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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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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A Transported Livengood–Wu Integral Model for Knock Prediction in Computational Fluid Dynamics Simulation

This work describes the development of a transported Livengood–Wu (L–W) integral model for computational fluid dynamics (CFD) simulation to predict autoignition and engine knock tendency. The currently employed L–W integral model considers both single-stage and two-stage ignition processes, thus can be generally applied to different fuels such as paraffin, olefin, aromatics, and alcohol. The model implementation is first validated in simulations of homogeneous charge compression ignition (HCCI) combustion for three different fuels, showing good accuracy in prediction of autoignition timing for fuels with either single-stage or two-stage ignition characteristics. Then, the L–W integral model is coupled with G-equation model to indicate end-gas autoignition and knock tendency in CFD simulations of a direct-injection spark-ignition engine. This modeling approach is about 10 times more efficient than the ones that based on detailed chemistry calculation and pressure oscillation analysis. Two fuels with same Research Octane Number (RON) but different octane sensitivity are studied, namely, Co-Optima alkylate and Co-Optima E30. Feed-forward neural network model in conjunction with multivariable minimization technique is used to generate fuel surrogates with targets of matched RON, octane sensitivity, and ethanol content. The CFD model is validated against experimental data in terms of pressure traces and heat release rate for both fuels under a wide range of operating conditions. The knock tendency—indicated by the fuel energy contained in the autoignited region—of the two fuels at different load conditions correlates well with the experimental results and the fuel octane sensitivity, implying the current knock modeling approach can capture the octane sensitivity effect and can be applied to further investigation on composition of octane sensitivity.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2020

Equation of state of hot, dense magnesium derived with first-principles computer simulations

Using two first-principles computer simulation techniques, path integral Monte Carlo and density functional theory molecular dynamics, we derive the equation of state of magnesium in the regime of warm dense matter, with densities ranging from 0.43 to 86.11 g cm –3 and temperatures from 20,000 K to 5×10 8 K. These conditions are relevant for the interiors of giant planets and stars as well as for shock compression measurements and inertial confinement fusion experiments. Here, we study ionization mechanisms and the electronic structure of magnesium as a function of density and temperature. We show that the L shell electrons, 2s and 2p energy bands, merge at high densities. This results in gradual ionization of the L-shell with increasing density and temperature. In this regard, Mg differs from MgO, which is also reflected in the shape of its principal shock Hugoniot curve. For Mg, we predict a single broad pressure-temperature region, where the shock compression ratio is approximately 4.9. Mg thus differs from Si and Al plasmas that exhibit two well-separated compression maxima on the Hugoniot curve for L and K shell ionizations. Finally, we study multiple shocks and effects of preheat and precompression.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

kynema-fmb [SWR-23-07]

