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DOE OSTI2023

Addendum to ICSBEP Logbooks 12r, 13r, 14r and 15r for Polyethylene and Graphite Reflected HEU Metal Critical Experiments

This report documents the experimenters’ data sheets that were recently (2023) discovered for critical experiments with highly enriched uranium metal with polyethylene and graphite reflectors. These data sheets were produced at the time of the measurements, when the dimensional inspection reports for the polyethylene and graphite were available. However, at this writing, those inspection reports are not available but may be in unmarked storage for the Y-12 National Security Complex. However, the data sheets presented herein contain sketches of the experimental configurations and other additional information that is not in the logbooks, such as dimensions and masses of the graphite measurements. This report reproduces the experimental data sheets that complement the logbooks. Some of the data on these sheets and the logbooks can be used to infer the dimensions and masses that are not documented. Some obvious mistakes in the logbook and data sheets have been corrected. In the reproduced data sheets, some of the information is not clearly visible: some information, such as average values, can be obtained from other data in the sheets or logbook. This report should be sent to the International Criticality Safety Benchmark Program at Idaho National Laboratory to complement the existing Oak Ridge Critical Facility logbooks there.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

Dynamics and Formation of Antiferromagnetic Textures in MnBi 2 Te 4 Single Crystal

We report coherent X-ray imaging of antiferromagnetic (AFM) domains and domain walls in MnBi 2 Te 4 , an intrinsic AFM topological insulator. This technique enables direct visualization of domain morphology without reconstruction algorithms, allowing us to resolve antiphase domain walls as distinct dark lines arising from the A-type AFM structure. The wall width is determined to be 550(30) nm, in good agreement with earlier magnetic force microscopy results. The temperature dependence of the AFM order parameter extracted from our images closely follows previous neutron scattering data. Remarkably, however, we find a pronounced hysteresis in the evolution of domains and domain walls: upon cooling, dynamic reorganizations occur within a narrow ∼1 K interval below 𝑇 𝑁 , whereas upon warming, the domain configuration remains largely unchanged until AFM order disappears. These findings reveal a complex energy landscape in MnBi 2 Te 4 , governed by the interplay of exchange, anisotropy, and domain-wall energies, and underscore the critical role of AFM domain-wall dynamics in shaping its physical properties. These sharply defined and hysteretically evolving walls may provide a controllable AFM texture in MnBi 2 Te 4 , hinting at potential use in low-power spintronic devices based on domain-wall dynamics.

36 MATERIALS SCIENCE↗

DOE OSTI2022

The many-body electronic interactions of Fe(II)–porphyrin

Fe(II)–porphyrin complexes exhibit a diverse range of electronic interactions between the metal and macrocycle. Herein, the incremental full configuration interaction method is applied to the entire space of valence orbitals of a Fe(II)–porphyrin model using a modest basis set. A novel visualization framework is proposed to analyze individual many-body contributions to the correlation energy, providing detailed maps of this complex’s highly correlated electronic structure. Furthermore, this technique is used to parse the numerous interactions of two low-lying triplet states ( 3 A 2 g and 3 E g ) and to show that strong metal d–d and macrocycle π–π orbital interactions preferentially stabilize the 3 A 2 g state. d–π interactions, on the other hand, preferentially stabilize the 3 E g state and primarily appear when correlating six electrons at a time. Ultimately, the Fe(II)–porphyrin model’s full set of 88 valence electrons are correlated in 275 orbitals, showing the interactions up to the 4-body level, which covers the great majority of correlations in this system.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Probing magnetic configuration-mediated topological phases via high harmonic generation in MnBi 2 Te 4

Compared to a space group, a magnetic space group is much more complex, as both magnetic structure and magnetic moment direction can change the original symmetries of materials. The interplay between space symmetry and magnetism can generate versatile novel quantum states. However, detecting these topological phases experimentally, achieved through manipulating the magnetic configuration, has been restricted. It is mainly because the intrinsic link between the theory and the available experimental technique remains elusive. Here, we show that high harmonic generation (HHG) can identify these topological quantum states. In this work, we use rhombohedral MnBi 2 Te 4 film as an example, and analyze the symmetry-dependent harmonic order and signal by combining first-principles calculations and time-dependent Liouville equation numerical computations. Our results provide a fundamental basis for using HHG to study the topological quantum phases mediated by various magnetic configurations that can be easily realized by applying an external magnetic field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Holistic fleet optimization incorporating system design considerations

