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At least 1,081 records · Page 60

Hyperheavy spherical and toroidal nuclei: The role of shell structure

The properties of toroidal hyperheavy even-even nuclei and the role of toroidal shell structure are extensively studied within covariant density functional theory. The general trends in the evolution of toroidal shapes in the Z ≈ 130–180 region of the nuclear chart are established for the first time. These nuclei are stable with respect to breathing deformations. The most compact fat toroidal nuclei are located in the Z ≈ 136, N ≈ 206 region of the nuclear chart, but thin toroidal nuclei become dominant with increasing proton number and toward proton and neutron drip lines. The roles of toroidal shell structure, its regularity, supershell structure, and shell gaps as well as the role of different groups of the pairs of the orbitals in its formation are investigated in detail. The lowest in energy solutions at axial symmetry are characterized either by large shell gaps or low density of the single-particle states in the vicinity of the Fermi level in at least one of the subsystems (proton or neutron). Related quantum shell effects are expected to act against the instabilities in breathing and sausage deformations for these subsystems. The investigation with a large set of covariant energy density functionals reveals that substantial proton Z = 154 and 186 and neutron N = 228, 308, and 406 spherical shell gaps exist in all functionals. The nuclei in the vicinity of the combination of these particle numbers form the islands of stability of spherical hyperheavy nuclei. Furthermore, the study suggests that the N = 210 toroidal shell gap plays a substantial role in the stabilization of fat toroidal nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Pairing Correlations across the Superfluid Phase Transition in the Unitary Fermi Gas

In the two-component Fermi gas with a contact interaction, a pseudogap regime can exist at temperatures between the superfluid critical temperature $T_c$ and a temperature $T^\ast > T_c$. This regime is characterized by pairing correlations without superfluidity. However, in the unitary limit of infinite scattering length, the existence of this regime is still debated. To help address this, we have applied finite-temperature auxiliary-field quantum Monte Carlo (AFMC) methods to study the thermodynamics of the superfluid phase transition and signatures of the pseudogap in the spin-balanced homogeneous unitary Fermi gas. We present results at finite filling factor $\textit{ν}$ ≃ 0.06 for the condensate fraction, an energy-staggering pairing gap, the spin susceptibility, and the heat capacity, and compare them to experimental data when available. In contrast to previous AFMC simulations, our model space consists of the complete first Brillouin zone of the lattice, and our calculations are performed in the canonical ensemble of fixed particle number. The canonical ensemble AFMC framework enables the calculation of a model-independent gap, providing direct information on pairing correlations without the need for numerical analytic continuation. We use finite-size scaling to estimate $T_c$ at the corresponding filling factor. In this work, we find that the energy-staggering pairing gap vanishes above $T_c$, showing no pseudogap effects, and that the spin susceptibility shows a substantially reduced signature of a spin gap compared to previously reported AFMC simulations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Coexistence of Interacting Charge Density Waves in a Layered Semiconductor

Coexisting orders are key features of strongly correlated materials and underlie many intriguing phenomena from unconventional superconductivity to topological orders. Here, we report the coexistence of two interacting charge-density-wave (CDW) orders in EuTe 4 , a layered crystal that has drawn considerable attention owing to its anomalous thermal hysteresis and a semiconducting CDW state despite the absence of perfect FS nesting. By accessing unoccupied conduction bands with time- and angle-resolved photoemission measurements, we find that mono- and bi-layers of Te in the unit cell host different CDWs that are associated with distinct energy gaps. The two gaps display dichotomous evolutions following photoexcitation, where the larger bilayer CDW gap exhibits less renormalization and faster recovery. Surprisingly, the CDW in the Te monolayer displays an additional momentum-dependent gap renormalization that cannot be captured by density-functional theory calculations. This phenomenon is attributed to interlayer interactions between the two CDW orders, which account for the semiconducting nature of the equilibrium state. Finally, our findings not only offer microscopic insights into the correlated ground state of EuTe 4 but also provide a general non-equilibrium approach to understand coexisting, layer-dependent orders in a complex system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Anisotropic Thermal Conductivity Oscillations in Relation to the Putative Kitaev Spin Liquid Phase of α-RuCl 3

