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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Ab initio generalized Langevin equation

We introduce a machine learning–based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables (CVs) in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori–Zwanzig formalism, under the constraint of the fluctuation–dissipation theorem. Combined with deep potential molecular dynamics and electronic density functional theory, this approach opens the way to multiscale modeling in a variety of situations. Here, we demonstrate this capability with a study of two mesoscale processes in crystalline lead titanate, namely the field-driven dynamics of a planar ferroelectric domain wall, and the dynamics of an extensive lattice of coarse-grained electric dipoles. In the first case, AIGLE extends the reach of ab initio simulations to a regime of noise-driven motions not accessible to molecular dynamics. In the second case, AIGLE deals with an extensive set of CVs by adopting a local approximation for the memory kernel and retaining only short-range noise correlations. The scheme is computationally more efficient than molecular dynamics by several orders of magnitude and mimics the microscopic dynamics at low frequencies where it reproduces accurately the dominant far-infrared absorption frequency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Coulomb Interaction-Driven Entanglement of Electrons on Helium

The generation and evolution of entanglement in many-body systems is an active area of research that spans multiple fields, from quantum information science to the simulation of quantum many-body systems encountered in condensed matter, subatomic physics, and quantum chemistry. Motivated by recent experiments exploring quantum information processing systems with electrons trapped above the surface of cryogenic noble gas substrates, we theoretically investigate the generation of entanglement between two electrons via their unscreened Coulomb interaction. The model system consists of two electrons confined in separate electrostatic traps that establish microwave-frequency quantized states of their motion. We compute the motional energy spectra of the electrons, as well as their entanglement, by diagonalizing the model Hamiltonian with respect to a single-particle Hartree product basis. We also compare our results with the predictions of an effective Hamiltonian. The computational procedure outlined here can be employed for device design and guidance of experimental implementations. In particular, the theoretical tools developed here can be used for fine-tuning and optimization of control parameters in future experiments with electrons trapped above the surface of superfluid helium or solid neon. Published by the American Physical Society 2024

Physics↗
DOE OSTI2021

Indoor Occupant Counting by RF Backscattering

Building HVAC (heating, ventilation and air conditioning) consumes approximately 13% of all energy consumption in USA. Motion detectors, cameras and user programmable thermostats have been shown to be ineffective for HVAC controls to save energy, mostly due to the user concerns of comfort, reliability and privacy. A new HVAC control system based on real-time occupant counting that is fully automated, highly accurate, economically sensible and preserving privacy and aesthetics can thus bring forth a disruptive impact to this large energy sector. Our indoor occupant monitoring technology is based on the radio-frequency identification system (RFID), deployed in the room, not on the occupants. One reader with four antennas can be deployed on the ceiling or behind the ceiling panels for every thousand square feet in home, office and assisted living, with or without room partitions. The sticker-like passive tag, 10 cents each and maintenance-free, are profusely hidden on the wall or inside the furniture at arbitrary position, preserving privacy and aesthetics. The large number of tags can realize diverse observation points to accommodate arbitrary room layouts, which is impractical by other active units of camera, infrared, radar or lidar. With 20 tags, the system can reliably detect the number of occupants. For 100 tags, occupant posture and location can be known. The technology has been verified in the research labs and test buildings with very high accuracy. When the real-time occupant number can be accurately known without assuming devices on occupants or occupant motion, the building HVAC system can be automated to achieve building energy saving without sacrificing occupant comfort. According to our limited testing in a few types of building models and the simplified cost calculation, the RFID system has low overall cost in production, deployment, operation and maintenance. The signal processing algorithm based on machine learning requires very small number of training cases as most learning is transferrable for various layouts, and very low computational needs during operation, according to our testing in four different room sizes and layouts. In our preliminary estimate from HVAC saving alone, the RFID system can potentially pay for itself within 1.5 years, in addition to the other enhancement in building automation systems (BAS). Our commercialization strategy and business pitch deck focus on venturing this Cornell occupant monitoring technology into BAS and energy management markets. We have identified three broad BAS market segments of senior living, residential buildings, and office buildings. We have put together the minimum viable product characteristics for these identified segments, including analyses on total cost and competing technologies, as well as the fit and technical gaps for these market segments. We intend to bring the technology to market by licensing or partnering with existing BAS vendors. A list of potential collaborators and licensing partner candidates was assembled for different aspects of integrating our technology into a potential product that can be used with BAS.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Physics-Based Real-time Analysis and Control to Achieve Transient-Free Operations for the ITER Era (Final Report)

