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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 OSTI2024

Real-Time Time-Dependent Density Functional Theory for Simulating Nonequilibrium Electron Dynamics

The explicit real-time propagation approach for time-dependent density functional theory (RT-TDDFT) has increasingly become a popular first-principles computational method for modeling various time-dependent electronic properties of complex chemical systems. Here, in this Perspective, we provide a nontechnical discussion of how this first-principles simulation approach has been used to gain novel physical insights into nonequilibrium electron dynamics phenomena in recent years. Following a concise overview of the RT-TDDFT methodology from a practical standpoint, we discuss our recent studies on the electronic stopping of DNA in water and the Floquet topological phase as examples. Our discussion focuses on how RT-TDDFT simulations played a unique role in deriving new scientific understandings. We then discuss existing challenges and some new advances at the frontier of RT-TDDFT method development for studying increasingly complex dynamic phenomena and systems.

Hamiltonians↗

DOE OSTI2024

Estimating the Contributions to Human Error Probability from the Convolution of the Distribution of Time Available and Time Required

As part of their duties, Human Reliability Analysis must often evaluate if crews in nuclear power plants (NPPs) can complete tasks associated with a human-failure event within time limits. For example, the time required in NPP scenarios is determined by systematic and structured walkthroughs, feasibility studies, recorded times from training exercises, and interviews with experienced operators and experts. Typically, a point estimate is derived for the estimate (mean, maximum, or 95th percentile of time required). Using point-estimate values can mask the risk associated with variability among crews, plant conditions and set-up, environmental conditions, and other impact factors under which these actions are executed. While point estimates for time required and time available have served the industry well, without considering the uncertainty they could lead to biased understanding about the risk. The Integrated Human Event Analysis System - General Methodology (IDHEAS-G) model (developed by the US Nuclear Regulatory Commission, NRC) for human error probability calculates human error probability by summing two probabilities: insufficient time and cognitive error. As such, the model takes a more holistic approach by considering the full distributions for time required and time available to calculate the human error probability because the time available to complete the task is insufficient. In this study, we expand on the work of the NRC and discuss methods for estimating these time considerations. For example, for the time required, the impact of Performance Influencing Factors (PIFs) on the distribution was divided into impacts that are aleatory in nature, such as crew-to-crew variability, and those that are epistemic (i.e., the PIFs). Starting with the factors that introduce aleatory uncertainty, a first-order distribution was developed from a large set of time required (i.e., NPP task completion times) data for the range of operator actions that occur in the NPP control room under simulated accident conditions. The first-order distribution can then be adjusted to account for epistemic uncertainty using research associated with the impact of applicable PIFs on the time required. We also develop guidance for analysts to address the probability distributions for the time available. The guidance we developed on how to estimate time required and time available distributions is based on the identification of pertinent research and data, data analyses, and expert knowledge elicitation.

human error probability, human performance, time e↗

DOE OSTI2023

A large area 100-channel PICOSEC Micromegas detector with time resolution at the 20 ps level

Abstract The PICOSEC Micromegas precise timing detector is based on a Cherenkov radiator coupled to a photocathode operating in a semi-transparent mode and a Micromegas amplification structure. The first proof of concept single-channel prototype was able to achieve a time resolution below 25 ps. One of the crucial aspects in the development of precise timing gaseous detectors applicable in high-energy physics experiments is a modular design that enables large area coverage. The first 19-channel multi-pad prototype with an active area of approximately 10 cm 2 suffered from degraded timing resolution due to the non-uniformity of the preamplification gap thickness. A new 100 cm 2 detector module with 100 channels based on a rigid hybrid ceramic/FR4 Micromegas board for improved drift gap uniformity was developed. Initial measurements with 80 GeV/c muons showed improvements in timing response over the measured pads and a time resolution below 25 ps. More recent measurements with a thinner drift gap detector module and newly developed RF pulse amplifiers show that the pad centre resolution can be enhanced to the level of 17 ps. This work will present the development of the detector from structural simulations, design, and beam test commissioning with a focus on the timing performance of a thinner drift gap detector module in combination with new electronics using an automated timing scan method.

