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DOE OSTI2025

Circles and triangles, the NLSM and Tr(Φ 3 )

A surprising connection has recently been made between the amplitudes for Tr(Φ 3 ) theory and the non-linear sigma model (NLSM). A simple shift of kinematic variables naturally suggested by the associahedron/stringy representation of Tr(Φ 3 ) theory yields pion amplitudes at all loops. In this note we provide an elementary motivation and proof for this link going in the opposite direction, starting from the non-linear sigma model and discovering its formulation as a sum over triangulations of surfaces with simple numerator factors. This uses an ancient connection between “circles” and “triangles”, interpreting the equation y = $\sqrt{1 – x^2}$ both as parametrizing points a circle as well as generating the number of triangulations of polygons. A further simplification of the numerator factors exposes them as arising from the kinematically shifted Tr(Φ3) theory, and gives rise to novel tropical representations of NLSM amplitudes. The connection to Tr(Φ 3 ) theory defines a natural notion of “surface-soft limit” intrinsic to curves on surfaces. Remarkably, with this definition, the soft limit of pion amplitudes vanishes directly at the level of the integrand, via obvious pairwise cancellations. We also give simple, explicit expressions for the multi-soft factors for tree and loop-level integrands in the limit as any number of pions are taken “surface-soft”.

Scattering Amplitudes↗

DOE OSTI2023

Extending the thermodynamic form factor bootstrap program: multiple particle-hole excitations, crossing symmetry, and reparameterization invariance

In this study, we further the thermodynamic bootstrap program which involves a set of recently developed ideas used to determine thermodynamic form factors of local operators in integrable quantum field theories. These form factors are essential building blocks for dynamic correlation functions at finite temperatures or non-equilibrium stationary states. In this work we extend this program in three ways. Firstly, we demonstrate that the conjectured annihilation pole axiom is valid in the low energy particle-hole excitations. Secondly, we introduce a crossing relation, which establishes a connection between form factors with different excitation content. Typically, the crossing relation is a consequence of Lorentz invariance, but due to the finite energy density of the considered states, Lorentz invariance is broken. Nonetheless a crossing relation involving excitations with both particles and holes can established using the finite volume representation of the thermodynamic form factors. Finally, we demonstrate that the thermodynamic form factors satisfy a reparameterization invariance, an invariance which encompasses crossing. Reparameterization invariance exploits the fact that the details of the representation of the thermodynamic state are unimportant. In the course of developing these results, we demonstrate the internal consistency of the thermodynamic form factor bootstrap program in a number of ways. Finally, we provide explicit computations of form factors of conserved charges and densities with crossed excitations and show our results can be used to infer information about thermodynamic form factors in the Lieb-Liniger model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Zwanziger’s pairwise little group on the celestial sphere

We generalize Zwanziger’s pairwise little group to include a boost subgroup. We do so by working in the celestial sphere representation of scattering amplitudes. We propose that due to late time soft photon and graviton exchanges, matter particles in the asymptotic states in massless QED and gravity transform under the Poincaré group with an additional pair of pairwise celestial representations for each pair of matter particles. We demonstrate that the massless abelian and gravitational exponentiation theorems are consistent with the proposed pairwise Poincaré transformation properties. For massless QED we demonstrate that our results are consistent with the effects of the Faddeev-Kulish dressing and the abelian exponentiation theorem for celestial amplitudes found in arXiv:2012.04208. We discuss electric and magnetic charges simultaneously as it is especially natural to do so in this formalism.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Brill-Noether-general limit root bundles: absence of vector-like exotics in F-theory Standard Models