Kynema-FMB (FKA: Kynema) is an open-source performance portable flexible multibody (FMB) dynamics solver designed for time-domain simulations. While originally tailored for wind turbine structural dynamics, the formulation and implementation are those of a general flexible-multidbody dynamics solver that can readily be applied to a wide range of systems. Kynema was designed with a narrow focus, namely to provide a lightweight, fast, accurate FMD solver for coupling to computational-fluid-dynamics (CFD) codes, especially the CFD codes in the Kynema suite, for fluid-structure-interaction (FSI) simulations. Kynema-FMB is equipped to model systems that can be represented as a collection of beams and rigid bodies that are connected through constraints. Degrees of freedom are defined in the inertial/global frame of reference and include displacements and rotations (formally as rotation matrices, but stored as quaternions). The underlying formulation is built on a Lie-group time integrator designed for index-3 differential-algebraic equations, which is second-order accurate in time (Bruls et al., 2012). Beam models are based on geometrically exact beam theory and are discretized as high-order spectral finite elements similar to those in BeamDyn (Wang et al., 2017). The governing equations for a FMD system like a wind turbine constitute a highly nonlinear system of constrained partial-differential equations. Kynema-FMB uses analytical Jacobians in the nonlinear-system solves in each time step. Linear systems use sparse storage and several third-party sparse-linear-system solvers are enabled. Ill conditioning of linear systems is mitigated with preconditioning described in Bottasso et al, 2008. Kynema-FMB is integrated with a simple open-source controller (ROSCO). There is an application programming interface (API) for coupling to geometry-resolved CFD (like that in Sharma et al., 2023) and actuator-force CFD (like that in Kuhn et al., 2025). In the latter, for actuator-line models, Kynema-FMB includes an internal blade-element solver that depends on user-provided lookup tables for coefficients of lift and drag, i.e., aerodynamic polars. Kynema-FMB is written in C++ and leverages Kokkos and Kokkos-Kernels (KokkosEcosystem) as its performance portability layer enabling simulations on both CPU and GPU systems. The repository is equipped with extensive automated testing at the unit and regression/system levels. The following describes the high-level development objectives conceived for Kynema: *Kynema will follow modern software development best practices, including test-driven development (TDD), version control, hierarchical automated testing, and continuous integration (CI) for a robust development environment. *The core data structures are memory efficient and enable vectorization and parallelization at multiple levels. *Data structures are data-oriented to exploit methods for accelerated computing including high utilization of chip resources (e.g., single instruction multiple data (SIMD) instruction sets) and parallelization using GP-GPUs. *The computational algorithms incorporate robust open-source libraries for mathematical operations, resource allocation, and data management. *The API design considers multiple stakeholder needs and ensure integration with existing and future ecosystems for data science, machine learning, and AI. *Kynema-FMB is written in modern C++ and leverages Kokkos as its performance-portability library with inspiration from the kynema stack.

Sprague, MichaelA.↗
DOE OSTI2025

Electron and photon structure functions at two loops

We present a fully analytic computation of the complete electron and photon structure functions, or QED lepton parton distribution functions (PDFs) up to two-loop order. Our computation is performed using modern techniques of reduction to Master Integrals and solving them with the differential equation method. We obtain explicit expressions for the electron-in-electron, positron-in-electron, photon-in-electron, electron-in-photon, and photon-in-photon distributions at next-to-next-to-leading order (NNLO). Cross-checks against one-loop results, existing two-loop calculations, and a recent soft-collinear effective theory (SCET) analysis of the electron structure functions are presented.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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

Model-based optimization strategies for direct hydrogenation of carbon dioxide to dimethyl ether

Here, this study discusses model-based optimization strategies for CO 2 hydrogenation to dimethyl ether (DME) over aCuZnZr (CZZ) and ferrite (FER) mixed catalyst system in a packed-bed reactor configuration. A two-dimensional axisymmetric, nonisothermal packed-bed reactor model was developed using COMSOL Multiphysics 6.2 software. The model solves two-dimensional (radial and axial) heat and mass transport equations in the packed-bed and integrates intraparticle diffusion and heat transfer in a 1D approach. This powerful feature differs from a traditional porous media approach and takes into account any heat and mass transfer limitations that may exist. Analysis shows that the heat transfer limitations are negligible, but strong internal mass transfer limitations were observed at 10 ≤ WHSV ≤ 90 h -1 on the FER catalyst and at 240 °C. The optimum catalyst composition (i.e., mixing ratio) varies depending on the operating regime. The FER catalyst weight in the mixture can be as low as 5 wt.%, but the ideal composition de-pends on the internal mass transfer limitation and its relationship with the operating regime (i.e., weight hourly space velocity, temperature). A catalyst composition of 80 wt.% CZZ and 20 wt.% FER was suggested; this composition can provide high CO 2 conversion and DME production rates at a wide range of temperatures and flow rates.

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

ElasTool v3.0: Efficient computational and visualization toolkit for elastic and mechanical properties of materials

Efficient computation and visualization of elastic and mechanical properties are crucial in the selection of materials and the design of new materials. Here, the ElasTool v3.0 toolkit marks a significant advancement in the computational analysis and visualization of elastic and mechanical properties of materials, essential in material selection and design. This enhanced version extends beyond standard calculations like elastic tensor, Young's modulus, bulk modulus, and Poisson's ratio. It introduces capabilities for computing minimum thermal conductivity, linear compressibility, rendering the Christoffel equation, and elastic energy density. Notably, it integrates advanced visualization tools, including compatibility with Plotly and Elate web platforms for interactive web-based property exploration. A key feature of ElasTool v3.0 is the implementation of second-order elastic constants (SOECs) for tubular 2D-based nanostructures and nanotubes. Leveraging high-efficiency strain-matrix sets (OHESS), the toolkit now facilitates efficient computation of elastic constants and mechanical properties at both zero and finite temperatures for 1D, 2D, and 3D dimensions. ElasTool is openly accessible on GitHub: https://github.com/gmp007/elastool.

