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At least 109 records · Page 6

Density and temperature profiles after low-Z and high-Z shattered pellet injections on DIII-D

Abstract In this work we utilize the recently upgraded Thomson scattering diagnostic to resolve density and temperature plasma profiles after pure deuterium and mixed neon/deuterium shattered pellet injections (SPIs) on DIII-D. This allows us to study individual components of the staggered scheme proposed for disruption mitigation on ITER, consisting of a low-Z material SPI followed by a delayed high-Z SPI. Obtained spatio-temporal density profiles exhibit very different dynamics after dominantly neon and pure deuterium SPIs. The neon SPI causes a fast radiative plasma collapse in a few milliseconds and results in almost flat density profile once the impurity mixes with the plasma during and after the thermal quench (TQ). The deuterium SPI leads to a disruption delayed by ten and more milliseconds, but very limited core fueling can be observed before the disruption. Even during and after the TQ, the edge deuterium density significantly exceeds the core density. 1D transport modeling suggests that this poor core fueling can be explained by strong outward grad-B-induced drift of the injected deuterium. Preliminary simulations show that larger pellet shards and greater injected quantity can be used to improve the penetration of the low-Z material into the core. These results call for optimization and further evaluation of the staggered SPI on ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Quasi-deuteron model at low renormalization group resolution

The quasi-deuteron model introduced by Levinger is used to explain cross sections for knocking out high-momentum protons in photoabsorption on nuclei. This is within a framework we characterize as exhibiting high renormalization group (RG) resolution. Assuming a one-body reaction operator, the nuclear wave function must include two-body short-range correlations (SRCs) with deuteronlike quantum numbers. In Phys. Rev. C 104, 034311 (2021), we showed that SRC physics can be naturally accounted for at low RG resolution. We describe the quasi-deuteron model at low RG resolution and determine the Levinger constant, which is proportional to the ratio of nuclear photoabsorption to that for photodisintegration of a deuteron. We extract the Levinger constant based on the ratio of momentum distributions at high relative momentum. We compute momentum distributions evolved under similarity RG (SRG) transformations where the SRC physics is shifted into the operator as a universal two-body term. The short-range nature of this operator motivates using local-density approximations with uncorrelated wave functions in evaluating nuclear matrix elements, which greatly simplifies the analysis. The operator must be consistently matched to the RG scale and scheme of the interaction for a reliable extraction. We apply SRG transformations to different nucleon-nucleon (NN) interactions and use the deuteron wave functions and Weinberg eigenvalues to determine approximate matching scales. We predict the Levinger constant for several NN interactions and a wide range of nuclei comparing to experimental extractions. The predictions at low RG resolution are in good agreement with experiment when starting with a hard NN interaction and the initial operator. Similar agreement is found using soft NN interactions when the additional two-body operator induced by evolution from hard to soft is included.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

High sensitivity of simulated fog properties to parameterized aerosol activation in case studies from ParisFog

Aerosols influence fog properties such as visibility and lifetime by affecting fog droplet number concentrations (N d ). Numerical weather prediction (NWP) models often represent aerosol–fog interactions using highly simplified approaches. Incorporating prognostic size-resolved aerosol microphysics from climate models could allow them to simulate N d and aerosol–fog interactions without incurring excessive computational expense. However, microphysics code designed for coarse spatial resolution may struggle with sub-kilometer-scale grid spacings. Here, we test the ability of the UK Met Office Unified Model to simulate aerosol and fog properties during case studies from the ParisFog field campaign in 2011. We examine the sensitivity of fog properties to variations in N d caused by modifications to simulated aerosol activation. Our model, with a 500 m horizontal resolution and interactive aerosol and cloud microphysics, significantly underpredicts N d , although it only slightly underestimates the cloud condensation nuclei concentration. With an updated version of the Abdul-Razzak and Ghan (2000) activation scheme, we produce N d that are more consistent with those predicted by a cloud parcel model under fog-like conditions. We activate droplets only by adiabatic cooling. We incorporate more realistic hygroscopicities for sulfate and organic aerosols and explore the sensitivity of simulated N d to unresolved updrafts. We find that both N d and simulated fog liquid water content are very sensitive to the updated activation scheme but remain less affected by the update to hygroscopicities. Our improvements offer insights into the physical processes regulating N d in stable conditions, potentially laying foundations for improved operational fog forecasts that incorporate interactive aerosol simulations or aerosol climatologies.

