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Results for “Mathematical crystallography”

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

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13 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Combined molecular and spin dynamics simulation of BCC iron with vacancy defects

Utilizing an atomistic computational model, which handles both translational and spin degrees of freedom, combined molecular and spin dynamics simulations have been performed to investigate the effect of vacancy defects on spin wave excitations in ferromagnetic iron. Fourier transforms of space- and time-displaced correlation functions yield the dynamic structure factor, providing characteristic frequencies and lifetimes of the spin wave modes. A comparison of the system with a 5% vacancy concentration with pure lattice data shows a decrease in frequency and a decrease in lifetime for all transverse spin wave excitations observed. In addition, the clearly defined transverse spin wave excitations are distorted with the introduction of vacancy defects, and we observe reduced excitation lifetimes due to increased magnon–magnon scattering. We observe further evidence of increased magnon–magnon scattering, as the peaks in the longitudinal spin wave spectrum become less distinct. Finally, similar impacts are observed in the vibrational subsystem, with a decrease in characteristic phonon frequency and flattening of lattice excitation signals due to vacancy defects.

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

Correlation function metrology for warm dense matter: Recent developments and practical guidelines

X-ray Thomson scattering (XRTS) has emerged as a valuable diagnostic for matter under extreme conditions, as it captures the intricate many-body physics of the probed sample. Recent advances, such as the model-free temperature diagnostic of Dornheim et al. [Nat. Commun. 13 , 7911 (2022)], have demonstrated how much information can be extracted directly within the imaginary-time formalism. However, since the imaginary-time formalism is a concept often difficult to grasp, we provide here a systematic overview of its theoretical foundations and explicitly demonstrate its practical applications to temperature inference, including relevant subtleties. Furthermore, we present recent developments that enable the determination of the absolute normalization, Rayleigh weight, and density from XRTS measurements without reliance on uncontrolled model assumptions. Finally, we outline a unified workflow that guides the extraction of these key observables, offering a practical framework for applying the method to interpret experimental measurements.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Integrable symplectic maps with a polygon tessellation

Identifying integrable dynamics remains a formidable challenge, and despite centuries of research, only a handful of examples are known to date. In this article, we explore a distinct form of area-preserving (symplectic) mappings derived from the stroboscopic Poincaré cross section of a kicked rotator—an oscillator subjected to an external force periodically switched on in short pulses. The significance of this class of problems extends to various applications in physics and mathematics, including particle accelerators, crystallography, and studies of chaos. Notably, Suris's theorem constrains the integrability within this category of mappings, outlining potential scenarios with analytic invariants of motion. In this paper, we challenge the assumption of the analyticity of the invariant by exploring piecewise linear transformations on a torus ( T 2 ) and associated systems on the plane ( R 2 ), incorporating arithmetic quasiperiodicity and discontinuities. Introducing a new automated technique, we discovered previously unknown scenarios featuring polygonal invariants that form perfect tessellations and, moreover, fibrations of the plane or torus. This work reveals a novel category of planar tilings characterized by discrete symmetries that emerge from the invertibility of transformations and are intrinsically linked to the presence of integrability. Our algorithm relies on the analysis of the Poincaré rotation number and its piecewise monotonic nature for integrable cases, contrasting with the noisy behavior in the case of chaos, thereby allowing for clear separation. Some of the newly discovered systems exhibit the peculiar behavior of “integrable diffusion,” characterized by infinite and quasirandom hopping between tiles while being confined to a set of invariant segments. Finally, through the implementation of a smoothening procedure, all mappings can be generalized to quasi-integrable scenarios with suppressed volume occupied by chaotic trajectories, thereby opening doors to potential practical applications. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

ExaFEL: extreme-scale real-time data processing for X-ray free electron laser science

ExaFEL is an HPC-capable X-ray Free Electron Laser (XFEL) data analysis software suite for both Serial Femtosecond Crystallography (SFX) and Single Particle Imaging (SPI) developed in collaboration with the Linac Coherent Lightsource (LCLS), Lawrence Berkeley National Laboratory (LBNL) and Los Alamos National Laboratory. ExaFEL supports real-time data analysis via a cross-facility workflow spanning LCLS and HPC centers such as NERSC and OLCF. Our work therefore constitutes initial path-finding for the US Department of Energy's (DOE) Integrated Research Infrastructure (IRI) program. We present the ExaFEL team's 7 years of experience in developing real-time XFEL data analysis software for the DOE's exascale supercomputers. We present our experiences and lessons learned with the Perlmutter and Frontier supercomputers. Furthermore we outline essential data center services (and the implications for institutional policy) required for real-time data analysis. Finally we summarize our software and performance engineering approaches and our experiences with NERSC's Perlmutter and OLCF's Frontier systems. This work is intended to be a practical blueprint for similar efforts in integrating exascale compute resources into other cross-facility workflows.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Crystal Orientation and Defect Mapping in Electron-Beam-Sensitive Zeolites with Near-Axis Transmission Kikuchi Diffraction

