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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Atmospheric velocity spectral width measurements using the statistical distribution of pulsed CO2 lidar return signal intensities

A pulsed CO2 lidar with coherent detection has been used to measure the correlation time of backscatter from an ensemble of atmospheric aerosol particles which are illuminated by the pulsed radiation. The correlation time of the backscatter of the return signal, which is directly related to the velocity spectral width, can be used to study the velocity structure constant of atmospheric turbulence and wind shear. Various techniques for correlation time measurement are discussed, and several measurement results are presented for the technique using the information contained in the statistical distribution of a set of lidar return signal intensities.

Ancellet, Gerard M.↗
DOE OSTI2021

mystic : software for autonomous discovery and design under uncertainty

Throughout the diverse range of science and engineering applications, there is a growing desire to develop computational methods that can reliably predict the behavior of complex systems. Specifically, there is a strategic need for tools that can robustly forecast the behavior of complex physical systems, where data may be high-dimensional, noisy, or sparse, and models of the system may be time-dependent or include uncertainty. We use mystic to build tools that leverage statistical learning, physics-informed learning, and active learning in the efficient generation of reliably predictive surrogates for complex physical systems. mystic is a robust, proven, open-source optimization and uncertainty quantification toolkit with over a decade of use in the design and optimization of neutron instrumentation, solar-powered drones, and gasguns, and in iterative tuning of models for Raman spectroscopy and elastoplastic materials strength. Recent developments have focused on automated learning of statistically robust surrogates under uncertainty, with applications in materials in extreme environments, nanostructures, materials simulations and strength models, and the failure of shielding under particle radiation. In 2020, McKerns demonstrated active learning of optimally robust surrogates with respect to new simulated data for molecular dynamics simulations of materials mixing in warm dense matter, and is currently applying active learning to the automated steering of particle accelerator beams and the optimal design and control of quantum optical sensor instrumentation.

42 ENGINEERING↗
DOE OSTI2024

Primordial non-Gaussianities with weak lensing: information on non-linear scales in the Ulagam full-sky simulations

Abstract Primordial non-Gaussianities (PNGs) are signatures in the density field that encode particle physics processes from the inflationary epoch. Such signatures have been extensively studied using the Cosmic Microwave Background, through constraining their amplitudes,f X NL , with future improvements expected from large-scale structure surveys; specifically, the galaxy correlation functions. We show that weak lensing fields can be used to achieve competitive and complementary constraints. This is shown via theUlagamsuite of N-body simulations, a subset of which evolves primordial fields with four types of PNGs. We create full-sky lensing maps and estimate the Fisher information from three summary statistics measured on the maps: the moments, the cumulative distribution function, and the 3-point correlation function. We find that the year 10 sample from the Rubin Observatory Legacy Survey of Space and Time (LSST) can constrain PNGs toσ(f NL eq ) ≈ 110,σ(f NL or, lss ) ≈ 120,σ(f NL loc ) ≈ 40. For the former two, this is better than or comparable to expected galaxy clustering-based constraints from the Dark Energy Spectroscopic Instrument (DESI). The PNG information in lensing fields is on non-linear scales and at low redshifts (z≲ 1.25), with a clear origin in the evolution history of massive halos. The constraining power degrades by ∼60% under scale cuts of ≳ 20 Mpc, showing there is still significant information on scales mostly insensitive to small-scale systematic effects (e.g., baryons). We publicly release theUlagamsuite to enable more survey-focused analyses.

Astronomy & Astrophysics↗
NASA NTRS1973

Problems in the simulation of atmospheric boundary layer flows

The realistic simulation of flow in the atmospheric boundary layers at heights greater than two kilometers is discussed. Information concerning horizontally homogeneous and statistically stationary atmospheric boundary layer flows is presented. The problems related to the incorporation of the information into atmospheric wind simulation programs are analyzed. The information which the meteorologist must acquire in order to provide a basis for improving the simulation of atmospheric boundary flows is explained.