In the presence of an external magnetic field, the Kitaev model could host either gapped topological anyons or gapless Majorana fermions. In α-RuCl 3 , the gapped and gapless cases are only separated by a 30° rotation of the in-plane magnetic field vector. The presence or absence of the spectral gap is key for understanding the thermal transport behavior in α-RuCl 3 . Here, we study the anisotropy of the oscillatory features of thermal conductivity in α-RuCl 3 . We examine the oscillatory features of thermal conductivities (κ / / a, κ / / b) with fixed external fields and find distinct behavior for the gapped (B / / a) and gapless (B / / b) scenarios. Furthermore, we track the evolution of thermal resistivity (λ α ) and its oscillatory features with the rotation of in-plane magnetic fields from B / / b to B / / a. The thermal resistivity λ(B, φ) displays distinct rotational symmetries before and after the emergence of the field-induced Kitaev spin liquid phase. These results suggest that oscillatory features of thermal conductivity in α-RuCl 3 are closely linked to the putative Kitaev spin liquid phase and its excitations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Circumventing superexponential runtimes for hard instances of quantum adiabatic optimization

Classical optimization problems can be solved by adiabatically preparing the ground state of a quantum Hamiltonian that encodes the problem. The performance of this approach is determined by the smallest gap encountered during the evolution. Here, we consider the maximum independent set problem, which can be efficiently encoded in the Hamiltonian describing a Rydberg atom array. We present a general construction of instances of the problem for which the minimum gap decays superexponentially with system size, implying a superexponentially large time to solution via adiabatic evolution. The small gap arises from locally independent choices which cause the system to initially evolve and localize into a configuration far from the solution in terms of Hamming distance. We investigate remedies to this problem. Specifically, we show that quantum quenches in these models can exhibit signatures of quantum many-body scars, which in turn, can circumvent the superexponential gaps. By quenching from a suboptimal configuration, states with a larger ground-state overlap can be prepared, illustrating the utility of quantum quenches as an algorithmic tool. Published by the American Physical Society 2024

Schiffer, Benjamin F. (ORCID:0000000189512157)↗

Dynamical control in a prethermalized molecular ultracold plasma: Local dissipation drives global relaxation

Prethermalization occurs as an important phase in the dynamics of isolated many-body systems when coupled degrees of freedom relax in a subspace separated from a state of complete thermodynamic equilibrium by a gap in energy or other conserved quantity. Slow equilibration from a prethermal phase can localize the dynamics of natural and model systems despite high dimensionality and limited disorder. Here, we report the signature of an enduring prethermal regime of arrested relaxation in the molecular ultracold plasma that forms following the avalanche of a state-selected Rydberg gas of nitric oxide. For a wide range of initial conditions, this system enters a critical phase in which a density of NO + and electrons balances a population of Rydberg molecules. Electron collisions mix orbital angular momentum, scattering Rydberg electrons to states of very high ℓ . The rapid predissociation of molecules in states of low- ℓ purifies this high- ℓ ensemble. The angular momentum barrier that separates NO + ions and electrons creates an extraordinary gap between the plasma states of n ≈ ℓ , with measured n > 200 and penetrating states of ℓ = 0 , 1 , and 2. Evolution to a statistically equilibrated state of N and O atoms cannot occur without Rydberg electron penetration, and this gap blocks relaxation for a millisecond or more. A weak radiofrequency (RF) field drives ℓ -mixing electron collisions that erase this gap, causing wholesale dissipation. Remarkably, a local quantum-state transition promoting an exceedingly small fraction of the molecules in the prethermalized ensemble to a predissociative state also acts with a global effect, driving the entire system to a dissipative equilibrium. Using the Lindblad master equation, we illustrate qualitatively similar dynamics for a toy model of an open quantum system that consists of a localized set of spins on which dissipation acts at a single site as a gateway to equilibrium. Published by the American Physical Society 2025

Wang, Ruoxi↗

Separate Surface and Bulk Topological Anderson Localization Transitions in Disordered Axion Insulators

