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15 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Operator evolution from the similarity renormalization group and the Magnus expansion

The Magnus expansion is an efficient alternative to solving similarity renormalization group (SRG) flow equations with high-order, memory-intensive ordinary differential equation solvers. The numerical simplifications it offers for operator evolution are particularly valuable for in-medium SRG calculations, though challenges remain for difficult problems involving intruder states. Here we test the Magnus approach in an analogous but more accessible situation, which is the free-space SRG treatment of the spurious bound states arising from a leading-order chiral effective field theory (EFT) potential with very high cutoffs. In this work, we show that the Magnus expansion passes these tests and then use the investigations as a springboard to address various aspects of operator evolution that have renewed relevance in the context of the scale and scheme dependence of nuclear processes. These aspects include SRG operator flow with band- versus block-diagonal generators, universality for chiral EFT Hamiltonians and associated operators with different regularization schemes, and the impact of factorization arising from scale separation. Implications for short-range correlations physics and the possibilities for reconciling high- and low-resolution treatments of nuclear structure and reactions are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Simple and General Unitarity Conserving Numerical Real-Time Propagators of the Time-Dependent Schrödinger Equation Based on Magnus Expansion

Magnus expansion (ME) provides a general way to expand the real-time propagator of a time-dependent Hamiltonian within the exponential such that the unitarity is satisfied at any order. Here, we use this property and explicit integration of Lagrange interpolation formulas for the time-dependent Hamiltonian within each time interval and derive approximations that preserve unitarity for the differential time evolution operators of general time-dependent Hamiltonians. The resulting second-order approximation is the same as using the average of Hamiltonians for two end points of time. We identify three fourth-order approximations involving commutators of Hamiltonians at different times and also derive a sixth-order expression. A test of these approximations along with other available expressions for a two-state time-dependent Hamiltonian with sinusoidal time dependences provides information on the relative performance of these approximations and suggests that the derived expressions can serve as useful numerical tools for time evolution in time-resolved spectroscopy, quantum control, quantum sensing, real-time ab initio quantum dynamics, and open system quantum dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Classical eikonal from Magnus expansion

In a classical scattering problem, the classical eikonal is defined as the generator of the canonical transformation that maps in-states to out-states. It can be regarded as the classical limit of the log of the quantum S-matrix. In a classical analog of the Born approximation in quantum mechanics, the classical eikonal admits an expansion in oriented tree graphs, where oriented edges denote retarded/advanced worldline propagators. The Magnus expansion, which takes the log of a time-ordered exponential integral, offers an efficient method to compute the coefficients of the tree graphs to all orders. We exploit a Hopf algebra structure behind the Magnus expansion to develop a fast algorithm which can compute the tree coefficients up to the 12th order (over half a million trees) in less than an hour. In a relativistic setting, our methods can be applied to the post-Minkowskian (PM) expansion for gravitational binaries in the worldline formalism. We demonstrate the methods by computing the 3PM eikonal and find agreement with previous results based on amplitude methods. Importantly, the Magnus expansion yields a finite eikonal, while the naïve eikonal based on the time-symmetric propagator is infrared-divergent from 3PM on.

Black Holes↗
DOE OSTI2026

A simple fourth order propagator based on the Magnus expansion in the Liouville space: Application to a Λ-system and assessment of the rotating wave approximation

A simple fourth-order propagator [Ture and Jang, J. Phys. Chem. A 128, 2871 (2024)] based on the Magnus expansion is extended to the Liouville space for both closed-system and Lindbladian open-system quantum dynamics. For both dynamics, commutator free versions of fourth-order propagators are provided as well. These propagators are then applied to the dynamics of a driven Λ-system, where Lindblad terms represent the effect of a photonic bath. For both dynamics, the accuracy of the rotating wave approximation (RWA) for the matter–radiation interaction is assessed. We confirmed reasonable performance of RWA for weak and resonant fields. However, small errors appear for moderate fields and substantial errors can be found for strong fields where coherent population trapping can still be expected. We also found that the presence of bath for open-system quantum dynamics consistently reduces the errors of the RWA. These results provide quantitative information on how the RWA breaks down beyond weak field or for non-resonant cases. Major results are benchmarked against results of our sixth-order ME-based propagator. Finally, we also provide numerical comparison of our algorithms with other fourth-order algorithms for the Λ-system. These confirm reasonable performance of our simple propagators and the improvement gained through commutator-free expressions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Optimal control of coupled quantum systems based on the first-order Magnus expansion: Application to multiple dipole-dipole-coupled molecular rotors