Porous materials are vital in catalysis, energy conversion, and environmental remediation. Understanding structural heterogeneity in zeolites is key to linking synthesis, framework intergrowths, and catalytic performance, yet current methods for phase identification and spatial mapping lack sufficient resolution or throughput. We present a high-throughput approach using near-axis transmission Kikuchi diffraction in a scanning electron microscope, achieving high phase and spatial resolution for electron-beam-sensitive zeolites, including ZSM-5 and, for the first time, Zeolite A. Here, this method enables direct visualization of intergrowth features that critically affect catalytic and adsorption behavior, bridging the gap between ensemble-averaged X-ray diffraction and high-resolution but low-throughput transmission electron microscopy. Combining nanoscale mapping with statistical sampling is highly suited for machine-learning pipelines guiding new structure function understanding and could be extended to other beam-sensitive porous materials such as metal–organic or covalent–organic frameworks.

crystallography↗
DOE OSTI2024

Deconvolution of dynamic heterogeneity in protein structure

Heterogeneity is intrinsic to the dynamic process of a chemical reaction. As reactants are converted to products via intermediates, the nature and extent of heterogeneity vary temporally throughout the duration of the reaction and spatially across the molecular ensemble. The goal of many biophysical techniques, including crystallography and spectroscopy, is to establish a reaction trajectory that follows an experimentally provoked dynamic process. It is essential to properly analyze and resolve heterogeneity inevitably embedded in experimental datasets. We have developed a deconvolution technique based on singular value decomposition (SVD), which we have rigorously practiced in diverse research projects. In this review, we recapitulate the motivation and challenges in addressing the heterogeneity problem and lay out the mathematical foundation of our methodology that enables isolation of chemically sensible structural signals. We also present a few case studies to demonstrate the concept and outcome of the SVD-based deconvolution. Finally, we highlight a few recent studies with mechanistic insights made possible by heterogeneity deconvolution.

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

Growth functions of periodic space tessellations

This work analyzes the rules governing the growth of the numbers of vertices, edges and faces in all possible periodic tessellations of the 2D Euclidean space, and encodes those rules in several types of polynomial growth functions. These encodings map the geometric, combinatorial and topological properties of the tessellations into sets of integer coefficients. Several general statements about these encodings are given with rigorous mathematical proof. The variation of the growth functions is represented graphically and analyzed in orphic diagrams, so named because of their similarity to orphic art. Several examples of 3D space groups are included, to emphasize the complexity of the growth functions in higher dimensions. A freely available Python library is presented to facilitate the discovery of the growth functions and the generation of orphic diagrams.

Chemistry↗
DOE OSTI2024

Structure analysis of the telomere resolvase from the Lyme disease spirochete Borrelia garinii reveals functional divergence of its C-terminal domain

Borrelia spirochetes are the causative agents of Lyme disease and relapsing fever, two of the most common tick-borne illnesses. A characteristic feature of these spirochetes is their highly segmented genomes which consists of a linear chromosome and a mixture of up to approximately 24 linear and circular extrachromosomal plasmids. The complexity of this genomic arrangement requires multiple strategies for efficient replication and partitioning during cell division, including the generation of hairpin ends found on linear replicons mediated by the essential enzyme ResT, a telomere resolvase. Using an integrative structural biology approach employing advanced modelling, circular dichroism, X-ray crystallography and small-angle X-ray scattering, we have generated high resolution structural data on ResT from B. garinii. Our data provides the first high-resolution structures of ResT from Borrelia spirochetes and revealed active site positioning in the catalytic domain. We also demonstrate that the C-terminal domain of ResT is required for both transesterification steps of telomere resolution, and is a requirement for DNA binding, distinguishing ResT from other telomere resolvases from phage and bacteria. These results advance our understanding of the molecular function of this essential enzyme involved in genome maintenance in Borrelia pathogens.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Robust error calibration for serial crystallography

Serial crystallography is an important technique with unique abilities to resolve enzymatic transition states, minimize radiation damage to sensitive metalloenzymes and perform de novo structure determination from micrometre-sized crystals. This technique requires the merging of data from thousands of crystals, making manual identification of errant crystals unfeasible. cctbx.xfel.merge uses filtering to remove problematic data. However, this process is imperfect, and data reduction must be robust to outliers. We add robustness to cctbx.xfel.merge at the step of uncertainty determination for reflection intensities. This step is a critical point for robustness because it is the first step where the data sets are considered as a whole, as opposed to individual lattices. Robustness is conferred by reformulating the error-calibration procedure to have fewer and less stringent statistical assumptions and incorporating the ability to down-weight low-quality lattices. We then apply this method to five macromolecular XFEL data sets and observe the improvements to each. The appropriateness of the intensity uncertainties is demonstrated through internal consistency. This is performed through theoretical CC 1/2 and I /σ relationships and by weighted second moments, which use Wilson's prior to connect intensity uncertainties with their expected distribution. This work presents new mathematical tools to analyze intensity statistics and demonstrates their effectiveness through the often underappreciated process of uncertainty analysis.