Ghosh, Pratapaditya [Carnegie Mellon University, P↗

A mass–momentum consistent coupling for mesh-adaptive two-phase flow simulations

Here, we present a novel mass-momentum consistent coupling between a geometric volume-of-fluid scheme and an incompressible flow solver with differing directional-splitting approaches. The advection of the volume fraction is performed using a direction-split algorithm, whereas the momentum advection algorithm uses a traditional unsplit, fractional-step approach. Both algorithms employ finite-volume discretizations based on Cartesian meshes. In solving the mass-momentum consistency problem, momentum fluxes at the cell faces are weighted by the density fluxes based on the already advected volume fraction. The success of our approach lies on introducing a Favre-averaged velocity interpolation at the liquid/gas interface along with a minmod slope limiter. Mesh-convergence studies show that when the minmod slope limiter is used, the two-phase solver retains an accuracy between first and second order, but when a purely upwind scheme is considered, its accuracy drops to first order. Finally, after considering several validation problems, the solver is shown to agree well with reference numerical and experimental data while retaining its robustness and efficiency.

97 MATHEMATICS AND COMPUTING↗

High precision tests of QCD without scale or scheme ambiguities: The 40th anniversary of the Brodsky–Lepage–Mackenzie method

A key issue in making precise predictions in QCD is the uncertainty in setting the renormalization scale μ r and thus determining the correct values of the QCD running coupling α s (μ r ) at each order in the perturbative expansion of a QCD observable. It has often been conventional to simply set the renormalization scale to the typical scale of the process Q and vary it in the range μ r $\in$ [Q/2, 2Q] in order to estimate the theoretical error. This is the practice of Conventional Scale Setting (CSS). The resulting CSS prediction will however depend on the theorist’s choice of renormalization scheme and the resulting pQCD series will diverge factorially. It will also disagree with renormalization scale setting used in QED and electroweak theory thus precluding grand unification. A solution to the renormalization scale-setting problem is offered by the Principle of Maximum Conformality (PMC), which provides a systematic way to eliminate the renormalization scale-and-scheme dependence in perturbative calculations. The PMC method has rigorous theoretical foundations, it satisfies Renormalization Group Invariance (RGI) and preserves all self-consistency conditions derived from the renormalization group. The PMC cancels the renormalon growth, reduces to the Gell-Mann–Low scheme in the N c → 0 Abelian limit and leads to scale- and scheme-invariant results. The PMC has now been successfully applied to many high-energy processes. In this article we summarize recent developments and results in solving the renormalization scale and scheme ambiguities in perturbative QCD. In particular, we present a recently developed method the PMC ∞ and its applications, comparing the results with CSS. The method preserves the property of renormalizable SU(N)/U(1) gauge theories defined as Intrinsic Conformality (iCF). This property underlies the scale invariance of physical observables and leads to a remarkably efficient method to solve the conventional renormalization scale ambiguity at every order in pQCD. This new method reflects the underlying conformal properties displayed by pQCD at NNLO, eliminates the scheme dependence of pQCD predictions and is consistent with the general properties of the PMC. A new method to identify conformal and β-terms, which can be applied either to numerical or to theoretical calculations is also shown. We present results for the thrust and C-parameter distributions in e + e - annihilation showing errors and comparison with the CSS. We also show results for a recent innovative comparison between the CSS and the PMC ∞ applied to the thrust distribution investigating both the QCD conformal window and the QED N c → 0 limit. In order to determine the thrust distribution along the entire renormalization group flow from the highest energies to zero energy, we consider the number of flavors near the upper boundary of the conformal window. In this flavor-number regime the theory develops a perturbative infrared interacting fixed point. These results show that PMC ∞ leads to higher precision and introduces new interesting features in the PMC. In fact, this method preserves with continuity the position of the peak, showing perfect agreement with the experimental data already at NNLO. We also show a detailed comparison of the PMC ∞ with the other PMC approaches: the multi-scale-setting approach (PMCm) and the single-scale-setting approach (PMCs) by comparing their predictions for three important fully integrated quantities R e+e- , R$_Τ$ and Γ (H→$b\bar{b}$) up to the four-loop accuracy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