The methodology described in this article enables a type of holistic fleet optimization that simultaneously considers the composition and activity of a fleet through time as well as the design of individual systems within the fleet. Often, real-world system design optimization and fleet-level acquisition optimization are treated separately due to the prohibitive scale and complexity of each problem. Importantly, this means that fleet-level schedules are typically limited to the inclusion of predefined system configurations and are blind to a rich spectrum of system design alternatives. Similarly, system design optimization often considers a system in isolation from the fleet and is blind to numerous, complex portfolio-level considerations. In reality, these two problems are highly interconnected. To properly address this system-fleet design interdependence, we present a general method for efficiently incorporating multi-objective system design trade-off information into a mixed-integer linear programming (MILP) fleet-level optimization. This work is motivated by the authors' experience with large-scale DOD acquisition portfolios. However, the methodology is general to any application where the fleet-level problem is a MILP and there exists at least one system having a design trade space in which two or more design objectives are parameters in the fleet-level MILP.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Reconnection and particle acceleration in three-dimensional current sheet evolution in moderately magnetized astrophysical pair plasma

Magnetic reconnection, a plasma process converting magnetic energy to particle kinetic energy, is often invoked to explain magnetic energy releases powering high-energy flares in astrophysical sources including pulsar wind nebulae and black hole jets. Reconnection is usually seen as the (essentially two-dimensional) nonlinear evolution of the tearing instability disrupting a thin current sheet. To test how this process operates in three dimensions, we conduct a comprehensive particle-in-cell simulation study comparing two- and three-dimensional evolution of long, thin current sheets in moderately magnetized, collisionless, relativistically hot electron–positron plasma, and find dramatic differences. We first systematically characterize this process in two dimensions, where classic, hierarchical plasmoid-chain reconnection determines energy release, and explore a wide range of initial configurations, guide magnetic field strengths and system sizes. We then show that three-dimensional (3-D) simulations of similar configurations exhibit a diversity of behaviours, including some where energy release is determined by the nonlinear relativistic drift-kink instability. Thus, 3-D current sheet evolution is not always fundamentally classical reconnection with perturbing 3-D effects but, rather, a complex interplay of multiple linear and nonlinear instabilities whose relative importance depends sensitively on the ambient plasma, minor configuration details and even stochastic events. It often yields slower but longer-lasting and ultimately greater magnetic energy release than in two dimensions. Intriguingly, non-thermal particle acceleration is astonishingly robust, depending on the upstream magnetization and guide field, but otherwise yielding similar particle energy spectra in two and three dimensions. Although the variety of underlying current sheet behaviours is interesting, the similarities in overall energy release and particle spectra may be more remarkable.

Physics↗

DOE OSTI2022

Structures of RNA ligase RtcB in complexes with divalent cations and GTP

Pyrococcus horikoshii (Pho) RtcB exemplifies a family of binuclear transition metal- and GTP-dependent RNA ligases that join 3'-phosphate and 5'-OH ends via RtcB-(histidinyl-N)–GMP and RNA 3' pp 5' G intermediates. We find that guanylylation of PhoRtcB is optimal with manganese and less effective with cobalt and nickel. Zinc and copper are inactive and potently inhibit manganese-dependent guanylylation. We report crystal structures of PhoRtcB in complexes with GTP and permissive (Mn, Co, Ni) or inhibitory (Zn, Cu) metals. Zinc and copper occupy the M1 and M2 sites adjacent to the GTP phosphates, as do manganese, cobalt, and nickel. The identity/positions of enzymic ligands for M1 (His234, His329, Cys98) and M2 (Cys98, Asp95, His203) are the same for permissive and inhibitory metals. The differences pertain to: (i) the coordination geometries and phosphate contacts of the metals; and (ii) the orientation of the His404 nucleophile with respect to the GTP α-phosphate and pyrophosphate leaving group. M2 metal coordination geometry correlates with metal cofactor activity, whereby inhibitory Zn2 and Cu2 assume a tetrahedral configuration and contact only the GTP γ-phosphate, whereas Mn2, Co2, and Ni2 coordination complexes are pentahedral and contact the β- and γ-phosphates. The His404-Nε–Pα–O(α-β) angle is closer to apical in Mn (179°), Co (171°), and Ni (169°) structures than in Zn (160°) and Cu (155°) structures. The octahedral Mn1 geometry in our RtcB•GTP•Mn 2+ structure, in which Mn1 contacts α-, β-, and γ-phosphates, transitions to a tetrahedral configuration after formation of RtcB•(His404)–GMP•Mn 2+ and departure of pyrophosphate.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Perturbing the spin state and conduction of Fe (II) spin crossover complexes with TCNQ

