial algorithm mapping ground settlements across a region through the superposition of poroelastic computations at multiple wells. The model computes the delay between depletion history and reservoir compaction in proximity of a producing well by assuming basal depletion of a fluid-saturated deformable disk, while the Geertsma solution of nucleus of strain is used to extrapolate the impact of such time-varying reservoir compaction around the well. This approach has been used to back-analyze the spatio-temporal progression of subsidence at the Groningen gas field. The results are compared against measurements collected over 50 year of production at 25 benchmark locations scattered over an area of 900 km 2 . It is shown that coupled simulations based on average values of rock compressibility and permeability lead to nonlinear trends of subsidence evolution in good agreement with field measurements, while uncoupled analyses overpredict settlements by more than 70%. Lastly, synthetic forecasts based on different rates of depletion were provided. The results suggest that slower depletion rates lead to lower subsidence at a given time, and that residual subsidence may continue to develop for several decades after interruption of production activities.

58 GEOSCIENCES↗

DOE OSTI2021

Modeling laser-driven ion acceleration with deep learning

Developments in machine learning promise to ameliorate some of the challenges of modeling complex physical systems through neural-network-based surrogate models. High-intensity, short-pulse lasers can be used to accelerate ions to mega-electronvolt energies, but to model such interactions requires computationally expensive techniques such as particle-in-cell simulations. Multilayer neural networks allow one to take a relatively sparse ensemble of simulations and generate a surrogate model that can be used to rapidly search the parameter space of interest. In this study, we created an ensemble of over 1,000 simulations modeling laser-driven ion acceleration and developed a surrogate to study the resulting parameter space. A neural-network-based approach allows for rapid feature discovery not possible for traditional parameter scans given the computational cost. A notable observation made during this study was the dependence of ion energy on the pre-plasma gradient length scale. While this methodology harbors great promise for ion acceleration, it has ready application to all topics in which large-scale parameter scans are restricted by significant computational cost or relatively large, but sparse, domains.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

An adaptive, data-driven multiscale approach for dense granular flows

The accuracy of coarse-grained continuum models of dense granular flows is limited by the lack of high-fidelity closure models for granular rheology. One approach to addressing this issue, referred to as the hierarchical multiscale method, is to use a high-fidelity fine-grained model to compute the closure terms needed by the coarse-grained model. The difficulty with this approach is that the overall model can become computationally intractable due to the high computational cost of the high-fidelity model. In this work, we describe a multiscale modeling approach for dense granular flows that utilizes neural networks trained using high-fidelity discrete element method (DEM) simulations to approximate the constitutive granular rheology for a continuum incompressible flow model. Our approach leverages an ensemble of neural networks to estimate predictive uncertainty that allows us to determine whether the rheology at a given point is accurately represented by the neural network model. Additional DEM simulations are only performed when needed, minimizing the number of additional DEM simulations required when updating the rheology. This adaptive coupling significantly reduces the overall computational cost of the approach while controlling the error. In addition, the neural networks are customized to learn regularized rheological behavior to ensure well-posedness of the continuum solution. We first validate the approach using two-dimensional steady-state and decelerating inclined flows. We then demonstrate the efficiency of our approach by modeling three-dimensional sub-aerial granular column collapse for varying initial column aspect ratios, where our multiscale method compares well with the computationally expensive computational fluid dynamics (CFD)-DEM simulation.

Dense granular flows↗

DOE OSTI2026

Fast and accurate calculation of EXAFS Debye-Waller factors in U⁢O2 using the dynamical matrix method

Theoretical modeling of bonding dynamics in metal oxides is required for predicting their thermal conductivity, catalytic activity, and mechanical properties. A primary challenge is the scarcity of experimental methods for validating theoretical predictions of these atomic-scale dynamics. This work presents a workflow that uses experimental extended x-ray absorption fine structure (EXAFS) data collected at high temperatures to validate an interatomic force field for uranium dioxide (UO2), an important model material. The validated force field is then used to drive computationally intensive molecular dynamics (MD) simulations and as input for the much faster dynamical matrix Debye-Waller (DMDW) method. The predicted values of the Debye-Waller factors from the DMDW calculations are in good agreement with those obtained from the MD simulations, with residual pair-specific differences attributable to quantum zero-point motion at low temperatures and lattice anharmonicity at high temperatures. We further show that theoretical EXAFS spectra constructed directly from DMDW-derived Debye-Waller factors reproduce the experimental data (at relatively low temperatures) with accuracy comparable to full MD-EXAFS, providing an additional validation of the choice of the potential. This study establishes a validated, rapid computational pathway for modeling bond dynamics, naturally incorporating quantum nuclear\\\\r\\\\nstatistics absent in classical simulations, which are essential for the mechanistic understanding of complex oxide materials.

58 GEOSCIENCES↗

DOE OSTI2024

Challenging Common Assumptions of Thick-Wall Chamber Dynamics in Inertial Fusion Systems Using MOOSE-based Multiphysics Simulations

