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DOE OSTI2025

Strong Correlation DMRG and DFT

This project developed new ways to improve computer simulations of materials where electrons interact strongly with each other, a challenge for today’s most widely used method, density functional theory (DFT). We used an exact numerical method, the density matrix renormalization group (DMRG), to create highly accurate reference results for simple model systems, and used these to test DFT, prove when it will converge, and even train machine-learned functionals. We also invented new kinds of localized basis functions (“gausslets” and “multi-sliced gausslets”) and a “sliced-basis” approach that make high-accuracy simulations faster and more practical. These methods were applied to extended hydrogen systems, enabling the direct derivation of accurate low-energy models from first-principles calculations. We also introduced a new formalism, Conditional-Probability DFT, which could bypass traditional approximations. The tools and results from this work, including open-source software releases, will help scientists design and understand complex quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2017

Sensitivity analysis for III–V/Si tandem solar cells: A theoretical study

Material and structural parameters may affect the efficiency of a tandem solar cell differently from the way they do in a single-junction solar cell. Here, we fabricated a III–V/Si four-terminal tandem solar cell and developed an opto-electronic model simulating this device. The optical properties were simulated with the transfer matrix method, while the electrical properties were simulated using the numerical device simulator PC1D. For this simulated tandem structure, we determined the parameters which have the largest potential impact on the device efficiency. A sensitivity analysis of the impact of these parameters on the device efficiency was also performed. Furthermore, to reduce the cost of the tandem solar cells, we identified the parameters that do not require tight control during the manufacturing process. The Si cell was simulated both as a single-junction cell and as the bottom cell of a tandem device. Lastly, we determined those device parameters that are more critical in a tandem configuration than in a single-junction configuration.

14 SOLAR ENERGY↗

DOE OSTI2015

Liquid-phase diffusion bonding: Temperature effects and solute redistribution in high temperature lead-free composite solders

Liquid-phase diffusion bonding (LPDB) is being studied as the primary phenomena occurring in the development of a high temperature lead-free composite solder paste composed of gas-atomized Cu-10Ni, wt.% (Cu-11Ni, at.%) powder blended with Sn-0.7Cu-0.05Ni-0.01Ge (Sn-1.3Cu-0.1Ni-0.02Ge, at.%) Nihon-Superior SN100C solder powder. Powder compacts were used as a model system. LPDB promotes enhanced interdiffusion of the low-melting alloy matrix with the solid Cu-10Ni reinforcement powder above the matrix liquidus temperature. The initial study involved the effective intermetallic compound (IMC) compositions and microstructures that occur at varying reflow temperatures and times between 250-300°C and 30-60s, respectively. Certain reflow temperatures encourage adequate interdiffusion to form a continuous highly-conductive network throughout the composite solder joints. The diffusion of nickel, in particular, has a disperse pattern that foreshadows the possibility of a highly-conductive low-melting solder that can be successfully utilized at high temperatures.

42 ENGINEERING↗

DOE OSTI2021

Impact of three-body forces on elastic nucleon-nucleus scattering observables

In a previous series of papers we investigated the domain of applicability of chiral potentials to the construction of a microscopic optical potential (OP) for elastic nucleon-nucleus scattering. The OP was derived at the first order of the spectator expansion of the Watson multiple scattering theory and its final expression was a folding integral between the nucleon-nucleon ( N N ) t matrix and the nuclear density of the target. In the calculations N N and three-nucleon ( 3 N ) chiral interactions were used for the target density and only the N N interaction for the N N t matrix. The purpose of this study is to achieve another step towards the calculation of a more consistent OP introducing the 3 N force also in the dynamic part of the OP. The full treatment of the 3 N interaction is beyond our present capabilities. Thus, here it is approximated with a density dependent N N interaction obtained after the averaging over the Fermi sphere. In practice, in our model the 3 N force acts as a medium correction of the bare N N interaction used to calculate the t matrix. Even if the 3 N force is treated in an approximate way, this method naturally extends our previous model of the OP and allows a direct comparison of our present and previous results. We consider as case studies the elastic scattering of nucleons off C 12 and O 16 . We present results for the differential cross section and the spin observables for different values of the projectile energy. From the comparison with the experimental data and with the results of our previous model we assess the importance of the 3 N interaction in the dynamic part of the OP. Conclusions: Our analysis indicates that the contribution of the 3 N force in the t matrix is small for the differential cross section and it is sizable for the spin observables, in particular, for the analyzing power. We find that the two-pion exchange term is the major contributor to the 3 N force. A chiral expansion order-by-order analysis of the scattering observables confirms the convergence of our results at the next-to-next-to-next-to-leading-order, as already established in our previous work.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Genomic selection in algae with biphasic lifecycles: A Saccharina latissima (sugar kelp) case study

