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DOE OSTI2026

Validated ligand geometries for macromolecular refinement restraints and molecular-mechanics force fields

In macromolecular structure refinement, the low observation-to-parameter ratio and the lack of high-resolution data are countered by using a priori information in the form of restraints. Having accurate geometries of the chemical entities in the sample is paramount for generating accurate chemical restraints and, therefore, accurate macromolecular structures. In particular, it is desirable to have accurate restraints for known and novel ligand entities. Quantum mechanics (QM) can minimize the energy of a ligand by adjusting its geometry, and these geometries can be used to generate restraints for macromolecular refinement. This article describes a library of approximately 37 000 small molecules extracted from the Chemical Component Dictionary in the Protein Data Bank and minimized by density-functional QM. The library includes restraint files for use in crystallography or cryo-EM refinement, along with files suitable for molecular-dynamics simulation. Because the geometries are validated using the Cambridge Structural Database, the restraints library provides users with both functional restraints and minimized geometries. This work also provides procedures for generating new and accurate restraints.

Amber↗

DOE OSTI2023

In-Situ Detection and Prediction of WAAM Cross Feature Geometry

Abstract Wire arc additive manufacturing (WAAM) is increasingly used by manufacturers due to its relatively low cost and high deposition rate compared to other metal AM methods, but the parts produced by WAAM can be subject to localized variations in part quality. One such variation is the cross-feature defect, whereby a localized part height increase occurs due to the crossing of deposition toolpaths. Mitigation of this defect is typically achieved using manual path planning strategies, but closed-loop control is underutilized. Since the nature of this defect and of the WAAM process is such that the previous layer’s geometry influences that of the subsequent layer’s, the cross-feature defect geometry changes throughout the deposition. Therefore, any closed-loop control strategy will need to incorporate the dynamic trait of this defect. The present work seeks to implement an in-situ process modeling approach where a regression model can be continuously updated to predict the defect geometry of the subsequent deposition layer based on the historical process data. Several multi-layer cross-feature geometries are deposited and current, voltage, and optical camera data is taken for each layer. The resulting cross-feature geometries are characterized using 3D scanning and the performance and accuracy of the in-situ modeling approach is evaluated.

Thien, Austen↗

DOE OSTI2022

Stereolithographic geometry model of the IBR-2M experimental facility

The IBR-2M is a fast research reactor that operates in supercritical condition for ∼ 800 μs every 200 ms. Two reflector parts in nickel rotate in opposite directions generating 1.8 GWth peak power when they align with the fuel zone changing the reactor status from deep subcritical to supercritical. The reactor core uses high-enriched plutonium fuel and is cooled by sodium. This reactor has been modeled by MCNP and SERPENT computer programs. The MCNP model uses combinatorial geometry, whereas the SERPENT model employs the Stereolithographic (STL) geometry representation that can be used by 3D printers. The STL geometry was constructed using the CUBIT computer program. The CUBIT program was also used for a three-dimensional visualization of the Monte Carlo models. SERPENT and MCNP models use the same geometry, material specifications, and nuclear data. The latter are based on the ENDF/B-7.0 library. SERPENT and MCNP using same geometry and same material specifications produce similar k{sub eff} values within 120 pcm.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2022

Universal suppression of superfluid weight by non-magnetic disorder in $s$-wave superconductors independent of quantum geometry and band dispersion

Motivated by the experimental progress in controlling the properties of the energy bands in superconductors, significant theoretical efforts have been devoted to study the effect of the quantum geometry and the flatness of the dispersion on the superfluid weight. In conventional superconductors, where the energy bands are wide and the Fermi energy is large, the contribution due to the quantum geometry is negligible, but in the opposite limit of flat-band superconductors the superfluid weight originates purely from the quantum geometry of Bloch wave functions. Here, we study how the energy band dispersion and the quantum geometry affect the disorder-induced suppression of the superfluid weight. In particular, we consider non-magnetic disorder and s-wave superconductivity. Surprisingly, we find that the disorder-dependence of the superfluid weight is universal across a variety of models, and independent of the quantum geometry and the flatness of the dispersion. Our results suggest that a flat-band superconductor is as resilient to disorder as a conventional superconductor.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Parametric Study of SANSMIC Input and Resulting Impact on Predicted Cavern Geometry and Leaching Efficiency

