Search NASASearch

SEARCH · Search NASA

Results for “TIMING”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

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

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

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

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

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

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

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

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

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)

Real-time inference and extrapolation with Time-Conditioned UNet: Applications in hypersonic flows, incompressible flows, and global temperature forecasting

Neural Operators are fast and accurate surrogates for nonlinear mappings between functional spaces within training domains. Extrapolation beyond the training domain remains a grand challenge across all application areas. We present Time-Conditioned UNet (TC-UNet) as an operator learning method to solve time-dependent PDEs continuously in time without any temporal discretization, including in extrapolation scenarios. TC-UNet incorporates the temporal evolution of the PDE into its architecture by combining a parameter conditioning approach with the attention mechanism from the Transformer architecture. After training, TC-UNet makes real-time inferences on an arbitrary temporal grid. We demonstrate its extrapolation capability on a climate problem by estimating the global temperature for several years and also for inviscid hypersonic flow around a double cone. We propose different training strategies involving temporal bundling and sub-sampling. We demonstrate performance improvements for several benchmarks, performing extrapolation for long time intervals and zero-shot super-resolution time.

Deep learning

ETROC1: the first full chain precision timing prototype ASIC for CMS MTD endcap timing layer upgrade

We present the design and characterization of the first fullchain precision timing prototype ASIC, named ETL Readout Chipversion 1 (ETROC1) for the CMS MTD endcap timing layer (ETL)upgrade. The ETL utilizes Low Gain Avalanche Diode (LGAD) sensors todetect charged particles, with the goal to achieve a time resolutionof 40–50 ps per hit, and 30–40 ps per track with hits from twodetector layers. The ETROC1 is composed of a 5 × 5 pixelarray and peripheral circuits. The pixel array includes a4 × 4 active pixel array with an H-tree shaped networkdelivering clock and charge injection signals. Each active pixel iscomposed of various components, including a bump pad, a chargeinjection circuit, a pre-amplifier, a discriminator, adigital-to-analog converter, and a time-to-digital converter. Thesecomponents play essential roles as the front-end link in processingLGAD signals and measuring timing-related information. Theperipheral circuits provide clock signals and readoutfunctionalities. The size of the ETROC1 chip is7 mm× 9 mm. ETROC1 has been fabricated in a 65 nmCMOS process, and extensively tested under stimuli of chargeinjection, infrared laser, and proton beam. The time resolution ofbump-bonded ETROC1 + LGAD chipsets reaches 42–46 ps per hit in thebeam test.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND

A real-time search for Type Ia Supernovae with late-time interactions with circumstellar material in ZTF data

While it is generally accepted that Type Ia supernovae (SNe Ia) are the terminal explosions of white dwarfs (WDs), the nature of their progenitor systems and the mechanisms that lead up to these explosions remain widely debated. In rare cases, the SN ejecta interact with circumstellar material (CSM) that had previously been ejected from the progenitor system. The longer the delay between the creation of the CSM and the SN explosion, the greater the distance between the SN explosion site and the CSM and the later the onset of the interaction. The unknown distance between the CSM and SN explosion site makes it impossible to predict when the interaction will start. If the time between the SN explosion and the onset of the CSM interaction is of the order of several months to years, the SN has generally faded and it is no longer actively followed up on. This makes it even more difficult to detect the interaction while it is happening. In this work, we report on a real-time monitoring programme running between 13 November 2023 and 9 July 2024. It monitored 6914 SNe Ia for signs of late-time rebrightening using the Zwicky Transient Facility (ZTF). Flagged candidates were rapidly followed up on with photometry and spectroscopy to confirm the late-time excess and its position. We report the discovery of a ∼50 day rebrightening event in SN 2020qxz around 1200 rest-frame days after the peak of its light curve. SN 2020qxz exhibited signs of an early CSM interaction, but had faded from view over two years before its reappearance. Initial follow-up spectroscopy revealed the presence of four emission lines, while later follow-up spectroscopy showed that these had faded shortly after the end of the ZTF-detected rebrightening event. Our best match for these emission lines are H β (blueshifted by ∼5900 km s −1 ) and Ca II λ8542 , N I λ8567 , and K I λλ8763, 8767 (all blueshifted by 5100 km s −1 ; although we note that the line identifications are uncertain). This shows that catching and following up on late-time interactions as they occur can offer new clues on the nature of the progenitor systems that produce these SNe by putting constraints on the possible type of donor star. The only way to do this systematically is to use large sky surveys such as ZTF and the upcoming Vera C. Rubin Observatory’s Legacy Survey of Space and Time (LSST) to monitor a large sample of objects for the rare events that reappear long after the object has faded from view.

