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DOE OSTI2022

Kinetic theory of particle-in-cell simulation plasma and the ensemble averaging technique

Abstract We derive the kinetic theory of fluctuations in physically and numerically stable particle-in-cell (PIC) simulations of electrostatic plasmas. The starting point is the single-time correlation at the start of the simulation between the statistical fluctuations of the weighted densities of macroparticle centers in the plasma particle phase-space. The fluctuations are associated with different initial conditions, typically due to the random initial conditions (in velocity space) of the macroparticles/simulation plasma, assigned according to their initial distribution of probability. The single-time correlations at all time steps and in each spatial grid cell are then determined from the Laplace–Fourier transforms of the discretized Klimontovich-like equation for the macroparticles and Maxwell’s equations for the fields, as computed by modern PIC codes. We recover the expressions for the electrostatic field and the plasma particle density fluctuation autocorrelation spectra as well as the kinetic equations describing the average evolution of PIC-simulated plasma particles, first derived by Langdon (1970b Proc. 4th Conf. Numerical Simulation of Plasmas ) using a test macroparticle approach perturbing a discretized Vlasovian plasma and then averaging the obtained physical quantity over the initial macroparticle velocity distribution. We generalize and extend these results to the modern algorithms in PIC codes using arbitrary macroparticle weights. Analytical estimates of statistical fluctuation amplitudes are derived as a function of the plasma simulation parameters, using the central limit theorem in the limit of a large number of macroparticles per cell. The theory is then used to analyze the ensemble averaging technique of PIC simulations where statistical averages are performed over ensembles of PIC simulations, modeling the same plasma physics problem but using different statistical realizations of the initial distribution functions of the macroparticles. This method is illustrated by linear Landau damping uncovering (from noise, which is usually considered numerical) the physical fluctuations driven by a single small amplitude electrostatic wave perturbing a PIC simulation plasma in equilibrium.

fluctuations correlations↗

DOE OSTI2023

Grid Optimization Competition on Synthetic and Industrial Power Systems

This paper summarizes a grid optimization (GO) competition effort in the United States to find the best solution strategies for up to interconnect-scale power system networks with around 32,000 buses. The optimization problem is a mixedinteger, non-convex non-linear problem, (MINLP) and includes discrete variables such as unit commitment and line switching, control settings (transformer taps and phase shifters with impedance correction tables), and bus shunts. The case study includes six actual industry grids as well as 16 realistic synthetic grids created by three different dataset teams. The winners are selected and ranked based on scoring criteria, which consider the solution quality (such as objective functions) within time limits. Nine winner teams are selected from 26 competitor teams. The results achieved by different teams are described and the performance of different algorithms on synthetic grids and actual industry grids are compared and analyzed.

mixed-integer non-linear programming↗

DOE OSTI2025

Enhanced MPM framework with multipatch isogeometric analysis for geotechnical applications

Achieving stable stress solutions at large strains using the Material Point Method (MPM) is challenging due to the accumulation of errors associated with geometry discretization, cell-crossing noise, and volumetric locking. Several simplified attempts exist in the literature to mitigate these errors, including higher-order frameworks. However, the stability of the MPM solution in such frameworks has been limited to simple geometries and the single-phase formulation (i.e., neglecting pore fluid). Although never explored, multipatch isogeometric analysis offers desirable qualities to simulate complex geometries while mitigating errors in the MPM. The degree of required high-order spatial integration has also never been investigated to infer a minimum limit for the stability of the stress solution in MPM. This paper presents a general-purpose numerical framework for simulating stable stresses in porous media, capturing both near incompressibility and multiphase interactions. First, the numerical framework is presented considering Non-Uniform Rational B-splines (NURBS) to perform isogeometric analysis (IGA) in MPM. Additionally, a volumetric strain smoothing algorithm is used to alleviate errors associated with volumetric locking. Second, the manifestation of cell-crossing errors is assessed via a series of problems with orders ranging from linear to cubic interpolation functions. Third, the use of NURBS is investigated and verified for problems with circular geometries. Finally, multipatch analysis is deployed to simulate plane strain and 3D penetration in soils, considering nearly incompressible elastoplastic (total stress) analysis and fully-coupled hydro-mechanical (effective stress) analysis. The stability of the solution is also analyzed for different constitutive models. From the results, it can be concluded that the framework using cubic interpolation functions with strain smoothing is the most convenient, presenting stable stress solutions for a broad range of multiphase geotechnical applications.