In topological phases of matter for which the bulk and boundary support distinct electronic gaps, there exists the possibility of decoupled mobility gaps in the presence of disorder. This is in analogy with the well-studied problem of realizing separate or concomitant bulk-boundary criticality in conventional Landau theory. Using a three-dimensional axion insulator having clean, gapped surfaces with 𝑒 2 /2⁢ℎ quantized Hall conductance, we show that the bulk and surface mobility gap evolve differently in the presence of disorder. The decoupling of the bulk and surface topology yields a regime that realizes a two-dimensional, unquantized anomalous Hall metal in the Gaussian unitary ensemble on each surface, which shares some spectral and response properties akin to the surface states of a conventional 3D topological insulator. The generality of these results, as well as extensions to other insulators and superconductors, is discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Effective Missing Value Imputation Methods for Building Monitoring Data

To understand behaviors of natural and man-made events, such as energy consumption of buildings, which accounts for 40% of energy uses in the US, we deploy automated monitoring devices to record periodic observations. However, such experimental and observation data often contains problems and irregularities that have to be cleaned up before analyses. Due to various conditions affecting sensor operations, the communication channels, recording steps, or the recording media, the recorded data might have missing values, errors, or anomalous values. An effective way to clean up these problems is to replace these missing values, errors and anomalous values with expected values, a process generally known as imputation. In this work, we survey commonly used missing value imputation techniques and compare their performance on a set of building monitoring data. To compare the different types of sensor measurements with widely varying characteristics, we use normalized root mean squared error (NRMSE) as the key metric for the effectiveness of the imputation methods. We additionally consider periodicity and run time when considering comparing methods. Through extensive testing, we find that for small gap sizes, up to 8 consecutive missing values, linear interpolation performs the best; for larger gaps stretching up to 48 consecutive missing values, K-nearest neighbors provides the most accurate imputations; for even larger gaps, more computational intensive methods, such as matrix factorization, achieve the smallest NRMSE. Additionally, we observe that these computationally intensive algorithms not only provide accurate imputations for large gaps, but are also more robust across all types of sensors.

Cho, B↗

The Implications of Collisions on the Spatial Profile of Electric Potential and the Space-Charge-Limited Current

The space-charge-limited current (SCLC) in a vacuum diode is given by the Child-Langmuir law (CLL), whose electric potential ϕ(x) ∝ (x/D) 4/3 , where x is the spatial coordinate across the gap and D is the gap separation distance. For a collisional diode, SCLC is given by the Mott-Gurney law (MGL) and ϕ(x) ∝ (x/D) 3/2 . Here, we apply a capacitance argument for SCLC and use the transit time from a recent exact solution for collisional SCLC to show that ϕ(x) ∝ (x/D)ξ for a general collisional gap, where 4/3 ≤ ξ ≤ 3/2 . Furthermore, ξ is strictly a function of νT, where ν is the collision frequency and T is the electron transit time. Using this definition of ξ, we estimate the spatial dependence of the electron velocity and use the gap capacitance to derive an analytic equation for collisional SCLC that agrees within ~4.5% of the exact solution that requires solving parametrically through T. This analytic equation for general ξ asymptotically recovers the CLL as ν → 0 and the MGL as ν → ∞. As a result, matching these limits shows that ξ ≈ 1.40 and V ∝ D 2 ν 2 at the transition from a vacuum to a collisional diode for any device condition.

Anodes↗

Twisted bulk-boundary correspondence of fragile topology

A topological insulator reveals its nontrivial bulk through the presence of gapless edge states: This is called the bulk-boundary correspondence. However, the recent discovery of “fragile” topological states with no gapless edges casts doubt on this concept. We propose a generalization of the bulk-boundary correspondence: a transformation under which the gap between the fragile phase and other bands must close. We derive specific twisted boundary conditions (TBCs) that can detect all the two-dimensional eigenvalue fragile phases. We develop the concept of real-space invariants, local good quantum numbers in real space, which fully characterize these phases and determine the number of gap closings under the TBCs. Realizations of the TBCs in metamaterials are proposed, thereby providing a route to their experimental verification.