1D, 2D, 3D, and tubular 2D nanostructure and nanot↗
DOE OSTI2026

Flow dynamics and heat transfer in simplified battery energy storage systems with heated battery modules

Large-scale energy storage systems (ESSs) composed of batteries show promise in addressing current energy challenges, but dissipation of generated heat is important. Here, this paper focuses on buoyant convective flows in simplified ESS battery racks. Natural convection is not generally the primary cooling strategy but can be important in abnormal scenarios where there is module overheat or potentially thermal runaway. We use computational fluid dynamics to investigate the flow dynamics and heat transfer mechanisms in a simplified parameterized rack design. Despite its simplicity, this configuration produces many of the relevant features expected in real ESSs without details of module geometry or hardware, allowing broad conclusions independent of manufacture-specific designs. We start by providing visualizations of the flowfield and measurements of entrainment, heat flux, and pressure. To characterize the dependence on the system parameters, we develop an integral-scale analysis of the average temperature equation to highlight the dominant source terms. We use results from this analysis to derive a steady network model composed of simple algebraic expressions to provide first-order predictions of entrainment through the rack. The network model leads to a linear scaling of the Reynolds number based on convective mass flux with respect to the Grashof number based on the heat source. We deduce empirical relationships that relate the heat exchanged between modules using a surface-averaged Nusselt number as a function of the local Reynolds and Rayleigh numbers. Lastly, we investigate how space between the modules and rack in the spanwise direction creates flow bypass, resulting in different flow pathways.

Battery thermal management↗
DOE OSTI2026

WellPINN: Accurate Well Representation for Transient Fluid Pressure Diffusion in Subsurface Reservoirs With Physics‐Informed Neural Networks

Accurate representation of pumping wells is essential for reliable reservoir characterization and simulation of operational scenarios in subsurface flow models. Physics-informed neural networks (PINNs) are emerging as a promising alternative to numerical models for reservoir modeling, offering seamless integration of monitoring data and governing physical equations. However, existing PINN-based studies face major challenges in capturing fluid pressure near wells when using a source/sink term, particularly during the early stages after pumping begins. We address this problem by introducing WellPINN, a workflow in which an initially trained PINN infers fluid pressure across the entire reservoir domain using a large equivalent well radius. This initial PINN solution is then locally refined around the well by a set of subdomain PINNs that are trained for smaller equivalent well radii. Continuity across these subdomain interfaces as well as at the initial condition is ensured by hard-constraining each PINN on its subdomain boundary. Our results demonstrate WellPINN as the first workflow of its kind to focus on accurate inference of fluid pressure from pumping rates throughout the entire injection period, significantly advancing the potential of PINNs for inverse modeling and operational scenario simulations. All data and code for this paper are openly available at https://doi.org/10.20350/DIGITALCSIC/17260.

58 GEOSCIENCES↗
DOE OSTI2023

Phonon-Induced Localization of Excitons in Molecular Crystals from First Principles

The spatial extent of excitons in molecular systems underpins their photophysics and utility for optoelectronic applications. Phonons are reported to lead to both exciton localization and delocalization. However, a microscopic understanding of phonon-induced (de)localization is lacking, in particular, how localized states form, the role of specific vibrations, and the relative importance of quantum and thermal nuclear fluctuations. Here, we present a first-principles study of these phenomena in solid pentacene, a prototypical molecular crystal, capturing the formation of bound excitons, exciton-phonon coupling to all orders, and phonon anharmonicity, using density functional theory, the ab initio GW-Bethe-Salpeter equation approach, finite-difference, and path integral techniques. In this study, we find that for pentacene zero-point nuclear motion causes uniformly strong localization, with thermal motion providing additional localization only for Wannier-Mott-like excitons. Anharmonic effects drive temperature-dependent localization, and, while such effects prevent the emergence of highly delocalized excitons, we explore the conditions under which these might be realized