Introduction Sugar kelp ( Saccharina latissima ) has a biphasic life cycle, allowing selection on both thediploid sporophytes (SPs) and haploid gametophytes (GPs). Methods We trained a genomic selection (GS) model from farm-tested SP phenotypic data and used a mixed-ploidy additive relationship matrix to predict GP breeding values. Topranked GPs were used to make crosses for further farm evaluation. The relationship matrix included 866 individuals: a) founder SPs sampled from the wild; b) progeny GPs from founders; c) Farm-tested SPs crossed from b); and d) progeny GPs from farm-tested SPs. The complete pedigree-based relationship matrix was estimated for all individuals. A subset of founder SPs ( n = 58) and GPs ( n = 276) were genotyped with Diversity Array Technology and whole genome sequencing, respectively. We evaluated GS prediction accuracy via cross validation for SPs tested on farm in 2019 and 2020 using a basic GBLUP model. We also estimated the general combining ability (GCA) and specific combining ability (SCA) variances of parental GPs. A total of 11 yield-related and morphology traits were evaluated. Results The cross validation accuracies for dry weight per meter ( r ranged from 0.16 to 0.35) and wet weight per meter ( r ranged 0.19 to 0.35) were comparable to GS accuracy for yield traits in terrestrial crops. For morphology traits, cross validation accuracy exceeded 0.18 in all scenarios except for blade thickness in the second year. Accuracy in a third validation year (2021) was 0.31 for dry weight per meter over a confirmation set of 87 individuals. Discussion Our findings indicate that progress can be made in sugar kelp breeding by using genomic selection.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2018

Heavy Physics Contributions to Neutrinoless Double Beta Decay from QCD

Observation of neutrinoless double beta decay, a lepton number violating process that has been proposed to clarify the nature of neutrino masses, has spawned an enormous world-wide experimental effort. Relating nuclear decay rates to high-energy, beyond the standard model (BSM) physics requires detailed knowledge of nonperturbative QCD effects. Using lattice QCD, we compute the necessary matrix elements of short-range operators, which arise due to heavy BSM mediators, that contribute to this decay via the leading order 𝜋 − → 𝜋 + exchange diagrams. Utilizing our result and taking advantage of effective field theory methods will allow for model-independent calculations of the relevant two-nucleon decay, which may then be used as input for nuclear many-body calculations of the relevant experimental decays. Furthermore, contributions from short-range operators may prove to be equally important to, or even more important than, those from long-range Majorana neutrino exchange.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Status of SAS4A/SASSYS-1 Software Development and Application (FY2024)

SAS4A/SASSYS-1 is a simulation tool used to perform deterministic analysis of anticipated events as well as design basis and beyond design basis accidents for advanced liquid-metal-cooled nuclear reactors. With its origin as SAS1A in the late 1960s, the SAS series of codes has been under continuous use and development for over fifty years. It has been identified as a critical element of safety analysis capabilities for the U.S. Department of Energy and is utilized within industry to perform the transient safety analyses required to support the licensing of Liquid Metal-cooled Fast Reactors (LMFRs). This report summarizes the code development and update activities carried out during FY2024. In FY2024, programmatic activities focused on key improvements to software useability, such as enhanced user interfaces for reactivity feedback modeling, improvements in stability/useability of the Code Manual, and improvements to the acceptance testing infrastructure, including automation of acceptance testing and generation of the Acceptance Testing Report. To support end user applications, an open training was held, a semi-public forum was maintained, and a practical benchmarking and validation matrix was developed which allowed limitations of existing testing capabilities to be assessed. The existing fuel models were also enhanced with improved modeling capabilities and testing for the oxide and annular fuel models.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2017

Zinc sparks induce physiochemical changes in the egg zona pellucida that prevent polyspermy

