Stress-hybrid virtual element method on ten-noded tetrahedral meshes for nearly-incompressible elastic solids and thin structures
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Chen, Alvin [Sandia National Laboratories (SNL-NM)↗
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Virtual element approximations of the time-fractional nonlinear convection-diffusion equation on polygonal meshes
We extend the Virtual Element Method to a two-dimensional unsteady nonlinear convection-diffusion equation characterized by a fractional-order derivative with respect to the time variable. Our methodology is based on three fundamental technical components: a fractional version of the Grunwald-Letnikov approximation, discrete maximal regularity, and the regularity theory associated with non-linearity. We prove the method's well-posedness, i.e., the approximate solution's existence and uniqueness to the time-fractional convection-diffusion equation with a Lipschitz nonlinear source term. The fully discrete scheme inherently maintains stability and consistency by leveraging the discrete maximal regularity and the energy projection operator. The convergence in the L 2 -norm and H 1 -norm to various mesh configurations is validated by numerical results, underlining the practical effectiveness of the proposed method.
97 MATHEMATICS AND COMPUTING↗
Hourglass control in staggered-grid hydrodynamics using virtual element stabilization techniques
Numerical simulations using the staggered-grid hydrodynamics (SGH) discretization suffer from hourglass instabilities. In this work, we develop a stabilization method to suppress the hourglass instabilities using techniques from the virtual element method (VEM). The stiffness matrix of the VEM consists of two terms: the consistency matrix which is rank deficient and the stability matrix. Here, we first show that in two dimensions and on general polygons, the stiffness matrix of the SGH is identical to the consistency matrix of the linear VEM for both the diffusion equation and the linear elasticity equation. These analyses explain the origin of the hourglass instabilities of the SGH discretization method, and establish a theoretical foundation for our proposed stabilization method by augmenting the stiffness matrix of the SGH discretization using the VEM stability matrix. Then, we present numerical examples using Lagrangian SGH simulations. The numerical experiments demonstrate that the proposed VEM stabilization method is effective at eliminating hourglass modes in the SGH discretization.
97 MATHEMATICS AND COMPUTING↗
A comparative study of calibration techniques for finite strain elastoplasticity: Numerically-exact sensitivities for FEMU and VFM
Accurate identification of material parameters is crucial for predictive modeling in computational mechanics. Here, the two primary approaches in the experimental mechanics community for calibration from full-field digital image correlation data are known as finite element model updating (FEMU) and the virtual fields method (VFM). In VFM, the objective function is a squared mismatch between internal and external virtual work or power. In FEMU, the objective function quantifies the weighted mismatch between model predictions and corresponding experimentally measured quantities of interest. It is minimized by iteratively updating the parameters of an FE model. While FEMU is seen as more flexible, VFM is commonly used instead of FEMU due to its considerably greater computational expense. However, comparisons between the two methods usually involve approximations of gradients or sensitivities with finite difference schemes, thereby making direct assessments difficult. Hence, in this study, we compare VFM and FEMU in the context of numerically-exact sensitivities obtained through local sensitivity analyses and the application of automatic differentiation software. To this end, we conduct a series of test cases to assess both methods under practical challenges using a finite strain elastoplasticity model.
Automatic differentiation↗
Gluon unpolarized, polarized, and transversity GPDs from lattice QCD: Lorentz-covariant parametrization
We identify the matrix elements necessary to determine the leading-twist gluon generalized parton distributions (GPDs) H g , E g , H ˜ g , E ˜ g , H g T , E g T , H ˜ g T , E ˜ g T in lattice QCD calculations. We present a method to achieve a Lorentz-covariant parameterization of the matrix elements in terms of a linearly independent basis of tensor structures. This parameterization is crucial for projecting lattice QCD matrix elements onto light cone distributions. For the first time, we determine the corresponding components that project onto the linear combinations of invariant amplitudes, which reduce to the different gluon GPDs in the light cone limit and enable their separation in a lattice QCD calculation for spin-0 and spin- 1 2 hadrons. Hence, this work lays the foundation for the numerical determination of the gluon GPDs from first-principle lattice QCD calculations, directly advancing our understanding of the mass and spin structures and mechanical properties of the nucleon, as well as the physics underlying deeply virtual Compton scattering and deeply virtual meson production in a range of experimental processes. Published by the American Physical Society 2025
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Inertia estimation for power grids: A review of methods, challenges, and future prospects
The electric power grid is undergoing a significant transformation, shifting from traditional synchronous generators to inverter-based resources (IBRs) such as solar photovoltaics, wind turbines, and energy storage systems. This evolution leads to a reduction in system inertia, a critical attribute for maintaining frequency stability in response to disturbances. Consequently, the ability to monitor and estimate system inertia has become increasingly essential. This paper provides a comprehensive review of existing inertia estimation methodologies, analyzing them from multiple perspectives, including the types of data utilized, underlying estimation principles, operational modes, and system-wide applicability. A comparative summary table is included to distill commonalities and key characteristics across various studies. In addition, the paper examines practical implementations of inertia estimation across several major power systems worldwide, including the U.S. interconnections, the Nordic power system, and the U.K. grid. Key challenges are identified, particularly in estimating contributions from virtual inertia sources and load-induced inertia in increasingly converter-dominated networks. To address these emerging challenges, the paper proposes an integrated framework for real-time inertia estimation and monitoring. This framework encompasses critical components such as data acquisition, inertia estimation from both synchronous and non-synchronous sources, load-induced effects, optimization techniques, forecasting, and virtual inertia scheduling. Collectively, these elements enable dynamic, system-wide monitoring and adaptive control of grid inertia.
