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At least 127 records · Page 7

Materials Characterization, Prediction, and Control Project: Summary Report on Material Characterization, Part 2

The Pacific Northwest National Laboratory (PNNL) undertook the Materials Characterization, Prediction, and Control (MCPC) Laboratory Directed Research and Development Project to advance understanding of nuclear material processing and enable multifold acceleration in the development and qualification of new material systems in national security and advanced energy applications (Smith 2021). The MCPC Project executed research across three scientific vertices—material characterization, predictive modeling, and data analytics—with extensive support by a data curation and management team. The central technical objective in the MCPC Project was to improve the prediction and characterization of the process-structure-property relationships within the microstructurally refined region of stainless-steel samples prepared utilizing friction stir processing (FSP). Application of the FSP technique is well established at PNNL within the Solid Phase Processing capability through many years of investment across a range of materials and applications (PNNL 2024).

36 MATERIALS SCIENCE↗

Materials Characterization, Prediction, and Control Project: Summary Report on Material Characterization, Part 3

The Pacific Northwest National Laboratory (PNNL) undertook the Materials Characterization, Prediction, and Control (MCPC) Laboratory Directed Research and Development Project to advance understanding of nuclear material processing and enable multifold acceleration in the development and qualification of new material systems in national security and advanced energy applications (Smith 2021). The MCPC Project executed research across three scientific vertices—material characterization, predictive modeling, and data analytics—with extensive support by a data curation and management team. The central technical objective in the MCPC Project was to improve the prediction and characterization of the process-structure-property relationships within the microstructurally refined region of stainless-steel samples prepared utilizing friction stir processing (FSP). Application of the FSP technique is well established at PNNL within the Solid Phase Processing capability through many years of investment across a range of materials and applications (PNNL 2024).

36 MATERIALS SCIENCE↗

Materials Characterization, Prediction, and Control Project: Summary Report on Material Characterization, Part 4

The Pacific Northwest National Laboratory (PNNL) undertook the Materials Characterization, Prediction, and Control (MCPC) Laboratory Directed Research and Development Project to advance understanding of nuclear material processing and enable multifold acceleration in the development and qualification of new material systems in national security and advanced energy applications (Smith 2021). The MCPC Project executed research across three scientific vertices—material characterization, predictive modeling, and data analytics—with extensive support by a data curation and management team. The central technical objective in the MCPC Project was to improve the prediction and characterization of the process-structure-property relationships within the microstructurally refined region of stainless-steel samples prepared utilizing friction stir processing (FSP). Application of the FSP technique is well established at PNNL within the Solid Phase Processing capability through many years of investment across a range of materials and applications (PNNL 2024).

36 MATERIALS SCIENCE↗

Creep suppression and fatigue in bio-based composites manufactured via conventional and large format additive manufacturing processes

The emergence of novel extrusion-based additive manufacturing (AM) processes has prompted the development of new thermoplastic composite feedstocks, and broadening sustainability initiatives have driven the development of bio-based and recyclable material for AM feedstocks. Poly(lactic acid) (PLA) with wood flour (WF) is one composite system that has been demonstrated in numerous AM applications, as well as traditional processing methods (i.e., compression and injection molding); however, there has been a need to understand how the variation in processing methodology impacts the material performance of these bio-based feedstocks from a fundamental perspective, with particular emphasis on creep for an extended application use-life. Herein, PLA/WF is explored as a feedstock material for large format additive manufacturing (LFAM) and the performance of additively manufactured materials is compared to those produced via more traditional processing methods. It is also demonstrated that the addition of WF decreases the material’s coefficient of thermal expansion (CTE) while increasing its Young’s modulus, susceptibility to water uptake, and creep fatigue resistance. Essentially, the addition of 20 wt% WF results in a 92 % decrease in rubbery regime CTE while simultaneously resulting in a 14 % increase in modulus, 190 % increase in water uptake, and a 31 % decrease in residual strain after cyclic creep tests. The processing method was also found to play a large role in the final part performance, with the printed material increasing the crystallinity by 183 % and 214 % compared to its compression and injection molded counterparts. Furthermore, the porosity of printed samples increased by two orders of magnitude compared to samples prepared via traditional processing methods.