This is the final report for the early career award for Prof. Egemen Kolemen that aimed to develop the physics and technical basis of real-time transient – i.e. disruptions and Edge Localized Modes (ELMs) – avoidance and feedback control at the DIII-D nuclear fusion facility for the ITER era. During this project, we reconstructed high quality real-time DIII-D equilibria using kinetic information from the motional Stark effect (MSE), Thomson Scattering (TS), and Charge Exchange Recombination (CER) spectroscopy. These equilibria were analyzed in real-time to determine the low-n ideal MHD stability and the pedestal stability thresholds, and to obtain plasma response models. These calculations were used to understand which physical process evolves to lead to the onset of disruption in ITER-relevant scenarios at DIII-D, and how disruption can be predicted using stability analysis as opposed to the current methods of correlation of various signals, which are descriptive but lack predictive power. In the disruption studies, we focused on tearing modes, since these constitute the vast majority of disruptions in this regime. With this knowledge, real-time disruption avoidance algorithms were developed and tested. The enhanced situation awareness and physics insight were used in advanced real-time feedback control of pedestal and core profiles, which allowed the pursuit and sustainment of transient-free high-confinement regimes that cannot be achieved via feed-forward design based on in-between shot analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Self-Propulsion Enhances Polymerization

Self-assembly is a spontaneous process through which macroscopic structures are formed from basic microscopic constituents (e.g., molecules or colloids). By contrast, the formation of large biological molecules inside the cell (such as proteins or nucleic acids) is a process more akin to self-organization than to self-assembly, as it requires a constant supply of external energy. Recent studies have tried to merge self-assembly with self-organization by analyzing the assembly of self-propelled (or active) colloid-like particles whose motion is driven by a permanent source of energy. Here we present evidence that points to the fact that self-propulsion considerably enhances the assembly of polymers: self-propelled molecules are found to assemble faster into polymer-like structures than non self-propelled ones. The average polymer length increases towards a maximum as the self-propulsion force increases. Beyond this maximum, the average polymer length decreases due to the competition between bonding energy and disruptive forces that result from collisions. The assembly of active molecules might have promoted the formation of large pre-biotic polymers that could be the precursors of the informational polymers we observe nowadays.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Semi-empirical simulation of in-motion radiation detection systems

The Replicative Assessment of Spectroscopic Equipment (RASE) is an open-source software that uses experimental data as the basis to simulate the response of commercial radiation detectors to sources in various situations, particularly in the context of nuclear security and safeguards applications. Dynamic RASE introduces the capability to simulate scenarios where sources and detector are in relative motion. Position-dependent experimentally acquired gamma spectra are ingested by Dynamic RASE to build maps that describe the detector response over all space. These response maps are used to replicate the time-dependent energy spectra collected as sources move on a path near the detector. Here, a Gaussian process is used to build each map, incorporating a novel kernel adapted to the special case of radiation detection. The approach has been validated against experimental data acquired using a NaI-based detector for 137 Cs and 54 Mn sources. The capability to create accurate simulations using either long-dwell static measurements or dynamic pass-by measurements as source data has been demonstrated. Quantitative relative performance, benefits, and shortcomings are discussed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2020

Hypothetical Efficiency of Electrical to Mechanical Energy Transfer during Individual Stochastic Molecular Switching Events