The Sandia Solution Mining Code (SANSMIC) has been used for many years to examine the development of salt cavern geometry, both in a confirmatory manner with comparisons made to real-world sonar data and in a predictive manner when updated sonar data are not available. SANSMIC models require some modeling choices in order to incorporate real-world data. Key modeling choices include the vertical resolution of cavern geometry to implement, as well as how to incorporate daily raw water injection data into the SANSMIC model. This report documents five studies that address the impact of the modeling choices on the predicted cavern geometries and calculated leaching efficiencies. In most cases, hypothetical cylindrical initial cavern geometries are used to provide a common baseline against which to test the systematic variation of input variables including cavern radius, oil-brine-interface (OBI) depth, vertical cell size, raw water injection rate, raw water injection duration, workover time, and number of leaching stages. The use of smaller cell sizes is recommended moving forward to provide a better one-to-one relationship between sonar data and the modeled cavern. A new methodology for incorporating raw water injection data is also recommended, in order to more closely model real-world injection and workover times. Overall, the systematic studies performed here have increased our confidence in previous SANSMIC model results, as well future use of the code for predicting leaching effects on cavern geometries. Some minor changes to modeling choices are recommended, which can easily be applied with the version of SANSMIC currently under development.

42 ENGINEERING↗

DOE OSTI2021

Generalising G 2 geometry: involutivity, moment maps and moduli

We analyse the geometry of generic Minkowski N = 1, D = 4 flux compactifications in string theory, the default backgrounds for string model building. In M-theory they are the natural string theoretic extensions of G2 holonomy manifolds. In type II theories, they extend the notion of Calabi-Yau geometry and include the class of flux backgrounds based on generalised complex structures first considered by Graña et al. (GMPT). Using E 7(7) × $\mathbb{R}$ + generalised geometry we show that these compactifications are characterised by an SU(7) ⊂ E 7(7) structure defining an involutive subbundle of the generalised tangent space, and with a vanishing moment map, corresponding to the action of the diffeomorphism and gauge symmetries of the theory. The Kähler potential on the space of structures defines a natural extension of Hitchin’s G 2 functional. Using this framework we are able to count, for the first time, the massless scalar moduli of GMPT solutions in terms of generalised geometry cohomology groups. It also provides an intriguing new perspective on the existence of G 2 manifolds, suggesting possible connections to Geometrical Invariant Theory and stability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Heterotic backgrounds via generalised geometry: moment maps and moduli

We describe the geometry of generic heterotic backgrounds preserving minimal supersymmetry in four dimensions using the language of generalised geometry. They are characterised by an SU(3) × Spin(6 + n) structure within O(6, 6 + n) x $\mathbb{R}$ + generalised geometry. Supersymmetry of the background is encoded in the existence of an involutive subbundle of the generalised tangent bundle and the vanishing of a moment map for the action of diffeomorphisms and gauge symmetries. We give both the superpotential and the Kähler potential for a generic background, showing that the latter defines a natural Hitchin functional for heterotic geometries. Intriguingly, this formulation suggests new connections to geometric invariant theory and an extended notion of stability. Finally we show that the analysis of infinitesimal deformations of these geometric structures naturally reproduces the known cohomologies that count the massless moduli of supersymmetric heterotic backgrounds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Standard Model in conformal geometry: Local vs gauged scale invariance

Here, we discuss comparatively local versus gauged Weyl symmetry beyond Standard Model (SM) and Einstein gravity and their geometric interpretation. The SM and Einstein gravity admit a natural embedding in Weyl integrable geometry which is a special limit of Weyl conformal (non-metric) geometry. The theory has a local Weyl scale symmetry but no associated gauge boson. Unlike previous models with such symmetry, this embedding is truly minimal i.e. with no additional fields beyond SM and underlying geometry. This theory is compared to a similar minimal embedding of SM and Einstein gravity in Weyl conformal geometry (SMW) which has a full gauged scale invariance, with an associated Weyl gauge boson. At large field values, both theories give realistic, Starobinsky–Higgs like inflation. The broken phase of the current model is the decoupling limit of the massive Weyl gauge boson of the broken phase of SMW, while the local scale symmetry of the current model is part of the larger gauged scale symmetry of SMW. Hence, the current theory has a gauge embedding in SMW. Unlike in the SMW, we note that in models with local scale symmetry the associated current is trivial, which is a concern for the physical meaning of this symmetry. Therefore, the SMW is a more fundamental UV completion of SM in a full gauge theory of scale invariance that generates Einstein gravity in the (spontaneously) broken phase, as an effective theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Simulation of Liquid Lithium Divertor Geometry Using SOLPS-ITER

