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At least 451 records · Page 25

Understanding the setting and hardening process of wollastonite-based brushite cement. Part 2: Influence of the boron and aluminum concentrations in the mixing solution

The mixing solution of wollastonite-based brushite cement is a phosphoric acid solution containing metallic cations and borax. This work complements a previous study devoted to the influence of the H{sub 3}PO{sub 4} concentration, Ca/P and liquid-to-solid (l/s) ratios on the setting and hardening process of the binder by providing new insight into the role of aluminum and boron. Boron retards the setting and decreases the heat released during the process. It also contributes to reduce the macroporosity of the hardened material but yields to poor compressive strength. With aluminum in the mixing solution, the mechanical properties are greatly improved thanks to the precipitation of an amorphous aluminophosphate which increases the density of the cement matrix. But aluminum alone leads to fast setting. A joint addition of boron and aluminum to the mixing solution makes it possible to get a material with optimized properties both in fresh and hardened states.

36 MATERIALS SCIENCE↗

Low correlation between household carbon monoxide and particulate matter concentrations from biomass-related pollution in three resource-poor settings

Household air pollution from the burning of biomass fuels is recognized as the third greatest contributor to the global burden of disease. Incomplete combustion of biomass fuels releases a complex mixture of carbon monoxide (CO), particulate matter (PM) and other toxins into the household environment. Some investigators have used indoor CO concentrations as a reliable surrogate of indoor PM concentrations; however, the assumption that indoor CO concentration is a reasonable proxy of indoor PM concentration has been a subject of controversy. We sought to describe the relationship between indoor PM{sub 2.5} and CO concentrations in 128 households across three resource-poor settings in Peru, Nepal, and Kenya. We simultaneously collected minute-to-minute PM{sub 2.5} and CO concentrations within a meter of the open-fire stove for approximately 24 h using the EasyLog-USB-CO data logger (Lascar Electronics, Erie, PA) and the personal DataRAM-1000AN (Thermo Fisher Scientific Inc., Waltham, MA), respectively. We also collected information regarding household construction characteristics, and cooking practices of the primary cook. Average 24 h indoor PM{sub 2.5} and CO concentrations ranged between 615 and 1440 μg/m{sup 3}, and between 9.1 and 35.1 ppm, respectively. Minute-to-minute indoor PM{sub 2.5} concentrations were in a safe range (<25 μg/m{sup 3}) between 17% and 65% of the time, and exceeded 1000 μg/m{sup 3} between 8% and 21% of the time, whereas indoor CO concentrations were in a safe range (<7 ppm) between 46% and 79% of the time and exceeded 50 ppm between 4%, and 20% of the time. Overall correlations between indoor PM{sub 2.5} and CO concentrations were low to moderate (Spearman ρ between 0.59 and 0.83). There was also poor agreement and evidence of proportional bias between observed indoor PM{sub 2.5} concentrations vs. those estimated based on indoor CO concentrations, with greater discordance at lower concentrations. Our analysis does not support the notion that indoor CO concentration is a surrogate marker for indoor PM{sub 2.5} concentration across all settings. Both are important markers of household air pollution with different health and environmental implications and should therefore be independently measured. - Highlights: • We summarized indoor PM2.5 and CO concentrations across three resource-poor settings. • Overall correlations between indoor PM2.5 and CO were low to moderate. • Agreement between observed indoor PM2.5 vs. those estimated based on indoor CO was poor.

54 ENVIRONMENTAL SCIENCES↗

Modeling the dynamic response of rock masses with multiple compliant fluid saturated joint sets - Part II: Continuum modeling

Part I of this two-part paper describes enhancements of a mesoscale model to include: many non-persistent fluid saturated joints with finite area, normal compliance with hysteresis and the weakening effects of angular deviation in the joint sets and of fluid pressure in the joints. The objective of this Part II is to use the results of the mesoscale model as simulated data to inspire functional forms in a continuum model for rock masses with multiple compliant fluid saturated joint sets which include these enhancements. Also, an algorithm is proposed for reducing the number of joint sets being modeled. Examples are presented here which show that the continuum model can predict similar anisotropic response to that observed in mesoscale simulations. In contrast with the mesoscale model, the continuum model can be used for large scale simulations of real applications, smoothly transitioning from coupled inelastic thermomechanical response near an explosive source to orthotropic elastic response far from the source.