High-Temperature Thermodynamics of Uranium from Ab Initio Modeling

We present high-temperature thermodynamic properties for uranium in its γ phase (γ-U) from first-principles, relativistic, and anharmonic theory. The results are compared to CALPHAD modeling. The ab initio electronic structure is obtained from density-functional theory (DFT) that includes spin–orbit coupling and an added self-consistent orbital-polarization (OP) mechanism for more accurate treatment of magnetism. The first-principles method is coupled to a lattice dynamics scheme that is used to model anharmonic lattice vibrations, namely, Self-Consistent Ab Initio Lattice Dynamics (SCAILD). The methodology can be summarized in the acronym DFT + OP + SCAILD. Upon thermal expansion, γ-U develops non-negligible magnetic moments that are included for the first time in thermodynamic theory. The all-electron DFT approach is shown to model γ-U better than the commonly used pseudopotential method. In addition to CALPHAD, DFT + OP + SCAILD thermodynamic properties are compared with other ab initio and semiempirical modeling and experiments. Our first-principles approach produces Gibbs free energy that is essentially identical to CALPHAD. The DFT + OP + SCAILD heat capacity is close to CALPHAD and most experimental data and is predicted to have a significant thermal dependence due to the electronic contribution.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

The potential role of organics in new particle formation and initial growth in the remote tropical upper troposphere

Abstract. Global observations and model studies indicate that new particle formation (NPF) in the upper troposphere (UT) and subsequent particles supply 40 %–60 % of cloud condensation nuclei (CCN) in the lower troposphere, thus affecting the Earth's radiative budget. There are several plausible nucleation mechanisms and precursor species in this atmospheric region, which, in the absence of observational constraints, lead to uncertainties in modeled aerosols. In particular, the type of nucleation mechanism and concentrations of nucleation precursors, in part, determine the spatial distribution of new particles and resulting spatial distribution of CCN from this source. Although substantial advances in understanding NPF have been made in recent years, NPF processes in the UT in pristine marine regions are still poorly understood and are inadequately represented in global models. Here, we evaluate commonly used and state-of-the-art NPF schemes in a Lagrangian box model to assess which schemes and precursor concentrations best reproduce detailed in situ observations. Using measurements of aerosol size distributions (0.003 < Dp < 4.8 µm) in the remote marine troposphere between ∼0.18 and 13 km altitude obtained during the NASA Atmospheric Tomography (ATom) mission, we show that high concentrations of newly formed particles in the tropical UT over both the Atlantic and Pacific oceans are associated with outflow regions of deep convective clouds. We focus analysis on observations over the remote Pacific Ocean, which is a region less perturbed by continental emissions than the Atlantic. Comparing aerosol size distribution measurements over the remote Pacific with box model simulations for 32 cases shows that none of the NPF schemes most commonly used in global models, including binary nucleation of sulfuric acid and water (neutral and ion-assisted) and ternary involving sulfuric acid, water, and ammonia, are consistent with observations, regardless of precursor concentrations. Through sensitivity studies, we find that the nucleation scheme among those tested that is able to explain most consistently (21 of 32 cases) the observed size distributions is that of Riccobono et al. (2014), which involves both organic species and sulfuric acid. The method of Dunne et al. (2016), involving charged sulfuric acid–water–ammonia nucleation, when coupled with organic growth of the nucleated particles, was most consistent with the observations for 5 of 32 cases. Similarly, the neutral sulfuric acid–water–ammonia method of Napari (2002), when scaled with a tuning factor and with organic growth added, was most consistent for 6 of 32 cases. We find that to best reproduce both nucleation and growth rates, the mixing ratios of gas-phase organic precursors generally need to be at least twice that of SO2, a proxy for dimethyl sulfide (DMS). Unfortunately, we have no information on the nature of oxidized organic species that participated in NPF in this region. Global models rarely include organic-driven nucleation and growth pathways in UT conditions where globally significant NPF takes place, which may result in poor estimates of NPF and CCN abundance and contribute to uncertainties in aerosol–cloud–radiation effects. Furthermore, our results indicate that the organic aerosol precursor vapors may be important in the tropical UT above marine regions, a finding that should guide future observational efforts.

54 ENVIRONMENTAL SCIENCES↗

Three-dimensional continuum point cloud method for large deformation and its verification

This study presents a strong form based meshfree collocation method, which is named Continuum Point Cloud Method, to solve nonlinear field equations derived from classical mechanics for deformed bodies in three-dimensional Euclidean space. The method and its implementation are benchmarked against a nonlinear vector field using manufactured solutions. The analysis of mechanical fields firstly focuses on the study of St. Venant Kirchhoff and compressible neo-Hookean materials. Results for various initial boundary value problems are presented, including benchmark cases involving unidirectional tension and simple shear. Subsequently, the study concludes with an analysis of a displacement-controlled simulation of a compressible neo-Hookean material, specifically a bar that is pulled to 50% of its original length and rotated 90°. The pure tension case yields a 1.5% error in displacement between computed and expected values and a combined tension and torsion loading case provides further insight into material behavior under complex loading conditions. The resulting normal axial and transverse stress-strain curves are also presented. Lastly, the consistency and robustness of the proposed nonlinear numerical schemes are successfully demonstrated through various numerical experiments.