During fertilization or chemically-induced egg activation, the mouse egg releases billions of zinc atoms in brief bursts known as ‘zinc sparks.’ The zona pellucida (ZP), a glycoprotein matrix surrounding the egg, is the first structure zinc ions encounter as they diffuse away from the plasma membrane. Following fertilization, the ZP undergoes changes described as ‘hardening’, which prevent multiple sperm from fertilizing the egg and thereby establish a block to polyspermy. A major event in zona hardening is cleavage of ZP2 proteins by ovastacin; however, the overall physiochemical changes contributing to zona hardening are not well understood. Using x-ray fluorescence microscopy, transmission and scanning electron microscopy, and biological function assays, we tested the hypothesis that zinc release contributes to ZP hardening. We found that the zinc content in the ZP increases by 300% following activation and that zinc exposure modulates the architecture of the ZP matrix. Importantly, zinc-induced structural changes of the ZP have a direct biological consequence; namely, they reduce the ability of sperm to bind to the ZP. These results provide a paradigm-shifting model in which fertilization-induced zinc sparks contribute to the polyspermy block by altering conformations of the ZP matrix. Finally, this adds a previously unrecognized factor, namely zinc, to the process of ZP hardening.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2017

Development of the self-consistent approximation and its application to the problem of magnetoelastic resonance in an inhomogeneous medium

Our previously proposed approximation involving both the first and second terms of the expansion of the vertex function is generalized to the system of two interacting wavefields of different physical nature. A system of self-consistent equations for the matrix Green’s function and matrix vertex function is derived. On the basis of this matrix generalization of the new self-consistent approximation, a theory of magnetoelastic resonance is developed for a ferromagnetic model, where the magnetoelastic coupling parameter ε(x) is inhomogeneous. Equations for magnetoelastic resonance are analyzed for one-dimensional inhomogeneities of the coupling parameter. The diagonal and off-diagonal elements of the matrix Green’s function of the system of coupled spin and elastic waves are calculated with the change in the ratio between the average value ε and rms fluctuation Δε of the coupling parameter between waves from the homogeneous case (ε ≠ 0, Δε = 0) to the extremely randomized case (ε = 0, Δε ≠ 0) at various correlation wavenumbers of inhomogeneities k{sub c}. For the limiting case of infinite correlation radius (k{sub c} = 0), in addition to approximate expressions, exact analytical expressions corresponding to the summation of all diagrams of elements of the matrix Green’s function are obtained. The results calculated for an arbitrary k{sub c} value in the new self-consistent approximation are compared to the results obtained in the standard self-consistent approximation, where only the first term of the expansion of the vertex function is taken into account. It is shown that the new approximation corrects disadvantages of the Green’s functions calculated in the standard approximation such as the dome shape of resonances and bends on the sides of resonance peaks. The appearance of a fine structure of the spectrum in the form of a narrow resonance on the Green’s function of spin waves and a narrow antiresonance on the Green’s function of elastic waves, which was previously predicted in the standard self-consistent approximation, is confirmed. With an increase in the parameter k{sub c}, the Green’s functions calculated in the standard and new approximations approach each other and almost coincide with each other at k{sub c}/k ≥ 0.5. At the same time, the results of this work indicate that the new self-consistent approximation has a certain advantage for studying the problems of stochastic radiophysics in media with long-wavelength inhomogeneities (small k{sub c} values), because it describes both the shape and width of peaks much better than the standard approximation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2013

Leptogenesis with heavy neutrino flavours: from density matrix to Boltzmann equations

Leptogenesis with heavy neutrino flavours is discussed within a density matrix formalism. We write the density matrix equation, describing the generation of the matter-antimatter asymmetry, for an arbitrary choice of the right-handed (RH) neutrino masses. For hierarchical RH neutrino masses lying in the fully flavoured regimes, this reduces to multiple-stage Boltzmann equations. In this case we recover and extend results previously derived within a quantum state collapse description. We confirm the generic existence of phantom terms. However, taking into account the effect of gauge interactions, we show that they are washed out at the production with a wash-out rate that is halved compared to that one acting on the total asymmetry. In the N{sub 1}-dominated scenario they cancel without contributing to the final baryon asymmetry. In other scenarios they do not in general and they have to be taken into account. We also confirm that there is a (orthogonal) component in the asymmetry produced by the heavier RH neutrinos which completely escapes the washout from the lighter RH neutrinos and show that phantom terms additionally contribute to it. The other (parallel) component is washed out with the usual exponential factor, even for weak washout. Finally, as an illustration, we study the two RH neutrino model in the light of the above findings, showing that phantom terms can contribute to the final asymmetry also in this case.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