58 GEOSCIENCES↗

Low-dose-rate Brachytherapy for Prostate Cancer in Low-resource Settings

Purpose: In areas with limited health care, it is important to identify and implement effective treatment methods and to optimize available resources. We investigated the implementation of a low-dose-rate (LDR) brachytherapy program for the treatment of prostate cancer (PCa) in a low-resource setting such as Puerto Rico (PR), where PCa is the main cause of cancer-associated death. Methods and Materials: After institutional approval, the medical records of patients with nonmetastatic PCa undergoing LDR brachytherapy from 2008 to 2013 were reviewed from PR. The factors analyzed included adequate D{sub 90} (radiation dose delivered to 90% of the target volume) coverage (≥140 Gy), early and late toxicity (Common Terminology Criteria for Adverse Events grade >2), and prostate-specific antigen failure. Freedom from biochemical failure was evaluated using Kaplan-Meier analysis. Results: The barriers to implementation of LDR brachytherapy in a country with limited resources were identified. These included lack of access to funding for startup costs, specific referral patterns, lack of trained support staff, such as dosimetrists and physicists, and initial opposition from insurance companies for reimbursement. The initial results from 191 patients were included in the present study with a median follow-up period of 26 months. Prostate-specific antigen failure occurred in 6 patients (3%). No early or late gastrointestinal toxicity (grade >2) developed. Only 3 (2%) and 2 (1%) patients experienced early and late genitourinary toxicity (grade >2), respectively. The 2- and 3-year freedom from biochemical failure in this population was 97% and 95.9%, respectively. Conclusions: At present, limited data are available delineating the barriers faced by low-resource settings in the implementation of LDR brachytherapy. Our data highlight the issues unique to this environment and support the use of LDR brachytherapy as a reliable and effective treatment modality for patients with PCa in low-resource settings.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Evaluating vaccination strategies for tuberculosis in endemic and non-endemic settings

According to the World Health Organization, tuberculosis (TB) is the leading cause of death from infectious disease worldwide. While there is no effective vaccine against adult pulmonary TB, more than a dozen vaccine candidates are in the clinical trial pipeline. These include both pre-exposure vaccines to prevent initial infections and post-exposure vaccines to prevent reactivation of latent disease. Many epidemiological models have been used to study TB, but most have not included a continuous age structure and the possibility of both pre- and post-exposure vaccination. Incorporating age-dependent death rates, disease properties, and social contact data allows for more realistic modeling of disease spread. Here, we propose a continuous age-structured model for the epidemiology of tuberculosis with pre- and post-exposure vaccination. We use uncertainty and sensitivity analysis to make predictions about the efficacy of different vaccination strategies in a non-endemic setting (United States) and an endemic setting (Cambodia). In particular, we determine optimal age groups to target for pre-exposure and post-exposure vaccination in both settings. We find that the optimal age groups tend to be younger for Cambodia than for the US, and that post-exposure vaccination has a significantly larger effect than pre-exposure vaccination in the US.

60 APPLIED LIFE SCIENCES↗

The Impact of Gate Width Setting and Gate Utilization Factors on Plutonium Assay in Passive Correlated Neutron Counting

In the field of nuclear safeguards, passive neutron multiplicity counting (PNMC) is a method typically employed in non-destructive assay (NDA) of special nuclear material (SNM) for nonproliferation, verification and accountability purposes. PNMC is generally performed using a well-type thermal neutron counter and relies on the detection of correlated pairs or higher order multiplets of neutrons emitted by an assayed item. To assay SNM, a set of parameters for a given well-counter is required to link the measured multiplicity rates to the assayed item properties. Detection efficiency, die-away time, gate utilization factors (tightly connected to die-away time) as well as optimum gate width setting are among the key parameters. These parameters along with the underlying model assumptions directly affect the accuracy of the SNM assay. In this paper we examine the role of gate utilization factors and the single exponential die-away time assumption and their impact on the measurements for a range of plutonium materials. In addition, we examine the importance of item-optimized coincidence gate width setting as opposed to using a universal gate width value. Finally, the traditional PNMC based on multiplicity shift register electronics is extended to Feynman-type analysis and application of this approach to Pu mass assay is demonstrated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

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↗

Achieving performance portability in Gaussian basis set density functional theory on accelerator based architectures in NWChemEx