In this study, we investigated modifications driven by 7,7,8,8-tetracyanoquinodimethane (TCNQ) to the spin state configuration of [Fe(3-bpp) 2 ](TCNQ) 2 co-crystal and both spin state and electric conductivity of [Fe{H 2 B(pz) 2 } 2 (bipy)] and TCNQ mixtures. The Fe 2+ site in the [Fe(3-bpp) 2 ](TCNQ) 2 co-crystal has a sizable orbital moment. During X-ray absorption measurements, the iron ion is partially excited to the high spin state and strong surface effects are indicated. Mixing TCNQ with the [Fe{H 2 B(pz) 2 } 2 (bipy)] spin crossover complex leads to a molecular combination with increased conductivity and drift carrier lifetimes. [Fe{H 2 B(pz) 2 } 2 (bipy)] thin films with TCNQ, grown using dimethylformamide (DMF), are to great extent locked mainly in the low spin (LS) state across a broad temperature range and exhibit drift carrier lifetimes approaching 0.5 s. When deposited onto a ferroelectric polyvinylidenefluoride-hexafluoropropylene thin film substrate, [Fe{H 2 B(pz) 2 } 2 (bipy)], shows enhanced transistor carrier mobility, likely associated with the increasing cationic character of [Fe{H 2 B(pz) 2 } 2 (bipy)] thin films with TCNQ.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Tracking the Light-Induced Excited-State Dynamics and Structural Configurations of an Extraordinarily Long-Lived Metastable State at Room Temperature

Time-resolved X-ray (Tr-XAS) and optical transient absorption (OTA) spectroscopy in the pico-microsecond time scale coupled with Density Functional theory calculations are applied to study the light-induced spin crossover processes of a Fe-based macrocyclic complex in solution. Tr-XAS analysis after light illumination shows the formation of a seven-coordinated high spin quintet metastable state which relaxes to a six-coordinated high spin configuration before decaying to ground state. Kinetic analysis of the macrocyclic complex reveals an unprecedented long-lived decay lifetime of ~42.6 µs. Comparative studies with a non-macrocyclic counterpart illustrate a significantly shortened ~568-old decay lifetime of ~75 ns, and highlight the importance of the ligand arrangement in stabilizing the reactivity of the excited state. Lastly, OTA analysis shows the seven-coordinated high spin state to be formed within ~6.2 ps. Finally, these findings provide a complete understanding of the spin crossover reaction and relaxation pathways of the macrocyclic complex, and reveal the importance of a flexible coordination environment for their rational design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Mechanics of the Ring Tension Test (RTT): A Finite Element-based Investigation