Root bundles appear prominently in studies of vector-like spectra of 4d F-theory compactifications. Of particular importance to phenomenology are the Quadrillion F-theory Standard Models (F-theory QSMs). In this work, we analyze a superset of the physical root bundles whose cohomologies encode the vector-like spectra for the matter representations ($3$, $2$) 1/6 , ($\overline{3}$, $1$) -2/3 and ($1$, $1$) 1 . For the family B 3 (Δ$^{°}_{4}$) consisting of $\mathcal{O}$(10 11 ) F-theory QSM geometries, we argue that more than 99.995% of the roots in this superset have no vector-like exotics. This indicates that absence of vector-like exotics in those representations is a very likely scenario in the O(10 11 ) QSM geometries B 3 (Δ$^{°}_{4}$). The QSM geometries come in families of toric 3-folds B 3 (Δ°) obtained from triangulations of certain 3-dimensional polytopes Δ°. The matter curves in X Σ $\large{ϵ}$ B 3 (Δ°) can be deformed to nodal curves which are the same for all spaces in B 3 (Δ°). Therefore, one can probe the vector-like spectra on the entire family B 3 (Δ°) from studies of a few nodal curves. We compute the cohomologies of all limit roots on these nodal curves. In our applications, for the majority of limit roots the cohomologies are determined by line bundle cohomology on rational tree-like curves. For this, we present a computer algorithm. The remaining limit roots, corresponding to circuit-like graphs, are handled by hand. The cohomologies are independent of the relative position of the nodes, except for a few circuits. On these jumping circuits, line bundle cohomologies can jump if nodes are specially aligned. This mirrors classical Brill-Noether jumps. B 3 (Δ°) admits a jumping circuit, but the root bundle constraints pick the canonical bundle and no jump happens.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Gauge loop-string-hadron formulation on general graphs and applications to fully gauge fixed Hamiltonian lattice gauge theory

We develop a gauge invariant, Loop-String-Hadron (LSH) based representation of SU(2) Yang-Mills theory defined on a general graph consisting of vertices and half-links. Inspired by weak coupling studies, we apply this technique to maximal tree gauge fixing. This allows us to develop a fully gauge-fixed representation of the theory in terms of LSH quantum numbers. We explicitly show how the quantum numbers in this formulation directly relate to the variables in the magnetic description. In doing so, we will also explain in detail how the Kogut-Susskind formulation, prepotentials, and point splitting work for general graphs. In the appendix of this work, we provide a self-contained exposition of the mathematical details of Hamiltonian pure gauge theories defined on general graphs.

Algorithms and Theoretical Developments↗

DOE OSTI2020

Assessing mean climate change signals in the global CORDEX-CORE ensemble

The new Coordinated Output for Regional Evaluations (CORDEX-CORE) ensemble provides high-resolution, consistent regional climate change projections for the major inhabited areas of the world. It serves as a solid scientific basis for further research related to vulnerability, impact, adaptation and climate services in addition to existing CORDEX simulations. The aim of this study is to investigate and document the climate change information provided by the CORDEX-CORE simulation ensemble, as a part of the World Climate Research Programme (WCRP) CORDEX community. An overview of the annual and monthly mean climate change information in selected regions in different CORDEX domains is presented for temperature and precipitation, providing the foundation for detailed follow-up studies and applications. Initially, two regional climate models (RCMs), REMO and RegCM were used to downscale global climate model output. The driving simulations by AR5 global climate models (AR5-GCMs) were selected to cover the spread of high, medium, and low equilibrium climate sensitivity at a global scale. The CORDEX-CORE ensemble has doubled the spatial resolution compared to the previously existing CORDEX simulations in most of the regions (25 $\,\mathrm {km}$ (0.22 $^{\circ }$ /jats:inline-formula>) versus 50 $\,\mathrm {km}$ (0.44 $^{\circ }$ )) leading to a potentially improved representation of, e.g., physical processes in the RCMs. The analysis focuses on changes in the IPCC physical climate reference regions. The results show a general reasonable representation of the spread of the temperature and precipitation climate change signals of the AR5-GCMs by the CORDEX-CORE simulations in the investigated regions in all CORDEX domains by mostly covering the AR5 interquartile range of climate change signals. The simulated CORDEX-CORE monthly climate change signals mostly follow the AR5-GCMs, although for specific regions they show a different change in the course of the year compared to the AR5-GCMs, especially for RCP8.5, which needs to be investigated further in region specific process studies.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Challenges in simulating economic effects of climate change on global agricultural markets