As an increasing number of companies look toward commercial Inertial Fusion Energy (IFE) designs, there is a pressing need to understand the physics of thick-wall chamber gas dynamics. The thick liquid wall approach implements a renewable wall to mitigate the fusion target emissions, thereby reducing the radiation damage rate and significantly extending the lifetime of chamber structures, leading to increased plant availability and reduced waste streams in comparison to dry wall chamber designs. It is necessary, however, to assess the critical performance and safety aspects of these systems. For example, it is crucial to predict (1) where the mass ablated from the liquid walls will vent, which determines the placement of condensing surfaces; (2) debris propagation up the beam lines, which provides essential information for design and protection requirements; (3) peak pressures and impulse on chamber walls, which affect chamber structural design; and (4) momentum transfer to the liquid jets, which constrains the shape and positioning of the jets. In turn, the chamber design and its liquid walls affect shielding requirements, material activation, and tritium fuel cycle. Currently available simulation tools, however, are unable to accurately capture key thick-wall chamber dynamics. Significant assumptions are often made to simplify the system and reduce computational cost and modeling capability needs, but the impact of these assumptions on simulation predictions has not been evaluated. For example, no three-dimensional simulations can be found in the open literature to evaluate gas venting and momentum transfer to the jets with simulations using two-dimensional domains to represent complex three-dimensional geometries. Moreover, limited studies have been dedicated to jet breakup due to both turbulence and neutron heating, and no studies have been found that evaluate how jet breakup can impact shock-jet interaction. Furthermore, effects of radiative heat transfer have rarely been included for the hydrodynamic phase of shock propagation, and integration of proper equations of state in shock dynamics codes has been mostly exploratory. In this study, we use the flexible, high-fidelity Multiphysics Object-Oriented Simulation Environment (MOOSE) to model these complex phenomena and inform design and safety studies. Capabilities to model thick-wall chamber gas dynamics are being developed, and the impact of the assumptions listed above (i.e., two-dimensional vs three-dimensional, absence of jet breakout, no radiative heat transfer, and ideal gas behavior) are being quantified.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Multidisciplinary design optimization in Architecture, Engineering, and Construction: a detailed review and call for collaboration

The design of buildings has become a complex and multidisciplinary problem involving multiple conflicting objectives as architects and designers address competing technical, economic, environmental, and societal concerns. This has been driving research in Architecture, Engineering, and Construction (AEC) toward rigorous multidisciplinary decision-making frameworks that generate and evaluate numerous design alternatives using multi-objective optimization in concert with simulation and analysis models of varying fidelity and computational expense. While such frameworks are well known and widely employed in the aerospace and systems engineering domains, efforts by design professionals and researchers in the AEC field are scattered at best. In this paper, we provide a detailed review of recent developments in optimization frameworks in the AEC field and subsequently highlight how such developments are largely compartmentalized into separate domains such as structural, energy, daylighting, and other performance factors. Herein, we further discuss the technical challenges involved in concurrent coupled multidisciplinary design optimization (MDO) in the AEC field such as interoperability issues between Building Information Modeling (BIM) environments, analysis/simulation tools, and optimization frameworks. We conclude by outlining research needed for more unified modeling and simulation-based optimization frameworks to aid in complex and multidisciplinary building design processes. We also highlight the need for the identification and development of multi-fidelity simulation tools for use across multiple design phases. As such, this paper contributes a novel roadmap to leverage aerospace and systems engineering research in MDO into the field of AEC, along with a call for researchers in the MDO community to seek collaborations in AEC field.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2022

Towards Z-Next: The Integration of Theory, Experiments, and Computational Simulation in a Bayesian Data Assimilation Framework

Making reliable predictions in the presence of uncertainty is critical to high-consequence modeling and simulation activities, such as those encountered at Sandia National Laboratories. Surrogate or reduced-order models are often used to mitigate the expense of performing quality uncertainty analyses with high-fidelity, physics-based codes. However, phenomenological surrogate models do not always adhere to important physics and system properties. This project develops surrogate models that integrate physical theory with experimental data through a maximally-informative framework that accounts for the many uncertainties present in computational modeling problems. Correlations between relevant outputs are preserved through the use of multi-output or co-predictive surrogate models; known physical properties (specifically monotoncity) are also preserved; and unknown physics and phenomena are detected using a causal analysis. By endowing surrogate models with key properties of the physical system being studied, their predictive power is arguably enhanced, allowing for reliable simulations and analyses at a reduced computational cost.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Challenging Common Assumptions of Thick-Wall Chamber Dynamics in Inertial Fusion Systems using MOOSE

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

The confluence of machine learning and multiscale simulations

Multiscale modeling has a long history of use in structural biology, as computational biologists strive to overcome the time- and length-scale limits of atomistic molecular dynamics. Contemporary machine learning techniques, such as deep learning, have promoted advances in virtually every field of science and engineering and are revitalizing the traditional notions of multiscale modeling. Deep learning has found success in various approaches for distilling information from fine-scale models, such as building surrogate models and guiding the development of coarse-grained potentials. However, perhaps its most powerful use in multiscale modeling is in defining latent spaces that enable efficient exploration of conformational space. In conclusion, this confluence of machine learning and multiscale simulation with modern high-performance computing promises a new era of discovery and innovation in structural biology.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Coordinate-based simulation of pair distance distribution functions for small and large molecular assemblies: implementation and applications

X-ray scattering has become a major tool in the structural characterization of nanoscale materials. Thanks to the widely available experimental and computational atomic models, coordinate-based X-ray scattering simulation has played a crucial role in data interpretation in the past two decades. However, simulation of real-space pair distance distribution functions (PDDFs) from small- and wide-angle X-ray scattering, SAXS/WAXS, has been relatively less exploited. This study presents a comparison of PDDF simulation methods, which are applied to molecular structures that range in size from β-cyclodextrin [1 kDa molecular weight (MW), 66 non-hydrogen atoms] to the satellite tobacco mosaic virus capsid (1.1 MDa MW, 81 960 non-hydrogen atoms). The results demonstrate the power of interpretation of experimental SAXS/WAXS from the real-space view, particularly by providing a more intuitive method for understanding of partial structure contributions. Furthermore, the computational efficiency of PDDF simulation algorithms makes them attractive as approaches for the analysis of large nanoscale materials and biological assemblies. The simulation methods demonstrated in this article have been implemented in stand-alone software, SolX 3.0 , which is available to download from https://12idb.xray.aps.anl.gov/solx.html.

Zuo, Xiaobing (ORCID:0000000201344804)↗