58 GEOSCIENCES↗

DOE OSTI2023

Geothermal Play Fairway Analysis, Part 2: GIS methodology

Play Fairway Analysis (PFA) in geothermal exploration originates from a systematic methodology developed within the petroleum industry and is based on a geologic, geophysical, and hydrologic framework of identified geothermal systems. We tailored this methodology to study the geothermal resource potential of the Snake River Plain and surrounding region, but it can be adapted to other geothermal resource settings. We adapted the PFA approach to geothermal resource exploration by cataloging the critical elements controlling exploitable hydrothermal systems, establishing risk matrices that evaluate these elements in terms of both probability of success and level of knowledge, and building a code-based ‘processing model’ to process results. A geographic information system was used to compile a range of different data types, which we refer to as elements (e.g., faults, vents, heat flow, etc.), with distinct characteristics and measures of confidence. Discontinuous discrete data (points, lines, or polygons) for each element were transformed into continuous interpretive 2D grid surfaces called evidence layers. Because different data types have varying uncertainties, most evidence layers have an accompanying confidence layer which reflects spatial variations in these uncertainties. Risk layers, as defined here, are the product of evidence and confidence layers, and are the building blocks used to construct Common Risk Segment (CRS) maps for heat, permeability, and seal, using a weighted sum for permeability and heat, but a different approach with seal. CRS maps quantify the variable risk associated with each of these critical components. In a final step, the three CRS maps were combined into a Composite Common Risk Segment (CCRS) map, using a modified weighted sum, for results that reveal favorable areas for geothermal exploration. Additional maps are also presented that do not mix contributions from evidence and confidence (to allow an isolated view of evidence and confidence), as well as maps that calculate favorability using the product of components instead of a weighted sum (to highlight where all components are present). Our approach helped to identify areas of high geothermal favorability in the western and central Snake River Plain during the first phase of study and helped identify more precise local drilling targets during the second phase of work. By identifying favorable areas, this methodology can help to reduce uncertainty in geothermal energy exploration and development.

15 GEOTHERMAL ENERGY↗

DOE OSTI2021

Predicting large-scale pool fire dynamics using an unsteady flamelet- and large-eddy simulation-based model suite

A low-Mach, unstructured, large-eddy-simulation-based, unsteady flamelet approach with a generalized heat loss combustion methodology (including soot generation and consumption mechanisms) is deployed to support a large-scale, quiescent, 5-m JP-8 pool fire validation study. The quiescent pool fire validation study deploys solution sensitivity procedures, i.e., the effect of mesh and time step refinement on capturing key fire dynamics such as fingering and puffing, as mesh resolutions approach O(1) cm. A novel design-order, discrete-ordinate-method discretization methodology is established by use of an analytical thermal/participating media radiation solution on both low-order hexahedral and tetrahedral mesh topologies in addition to quadratic hexahedral elements. Here, the coupling between heat losses and the flamelet thermochemical state is achieved by augmenting the unsteady flamelet equation set with a heat loss source term. Soot and radiation source terms are determined using flamelet approaches for the full range of heat losses experienced in fire applications including radiative extinction. The proposed modeling and simulation paradigm are validated using pool surface radiative heat flux, maximum centerline temperature location, and puffing frequency data, all of which are predicted within 10% accuracy. Simulations demonstrate that under-resolved meshes predict an overly conservative radiative heat flux magnitude with improved comparisons as compared to a previously deployed hybrid Reynolds-averaged Navier–Stokes/eddy dissipation concept-based methodology.

42 ENGINEERING↗

DOE OSTI2025

CLPNets: Coupled Lie–Poisson neural networks for multi-part Hamiltonian systems with symmetries