There are now many examples of single molecule rotors, motors and switches in the literature that, when driven by photons, electrons or chemical reactions, exhibit well defined motions. As a step towards using these single molecule devices to perform useful functions one must understand how they interact with their environment and quantify their ability to perform work on it. Using a single molecule rotary switch we examine the transfer of electrical energy, delivered via electron tunneling, to mechanical motion and measure the forces the switch experiences with a non-contact q-plus atomic force microscope. Action spectra reveal that the molecular switch has two stable states and can be excited resonantly between them at a bias of 100 mV via a one-electron inelastic tunneling process which corresponds to an energy input of 16 zepto Joules. Furthermore, while the electrically induced switching events are stochastic and no net work is to done on the cantilever, by measuring the forces between the molecular switch and the AFM cantilever we can derive the maximum hypothetical work the switch could perform during a single switching event which is ~55 meV, equal to 8.9 zepto Joules which translates to a hypothetical efficiency ~55% per individual inelastic tunneling electron induced switching event. When co considering the total electrical energy input this drops to 1x10 -7 % due to elastic tunneling events that dominate the tunneling current. However, this approach constitutes a general method for quantifying and comparing the energy input and output of molecularmechanical devices.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Operando neutron diffraction reveals mechanisms for controlled strain evolution in 3D printing

Abstract Residual stresses affect the performance and reliability of most manufactured goods and are prevalent in casting, welding, and additive manufacturing (AM, 3D printing). Residual stresses are associated with plastic strain gradients accrued due to transient thermal stress. Complex thermal conditions in AM produce similarly complex residual stress patterns. However, measuring real-time effects of processing on stress evolution is not possible with conventional techniques. Here we use operando neutron diffraction to characterize transient phase transformations and lattice strain evolution during AM of a low-temperature transformation steel. Combining diffraction, infrared and simulation data reveals that elastic and plastic strain distributions are controlled by motion of the face-centered cubic and body-centered cubic phase boundary. Our results provide a new pathway to design residual stress states and property distributions within additively manufactured components. These findings will enable control of residual stress distributions for advantages such as improved fatigue life or resistance to stress-corrosion cracking.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Spin-lattice and spin-electronic interactions in the van der Waals semiconductor C⁢o 2 ⁢P 2 ⁢S 6

Here, we report the results of a temperature-dependent reflection spectroscopy study, across a wide energy range (~ 0.01 to 3 eV), of unsubstituted and 40% Zn substituted for Co, for the transition-metal phosphorus trichalcogenide, C⁢o 2 ⁢P 2 ⁢S 6 . We observe a transition from a paramagnetic to antiferromagnetic state with a Néel temperature at T N ~ 120 K that is completely suppressed in Zn-substituted samples. At 300 K we identify four narrow (~ 1 meV) infrared active phonon modes while at 70 K (below T N ) we observe that the low-energy phonons, dominated by Co motion, resolve into two modes. These low-energy modes are asymmetric, indicating coupling to a broad electronic continuum. We also report a broad (~ 30 meV) low-temperature infrared absorption band that appears near T N that we suggest is determined by a multiphonon-assisted 2-magnon absorption process. At 300 K in higher-energy spectra, we observe considerable absorption starting from 0.20 ± 0.02 eV which we associate with inter-C⁢o 2+ ion 3⁢d transitions. At temperatures below T N the number of electronic absorption bands increases from 4 to 6, indicating a lowering of the symmetry around the C⁢o 2+ ions. On substituting 40% Zn for Co, the antiferromagnetic transition is suppressed along with temperature-dependent changes in the phonon and electronic spectra. The temperature-dependent spectral changes indicate strongly correlated behavior between the infrared active lattice vibrations, the electronic excitations, and magnetism in unsubstituted C⁢o 2 ⁢P 2 ⁢S 6 .

2-dimensional systems↗
DOE OSTI2020

Theory Manual for the Fuel Cycle Analysis Code REBUS

REBUS is a system of programs designed for the fuel cycle analysis of fast reactors and accelerator-driven systems. The first version of REBUS was developed in 1970 for calculating the equilibrium operating conditions of liquid metal fast breeder reactors. During the past five decades, various extensions and refinements have been made in the simulation of material motions in fuel cycle facilities and the solution of the neutronics and isotopic transmutation equations that govern the reactor behavior. The latest version complies with the standard code practices and interface dataset specifications of the committee on computer code coordination (CCCC). This report provides a detailed description of the physical processes and their mathematical models and solution methods of the current production version of REBUS. The models of the facilities and physical processes involved in fast reactor fuel cycle are first discussed. Then the mathematical formulation of these physical models is presented, followed by detailed discussions of solution methods of the resulting set of equations. Finally the output edit quantities are discussed along with their definitions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Fragmentation in Gravitationally Unstable Collapsar Disks and Subsolar Neutron Star Mergers