36 MATERIALS SCIENCE↗

An Overview of Manufacturing Controls for Production of High-Consequence, Single-Use Systems

Extended Testing (Crowder, et al. (2025) ) is a reliability demonstration technique that can be used to dramatically reduce sample size requirements. Manufacturing controls are needed to supplement extended testing by identifying production issues that a reduced sample sizes might overlook, especially built-in, or latent, manufacturing defects. This report focuses on some of the most commonly used, yet most impactful, manufacturing control tools that are used to limit production-related defects and efficiently screen any remaining defects at final inspection. These tools include statistical process control (SPC), acceptance sampling, environmental stress screening (HASS and ESS), and mistake proofing. The goal is to minimize the probability that built-in defects ever reach the customer. In terms of nuclear weapons (NW), the goal is to prevent defective units from ever entering the nation’s NW stockpile. Examples of each of the techniques are illustrated with case studies.

42 ENGINEERING↗

Performance Testing of a Moving-Bed Gasifier Using Coal, Biomass, and Waste Plastic Blends with Washed and Unwashed Legacy Coals and Other Waste Fuels to Generate White Hydrogen

The objective of this effort, primarily funded by the United States Department of Energy (DOE), and led by the Electric Power Research Institute, Inc. (EPRI), with support by Hamilton Maurer International (HMI) and Sotacarbo S.p.A. (Sotacarbo), has been to qualify coal, biomass, and plastic waste blends based on performance testing of selected fuel pellet compositions in a pilot-scale updraft moving-bed (UDMB) gasifier. The testing provided relevant data to advance the commercial-scale design of the moving-bed gasifier to be able to successfully use these feedstocks to produce hydrogen. In particular, the effects of waste plastics on feedstock development (i.e., blending and pelletizing) and the resulting products (i.e., syngas compositions, organic condensate production, and ash characteristics) are the focus. The gasifier used for testing is HMI’s moving-bed gasifier, which has been proven capable of gasifying nearly all coal ranks. It has also shown the ability in prior testing work to gasify wood chips (biomass). However, mixtures of these fuels with plastic wastes have not been prepared and gasified together. The three feedstocks were densified and pelletized by California Pellet Mill (CPM) to meet the feedstock size required by Sotacarbo’s 30mm ID UDMB gasifier, under contract to HMI. The technical tasks and results from this two-year research project included: (1) Feed Procurement and Preparation: Nine different tri-fuel pellets were prepared from varying compositions of fresh mined PRB coal, corn stover biomass, and car fluff waste plastics. Tri-fuel pellets were produced by CPM and shipped to Sotacarbo’s test facility in Carbonia, Sardinia, Italy. (2) Test Plan Development: A test plan was created to define the test runs to be performed. The test plan detailed the different UDMB gasification tests to be performed in Sotacarbo’s 12-inch ID pilot scale gasifier, the process monitoring instrumentation used, and the extractive samples recovered for analysis of the total gasification process mass and energy balance. (3) Gasifier Testing: Nine different gasification runs were performed in the pilot-scale gasifier at Sotacarbo using nine different fuel feedstock compositions generated from varying mixtures of PRB coal, biomass, and plastic wastes. The testing generated performance data on gasification reaction efficiency and performance, yielding relevant data for models used to scale up the gasifier design. This task also included work to refurbish and reassemble the pilot gasifier at Sotacarbo and perform a baseline 100% PRB coal run. (4) Data Analysis and Reporting: Review of the data, determination of figures of merit, and interpretation of the results are reported in the project’s final report, published in March 2024. The results show that all tri-fuel pellets gasified well and maintained structural integrity throughout the gasification process. The syngas generated can be shifted to hydrogen by using commercial syngas shifting technologies. (5) High Fidelity computational fluid dynamics (CFD) Simulation: The National Energy Technology Laboratory (NETL) team performed CFD simulations of the UDMB gasifier for two of the tri-fuel pellets gasified in Sotacarbo’s pilot scale gasifier. The kinetic mechanisms for the pyrolysis of each constituent, PRB coal, corn stover biomass, and waste plastics are based on thermogravimetric analysis performed by Sotacarbo. The gasification model was validated by comparing the predicted syngas composition at the exit of the gasifier with the measured syngas composition. In addition, the reactor’s measured internal temperature profile agreed well with the predicted internal reactor temperature profile. These results validate that the model can be used to predict the performance of the updraft moving bed gasifier for different feedstocks and operating conditions. This paper summarizes the results of the completed work in which the pelletizing procedure was validated to ensure the viability of the tri-fuel pellets for the gasification runs performed at Sotacarbo’s 30 mm UDMB gasifier. The gasification performance data from this series of nine runs will enable modeling of a full-scale HMI industrial scale gasifier supporting both combined heat and power, and Hydrogen production from coal (both fresh mined and legacy) combined with various biomass and waste plastics. Additionally, plans and progress on a follow-up project, being executed by the same project team, will be presented. In this project, a total of twenty (20) different feedstocks are being prepared from varying compositions of biomass (both woody biomass and corn stover) with a mixture of legacy coal waste, plastic waste, and refuse-derived fuel (RDF). The testing will provide information on gasification reaction efficiency/performance, yielding relevant data for models used to scale up the gasifier design to 50 megawatt electric (MWe) (equivalent hydrogen production). Tests will also be performed on a bench-scale fluidized-bed gasifier for comparison purposes. The results of this testing will be used to specify the range of feedstock blends that can be successfully gasified as well as quantify gasifier outputs based on specific blends.

