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DOE OSTI2021

Synchronous and Concurrent Multidomain Computing Method for Cloud Computing Platforms

We present a numerical method for synchronous and concurrent solution of transient elastodynamics problem where the computational domain is divided into subdomains that may reside on separate computational platforms. Here, this work employs the variational multiscale discontinuous Galerkin (VMDG) method to develop interdomain transmission conditions for transient problems. The fine-scale modeling concept leads to variationally consistent coupling terms at the common interfaces. The method admits a large class of time discretization schemes, and decoupling of the solution for each subdomain is achieved by selecting any explicit algorithm. Numerical tests with a manufactured solution problem show optimal convergence rates. The energy history in a free vibration problem is in agreement with that of the solution from a monolithic computational domain.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

A note on the reliability of goal-oriented error estimates for Galerkin finite element methods with nonlinear functionals

Here, we consider estimating the discretization error in a nonlinear functional J (u) in the setting of an abstract variational problem: find u ϵ $\mathscr{V}$ such that B (u, φ) = L (φ) ∀φ ϵ $\mathscr{V}$, as approximated by a Galerkin finite element method. Here, $\mathscr{V}$ is a Hilbert space, B (. , .) is a bilinear form, and L (∙) is a linear functional. We consider well-known error estimates η of the form J (u) - J (u h ) ≈ η = L (z) - B (u h , z), where u h denotes a finite element approximation to u, and z denotes the solution to an auxiliary adjoint variational problem. We show that there exist nonlinear functionals for which error estimates of this form are not reliable, even in the presence of an exact adjoint solution z. An estimate η is said to be reliable if there exists a constant C ϵ $\mathbb{R}$ >0 independent of u h such that |J (u) - J (u h )| ≤ C|η|. We present several example pairs of bilinear forms and nonlinear functionals where reliability of η is not achieved.

A posteriori↗

DOE OSTI2023

Deep reinforcement learning assisted co-optimization of Volt-VAR grid service in distribution networks

With the increasing penetration of distributed energy resources in distribution networks, Volt-VAR control and optimization (VVC/VVO) have become very important to ensure an acceptable quality of service to all customers. System operators can rely on slow-responding utility devices, including capacitor banks and on-load tap changing transformers, along with fast-responding battery and photovoltaic (PV) inverters for the VVC/VVO implementation. Because of variations in response time of these two classes of devices, and different control actions (discrete versus continuous), coordinated and optimal scheduling and operation have become of utmost importance. Here, this paper develops a look-ahead deep reinforcement learning (DRL)-based multi-objective VVO technique to improve the voltage profile of active distribution networks, decrease network and inverter power loss, and save the operational cost of the grid. It proposes a deep deterministic policy gradient (DDPG)-based approach to schedule the optimal reactive and/or active power set-points of fast-responding inverters, and a deep Q-network (DQN)-based DRL agent to schedule the discrete decisions variables of slow-responding assets. The reactive power output of PV and battery smart inverters are scheduled at 30-minute intervals and the capacitors’ commitment status is scheduled with several hour intervals. The proposed framework is validated on the modified IEEE 34-bus and 123-bus test cases with embedded PV and PV-plus-storage. To validate the efficacy of the proposed VVO, it is compared with several scenarios, including the base case without VVO, localized droop control of DERs, DDPG-only, and twin delayed DDPG (TD3) agent-based DRL techniques. The results justify the superior performance of the proposed method to improve the voltage profile, reduce network power loss, and minimize the look-ahead grid operational cost while minimizing the undesirable power losses in inverters as a result of power factor adjustments.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Stress Field Dynamics and Fault Slip Potential in the Paradox Basin