Inertia estimation↗
The Dynamic Networks Experiments: Virtual Experiments to Quantify Gains in Nuclear Explosion Monitoring
We describe an ongoing series of virtual experiments conducted collaboratively by four United States National Laboratories: Sandia National Laboratories, Los Alamos National Laboratory, Lawrence Livermore National Laboratory, and Pacific Northwest National Laboratory. These Dynamic Network Experiments (DNEs) provide an experimental framework to evaluate the potential impact of new research tools on nuclear explosion monitoring. The second DNE (DNE2), completed in 2024, exploited waveform data (seismic, infrasound, and electromagnetic) that was recorded by multi-modal sensors within and near the Nevada National Security Site and synthetic radionuclide signatures over multiple time periods. During the execution of DNE2, we processed and analyzed data through a multi-stage event processing pipeline that ingested raw data, performed quality control, detected signals, built events from these signals, located these events, and characterized the events’ source types and sizes. For each stage and over the entire event processing pipeline, we evaluated performance changes by comparing the performance of new data processing methods, models, and algorithms against a baseline. We also performed an additional execution phase to assess event processing pipeline function, speed, and efficiency against that of an expert analyst, including computational and manual efforts. Finally, we assessed the impact and effort of modern computing infrastructure on the monitoring pipeline. This paper describes key elements of the DNEs, from formulation through execution, as demonstrated in DNE2. The DNEs introduce several novel concepts to quantitatively measure the potential impact of new methods on explosion monitoring, including the collaborative design of multi-modal datasets, performance and logistical metrics, and integrated analyses.
42 ENGINEERING↗
NewLife Nuclear - An Environmentally and Economically Minded Solution for Fusion Energy Waste Handling
Energy demand is rising as a result of innovative and increasingly more energy intensive processes coming to fruition, particularly through the recent interest in the development of AI data centers as well as manufacturing with the push towards increasing domestic manufacturing interest. Fusion energy can provide virtually limitless energy to support this increase in energy demand. Fusion energy concepts, largely classified as magnetic fusion energy (MFE) and inertial fusion energy (IFE) are being pursued, each having unique challenges to overcome before the successful deployment of electricity to the grid. Achieving fusion ignition on the National Ignition Facility, first in December 2022, and eight times since, has demonstrated the scientific viability of the IFE approach. Meanwhile, MFE test stands continue to improve confinement times, making meaningful strides in progressing towards experimental scientific viability. In each of these approaches, an emphasis is placed on generating more power out of the system than what is required to power the system. An under-researched area applicable to both IFE and MFE is handling activated waste coming out of fusion energy systems, both in the course of normal daily operations, as well as in intermittent periods as structural materials may need to be replaced. In the context of an IFE plant system, commonly discussed plant designs suggest targets are ignited within a chamber at a rate of up to one million targets per day. Between each shot, the chamber housing the ignition event will clear a portion of the chamber – resulting in a mixture of vaporized target gas, target debris, and other materials being expelled from the chamber [source]. Additionally, IFE system concepts typically discuss the modularization of plant designs, which are expected to be replaced periodically as the components degrade over time. This would result in the irradiated chamber structure materials, likely metals and alloys, needing to be removed and safely stored. In MFE plant systems, while targets are not ignited at a repetition rate with the frequent chamber clearing as is expected in IFE plant systems, it is anticipated that portions of the confinement area interfacing with the hot plasma will need to be replaced periodically. In each system, without additional investment and research into alternative processing and recycling methods, the result is storing irradiated materials, and other elements in a safe containment area until they are no longer activated. – resulting in significant waste both economic and environmental.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