Here, plasma-facing component (PFC) geometries are evaluated for a Fusion Nuclear Science Facility (FNSF) design to find solutions that are compatible with flowing liquid lithium components while satisfying requirements from the perspective of plasma and neutral particle transport. Flowing liquid metal (LM) divertor systems offer important advantages due to continual regeneration of the surface material, but may require modifications from standard optimized tokamak divertor designs. Scrape Off Layer Plasma Simulator for the International Thermonuclear Experimental Reactor (SOLPS-ITER) simulations are used to compare standard vertical target, open, and balanced baffled geometries. It is found that the open geometry offers little control of neutral particles and has narrow operating windows where the divertor fluxes can be lowered to acceptable levels, while maintaining the required upstream density. The addition of neutral baffles allows greater control over the divertor conditions with less impact on the upstream density. The divertor neutral pressure in the baffled geometry is slightly higher than the open divertor, but not as large with a vertical target. A first-pass coupling of the SOLPS solution with sheath and implantation/erosion models to compute the lithium emission shows that the lithium is largely confined to the near-surface region due to the small ionization mean free path and large main ion flow toward the surface. The lithium source was varied by three orders of magnitude. At the highest rate, when the sourced lithium approaches the level of the main ion recycling flux, a high core lithium concentration (~10%) is observed with only moderate power dissipation to affect the divertor plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Using AMReX's Embedded Boundaries to Support MFIX-Exa’s Geometry Capabilities

MFIX-Exa is an AMReX-based application used for the simulation of chemically reacting multiphase flows inside reactors. The reactor geometry is mostly a combination of primitive shapes such as cylinders, cubes and spheres of varying dimensions connected together with potentially a lot of dead space between them. Additionally, the reactors may have particle-laden jets introduced at different parts of their geometry to enhance reactant mixing. This talk presents how MFIX-Exa uses OpenSCAD’s csg format to allow users to define the embedded boundary (EB) geometry and how it supports specifying inflow through certain sections of the EB. The talk will describe how MFIX-Exa leverages the EB features of grid-pruning, restart files and redistribution. Finally, the talk goes over some capabilities which are currently not available in MFIX-Exa but planned for the future, such as moving parts of the reactor geometry.

embedded boundaries↗

DOE OSTI2021

The great escape: tunneling out of microstate geometries

We compute the quasi-normal frequencies of scalars in asymptotically-flat microstate geometries that have the same charge as a D1-D5-P black hole, but whose long BTZ-like throat ends in a smooth cap. In general the wave equation is not separable, but we find a class of geometries in which the non-separable term is negligible and we can compute the quasi-normal frequencies using WKB methods. We argue that our results are a universal property of all microstate geometries with deeply-capped BTZ throats. These throats generate large redshifts, which lead to exceptionally-low-energy states with extremely long decay times, set by the central charge of the dual CFT to the power of twice the dimension of the operator dual to the mode. While these decay times are extremely long, we also argue that the energy decay is bounded, at large t , by (log( t )) – 2 and is comparable with the behavior of ultracompact stars, as one should expect for microstate geometries.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Non-planar BCFW Grassmannian geometries

In this paper, we study non-adjacent BCFW recursion relations and their connection to positive geometry. For an adjacent BCFW shift, the n-point N k MHV tree-level amplitude in N = 4 SYM theory is expressed as a sum over planar on-shell diagrams, corresponding to canonical “dlog” forms on the cells in the positive Grassmannian G+(k, n). Non-adjacent BCFW shifts naturally lead to an expansion of the amplitude in terms of a different set of objects, which do not manifest the cyclic ordering and the hidden Yangian symmetry of the amplitude. We show that these terms can be interpreted as dlog forms on the non-planar Grassmannian geometries, generalizing the cells of the positive Grassmannian G+(k, n) to a larger class of objects which live in G(k, n). We focus mainly on the case of NMHV amplitudes and discuss in detail the Grassmannian geometries. We also propose an alternative way to calculate the associated on-shell functions and dlog forms using an intriguing connection between Grassmannian configurations and the geometry in the kinematical space.