Compressible neo-Hookean materials↗

Advances for QCD and the standard model: color-confining light-front holography and the principle of maximum conformality

Here, I review how the application of superconformal quantum mechanics and light-front holography leads to new insights into the physics of color confinement, the spectroscopy and dynamics of hadrons, as well as surprising supersymmetric relations between the masses of mesons, baryons, and tetraquarks. Spontaneous chiral symmetry breaking is automatically fulfilled by supersymmetric Light-Front QCD. The light-front holographic approach (HLFQCD) also predicts the behavior of the QCD running coupling and other observables from the nonperturbative color-confining domain to the perturbative domain. One can determine the QCD running coupling to high precision from the data of just a single experiment over the entire perturbative regime by using the Principle of Maximum Conformality (PMC). The PMC, which generalizes the conventional Gell-Mann-Low method for scale-setting in perturbative QED to non-Abelian QCD, provides a rigorous method for achieving unambiguous scheme-independent, fixed-order Standard Model predictions, consistent with the principles of the renormalization group. I also briefly review a novel feature of hadronic physics predicted by QCD: intrinsic heavy quarks.

Brodsky, Stanley J. [SLAC National Accelerator Lab↗

Developing and Managing Data Acquisition Software Using Spack

The Data Acquisition systems of particle physics experiments regularly push the boundaries of high-throughput computing, demanding low-latency collection of data from thousands of devices, collating data into time-sliced events, processing these events and making trigger decisions, and writing the selected data streams to disk. To accomplish these tasks, the DAQ Engineering and Operations department at Fermilab leverages multiple software libraries and builds reusable DAQ frameworks on top. These libraries must be delivered in well-defined bundles and are thoroughly tested for compatibility and functionality before being deployed to live detectors. We have several techniques used to ensure that a consistent set of dependencies can be delivered and re-created at need. We must also support active development of DAQ software components, ideally in an environment as close as possible to that of the detectors. This development often occurs across multiple packages which have to be built in concert and features tested in a consistent and reproducible manner. I will present our scheme for accomplishing these goals using Spack environments, bundle packages, and Github Actions-based CI.

Flumerfelt, Eric [Fermilab]↗

Snowflake: An Adaptive Energy and Delay Efficient Scheme for Source Location Privacy in Wireless Sensor Networks

Wireless Sensor Networks (WSNs) consist of a number of resource-constrained sensor nodes and a designated node called a sink, which collects data from the sensor nodes. A WSN can be used in numerous applications such as subject tracking and monitoring, where it is often desirable to keep the location of the subject private. In these types of applications, an adversary can locate the monitored subject, if a location privacy protection scheme is not applied. In this paper, we propose an adaptive energy and delay efficient scheme, called Snowflake, that conceals the location of subjects from a global adversary. Snowflake can be adapted to make the delivery delay smaller, or to make the packet overhead low. The simulation results show that Snowflake performs better than an existing algorithm.

97 MATHEMATICS AND COMPUTING↗

Metrics for Intercomparison of Remapping Algorithms (MIRA) protocol applied to Earth system models

