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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 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Nonlinear Optimal Control of Electron Dynamics Within Hartree-Fock Theory

Consider the problem of determining the optimal applied electric field to drive a molecule from an initial state to a desired target state. For even moderately sized molecules, solving this problem directly using the exact equations of motion—the time-dependent Schrödinger equation (TDSE)—is numerically intractable. Here, we present a solution of this problem within time-dependent Hartree-Fock (TDHF) theory, a mean field approximation of the TDSE. Optimality is defined in terms of minimizing the total control effort while maximizing the overlap between desired and achieved target states. We frame this problem as an optimization problem constrained by the nonlinear TDHF equations; we solve it using trust region optimization with gradients computed via a custom-built adjoint state method. For three molecular systems, we show that with very small neural network parametrizations of the control, our method yields solutions that achieve desired targets within acceptable constraints and tolerances.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2015

Memory-Efficient Simulation of Frequency-Dependent Q

Memory-variable methods have been widely applied to approximate frequency-independent quality factor Q in numerical simulation of wave propagation. The frequency-independent model is often appropriate for frequencies up to about 1 Hz but at higher frequencies is inconsistent with some regional studies of seismic attenuation. We apply the memory-variable approach to frequency-dependent Q models that are constant below, and follow a power-law above, a chosen transition frequency. We present numerical results for the corresponding memory-variable relaxation times and weights, obtained by nonnegative least-squares fitting of the Q(f) function, for a range of exponent values; these times and weights can be scaled to an arbitrary transition frequency and a power-law prefactor, respectively. The resulting memory-variable formulation can be used with numerical wave-propagation solvers based on methods such as finite differences (FDs) or spectral elements and may be implemented in either conventional or coarse-grained form. In the coarse-grained approach, we fit effective Q for low-Q values (<200) using a nonlinear inversion technique and use an interpolation formula to find the corresponding weighting coefficients for arbitrary Q. A 3D staggered-grid FD implementation closely approximates the frequency–wavenumber solution to both a half-space and a layered model with a shallow dislocation source for Q as low as 20 over a bandwidth of two decades. We compare the effects of different power-law exponents using a finite-fault source model of the 2008 Mw 5.4 Chino Hills, California, earthquake and find that Q(f) models generally better fit the strong-motion data than the constant Q models for frequencies above 1 Hz.

Geochemistry & Geophysics↗
DOE OSTI2015

Generation of longitudinal current by a transverse electromagnetic field in classical and quantum plasmas

A distribution function for collisionless plasma is derived from the Vlasov kinetic equation in the quadratic approximation with respect to the electromagnetic field. Formulas for calculation of the electric current at an arbitrary temperature (arbitrary degree of degeneration of the electron gas) are deduced. The case of small wavenumbers is considered. It is shown that nonlinearity leads to the generation of an electric current directed along the wave vector. This longitudinal current is orthogonal to the classical transverse current, well known in the linear theory. A distribution function for collisionless quantum plasma is derived from the kinetic equation with the Wigner integral in the quadratic approximation with respect to the vector potential. Formulas for calculation of the electric current at an arbitrary temperature are deduced. The case of small wavenumbers is considered. It is shown that, at small values of the wavenumber, the value of the longitudinal current for quantum plasma coincides with that for classical plasma. The dimensionless currents in quantum and classical plasmas are compared graphically.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

A fast mollified impulse method for biomolecular atomistic simulations

Classical integration methods for molecular dynamics are inherently limited due to resonance phenomena occurring at certain time-step sizes. The mollified impulse method can partially avoid this problem by using appropriate filters based on averaging or projection techniques. However, existing filters are computationally expensive and tedious in implementation since they require either analytical Hessians or they need to solve nonlinear systems from constraints. In this work we follow a different approach based on corotation for the construction of a new filter for (flexible) biomolecular simulations. The main advantages of the proposed filter are its excellent stability properties and ease of implementation in standard softwares without Hessians or solving constraint systems. By simulating multiple realistic examples such as peptide, protein, ice equilibrium and ice–ice friction, the new filter is shown to speed up the computations of long-range interactions by approximately 20%. The proposed filtered integrators allow step sizes as large as 10 fs while keeping the energy drift less than 1% on a 50 ps simulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Theory of critical balance in plasma turbulence