circumstellar matter

Real time computations of cryogenic He properties

The Fermilab PIP-II (proton improvement plan - II) project is being constructed at Fermilab to deliver $800\,MeV$ protons of $>1\,MW$ beam power to replace the present LINAC and provide protons to the remainder of the existing accelerator complex. The new LINAC consists of a warm front end, 23 superconducting RF cryomodules, and a beam transfer line to the existing complex. The cryomodules (CMs) are to be tested at Fermilab's CryoModule Test Facility (CMTF).An important measurement in cryogenic testing is the heat load of each CM. Traditionally, at Fermilab, these measurements were made collecting archived data offline and analyzing it. The new control system for PIP-II is being developed with the EPICS (Experimental Physics and Industrial Control System) framework, which allows us to compute the heat load in real time using the HePak library.We are exploring other $He$ properties, such as flow, where flow meters are not available, which can also be calculated in real time and fed back to the cryogenics engineers.This paper details the real time heat load calculation and $He$ flow software developed for CM testing at CMTF, as well as the first results from the prototype HB650 CM. Future plans for 2-phase $LHe$ flow will also be outlined.

Hanlet, Pierrick [Fermilab]

Time evolution of a pumped molecular magnet—A time-resolved inelastic neutron scattering study

Introducing an experimental technique of time-resolved inelastic neutron scattering (TRINS), we explore the time-dependent effects of resonant pulsed microwaves on the molecular magnet Cr 8 F 8 Piv 16 . The octagonal rings of magnetic Cr 3+ atoms with antiferromagnetic interactions form a singlet ground state with a weakly split triplet of excitations at 0.8 meV. A 4.6 tesla field was applied to tune the splitting between two members of the triplet excited level |1$\rangle$ ↔ |2$\rangle$ to resonance with 105 GHz (0.434 meV) microwaves. The time-dependent occupations of the ground state |0$\rangle$, lower lying levels |1$\rangle$ and |2$\rangle$, and higher energy states |λ ≥ 3$\rangle$ were extracted during and after 20 s long microwave pulses incident along the (101) direction of a Cr 8 F 8 Piv 16 crystal held at 1.9 K. At significantly elevated spin temperatures, we found underpopulation relative to thermal equilibrium of |2$\rangle$ and spin-lattice thermalization time scales ranging from 1.6(2) s to 5.7(2) s depending on the power level. This contrasts with the relaxation time τ 1 (T → 0) = 27(5) 𝛍 s inferred for |2$\rangle$ from in situ Electron Spin Resonance measurements. By probing a broad range of excited states during intense microwave pumping, TRINS thus provides a first view of long lived excited states in a molecular antiferromagnet.

Science & Technology - Other Topics

Toward quantum tunneling from excited states: Recovering imaginary-time instantons from a real-time analysis

We revisit the path integral description of quantum tunneling and its generalization to excited states. For clarity, we focus on the simple toy model of a point particle in a double-well potential, for which we perform all steps explicitly. Instead of performing the familiar Wick rotation from physical to imaginary time—which is inconsistent with the requisite boundary conditions when treating tunneling from excited states—we regularize the path integral by adding an infinitesimal complex contribution to the Hamiltonian, while keeping time strictly real. We find that this gives rise to a complex stationary-phase solution, in agreement with recent insights from Picard-Lefshetz theory. We then show that there exists a class of analytic solutions for the corresponding equations of motion, which can be made to match the appropriate boundary conditions in the physically relevant limits of a vanishing regulator and an infinite physical time. We provide a detailed discussion of this nontrivial limit. We find that, for systems without an explicit time-dependence, our approach reproduces the picture of an instantonlike solution defined on a finite Euclidean-time interval. Lastly, we discuss the generalization of our approach to broader classes of systems, for which it serves as a reliable framework for high-precision calculations. Published by the American Physical Society 2025