Abstract The Paradox Basin, straddling Utah, Colorado, Arizona, and New Mexico is characterized by an intricate amalgamation of evaporites and clastic layers and is dominated by prominent salt walls and related subsurface structures. Our research offers a new examination of the stress distribution across the basin, deriving from continuous and discrete stress measurements conducted in boreholes in the region and focal mechanism analysis, emphasizing variations over salt structures. Integrating Coulomb failure criteria with probabilistic methods, we assess potential fault movements resulting from fluid pressure alterations. Our approach provides a comprehensive understanding of the Paradox Basin's state of stress, showing a continuous change of the maximum horizontal stress orientation from N‐S at the Wasatch Fault Zone to WNW‐ESE in the northern part of the Paradox Basin and to WSW‐ENE in the southern part of the basin. Further East, into the Colorado Plateau and the Uncompahgre Uplift, the S H max orientation becomes E‐W. Decoding stress orientation dynamics has enabled critical insights into fault slip potential, especially in the basin's northern region. The salt wall faults are less likely to slip, and the Paradox Formation's evaporite and clastic rock sequence can serve as a potential low seismic risk target for carbon storage and hydrocarbon extraction.

Geochemistry & Geophysics↗

DOE OSTI2026

Parametric reduced order models for graded lattice structures

Graded lattice structures, characterized by smoothly varying mechanical properties, hold significant promise for optimizing material distribution in advanced engineering applications. However, accurately modeling these structures poses substantial computational challenges due to the continuous geometric variations within their unit cells. Here, to address these challenges, this paper introduces a novel Efficient Reduced Order Model (EROM) that integrates the Matrix Discrete Empirical Interpolation Method (MDEIM) and Discrete Empirical Interpolation Method (DEIM) with polynomial regression to efficiently manage geometric parametrization in lattice structures. Unlike traditional reduced order models (ROMs) that require extensive precomputed libraries for each geometric configuration, our approach enables continuous geometric variations through a flexible algebraic formulation, significantly reducing computational costs while preserving high accuracy. The method constructs projection matrices for individual unit cells that can be efficiently assembled into global systems, leveraging the repetitive nature of lattice structures. Numerical studies demonstrate that our EROM achieves displacement errors below 1% and von Mises stress prediction errors below 4%, coupled with computational speedups exceeding two orders of magnitude compared to full-order simulations. The proposed method's modularity and scalability make it particularly suitable for design optimization and real-time simulation of functionally graded lattice structures, with applications spanning aerospace to biomedical engineering.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

An Orthogonal Recursive Bisection (ORB) Based Time Advancement Algorithm for CFD-DEM Solvers

The time integration of the granular phase in coupled computational fluid dynamics (CFD) – discrete element method (DEM) simulations presents a unique computational challenge brought about by the large variations in particle collisional time scales. Particles in the dilute regions of the computational domain can be advanced with large time steps while dense regions require much smaller time increments. However, the time step size in most solvers is globally set as the limit for accuracy and stability imposed by the collisions and is typically orders of magnitude less than that required away from collisions. This work addresses this precise issue and provides a strategy to avoid the use of a global conservative small time step size for the entire set of particles.A novel time stepping algorithm for CFD-DEM solvers using a partitioning approach using orthogonal recursive bisection (ORB) that allows for variable time steps among particles is described and its computational performance is compared against baseline explicit methods, typically used in several CFD-DEM solvers. ORB has advantages of being relatively quick and easy to update incrementally and has the required heuristic behavior (i.e., it will split the region in half with a cluster on each side) when groups of particles are well separated (clustered). The algorithm presented in this work uses a local time stepping approach to resolve collisional time scales for subsets of particles that are present at the leaves of the ORB, thereby resulting in substantial reduction of computational cost. The parallel implementation of this method where a ``knapsack” algorithm is used in tandem with ORB for effective load-balancing is also presented, where a best possible partitioning is obtained based on number of particles and local time-stepping costs. The algorithm is tested against benchmark problems with varying particle distributions that include fluidized bed and riser flow scenarios. Preliminary results indicate that the approach is 2-3X faster than traditional explicit methods for problems that involve both dense and dilute regions, while maintaining the same level of accuracy.

adaptive timestepping↗

DOE OSTI2024

Structural Trends and Vibrational Analysis of N,N,N′,N′−Tetramethylmalonamide Complexes Across the Lanthanide Series