This paper presents a method for performing approximate optimal control simulations for quantum systems with multiple coupled degrees of freedom. In this work, the time evolution is simulated using the first-order Magnus expansion in the interaction picture, where the couplings between different degrees of freedom are treated as the perturbation. A numerical implementation procedure is presented that leverages upon pairwise couplings and the separability of the zeroth-order time evolution operator to achieve a reduced computational cost, which is analyzed with respect to the number of degrees of freedom. The formulation is compatible with gradient-free methods to optimize the control field, and a stochastic hill climbing algorithm is adopted for this purpose. As illustrations, optimal control simulations are performed for systems of two and three dipole-dipole-coupled molecular rotors under the influence of a control field. For the two-rotor system, the field is optimized to achieve either orientation or entanglement objectives. For the three-rotor system, the field is optimized either to orient all three rotors in the same direction or to orient one rotor in a particular direction while the other two rotors point in the opposite direction.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Computational schemes for the Magnus expansion of the in-medium similarity renormalization group

The in-medium similarity renormalization group (IMSRG) is a popular many-body method used for computations of nuclei. It solves the many-body Schrödinger equation through a continuous unitary transformation of the many-body Hamiltonian. The IMSRG transformation is typically truncated at the normal-ordered two-body level, the IMSRG(2), but recently several approaches have been developed to capture the effects of normal-ordered three-body operators, the IMSRG(3). In particular, a factorized approximation to the IMSRG(3) proposes to capture the leading effects of three-body operators at the same computational cost as the IMSRG(2) approximation. This approach often employs an approximate scheme for solving the IMSRG equations, the so-called hunter-gatherer scheme. In this work, I study the uncertainty associated with this scheme. I find that the hunter-gatherer scheme differs by up to 7MeV for ground-state energies and 0.5MeV for excitation energies from standard IMSRG(2) approaches. These differences are in some cases comparable to the expected size of IMSRG(3) corrections.

39 ≤ A ≤ 58↗
DOE OSTI2022

ADG: automated generation and evaluation of many-body diagrams

The goal of the present paper is twofold. First, a novel expansion many-body method applicable to superfluid open-shell nuclei, the so-called Bogoliubov in-medium similarity renormalization group (BIMSRG) theory, is formulated. This generalization of standard single-reference IMSRG theory for closed-shell systems parallels the recent extensions of coupled cluster, self-consistent Green’s function or many-body perturbation theory. Within the realm of IMSRG theories, BIMSRG provides an interesting alternative to the already existing multi-reference IMSRG (MR-IMSRG) method applicable to open-shell nuclei. The algebraic equations for low-order approximations, i.e., BIMSRG(1) and BIMSRG(2), can be derived manually without much difficulty. However, such a methodology becomes already impractical and error prone for the derivation of the BIMSRG(3) equations, which are eventually needed to reach high accuracy. Based on a diagrammatic formulation of BIMSRG theory, the second objective of the present paper is thus to describe the third version (v3.0) of the code that automatically (1) generates all valid BIMSRG(n) diagrams and (2) evaluates their algebraic expressions in a matter of seconds. This is achieved in such a way that equations can easily be retrieved for both the flow equation and the Magnus expansion formulations of BIMSRG. Expanding on this work, the first future objective is to numerically implement BIMSRG(2) (eventually BIMSRG(3)) equations and perform ab initio calculations of mid-mass open-shell nuclei.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Locality and heating in periodically driven, power-law-interacting systems

In this work, we study the heating time in periodically driven D-dimensional systems with interactions that decay with the distance r as a power law 1 / r α Using linear-response theory, we show that the heating time is exponentially long as a function of the drive frequency for α > D. For systems that may not obey linear-response theory, we use a more general Magnus-like expansion to show the existence of quasiconserved observables, which imply exponentially long heating time, for α > 2D. We also generalize a number of recent state-of-the-art Lieb-Robinson bounds for power-law systems from two-body interactions to k-body interactions and thereby obtain a longer heating time than previously established in the literature. Additionally, we conjecture that the gap between the results from the linear-response theory and the Magnus-like expansion does not have physical implications, but is, rather, due to the lack of tight Lieb-Robinson bounds for power-law interactions. We show that the gap vanishes in the presence of a hypothetical, tight bound.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Parallel-In-Time Magnus Integrators