Mittan-Moreau, David W.↗
DOE OSTI2024

Towards Autonomous Experiments by Connecting High Performance Microscopy with High Performance Computing

The digitization of controls, data, and analysis in microscopy is bringing the idea of autonomous microscopes closer to reality than ever before. Automated transmission electron microscopy (TEM) is already fairly routine for some experiments the only require simple repetitive tasks such as imaging biological macromolecules for single particle cryoEM [1], tilt series for electron tomography [2], and movies for crystallography [3]. The vast majority of TEM experiments are conducted completely by human operators who choose the regions of interest, optimize experimental parameters, and make decisions about data quality visually during an experiment. The field is still a long way from having completely autonomous TEMs that can adapt to sample difficulties and tune experimental parameters based on data quality and desired experimental outcomes. Part of the issue is the lack of capability for feeding information learned from on-line, live data analysis back into the on-going experiment [4]. Furthermore, this presentation will discuss current capabilities for large scale data reduction and analysis using high performance computing (i.e. supercomputing) and progress towards developing a true feed-back loop that places data analysis and theory in the experimental loop.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Combining Reactive Quantum-Mechanical Molecular-Dynamics Simulations with Mutagenesis, Crystallography, and Enzyme Kinetics to Reveal Plausible Steps of Isocyanide Hydratase Catalysis

A complete understanding of enzyme mechanisms requires atomistic details of chemical reactions. Quantum-based molecular dynamics simulations (QMD) are a potential source of this information, but trade-offs between accuracy and computational cost have limited their use. We previously developed extended Lagrangian Born–Oppenheimer molecular dynamics (XL-BOMD) methods that leverage a negligible compromise in accuracy to substantially decrease the cost of QMD simulations. Here, we develop a reactive QMD approach using the latest XL-BOMD formulation, which enables efficient simulations of highly reactive systems, and use it to investigate mechanisms of intermediate formation in isocyanide hydratase (ICH) catalysis. In QMD simulations, molecular analogs of ICH active site residues reacted with para-nitrophenyl isocyanide, forming a thioimidate. Analysis of simulated atomic configurational and charge dynamics revealed a pathway where protonation of the isocyanide carbon occurs prior to thioimidate formation and suggested a possible role of Asp17 as a proton donor in the early phase of ICH catalysis. To test whether the pathway seen using the reactive QMD approach might be relevant to ICH catalysis, we performed X-ray crystallography and pre-steady-state enzyme kinetics studies of wild-type and D17N mutant ICH. Both the structure and kinetics are sensitive to the D17N mutation in a manner that is consistent with the order of the reaction steps seen in the simulations. Mobile protons play essential roles in many enzymes, yet they are difficult to observe experimentally, making the ordering of proton-dependent steps ambiguous in many enzyme mechanisms. The ability to directly simulate model reactions for the design of experiments that provide information about enzyme mechanisms involving mobile protons demonstrates the significance of our reactive QMD approach and motivates further biological applications.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Integrated edge-to-exascale workflow for real-time steering in neutron scattering experiments

We introduce a computational framework that integrates artificial intelligence (AI), machine learning, and high-performance computing to enable real-time steering of neutron scattering experiments using an edge-to-exascale workflow. Focusing on time-of-flight neutron event data at the Spallation Neutron Source, our approach combines temporal processing of four-dimensional neutron event data with predictive modeling for multidimensional crystallography. At the core of this workflow is the Temporal Fusion Transformer model, which provides voxel-level precision in predicting 3D neutron scattering patterns. The system incorporates edge computing for rapid data preprocessing and exascale computing via the Frontier supercomputer for large-scale AI model training, enabling adaptive, data-driven decisions during experiments. This framework optimizes neutron beam time, improves experimental accuracy, and lays the foundation for automation in neutron scattering. Although real-time experiment steering is still in the proof-of-concept stage, the demonstrated potential of this system offers a substantial reduction in data processing time from hours to minutes via distributed training, and significant improvements in model accuracy, setting the stage for widespread adoption across neutron scattering facilities and more efficient exploration of complex material systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

X-ray thermal diffuse scattering as a texture-robust temperature diagnostic for dynamically compressed solids

We present a model of x-ray thermal diffuse scattering (TDS) from a cubic polycrystal with an arbitrary crystallographic texture, based on the classic approach of Warren [B. E. Warren, Acta Crystallogr. 6, 803 (1953)]. We compare the predictions of our model with femtosecond x-ray diffraction patterns gathered from ambient and dynamically compressed rolled copper foils obtained at the High Energy Density instrument of the European X-Ray Free-Electron Laser facility and find that the texture-aware TDS model yields more accurate results than does the conventional powder model owed to Warren. Nevertheless, we further show: with sufficient angular detector coverage, the TDS signal is largely unchanged by sample orientation and in all cases strongly resembles the signal from a perfectly random powder; shot-to-shot fluctuations in the TDS signal resulting from grain-sampling statistics are at the percent level, in stark contrast to the fluctuations in the Bragg-peak intensities (which are over an order of magnitude greater); and TDS is largely unchanged even following texture evolution caused by compression-induced plastic deformation. We conclude that TDS is robust against texture variation, making it a flexible temperature diagnostic applicable just as well to off-the-shelf commercial foils as to ideal powders.

Crystal lattices↗