The ring tension test (RTT) is an experimental method for determining mechanical behavior in a material’s circumferential or hoop direction. It is a crucial test for testing anisotropic materials with tube geometry, such as nuclear fuel cladding or irradiated pipes. Several RTT configurations exist, each with their own advantages and disadvantages. However, this test is significantly more complex than traditional tensile testing and can be especially sensitive to small differences and inconsistencies in the test setup and geometry, ultimately affecting the derived mechanical properties. Previous research has focused on method development, and little work has been done on understanding the subtle differences between an ideal test and experiments, specifically when the tests are performed on highly irradiated materials in hot cells. In this work, a finite element-based investigation of the RTT is conducted. Two promising test configurations are investigated, comparing their ability to determine accurate material strengths through plastic deformation. Several non-ideal conditions and uncontrollable effects which are likely to occur during experimental testing such as machining tolerances, variations of specimen geometry from nominal dimensions, rotation of specimens and fixturing, and other test setup discrepancies are studied. The sensitivity of measured strengths to these conditions is presented. A mechanics-based approach to describing and correcting raw data to determine actual strengths is also included for one of the configurations, resulting in a robust correction method with highly accurate material strength measurements. Based on these analyses, the hemicylindrical mandrel configuration is recommended with a gauge region oriented at a 45° angle.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Evaluation of the ring tension test (RTT) for robust determination of material strengths

The ring tension test (RTT) is an experimental method for determining mechanical behavior in a material’s circumferential or hoop direction. It is a crucial test for testing anisotropic materials with tube geometry, such as nuclear fuel cladding or irradiated pipes. Several RTT configurations exist, each with their own advantages and disadvantages. However, this test is significantly more complex than traditional tensile testing and can be especially sensitive to small differences and inconsistencies in the test setup and geometry, ultimately affecting the derived mechanical properties. Previous research has focused on method development, and little work has been done on understanding the subtle differences between an ideal test and experiments, specifically when the tests are performed on highly irradiated materials in hot cells. In this work, a finite element-based investigation of the RTT is conducted to fill this gap. The two most used test configurations are investigated, comparing their ability to determine accurate material strengths through plastic deformation. Several non-ideal conditions and uncontrollable effects which are likely to occur during experimental testing such as machining tolerances, variations of specimen geometry from nominal dimensions, rotation of specimens and fixturing, and other test setup discrepancies are studied. The sensitivity of measured strengths to these conditions is presented. A mechanics-based approach to describing and correcting raw data to determine actual strengths is also included for one of the configurations, resulting in a robust correction method with highly accurate material strength measurements. Finally, based on these analyses, the hemicylindrical mandrel configuration is recommended with a gauge region oriented at a 45° angle.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Mixed gain detector configurations for time-resolved X-ray solution scattering

X-ray detection at X-ray free-electron lasers is challenging in part due to the XFEL's extremely short and intense X-ray pulses. Experimental measurements are further complicated by the large fluctuations inherent to the self-amplified spontaneous emission process producing the X-rays. At the Linac Coherent Light Source the ePix10ka2M detector offers multiple gain modes, and auto-ranging between these, to increase the dynamic range while retaining low noise. For diffuse scattering techniques, such as time-resolved X-ray solution scattering, where the shape of the scattering pattern largely does not change between exposures, a fixed mix of different gain modes offers many of the same advantages as auto-ranging. We find that configuring individual ASICs in separate gain modes does not impact the intensity linearity of the gain response and has a limited effect on the effective dynamic range in regions with different gain mode settings while avoiding the complexities of auto-ranging. Small (<5%) non-linear gain contributions arise when pixels on the same ASIC are configured in different gain modes. We present a configuration scheme that is designed to select the optimal mixed gain configuration to minimize effects of saturation in the high-/medium-gain region, while maximizing the number of pixels with higher gain to improve the signal-to-noise ratio.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Exploring the impact of surface topography on Rayleigh-Bénard dry convection in the Pi cloud chamber using OpenFOAM: In cylindrical and rectangular geometries