Fundamental understanding of coordination chemistry across the lanthanide series is essential for explaining chemical behavior of rare-earth metals in complex liquid-liquid extraction processes, which in turn affects the distribution ratios and efficacy of separations as a whole. In this work, we explore the structural trends between the lanthanides and a neutral N,N,N',N'-tetramethylmalonamide (TMMA) ligand within four isolated families of solid-state compounds: Ln(trans-TMMA) 2 (NO 3 ) 3 Ln=La-Nd, Sm; Ln(cis-TMMA) 2 (NO 3 ) 3 Ln=Eu-Tb, Er; [Ln(TMMA) 3 (NO 3 ) 2 ][Ln(TMMA)(NO 3 ) 4 ] Ln=Dy-Tm; Ln(Κ 2 -TMMA)(iPrOH)(NO 3 ) 3 and Ln(Κ 1 -TMMA)(Κ 2 -TMMA)(NO 3 ) 3 Ln=Yb, Lu. Moving across the lanthanide series, we note the formation of both discrete charge-neutral complexes, as well as charged molecular anion-cation pairs, with variations in spatial ligand arrangement, coordination numbers, and ligand denticities. IR and Raman spectroscopy paired with DFT frequency calculations were used for an in-depth investigation of vibrational modes unique to each structural family. The collection of isolated model compounds was also discussed in the context of liquid-liquid separations based on reported distribution ratios from malonamide extraction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

FSISPH: An SPH formulation for impacts between dissimilar materials

Here, we present an SPH formulation with several new features designed to better model the fully-compressible interaction of dissimilar materials. We developed the new method to simulate the atmospheric entry and break-up of small celestial bodies in planetary atmospheres. The formulation uses a unity-based, density-energy discretization of the hydrodynamic conservation laws with linear-corrected kernel gradients. To account for variations in compressibility, we use an HLLC approximate Riemann solver to adjust the velocity gradient at material interfaces. To handle large transverse velocity discontinuities, we introduce a simple slip interface model that limits the artificial viscosity at material interfaces. Diffusion is optionally applied through the velocity gradient and this allows the density and specific thermal energy to evolve in a manner more consistent with the first law of thermodynamics in comparison to other more direct diffusion schemes. We also introduce a material-local second-order artificial conduction scheme used to smooth the specific thermal energy field. Material damage fits neatly under this framework by treating the damage front as a material interface. The method has been implemented as a solver, FSISPH, within the code, Spheral++, and is publicly available on github. We test our new solver on a number of classic shock, mixing, and multi-material problem. The components we outline can significantly improve accuracy of SPH for problems with sharp contact discontinuities.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Electron-Proton Scattering Event Generation using Structured Tokenization

Recent work such as Omnijet-$\alpha$ has demonstrated that effective tokenization combined with transformer-based architectures can produce effective foundation models for jet physics. While tokenization may help models capture generalizable event characteristics, it also introduces discretization errors that may compromise the precision required for downstream physics analyses. As the number and complexity of the particle features grow, these errors are likely to grow proportionally. In this study, we investigate new tokenization strategies to improve the application of generative transformer models to \textsc{Pythia8} simulations of electron-proton scattering at the Electron-Ion Collider. Specifically, we propose a feature-based structured tokenization approach that utilizes multiple tokens per particle, improving expressivity, while reducing the total number of unique tokens needed. We evaluate this method against grid-based binning, K-means clustering, and vector-quantized variational auto-encoders on the event simulations. Our results show that feature-based structured tokenization reduces discretization error, leading to more accurate generative modeling of particle-level events.

Goldenberg, Steven [Thomas Jefferson National Acce↗

DOE OSTI2025

Electron-Proton Scattering Event Generation using Structured Tokenization

Goldenberg, Steven [Thomas Jefferson National Acce↗

DOE OSTI2023

Engineering Relaxor Behavior in (BaTiO 3 ) n /(SrTiO 3 ) n Superlattices

Complex-oxide superlattices provide a pathway to numerous emergent phenomena because of the juxtaposition of disparate properties and the strong interfacial interactions in these unit-cell-precise structures. This is particularly true in superlattices of ferroelectric and dielectric materials, wherein new forms of ferroelectricity, exotic dipolar textures, and distinctive domain structures can be produced. Here, in this study, relaxor-like behavior, typically associated with the chemical inhomogeneity and complexity of solid solutions, is observed in (BaTiO 3 ) n /(SrTiO 3 ) n (n = 4–20 unit cells) superlattices. Dielectric studies and subsequent Vogel–Fulcher analysis show significant frequency dispersion of the dielectric maximum across a range of periodicities, with enhanced dielectric constant and more robust relaxor behavior for smaller period n. Bond-valence molecular-dynamics simulations predict the relaxor-like behavior observed experimentally, and interpretations of the polar patterns via 2D discrete-wavelet transforms in shorter-period superlattices suggest that the relaxor behavior arises from shape variations of the dipolar configurations, in contrast to frozen antipolar stripe domains in longer-period superlattices (n = 16). Moreover, the size and shape of the dipolar configurations are tuned by superlattice periodicity, thus providing a definitive design strategy to use superlattice layering to create relaxor-like behavior which may expand the ability to control desired properties in these complex systems.

36 MATERIALS SCIENCE↗

DOE OSTI2020

A mathematical model of asynchronous data flow in parallel computers *

Abstract We present a simplified model of data flow on processors in a high-performance computing framework involving computations necessitating inter-processor communications. From this ordinary differential model, we take its asymptotic limit, resulting in a model which treats the computer as a continuum of processors and data flow as an Eulerian fluid governed by a conservation law. We derive a Hamilton–Jacobi equation associated with this conservation law for which the existence and uniqueness of solutions can be proven. We then present the results of numerical experiments for both discrete and continuum models; these show a qualitative agreement between the two and the effect of variations in the computing environment’s processing capabilities on the progress of the modelled computation.

Barnard, Richard C.↗

DOE OSTI2023

Trapping-induced quantum beats in a van-der-Waals heterostructure microcavity observed by two-dimensional micro-spectroscopy

Spatial confinement has been frequently engineered to control the flow and relaxation dynamics of exciton polaritons. While widely investigated in GaAs microcavities, exciton-polariton coupling between discretized polariton modes arising from spatially confined 2D crystals been has been less exhaustively studied. Here, we use coherent 2D photoluminescence-detected micro-spectroscopy to detect oscillating 2D peaks exclusively from a spatial trap in a microcavity with an embedded van-der-Waals heterostructure at room temperature. We observe a wide variation of oscillatory phases as a function of spectral position within the 2D spectrum, which suggests the existence of a coupling between the discretized polariton modes. The latter is accompanied by the generation of coherent phonons.

Materials Science↗

DOE OSTI2020

Detection Limits and Near‐Field Ground Motions of Fast and Slow Earthquakes

Abstract We investigate theoretical limits to detection of fast and slow seismic events, and spatial variations of ground motion expected from M 6 earthquakes at short epicentral distances. The analyses are based on synthetic velocity seismograms calculated with the discrete wavenumber method assuming seismic velocities and attenuation properties of the crust in Southern California. The examined source properties include different magnitudes ( M −1.0 to M 6.0), static stress drops (0.1–10 MPa), and slow and fast ruptures (0.1–0.9 of shear wave velocity). For the M 6 events we also consider variations in rise times producing crack‐ and pulse‐type events and different rupture directivities. Slow events produce ground motion with considerably lower amplitude than corresponding regular fast earthquakes with the same magnitude, and hence are significantly more difficult to detect. The static stress drop and slip rise time also affect the maximum radiated seismic motion, and hence event detectability. Apart from geometrical factors, the saturation and depletion of seismic ground motion at short epicentral distances stem from radiation pattern, earthquake size (magnitude, stress drop), and rupture directivity. The rupture velocity, rise time, and directivity affect significantly the spatial pattern of the ground motions. The results can help optimizing detection of slow and fast small earthquakes and understand the spatial distribution of ground motion generated by large events.