Steingasser, Thomas (ORCID:0000000217262117)

Integration of a real-time orientation measurement system for a real-time evaluator (RTE) to measure the position and orientation of crane-lifted components

Prefabrication of building components holds the potential to revolutionize the construction industry. Prefabrication consists of manufacturing building components, modules, and other elements in a factory to be shipped and installed on a construction site. Prefabricated components have been produced for various applications including precast concrete panels for new construction and exterior wall retrofits. The manufacturing process has seen much innovation in recent years; however, the installation process has seen minimal advancements. A real-time evaluator (RTE) was developed to reduce the installation cost of prefabricated components by reducing installation time, decreasing rework, and improving accuracy. The RTE uses off-the-shelf hardware and novel algorithms to assist erectors with component installation by measuring the real-time positions of connections and prefabricated components, providing installation guidance through a graphical user interface, and monitoring the accumulated installation errors. An overview of the RTE and the proposed workflow is presented. Previous on-site demonstrations provided valuable feedback from users on the potential areas for improvement of the system. One common request was real-time measurement of component orientation during lifting, a process that previously required that the component remain stationary while the laser tracker cycled through target prisms. This paper will present the incorporation and testing of a real-time orientation measurement system as it was implemented into the RTE, allowing for measurement of component orientation during movement.

Selvakumar, Balaji [ORNL]

Neutrino beam bunch structure reconstruction with precision timing in the ICARUS liquid argon time projection chamber

The ICARUS detector has been operating smoothly since 2021 as the far detector in the Short Baseline Neutrino (SBN) program at Fermilab, collecting neutrino interactions from both the Booster Neutrino Beam (BNB) and off-axis from the Neutrinos at the Main Injector (NuMI) beam. Analysis of neutrino interactions in ICARUS requires mitigation of substantial cosmogenic backgrounds. This is achieved by using an external Cosmic Ray Tagger (CRT) and a Photomultiplier Tube (PMT) system embedded in the liquid argon. The intrinsic neutrino beam bunch structure, inherited time structure from the Radio Frequency (RF) system used to accelerate the protons, can be resolved at the ICARUS detector using precise timing information. Located at shallow depth, ICARUS is exposed to a high flux of cosmic rays that can be mistaken for neutrino interactions. To mitigate this background, the CRT and a 3-meter-thick concrete overburden were installed. To better model backgrounds, ICARUS makes use of an overlay technique where simulated neutrino events are superimposed on detector beam-off data. PMTs installed within a Time Projection Chamber detect argon scintillation light emitted by high energy charged particles passing through the chamber and provide the event timing of neutrino interactions. The nanosecond-level beam bunch structure is reconstructed with the PMT system and can be used to further understand backgrounds and enhance neutrino physics capabilities. In this thesis, I will discuss background mitigation techniques using precision timing and present a novel technique to select neutrino events from our unbiased data stream using the beam bunch structure.

Heggestuen, Anna [Colorado State U.] (ORCID:000000

Simulation of 24,000 Electron Dynamics: Real-Time Time-Dependent Density Functional Theory (TDDFT) with the Real-Space Multigrids (RMG)

Here, we present the theory, implementation, and benchmarking of a real-time time-dependent density functional theory (RT-TDDFT) module within the RMG code, designed to simulate the electronic response of molecular systems to external perturbations. Our method offers insights into nonequilibrium dynamics and excited states across a diverse range of systems, from small organic molecules to large metallic nanoparticles. Benchmarking results demonstrate excellent agreement with established TDDFT implementations and showcase the superior stability of our time integration algorithm, enabling long-term simulations with minimal energy drift. The scalability and efficiency of RMG on massively parallel architectures allow for simulations of complex systems, such as plasmonic nanoparticles with thousands of atoms. Future extensions, including nuclear and spin dynamics, will broaden the applicability of this RT-TDDFT implementation, providing a powerful toolset for studies of photoactive materials, nanoscale devices, and other systems where real-time electronic dynamics is essential.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH