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At least 865 records · Page 48
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Addressing spreading pressure dependence of real adsorbed solution theory with generalized Langmuir isotherm

This work addresses spreading pressure dependence of Real Adsorbed Solution Theory (RAST) for mixed-gas adsorption equilibria using generalized Langmuir (gL) isotherm. Considering vacant sites as an integral part of competitive multicomponent adsorption on a constant adsorbent surface area, the gL isotherm properly accounts for surface heterogeneity and loading, adsorbate composition, and temperature dependence. We show the spreading pressure dependence of adsorbate activity coefficient expression in the RAST framework can be generated from the gL isotherm. The procedure is illustrated with a spreading pressure dependent adsorption Nonrandom Furthermore, two-Liquid activity coefficient model, and the results are validated for ten binary mixed-gas adsorption equilibria systems including two highly nonideal azeotropic systems.

42 ENGINEERING↗
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 OSTI2020

Space-energy separated representations for multigroup neutron diffusion using proper generalized decompositions

Proper generalized decomposition (PGD) can be described as a numerical extension of separation of variables and thus be employed as a solution technique for multi-dimensional problems, where dimensions should be understood in the phase-space context of the governing law at hand. This paper presents a PGD approach on efficiently solving problems involving multigroup neutron diffusion. Two PGD approaches are described: space-only and space-energy decompositions. Numerical results include 2-D and 3-D examples with two-, seven-, and 145-group structures. The PGD solutions are compared against traditional multi-dimensional finite element discretization. For few-group problems, both PGD approaches prove effective for mildly heterogeneous geometries, but showed reduced performance with increasing heterogeneity. The space-energy representation was found to be slower than the space-only approach for two-group problems, but proved more effective for seven-group problems. For even larger numbers of groups, the space-energy PGD decomposition was very effective at reducing the computational time.

42 ENGINEERING↗
DOE OSTI2021

Dirac systems with magnetic field and position-dependent mass: Darboux transformations and equivalence with generalized Dirac oscillators

Highlights: • We construct Darboux transformations for Dirac systems with position-dependent mass. • Our systems are either Dirac oscillators or coupled to a magnetic field. • We use our Darboux transformation to construct new solvable Dirac systems. We construct a Darboux transformation for a class of two-dimensional Dirac systems at zero energy. Our starting equation features a position-dependent mass, a matrix potential, and an additional degree of freedom that can be interpreted either as a magnetic field perpendicular to the plane or a generalized Dirac oscillator interaction. We obtain a number of Darboux-transformed Dirac equations for which the zero energy solutions are exactly known.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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 OSTI2021

Simple, general, realistic, robust, analytic tokamak equilibria. Part 1. Limiter and divertor tokamaks

Tokamak equilibria have been derived that are analytic solutions to the Grad–Shafranov equation. Here in this paper, Part 1, describes a wide range of such equilibria including smooth limiter surfaces, double- and single-null divertor surfaces, arbitrary aspect ratio, elongation, triangularity and beta. Part 2 generalizes the analysis to include edge pedestals and toroidal flow.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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 OSTI2022

Exploring nonequilibrium phases of photo-doped Mott insulators with generalized Gibbs ensembles

Many experiments show that strong excitations of correlated quantum materials can cause non-thermal phases without equilibrium analogues. Understanding the origin and properties of these nonequilibrium states has been challenging due to the limitations of theoretical methods for nonequilibrium strongly correlated systems. In this work, we introduce a generalized Gibbs ensemble description that enables a systematic analysis of the long-time behavior of photo-doped states in Mott insulators based on equilibrium methods. We demonstrate the power of the method by mapping out the nonequilibrium phase diagram of the one-dimensional extended Hubbard model, which features η -pairing and charge density wave phases in a wide photo-doping range. We furthermore clarify that the peculiar kinematics of photo-doped carriers, and the interaction between them, play an essential role in the formation of these non-thermal phases. Our results establish a new path for the systematic analysis of nonequilibrium strongly correlated systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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 OSTI2021

Constructing tensor network influence functionals for general quantum dynamics

Here, we describe an iterative formalism to compute influence functionals that describe the general quantum dynamics of a subsystem beyond the assumption of linear coupling to a quadratic bath. We use a space-time tensor network representation of the influence functional and investigate its approximability in terms of its bond dimension and time-like entanglement in the tensor network description. We study two numerical models, the spin-boson model and a model of interacting hard-core bosons in a 1D harmonic trap. We find that the influence functional and the intermediates involved in its construction can be efficiently approximated by low bond dimension tensor networks in certain dynamical regimes, which allows the quantum dynamics to be accurately computed for longer times than with direct time evolution methods. However, as one iteratively integrates out the bath, the correlations in the influence functional can first increase before decreasing, indicating that the final compressibility of the influence functional is achieved via non-trivial cancellation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Nonuniqueness of generalized quantum master equations for a single observable

When deriving exact generalized master equations for the evolution of a reduced set of degrees of freedom, one is free to choose what quantities are relevant by specifying projection operators. However, obtaining a reduced description does not always need to be achieved through projections-one can also use conservation laws for this purpose. Such an operation should be considered as distinct from any kind of projection; that is, projection onto a single observable yields a different form of master equation compared to that resulting from a projection followed by the application of a constraint. Here, we give a simple example to show this point and give relationships that the different memory kernels must satisfy to yield the same dynamics.

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↗