Fichtl, G. H.↗
NASA NTRS1993

The helical decomposition and the instability assumption

Direct numerical simulations show that the triadic transfer function T(k,p,q) peaks sharply when q (or p) is much smaller than k. The triadic transfer function T(k,p,q) gives the rate of energy input into wave number k from all interactions with modes of wave number p and q, where k, p, q form a triangle. This observation was thought to suggest that energy is cascaded downscale through non-local interactions with local transfer and that there was a strong connection between large and small scales. Both suggestions were in contradiction with the classical Kolmogorov picture of the energy cascade. The helical decomposition was found useful in distinguishing between kinematically independent interactions. That analysis has gone beyond the question of non-local interaction with local transfer. In particular, an assumption about the statistical direction of triadic energy transfer in any kinematically independent interaction was introduced (the instability assumption). That assumption is not necessary for the conclusions about non-local interactions with local transfer recalled above. In the case of turbulence under rapid rotation, the instability assumption leads to the prediction that energy is transferred in spectral space from the poles of the rotation axis toward the equator. The instability assumption is thought to be of general validity for any type of triad interactions (e.g. internal waves). The helical decomposition and the instability assumption offer detailed information about the homogeneous statistical dynamics of the Navier-Stokes equations. The objective was to explore the validity of the instability assumption and to study the contributions of the various types of helical interactions to the energy cascade and the subgrid-scale eddy-viscosity. This was done in the context of spectral closures of the Direct Interaction or Quasi-Normal type.

Waleffe, Fabian A.↗
DOE OSTI2020

Dark Energy Survey Year 3 results: cosmology with moments of weak lensing mass maps – validation on simulations

ABSTRACT We present a simulated cosmology analysis using the second and third moments of the weak lensing mass (convergence) maps. The second moment, or variances, of the convergence as a function of smoothing scale contains information similar to standard shear two-point statistics. The third moment, or the skewness, contains additional non-Gaussian information. The analysis is geared towards the third year (Y3) data from the Dark Energy Survey (DES), but the methodology can be applied to other weak lensing data sets. We present the formalism for obtaining the convergence maps from the measured shear and for obtaining the second and third moments of these maps given partial sky coverage. We estimate the covariance matrix from a large suite of numerical simulations. We test our pipeline through a simulated likelihood analyses varying 5 cosmological parameters and 10 nuisance parameters and identify the scales where systematic or modelling uncertainties are not expected to affect the cosmological analysis. Our simulated likelihood analysis shows that the combination of second and third moments provides a 1.5 per cent constraint on S8 ≡ σ8(Ωm/0.3)0.5 for DES Year 3 data. This is 20 per cent better than an analysis using a simulated DES Y3 shear two-point statistics, owing to the non-Gaussian information captured by the inclusion of higher order statistics. This paper validates our methodology for constraining cosmology with DES Year 3 data, which will be presented in a subsequent paper.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2015

Rao-Blackwellization for Adaptive Gaussian Sum Nonlinear Model Propagation

When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented.

state estimation↗
DOE OSTI2023

A VOI Web Application for Distinct Geothermal Domains: Statistical Evaluation of Different Data Types within the Great Basin

The Great Basin region contains different domains that have different structural and hydrothermal flow patterns. Depending on the characteristics of these patterns, certain data types may be more successful at detecting hidden geothermal resources. In this paper, we quantitatively evaluate if certain data types are more successful in certain domains. Given different aquifer, strain and structural conditions, we explore which data types statistically reveal positively labeled geothermal sites. We utilize value of information (VOI) metrics to help quantify the reliability of data types to discriminate against "positive" and "negative" labeled geothermal sites. We also evaluate how kernel density estimation can help generalize the statistics that inform VOI, which is necessary given the limited data in geothermal exploration. Except for the Carbonate Aquifer, the highest ranking of the Vimperfect is the Local Structural Setting. Next, the slip and dilation tendency is first for Carbonate Aquifer and second for Central Nevada Seismic Belt and Western Great Basin. For the Carbonate Aquifer, heat flow is has the lowest Vimperfect value compared to the other three domains, which is consistent with the understanding of how heat flow measurements are masked by regional groundwater flow.

Bayesian analysis↗
NASA NTRS1983

Information theory analysis of sensor-array imaging systems for computer vision

Information theory is used to assess the performance of sensor-array imaging systems, with emphasis on the performance obtained with image-plane signal processing. By electronically controlling the spatial response of the imaging system, as suggested by the mechanism of human vision, it is possible to trade-off edge enhancement for sensitivity, increase dynamic range, and reduce data transmission. Computational results show that: signal information density varies little with large variations in the statistical properties of random radiance fields; most information (generally about 85 to 95 percent) is contained in the signal intensity transitions rather than levels; and performance is optimized when the OTF of the imaging system is nearly limited to the sampling passband to minimize aliasing at the cost of blurring, and the SNR is very high to permit the retrieval of small spatial detail from the extensively blurred signal. Shading the lens aperture transmittance to increase depth of field and using a regular hexagonal sensor-array instead of square lattice to decrease sensitivity to edge orientation also improves the signal information density up to about 30 percent at high SNRs.

