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At least 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

New heavenly double copies

The double copy relates scattering amplitudes and classical solutions in Yang-Mills theory, gravity, and related field theories. Previous work has shown that this has an explicit realisation in self-dual YM theory, where the equation of motion can be written in a form that maps directly to Plebański’s heavenly equation for self-dual gravity. The self-dual YM equation involves an area-preserving diffeomorphism algebra, two copies of which appear in the heavenly equation. In this paper, we show that this construction is a special case of a wider family of heavenly-type examples, by (i) performing Moyal deformations, and (ii) replacing the area-preserving diffeomorphisms with a less restricted algebra. As a result, we obtain a double-copy interpretation for hyper-Hermitian manifolds, extending the previously known hyper-Kähler case. We also introduce a double-Moyal deformation of the heavenly equation. The examples where the construction of Lax pairs is possible are manifestly consistent with Ward’s conjecture, and suggest that the classical integrability of the gravity-type theory may be guaranteed in general by the integrability of at least one of two gauge-theory-type single copies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Toward more mechanistic representations of biogeochemical processes in river networks: Implementation and demonstration of a multiscale model

A recently introduced multiscale model for representing the effects of small-scale hyporheic-zone biogeochemical processes is extended from the reach scale to river network scales. The model uses advection-dispersion-reaction equations for the channel network and one-dimensional advection-reaction subgrid models for the hyporheic zone. We summarize implementation in the integrated surface/subsurface hydrology modeling system Amanzi-ATS. The extension uses topologically defined meshes to represent stream/river networks and associates a hyporheic subgrid model with each channel grid cell. Biogeochemical reaction modeling capability residing in community software is accessed through an application programming interface. The implementation is verified against independent numerical solutions on a single reach. Mesh convergence studies show that commonly used semi-distributed representations can introduce significant spatial discretization error. Denitrification of farm runoff in a subbasin of the Portage River Basin in Ohio, USA is used to demonstrate the general-purpose reactive transport capability.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

The theory of transport in helical spin-structure crystals

Abstract We study helical structures in spin-spiral single crystals. In the continuum approach for the helicity potential energy the simple electronic band splits into two non-parabolic bands. For low exchange integrals, the lower band is described by a surface with a saddle shape in the direction of the helicity axis. Using the Boltzmann equation with the relaxation due to acoustic phonons, we discover the dependence of the current on the angle between the electric field and helicity axis leading to the both parallel and perpendicular to the electric field components in the electroconductivity. The latter can be interpreted as a planar Hall effect. In addition, we find that the transition rates depend on an electron spin allowing the transition between the bands. The electric conductivities exhibit nonlinear behaviors with respect to chemical potential µ . We explain this effect as the interference of the band anisotropy, spin conservation, and interband transitions. The proposed theory with the spherical model in the effective mass approximation for conduction electrons can elucidate nonlinear dependencies that can be identified in experiments. We find the excellent agreement between the theoretical and experimental data for parallel resistivity depending on temperature at the phase transition from helical to ferromagnetic state in a M n P single crystal. In addition, we predict that the perpendicular resistivity abruptly drops to zero in the ferromagnetic phase.

Physics↗
DOE OSTI2024

Infinite Family of Integrable Sigma Models Using Auxiliary Fields

We introduce a class of 2D sigma models which are parametrized by a function of one variable. In addition to the physical field g , these models include an auxiliary field v α which mediates interactions in a prescribed way. We prove that every theory in this family is classically integrable, in that it possesses an infinite set of conserved charges in involution, which can be constructed from a Lax representation for the equations of motion. This class includes the principal chiral model (PCM) and all deformations of the PCM by functions of the energy-momentum tensor. Published by the American Physical Society 2024

Physics↗
DOE OSTI2026

Direct Nonlinear Approximation for Security Region Boundary of Integrated Energy Systems: A Polynomial Chaos Expansion Solution

The strong interdependence of electricity, gas, and heating systems can facilitate fault propagation within integrated energy systems (IESs), posing significant challenges to secure operation. This paper proposes a polynomial chaos expansion (PCE)-based approximation method to accurately characterize the IES security region boundary (IES–SRB). By integrating the Karush-Kuhn-Tucker conditions with PCE theory, the IES-SRB approximation problem is reformulated as a set of nonlinear equations concerning the approximation coefficients. Using the Galerkin projection method, these equations are further transformed into a system of projection equations that govern the polynomial approximation coefficients in the IES-SRB approximation. To reduce computational complexity while maintaining high approximation accuracy, a piecewise polynomial approximation method is proposed. Numerical studies on the E39-G20-H6 and E118-G96-H52 IES test systems demonstrate that the proposed method can accurately and effectively construct IES security regions.