Utrobicic, A.↗

DOE OSTI2023

Towards robust PICOSEC Micromegas precise timing detectors

The PICOSEC Micromegas (MM) detector is a precise timing gaseous detector consisting of a Cherenkov radiator combined with a photocathode and a MM amplifying structure. A 100-channel PICOSEC MM prototype with 10 × 10 cm 2 active area equipped with a Cesium Iodide (CsI) photocathode demonstrated a time resolution below σ = 18 ps. The objective of this work is to improve the PICOSEC MM detector robustness aspects, i.e. integration of resistive MM and carbon-based photocathodes, while maintaining good time resolution. The PICOSEC MM prototypes have been tested in laboratory conditions and successfully characterised with 150 GeV/c muon beams at the CERN SPS H4 beam line. The excellent timing performance below σ = 20 ps for an individual pad obtained with the 10 × 10 cm 2 area resistive PICOSEC MM of 20 MΩ/$\square$ showed no significant time resolution degradation as a result of adding a resistive layer. A single-pad prototype equipped with a 12 nm thick Boron Carbide (B 4 C) photocathode presented a time resolution below σ = 35 ps, opening up new possibilities for detectors with robust photocathodes. The results made the concept more suitable for the experiments in need of robust detectors with good time resolution.

RETHGEM↗

DOE OSTI2022

Fast Quasi-Static Time-Series Simulation for Accurate PV Inverter Semiconductor Fatigue Analysis with a Long-Term Solar Profile

Power system simulations with long-term data typically have large time steps varying from one second to a few minutes. However, for PV inverter semiconductors, the minimum thermal stress cycle occurs over the fundamental grid frequency (50 or 60 Hz). This requires the time step of the fatigue simulation to be around 100 µs. This small time step requires long computation times to process yearly power production profiles. This paper proposes a fast fatigue simulation for inverter semiconductors using the quasi-static time series (QSTS) simulation concept. The proposed simulation calculates the steady state of the semiconductor junction temperature by using a Fast Fourier Transform (FFT). The small thermal cycling during a switching period and even over the fundamental waveform is disregarded to further accelerate the simulation speed. The resulting time step of the fatigue simulation is 15 minutes, which is consistent with the solar dataset. The error of the proposed simulation is 0.16% compared to the fatigue simulation results using the complete thermal stress profile. A PV inverter that responds to a Transactive Energy System (TES) is simulated to demonstrate the use of the proposed fatigue simulation. The proposed simulation has the potential to co-simulate with system level simulation tools that also adopt the QSTS concept.

Liu, Yunting↗

DOE OSTI2024

Endogeneity of pedestrian survival time and emergency medical service response time: Variations across disadvantaged and non-disadvantaged communities

The Vision Zero-Safe Systems Approach prioritizes fast access to Emergency Medical Services (EMS) to improve the survivability of road users in transportation crashes, especially concerning the recent increase in pedestrian-involved crashes. Pedestrian crashes resulting in immediate or early death are considerably more severe than those taking longer. The time gap between injury and fatality is known as survival time, and it heavily relies on EMS response time. The characteristics of the crash location may be associated with EMS response and survival time. A US Department of Transportation initiative identifies communities often facing challenges. Six disadvantaged community (DAC) indicators, including economy, environment, equity, health, resilience, and transportation access, enable an analysis of how survival and EMS response times vary across DACs and non-DACs. To this end, this study created a unique and comprehensive database by linking DACs data with 2017–2021 pedestrian-involved fatal crashes. This study utilizes two-stage residual inclusion models with segmentation for DACs and non-DACs accounting for the endogenous relationship between EMS response and pedestrian survival time. The results indicate that EMS response time is higher and pedestrian survival time is lower in DACs than in non-DACs. A delayed EMS response time is associated with a greater reduction in survival time in DACs compared to non-DACs. Factors, e.g., nighttime and interstate crashes, contribute to higher EMS response time, while pedestrian drugs, driver speeding, and hit-and-run behaviors are associated with a greater reduction in survival time in DACs than non-DACs. Finally, the implications of the findings are discussed in the paper.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2026

Explicit Monotone Stable Super-Time-stepping Methods for Finite Time Singularities