Critical balance, a statement of the approximate equality of a timescale of motion parallel to the magnetic field with a timescale of turbulent motion perpendicular to the field, is analyzed from a statistical description of the relative motion of two particles consistent with two-point correlation in a nonlinear gyrokinetic system with collisions. Critical balance is understood from a premise that the fastest time to any spatial scale that encounters decorrelated motions sets an overall correlation time for both perpendicular and parallel scales. For a regime of weak collisionality, this leads to the approximate equality of the parallel streaming time and the perpendicular turbulent correlation time, which is a standard statement of critical balance. These two timescales are only approximately equal because of effects in parallel streaming dynamics and collisions, the former producing deviations tied to variations of perpendicular and parallel wavenumbers. Finally, analysis of a collisional regime shows that critical balance also applies in that limit with a modified relation between parallel and perpendicular spatial scales.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Nonlinear nanomechanical resonators approaching the quantum ground state

It is an open question whether mechanical resonators can be made nonlinear with vibrations approaching the quantum ground state. This requires the engineering of a mechanical nonlinearity far beyond what has been realized so far. Here we discover a mechanism to boost the Duffing nonlinearity by coupling the vibrations of a nanotube resonator to single-electron tunnelling and by operating the system in the ultrastrong-coupling regime. We find that thermal vibrations become highly nonlinear when lowering the temperature. The average vibration amplitude at the lowest temperature is 13 times the zero-point motion, with approximately 42% of the thermal energy stored in the anharmonic part of the potential. Our work may enable the realization of mechanical Schrödinger cat states, mechanical qubits and quantum simulators emulating the electron–phonon coupling.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Stability of trapped solutions of a nonlinear Schrödinger equation with a nonlocal nonlinear self-interaction potential

This work focuses on the study of the stability of trapped soliton-like solutions of a (1 + 1)-dimensional nonlinear Schrödinger equation (NLSE) in a nonlocal, nonlinear, self-interaction potential of the form [|Ψ(x,t)| 2 +|Ψ(-x,t)| 2 ] κ where κ is an arbitrary nonlinearity parameter. Although the system with κ = 1 (i.e. fully integrable case) was first reported by Yang (2018 Phys. Rev. E 98 042202), here in the present work, we extend this model to the one in which κ is arbitrary. This allows us to compare the stability properties of the now trapped solutions to previously found solutions of the more usual NLSE with κ ≠ 1 which are moving soliton solutions. We show that there is a simple, one-component, nonlocal Lagrangian and corresponding action governing the dynamics of the system. Using a collective coordinate method derived from the action as well as assuming the validity of Derrick's theorem, we find that these trapped solutions are stable for 0 < κ < 2 and unstable when κ > 2. At the critical value of κ, i.e. κ = 2, the solution can either collapse or blowup linearly in time when q 0 = 0, where q 0 is the center of the initial density ρ(x, t = 0) = ψ*ψ of the solution. For q 0 ≠ 0 the displaced solution collapses. When κ > 2 initial small displacements from the origin also lead to collapse of the wave function. This phenomenon is not seen in the usual NLSE.

collective coordinates↗
DOE OSTI2019

Effect of Ge substitution on magnetic properties in the itinerant chiral magnet MnSi