08 HYDROGEN↗

Fluoride Analysis by Ion Chromatography in Support of Fast Critical Assembly (FCA) Spent Nuclear Fuel Processing

INTRODUCTION The Savannah River Site (SRS) is currently processing Fast Critical Assembly (FCA) fuel received from the Japan Atomic Energy Agency (JAEA) for disposition. Stainless steel-clad plate and rods in stainless steel containers are dissolved using electrolysis with a solution mixture of nitric acid (HNO3), potassium fluoride (KF), and gadolinium (Gd). An ion chromatography (IC) was developed and vetted to monitor fluoride at various sampling points of the process. To finalize the method, FCA test solution was analyzed to qualify the analytical method followed by real FCA process solution analysis using two different analytical columns. This presentation summarizes the development and vetting of the IC method.

White, Thomas L. [Savannah River National Laborato↗

Single-Molecule Fluorescence Microscopy Reveals Energy Transfer Active versus Inactive Nanocrystal/Dye Conjugate Pairs

Defect-mediated energy transfer (EnT) is a radiative process that occurs between donor defect states in the forbidden bandgap of semiconductor nanocrystals (NCs) and dye molecules bound to their surfaces. The EnT efficiency depends on the number of dye molecules attached to each NC, the donor–acceptor distance, and the dipole orientation factor between the donor and acceptor, all of which vary across all individual NCs in a sample. While ensemble-level fluorescence spectroscopy measurements have provided average values for donor–acceptor distances, dye-to-NC ratios, and EnT rate constants, questions remain about the impact of donor/acceptor heterogeneity on observed EnT efficiencies. Notably, ensemble-level measurements cannot distinguish between bare NCs and EnT-active versus inactive NC/dye pairs in the same sample batch, limiting the ability to design systems with 100% EnT efficiency. To address this, we studied defect-mediated EnT between AlexaFluor 555 dye acceptors chemically bound to ZnO NC donors at the level of single molecules and single NCs. Interestingly, 20% of bound NC/dye pairs are EnT-inactive, likely contributing to residual defect photoluminescence (PL) observed in ensemble-level measurements and reducing overall EnT efficiency. Single particle-level ZnO defect PL and acceptor fluorescence trajectories exhibited distinct microfluctuations, which are absent in bare ZnO NCs. We hypothesized that our observations can be explained with a competitive dye fluorescence quenching pathway, possibly due to charge transfer between the excited state dye and the ZnO NC. Numerical simulations of single-molecule PL traces for this scenario produced microfluctuations consistent with the experimental results. These findings highlight the impact of sample heterogeneity on EnT processes and provide insights for designing light-harvesting systems with optimized EnT efficiency.

25 ENERGY STORAGE↗

Generalizable Image Segmentation for Microstructure Characterization Through Integrated SEM and EBSD Analysis

We demonstrate generalizable semantic segmentation using minimal ground truth data. Correlated scanning electron microscopy (SEM) images and electron backscatter diffraction (EBSD) measurements of frictionstir processed 316L stainless steel plates were used to train deep learning models for grain boundary segmentation. Secondary electron (SE) imaging taken at an accelerating voltage of 10 keV correlated to EBSD-derived grain boundaries produced the best performing model. Notably, an ensemble of three models trained on a single SE image produced accurate segmentation over a series of BSE images of samples manufactured under different processing parameters, with a resultant mean absolute error in grain size of 0.34 µm. The striking generalizability of the models likely results from the similar escape depths of the SE training input and the EBSD training output and the reduced probability of dislocation artifacts appearing in the image. This finding highlights the importance of considering the physical principles behind imaging in the development of robust segmentation models for microstructure characterization.