We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge–Kutta–Legendre (RKL) and Runge–Kutta–Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multistage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the time-step size for stability scales with stage number 𝑠 as $\mathcal{O}$⁡(𝑠 2 ). Many interesting nonlinear PDEs have finite-time singularities, and the presence of diffusion often limits one to using implicit or semi-implicit time-step methods for stability constraints. Finite-time singularities are particularly challenging due to the large range of scales that one desires to resolve, often with adaptive spatial grids and adaptive time steps. Here, in this study, we show two examples of nonlinear PDEs for which the self-similar singularity structure has time and space scales that are resolvable using the RKL and RKG methods, without forcing even smaller time steps. Compared to commonly used implicit numerical methods, we achieve a significantly smaller run time while maintaining comparable accuracy. We also prove numerical monotonicity for both the RKL and RKG methods under their linear stability conditions for the constant coefficient heat equation, in the case of infinite domain and periodic boundary condition, leading to a theoretical guarantee of the superiority of the RKL and RKG methods over traditional super-time-stepping methods, such as the Runge-Kutta-Chebyshev and the orthogonal Runge-Kutta-Chebyshev methods. Code can be found at https://github.com/ZT220501/SRK-Singularity.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

X-ray Spectral-Timing Pipeline to Investigate an Electron-Scattering Time Delay in Black Hole Accretion Disks [Slides]

The soft lag in black hole X-ray binaries (BHXRBs) refers to the time delay for the soft, thermal disk to respond to hard, variable coronal irradiation. This time lag increases from less than 1 ms to ~10 ms during the hard-to-soft state transition. Interpretations of soft lag trends appeal to changing the light-travel path via an evolving coronal height and/or inner accretion disk radius. Both interpretations neglect a time delay contribution from the reprocessing of irradiation inside the disk, where electron-scattering opacity dominates. A new theory considering a thermalization (electron scattering) time delay in the disk can plausibly produce ~10 ms time delays in the intermediate state. To further investigate the impacts of adding a time delay component from electron scattering in the disk, we are creating a spectral-timing pipeline that can analyze NICER (Neutron Star Interior Composition Explorer) X-ray observations of BHXRBs in outburst. In the near future, we will apply this spectral timing pipeline to develop a reverberation lag model from simulations that include the thermalization time delay from electron scattering in the disk.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Topology property analysis and application of stable time-delay regions for linear multiple time-delay systems

This study examines the relationship between the topology of stable time-delay regions and the stability analysis of an linear multiple time delay system. To analyze the topology of stable time-delay regions, we construct a function with a value equal to zero for the time-delay points on the boundaries of stable time-delay regions. The function is continuous and differentiable in the whole defining field with a global minimum of zero so that we can locate the boundaries by minimizing the value of the function. Based on the topology analysis, we proposed a performance validation approach for controllers that are designed to stabilize the system using feedback signals with time delays. The method based on the topology analysis is simple and reliable so that can deal with a linear time-invariant system with high order and multiple time delays (more than 3). The example case study shows that the above method is reliable and enables ultra-low latency coordination and control for the future power grid with ubiquitous power electronics.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Real-Time High-Accuracy Digital Wireless Time, Frequency, and Phase Calibration for Coherent Distributed Antenna Arrays

his work presents a fully-digital high-accuracy real-time calibration procedure for frequency and time alignment of open-loop wirelessly coordinated coherent distributed antenna array (CDA) modems, enabling radio frequency (RF) phase coherence of spatially separated commercial off-the-shelf (COTS) software-defined radios (SDRs) without cables or external references such as the global navigation satellite system (GNSS). Building on previous work using high-accuracy spectrally-sparse time of arrival (ToA) waveforms and a multistep ToA refinement process, a high-accuracy two-way time transfer (TWTT)-based time–frequency coordination approach is demonstrated. Due to the two-way nature of the high-accuracy TWTT approach, the time and frequency estimates are Doppler and multipath tolerant, so long as the channel is reciprocal over the synchronization epoch. This technique is experimentally verified using COTS SDRs in a lab environment in static and dynamic scenarios and with significant multipath scatterers. Time, frequency, and phase stability were evaluated by beamforming over coaxial cables to an oscilloscope which achieved time and phase precisions of ~60– 70 ps , with median coherent gains above 99% using optimized coordination parameters, and a beamforming frequency root-mean-square error (RMSE) of 3.73 ppb in a dynamic scenario. Finally, experiments were conducted to compare the performance of this technique with previous works using an analog continuous-wave two-tone (CWTT) frequency reference technique in both static and dynamic settings.