To accurately compute data-based prediction of Hamiltonian systems, it is essential to utilize methods that preserve the structure of the equations over time. We consider a particularly challenging case of systems with interacting parts that do not reduce to pure momentum evolution. Such systems are essential in scientific computations, such as discretization of a continuum elastic rod, which can be viewed as the group of rotations and translations $SE(3)$. The evolution involves not only the momenta but also the relative positions and orientations of the particles. The presence of Lie group-valued elements, such as relative positions and orientations, poses a problem for applying previously derived methods for data-based computing. We develop a novel method of data-based computation and complete phase space learning of such systems. We follow the original framework of SympNets (Jin et al., 2020) and LPNets (Eldred et al., 2024), building the neural network from phase space mappings that preserve the Lie–Poisson structure. We derive a novel system of mappings that are built into neural networks describing the evolution of such systems. We call such networks Coupled Lie–Poisson Neural Networks, or CLPNets. We consider increasingly complex examples for the applications of CLPNets, starting with the rotation of two rigid bodies about a common axis, progressing to the free rotation of two rigid bodies, and finally to the evolution of two connected and interacting $SE(3)$ components, describing the discretization of an elastic rod into two elements. Our method preserves all Casimir invariants to machine precision, preserves energy to high accuracy, and shows good resistance to the curse of dimensionality, requiring only a few thousand data points for all cases studied (three to eighteen dimensions). Additionally, the method is highly economical in memory requirements, requiring only about 200 parameters for the most complex case considered.

Data-based modeling↗

DOE OSTI2020

Evaluation of Nuclear Spent Fuel Disposal in Clay-Bearing Rock - Process Model Development and Experimental Studies

The DOE R&D program under the Spent Fuel Waste Science Technology (SFWST) campaign has made key progress in modeling and experimental approaches towards the characterization of chemical and physical phenomena that could impact the long-term safety assessment of heat-generating nuclear waste disposition in deep clay/shale/argillaceous rock. International collaboration activities such as heater tests and postmortem analysis of samples recovered from these have elucidated key information regarding changes in the engineered barrier system (EBS) material exposed to years of thermal loads. Chemical and structural analyses of sampled bentonite material from such tests has as well as experiments conducted on these are key to the characterization of thermal effects affecting bentonite clay barrier performance and the extent of sacrificial zones in the EBS during the thermal period. Thermal, hydrologic, and chemical data collected from heater tests and laboratory experiments has been used in the development, validation, and calibration of THMC simulators to model near-field coupled processes. This information leads to the development of simulation approaches (e.g., continuum vs. discrete) to tackle issues related to flow and transport at various scales of the host-rock and EBS design concept. Consideration of direct disposal of large capacity dual-purpose canisters (DPCs) as part of the back-end SNF waste disposition strategy has generated interest in improving our understanding of the effects of elevated temperatures on the EBS design. This is particularly important for backfilled repository concepts where temperature plays a key role in the EBS behavior and long-term performance. This report describes multiple R&D efforts on disposal in argillaceous geologic media through development and application of coupled THMC process models, experimental studies on clay/metal/cement barrier and host-rock (argillite) material interactions, molecular dynamic (MD) simulations of water transport during (swelling) clay dehydration, first-principles studies of metaschoepite (UO 2 corrosion product) stability, and advances in thermodynamic plus surface complexation database development. Drift-scale URL experiments provides key data for testing hydrological-chemical (HC) model involving strong couplings of fluid mixing and barrier material chemical interactions. The THM modeling focuses on heater test experiments in argillite rock and gas migration in bentonite as part of international collaboration activities at underground research laboratories (URLs). In addition, field testing at an URL involves in situ analysis of fault slip behavior and fault permeability. Pore-scale modeling of gas bubble migration is also being investigated within the gas migration modeling effort. Interaction experiments on bentonite samples from heater test under ambient and elevated temperatures permit the evaluation of ion exchange, phase stability, and mineral transformation changes that could impact clay swelling. Advances in the development, testing, and implementation of a spent nuclear fuel (SNF) degradation model coupled with canister corrosion focus on the effects of hydrogen gas generation and its integration with Geologic Disposal Safety Assessment (GDSA). GDSA integration activities includes evaluation of groundwater chemistries in shale formations.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2023

Enhancement of charge density wave correlations in a Holstein model with an anharmonic phonon potential

The Holstein Hamiltonian describes itinerant electrons whose site density couples to local phonon degrees of freedom. In the single-site limit, at half filling, the electron-phonon coupling results in a double-well structure for the lattice displacement, favoring empty or doubly occupied sites. In two dimensions and on a bipartite lattice in d ≥ 2, intersite hopping causes these doubly occupied and empty sites to alternate in a charge density wave (CDW) pattern when the temperature is lowered. Because a discrete symmetry is broken, this occurs in a conventional second-order transition at finite T cdw . In this paper, we investigate the effect of changing the phonon potential energy to one with an intrinsic double-well structure even in the absence of electron-phonon coupling. While this aids in the initial process of pair formation, the implications for subsequent CDW order are nontrivial. One expects that, when the electron-phonon coupling is too strong, the double wells become deep and the polaron mass gets large, an effect which reduces T cdw . Here, we show here the existence of regions of parameter space where the double-well potential, while aiding local pair formation, does so in a way which also substantially enhances long-range CDW order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Physical properties and anisotropic magnetism of EuBi 2