The numerical integration of the exchange–correlation (XC) potential is one of the primary computational bottlenecks in Gaussian basis set Kohn–Sham density functional theory (KS-DFT). To achieve optimal performance and accuracy, care must be taken in this numerical integration to preserve local sparsity as to allow for near linear weak scaling with system size. This leads to an integration scheme with several performance critical kernels which must be hand optimized for each architecture of interest. As the set of available accelerator hardware goes more diverse, a key challenge for developers of KS-DFT software is to maintain performance portability across a wide range of computational architectures. In this article, we examine a modular software design pattern which decouples the implementation details of performance critical kernels from the expression of high-level algorithmic workflows in a device-agnostic language such as C++; thus allowing for developers to target existing and emerging accelerator hardware within a single code base. We consider the efficacy of such a design pattern in the numerical integration of the XC potential by demonstrating its ability to achieve performance portability across a set of accelerator architectures which are representative of those on current and future U.S. Department of Energy Leadership Computing Facilities.

97 MATHEMATICS AND COMPUTING↗

Use of genomic data in risk assessment case study: II. Evaluation of the dibutyl phthalate toxicogenomic data set

An evaluation of the toxicogenomic data set for dibutyl phthalate (DBP) and male reproductive developmental effects was performed as part of a larger case study to test an approach for incorporating genomic data in risk assessment. The DBP toxicogenomic data set is composed of nine in vivo studies from the published literature that exposed rats to DBP during gestation and evaluated gene expression changes in testes or Wolffian ducts of male fetuses. The exercise focused on qualitative evaluation, based on a lack of available dose–response data, of the DBP toxicogenomic data set to postulate modes and mechanisms of action for the male reproductive developmental outcomes, which occur in the lower dose range. A weight-of-evidence evaluation was performed on the eight DBP toxicogenomic studies of the rat testis at the gene and pathway levels. The results showed relatively strong evidence of DBP-induced downregulation of genes in the steroidogenesis pathway and lipid/sterol/cholesterol transport pathway as well as effects on immediate early gene/growth/differentiation, transcription, peroxisome proliferator-activated receptor signaling and apoptosis pathways in the testis. Since two established modes of action (MOAs), reduced fetal testicular testosterone production and Insl3 gene expression, explain some but not all of the testis effects observed in rats after in utero DBP exposure, other MOAs are likely to be operative. A reanalysis of one DBP microarray study identified additional pathways within cell signaling, metabolism, hormone, disease, and cell adhesion biological processes. These putative new pathways may be associated with DBP effects on the testes that are currently unexplained. This case study on DBP identified data gaps and research needs for the use of toxicogenomic data in risk assessment. Furthermore, this study demonstrated an approach for evaluating toxicogenomic data in human health risk assessment that could be applied to future chemicals. - Highlights: ► We evaluate the dibutyl phthalate toxicogenomic data for use in risk assessment. ► We focus on information about the mechanism of action for the developing testis. ► Multiple studies report effects on testosterone and insl3-related pathways. ► We identify additional affected pathways that may explain some testis effects. ► The case study is a template for evaluating toxicogenomic data in risk assessment.

60 APPLIED LIFE SCIENCES↗

Application of a set of complementary techniques to understand how varying the proportion of two wastes affects humic acids produced by vermicomposting

Highlights: • A set of techniques was used to characterize humic acids content of vermicomposts. • The properties of the humic acids produced from different waste mixtures were similar. • This set of techniques allowed distinguishing the humic acids of each vermicomposts. • Increasing humic acid contents in initial mixtures would produce richer vermicomposts. - Abstract: A better understanding of how varying the proportion of different organic wastes affects humic acid (HA) formation during vermicomposting would be useful in producing vermicomposts enriched in HAs. With the aim of improving the knowledge about this issue, a variety of analytical techniques [UV–visible spectroscopic, Fourier transform infrared, fluorescence spectra, solid-state cross-polarization magic-angle spinning (CPMAS) {sup 13}C nuclear magnetic resonance (NMR) spectra, and thermal analysis] was used in the present study to characterize HAs isolated from two mixtures at two different ratios (2:1 and 1:1) of tomato-plant debris (TD) and paper-mill sludge (PS) before and after vermicomposting. The results suggest that vermicomposting increased the HA content in the TD/PS 2:1 and 1:1 mixtures (15.9% and 16.2%, respectively), but the vermicompost produced from the mixture with a higher amount of TD had a greater proportion (24%) of HAs. Both vermicomposting processes caused equal modifications in the humic precursors contained in the different mixtures of TD and PS, and consequently, the HAs in the vermicomposts produced from different waste mixtures exhibited analogous characteristics. Only the set of analytical techniques used in this research was able to detect differences between the HAs isolated from each type of vermicompost. In conclusion, varying the proportion of different wastes may have a stronger influence on the amount of HAs in vermicomposts than on the properties of HAs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Curating a comprehensive set of enzymatic reaction rules for efficient novel biosynthetic pathway design