Taufique, Mohammad Fuad Nur↗

Lignin molecular weights of Populus trichocarpa residues after CELF pretreatment

Here we present a dataset of molecular weights of lignin from a woody energy crop (Populus trichocarpa) residues after a series of co-solvent enhanced lignocellulosic fractionation (CELF) pretreatment. The natural poplar variant GW-9947 from the Center for Bioenergy Innovation (CBI) was used. The poplar was knife milled and passed through a 1 mm sieve and CELF pretreatment was performed in a Parr autoclave reactor with 7.5 wt % solids loading, 0.5 wt% H2SO4 as catalyst at 150°C with various time. Tetrahydrofuran was added in a 1:1 mass ratio with water as the pretreatment solvent. Lignin was isolated from the pretreated samples after ball-milling in a porcelain jar with ceramic balls via Retsch PM 200 at 580 rpm for 2.5 h followed by enzymatic hydrolysis in acetate buffer (pH 4.8, 50 °C) for 48 h. The solid residue was isolated by centrifugation and hydrolyzed again with freshly added buffer and enzymes for another 48 h. After filtration, the solid residue was extracted twice with 96% (v/v) 1,4-dioxane/water mixture at room temperature overnight. The extracts were combined, rotary evaporated, and freeze-dried to recover lignin. The lignin samples were then derivatized in an acetic anhydride/pyridine (1:1, v/v) mixture and stirred at room temperature for 24 h. Ethanol was added to the reaction mixture, left for 30 min and then removed with a rotary evaporator. The addition and removal of ethanol was repeated at least 3 times until all traces of acetic acid were removed. Acetylated lignin samples were then dissolved in tetrahydrofuran (THF) at a concentration of 1.0 mg/mL. The molecular weight of acetylated lignin was measured by a gel permeation chromatography (GPC) on a PSS-Polymer Standards Service (Warwick, RI, USA) GPC SECurity 1200 system featuring Agilent HPLC 1200 components equipped with four Waters Styragel columns (HR1, HR2, HR4 and HR6) and an UV detector (270 nm). Tetrahydrofuran was used as the mobile phase and flow rate was 0.3 mL/min. The Polymer Standards Service WinGPC Unity software (Build 6807) was used for data processing for all the samples. The data provides information about the effects of CELF pretreatment time at 150 ºC on lignin molecular weights.

09 BIOMASS FUELS↗

Filtration Performance of Simulated 200 West Area Waste Feeds

This report describes the scaled experimental system and approach used to examine dead-end filtration performance of representative 200W waste feeds. The scaled system, which was originally designed and assembled to test Tank Side Cesium Removal (TSCR) system performance with higher-than-expected solid loadings in 2021 (Schonewill et al. 2021), was repurposed to conduct the current experiments at ~1/145 of full scale (based on throughput). Six experimental runs were conducted with five different 200W waste feed simulants: three using a DEF module scaled for TSCR and three using a DEF module scaled for the 200W process modules (based on the current design for the Advanced Modular Pretreatment System). Each experiment was run continuously for multiple days with an operating approach prototypic of the full-scale system. Staff performing the experimental runs monitored performance, obtained data from calibrated process instruments, and collected samples for observation and analysis. The measured data are presented with a focus on assessing DEF performance – specifically, the filters’ differential pressure response to the five waste simulants, frequency and efficacy of backwashing, and baseline recovery between experimental runs; data related to ion exchange column performance are also discussed in cases where the opportunity arose. The experimental campaign demonstrated that the DEFs satisfied their primary function of protecting the ion exchange column from solid intrusion for all the representative simulants used. The filters readily handled solids loadings of =500 ppm (and even greater), especially the modules scaled to the 200W process modules. Adjustments to the processing flow rate and reductions in feed temperature were observed to affect the rate of differential pressure increase on the filters, but neither adversely affected the ability of the DEFs to perform their primary function. Backflushing reliably recovered filter performance in all runs, although it did not prevent irreversible fouling for one simulant. The run that exhibited irreversible fouling established that both the quantity and the nature of the solids being filtered need to be considered when projecting filter performance.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Effect of Plutonium on Uranium Oxide Microstructural Fingerprint