Abstract Many approaches have been used to investigate climate change impacts on agriculture. However, several caveats remain in this field: (i) analyses focus only on a few major crops, (ii) large differences in yield impacts are observed between projections from site-based crops models and Global Gridded Crop Models (GGCMs), (iii) climate change impacts on livestock are rarely quantified, and (iv) several causal relations among biophysical, environmental, and socioeconomic aspects are usually not taken into account. We investigate how assumptions about these four aspects affect agricultural markets, food supply, consumer well-being, and land use at global level by deploying a large-scale socioeconomic model of the global economy with detailed representation of the agricultural sector. We find global welfare impacts several times larger when climate impacts all crops and all livestock compared to a scenario with impacts limited to major crops. At the regional level, food budget can decrease by 10 to 25% in developing countries, challenging food security. The role of land area expansion as a major source of adaptation is highlighted. Climate impacts on crop yields from site-based process crop models generate more challenging socioeconomic outcomes than those from GGCMs. We conclude that the agricultural research community should expand efforts to estimate climate impacts on many more crops and livestock. Also, careful comparison of the GGCMs and traditional site-based process crop models is needed to understand their major implications for agricultural and food markets.

Gurgel, Angelo C. (ORCID:0000000183319508)↗

DOE OSTI2022

Conservative Numerical Schemes with Optimal Dispersive Wave Relations: Part II. Numerical Evaluations

A new energy and enstrophy conserving scheme (EEC) for the shallow water equations is proposed and evaluated using a suite of test cases over the global spherical or bounded domain. The evaluation is organized around a set of pre-defined properties: accuracy of individual operators, accuracy of the whole scheme, conservation of key quantities, control of the divergence variable, representation of the energy and enstrophy spectra, and simulation of nonlinear dynamics. The results confirm that the scheme is between the first and second order accurate, and conserves the total energy and potential enstrophy up to the time truncation errors. Here, the scheme is capable of producing more physically realistic energy and enstrophy spectra, indicating that it can help prevent the unphysical energy cascade towards the finest resolvable scales. With an optimal representation of the dispersive wave relations, the scheme is able to keep the flow close to being non-divergent, and maintain the geostrophically balanced structures with large-scale geophysical flows over long-term simulations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

X-ray Inspection Model Validation with Physical Dosimetry

A non-functional printed circuit board assembly was developed using ULTIboard and a simple computational transport model was created for use with the Monte Carlo software MCNP. EBT 3 film radiography was used to compare with Monte Carlo simulation to validate the board representation. The computational transport model was then revised to include connection pins, solder balls, highly attenuating internal structures, and copper trace distribution. Results from the revised model were compared to the EBT 3 films to observe improvements to dose profiles. It was found that this method was useful in verifying the placement of components, as the dose profiles were observed to follow the same trends. The experiment was then repeated using XRQA 2 films to achieve the same level of contrast with 1% the dose of EBT 3 films. It was found that high contrast may be achieved using these films to identify major issues with the model geometry, at a cost of dose profile accuracy. A second validation method was applied to the model using 37 CaF 2 thermoluminescent dosimeters (TLDs). TLD measurements were compared with the simplified and complex transport models to identify the features that have the greatest impact on simulation accuracy. The TLD calibration to CaF 2 was found to be accurate within 5.6%, while calibration to dose in Si was found to be accurate within 4.7%. Finally, it was observed that the accurate representation of solder balls and proper modeling of highly attenuating internal structures had the greatest impact on simulation accuracy.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2021

Multilevel Graph Partitioning for Three-Dimensional Discrete Fracture Network Flow Simulations