Huck, F. O.↗
NASA NTRS1993

Federal Communications Commission (FCC) Transponder Loading Data Conversion Software. User's guide and software maintenance manual, version 1.2

This volume contains the complete software system documentation for the Federal Communications Commission (FCC) Transponder Loading Data Conversion Software (FIX-FCC). This software was written to facilitate the formatting and conversion of FCC Transponder Occupancy (Loading) Data before it is loaded into the NASA Geosynchronous Satellite Orbital Statistics Database System (GSOSTATS). The information that FCC supplies NASA is in report form and must be converted into a form readable by the database management software used in the GSOSTATS application. Both the User's Guide and Software Maintenance Manual are contained in this document. This volume of documentation passed an independent quality assurance review and certification by the Product Assurance and Security Office of the Planning Research Corporation (PRC). The manuals were reviewed for format, content, and readability. The Software Management and Assurance Program (SMAP) life cycle and documentation standards were used in the development of this document. Accordingly, these standards were used in the review. Refer to the System/Software Test/Product Assurance Report for the Geosynchronous Satellite Orbital Statistics Database System (GSOSTATS) for additional information.

Mallasch, Paul G.↗
DOE OSTI2020

Neutron scattering in photosynthesis research: recent advances and perspectives for testing crop plants

The photosynthetic performance of crop plants under a variety of environmental factors and stress conditions, at the fundamental level, depends largely on the organization and structural flexibility of thylakoid membranes. These highly organized membranes accommodate virtually all protein complexes and additional compounds carrying out the light reactions of photosynthesis. Most regulatory mechanisms fine-tuning the photosynthetic functions affect the organization of thylakoid membranes at different levels of the structural complexity. In order to monitor these reorganizations, non-invasive techniques are of special value. On the mesoscopic scale, small-angle neutron scattering (SANS) has been shown to deliver statistically and spatially averaged information on the periodic organization of the thylakoid membranes in vivo and/or, in isolated thylakoids, under physiologically relevant conditions, without fixation or staining. More importantly, SANS investigations have revealed rapid reversible reorganizations on the timescale of several seconds and minutes. In this paper, we give a short introduction into the basics of SANS technique, advantages and limitations, and briefly overview recent advances and potential applications of this technique in the physiology and biotechnology of crop plants. We also discuss future perspectives of neutron crystallography and different neutron scattering techniques, which are anticipated to become more accessible and of more use in photosynthesis research at new facilities with higher fluxes and innovative instrumentation.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Enhanced accuracy through ensembling of randomly initialized auto-regressive models for dynamical systems

Computational mechanics simulations using traditional finite element methods (FEM) require prohibitively expensive computational resources for real-time engineering applications, design optimization, and digital twin implementations. While machine learning (ML) surrogate models offer significant computational speedups, autoregressive ML models for time-dependent mechanical systems suffer from error accumulation that compromises long-term prediction reliability - a critical concern for engineering applications where accuracy over extended time horizons is essential for safety and performance assessments. Here, we propose a deep ensemble framework specifically designed to address this challenge in computational mechanics applications, where multiple ML surrogate models with random weight initializations are trained in parallel and their predictions aggregated during inference. This approach leverages statistical diversity to maximize information gain from a fixed set of training data and to mitigate error propagation, while maintaining the computational efficiency that makes ML surrogates attractive for engineering practice. We validate the framework on three representative problems spanning critical areas of computational mechanics: stress field evolution in heterogeneous microstructures under complex loading (relevant to advanced materials design and composite analysis), planetary-scale shallow water dynamics (applicable to environmental and geotechnical engineering), and Gray-Scott reaction-diffusion systems (relevant to mass transport and chemical process engineering). Across all test cases, the ensemble approach demonstrates consistent error reduction of 15-33% compared to individual models. The codes for this work are available on GitHub (https://github.com/Graham-Brady-Research-Group/AutoregressiveEnsemble_SpatioTemporal_Evolution).

autoregressive prediction↗
DOE OSTI2021

Machine learning in materials science: From explainable predictions to autonomous design