We report the synthesis of EuBi 2 single crystals and their magnetic and electronic properties. Plate-like crystals were grown in excess bismuth, and X-ray diffraction data confirm the previously reported tetragonal space group, I 4 1 /amd (No. 141). A Néel temperature of T N = 18.6 K was determined from the specific heat data, and corresponding anomalies occur in the magnetization and resistivity. We only observe one magnetic transition in zero magnetic field. The magnetization data above 70 K are well described by a Curie-Weiss model with a Weiss temperature of Θ CW ≈ −35 K and an effective moment near that of the expected spin-only moment of Eu 2+ (S = 7/2). Isothermal magnetization measurements reveal field-induced transitions for H||[100], including a hysteretic spin-flop centered at 10.1 T and a change in slope at 12 T and 2 K. However, while the isothermal magnetization for H||[110] displays nonlinear behavior, discrete metamagnetic transitions are not observed for H||[110] or H||[001], indicating significant magnetic anisotropy. The magnetization does not saturate by 13.5 T for any orientation. EuBi 2 is metallic and our crystals possess an in-plane residual resistivity ratio of ⍴300 K/⍴2 K ≈ 40. Single crystal neutron diffraction data reveal a large magnetic unit cell and non-trivial antiferromagnetic ordering. These results demonstrate that strong antiferromagnetic coupling drives complex magnetism in EuBi 2 .

36 MATERIALS SCIENCE↗

DOE OSTI2020

Charge transfer rate constants for the carotenoid-porphyrin-C 60 molecular triad dissolved in tetrahydrofuran: The spin-boson model vs the linearized semiclassical approximation

Charge transfer rate constants were calculated for the carotenoid-porphyrin-C 60 (CPC 60 ) molecular triad dissolved in explicit tetrahydrofuran. The calculation was based on mapping the all-atom anharmonic Hamiltonian of this system onto the spin-boson Hamiltonian. The mapping was based on discretizing the spectral density from the time correlation function of the donor–acceptor potential energy gap, as obtained from all-atom molecular dynamics simulations. Different spin-boson Hamiltonians were constructed for each of the possible transitions between the three excited electronic states in two different triad conformations. The rate constants of three possible transitions were calculated via the quantum-mechanically exact Fermi’s golden rule (FGR), as well as a progression of more approximate expressions that lead to the classical Marcus expression. The advantage of the spin-boson approach is that once the mapping is established, the quantum-mechanically exact FGR and the hierarchy of approximations are known in closed form. The classical Marcus charge transfer rate constants obtained with the spin-boson Hamiltonians were found to reproduce those obtained from all-atom simulations with the linearized semiclassical approximation, thereby confirming the equivalence of the two approaches for this system. Furthermore, within the spin-boson Hamiltonian, we also found that the quantum-mechanically exact FGR rate constants were significantly enhanced compared to the classical Marcus theory rate constants for two out of three transitions in one of the two conformations under consideration. The results confirm that mapping to the spin-boson model can yield accurate predictions for charge transfer rate constants in a system as complex as CPC 60 dissolved in tetrahydrofuran.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

A discretized representation for Monte Carlo simulation of deformed semiflexible chains

In this study, we present a novel orientation discretization approach based on the rhombic triacontahedron for Monte Carlo simulations of semiflexible polymer chains, aiming at enhancing structural analysis through rheo-small-angle scattering (rheo-SAS). Our approach provides a more accurate representation of the geometric features of semiflexible chains under deformation, surpassing the capabilities of traditional lattice structures. Validation against the Kratky–Porod chain system demonstrated superior consistency, underscoring its potential to significantly improve the precision of uncovering geometric details from rheo-SAS data. Further, this approach opens new avenues for investigating the conformations of semiflexible polymers and mechanically induced phase transitions in more complex polymer structures, offering deeper insights into their behavior under various conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