Science & Technology - Other Topics↗

Inversion of downhole electrical measurements for proppant mapping using very fast simulated annealing

Proppant mapping is critical for optimizing fracture treatment design and improving wells’ productivity. An electrode-based resistivity tool concept was developed earlier for proppant mapping in cased-hole wells. An array of insulating gaps is installed and cemented in place as a permanent part of the casing string. The electrical measurements are performed by imposing a voltage across each insulating gap, one at a time, before and after hydraulic fracture operations. The voltages across other insulating gaps near the transmitter gap are recorded. The method relies on direct excitation of the casing, which is expected to overcome the severe limitations of induction tools in cased-hole wells. A forward model based on a finite volume method has been developed to simulate the tool’s response to one or multiple fractures. To enable the implementation of such a practical system in multistage fractured horizontal wells, a fast and robust inversion approach is required. To that end, we have developed a divide-and-conquer approach based on a global optimization algorithm very fast simulated annealing (VFSA). Specifically, the original inverse problem is divided into subproblems and each subproblem can be solved separately using VFSA. The results indicate that our approach can invert the data and output widths and radii of multiple fractures without requiring a large number of forward simulations. The robustness of the inverse solver is also tested by adding Gaussian noise to the synthetic data. We tested example cases that demonstrate that when up to 5% noise is introduced, VFSA still provides very accurate inversion results with moderate uncertainties. Inversion results with some more realistic conditions, e.g., tilted fractures, complex fractures, and so on, are also presented.

Geochemistry & Geophysics↗

Data for Clumping Index Estimation With 30°-tilted Cameras in Row Crops: Evaluation of Methods and Segment Size Effects

The clumping index (CI) quantifies the spatial distribution of foliage elements and is essential for accurately estimating the plant area index (PAI), canopy radiative transfer, and photosynthesis. Traditionally, the finite-length averaging method (LX), the gap size distribution method (CC), and a combined approach of CC and LX (CLX) have been applied to instruments like TRAC and digital hemispherical photography to estimate CI. However, a comprehensive evaluation of these methods in row crops remains limited, especially regarding the influence of segment size on CI. Meanwhile, digital cameras offer a cost-effective and user-friendly solution for canopy measurements in row crops, yet their application in this context remains underexplored. In this study, we employed a new approach using a 30°-tilted digital camera to estimate CI in corn and soybean fields, applying the LX, CC, and CLX methods. We systematically assessed the performance of these three methods by combining field measurements in real-world fields with simulations using the LESS 3D radiative transfer model. Our results showed that CLX applied to the whole image and 45° segment offered accurate estimation of CI (bias within ±0.1, RMSE < 0.2) and PAI (bias within ±0.4, RMSE < 1) in real-world fields and LESS simulations. The accuracy of the LX method was highly sensitive to segment size, with the best performance observed at the 15° segment (PAI bias within ±0.4). In contrast, the CC method remained stable across different segment sizes, and its performance was generally comparable to that of LX, except at the 15° segment. Across view zenith angles, CI derived from CC generally showed a continuous increase, while those from LX and CLX followed a rising trend at small zenith angles but began to decline at 68°, likely due to an increasing proportion of no-gap segments. Seasonally, LX tended to show decreasing CI during early growth stages but increased as the canopy matured, whereas CC and CLX showed gradually increasing CI before plateauing at peak PAI. The 30°-tilted camera effectively captured CI variations across different angles and growth stages, making it a practical and robust instrument for row crop canopy structure analysis. Applying these CI methods to digital cameras offers a low-cost and accessible CI estimation alternative, improving canopy structure monitoring accuracy in row crops.

Modeling↗

Assessment of Cold Spray Technology for Nuclear Power Applications

This report provides an overview of cold spray (CS) technology as it relates to repair and fabrication of metal alloys in the nuclear power industry. CS is a relatively new technology with applications established in other industries (e.g., aerospace, defense), and greater use of CS is anticipated within the nuclear power industry. This report is prepared in support of the United States Nuclear Regulatory Commission (NRC) Action Plan for Advanced Manufacturing Technologies (AMTs) Rev. 1, which includes objectives to identify the AMTs most likely to be used for nuclear power applications that require NRC approval, and to prepare NRC staff to review regulatory submittals containing components manufacturing using AMTs. In addition to providing an overview of CS technology, this report highlights engineering and scientific knowledge gaps of CS and rates the size of the knowledge gaps. It also assesses importance rankings of the knowledge gaps as they relate to several application categories. The application categories considered in this exercise include factory-applied CS for chloride induced stress corrosion cracking (CISCC) mitigation, field CISCC repair, light water reactor (LWR) factory structural fabrication, and LWR field dimensional restoration and corrosion protection. The combination of a knowledge gap size rating and importance ranking for an application can be used to prioritize additional data or information gathering efforts.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Roadmap for Advanced Power System Measurements