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

A transported Livengood-Wu integral model for knock prediction in CFD simulation

This work describes the development of a transported Livengood-Wu (L-W) integral model for computational fluid dynamics (CFD) simulation to predict auto-ignition and engine knock tendency. The currently employed L-W integral model considers both single-stage and two-stage ignition processes, thus can be generally applied to different fuels such as paraffin, olefin, aromatics and alcohol. The model implementation is first validated in simulations of homogeneous charge compression ignition combustion for three different fuels, showing good accuracy in prediction of auto-ignition timing for fuels with either single-stage or two-stage ignition characteristics. Then, the L-W integral model is coupled with G-equation model to indicate end-gas auto-ignition and knock tendency in CFD simulations of a direct injection spark ignition engine. This modeling approach is about 10 times more efficient than the ones that based on detailed chemistry calculation and pressure oscillation analysis. Two fuels with same Research Octane Number (RON) but different octane sensitivity are studied, namely Co-Optima Alkylate and Co-Optima E30. Feed-forward neural network model in conjunction with multi-variable minimization technique is used to generate fuel surrogates with targets of matched RON, octane sensitivity and ethanol content. The CFD model is validated against experimental data in terms of pressure traces and heat release rate for both fuels under a wide range of operating conditions. The knock tendency indicated by the fuel energy contained in the auto-ignited region of the two fuels at different load conditions correlates well with the experimental results and the fuel octane sensitivity, implying the current knock modeling approach can capture the octane sensitivity effect and can be applied to further investigation on composition of octane sensitivity.

Yue, Zongyu↗
DOE OSTI2022

Phase Field Dislocation Dynamics (PFDD) version 2.x

This disclosure is for version 2.x of a mesoscale model called Phase Field Dislocation Dynamics (PFDD). PFDD is used for investigating deformation in nanoscale (grain sizes of ~300 nm and less) materials, such as metals and alloys. This approach models the motion and interaction of individual defects, namely dislocations, in the material using scalar-valued phase field variables, also called order parameters. The system is evolved through energy minimization thus the model calculates the total energy density in terms of the phase field variables. The energy minimization is completed using the Ginzburg-Landau equation, and is implemented with explicit time integration. The total system energy can be comprised of several terms, including the strain energy (which describes dislocation-dislocation interactions), the energy due to an applied stress (dislocation interactions with the applied stress), and a core/lattice (perfect dislocations) or generalized stacking fault (partial dislocations) energy (described the dislocation core structure). The latter term in particular may vary based on the crystal structure being modeled and is typically informed using lower length scale (e.g., atomistic) approaches, although no such (atomistic) calculations are completed within the PFDD algorithm. This basic formulation was previously reviewed by Los Alamos National Laboratory and released under license number C17113. This previously reviewed version we will henceforth refer to as PFDD v1.0. PFDD v1.0 consisted of 2 codes (one parallel and one serial) plus input files, all written in the C language. This new disclosure is addressing the next versions of the PFDD, versions 2.x. There have been several enhancements of PFDD v1.0, which are described here and included in the attached code, which we will refer to as PFDD v2.0. There are also several new features described here that are either planned or already in process and are expected to be subsequent releases, i.e., v2.1, v2.2, ...v2.x.