Enzyme substrate promiscuity has significant implications for metabolic engineering. The ability to predict the space of possible enzymatic side reactions is crucial for elucidating underground metabolic networks in microorganisms, as well as harnessing novel biosynthetic capabilities of enzymes to produce desired chemicals. Reaction rule-based cheminformatics platforms have been implemented to computationally enumerate possible promiscuous reactions, relying on existing knowledge of enzymatic transformations to inform novel reactions. However, past versions of curated reaction rules have been limited by a lack of comprehensiveness in representing all possible transformations, as well as the need to prune rules to enhance computational efficiency in pathway expansion. To this end, we curated a set of 1224 most generalized reaction rules, automatically abstracted from atom-mapped MetaCyc reactions and verified to uniquely cover all common enzymatic transformations. Additionally, we developed a framework to systematically identify and correct redundancies and errors in the curation process, resulting in a minimal, yet comprehensive, rule set. These reaction rules were capable of reproducing more than 85% of all reactions in the KEGG and BRENDA databases, for which a large fraction of reactions is not present in MetaCyc. Our rules exceed all previously published rule sets for which reproduction was possible in this coverage analysis, which allows for the exploration of a larger space of known enzymatic transformations. By leveraging the entire knowledge of possible metabolic reactions through generalized enzymatic reaction rules, we are able to better utilize underground metabolic pathways and accelerate novel biosynthetic pathway design to enable bioproduction towards a wider range of new molecules.

59 BASIC BIOLOGICAL SCIENCES↗

Accurate Prediction of HSE06 Band Structures for a Diverse Set of Materials Using Δ-Learning

Here we used machine learning (ML) to accurately predict eigenvalues of the hybrid HSE06 functional using eigenvalues computed by the less computationally expensive PBE functional and associated electronic features based on the k-point resolved atomic band character. The ML model was trained by using eigenvalues from only one k-point for each of the 168 compounds in the training set. The HSE06 eigenvalues across all k-points were then predicted for a separate set of 169 compounds with a mean absolute error (MAE) of 0.13 eV, representing a significant improvement over the error of PBE-computed eigenvalues relative to that of HSE06 (MAE = 0.96 eV). These accurately predicted eigenvalues result in remarkably accurate predictions for the band structures, projected density of states, and band gaps, even though the model was not explicitly trained on these other properties. Finally, we demonstrate that our ML model has a similar accuracy for both ternary and quaternary compounds well outside the initial training set and on systems with 112 and 160 atoms, demonstrating its potential to rapidly predict HSE06-quality electronic structures of complex materials that are practically unfeasible for HSE06.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

MS25: Materials Science-Focused Benchmark Data Set for Machine Learning Interatomic Potentials

Here, we present MS25, a benchmark data set for evaluating machine learning interatomic potentials (MLIPs) across diverse materials-relevant systems including MgO surfaces, liquid water, zeolites, a catalytic Pt surface reaction, high-entropy alloys (HEAs), and disordered Zr-oxides. Five MLIP architectures (MACE, NequIP, Allegro, MTP, and Torch-ANI) are trained and tested, focusing not only on traditional metrics (energies, forces, and stresses) but also explicitly validating derived physical observables such as lattice constants, volumes, and reaction barriers. We find that most models reach comparable accuracy on standard error metrics across the simple systems, although equivariant MLIPs offer 1.5–2× improvements over nonequivariant MLIPs in energy and force error for structurally complex or compositionally disordered environments such as HEAs and Zr–O systems. Our analysis highlights that low errors in energy and force predictions do not guarantee reliable observables, emphasizing the necessity of explicit validation. We demonstrate limitations in cross-framework transferability, as models trained on one zeolite framework (CHA) fail to reliably generalize to predictions of structurally distinct frameworks (e.g., MFI). Size-extensive tests show some dependence on system size for MgO, resulting from forced periodicity. The HEA and Zr–O data sets are identified as challenging tests for future benchmarks and MLIP model architecture developments as they show significant differentiation in error between MLIP architectures and are still relatively difficult at 1000 training images. Moving forward, we recommend that benchmarking efforts shift their focus from marginal accuracy improvements in energy and force errors toward identifying and understanding model failure modes, rigorously assessing transferability, and evaluating how their errors affect observable predictions. For researchers looking to choose an MLIP architecture, we suggest selecting equivariant MLIP architectures if the complexity of the system is a challenge. For simple materials problems, auxiliary features such as integration with molecular dynamics engines, trade-offs between computational data set generation cost vs MLIP inference speed, and framework integration may play a more important decision factor than small differences in error metrics that are unlikely to matter for production-level research.