Clock synchronization↗

DOE OSTI2023

Assessment and Commissioning of Electrical Substation Grid Testbed with a Real-Time Simulator and Protective Relays/Power Meters in the Loop

Electrical utility substations are wired with intelligent electronic devices (IEDs), such as protective relays, power meters, and communication switches. Substation engineers commission these IEDs to assess the appropriate measurements for monitoring, control, power system protection, and communication applications. Like real electrical utility substations, complex electrical substation grid testbeds (ESGTs) need to be assessed for measuring current and voltage signals in monitoring, power system protection, control (synchro check), and communication applications that are limited by small measurement percentage errors. In the process of setting an ESGT with real-time simulators and IEDs in the loop, protective relays, power meters, and communication devices must be commissioned before running experiments. In this study, an ESGT with IEDs and distributed ledger technology was developed. The ESGT with a real-time simulator and IEDs in the loop was satisfactorily assessed and commissioned. The commissioning and problem-solving tasks of the testbed are described to define a method with flowcharts to assess possible trouble-shooting in ESGTs. This method was based on comparing the simulations versus IED measurements for the phase current and voltage magnitudes, three-phase phasor diagrams, breaker states, protective relay times with selectivity coordination at electrical faults, communication data points, and time-stamp sources.

Piesciorovsky, Emilio↗

DOE OSTI2024

Tensor Network Space-Time Spectral Collocation Method for Time-Dependent Convection-Diffusion-Reaction Equations

Emerging tensor network techniques for solutions of partial differential equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical methods for ultra-fast numerical solutions of high-dimensional problems. Here, we introduce a Tensor Train (TT) Chebyshev spectral collocation method, in both space and time, for the solution of the time-dependent convection-diffusion-reaction (CDR) equation with inhomogeneous boundary conditions, in Cartesian geometry. Previous methods for numerical solution of time-dependent PDEs often used finite difference for time, and a spectral scheme for the spatial dimensions, which led to a slow linear convergence. Spectral collocation space-time methods show exponential convergence; however, for realistic problems they need to solve large four-dimensional systems. We overcome this difficulty by using a TT approach, as its complexity only grows linearly with the number of dimensions. We show that our TT space-time Chebyshev spectral collocation method converges exponentially, when the solution of the CDR is smooth, and demonstrate that it leads to a very high compression of linear operators from terabytes to kilobytes in TT-format, and a speedup of tens of thousands of times when compared to a full-grid space-time spectral method. These advantages allow us to obtain the solutions at much higher resolutions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

A Practical Framework for Simulating Time-Resolved Spectroscopy Based on a Real-Time Dyson Expansion

Time-resolved spectroscopy is a powerful tool for probing electron dynamics in molecules and solids, revealing transient phenomena on subfemtosecond time scales. The interpretation of experimental results is often enhanced by parallel numerical studies, which can provide insight and validation for experimental hypotheses. However, developing a theoretical framework for simulating time-resolved spectra remains a significant challenge. The most suitable approach involves the many-body nonequilibrium Green's function formalism, which accounts for crucial dynamical many-body correlations during time evolution. While these dynamical correlations are essential for observing emergent behavior in time-resolved spectra, they also render the formalism prohibitively expensive for large-scale simulations. Substantial effort has been devoted to reducing this computational cost─through approximations and numerical techniques─while preserving the key dynamical correlations. The ultimate goal is to enable first-principles simulations of time-dependent systems ranging from small molecules to large, periodic, multidimensional solids. Here, in this perspective, we outline key challenges in developing practical simulations for time-resolved spectroscopy, with a particular focus on Green's function methodologies. We highlight a recent advancement toward a scalable framework: the real-time Dyson expansion (RT-DE) [Phys. Rev. Lett. 2024, 133, 226902]. We introduce the theoretical foundation of RT-DE and discuss strategies for improving scalability, which have already enabled simulations of system sizes beyond the reach of previous fully dynamical approaches. We conclude with an outlook on future directions for extending RT-DE to first-principles studies of dynamically correlated, nonequilibrium systems.