Conditions in the electric power grid are changing rapidly. Changes are driven, in particular, by the increased penetration of renewable resources in the generation mix. Part of the solution to dealing with the changing conditions is the better use of measurement systems, taking advantage of the better understanding of measurements that was heralded by digital technology. Another part of the solution is the communication of samples of the directly observable voltages and currents by means of continuous point-on-wave values. The increased bandwidth capability of such a system allows more complicated measurement models to be built at the point of use. Additional measurements and analyses can then be performed. This Roadmap hinges on these two aspects of measuring: improved measurements supported by high-bandwidth (raw data) communications. Following an introduction to the overall subject, the report explores the impact of what can be thought of as the digital revolution in measurement. In essence, that revolution has served to clarify ideas about measurement and is continuing to lead to improved processes. An extensive survey of the relevant literature was performed . Webinars were held to learn from the wider community of practitioners. Based on this information, a number of gaps were identified whose continued existence would hamper the solution of the challenges now facing measurement and communication in the power grid. The underlying value propositions are interoperability (presently not very satisfactory in many measurements); greater (and less challenging) adoption of distributed energy resources; and improved international competitiveness. Underlying all that, of course, is progress toward a more reliable and resilient power system. The identified gaps were addressed in four major thrusts: technology deployment and demonstration, education, instrumentation testing and standards, and analytical methods. For each of the thrusts, multiple goals are defined to guide the implementation. The thrusts were designed to close gaps and unlock high-value use cases. After discussing the literature review, gap analysis, high-value use cases, and research thrusts in chapters 2-5, the report culminates in chapter 6 with a roadmap that links each aspect together to form a unified plan. Developing a research portfolio aligned with this plan will ensure that advanced measurement systems are in place to support reliable operation of the power system as it modernizes.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Collisional Effects on Electron Trajectories in Crossed-Field Devices

Crossed-field diodes (CFDs) are used in multiple high-power applications and are characterized by an applied magnetic field orthogonal to the electric field, induced by the applied voltage across the anode-cathode gap. In vacuum, the Hull cutoff magnetic field (HCMF) represents the maximum applied magnetic field for which an electron from the cathode can reach the anode. This study investigates the effects of non-vacuum conditions on electron trajectories by introducing electron mobility, which represents particle collisions. We used numerical solutions of the electron force law and particle-in-cell simulations (XPDP1) to assess electron motion for various electron mobilities. For magnetic fields above the HCMF in vacuum, reducing the electron mobility increases the time for an electron emitted from the cathode to reach the anode. Reducing mobility below 22 C s/kg eliminates the HCMF for any magnetic field, meaning that an emitted electron will always cross the gap. We derived the magnetic field, mobility, and electron transit time corresponding to this condition by solving for the condition when the electron velocity in the direction across the anode-cathode gap going to zero at the anode. A parametric study of these conditions using theory and XPDP1 is performed under different gap distances, voltages, and magnetic fields.

42 ENGINEERING↗

FY2022 Progress Report on Viscosity and Thermal Conductivity Measurements of Molten Salts

This report describes the development of and experimental measurements made with the thermal conductivity and viscosity measurement systems for molten salts at Oak Ridge National Laboratory. The thermal conductivity system is based on a steady-state measurement technique in which a heat flux is driven across a variable gap, and the changes in temperature difference across the gap are measured as the gap size is varied. The system comprises an inner containment, which possesses the heating element, and an outer containment, which possesses the salt specimen and cooling channels. The gap is formed between the outer bottom of the inner containment and the inner bottom of the outer containment. The viscosity system is based on the falling-ball technique in which a salt-filled tubular crucible is fixed at an angle and a ball rolls through the salt. The terminal velocity of the ball can be converted into viscosity via a calibration factor calculated for crucible-ball combinations which account for thermal expansion and flow characteristics. Modifications were made to both systems this fiscal year. Modifications to the thermal conductivity system included adding guard heaters to prevent axial heating losses, and modifications to the viscosity system included changing the crucible design to prevent air pocket formation and providing the ability to conduct measurements with a glass or steel crucible.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Regulations, Codes, and Standards Review for Underground Hydrogen Storage