Magnus integrators are a subset of geometric integration methods for the numerical solution of ordinary differential equations that conserve certain invariants in the numerical solution. Our report explores temporal parallelism of Magnus integrators, particularly in the context of nonlinear problems. The method combines the concurrent computation of matrix commutators and exponentials within a time step with a pipelined iteration applied to multiple time steps in parallel. The accuracy and efficiency of time parallel Magnus methods up to order six are highlighted through numerical examples and demonstrate that critical parallel speedup is possible compared to serial methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Energy storage solutions to decarbonize electricity through enhanced capacity expansion modelling

To meet ambitious global decarbonization goals, electricity system planning and operations will change fundamentally. With increasing reliance on variable renewable energy resources, energy storage is likely to play a critical accompanying role to help balance generation and consumption patterns. As grid planners, non-profit organizations, non-governmental organizations, policy makers, regulators and other key stakeholders commonly use capacity expansion modelling to inform energy policy and investment decisions, it is crucial that these processes capture the value of energy storage in energy-system decarbonization. Here we conduct an extensive review of literature on the representation of energy storage in capacity expansion modelling. We identify challenges related to enhancing modelling capabilities to inform decarbonization policies and electricity system investments, and to improve societal outcomes throughout the clean energy transition. Additionally, we further identify corresponding research activities that can help overcome these challenges and conclude by highlighting tangible real-world outcomes that will result from pursuing these research activities. Capacity expansion modelling (CEM) approaches need to account for the value of energy storage in energy-system decarbonization. A new Review considers the representation of energy storage in the CEM literature and identifies approaches to overcome the challenges such approaches face when it comes to better informing policy and investment decisions.

25 ENERGY STORAGE↗
DOE OSTI2025

Synergies and trade-offs between storage, transmission, and sector coupling in high renewable energy systems

Energy storage, transmission, and sector coupling are some prominent flexibility solutions to support variable renewable energy (VRE) integration. However, investment cost uncertainties and public acceptance could hamper the deployment of these flexibility solutions. This raises questions about the development and cost-effectiveness of future energy systems, especially on how the dependence on local and cross-border solutions of flexibility would evolve if the uptake of these solutions is restricted. In this context, this paper identifies the synergies among flexibility options under restrictions on transmission expansion or increased costs of energy storage. It contributes to determining whether investments in energy storage and/or transmission expansion offer the least-cost transition and investigates the impact of sector coupling on these solutions. A long-term energy system planning and optimisation model towards 2050 is developed using the open-source energy system optimisation tool Balmorel, and a case study of the countries surrounding the Baltic Sea and the North Sea is established. Five cases with restrictions imposed on transmission expansion and higher energy storage technology costs are analysed at different levels of sector coupling. The results highlight the importance of transmission expansion at all levels of sector coupling. As the level of sector coupling increases, uncertainties around the cost of energy storage drive the least-cost pathways. Optimal investment solutions are found to have a mix of transmission and energy storage in capacity expansion at all levels of sector coupling.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRSDate not supplied

Measurement of Material Recession and Shock Standoff in Plasma Windtunnel using Neural Nets

Arcjets are plasma wind tunnels used to test the performance of heatshield materials for spacecraft atmospheric entry. These facilities present an extremely harsh flow environment with heat fluxes up to 109 W/m2 for up to 30 minutes. The plasma is low-temperature (∼1 eV) but high pressure (> 10 kPa) creating high-enthalpy supersonic flows similar to atmospheric entry conditions. Typically, material samples are measured before and after a test to characterize the total recession. However, this does not capture time-dependent effects such as material expansion and non-linear recession. This work will present new analysis of arcjet test videos which measure both the time-dependent 2D recession of the material samples and the shock standoff distance. The results show non-linear time-dependent effects are present for some conditions. The material and shock edges are extracted from the videos by training and applying a convolutional neural network. Due to the consistent camera settings, the machine learning model achieves high accuracy (± 2 px) relative to manually segmented images with only a small number of training frames (80).