Reeves, Cian C. [Univ. of California, Santa Barbar↗

DOE OSTI2025

Parallel-in-time quantum simulation via Page and Wootters quantum time

In the past few decades, researchers have created a veritable zoo of quantum algorithms by drawing inspiration from classical computing, information theory, and even from physical phenomena. Here, we present quantum algorithms for parallel-in-time simulations that are inspired by the Page and Wootters formalism. In this framework, and thus in our algorithms, the classical time variable of quantum mechanics is promoted to the quantum realm by introducing a Hilbert space of “clock” qubits that are then entangled with the “system” qubits. We show that our algorithms can compute temporal properties over 𝑁 different times of many-body systems by only using log⁡(𝑁) clock qubits. As such, we achieve an exponential trade-off between time and spatial complexities. In addition, we rigorously prove that the entanglement created between the system qubits and the clock qubits has operational meaning, as it encodes valuable information about the system’s dynamics. We also provide a circuit depth estimation of all the protocols, showing a running time advantage in computation times over traditional sequential-in-time algorithms. In particular, for the case when the dynamics are determined by the Aubry-Andre model, we present a hybrid method for which our algorithms have a depth that only scales as 𝒪⁡(log⁡(𝑁)⁢𝑛). As a by-product, we can relate the previous schemes to the problem of equilibration of an isolated quantum system, thus indicating that our framework enables a new dimension for studying dynamical properties of many-body systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Compact representation and long-time extrapolation of real-time data for quantum systems using the ESPRIT algorithm

Representing real-time data as a sum of complex exponentials provides a compact form that enables both denoising and extrapolation. As a fully data-driven method, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm is agnostic to the underlying physical equations, making it broadly applicable to various observables and experimental or numerical setups. In this work, we consider applications of the ESPRIT algorithm primarily to extend real-time dynamical data from simulations of quantum systems. We evaluate ESPRIT's performance in the presence of noise and compare it to other extrapolation methods. We demonstrate its ability to extract information from short-time dynamics to reliably predict long-time behavior and determine the minimum time interval required for accurate results. We discuss how this insight can be leveraged in numerical methods that propagate quantum systems in time, and we show how ESPRIT can predict infinite-time values of dynamical observables, offering a purely data-driven approach to characterizing quantum phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Instrumentation and methods for efficient time-resolved X-ray crystallography of biomolecular systems with sub-10 ms time resolution

Time-resolved X-ray crystallography has great promise to illuminate structure–function relations and key steps of enzymatic reactions with atomic resolution. The dominant methods for chemically-initiated reactions require complex instrumentation at the X-ray beamline, significant effort to operate and maintain this instrumentation, and enormous numbers (∼10 5 –10 9 ) of crystals per time point. We describe instrumentation and methods that enable high-throughput time-resolved study of biomolecular systems using standard crystallography sample supports and mail-in X-ray data collection at standard high-throughput cryocrystallography synchrotron beamlines. The instrumentation allows rapid reaction initiation by mixing of crystals and substrate/ligand solution, rapid capture of structural states via thermal quenching with no pre-cooling perturbations, and yields time resolutions in the single-millisecond range, comparable to the best achieved by any non-photo-initiated method in both crystallography and cryo-electron microscopy. Our approach to reaction initiation has the advantages of simplicity, robustness, low cost, adaptability to diverse ligand solutions and small minimum volume requirements, making it well suited to routine laboratory use and to high-throughput screening. We report the detailed characterization of instrument performance, present structures of binding of N -acetylglucosamine to lysozyme at time points from 8 ms to 2 s determined using only one crystal per time point, and discuss additional improvements that will push time resolution toward 1 ms.

Indergaard, John A. (ORCID:000000022367699X)↗

DOE OSTI2022

Quantitative interpretation of time-lapse seismic data at Farnsworth field unit: Rock physics modeling, and calibration of simulated time-lapse velocity responses

Here, this study investigates the contribution of fluid saturation variation to the time-lapse velocity response by performing fluid substitution modeling. The methodology is exemplified by the time-lapse seismic monitoring of carbon dioxide at Farnsworth field unit (FWU). In order to evaluate the fluid distribution in a matured oil reservoir, the Southwest Regional Partnership (SWP) acquired multiple vertical seismic profile (VSP) surveys at different times during the CO 2 –water alternatinggas (WAG) injection period. In this work, we present a thorough methodology for computing the elastic response of the saturated rock for different fluid saturations using a site-specific petro-elastic model (PEM). The output from the PEM was combined with results from a fluid compositional model to compute the seismic velocities at times corresponding to each VSP survey. To produce a calibrated simulated response, the measured time-lapse seismic velocities were integrated into the numerical simulation model. The mismatches between the predicted and measured time-lapse velocities were minimized through an iterative calibration process using a trained artificial neural network proxy (ANN) coupled with a particle swarm optimizer (PSO). Our study indicates that the hybrid optimization workflow can effectively perform the history matching. With an accurate prediction of the hydrodynamic properties, the migration of CO 2 within the subsurface was modeled by predicting the spatial velocity distribution for a radius of 305 m around the injection well. The technology demonstrated and the expertise gained from this study can guide similar CO 2 -WAG projects.

58 GEOSCIENCES↗