Hydrogen continues to show promise as a viable contributor to achieving energy storage goals such as energy security and decarbonization in the United States. However, many new and expanded hydrogen use applications will require identifying methods of larger-scale storage than the solutions that currently exist for smaller storage applications. One possibility is to store large quantities of gaseous hydrogen below ground level. Underground storage of other fuels such as natural gas is already currently utilized, so much of the infrastructure and basic technologies can be used as a basis for underground hydrogen storage (UHS). A few commercial UHS facilities currently exist in the United States, including salt caverns owned and operated by Air Liquide, Linde, and Conoco Philips, but UHS is still a relatively new concept that has not been widely deployed. It is necessary to understand the safety risks and hazards associated with UHS before its use can be expanded and accepted more broadly. Many of these risks are addressed through regulations, codes, and standards (RCS) issued by governing bodies and organizations with expertise in certain hazards. This report is a review of RCS documents relevant to UHS, with a particular lens on potential technical gaps in existing guidance. These gaps may be specific to the physical properties of hydrogen or due to the different technologies relevant for hydrogen vs. natural gas storage. This is meant to be a high-level review to identify relevant documents and potential gaps. Formally addressing the individual gaps identified here within the codes and standards themselves would involve a more intensive analysis and differ based on the code or standard revision processes of the various publishing organizations. Therefore, presenting specific recommendations for revising the verbiage of the documents for UHS applications is left for future work and other publications.

08 HYDROGEN↗

Fiscal Year 2024 Software Quality Assurance Activities for the ARC Software

The continued goal of the ARC SQA project in the Advanced Reactor Technologies program of DOE is to resolve the QA gaps for the ARC software that limit, or prevent, commercialization of the software for industry users. This project started in earnest in fiscal year 2023 which saw the entire code system moved from a SVN repository to a GitLab repository and an associated software quality assurance plan (SQAP) developed and ratified. Most of the QA gaps in the ARC software were identified in collaboration with industry partners and work begin in fiscal year 2023 and continued in 2024. The primary documentation that is missing includes user manuals, user guides, software verification reports, and code coverage assessments. The SUMMAR manual was completed this fiscal year and work was started on creating manuals for SE2ANL, SE2RCT, and DASSH. Software verification work was carried out for DIF3D and REBUS in a previous program and the current fiscal year saw the completion of software verification reports for GAMSOR, GAMSRC, VARPOW, EvaluateFlux, and SUMMAR. The goal for the next fiscal year is to complete the PERSENT software verification work and begin planning the software verification work for DASSH, SE2ANL, and SE2RCT. The code coverage reports for DIF3D and MC2-3 were completed in the previous fiscal year and the goal is to generate code coverage reports for REBUS, GAMSOR, PERSENT, and DASSH in the coming fiscal year. A considerable amount of effort was spent in the current fiscal year working on the continuous integration capability for automated regression testing in GitLab. The first version of the testing was created in the previous fiscal year and applied to DIF3D and its utility programs. That testing was extended this year to cover GAMSOR, REBUS, and PERSENT. To accomplish this, the first version of the new testing methodology had to be updated to make a single output checking methodology viable for all of the ARC software. This will result in a single document to detail the automated regression testing methodology and minor documents to detail the tolerance settings that have been applied to the output for each ARC code. The previous methodology put into place with SVN would have required a separate document for each ARC code to detail the output checking methodology and the tolerance settings for the output from each code. Because some of our industry partners are providing funds to add new capabilities to the ARC software to meet their needs, all of which must be reviewed and approved by the SQA program funded by this project, a summary of that development work is detailed in this report. Overall progress on resolving the QA gaps has been good this year with the most impactful improvement for our industry partners in capability being the creation of a threaded version of DIF3D-VARIANT that allows the DIF3D, REBUS, and GAMSOR run times to be reduced by a factor of 4-6. The most impactful QA gap that was resolved was the software verification of GAMSRC and VARPOW.

97 MATHEMATICS AND COMPUTING↗