We present a topology-based method for mesh-partitioning in three-dimensional discrete fracture network (DFN) simulations that takes advantage of the intrinsic multi-level nature of a DFN. DFN models are used to simulate flow and transport through low-permeability fractured media in the subsurface by explicitly representing fractures as discrete entities. The governing equations for flow and transport are numerically integrated on computational meshes generated on the interconnected fracture networks. Modern high-fidelity DFN simulations require high-performance computing on multiple processors where performance and scalability depends partially on obtaining a high-quality partition of the mesh to balance work-loads and minimize communication across all processors. The discrete structure of a DFN naturally lends itself to various graph representations, which can be thought of as coarse-scale representations of the computational mesh. Using this concept, we develop two applications of the multilevel graph partitioning algorithm to partition the mesh of a DFN. In the first, we project a partition of the graph based on the DFN topology onto the mesh of the DFN and in the second, this DFN-based projection is used as the initial condition for further partitioning refinement of the mesh. We compare the performance of these methods with standard multi-level graph partitioning using graph-based metrics (cut, imbalance, partitioning time), computational-based metrics (FLOPS, iterations, solver time), and total run time. The DFN-based and the mesh-based partitioning methods are comparable in terms of the graph-based metrics, but the time required to obtain the partition is several orders of magnitude faster using the DFN-based partitions. The computation-based metrics show comparable performance between both methods so, in combination, the DFN-based partitions are several orders of magnitude faster than the mesh-based partition. Furthermore, the method which uses the DFN-partition solution as the initial condition of the mesh partition provided cut and imbalance values that were close to the mesh-based partition but in a fraction of the time. In turn, this hybrid method outperformed both of the other methods in terms of the total run time.

58 GEOSCIENCES↗

DOE OSTI2024

Performance characterization and modeling of an oscillating surge wave energy converter

Abstract Testing wave energy converters in the ocean could be expensive and complex, which necessitates the use of numerical modeling. However, accurately modeling the response of wave energy converters with high-fidelity simulations can be computationally intensive in the design stage where different configurations must be considered. Reduced-order models based on simplified equations of motion can be very useful in the design, optimization, or control of wave energy converters. Given the complex dynamics of wave energy converters, accurate representation, and evaluation of relative contributions by different forces are required. This effort is concerned with a performance characterization of the hydrodynamic response of an oscillating surge wave energy converter that is based on a reduced-order model. A state-space model is used to represent the radiation damping term. Morison’s representation of unsteady forces is used to account for the nonlinear damping. Wave tank tests are performed to validate simulations. A free response simulation is used to determine the coefficients of the state-space model. Torque-forced simulations are used to identify the coefficients of the nonlinear damping term for different amplitudes and wave frequencies. The impact of varying these coefficients on the response is investigated. An assessment of the capability of the model in predicting the hydrodynamic response under irregular forcing is performed. The results show that the maximum error is 3% when compared with high-fidelity simulations. It is determined that the nonlinear damping is proportional to the torque amplitude and its effects are more pronounced as the amplitude of the flap oscillations increases.

16 TIDAL AND WAVE POWER↗

DOE OSTI2020

Host-specific and tissue-dependent orchestration of microbiome community structure in traditional rice paddy ecosystems