Hunter, Abigail↗
DOE OSTI2020

TChem v2.0 - A Software Toolkit for the Analysis of Complex Kinetic Models

TChem is an open source software library for solving complex computational chemistry problems and analyzing detailed chemical kinetic models. The software provides support for: complex kinetic models for gas-phase and surface chemistry; thermodynamic properties based on NASA polynomials; species production/consumption rates; stable time integrator for solving stiff time ordinary differential equations; and, reactor models such as homogenous gas-phase ignition (with analytical Jacobian matrices), continuously stirred tank reactor, plug-flow reactor. This toolkit builds upon earlier versions that were written in C and featured tools for gas-phase chemistry only. The current version of the software was completely refactored in C++, uses an object-oriented programming model, and adopts Kokkos as its portability layer to make it ready for the next generation computing architectures i.e., multi/many core computing platforms with GPU accelerators. We have expanded the range of kinetic models to include surface chemistry and have added examples pertaining to Continuously Stirred Tank Reactors (CSTR) and Plug Flow Reactor (PFR) models to complement the homogenous ignition examples present in the earlier versions. To exploit the massive parallelism available from modern computing platforms, the current software interface is designed to evaluate samples in parallel, which enables large scale parametric studies, e.g. for sensitivity analysis and model calibration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Computational Materials Design for Ceramic Nuclear Waste Forms Using Machine Learning, First-Principles Calculations, and Kinetics Rate Theory

Ceramic waste forms are designed to immobilize radionuclides for permanent disposal in geological repositories. One of the principal criteria for the effective incorporation of waste elements is their compatibility with the host material. In terms of performance under environmental conditions, the resistance of the waste forms to degradation over long periods of time is a critical concern when they are exposed to natural environments. Due to their unique crystallographic features and behavior in nature environment as exemplified by their natural analogues, ceramic waste forms are capable of incorporating problematic nuclear waste elements while showing promising chemical durability in aqueous environments. Recent studies of apatite- and hollandite-structured waste forms demonstrated an approach that can predict the compositions of ceramic waste forms and their long-term dissolution rate by a combination of computational techniques including machine learning, first-principles thermodynamics calculations, and modeling using kinetic rate equations based on critical laboratory experiments. By integrating the predictions of elemental incorporation and degradation kinetics in a holistic framework, the approach could be promising for the design of advanced ceramic waste forms with optimized incorporation capacity and environmental degradation performance. Such an approach could provide a path for accelerated ceramic waste form development and performance prediction for problematic nuclear waste elements.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

A coupled ground heat flux–surface energy balance model of evaporation using thermal remote sensing observations

Abstract. One of the major undetermined problems in evaporation (ET) retrieval using thermal infrared remote sensing is the lack of a physically based ground heat flux (G) model and its integration within the surface energy balance (SEB) equation. Here, we present a novel approach based on coupling a thermal inertia (TI)-based mechanistic G model with an analytical surface energy balance model, Surface Temperature Initiated Closure (STIC, version STIC1.2). The coupled model is named STIC-TI. The model is driven by noon–night (13:30 and 01:30 local time) land surface temperature, surface albedo, and a vegetation index from MODIS Aqua in conjunction with a clear-sky net radiation sub-model and ancillary meteorological information. SEB flux estimates from STIC-TI were evaluated with respect to the in situ fluxes from eddy covariance measurements in diverse ecosystems of contrasting aridity in both the Northern Hemisphere and Southern Hemisphere. Sensitivity analysis revealed substantial sensitivity of STIC-TI-derived fluxes due to the land surface temperature uncertainty. An evaluation of noontime G (Gi) estimates showed 12 %–21 % error across six flux tower sites, and a comparison between STIC-TI versus empirical G models also revealed the substantially better performance of the former. While the instantaneous noontime net radiation (RNi) and latent heat flux (LEi) were overestimated (15 % and 25 %), sensible heat flux (Hi) was underestimated (22 %). Overestimation (underestimation) of LEi (Hi) was associated with the overestimation of net available energy (RNi−Gi) and use of unclosed surface energy balance flux measurements in LEi (Hi) validation. The mean percent deviations in Gi and Hi estimates were found to be strongly correlated with satellite day–night view angle difference in parabolic and linear pattern, and a relatively weak correlation was found between day–night view angle difference versus LEi deviation. Findings from this parameter-sparse coupled G–ET model can make a valuable contribution to mapping and monitoring the spatiotemporal variability of ecosystem water stress and evaporation using noon–night thermal infrared observations from future Earth observation satellite missions such as TRISHNA, LSTM, and SBG.