Abstract. Strongly coupled nonlinear phenomena such as those described by Earth system models (ESMs) are composed of multiple component models with independent mesh topologies and scalable numerical solvers. A common operation in ESMs is to remap or interpolate component solution fields defined on their computational mesh to another mesh with a different combinatorial structure and decomposition, e.g., from the atmosphere to the ocean, during the temporal integration of the coupled system. Several remapping schemes are currently in use or available for ESMs. However, a unified approach to compare the properties of these different schemes has not been attempted previously. We present a rigorous methodology for the evaluation and intercomparison of remapping methods through an independently implemented suite of metrics that measure the ability of a method to adhere to constraints such as grid independence, monotonicity, global conservation, and local extrema or feature preservation. A comprehensive set of numerical evaluations is conducted based on a progression of scalar fields from idealized and smooth to more general climate data with strong discontinuities and strict bounds. We examine four remapping algorithms with distinct design approaches, namely ESMF Regrid (Hill et al., 2004), TempestRemap (Ullrich and Taylor, 2015), generalized moving least squares (GMLS) (Trask and Kuberry, 2020) with post-processing filters, and WLS-ENOR (Li et al., 2020). By repeated iterative application of the high-order remapping methods to the test fields, we verify the accuracy of each scheme in terms of their observed convergence order for smooth data and determine the bounded error propagation using challenging, realistic field data on both uniform and regionally refined mesh cases. In addition to retaining high-order accuracy under idealized conditions, the methods also demonstrate robust remapping performance when dealing with non-smooth data. There is a failure to maintain monotonicity in the traditional L2-minimization approaches used in ESMF and TempestRemap, in contrast to stable recovery through nonlinear filters used in both meshless GMLS and hybrid mesh-based WLS-ENOR schemes. Local feature preservation analysis indicates that high-order methods perform better than low-order dissipative schemes for all test cases. The behavior of these remappers remains consistent when applied on regionally refined meshes, indicating mesh-invariant implementations. The MIRA intercomparison protocol proposed in this paper and the detailed comparison of the four algorithms demonstrate that the new schemes, namely GMLS and WLS-ENOR, are competitive compared to standard conservative minimization methods requiring computation of mesh intersections. The work presented in this paper provides a foundation that can be extended to include complex field definitions, realistic mesh topologies, and spectral element discretizations, thereby allowing for a more complete analysis of production-ready remapping packages.

58 GEOSCIENCES↗

An Optimized Parameterization of Sub‐Grid Scale Advection for Convection Permitting Models

Convection‐permitting models (CPMs) explicitly resolve deep convection yet under‐resolve the organized lateral exchanges among drafts and their environment that control entrainment/detrainment, precipitation efficiency, and mesoscale structure. In this work, we introduce the Optimized Advection Scheme (OAS), which introduces a small rotation of the Cartesian frame of reference for the horizontal winds relative to other variables used in advection that induces cross‐gradient transport to mimic under‐resolved convective mixing. The rotation angle is selected to minimize the Kullback–Leibler divergence between the simulated and satellite observed precipitation intensity distributions, yielding a physically consistent perturbation that is computationally inexpensive and portable. Optimized Advection Scheme is implemented in WRF and evaluated over Amazon (April 2014). It shifts precipitation–precipitable‐water joint distributions toward lighter rain, reduces overly intense rates, and improves mesoscale convective system (MCS) lifetime and propagation. Mechanistically, the added cross‐gradient transport promotes convective detrainment and environmental mixing, which cools and moistens the mid‐troposphere, weakens downward momentum transport, alleviates excessive downwelling shortwave biases, and warms the surface temperature. The optimized rotation angle yields comparable improvements at 4‐km and 1‐km grid spacing, demonstrating resolution‐independent benefits across the CPM gray zone. By targeting the dynamical root of under‐mixed convective circulations, rather than tuning model microphysics or closures, OAS delivers robust, scale‐aware improvements in precipitation statistics, cloud vertical structure, and characteristics of MCS (MCSs), offering a practical pathway to more reliable CPM simulations for weather and climate applications.

CPM↗

Numerical integration in the virtual element method with the scaled boundary cubature scheme

Abstract The virtual element method (VEM) is a stabilized Galerkin method on meshes that consist of arbitrary (convex and nonconvex) polygonal and polyhedral elements. A crucial ingredient in the implementation of low‐ and high‐order VEM is the numerical integration of monomials and nonpolynomial functions over such elements. In this article, we apply the recently proposed scaled boundary cubature (SBC) scheme to compute the weak form integrals in various virtual element formulations over polygonal and polyhedral meshes. In doing so, we demonstrate the flexibility of the approach and the accuracy that it delivers on a broad suite of boundary‐value problems in 2D and 3D over polytopes with affine faces as well as on elements with curved boundaries. In addition, the use of the SBC scheme is exemplified in an enriched Poisson formulation of the VEM in which weakly singular functions are required to be integrated. This study establishes the SBC method as a simple, accurate and efficient integration scheme for use in the VEM.