Abstract Background and aim Rice and duckweed are two monocotyledonous plants that naturally coexist in paddy fields. While the presence of duckweed in paddy fields significantly improves rice productivity, the interplay between soil microbes and the two plant hosts in this agroecosystem remains unexplored. Methods We compared the bacterial community structure between duckweed, rice and soil from multiple rice paddies. We also isolated bacteria from these communities and characterized their modes of bacterial colonization and plant growth-promotion using model plants. Results Our data indicate that host-specific and tissue-dependent factors reproducibly orchestrate the bacterial community structure associated with their plant hosts. This is corroborated by results from culture-dependent approaches in which the dominant genus Pantoea isolated from rice aerial tissues can strongly attach and colonize gnotobiotic duckweed in spite of the low representation of this bacterial genus in the natural duckweed microbiome. Our study identified a core of 254 bacterial taxa that are consistently found in all rice and duckweed tissue samples from rice paddy fields. Furthermore, characterizing auxin-producing bacteria isolates from both plant species identified potential plant growth-promoting bacteria that may improve growth for both duckweed and rice in paddy fields. Conclusions Results from this work provide evidence for the importance of the host tissue and species context in determining plant colonization by microbes in the paddy field system. The resources generated in this study could facilitate the agronomic deployment of microbes for more sustainable rice production.

Agriculture↗

DOE OSTI2021

Entanglement types for two-qubit states with real amplitudes

We study the set of two-qubit pure states with real amplitudes and their geometrical representation in the three-dimensional sphere. In this representation, we show that the maximally entangled states—those locally equivalent to the Bell states—form two disjoint circles perpendicular to each other. We also show that taking the natural Riemannian metric on the sphere, the set of states connected by local gates are equidistant to this pair of circles. Moreover, the unentangled or so-called product states are π/4 units away to the maximally entangled states. This is, the unentangled states are the farthest away to the maximally entangled states. In this way, if we define two states to be equivalent if they are connected by local gates, we have that there are as many equivalent classes as points in the interval [0,π/4] with the point 0 corresponding to the maximally entangled states. The point π/4 corresponds to the unentangled states which geometrically are described by a torus. Finally, for every 0<d<π/4 the point d corresponds to a disjoint pair of torus. Finally, we also show how this geometrical interpretation allows to clearly see that any pair of two-qubit states with real amplitudes can be connected with a circuit that only has single-qubit gates and one controlled-Z gate.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

MFA-DVR: direct volume rendering of MFA models

3D volume rendering is widely used to reveal insightful intrinsic patterns of volumetric datasets across many domains. However, the complex structures and varying scales of volumetric data can make efficiently generating high-quality volume rendering results a challenging task. Multivariate functional approximation (MFA) is a new data model that addresses some of the critical challenges: high-order evaluation of both value and derivative anywhere in the spatial domain, compact representation for large-scale volumetric data, and uniform representation of both structured and unstructured data. Here, in this paper, we present MFA-DVR, the first direct volume rendering pipeline utilizing the MFA model, for both structured and unstructured volumetric datasets. We demonstrate improved rendering quality using MFA-DVR on both synthetic and real datasets through a comparative study. We show that MFA-DVR not only generates more faithful volume rendering than using local filters but also performs faster on high-order interpolations on structured and unstructured datasets. MFA-DVR is implemented in the existing volume rendering pipeline of the Visualization Toolkit (VTK) to be accessible by the scientific visualization community.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems

Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimension. In this paper, we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control. We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians. Additionally, we present an efficient, grid-free numerical solver based on our representation formulas, which is shown to scale linearly with the state dimension, and thus, to overcome the curse of dimensionality. Using existing optimization methods and the min-plus technique, we extend our numerical solvers to address more general classes of convex and nonconvex initial costs. We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit (CPU) and a field-programmable gate array (FPGA). In several cases, our FPGA implementation obtains over a 10 times speedup compared to the CPU, which demonstrates the promising performance boosts FPGAs can achieve. Furthermore, our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