Bhattacharya, Bimal K.↗
DOE OSTI2023

QES-Plume v1.0: a Lagrangian dispersion model

Low-cost simulations providing accurate predictions of transport of airborne material in urban areas, vegetative canopies, and complex terrain are demanding because of the small-scale heterogeneity of the features influencing the mean flow and turbulence fields. Common models used to predict turbulent transport of passive scalars are based on the Lagrangian stochastic dispersion model. The Quick Environmental Simulation (QES) tool is a low-computational-cost framework developed to provide high-resolution wind and concentration fields in a variety of complex atmospheric-boundary-layer environments. Part of the framework, QES-Plume, is a Lagrangian dispersion code that uses a time-implicit integration scheme to solve the generalized Langevin equations which require mean flow and turbulence fields. Here, QES-Plume is driven by QES-Winds, a 3D fast-response model that computes mass-consistent wind fields around buildings, vegetation, and hills using empirical parameterizations, and QES-Turb, a local-mixing-length turbulence model. In this paper, the particle dispersion model is presented and validated against analytical solutions to examine QES-Plume’s performance under idealized conditions. In particular, QES-Plume is evaluated against a classical Gaussian plume model for an elevated continuous point-source release in uniform flow, the Lagrangian scaling of dispersion in isotropic turbulence, and a non-Gaussian plume model for an elevated continuous point-source release in a power-law boundary-layer flow. In these cases, QES-Plume yields a maximum relative error below 6 % when compared with analytical solutions. In addition, the model is tested against wind-tunnel data for a uniform array of cubical buildings. QES-Plume exhibits good agreement with the experiment with 99 % of matched zeros and 59 % of the predicted concentrations falling within a factor of 2 of the experimental concentrations. Furthermore, results also emphasize the importance of using high-quality turbulence models for particle dispersion in complex environments. Finally, QES-Plume demonstrates excellent computational performance.

58 GEOSCIENCES↗
DOE OSTI2025

Differential equations for cosmological correlators

Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations satisfied by cosmological correlation functions. In this work, we provide a broader perspective on the origin and structure of these differential equations. As a concrete example, we study conformally coupled scalar fields in a power-law cosmology. The wavefunction coefficients in this model have integral representations, with the integrands being the product of the corresponding flat-space results and “twist factors” that depend on the cosmological evolution. Similar twisted integrals arise for loop amplitudes in dimensional regularization, and their recent study has led to the discovery of rich mathematical structures and powerful new tools for computing multi-loop Feynman integrals in quantum field theory. The integrals of interest in cosmology are also part of a finite-dimensional basis of master integrals, which satisfy a system of first-order differential equations. We develop a formalism to derive these differential equations for arbitrary tree graphs. The results can be represented in graphical form by associating the singularities of the differential equations with a set of graph tubings. Upon differentiation, these tubings grow in a local and predictive fashion. In fact, a few remarkably simple rules allow us to predict — by hand — the equations for all tree graphs. While the rules of this “kinematic flow” are defined purely in terms of data on the boundary of the spacetime, they reflect the physics of bulk time evolution. We also study the analogous structures in tr ϕ 3 theory, and see some glimpses of hidden structure in the sum over planar graphs. This suggests that there is an autonomous combinatorial or geometric construction from which cosmological correlations, and the associated spacetime, emerge.

Cosmological models↗
DOE OSTI2020

A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO

In this work, we provide a new approach for the efficient matrix-free application of the transpose of the Jacobian for the spectral element method for the adjoint-based solution of partial differential equation (PDE) constrained optimization. This results in optimizations of nonlinear PDEs using explicit integrators where the integration of the adjoint problem is not more expensive than the forward simulation. Solving PDE constrained optimization problems entails combining expertise from multiple areas, including simulation, computation of derivatives, and optimization. The Portable, Extensible Toolkit for Scientific computation (PETSc) together with its companion package, the Toolkit for Advanced Optimization (TAO), is an integrated numerical software library that contains an algorithmic/software stack for solving linear systems, nonlinear systems, ordinary differential equations, differential algebraic equations, and large-scale optimization problems and, as such, is an ideal tool for performing PDE-constrained optimization. This paper describes an efficient approach in which the software stack provided by PETSc/TAO can be used for large-scale nonlinear time-dependent problems. Time integration can involve a range of high-order methods, both implicit and explicit. The PDE-constrained optimization algorithm used is gradient-based and seamlessly integrated with the simulation of the physical problem.

97 MATHEMATICS AND COMPUTING↗