In this work, we present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system’s governing equations to identify a coordinate transformation in which the system dynamics have quadratic structure. This transformation is called a lifting map because it often adds auxiliary variables to the system state. The lifting map is applied to data obtained by evaluating a model for the original nonlinear system. This lifted data is projected onto its leading principal components, and low-dimensional linear and quadratic matrix operators are fit to the lifted reduced data using a least-squares operator inference procedure. Analysis of our method shows that the Lift & Learn models are able to capture the system physics in the lifted coordinates at least as accurately as traditional intrusive model reduction approaches. This preservation of system physics makes the Lift & Learn models robust to changes in inputs. Numerical experiments on the FitzHugh–Nagumo neuron activation model and the compressible Euler equations demonstrate the generalizability of our model.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Quasi-parton distribution functions: A study in the diquark spectator model

A set of quasi-parton distribution functions (quasi-PDFs) have been recently proposed by Ji. Defined as the matrix elements of equal-time spatial correlations, they can be computed on the lattice and should reduce to the standard PDFs when the proton momentum P z is very large. Since taking the P z → ∞ limit is not feasible in lattice simulations, it is essential to provide guidance for what values of P z the quasi-PDFs are good approximations of standard PDFs. Within the framework of the spectator diquark model, we evaluate both the up and down quarks' quasi-PDFs and standard PDFs for all leading-twist distributions (unpolarized distribution f 1 , helicity distribution g 1 , and transversity distribution h 1 ). We find that, for intermediate parton momentum fractions x, quasi-PDFs are good approximations to standard PDFs (within 20–30) when P z ≳ 1.5–2 GeV. On the other hand, for large x ~ 1 much larger P z > 4 GeV is necessary to obtain a satisfactory agreement between the two sets. We further test the Soffer positivity bound, and find that it does not hold in general for quasi-PDFs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2014

SU-E-T-380: Particle Microdosimetry Study Based On 3D-Cylindrical Silicon Radiaton Detectors

Purpose: A new design of a solid-state-microdetector based on silicon 3D microfabrication and its performance to characterise Lineal energy, Specific Energy, dose, LET and other microdosimetric variables required for modelling particle relative biological effectiveness (RBE) is presented. Methods: A microdosimeter formed by a matrix of independent sensors with well-defined micrometric cylindrical shape and with a volume similar to those of cellular dimensions is used to measure microdosimetric variables. Each sensor measures the radiation deposited energy which, divided by the mean cord length of the sensors, provides us with the Linear Energy (y) of the radiation as well as its energy distribution, and frequencymean. Starting from the these distributions in different points of a proton beam, we generate biophysical data (e.g. Linear Energy Transfer (LET), Specific Energy (z), etc…) needed for relative biological effectiveness (RBE) calculations radiation effect models used in particle radiotherapy treatment planning. In addition, a Tissue Equivalent Proportional Counter (TEPC) will be used as baseline to calibrate the “y” magnitude of the microdosimeter unit-cells. Results: The experimental measurements will soon be carried out at the Perelman Center for Advanced Medicine (University of Pennsylvania), which provides proton beam for clinical research proposals. The results of distributions measured of the microdosimetric variables from the first tests developed in the proton facility will be presented and compared with Monte Carlo simulations using the Geant4 code. Conclusion: The use of 3D microdosimeters such as the one presented here will enhance the accuracy of RBE calculations normally affected by the inherent uncertainty of monte carlo simulations due to the approximation of material composition and energy dependent physical laws involved in such calculations. The effect of such approximations will be quatified by comparison with absolute measurement of radiation quality parameters.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2021

Comparative study of He 6 β -decay based on different similarity-renormalization-group evolved chiral interactions

We report on a study of the Gamow-Teller matrix element contributing to ${}^6$He $\beta$-decay with similarity renormalization group (SRG) versions of momentum- and configuration-space two-nucleon interactions. These interactions are derived from two different formulations of chiral effective field theory ($\chi$EFT) -- without and with the explicit inclusion of $\Delta$-isobars. We consider evolution parameters $\Lambda_{\rm SRG}$ in the range between 1.2 and 2.0 fm$^{-1}$ and, for the $\Delta$-less case, also the unevolved (bare) interaction. The axial current contains one- and two-body terms, consistently derived at tree level (no loops) in the two distinct $\chi$EFT formulations we have adopted here. The ${}^6$He and ${}^6$Li ground-state wave functions are obtained from hyperspherical-harmonics (HH) solutions of the nuclear many-body problem. In $A\,$=$\,6$ systems, the HH method is limited at present to treat only two-body interactions and non-SRG evolved currents. Our results exhibit a significant dependence on $\Lambda_{\text{SRG}}$ of the contributions associated with two-body currents, suggesting that a consistent SRG-evolution of these is needed in order to obtain reliable estimates. We also show that the contributions from one-pion-exchange currents depend strongly on the model (chiral) interactions and on the momentum- or configuration-space cutoffs used to regularize them. These results might prove helpful in clarifying the origin of the sign difference recently found in No-Core-Shell-Model and Quantum Monte Carlo calculations of the ${}^6$He Gamow-Teller matrix element.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Tensor renormalization group for fermions