1/N expansion↗

DOE OSTI2025

Thermomechanics coupling to Monte Carlo particle transport on unstructured mesh geometries using Cardinal

Geometry deformation due to thermal expansion influences neutron transport in many systems. Studying this phenomenon involves coupling models for neutronics, thermal hydraulics, and solid mechanics. To enable high fidelity modeling of these coupled physics, new capabilities were introduced in Cardinal, coupling OpenMC Monte Carlo particle transport models with MOOSE thermomechanical physics on unstructured moving-mesh geometries. In this work, we present a fully open-source capability leveraging on-the-fly mesh skinning to automatically regenerate OpenMC geometry, which allows multiphysics feedback from temperature, density, and geometry changes. The new capability is verified using an analytic benchmark slab problem, which couples S 2 neutron transport with thermal conduction, convective boundary conditions, Doppler-broadened cross sections, and nonlinear thermal expansion effects along the heated slab. Cardinal reproduces the analytic solutions for the neutron flux, heating, k eff , and temperature with demonstrated convergence in various error terms including mesh resolution and cross section temperature library spacing. For the nominal benchmark conditions and with a fine mesh, maximum relative errors for neutron flux, temperature, and heating are lower than 1%, while errors in integral quantities such as k eff and slab length are within 1 pcm and 48 µm, respectively. This work (i) presents a new numerical approach to thermomechanics coupling with OpenMC models, (ii) is the first (to our knowledge) to utilize a mechanical partial differential equation (PDE) solution to solve the (Griesheimer and Kooreman, 2022) analytic benchmark, and (iii) develops this verified capability within an open-source package.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Smoothed boundary method for simulating incompressible flow in complex geometries

Simulating flow through porous media with explicit considerations of complex microstructures is very challenging using conventional sharp-interface methods because of the difficulties in generating meshes conformal to complex geometries. In this work, a diffuse interface embedded boundary method known as the Smoothed Boundary Method (SBM) is utilized to facilitate simulations of fluid dynamics involving complex geometries. In diffuse-interface methods, the geometry is described by a domain parameter. The SBM allows the straightforward reformulation of the time-dependent Navier-Stokes equations in terms of this domain parameter, using only algebraic identities. Thus, enforcing the appropriate boundary conditions at the irregular embedded boundary is greatly simplified. Adaptive mesh refinement is used to increase the accuracy of the diffuse interface method by allowing thinner interfacial thickness to be used in the domain parameter. Here, the SBM-formulated Navier-Stokes equations are solved with the Finite Difference Method on refined mesh systems. Sharp-interface Finite Element Method simulations using the commercial software COMSOL on body-conforming meshes are also provided for comparison. Favorable agreement between the two methods is observed. Since it is no longer necessary for the mesh to conform to the complex geometry, the grid system for the SBM simulations can be generated rapidly and without additional manual interventions, making the entire simulation process more expedient.

36 MATERIALS SCIENCE↗

DOE OSTI2021

A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries

Herein, we present a computational framework for solving the equations of inviscid gas dynamics using structured grids with embedded geometries. The novelty of the proposed approach is the use of high-order discontinuous Galerkin (dG) schemes and a shock-capturing Finite Volume (FV) scheme coupled via an hp adaptive mesh refinement (hp-AMR) strategy that offers high-order accurate resolution of the embedded geometries. The hp-AMR strategy is based on a multi-level block-structured domain partition in which each level is represented by block-structured Cartesian grids and the embedded geometry is represented implicitly by a level set function. The intersection of the embedded geometry with the grids produces the implicitly-defined mesh that consists of a collection of regular rectangular cells plus a relatively small number of irregular curved elements in the vicinity of the embedded boundaries. High-order quadrature rules for implicitly-defined domains enable high-order accuracy resolution of the curved elements with a cell-merging strategy to address the small-cell problem. The hp-AMR algorithm treats the system with a second-order finite volume scheme at the finest level to dynamically track the evolution of solution discontinuities while using dG schemes at coarser levels to provide high-order accuracy in smooth regions of the flow. On the dG levels, the methodology supports different orders of basis functions on different levels. The space-discretized governing equations are then advanced explicitly in time using high-order Runge-Kutta algorithms. Numerical tests are presented for two-dimensional and three-dimensional problems involving an ideal gas. The results are compared with both analytical solutions and experimental observations and demonstrate that the framework provides high-order accuracy for smooth flows and accurately captures solution discontinuities.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

K-shell radiation and bright spot characteristics of high-energy-density Fe-Cr-Ni plasmas influenced by X-pinch load geometry