The Pi convection-cloud chamber can generate steady-state turbulence in both rectangular and cylindrical shapes via Rayleigh-Bénard convection (RBC) by maintaining warm bottom and cold top surfaces. Although most experiments in the Pi chamber were conducted in cylindrical shapes, all previous Pi chamber simulations were conducted in a rectangular shape due to the limitations of those models to discretize a cylindrical domain when using the finite difference method therein. Here, we use OpenFOAM, an open-source finite-volume-based Computational Fluid Dynamics (CFD) software package, to conduct Large-Eddy Simulation (LES) of dry RBC in the Pi chamber at high Rayleigh numbers (10 8 to 10 9 ). Results show that large-scale circulation (LSC) direction varies in the chamber with a constant side wall temperature. Imposing a slight temperature imbalance at the side wall ranging from 0.1 to 0.7 degrees can lock the LSC, aligning better with Pi chamber observations, particularly at higher Rayleigh numbers. In addition, we examine the impact of surface topography on LSC and heat transfer in RBC systems within cylindrical and rectangular shapes under varying conditions. Results show that roughing top/bottom surfaces by adding bars of a few tens millimeters height can strengthen thermal plumes and enhance temperature fluctuations in the chamber. Furthermore, we observe that different bar height configurations lead to notable changes in LSC orientation and thermal stratification, highlighting the complex interactions between surface features and convection patterns. This finding highlights how surface topography and chamber geometry affect Rayleigh-Bénard convection, improving understanding of turbulent heat transfer and atmospheric boundary-layer processes. Direct Numerical Simulations (DNS) are also conducted to validate LES results. In conclusion, while LES effectively captures qualitative behaviors seen in DNS, it tends to underestimate velocity variances near walls, illustrating a trade-off between computational efficiency and accuracy.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Best of both worlds: Enforcing detailed balance in machine learning models of transition rates

The slow microstructural evolution of materials often plays a key role in determining material properties. When the unit steps of the evolution process are slow, direct simulation approaches such as molecular dynamics become prohibitive and Kinetic Monte-Carlo (kMC) algorithms, where the state-to-state evolution of the system is represented in terms of a continuous-time Markov chain, are instead frequently relied upon to efficiently predict long-time evolution. The accuracy of kMC simulations however relies on the complete and accurate knowledge of reaction pathways and corresponding kinetics. This requirement becomes extremely stringent in complex systems such as concentrated alloys where the astronomical number of local atomic configurations makes the a priori tabulation of all possible transitions impractical. Machine learning models of transition kinetics have been used to mitigate this problem by enabling the efficient on-the-fly prediction of kinetic parameters. While conventional KMC methods based on transition state theory naturally yield reversible dynamics that exactly obey the detailed balance criterion, providing strong guarantees on the properties of the stationary distribution, many recently-proposed ML-based approaches to barrier predictions provide no such guarantees. In this study, we derive conditions under which physics-informed ML architectures exactly enforce the detailed balance condition by construction, even when relying on non-extensive descriptions of states in terms of local environments around mobile defects. In conclusion, using the diffusion of a vacancy in a concentrated alloy as an example, we show that such ML architectures also exhibit superior performance in terms of prediction accuracy, demonstrating that the imposition of physical constraints can facilitate the accurate learning of barriers at no increase in computational cost.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Pb:Sn Ratio-Driven Polytypism and Band Modulation in Photoresponsive Hexagonal Perovskitoids

Three-dimensional (3D) perovskites of the formula AMX 3 are known for their excellent optoelectronic properties, but their design is limited by the narrow range of A-site cations that can template the 3D corner-sharing structure, and many of the viable options have already been explored. These materials also face structural instability under environmental conditions. In contrast, 3D hexagonal perovskitoids, with the same chemical formula, may offer enhanced stability and richer structural diversity through a range of corner- and face-sharing octahedral configuration options, providing greater opportunities for structural design; however, challenges such as synthesis complexity and wide band gaps have hindered optoelectronic performance achieved to date. Herein, we synthesized a structural homologous series of mixed-metal hexagonal perovskitoids with the formula APb 1-x Sn x I 3 (x = 0, 0.25, 0.50, 0.75, 1; A = ethylammonium, guanidinium) and identified three polytypes (9R, 12R, 6H) using single-crystal X-ray diffraction (SCXRD). These structures exhibited increasing corner-sharing connectivity with higher Sn content, revealing a previously unobserved relationship between metal composition and structural evolution in perovskitoid materials. The incorporation of Sn reduced the band gap (tunable from 2.51 eV to 1.87 eV) and drove structural transformations, a trend seen also in density functional theory (DFT) calculations, which suggest a thermodynamic preference for Pb at face-sharing sites and Sn at corner-sharing sites. DFT band structure calculations and optical spectroscopy also reveal an anomalous behavior in these materials, which we term polytypic band modulation. This phenomenon combines conventional band bowing with the structural transformations that occur as Sn content increases, as observed in the band gap and in photoluminescence spectra. Photodiodes fabricated from thin films of these materials exhibited stable and pronounced photoresponses across various light intensities over time. Furthermore, the combination of templating 3D perovskitoids with multiple cations and alloying Pb and Sn, suggests a vastly underexplored phase space that offers new parameters to tune perovskitoids.