The advent of big data and algorithmic developments in the field of machine learning (and artificial intelligence, in general) have greatly impacted the entire spectrum of physical sciences, including materials science. Materials data, measured or computed, combined with various techniques of machine learning have been employed to address a myriad of challenging problems, such as, development of efficient and predictive surrogate models for a range of materials properties, screening and down-selection of novel candidate materials for targeted applications, new methodologies to improve and further expedite molecular and atomistic simulations, with likely many more important developments to come in the foreseeable future. While the applications thus far have provided a glimpse of the true potential data-enabled routes have to offer, it has also become clear that further progress in this direction hinges on our ability to understand, explain and rationalize findings of a machine learning model in light of the domain-knowledge. This focused review provides an overview of the main areas where machine learning has been widely and successfully used in materials science. Subsequently, a brief discussion of several techniques that have been helpful in extracting physically-meaningful insights, causal relationships and design-centric knowledge from materials data is provided. Finally, we identify some of the imminent opportunities and challenges that materials community faces in this exciting and rapidly growing field.

36 MATERIALS SCIENCE↗
DOE OSTI2023

The gallium anomaly

In order to test the end-to-end operations of gallium solar neutrino experiments, intense electron-capture sources were fabricated to measure the responses of the radiochemical SAGE and GALLEX/GNO detectors to known fluxes of low-energy neutrinos. Such tests were viewed at the time as a cross-check, given the many tests of 71 Ge recovery and counting that had been routinely performed, with excellent results. However, the four 51 Cr and 37 Ar source experiments yielded rates below expectations, a result commonly known as the Ga anomaly. As the intensity of the electron-capture sources can be measured to high precision, the neutrino lines they produce are fixed by known atomic and nuclear rates, and the neutrino absorption cross section on 71 Ga is tightly constrained by the lifetime of 71 Ge, no simple explanation for the anomaly has been found. To check these calibration experiments, a dedicated experiment BEST was performed, utilizing a neutrino source of unprecedented intensity and a detector optimized to increase statistics while providing some information on counting rate as a function of distance from the source. The results BEST obtained are consistent with the earlier solar neutrino calibration experiments, and when combined with those measurements, yield a Ga anomaly with a significance of approximately 4𝜎, under conservative assumptions. But BEST found no evidence of distance dependence and thus no explicit indication of new physics. In this review we describe the extensive campaigns carried out by SAGE, GALLEX/GNO, and BEST to demonstrate the reliability and precision of their experimental procedures, including 71 Ge recovery, counting, and analysis. We also describe efforts to define uncertainties in the neutrino capture cross section, which now include estimates of effects at the ≲ 0.5% level such as radiative corrections and weak magnetism. With the results from BEST, an anomaly remains even if one retains only the transition to the 71 Ge ground state, whose strength is fixed by the known lifetime of 71 Ge. We then consider the new-physics solution most commonly suggested to resolve the Ga anomaly, oscillations into a sterile fourth neutrino, 𝜈 𝑒 → 𝜈 𝑠 . We find such a solution generates substantial tension with several null experiments, owing to the large mixing angle required. While this does not exclude such solutions – the sterile sector might include multiple neutrinos as well as new interactions – it shows the need for more experimental constraints, if we are to make progress in resolving the Ga and other low-energy neutrino anomalies. We conclude by consider the role future low-energy electron-capture sources could play in this effort.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

An algorithm to locate the centers of baryon acoustic oscillations

The cosmic structure formed from baryon acoustic oscillations (BAO) in the early universe is imprinted in the galaxy distribution observable in large-scale surveys and is used as a standard ruler in contemporary cosmology. Typically, BAOs are detected as a preferential length scale in two-point statistics, which gives little information about the location of the BAO structures in real space. The aim of the algorithm described in this paper is to find probable centers of BAOs in the cosmic matter distribution. The algorithm convolves the three-dimensional distribution of matter density with a spherical shell kernel of variable radius placed at different locations. The locations that correspond to the highest values of the convolution correspond to the probable centers of BAOs. This method is realized in an open-source, computationally efficient algorithm. Here, we describe the algorithm and present the results of applying it to the SDSS DR9 CMASS survey and associated mock catalogs. A detailed performance study demonstrates the ability of the algorithm to locate BAO centers and in doing so presents a novel detection of the BAO scale in galaxy surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Knowledge-guided learning with curated prior genetic biomarkers for robust model interpretation

