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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part II: Enforcing the Lorenz Gauge Condition

In a previous paper Christlieb et al. (A particle-in-cell method for plasmas with a generalized momentum formulation, part I: Model formulation, 2024), we developed a new particle-in-cell (PIC) method for the relativistic Vlasov–Maxwell system in which the electromagnetic fields and the equations of motion for the particles were cast in terms of scalar and vector potentials through a Hamiltonian formulation. This new method evolved the potentials under the Lorenz gauge using integral equation methods. New methods to construct spatial derivatives of the potentials that converge at the same rates as the fields were also presented. The new particle method was compared against standard explicit discretizations, including the well-known FDTD-PIC method, for a range of applications involving sheaths and particle beams. Here, this paper extends this new class of methods by focusing on the enforcement the Lorenz gauge condition in both exact and approximate forms using co-located meshes. A time-consistency property of the proposed field solver for the vector potential form of Maxwell’s equations is established, which is shown to preserve the equivalence between the semi-discrete Lorenz gauge condition and the analogous semi-discrete continuity equation. Using this property, we present three methods to enforce a semi-discrete gauge condition. The first method introduces an update for the continuity equation that is consistent with the discretization of the Lorenz gauge condition. Both the finite difference and spectral implementations satisfy this discrete gauge condition to machine precision. The second approach we propose enforces a semi-discrete continuity equation using the boundary integral solution to the field equations. The potential benefit of this approach is that it eliminates spatial derivatives that appear on the particle data, namely the current density, which is often calculated by linear combinations of low-order spline basis functions. This method is ideally suited to boundary integral equation methods that invert multi-dimensional operators without dimensional splitting techniques and will be the subject of future work. The third approach introduces a gauge correcting method that makes direct use of the gauge condition to modify the scalar potential and uses local maps for both the charge and current densities. This results in a gauge error, as the maps do not enforce the continuity equation. The vector potential coming from the current density is taken to be exact, and using the Lorenz gauge, we compute a correction to the scalar potential that makes the two potentials satisfy the gauge condition. This method also enforces the gauge condition to machine precision. We demonstrate two of the proposed methods in the context of periodic domains. Problems defined on bounded domains, including those with complex geometric features remain an ongoing effort. However, this work shows that it is possible to design computationally efficient methods that can effectively enforce the Lorenz gauge condition in a non-staggered PIC formulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation

Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Generalization error guaranteed auto-encoder-based nonlinear model reduction for operator learning

Many physical processes in science and engineering are naturally represented by operators between infinite-dimensional function spaces. The problem of operator learning, in this context, seeks to extract these physical processes from empirical data, which is challenging due to the infinite or high dimensionality of data. An integral component in addressing this challenge is model reduction, which reduces both the data dimensionality and problem size. In this paper, we utilize low-dimensional nonlinear structures in model reduction by investigating Auto-Encoder-based Neural Network (AENet). AENet first learns the latent variables of the input data and then learns the transformation from these latent variables to corresponding output data. Our numerical experiments validate the ability of AENet to accurately learn the solution operator of nonlinear partial differential equations. Furthermore, we establish a mathematical and statistical estimation theory that analyzes the generalization error of AENet. Finally, our theoretical framework shows that the sample complexity of training AENet is intricately tied to the intrinsic dimension of the modeled process, while also demonstrating the robustness of AENet to noise.

Auto-encoder↗
DOE OSTI2022

Conservative high-order data transfer method on generalized polygonal meshes

A conservative data transfer (remap) between two meshes is an important step of arbitrary Lagrangian-Eulerian (ALE) hydrodynamics simulations. High-order numerical methods for ALE simulations require both high-order (curvilinear) meshes and high-order remap algorithms. Here we develop a conservative and bounds-preserving method for accurate remapping of discrete fields on generalized polygonal meshes with curvilinear edges. The properties of the proposed method are studied theoretically and numerically for various (smooth and non-smooth) mesh deformations and discrete fields that represent smooth and discontinuous functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A phase-field fracture formulation for generalized standard materials: The interplay between thermomechanics and damage