The analysis of particulates from environmental sampling is routinely performed for nuclear forensics applications. In order to increase the tools available for nuclear forensics applications, capability development materials (CDMs), or reference particulates, are necessary for developing and benchmarking new analytical methods. Historically, these CDM particulates have been produced with highly controlled and characterized isotopic and size parameters for applications in developing and benchmarking particle sizers and mass spectrometry analytical methods [1- 4]. However, the development of CDMs with highly characterized particle morphology and phase of the particles is vital for aiding in the development and benchmarking of particle analytical methods for those parameters. In many cases, key properties such as crystallographic phase, morphology, and microstructure, may be correlated to processing history of environmental sampling particulates [5]. To that end, this work investigates determining the structural fingerprint of produced Pu-doped uranium oxide CDMs using transmission electron microscopy (TEM). The particulates, one of which shown in Figure 1, were synthesized to Fig. 1. Single particulate of uranium oxide fabricated using the THESEUS technique. develop capabilities for environmental sampling investigations. These particles are monodisperse at diameter of 1 μm and a range of plutonium concentrations from 0- 1,000 ppm. Given their small diameter, TEM analysis was ideal for studying the particulate structural fingerprint in detail. Previous investigations confirmed the external homogeneity of the particulates at different plutonium concentrations, however this analysis focuses on determining the grain structure, phase distribution, and porosity of the particulates.

Mayer, Jack [Univ. of Florida, Gainesville, FL (Un↗

Round Robin Analysis of Uranium Isotopics on Cotton Swipes Measured Using Microextraction-Based Sampling Versus Conventional Bulk Analysis

A comparison of microextraction sampling methods to directly analyze uranium isotopics on cotton swipes was performed concurrently with traditional bulk-processing methods. For the microextraction sampling approach, two different detection platforms were evaluated, a quadrupole-based inductively coupled plasma mass spectrometer (ICP-MS) and the liquid sampling-atmospheric pressure glow discharge (LS-APGD) coupled to an Orbitrap mass spectrometer. Results presented from this innovative sampling approach (i.e., microextraction) are compared with a more traditional approach employed for analysis of cotton-based environmental swipes, namely bulk ashing/digestion, separation, and subsequent analysis by high-precision multi-collector ICP-MS. Overall, the microextraction approach proved to be a reliable and accurate means to determine isotopic ratios of uranium collected on cotton swipes. The ICP-MS-based detection had relative standard deviations of <0.65% for the major isotopic determinations, whereas the LS-APGD-Orbitrap method had relative standard deviations of <3%. The percent relative difference for the 235 U/ 238 U ratios, in comparison to the expected values, was <1% for ICP-MS and <4% for the microplasma-Orbitrap method. Additionally, the microextraction ICP-MS accurately (<2%) and precisely (<5%) determined the minor isotopic compositions (i.e., 234 U/ 238 U and 236 U/ 238 U).

ICP-MS↗

Evaluation of Seismic Artificial Intelligence with Uncertainty

Artificial intelligence has transformed the seismic community with deep learning models (DLMs) that are trained to complete specific tasks within workflows. However, there is still a lack of robust evaluation frameworks for evaluating and comparing DLMs. Here, we address this gap by designing an evaluation framework that jointly incorporates two crucial aspects: performance uncertainty and learning efficiency. To target these aspects, we meticulously construct the training, validation, and test splits using a clustering method tailored to seismic data and enact an expansive training design to segregate performance uncertainty arising from stochastic training processes and random data sampling. The framework’s ability to guard against misleading declarations of model superiority is demonstrated through the evaluation of PhaseNet (Zhu and Beroza, 2018), a popular seismic phase picking DLM, under three training approaches. Our framework helps practitioners choose the best model for their problem and set performance expectations by explicitly analyzing model performance with uncertainty at varying budgets of training data.