Wu, Chenghao [Northeast Electric Power University]↗
DOE OSTI2021

Learning Forecasts of Rare Stratospheric Transitions from Short Simulations

Abstract Rare events arising in nonlinear atmospheric dynamics remain hard to predict and attribute. We address the problem of forecasting rare events in a prototypical example, sudden stratospheric warmings (SSWs). Approximately once every other winter, the boreal stratospheric polar vortex rapidly breaks down, shifting midlatitude surface weather patterns for months. We focus on two key quantities of interest: the probability of an SSW occurring, and the expected lead time if it does occur, as functions of initial condition. These optimal forecasts concretely measure the event’s progress. Direct numerical simulation can estimate them in principle but is prohibitively expensive in practice: each rare event requires a long integration to observe, and the cost of each integration grows with model complexity. We describe an alternative approach using integrations that are short compared to the time scale of the warming event. We compute the probability and lead time efficiently by solving equations involving the transition operator, which encodes all information about the dynamics. We relate these optimal forecasts to a small number of interpretable physical variables, suggesting optimal measurements for forecasting. We illustrate the methodology on a prototype SSW model developed by Holton and Mass and modified by stochastic forcing. While highly idealized, this model captures the essential nonlinear dynamics of SSWs and exhibits the key forecasting challenge: the dramatic separation in time scales between a single event and the return time between successive events. Our methodology is designed to fully exploit high-dimensional data from models and observations, and has the potential to identify detailed predictors of many complex rare events in meteorology.

Finkel, Justin↗
DOE OSTI2023

hIPPYlib-MUQ: A Bayesian Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty

Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the uncertainty in the solution of the inverse problem. However, the solution of Bayesian inverse problems governed by complex forward models described by partial differential equations (PDEs) remains prohibitive with black-box Markov chain Monte Carlo (MCMC) methods. We present hIPPYlib-MUQ, an extensible and scalable software framework that contains implementations of state-of-the art algorithms aimed to overcome the challenges of high-dimensional, PDE-constrained Bayesian inverse problems. These algorithms accelerate MCMC sampling by exploiting the geometry and intrinsic low-dimensionality of parameter space via derivative information and low rank approximation. The software integrates two complementary open-source software packages, hIPPYlib and MUQ. hIPPYlib solves PDE-constrained inverse problems using automatically-generated adjoint-based derivatives, but it lacks full Bayesian capabilities. MUQ provides a spectrum of powerful Bayesian inversion models and algorithms, but expects forward models to come equipped with gradients and Hessians to permit large-scale solution. By combining these two complementary libraries, we created a robust, scalable, and efficient software framework that realizes the benefits of each and allows us to tackle complex large-scale Bayesian inverse problems across a broad spectrum of scientific and engineering disciplines. To illustrate the capabilities of hIPPYlib-MUQ, we present a comparison of a number of MCMC methods available in the integrated software on several high-dimensional Bayesian inverse problems. These include problems characterized by both linear and nonlinear PDEs, various noise models, and different parameter dimensions. The results demonstrate that large (~ 50×) speedups over conventional black box and gradient-based MCMC algorithms can be obtained by exploiting Hessian information (from the log-posterior), underscoring the power of the integrated hIPPYlib-MUQ framework.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Model-based predictive control of multi-stage air-source heat pumps integrated with phase change material-embedded ceilings

This paper presents a model-based predictive control strategy to optimize the operations of phase change material (PCM) ceiling panels coupled with a multi-stage air-source heat pump. A three-stage prototype heat pump unit has been built and tested in the laboratory, with the low and medium stages designed for space heating/cooling and the high compression stage dedicated to charging of the PCM energy storage. To facilitate optimal control of the integrated heat pump system, a mixed-integer linear programming formulation is derived through linearization of the heat pump model and a mixed-integer reformulation of the PCM dynamic governing equations. A predictive control strategy is synthesized based on the resultant control formulation and implemented in a receding horizon scheme that optimizes the PCM charging and the zone temperature schedules simultaneously to leverage both the passive (associated with building construction materials) and active (PCM) storage capacities of a building. The control strategy has been tested along with three benchmarking control scenarios using a co-simulation platform for a prototypical detached house in Atlanta, GA. In this study, test results showed that application of the proposed control strategy to the PCM-integrated heat pump could provide 27.1% electricity cost savings while a fine tuned rule-based control strategy could achieve cost savings of 20.4%, compared to a baseline case without PCM storage, under a time-of-use rate tariff.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Finite domain solution of a KGD hydraulic fracture in the viscosity-dominated regime