K-shell radiation is diagnostically advantageous for the study of high-energy-density plasmas. Here, the current work investigates the influence of load geometry on K-shell x-rays in Z-pinch plasmas produced on the 1-MA Zebra generator. Stainless steel (Fe: 69%, Cr: 20%, Ni: 9%) X-pinch wire loads are fielded with an interwire angle of 31° (small-angle) or 62.5° (large-angle), respectively and studied using various x-ray diode, imaging, and spectroscopic diagnostics. The large-angle geometry produced large, individual x-ray-emitting bright spots (> 3 keV) at the wire cross-point averaging areas ≥ 1 mm 2 , with noteworthy soft x-ray (> 0.75 keV) bursts and radiation yields ≤ 14.6 kJ. The small-angle geometry produced multiple x-ray-emitting bright spots extending the pinch axis with smaller average sizes (≤ 0.5 mm 2 ), consistent with stronger current, increased radiation yield (≥ 15.5 kJ), and notable hard x-ray (> 9 keV) bursts, which peak with largest cumulative bright spot size. Spectroscopic analysis is performed with non-LTE collisional-radiative modeling, indicating a cold, nonthermal plasma region radiating from neutral to Ne-like ions, a hot, thermal region radiating from Fe and Cr He- and Li-like ions, and an intermediate region radiating Kα satellites from Li-like to O-like ions. Modeling of the nonthermal and satellite features imply a fractional hot electron abundance ~0.1% and ~0.5% for large- and small-angle geometries, respectively. Relative intensity analysis is performed on Heα and Kα lines, revealing intensity ratios that deviate from the original wire composition. Optical depth estimates allude to optically thick, thermal K-shell plasmas with densities consistent with non-LTE modeling.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Weyl-ambient geometries

Weyl geometry is a natural extension of conformal geometry with Weyl covariance mediated by a Weyl connection. We generalize the Fefferman-Graham (FG) ambient construction for conformal manifolds to a corresponding construction for Weyl manifolds. We first introduce the Weyl-ambient metric motivated by the Weyl-Fefferman-Graham (WFG) gauge. From a top-down perspective, we show that the Weyl-ambient space as a pseudo-Riemannian geometry induces a codimension-2 Weyl geometry. Then, from a bottom-up perspective, we start from promoting a conformal manifold into a Weyl manifold by assigning a Weyl connection to the principal R+-bundle realizing a Weyl structure. We show that the Weyl structure admits a well-defined initial value problem, which determines the Weyl-ambient metric. Through the Weyl-ambient construction, we also investigate Weyl-covariant tensors on the Weyl manifold and define extended Weyl-obstruction tensors explicitly.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Effects of the Grazing Incidence Geometry on X-ray Photon Correlation Spectroscopy Measurements

X-ray photon correlation spectroscopy (XPCS) is a versatile tool to measure dynamics on the nanometer to micrometer scale in bulk samples. XPCS has also been applied in grazing incidence (GI) geometry to examine the dynamics of surface layers. However, considering GI scattering experiments more universally, the GI geometry leads to a superposition of signals due to reflection and refraction effects, also known from the distorted-wave Born approximation (DWBA). In this paper, the impact of these reflection and refraction effects on the correlation analysis is determined experimentally by measuring grazing incidence transmission XPCS (GT-XPCS) and grazing incidence XPCS (GI-XPCS) simultaneously for a thin film sample, showing non-equilibrium dynamics. Here the results of the GI and GT geometry comparisons are combined within the framework of the standardly applied, simplified DWBA. These calculations allow identifying the main contributions of the detected signal from the leading scattering terms along the out-of-plane direction q z , which dominate the measured intensity pattern on the detector. In combination with the calculation of the non-linear effect of refraction in GTSAXS and GISAXS, it is possible to identify experimental conditions that can be chosen to run experiments and data analysis as close as possible to transmission XPCS and to explain which limitations for data interpretations are observed. Consequently, the beam exposure can be significantly reduced by using GI geometry only. Calculations of experimental settings prior to experiments are detailed to determine suitable q z regions for a variety of material systems measured in bulk-sensitive GI-XPCS experiments, allowing us to determine the scaling behavior of typical decay times as a function of q that is comparable to the scaling behavior obtained in distortion-free GT-XPCS or transmission XPCS experiments.

36 MATERIALS SCIENCE↗