58 GEOSCIENCES↗

Detection of Part Porosity in Additive Manufacturing Using Machining

Monitoring of part porosity in additive manufacturing is critical for part qualification and process parameter development. This article describes the monitoring of porosity in additive manufacturing using machining. Grade 91 steel samples with different levels of porosity were additively manufactured using a laser blown-powder process. The samples were machined, and the tool position and cutting power were monitored using the machine controller and an external power transducer, respectively. Results show that the power transducer is sensitive to machining porosities. A novel approach using the standard deviation of cutting power was developed to determine the location of porosities along the length of the machining pass. Test cuts were completed at different machining process parameters. Results showed that the probability of detection was one for pore volume greater than 0.3 mm 3 at different machining parameters. In conclusion, although the detection of porosity using machining is a destructive method for evaluation, it offers a low-cost and fast approach for monitoring porosity in additive manufacturing.

36 MATERIALS SCIENCE↗

Sample screening of uranium ore concentrates using portable spectrophotometers: investigating the correlation between visible colors and chemical signatures

A research collaboration between the Japan Atomic Energy Agency and the Department of Energy’s National Nuclear Security Administration examined nuclear forensic signatures and analytical methods for tracing the origins of uranium ore concentrates (UOCs). Here, this study focuses on utilizing portable spectrophotometers capable of reflectance measurements in the visible light spectrum as a potential rapid screening tool for nuclear forensics analysis. Unlike laboratory-based near-infrared spectroscopy or digital image analysis, this research investigated the potential to correlate visible color measurements with key nuclear forensics signatures using seven types of UOC samples with known origins and three UOC certified reference materials. Results demonstrated that distinct color groups, quantified using CIELAB values, correlated with major uranium compounds. Furthermore, the findings indicated that trace elements can influence the UOC colors, providing additional insights into material characteristics. Although this approach requires further validation across a broader range of UOC species, this study demonstrated that simple colorimetric analysis using visible spectrophotometry, which does not require complex sample preparation or data processing, can serve as a practical and novel rapid tool for preliminary screening and attribution in nuclear forensics investigations.

and nuclear chemistry↗

Machine learning models of intermittent operation of RO wellhead water treatment for salinity reduction and nitrate removal

Machine learning models were developed for intermittent multi-mode operation of a wellhead reverse osmosis water purification and desalination system to predict salt passage, nitrate passage, and permeate flux. The models, based on long short-term memory (LSTM) recurrent neural network (RNN) architecture, included an attention mechanism to increase model performance in proximity of the regulatory limit for nitrate. Training and testing of the models for the Startup, Production, Shutdown and Flushing operational modes were based on operational data (consisting of 22 process variables per data sample) acquired every 2–5 s over a six-month period. The significant sets of model input attributes for the different operational modes were assessed via Spearman ranking correlation, Self-Organizing Map (SOM) analysis and feed forward feature selection (FFFS). Although the variability of nitrate passage, salt passage and permeate flux was significant over the four operational modes, prediction performance for the three outcomes were with R2 and Average Absolute Relative Error (AARE) of 0.78–0.95 and 2.96–6.16 %, respectively. Model updates post membrane elements replacement demonstrated similar levels of prediction accuracy. The study results suggest that there is merit in exploring the utility of multi-mode models for sensor fault detection, data imputation, and for potential use in model-predictive control.

Intermittent RO operation↗

Polariton spectra under the collective coupling regime. II. 2D non-linear spectra

In our previous work [Mondal et al., J. Chem. Phys. 162, 014114 (2025)], we developed several efficient computational approaches to simulate exciton–polariton dynamics described by the Holstein–Tavis–Cummings (HTC) Hamiltonian under the collective coupling regime. Here, we incorporated these strategies into the previously developed Lindblad-partially linearized density matrix (⁠$\mathscr{L}$-PLDM) approach for simulating 2D electronic spectroscopy (2DES) of exciton–polariton under the collective coupling regime. In particular, we apply the efficient quantum dynamics propagation scheme developed in Paper I to both the forward and the backward propagations in the PLDM and develop an efficient importance sampling scheme and graphics processing unit vectorization scheme that allow us to reduce the computational costs from $\mathscr{O}$($\mathscr{K}$ 2 )$\mathscr{O}$(T 3 ) to $\mathscr{O}$($\mathscr{K}$)$\mathscr{O}$(T 0 ) for the 2DES simulation, where $\mathscr{K}$ is the number of states and T is the number of time steps of propagation. As a result, we further simulated the 2DES for an HTC Hamiltonian under the collective coupling regime and analyzed the signal from both rephasing and non-rephasing contributions of the ground state bleaching, excited state emission, and stimulated emission pathways.

2D non-linear spectra↗