Accurately modeling fracture of ductile materials poses open challenges in the field of computational mechanics due to the multiphysics nature of their failure processes. Integrating the interplay between thermodynamics and damage into ductile fracture models is vital for predicting critical failure modes. Here, in this paper, we develop a versatile phase-field (PF) framework for modeling ductile fracture, taking into account finite-strain elasto-plasticity. The framework stems from a variational formulation of constitutive relations for generalized standard materials (GSMs), whose response is described by a Helmholtz free energy and a dissipation pseudo-potential. Its variational structure is based on a minimum principle for a functional that expresses the sum of power densities for reversible and irreversible processes. By minimizing this functional with a constraint on a von Mises yield function, we derive the evolution equation for the equivalent plastic strain and an associative flow rule. This constrained optimization problem is analytically solved for a wide class of thermo-viscoplasticity models. The key innovations of the current work include (i) a cubic plastic degradation function that accounts for a non-vanishing damage-dependent yield stress, (ii) closed-form expressions of the Helmholtz free energy and dissipation pseudo-potential for three thermo-viscoplasticity models, (iii) an extended Johnson–Cook plasticity model with a nonlinear hardening law, and (iv) a plastic work heat source that depends on the plastic degradation function and a variable Taylor–Quinney (TQ) coefficient. The capabilities of the proposed framework are tested with the aid of four ductile fracture problems, including the Sandia Fracture Challenge. In each of these problems, we examine the evolution of relevant field variables such as the PF order parameter, the equivalent plastic strain, the temperature, and the internal power dissipation density, in addition to the overall structural response quantified by the force–displacement curve. These numerical studies demonstrate that the proposed framework effectively represents ductile fracture, yielding computational results that exhibit good agreement with experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Exclusive double quarkonium production and generalized TMDs of gluons

Being the “mother distributions” of all types of two-parton correlation functions, generalized transverse momentum dependent parton distributions (GTMDs) have attracted a lot of attention over the last years. We argue that exclusive double production of pseudoscalar quarkonia (η c or η b ) in nucleon-nucleon collisions gives access to GTMDs of gluons.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Multivariate degradation modeling using generalized cauchy process and application in life prediction of dye-sensitized solar cells

Recently, the Generalized Cauchy (GC) process has been applied to capture a Long Memory (LM) phenomenon in product degradation modeling and life prediction. Compared with the traditional fractional Brownian motion that captures the LM using a single Hurst parameter, the GC process has two free parameters (Hurst and fractal dimension parameters) that flexibly capture both global LM and local irregularity. However, all existing GC-based degradation models are for a single Degradation Characteristic (DC). In this article, motivated by a real degradation problem of dye-sensitized solar cells that jointly exhibits multiple DCs, global LM, local irregularity and DC-wise cross-correlation, we propose a novel GC-based Multivariate Degradation Model (GC-MDM) to simultaneously capture the aforementioned effects. A maximum likelihood estimation approach is developed to estimate parameters of the GC-MDM. Subsequently, product life prediction based on the GC-MDM is developed. The proposed GC-MDM is validated through a simulation study and a physical experiment of dye-sensitized solar cells. Furthermore, results show that the proposed GC-MDM fundamentally improves the life prediction accuracy in comparison with conventional degradation models which significantly misestimate the uncertainty of product life.

14 SOLAR ENERGY↗
DOE OSTI2024

Coarse-Graining Conformational Dynamics with Multidimensional Generalized Langevin Equation: How, When, and Why

A data-driven ab initio generalized Langevin equation (AIGLE) approach is developed to learn and simulate high-dimensional, heterogeneous, coarse-grained (CG) conformational dynamics. Constrained by the fluctuation–dissipation theorem, the approach can build CG models in dynamical consistency (DC) with all-atom molecular dynamics. Here, we also propose practical criteria for AIGLE to enforce long-term DC. Case studies of a toy polymer, with 20 CG sites, and the alanine dipeptide, with two dihedral angles, elucidate why one should adopt AIGLE or its Markovian limit for modeling CG conformational dynamics in practice.