A review of coarse mineral dust in the Earth system

Mineral dust particles suspended in the atmosphere span more than three orders of magnitude in diameter, from <0.1 µm to more than 100 µm. This wide size range makes dust a unique aerosol species with the ability to interact with many aspects of the Earth system, including radiation, clouds, hydrology, atmospheric chemistry, and biogeochemistry. This review focuses on coarse and super-coarse dust aerosols, which we respectively define as dust particles with a diameter of 2.5–10 µm and 10–62.5 µm. We review several lines of observational evidence indicating that coarse and super-coarse dust particles are transported farther than previously expected and that the abundance of these particles is substantially underestimated in current global models. We synthesize previous studies that used observations, theories, and model simulations to highlight the impacts of coarse and super-coarse dust aerosols on the Earth system, including their effects on dust-radiation interactions, dust-cloud interactions, atmospheric chemistry, and biogeochemistry. Specifically, coarse and super-coarse dust aerosols produce a net positive direct radiative effect (warming) at the top of the atmosphere and can modify temperature and water vapor profiles, influencing the distribution of clouds and precipitation. In addition, coarse and super-coarse dust aerosols contribute a substantial fraction of ice-nucleating particles, especially at temperatures above –23 °C. They also contribute a substantial fraction to the available reactive surfaces for atmospheric processing and the dust deposition flux that impacts land and ocean biogeochemistry by supplying important nutrients such as iron and phosphorus. Furthermore, we examine several limitations in the representation of coarse and super-coarse dust aerosols in current model simulations and remote-sensing retrievals. Because these limitations substantially contribute to the uncertainties in simulating the abundance and impacts of coarse and super-coarse dust aerosols, we offer some recommendations to facilitate future studies. Overall, we conclude that an accurate representation of coarse and super-coarse properties is critical in understanding the impacts of dust aerosols on the Earth system.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Quantifying Value and Representing Competitiveness of Electricity System Technologies in Economic Models

Evaluating competition between electricity technologies is challenging because it depends on both their costs and their values. While technology costs can typically be estimated from projections of the cost components - capital, fuel, and O&M - estimating a technology's value is more complex due to its dependence on its contributions to multiple different grid services, each with prices that can vary substantially over space and time. In this work, using an electricity model of the contiguous United States, we develop relationships between relative value and share of total generation for major electricity generation technologies which, when paired with projections of technology costs, can be used to estimate technology competitiveness. We identify significant differences in the relationship between relative value and generation share for variable renewable energy (VRE) and non-VRE sources, but we demonstrate that all technologies require consideration of their dynamic values (in addition to cost) when evaluating competitiveness. In addition, we demonstrate that relative value of a technology is substantially impacted by not only its own generation share but also other aspects of the system state, in particular the mix of other technologies present in the system. Finally, we use the developed relative value relationships in combination with projections of future technology costs in a coarse resolution model that competes technologies based on a comprehensive competitiveness metric: profitability-adjusted LCOE (PLCOE). We show that this simple representation of technology competition approximately recovers the generation mix from a detailed model, which is not possible using LCOE alone. Such an approach can be used to improve the representation of technology competition in coarse-resolution models such as integrated assessment models, for which simplified metrics are often needed.

electricity model↗

DOE OSTI2023

Power market models for the clean energy transition: State of the art and future research needs

As power systems around the world are rapidly evolving to achieve decarbonization objectives, it is crucial that power system planners and operators use appropriate models and tools to analyze and address the associated challenges. This paper provides a detailed overview of the properties of power market models in the context of the clean energy transition. We review common power market model methodologies, their readiness for low- and zero-carbon grids, and new power market trends. Based on the review, we suggest model improvements and new designs to increase modeling capabilities for future grids. The paper highlights key modeling concepts related to power system flexibility, with a particular focus on hydropower and energy storage, as well as the representation of grid services, price formation, temporal structure, and the importance of uncertainty. We find that a changing resource mix, market restructuring, and growing price uncertainty require more precise modeling techniques to adequately capture the new technology constraints and the dynamics of future power markets. In particular, models must adequately represent resource opportunity costs, multi-horizon flexibility, and energy storage capabilities across the full range of grid services. Moreover, at the system level, it is increasingly important to consider sub-hourly time resolution, enhanced uncertainty representation, and introduce co-optimization for dual market clearing of energy and grid services. Likewise, models should capture interdependencies between multiple energy carriers and demand sectors.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