Abstract Although stable neutron stars (NSs) can in principle exist down to massesM ns ≈ 0.1M ⊙ , standard models of stellar core-collapse predict a robust lower limitM ns ≳ 1.2M ⊙ , roughly commensurate with the Chandrasekhar massM Ch of the progenitor’s iron core (electron fractionY e ≈ 0.5). However, this limit may be circumvented in sufficiently dense neutron-rich environments (Y e < 0.5) for which M Ch ∝ Y e 2 is reduced to ≲1M ⊙ . Such physical conditions could arise in the black hole accretion disks formed from the collapse of rapidly rotating stars (“collapsars”), as a result of gravitational instabilities and cooling-induced fragmentation, similar to models for planet formation in protostellar disks. We confirm that the conditions to form subsolar-mass NS (ssNS) may be marginally satisfied in the outer regions of massive neutrino-cooled collapsar disks. If the disk fragments into multiple ssNSs, their subsequent coalescence offers a channel for precipitating subsolar mass LIGO/Virgo gravitational-wave mergers that does not implicate primordial black holes. The model makes several additional predictions: (1) ∼Hz frequency Doppler modulation of the ssNS-merger gravitational-wave signals due to the binary’s orbital motion in the disk; (2) at least one additional gravitational-wave event (coincident within ≲hours), from the coalescence of the ssNS-merger remnant(s) with the central black hole; (3) an associated gamma-ray burst and supernova counterpart, the latter boosted in energy and enriched withr-process elements from the NS merger(s) embedded within the exploding stellar envelope (“kilonovae inside a supernova”).

Astronomy & Astrophysics↗
DOE OSTI2026

One-Body Properties and Their Perturbative Accuracy with Aufbau Suppressed Coupled Cluster Theory

In this work we derived and implemented the calculation of the one-body reduced density matrix for Aufbau suppressed coupled cluster theory, from which excited state natural orbitals and one-body properties, like atomic populations and dipole moments, are obtained. We utilized the natural orbitals to refine the ASCC solution for simple valence and Rydberg systems, exploring the process of repeatedly solving the ASCC equations in successive natural orbital bases to achieve independence from the starting molecular orbitals. For dipole moments in small molecules where high-level comparison data is available, we find that the accuracy of ASCC essentially matches that of linear response and equation-of-motion coupled cluster as long as care is taken to preserve the response's perturbative completeness.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

General Testing Setup for Hyperelastic Transducers-DEEC-Tec & Marine Renewable Energy: Preprint

Distributed embedded energy conversion technologies (DEEC-Tec), an emerging domain for ocean wave energy conversion technology, is showing promise for a range of applications. Research is being conducted at the National Renewable Energy Laboratory that leverages this domain to investigate the potential of ocean wave energy converters (WECs) constructed from hyperelastic forms of distributable and embeddable energy transducers. These transducers are available in forms such as disks, rectangles, or hexagons and can be combined in various ways to form energy-producing metamaterials and flexible WECs. DEEC-Tec, therefore, could open doors that enhance ocean wave energy conversion in ways not previously thought possible by allowing for many WEC topologies and morphologies. However, the same diversity and adaptability pose challenges for the development of these DEEC-Tec-oriented hyperelastic transducers. A commercial tensile testing setup was not found that was adaptable enough to accommodate the varied transducers while providing precise force control, range of motion, and noncontact data collection. Because of this lack, a comprehensive test rig was designed in house to be used with a 3D laser scanning device-providing contactless measurements while also allowing for different geometries and various uniaxial loadings. This paper and presentation will discuss these unique challenges and the processes for overcoming them to provide a robust and general testing setup for hyperelastic transducers, of any form, for the DEEC-Tec marine renewable energy domain.