58 GEOSCIENCES↗

DOE OSTI2022

Modeling rarefied gas chemistry with QuiPS, a novel quasi-particle method

The goal of this work is to build up the capability of quasi-particle simulation (QuiPS), a novel flow solver, such that it can adequately model the rarefied portion of an atmospheric reentry trajectory. Direct simulation Monte Carlo (DSMC) is the conventional solver for such conditions, but struggles to resolve transient flows, trace species, and high-level internal energy states due to stochastic noise. Quasi-particle simulation (QuiPS) is a novel Boltzmann solver that describes a system with a discretized, truncated velocity distribution function. The resulting fixed-velocity, variable weight quasi-particles enable smooth variation of macroscopic properties. The distribution function description enables the use of a variance-reduced collision model, greatly minimizing expense near equilibrium. This work presents the addition of a neutral air chemistry model to QuiPS and some demonstrative 0D simulations. The explicit representation of internal distributions in QuiPS reveals some of the flaws in existing physics models. Overall, variance reduction, a key feature of QuiPS, can greatly reduce expense of multi-dimensional calculations, but is only cheaper when the gas composition is near chemical equilibrium.

42 ENGINEERING↗

DOE OSTI2023

On Practical Aspects of Variational Consistency in Contact Dynamics

Usage of contact mechanics methodologies is a pervasive modeling requirement in dynamic simulations. While for some trivial problems, solutions taken from analytical geometry are available, use of a finite element framework is common to achieve formulation generality. This work explores two dynamic contact formulations: one based on the traditional node-to-segment (NTS) approach, and a variationally consistent segment-to-segment (STS) mortar formulation. The NTS formulation employed here enforces the constraints kinematically (i.e., the interpenetration is enforced to the solver tolerance), whereas the mortar approach uses Lagrange multipliers to enforce the contact constraints. Both approaches are implemented in the open-source finite element framework Multiphysics Object-Oriented Simulation Environment (MOOSE). The results highlight two relevant contact-interface-related dynamic phenomena in finite element simulations. First, stabilization of contact constraints is discussed, taking into account the evolution of the total energy in a benchmark problem. Second, the influence of finite element discretization on both of the aforementioned contact formulations is analyzed by exercising a large-deformation example with continuous relative sliding. Variationally consistent contact approaches such as the mortar formulation lead to improved energy preservation and avoid spurious excitation of the system's frequencies. This is especially relevant in settings where inertia and vibrations are of importance.

42 ENGINEERING↗

DOE OSTI2024

Peridynamic Models for Random Media Found by Coarse Graining

Using coarse graining, the upscaled mechanical properties of a solid with small scale heterogeneities are derived. The method maps internal forces at the small scale onto peridynamic bond forces in the coarse grained mesh. These upscaled bond forces are used to calibrate a peridynamic material model with position-dependent parameters. These parameters incorporate mesoscale variations in the statistics of the small scale system. The upscaled peridynamic model can have a much coarser discretization than the original small scale model, allowing larger scale simulations to be performed efficiently. The convergence properties of the method are investigated for representative random microstructures. In conclusion, a bond breakage criterion for the upscaled peridynamic material model is also demonstrated.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Weak boundary conditions for Lagrangian shock hydrodynamics: A high-order finite element implementation on curved boundaries

Here, we propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations using high-order finite elements on curved boundaries. Specifically, the variational formulation is appropriately modified to enforce free-slip wall boundary conditions, without perturbing the structure of the function spaces used to represent the solution, with a considerable simplification with respect to traditional approaches. Total energy is conserved and the resulting mass matrices are constant in time. The robustness and accuracy of the proposed method are validated with an extensive set of tests involving nontrivial curved boundaries.

97 MATHEMATICS AND COMPUTING↗