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

Open quantum system violates generalized Pauli constraints on quantum device

Abstract The Pauli exclusion principle governs the fundamental structure and function of fermionic systems from molecules to materials. Nonetheless, when such a fermionic system is in a pure state, it is subject to additional restrictions known as the generalized Pauli constraints (GPCs). Here we verify experimentally the violation of the GPCs for an open quantum system using data from a superconducting-qubit quantum computer. We prepare states of systems with three-to-seven qubits directly on the quantum device and measure the one-fermion reduced density matrix (1-RDM) from which we can test the GPCs. We find that the GPCs of the 1-RDM are sufficiently sensitive to detect the openness of the 3-to-7 qubit systems in the presence of a single-qubit environment. Results confirm experimentally that the openness of a many-fermion quantum system can be decoded from only a knowledge of the 1-RDM with potential applications from quantum computing and sensing to noise-assisted energy transfer.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

An implementation of a high-order generalized finite difference method for solving the time-harmonic cold plasma wave equation in toroidal geometry

A high-order physics-informed meshless finite difference numerical technique is introduced for solving the time-harmonic cold plasma wave equation in toroidal geometries, presenting a novel application of the generalized finite difference (GFD) method to plasma wave simulations. The algorithm employs an irregular distribution of computational points, with local point density informed by the shortest wavelength derived from the cold plasma dispersion relation. Numerical stability and robustness are addressed using regularization techniques. The algorithm, implemented for two spatial dimensions, solves for the wave electric field and is demonstrated to achieve convergence rates of $\mathcal{O}$($\mathcal{h}$ $\mathcal{P}$ )⁠. Verification tests reproduce plane wave solutions, and example simulations of ion cyclotron resonance heating and electron cyclotron resonance heating demonstrate its capability, approaching realistic tokamak plasma scenarios. This work contributes to laying a foundation for the GFD method to be used in more sophisticated, optimized, and physically realistic full-wave simulations in time-harmonic plasma wave research.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Perspective of Fermi’s golden rule and its generalizations in chemical physics

This perspective provides a succinct history of Fermi’s golden rule (FGR), an overview of its derivation, assumptions, and representative forms. Major applications of FGR, mostly in the field of chemical physics, are reviewed. These illustrate the broad applicability and success of FGR. Ambiguities and open issues encountered in practical applications of FGR are clarified. Recent advances in generalizations of FGR and computational methods for practical applications are addressed.

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

Ab initio generalized Langevin equation

We introduce a machine learning–based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables (CVs) in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori–Zwanzig formalism, under the constraint of the fluctuation–dissipation theorem. Combined with deep potential molecular dynamics and electronic density functional theory, this approach opens the way to multiscale modeling in a variety of situations. Here, we demonstrate this capability with a study of two mesoscale processes in crystalline lead titanate, namely the field-driven dynamics of a planar ferroelectric domain wall, and the dynamics of an extensive lattice of coarse-grained electric dipoles. In the first case, AIGLE extends the reach of ab initio simulations to a regime of noise-driven motions not accessible to molecular dynamics. In the second case, AIGLE deals with an extensive set of CVs by adopting a local approximation for the memory kernel and retaining only short-range noise correlations. The scheme is computationally more efficient than molecular dynamics by several orders of magnitude and mimics the microscopic dynamics at low frequencies where it reproduces accurately the dominant far-infrared absorption frequency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Complete definition of 𝑁 →Δ transition generalized parton distributions

We revisit the definition of the leading-twist chiral-even generalized parton distributions (GPDs) for 𝑁 →Δ baryon transitions. We identify and address deficiencies in previous definitions of the transition GPDs inspired by the transition form factors of the vector and axial vector currents. Through systematic analysis of all possible covariant structures, respecting discrete symmetries and the baryon spinor equations of motion, we derive complete sets of independent structures for the transition matrix elements of the vector and axial vector partonic operators. They contain additional structures proportional to the light-cone vector, corresponding to transition GPDs of vanishing first moment, which were not included in previous parametrizations. Their presence is confirmed independently by the light-front multipole expansion and the cross-channel SO(3) partial-wave analysis of the transition matrix elements. Our analysis provides a complete definition of the 𝑁 →Δ transition GPDs for use in theoretical and phenomenological studies.

baryons↗
DOE OSTI2023

Cosmological consequences of first-order general-relativistic viscous fluid dynamics

In this work, we investigate the out-of-equilibrium dynamics of viscous fluids in a spatially flat Friedmann-LemaîtreRobertson-Walker cosmology using the most general causal and stable viscous energy-momentum tensor defined at first order in spacetime derivatives. In this new framework a pressureless viscous fluid having equilibrium energy density ρ can evolve to an asymptotic future solution in which the Hubble parameter approaches a constant while ρ → 0, even in the absence of a cosmological constant (i.e., Λ = 0). Thus, while viscous effects in this model drive an accelerated expansion of the universe, the equilibrium energy density itself vanishes, leaving behind only the acceleration. This behavior emerges as a consequence of causality in first-order theories of relativistic fluid dynamics and it is fully consistent with Einstein’s equations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Ameliorating the Courant-Friedrichs-Lewy condition in spherical coordinates: A double FFT filter method for general relativistic MHD in dynamical spacetimes