This paper describes a numerical algorithm for solving the classic problem of a plane strain (KGD) fracture propagating in an impermeable elastic medium with zero toughness. The method, which takes advantage of the self-similar nature of the solution, combines a domain-based scheme to solve the elasticity equations and a finite volume method to solve the nonlinear lubrication equation. This work represents a first step towards developing a model able to account for pore pressure diffusion in the medium and corresponding poroelastic effects, noting that these processes are more efficiently solved using a domain-based rather than a boundary integral method. To enhance the efficiency and accuracy of the numerical scheme, the far-field crack asymptotics is embedded in the discretized elastic relationship between the fluid pressure and the crack opening, while the coupled fluid-solid tip asymptote is enforced in a weak form when solving the nonlinear lubrication equation. The proposed technique yields results that closely match the analytical solution, even with a coarse mesh. This approach offers potential for addressing more complex hydraulic fracturing problems in the future.

Domain-based method↗
DOE OSTI2026

Reduced-action-integral approach for photon-photon interactions in vacuum

Electromagnetic waves propagating through vacuum can polarize virtual electron–positron pairs; this polarization, in turn, nonlinearly modifies their propagation. A semi-classical nonlinear wave equation describing the propagation is derived from the Euler–Heisenberg Lagrangian density, which captures vacuum polarization effects up to the one-loop level. In this article, we present a reduced-actionintegral approach that enables rapid modeling of nonlinear phenomena arising from the Euler– Heisenberg Lagrangian. Application of the variational principle to the reduced action provides equations of motion for familiar light-pulse parameters, such as spot size, phase, polarization, and phase-front curvature, without requiring full-field simulations. Three examples demonstrate the utility of the approach: phase modulation, birefringence, and frequency mixing.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

First-principles free energies by hybrid thermodynamic integration for phase equilibria and fission product solubility in molten salts

The overarching goal of this research project is quantitative microscopic modeling of phase diagrams and solubility of actinides and lanthanide-fission products in molten salts for molten salt reactors. Application of molten salts as coolants and liquid fuels for next-generation reactors requires quantitative understanding of phase diagrams, equations of state and transport properties of binary and ternary molten salt mixtures, as well as solubility of fuel, fission products and reactor-wall corrosion products, but these remain beyond the reach of current first-principles computational techniques. We will address this fundamental capability gap using a novel hybrid framework for thermodynamic integration to directly predict absolute free energies of solid and molten salts at any specified conditions of composition, temperature and pressure. This framework will combine a hierarchy of first-principles, molecular dynamics and continuum techniques to deliver first-principles-level accuracy at a fraction of the computational cost of conventional ab initio molecular dynamics approaches. In particular, this technique is expected to provide first-principles accuracy, while off-loading most of the computational work on much less expensive classical molecular dynamics and continuum techniques.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Slow manifolds of classical Pauli particle enable structure-preserving geometric algorithms for guiding center dynamics

Since variational symplectic integrators for the guiding center was proposed, structure-preserving geometric algorithms have become an active research field in plasma physics. We found that the slow manifolds of the classical Pauli particle enable a family of structure-preserving geometric algorithms for guiding center dynamics with long-term stability and accuracy. This discovery overcomes the difficulty associated with the unstable parasitic modes for variational symplectic integrators when applied to the degenerate guiding center Lagrangian. It is a pleasant surprise that Pauli's Hamiltonian for electrons, which predated the Dirac equation and marks the beginning of particle physics, reappears in classical physics as an effective algorithm for solving an important plasma physics problem. This technique is applicable to other degenerate Lagrangians reduced from regular Lagrangians.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Integrating Learning and Physics based Computation for Fast Online Transient Analysis