Neural network↗
NASA NTRSDate not supplied

Measurement of material recession and shock standoff in plasma windtunnel using neural nets

Arcjets are plasma wind tunnels used to test the performance of heatshield materials for spacecraft atmospheric entry. These facilities present an extremely harsh flow environment with heat fluxes up to 10^9 W/m^2 for up to 30 minutes. The plasma is low-temperature (~1 eV) but high pressure (> 10 kPa) creating high-enthalpy supersonic flows similar to atmospheric entry conditions. Typically, material samples are measured before and after a test to characterize the total recession. However, this does not capture time-dependent effects such as material expansion and non-linear recession. This work will present new analysis of arcjet test videos which measure both the time-dependent 2D recession of the material samples and the shock standoff distance. New results showing non-linear material erosion rates will be highlighted. The material and shock edges are extracted from the videos by training and applying a convolutional neural network. Due to the consistent camera settings, the machine learning model achieves high accuracy (~99%) on new data with only a small number of training frames (~80). The new results will be discussed in the context of temperature dependent plasma-surface interaction.

Magnus A Haw↗
DOE OSTI2020

Shallow soils are warmer under trees and tall shrubs across Arctic and Boreal ecosystems

Soils are warming as air temperatures rise across the Arctic and Boreal region concurrent with the expansion of tall-statured shrubs and trees in the tundra. Changes in vegetation structure and function are expected to alter soil thermal regimes, thereby modifying climate feedbacks related to permafrost thaw and carbon cycling. However, current understanding of vegetation impacts on soil temperature is limited to local or regional scales and lacks the generality necessary to predict soil warming and permafrost stability on a pan-Arctic scale. Here we synthesize shallow soil and air temperature observations with broad spatial and temporal coverage collected across 106 sites representing nine different vegetation types in the permafrost region. We showed ecosystems with tall-statured shrubs and trees (> 40 cm) have warmer shallow soils than those with short-statured tundra vegetation when normalized to a constant air temperature. In tree and tall shrub vegetation types, cooler temperatures in the warm season do not lead to cooler mean annual soil temperature indicating that ground thermal regimes in the cold-season rather than the warm-season are most critical for predicting soil warming in ecosystems underlain by permafrost. Our results suggest that the expansion of tall shrubs and trees into tundra regions can amplify shallow soil warming, and could increase the potential for increased seasonal thaw depth and increase soil carbon cycling rates and lead to increased carbon dioxide loss and further permafrost thaw.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

The influence of intake flow and coolant temperature on gasoline spray morphology during early-injection DISI engine operation

Multi-hole gasoline injectors operating at conditions spanning throttled early-intake stroke operation produce spray plumes that either remained separated or merge and collapse due to flash boiling. Flash boiling occurs due to the sudden expansion of gas bubbles in the liquid fuel at high fuel temperature and low ambient pressure. This study records high-speed images of spray-morphology changes due to in-cylinder flow, thereby revealing operating conditions that do and do not affect the self-induced morphology observed in quiescent vessels. Specifically, in a central-injection, four-valve, high-tumble engine, where the thermodynamic state and in-cylinder cross flow are dynamic. Motivated by cold start and hot restart operation, the fuel pressure, coolant temperature, in-cylinder air pressure, and engine rpm were systematically varied over relevant operating conditions, which bracketed the range from non- to flash-boiling sprays. The results reveal the operating conditions at which the in-cylinder cross flow disrupts the spray morphology as well as the extent of the disruption. At 650 rpm, the spray morphology was similar to that observed in quiescent vessels at nominally equivalent fuel temperature and in-cylinder pressure, indicating that the spray’s self-induced entrainment flow dominated the in-cylinder flow. However, for fuel temperature and ambient pressure near the transition between non- and flash-boiling, the intake cross flow at higher engine speed (1950 rpm) significantly disrupted the spray morphology. The high cross-flow velocity appears to induce plume merging and collapse, whereas none was evident at low rpm (650 rpm). This study led to the postulate that the spray merging and collapse are governed by the rate of atomization near the nozzle exit, presumed to be controlled by either or both aerodynamic atomization and flash-boiling intensity. It would then follow that spray modeling in CFD requires atomization models that blend the effects of both physical processes.

42 ENGINEERING↗