Chin, Eric B.↗

A conservative Galerkin solver for the quasilinear diffusion model in magnetized plasmas

We propose a conservative Galerkin scheme for the quasilinear model in three-dimensional momentum space and three-dimensional spectral space, with cylindrical symmetry. We construct an unconditionally conservative weak form and use a discretization that preserves conservation properties independent of the wave emission probability. The discrete operators, combined with a consistent quadrature rule, preserve all the conservation laws rigorously. The proposed scheme is quite general: it works for both relativistic and non-relativistic systems, for both magnetized and unmagnetized plasmas, and even for problems with time-dependent dispersion relations. We represent the particle distribution by continuous basis functions and use discontinuous basis functions for the wave spectral energy density, which enables the application of a positivity-preserving technique. We adopt the marching simplex algorithm, designed initially for computer graphics, for numerical integration on the resonance manifold. Furthermore, the numerical examples with a bump-on-tail initial configuration show how the unstable waves produce strong momentum space diffusion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Assessment of a Detailed Biomass Pyrolysis Kinetic Scheme in Multiscale Simulations of a Single-Particle Pyrolyzer and a Pilot-Scale Entrained Flow Pyrolyzer

A detailed biomass pyrolysis kinetic scheme was assessed in the multiscale simulations of a single-particle pyrolyzer with slow pyrolysis and a pilot-scale entrained flow pyrolyzer with fast pyrolysis. The detailed kinetic scheme of biomass pyrolysis developed by the CRECK group consists of 32 reactions and 58 species. A multiscale simulation model was developed, where the CRECK kinetics was employed to simulate biomass pyrolysis reactions, a one-dimensional particle model was utilized to simulate the intraparticle transport phenomena, and the particle-in-cell (PIC) model was employed to simulate the hydrodynamics. The multiscale model was first applied to simulate a single-particle pyrolysis experiment. The simulation with nonisothermal particles matched the experimental data better than the simulation with isothermal particles. Then the multiscale model was applied to simulate the pilot-scale entrained flow pyrolyzer. In this case, the simulation with isothermal particles matched the experimental data better than the simulation with nonisothermal particles. The reason for this difference might be that the kinetics itself already partially included the intraparticle transport effect as it was fitted using both TGA data (slow pyrolysis of small size biomass) and fluidized bed data (fast pyrolysis of relatively large size biomass). This study provides some insights into biomass pyrolysis kinetics development and pyrolyzer multiscale simulation for a future study.

09 BIOMASS FUELS↗

Detailed comparison of renormalization scale-setting procedures based on the principle of maximum conformality

The Principle of Maximum Conformality (PMC), which generalizes the conventional Gell-Mann-Low method for scale-setting in perturbative QED to non-Abelian QCD, provides a rigorous method for achieving unambiguous scheme-independent, fixed-order predictions for physical observables consistent with the principles of the renormalization group. In addition to the original multi-scale-setting approach (PMCm), two variations of the PMC have been proposed to deal with ambiguities associated with the uncalculated higher order terms in the pQCD series, i.e. the single-scale-setting approach (PMCs) and the procedures based on ``intrinsic conformality" (PMC ∞ ). In this paper, we will give a detailed comparison of these PMC approaches by comparing their predictions for three important quantities R e+e– , R τ , and $Γ(H→b\bar{b}$) up to four-loop pQCD corrections. The PMCs approach determines an overall effective running coupling α s (Q) by the recursive use of the renormalization group equation, whose argument Q represents the actual momentum flow of the process. Our numerical results show that the PMCs method, which involves a somewhat simpler analysis, can serve as a reliable substitute for the full multi-scale PMCm method, and that it leads to more precise pQCD predictions with small residual scale dependence.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

The Grassmann interpolation method for spin-unrestricted open-shell systems

The recently reported Grassmann interpolation (G-Int) method [J. A. Tan and K. U. Lao, J. Chem. Phys. 158, 051101 (2023)] has been extended to spin-unrestricted open-shell systems. In contrast to closed-shell systems, where G-Int has to be performed only once since the α and β density matrices are the same, spin-unrestricted open-shell systems require G-Int to be performed twice—one for the α spin and another for the β spin density matrix. In this work, we tested the performance of G-Int to the carbon monoxide radical cation CO●+ and nickelocene complex, which have the doublet and triple ground states, respectively. We found that the Frobenius norm errors associated with the interpolations for the α and β spin density matrices are comparable for a given molecular geometry. These G-Int density matrices, when used as an initial guess for a self-consistent field (SCF) calculation, outperform the conventional SCF guess schemes, such as the superposition of atomic densities, purified superposition of atomic densities, core Hamiltonian, and generalized Wolfsberg–Helmholtz approximation. Depending on the desired accuracy, these G-Int density matrices can be used to directly evaluate the SCF energy without performing SCF iterations. In addition, the spin-unrestricted G-Int density matrices have been used for the first time to directly calculate the atomic charges using the Mulliken and ChElPG population analysis.

Chemistry↗