Numerical simulations of merging compact objects and their remnants form the theoretical foundation for gravitational wave and multimessenger astronomy. While Cartesian-coordinate-based adaptive mesh refinement is commonly used for simulations, spherical-like coordinates are more suitable for nearly spherical remnants and azimuthal flows due to lower numerical dissipation in the evolution of fluid angular momentum, as well as requiring fewer numbers of computational cells. However, the use of spherical coordinates to numerically solve hyperbolic partial differential equations can result in severe Courant-Friedrichs-Lewy (CFL) stability condition time step limitations, which can make simulations prohibitively expensive. This paper addresses this issue for the numerical solution of coupled spacetime and general relativistic magnetohydrodynamics evolutions by introducing a double fast Fourier transform (FFT) filter and implementing it within the fully message passing interface (mpi)-parallelized sphericalnr framework in the einstein toolkit. In conclusion, we demonstrate the effectiveness and robustness of the filtering algorithm by applying it to a number of challenging code tests, and show that it passes these tests effectively, demonstrating convergence while also increasing the time step significantly compared to unfiltered simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Extracting transition generalized parton distributions from hard exclusive pion-nucleon scattering

We study the extraction of transition generalized parton distributions (GPDs) from production of two back-to-back high transverse momentum photons ( γ γ ) and a massive pair of leptons ( ℓ + ℓ − ) in hard exclusive pion-nucleon scattering. We argue that the exclusive scattering amplitude of both processes could be factorized into nonperturbative pion distribution amplitude and nucleon transition GPDs that are convoluted with perturbatively calculable short-distance matching coefficients. We demonstrate that the exclusive diphoton production not only is complementary to the Drell-Yan-type dilepton production for extracting the GPDs but also provides enhanced sensitivities for extracting the parton momentum fraction x dependence of the GPDs. We show that both exclusive observables are physically measurable at the J-PARC and AMBER experiment energies. If the target nucleon can be polarized, corresponding spin asymmetries can offer additional sensitivities for extracting transition GPDs. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Phase diagram of generalized XY model using the tensor renormalization group

We use the higher-order tensor renormalization group method to study the two-dimensional generalized XY model that admits integer and half-integer vortices. This model is the deformation of the classical XY model and has a rich phase structure consisting of nematic, ferromagnetic, and disordered phases and three transition lines belonging to the Berezinskii-Kosterlitz-Thouless and Ising class. We explore the model for a wide range of temperatures, T , and the deformation parameter, Δ , and compute specific heat along with integer and half-integer magnetic susceptibility, finding both Berezinskii-Kosterlitz-Thouless-like and Ising-like transitions and the region where they meet. Published by the American Physical Society 2024

2-dimensional systems↗
DOE OSTI2025

Chiral-odd generalized parton distributions in the large-𝑁 𝑐 limit of QCD: Spin-flavor structure, polynomiality, and sum rules

We study the nonperturbative properties of the nucleon’s chiral-odd generalized parton distributions (transversity GPDs) in the large-𝑁 𝑐 limit of QCD. This includes the parametric ordering of the spin-flavor components, the polynomiality property of the moments, and the sum rules connecting the GPDs with the tensor form factors. A multipole expansion in the transverse momentum transfer is used to enumerate and interpret the structures in the nucleon matrix element of the chiral-odd partonic operator, including monopole, dipole and quadrupole terms. The 1/𝑁 𝑐 expansion of the GPDs is performed using the abstract mean-field picture of baryons in the large-𝑁 𝑐 limit and its symmetries. We derive a large-𝑁 𝑐 relation between the flavor-nonsinglet GPDs 𝐸$^{𝑢−𝑑}_𝑇$ and $\tilde{𝐻}^{𝑢−𝑑}_𝑇$ and test it with recent lattice QCD results. We show that the polynomiality property and sum rules of the GPDs are fulfilled with the restricted realization of translational and rotational invariance in the mean-field picture. The results provide a basis for the phenomenological analysis of chiral-odd GPDs and hard exclusive processes in the large-𝑁 𝑐 limit, and for calculations in specific dynamical models.

generalized parton distributions↗