We have investigated the effect of Ge substitution on the magnetic ordering in the B20 itinerant chiral magnet MnSi prepared by melting and annealing under ambient pressure. From a metallurgical survey, the solubility limit of Ge was found to be x = 0.144(5) with annealing temperature T an = 1073 K. Magnetization measurements on MnSi 1–x Ge x samples show that the helical ordering temperature T c increases rapidly in the low-x range, whereas it becomes saturated at higher concentration x > 0.1. Here, the Ge substitution also increases both the saturation magnetization M s and the critical field to the fully polarized state H c2 . In contrast to the saturation behavior of T c , those parameters increase linearly up to the highest Ge concentration investigated. In the temperature-magnetic field phase diagram, we found enlargement of the skyrmion phase region for large x samples. We, furthermore, observed the nonlinear behavior of helical modulation vector k as a function of Ge concentration, which can be described qualitatively using the mean field approximation.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Two-stage State Estimation Algorithm for Distribution Network Analysis

Practical distribution system contains many nodes and short branches. As a result, a more efficient and stable distribution state estimation (DSE) algorithm is needed to properly handle the inverse operation of its large-scale ill-conditioned information matrix. This paper proposed a two-stage DSE algorithm to transform the inverse operation into addition and multiplication operations in a recursive manner. It includes pseudo measurement preprocessing in the offline stage where an approximate linear estimator is adopted to relieve most of computation burdens, and real-time correction in the online stage where a nonlinear estimator is used to update the estimation. Numerical results of the method applied to both IEEE standard test systems and an actual distribution system show the accuracy and effectiveness of the proposed algorithm.

Dong, Jiaojiao↗
DOE OSTI2021

Multilane Automated Driving With Optimal Control and Mixed-Integer Programming

Road vehicle lane changes often initiate traffic disturbances and can therefore impact road networks’ energy and time efficiency. Furthermore, unexpected changes in traffic conditions may also render lane changes counterproductive for the lane-changing vehicle. Vehicle-to-vehicle connectivity combined with anticipative control could address these challenges via improved lane change decisions by automated vehicles. In a move toward this objective, receding horizon control cast as a mixed-integer quadratic program is used to plan lane changing and acceleration in a coupled optimization. A long-term pacing module, based on Pontryagin’s minimum principle from optimal control theory, sets terminal and input references for receding horizon control to target a user’s expected travel time. To remove nonlinear vehicle dynamics from the receding horizon controller, lane change commands are passed to a pure pursuit steering module whose response is approximated by a second-order linear model. Here, comparison against a rule-based reactive algorithm in arterial and highway scenarios shows an 8.9%–13.7% reduction in energy consumption and a 5.2%–10.3% reduction in the travel time, along with navigational improvements.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2021

Vibronic and Environmental Effects in Simulations of Optical Spectroscopy

Including both environmental and vibronic effects is important for accurate simulation of optical spectra, but combining these effects remains computationally challenging. We outline two approaches that consider both the explicit atomistic environment and the vibronic transitions. Both phenomena are responsible for spectral shapes in linear spectroscopy and the electronic evolution measured in nonlinear spectroscopy. The first approach utilizes snapshots of chromophore-environment configurations for which chromophore normal modes are determined. We outline various approximations for this static approach that assumes harmonic potentials and ignores dynamic system-environment coupling. The second approach obtains excitation energies for a series of time-correlated snapshots. This dynamic approach relies on the accurate truncation of the cumulant expansion but treats the dynamics of the chromophore and the environment on equal footing. Both approaches show significant potential for making strides toward more accurate optical spectroscopy simulations of complex condensed phase systems.

Chemistry↗
DOE OSTI2021

Decomposing Loosely Coupled Mixed-Integer Programs for Optimal Microgrid Design

Microgrids are frequently employed in remote regions, in part because access to a larger electric grid is impossible, difficult, or compromises reliability and independence. Although small microgrids often employ spot generation, in which a diesel generator is attached directly to a load, microgrids that combine these individual loads and augment generators with photovoltaic cells and batteries as a distributed energy system are emerging as a safer, less costly alternative. In this work, we present a model that seeks the minimum-cost microgrid design and ideal dispatched power to support a small remote site for one year with hourly fidelity under a detailed battery model; this mixed-integer nonlinear program (MINLP) is intractable with commercial solvers but loosely coupled with respect to time. A mixed-integer linear program (MIP) approximates the model, and a partitioning scheme linearizes the bilinear terms. We introduce a novel policy for loosely coupled MIPs in which the system reverts to equivalent conditions at regular time intervals; this separates the problem into subproblems that we solve in parallel. We obtain solutions within 5% of optimality in at most six minutes across 14 MIP instances from the literature and solutions within 5% of optimality to the MINLP instances within 20 minutes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Scientific Summary Report for Early Career Award "High Precision Event Simulation for the LHC"