DEEC-Tec↗
DOE OSTI2025

Divergent evolution of slip banding in CrCoNi alloys

Abstract Metallic materials under high stress often exhibit deformation localization, manifesting as slip banding. Over seven decades ago, Frank and Read introduced the well-known model of dislocation multiplication at a source, explaining slip band formation. Here, we reveal two distinct types of slip bands (confined and extended) in compressed CrCoNi alloys through multi-scale testing and modeling from microscopic to atomic scales. The confined slip band, characterized by a thin glide zone, arises from the conventional process of repetitive full dislocation emissions at Frank–Read source. Contrary to the classical model, the extended band stems from slip-induced deactivation of dislocation sources, followed by consequent generation of new sources on adjacent planes, leading to rapid band thickening. Our findings provide insights into atomic-scale collective dislocation motion and microscopic deformation instability in advanced structural materials.

Science & Technology - Other Topics↗
DOE OSTI2022

Dynamics of the gold–silicon eutectic reaction studied at limited length scales using in situ $\mathrm{TEM}$ and $\mathrm{STEM}$

We report the dynamics of the gold–silicon eutectic reaction in limited dimensions were studied using in situ transmission electron microscopy and scanning transmission electron microscopy heating experiments. The phase transformation, viewed in both plan-view and cross-section of the film, occurs through a complex combination of dislocation and grain boundary motion and diffusion of silicon along gold grain boundaries, which results in a dramatic change in the microstructure of the film. The conversion observed in cross-section shows that the eutectic mixture forms at the Au–Si interface and proceeds into the Au film at a discontinuous growth rate. This complex process can lead to a variety of microstructures depending on sample geometry, heating temperature, and the ratio of gold to silicon which was found to have the largest impact on the eutectic microstructure. The eutectic morphology varied from dendrites to hollow rectangular structures to Au–Si eutectic agglomerates with increasing silicon to gold ratio.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Co-Firing Switchgrass and Waste Coal in A Power Plant: A Techno-Economic and Life Cycle Evaluation for The Ohio River Valley (SWITCH) (Final Technical Report for Ohio State/FE0032204)

Abandoned coal mine lands (AMLs) represent one of the most persistent environmental challenges in the United States. Prior to the enactment of the Surface Mining Control and Reclamation Act (SMCRA) in 1977, coal mining operations were not legally required to reclaim disturbed lands, leaving behind approximately 500,000 AML sites nationwide. These sites pose severe environmental and health risks, including acid mine drainage, soil and water contamination, and spontaneous combustion of waste coal piles. Millions of Americans live within one mile of these AMLs, underscoring the urgency of remediation. Traditional reclamation practices, such as planting cool-season grasses, often fail to fully restore ecological function or leverage the economic potential of these lands. This project addressed these challenges by developing integrated strategies for resource recovery, land reclamation, and sustainable energy production. This project evaluated an integrated strategy to convert this liability into an opportunity by recovering waste coal and co-firing it with switchgrass (Panicum virgatum L.) cultivated on reclaimed or marginal AML areas in existing coal-fired power plants. Switchgrass not only provides a renewable feedstock but also aids in land reclamation and carbon sequestration. 1) Remote Sensing and Machine Learning for Waste Coal Identification Using Sentinel-2 satellite imagery and supervised classification, we applied four machine learning models to detect historical waste coal piles. Random Forest achieved the highest accuracy (precision: 86%, recall: 77%). Time-series analysis revealed gradual vegetation recovery since 1986, indicating natural reclamation processes in historical sites, while active mining areas showed ongoing disturbance. This workflow enables scalable monitoring and prioritization of reclamation efforts. 2) UAS-Based Stockpile Volume Estimation To quantify recoverable waste coal, we evaluated Unmanned Aerial Systems (UAS) equipped with Light Detection and Ranging (LiDAR) and multispectral sensors. Structure-from-Motion (SfM) photogrammetry combined with interpolated Digital Terrain Models (DTMs) achieved strong agreement with LiDAR reference volumes (Root Mean Square Error (RMSE) ≈147 m 3 , Mean Absolute Percentage Error (MAPE) ≈2%). Sensitivity analysis confirmed that spatial resolution significantly influences accuracy, emphasizing the need for high-resolution data for precise volume estimation. This approach offers a scalable, cost-effective, and accurate alternative to conventional ground-based surveys. 3) Switchgrass Cultivation for Bioenergy and Water Quality Improvement We assessed the hydrological and water quality impacts of converting AMLs to switchgrass production areas using the Soil and Water Assessment Tool (SWAT). Results showed that converting 10% of the watershed area into the switchgrass production zone reduced streamflow by 3.1%, total suspended solids by 18.1%, total nitrogen by 7.6%, and total phosphorus by 6.2%, while achieving biomass yields of 8.6–9.2 metric tons per hectare. These findings highlight switchgrass as a dual-benefit strategy for land reclamation and bioenergy feedstock production. 4) Integrated Co-Firing and CCS for Carbon-Negative Power Generation We modeled co-firing scenarios using the Power Plant Flexible Model (PPFM) to evaluate plant efficiency, greenhouse gas (GHG) emissions, and levelized cost of electricity (LCOE). Without carbon capture and storage (CCS), increasing switchgrass co-firing ratios reduced LCOE from $\$$150/MWh at 0% biomass to $\$$110/MWh at full substitution. Under CCS, costs remained higher (~$\$$250/MWh at 0% biomass) but decreased to $\$$200/MWh at 100% biomass, while enabling net-zero or carbon-negative electricity due to switchgrass sequestration benefits. Although CCS introduced efficiency penalties, pairing it with biomass co-firing offset these impacts and maximized climate benefits. Overall, optimizing co-firing ratios between 60-100%, supported by reliable logistics and storage strategies, emerged as a practical pathway to balance affordability, sustainability, and net-zero or negative GHG emissions while promoting productive reuse of AMLs.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2025