In this work, a novel method that integrates learning and physics based computation is developed for greatly accelerating the simulation of full power system transient trajectories. To solve the dynamic algebraic equations, the method replaces the time-consuming dynamic computation for generator dynamics with trained predictors, while retaining the time-efficient algebraic computation of solving AC-power flow (PF) for power systems. In particular, a predictor is trained for each generator, and the system trajectories are computed by alternating steps of calling the predictors and solving AC-PF. The proposed method also allows fully parallelizable training strategies and a flexible trade-off between training time and testing accuracy. Comprehensive evaluations of the proposed method for transient/dynamic contingency analysis of the New York/New England 16-machine 68-bus power systems demonstrate excellent performance and significant acceleration of computation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Electromagnetic Transient (EMT) Simulation Algorithm for Evaluation of Photovoltaic (PV) Generation Systems

Use of inverter-based resources facilitating renewable energy resources such as photovoltaic (PV) generation is increasing rapidly with decreasing costs and reduced emissions associated. To accommodate such rapid growth of inverter-based resources like PV systems, electromagnetic transient (EMT) simulation models of both PV systems and grids are required to analyze the interaction of PVs in the grid (like the post-event analysis). In addition, the EMT simulation would help with the planning of future power grid with a large number of PVs as well as other inverter-based distributed generation systems. In this paper, the EMT simulation models of PV systems and grids are developed based on the differential algebraic equations (DAEs) representing their EMT dynamics. Furthermore, advanced simulation algorithms including numerical stiffness-based hybrid discretization, DAE clustering and aggregation, multi-order integration, and matrix splitting approaches are applied to accelerate the EMT simulation. The proposed algorithm was applied to 125 PV inverters within 52-bus medium-voltage (MV) distribution grid.

Choi, Jongchan↗
DOE OSTI2020

Efficient and Robust Dynamic Simulation of Power Systems With Holomorphic Embedding

Dynamic simulation is vitally important in power system analysis, but traditional approaches based on numerical integration over small time steps are time-consuming. Also, the Newton-Raphson method suffers from difficulty in convergence when solving nonlinear algebraic equations. In this paper, we propose a novel dynamic simulation approach based on holomorphic embedding. By obtaining a high-order approximation of system dynamics, it achieves a much larger time step and thus enhances the computational efficiency significantly. In addition, the new approach avoids non-convergence issues in solving algebraic equations, which improves robustness. The approach includes flexible modeling of synchronous generators and controllers, and we propose a method for modeling generator coordinate transformations. The approach is tested on the IEEE 39-bus, 10-generator system and a Polish 2383-bus, 327-generator system. The results demonstrate promising computational efficiency and satisfactory numerical robustness for the analysis of large-scale power systems.

42 ENGINEERING↗
DOE OSTI2024

Model Diagnostics for Equation Oriented Models: Roadblocks and the Path Forward

This poster was presented at the Foundations of Computer Aided Process Design (FOCAPD) 2024 conference with a paper describing efforts to develop a unified workflow and toolbox for diagnosing issues in equation-oriented models as part of the IDAES modeling framework. The poster presents the work currently underway within the IDAES project to develop and integrate cutting edge model analysis techniques into a common toolbox and workflow for model developers to use.

Lee, Andrew↗
DOE OSTI2025

A Quantum Approach for Implementing Fixed-Point Arithmetic in Solving Ordinary Differential Equations

Differential equations (DEs) serve as fundamental tools in mathematical modeling across scientific disciplines, yet classical numerical solvers face limitations with large-scale or computationally intensive problems. This study explores a quantum-inspired approach to solving DEs, combining quantum- inspired techniques with classical methods. It focuses on fixed- point arithmetic on quantum circuits, utilizing basic quantum gates to manipulate DE solutions. We expand upon the techniques introduced by Zanger et al. [Quantum, 5, 502 (2021)] by offering a precise computation for a fixed-point signed multiplication scheme, while also presenting a quantum circuit capable of executing the fixed-point division algorithm. We demonstrate the feasibility of our approach through the simulation of a linear Ordinary Differential Equation (ODE), where initial conditions and parameters are encoded into quantum circuits using fixed- point representation. By executing sequences of quantum gates mimicking numerical integration steps, we obtain approximate solutions to the ODE with specified fixed-point precision.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Model Diagnostics for Equation Oriented Models: Roadblocks and the Path Forward

Conference paper for FOCAPD24 describing efforts to develop a unified workflow and toolbox for diagnosing issues in equation-oriented models as part of the IDAES modeling framework. The paper presents the work currently underway within the IDAES project to develop and integrate cutting edge model analysis techniques into a common toolbox and workflow for model developers to use.

Lee, Andrew↗