Particle physics has entered a new era with the discovery of the Higgs boson at the CERN Large Hadron Collider (LHC). To determine all properties of the boson and to reveal possible signatures of physics beyond the Standard Model it is crucial to make reliable predictions for both signal and background reactions. Monte-Carlo event generators produce such predictions fully differentially at the level of observed particles. They rely on various approximations to cope with the many-body dynamics of the problem and on models to deal with the non-abelian, nonlinear nature of Quantum Chromodynamics (QCD), the quantum-field theoretical model of the strong nuclear force. Dependence on the model parameters is one of the main uncertainties affecting measurements and searches at the LHC. Whenever possible such dependence must be reduced or eliminated.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators

This paper examines the dynamics of power-electronic inverters in islanded microgrids that are controlled to emulate the dynamics of Van der Pol oscillators. The general strategy of controlling inverters to emulate the behavior of nonlinear oscillators presents a compelling time-domain alternative to ubiquitous droop control methods which presume the existence of a quasistationary sinusoidal steady state and operate on phasor quantities. We present two main results in this paper. First, by leveraging the method of periodic averaging, we demonstrate that droop laws are intrinsically embedded within a slower time scale in the nonlinear dynamics of Van der Pol oscillators. Second, we establish the global convergence of amplitude and phase dynamics in a resistive network interconnecting inverters controlled as Van der Pol oscillators. Furthermore, under a set of nonrestrictive decoupling approximations, we derive sufficient conditions for local exponential stability of desirable equilibria of the linearized amplitude and phase dynamics.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Operation of Natural Gas Pipeline Networks With Storage Under Transient Flow Conditions

Here, we formulate a nonlinear optimal control problem for intraday operation of a natural gas pipeline network that includes storage reservoirs. The dynamics of compressible gas flow through pipes, compressors, reservoirs, and wells are considered. In particular, a reservoir is modeled as a rigid, hollow container that stores gas under isothermal conditions and uniform density, and a well is modeled as a vertical pipe. For each pipe, flow dynamics are described by a coupled partial differential equation (PDE) system in density and mass flux variables, with momentum dissipation modeled using the Darcy–Wiesbach friction approximation. Compressors are modeled as scaling up the pressure of gas between the inlet and outlet. The governing equations for all network components are spatially discretized and assembled into a nonlinear differential-algebraic equation (DAE) system, which synthesizes above-ground pipeline and subsurface reservoir dynamics into a single reduced-order model. We seek to maximize an objective function that quantifies economic profit and network efficiency subject to the flow equations and inequalities that represent operating limitations. The problem is solved using a primal–dual interior point solver, and the solutions are validated in computational experiments and simulations on several pipeline test networks to demonstrate the effectiveness of the proposed methodology.

03 NATURAL GAS↗
DOE OSTI2015

A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: A dynamic variational multiscale approach [A simple, stable, and accurate tetrahedral finite element for transient, nearly incompressible, linear and nonlinear elasticity: A dynamic variational multiscale approach]

Here, we propose a new approach for the stabilization of linear tetrahedral finite elements in the case of nearly incompressible transient solid dynamics computations. Our method is based on a mixed formulation, in which the momentum equation is complemented by a rate equation for the evolution of the pressure field, approximated with piece-wise linear, continuous finite element functions. The pressure equation is stabilized to prevent spurious pressure oscillations in computations. Incidentally, it is also shown that many stabilized methods previously developed for the static case do not generalize easily to transient dynamics. Extensive tests in the context of linear and nonlinear elasticity are used to corroborate the claim that the proposed method is robust, stable, and accurate.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