Cations↗

DOE OSTI2026

A New 1D Model for Thermal Mixing and Stratification in Advanced Reactor Transients

Thermal mixing and stratification in large pools and enclosures play a critical role in the safety and performance of pool-type nuclear reactors, particularly during transient scenarios involving significant temperature differences between incoming and bulk coolant. Accurate modeling of these phenomena is essential for predicting system behavior and supporting passive safety features such as natural circulation. Here, this paper presents a new 1D model for thermal mixing and stratification, developed and implemented in the SAM code. The model represents a large pool as 1D coolant jet channels and zero-dimensional bulk pool volumes, enabling the simulation of a wide range of flow configurations, including hot and cold jet interactions, stratified layers, and the influence of complex geometries such as ceilings, free surfaces, and internal obstacles. Heat exchange between jet and pool regions is governed by closure relations calibrated against 3D computational fluid dynamics (CFD) simulations. The model improves upon earlier approaches by incorporating time-dependent jet characteristics and capturing the associated delay effects more accurately. Code-to-code comparisons and validation against experimental data from the Thermal Stratification Test Facility demonstrate the model’s accuracy and flexibility. This work offers two key contributions: (1) an efficient and robust method for simulating thermal mixing and stratification at the system level, eliminating the need for external coupling between system analysis codes and CFD, and (2) a significant enhancement of SAM’s capabilities to analyze thermal stratification phenomena in advanced reactor systems.

SAM↗

DOE OSTI2022

Comparison between MAST-U conventional and Super-X configurations through SOLPS-ITER modelling

Abstract MAST-U has recently started operating with a Super-X divertor, designed to increase total flux expansion and neutral trapping, both predicted through simple analytic models and SOLPS calculations to reduce the plasma and impurity density detachment thresholds. In this study, utilising the SOLPS-ITER code, we are quantifying the possible gain allowed by the MAST-U Super-X and neutral baffling geometry, in terms of access to detachment. We show that a significant reduction of the upstream density detachment threshold (up to a factor 1.6) could be achieved in MAST-U, for the Super-X, as opposed to conventional divertor geometry, mainly through an increased total flux expansion, neutral trapping being found very similar between the different configurations. We also show that variations of the strike-point angle are complex to interpret in such a tightly baffled geometry, and that a case in which the target normal points more towards the separatrix does not necessarily imply a lower detachment threshold. As in previous calculations for TCV, we quantify the role of neutral effects through developing and applying a quantitative definition of neutral trapping.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Scalar flux transport models for self-similar turbulent mixing

A common approach to closing turbulent species flux in multicomponent Reynolds-averaged Navier-Stokes models is to use the standard gradient diffusion approximation. While such an approach has been shown to work well when applied to many canonical turbulent mixing configurations, a gradient diffusion approach is fundamentally limited in its ability to capture complex phenomena such as countergradient transport. For this reason, complicated mixing applications may benefit by treating the turbulent diffusivity with a model transport equation in a manner analogous to second-moment momentum closure in Reynolds-stress transport models. Here, the present work explores the development and application of two different scalar flux transport (SFT) models. Self-similarity constraints are derived for these models, and they are evaluated against gradient-diffusion-based models in several one- and two-dimensional problems of turbulent mixing. It is found that the new SFT models out-perform gradient diffusion models in problems involving rapid acceleration reversal and in problems involving anisotropic transport of materials. In addition, it is found that even a hybrid-SFT approach, in which an SFT equation is utilized along with a gradient diffusion closure, provides some measure of improvement over models that transport the mass flux rather than the scalar flux.

Reynolds-averaged Navier Stokes↗