Abstract We review the basic ideas of the tensor renormalization group method and show how they can be applied for lattice field theory models involving relativistic fermions and Grassmann variables in arbitrary dimensions. We discuss recent progress for entanglement filtering, loop optimization, bond-weighting techniques and matrix product decompositions for Grassmann tensor networks. The new methods are tested with two-dimensional Wilson–Majorana fermions and multi-flavor Gross–Neveu models. We show that the methods can also be applied to the fermionic Hubbard model in 1+1 and 2+1 dimensions.

Physics↗

DOE OSTI2019

Fuel/Basket Degradation and Waste Package Pressure Effects Modeling (Progress Report)

Progress is reported on development and testing of the Fuel/Basket Degradation Model, and the Waste Package Breach Model. The work follows on reported FY19 model development (SNL-ICG 2019). Modeling has addressed questions framed in the deliverable description: 1) how fuel/basket damage, including from seismic ground motion, could impact reactivity; 2) whether dynamic degradation processes (e.g., caused by seismic ground motion) should be targets for further model development; and 3) what are the key model parameters and how do they affect the likelihood and energy of criticality events. For basket structure made from aluminum-based metal-matrix composite material, basket collapse would coincide with loss of neutron absorbers, and would occur within a few hundred years after waste package breach. Degradation models discussed in this report have thus far focused on a generic 32-PWR (pressurized water reactor fuel) basket with aluminum-based plates

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2019

Mathematical Reconstruction of Land Carbon Models From Their Numerical Output: Computing Soil Radiocarbon From C Dynamics

Radiocarbon ( 14 C) is a powerful tracer of the global carbon cycle that is commonly used to assess carbon cycling rates in various Earth system reservoirs and as a benchmark to assess model performance. Therefore, it has been recommended that Earth System Models (ESMs) participating in the Coupled Model Intercomparison Project Phase 6 report predicted radiocarbon values for relevant carbon pools. However, a detailed representation of radiocarbon dynamics may be an impractical burden on model developers. Here, we present an alternative approach to compute radiocarbon values from the numerical output of an ESM that does not explicitly represent these dynamics. The approach requires computed 12 C stocks and fluxes among all carbon pools for a particular simulation of the model. From this output, a time-dependent linear compartmental system is computed with its respective state-transition matrix. Using transient atmospheric 14 C values as inputs, the state-transition matrix is then applied to compute radiocarbon values for each pool, the average value for the entire system, and component fluxes. We demonstrate the approach with ELMv1-ECA, the land component of an ESM model that explicitly represents 12 C, and 14 C in 7 soil pools and 10 vertical layers. Results from our proposed method are highly accurate (relative error <0.01%) compared with the ELMv1-ECA 12 C and 14 C predictions, demonstrating the potential to use this approach in CMIP6 and other model simulations that do not explicitly represent 14 C.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

An SYK-inspired model with density–density interactions: Spectral & wave function statistics, Green’s function and phase diagram

The Sachdev–Ye–Kitaev (SYK) model is a rare example of a strongly-interacting system that is analytically tractable. Tractability arises because the model is largely structureless by design and therefore artificial: while the interaction is restricted to two-body terms, interaction matrix elements are “randomized” and therefore the corresponding interaction operator does not commute with the local density. Unlike conventional density–density-type interactions, the SYK-interaction is, in this sense, not integrable. We here investigate a variant of the (complex) SYK model, which restores this integrability. It features a randomized single-body term and a density–density-type interaction. We present numerical investigations suggesting that the model exhibits two integrable phases separated by several intermediate phases including a chaotic one. The chaotic phase carries several characteristic SYK-signatures including in the spectral statistics and the frequency scaling of the Green’s function and therefore should be adiabatically connected to the non-Fermi liquid phase of the original SYK model. Thus, our model Hamiltonian provides a bridge from the SYK-model towards microscopic realism.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