In-Situ Synchrotron X-Ray Diffraction of Ultrasonic Microstructural Refinement During Solidification in a Commercial Al–Si–Mg Alloy

This study reports the first use of in-situ synchrotron X-ray diffraction (SXRD) to study the effects of ultrasonic melt processing (USMP) on phase and grain size evolution during solidification in a commercial Al–Si–Mg casting alloy. USMP is a technique that, when applied to aluminum as it solidifies, can be used to refine the local microstructure of large-scale castings. Analysis of the in-situ SXRD data to estimate the average grain size of primary α-Al grains during USMP demonstrates that USMP slows the growth rate of α-Al grains and reduces grain size by 36 pct. Furthermore, there is also evidence that USMP causes the primary α-Al grains to move relative to the X-ray beam; such motion increases the probability of primary α-Al grains colliding and fragmenting. This movement becomes constrained at the onset of the Al–Si binary eutectic, suggesting that USMP ceases to effectively refine the microstructure once the Al–Si binary eutectic begins to form. Complementary laboratory-scale X-ray diffraction (XRD) data were used to correlate the lattice parameters of the α-Al and Si (D-A4) phases with temperature to estimate cooling rate during solidification. Thus, this study can guide the design of novel castings with spatially distributed fine-grained regions produced using local ultrasonic processing.

Aluminum Alloys↗
DOE OSTI2024

Generative deep-learning reveals collective variables of Fermionic systems

Complex processes of fermionic systems ranging from protein folding to nuclear fission often follow a low-dimensional reaction path parametrized in terms of a few collective variables. In nuclear theory, variables related to the shape of the nuclear density in a mean-field picture are key to describing the large amplitude collective motion of the neutrons and protons. Exploring the adiabatic energy landscape spanned by these degrees of freedom reveals the possible reaction channels while simulating the dynamics in this reduced space yields their respective probabilities. Unfortunately, this theoretical framework breaks down whenever the systems encounters a quantum phase transition with respect to the collective variables. Here, in this study, we introduce a novel generative deep-learning algorithm designed to build reaction paths that ensure that the many-fermion wave function stays differentiable with respect to the collective variables. This approach is applicable to any fermionic system described by a coherent state. We use the case of potential energy curves in the 16 O nucleus within the Hartree-Fock theory to illustrate its main features.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