Abstract Motivation Knowledge-guided learning offers effective and robust model training strategies in data-scarce settings by incorporating established domain knowledge, thereby enhancing generalization, robustness, and interpretability. By contrast, conventional deep learning approaches rely purely on data-driven learning, which can limit robust model interpretability, particularly in high-dimensional settings with limited size samples. In computational biology, knowledge-guided learning has primarily leveraged network- and structural-based knowledge, leading to biologically interpretable representations and enhanced predictive performance compared to conventional approaches. However, curated biomarkers, one of the most accessible forms of biological knowledge, remain largely unexplored within knowledge-guided paradigms. Results In this study, we propose a model-agnostic training paradigm, Biomarker-driven Explainable Prior-guided Learning (BioExPL), that can be applied to any neural networks that incorporates curated prior knowledge. BioExPL enforces neural networks to reflect curated biomarker priors in their latent representations through a novel knowledge-alignment loss. BioExPL consistently demonstrated significantly improved predictive performance and enhanced model interpretability with minimized computational overhead in simulation studies and intensive experiments on multiple cancer datasets. BioExPL not only integrates prior curated knowledge into the model but also accurately identifies unknown associated signals additionally. BioExPL is model-agnostic and domain-independent, enabling its integration into diverse neural network architectures. Availability and implementation The open-source is publicly available at: https://github.com/datax-lab/BioExPL.

Baek, Beomsu [Department of Computer Science, Univ↗
DOE OSTI2025

Production of neutron-rich heavy nuclei in deep-inelastic 208 Pb + 208 Pb collisions within the stochastic mean-field theory

In deep-inelastic collisions of heavy nuclei, reaction products with a wide range of mass and charge are produced. Such collisions been considered as a possible way to produce superheavy nuclei, as an alternative to fusion reactions. To provide reliable theoretical predictions, it is desired to develop microscopic approaches that correctly and accurately describe nucleon transfer processes in dissipative collisions of heavy nuclei. The purpose of the present work is (1) to investigate the mechanism of nucleon transfers in dissipative collisions of two heavy nuclei, and (2) to explore possible pathways to produce neutron-rich heavy nuclei, through detailed theoretical analyses of fluctuations and correlations in nucleon transfers in 208 Pb + 208 Pb reactions. Three-dimensional time-dependent Hartree-Fock (TDHF) calculations are performed for the collisions of 208 Pb + 208 Pb at 𝐸 c.m. = 832, 936, and 1040 MeV, using the Skyrme SLy4d energy density functional. To calculate fluctuations and correlations in nucleon transfers, we employ the stochastic mean-field (SMF) theory, and the results are compared with another theoretical framework currently available, the time-dependent random phase approximation (TDRPA). Primary and secondary production cross sections are calculated with the SMF theory combined with a statistical model, GEMINI ++ . Using information of nucleon flow across a neck of colliding nuclei in TDHF calculations, we solve quantal diffusion equations for fluctuations and correlations in nucleon transfers based on the SMF theory. From the SMF calculations, we obtain the time evolution of diffusion coefficients as well as fluctuations and correlations in nucleon transfers for a range of initial orbital angular momenta. We compare the results of the SMF calculations with those of TDRPA, showing that TDRPA tends to predict substantially larger fluctuations and correlations in strongly damped collisions of heavy nuclei, which exhibit complex initial angular momentum dependence, while the SMF results provide almost constant (stable) values. Using the obtained fluctuations and correlations, we calculate primary and secondary production cross sections for the 208 Pb + 208 Pb collisions. From the results, we find that both lighter and heavier reaction products as compared to 208 Pb are produced for a wide region in the 𝑁−𝑍 plane as primary products, thanks to the quantal diffusion mechanism in the dissipative collisions. However, we show that cross sections for production of heavy nuclei with 𝑍 ≳ 90 or 𝑁 ≳ 135 are washed out due to secondary particle evaporation and/or fission processes. On the other hand, we find that there remain sizable cross sections for production of neutron-rich nuclei along 𝑁 = 126 with 𝑍< 82, even after secondary disintegration processes. We demonstrate that the secondary production cross sections depend weakly on incident energies, but lower (higher) energy is slightly preferred for production of nuclei with smaller (larger) atomic numbers as compared to 𝑍 = 82. Here, based on the microscopic SMF calculations, it has been shown that deep-inelastic collisions of heavy nuclei, such as 208 Pb + 208 Pb examined in this study, can be a promising means to produce neutron-rich heavy nuclei along 𝑁=126. Discrepancies between the SMF and TDRPA approaches are left unsolved for future investigations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