chemical structure↗

Gold-Standard Chemical Database 137 (GSCDB137): A Diverse Set of Accurate Energy Differences for Assessing and Developing Density Functionals

We present GSCDB137, a rigorously curated benchmark library of 137 data sets (8377 entries) covering main-group and transition-metal reaction energies and barrier heights, (intra- and intermolecular) noncovalent interactions, dipole moments, polarizabilities, electric-field response energies, and vibrational frequencies. Legacy data from GMTKN55 and MGCDB84 have been updated to today's best reference values; redundant or low-quality points were removed, and many new, property-focused sets were added. Testing 29 popular density functional approximations (DFAs) confirms the expected Jacob's-ladder hierarchy overall but also reveals notable exceptions: functional performance for frequencies and electric-field properties correlates poorly with that for other ground-state energetics. ωB97M-V and ωB97X-V are the most balanced hybrid meta-GGA and hybrid GGA, respectively; B97M-V and revPBE-D4 lead the meta-GGA and GGA classes. Double hybrids lower mean errors by about 30% versus their hybrid analogues but demand careful frozen-core, basis set, and spin contamination treatment. GSCDB137 offers a comprehensive, openly documented platform for rigorous validation of DFA and universal machine learning potentials, and training of the next generation of exchange-correlation functionals.

Liang, Jiashu [University of California, Berkeley,↗

A Density Functional Tight Binding Model with an Extended Basis Set and Three-Body Repulsion for Hydrogen under Extreme Thermodynamic Conditions

Here, we present a new DFTB-p3b density functional tight binding model for hydrogen at extremely high pressures and temperatures, which includes a polarizable basis set ( p ) and a three-body environmentally dependent repulsive potential ( 3b ). We find that use of an extended basis set is necessary under dissociated liquid conditions to account for the substantial p-orbital character of the electronic states around the Fermi energy. The repulsive energy is determined through comparison to cold curve pressures computed from density functional theory (DFT) for the hexagonal close-packed solid, as well as pressures from thermally equilibrated DFT-MD simulations of the liquid phase. In particular, we observe improved agreement in our DFTB-p3b model with previous theoretical and experimental results for the shock Hugoniot of hydrogen up to 100 GPa and 25000 K, compared to a standard DFTB model using pairwise interactions and an s-orbital basis set, only. In conclusion, the DFTB-p3b approach discussed here provides a general method to extend the DFTB method for a wide variety of materials over a significantly larger range of thermodynamic conditions than previously possible.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

iVirus: facilitating new insights in viral ecology with software and community data sets imbedded in a cyberinfrastructure

Microbes affect nutrient and energy transformations throughout the world’s ecosystems, yet they do so under viral constraints. In complex communities, viral metagenome (virome) sequencing is transforming our ability to quantify viral diversity and impacts. Although some bottlenecks, for example, few reference genomes and nonquantitative viromics, have been overcome, the void of centralized data sets and specialized tools now prevents viromics from being broadly applied to answer fundamental ecological questions. Here we present iVirus, a community resource that leverages the CyVerse cyberinfrastructure to provide access to viromic tools and data sets. The iVirus Data Commons contains both raw and processed data from 1866 samples and 73 projects derived from global ocean expeditions, as well as existing and legacy public repositories. Through the CyVerse Discovery Environment, users can interrogate these data sets using existing analytical tools (software applications known as ‘Apps’) for assembly, open reading frame prediction and annotation, as well as several new Apps specifically developed for analyzing viromes. Because Apps are web based and powered by CyVerse supercomputing resources, they enable scalable analyses for a broad user base. Finally, a use-case scenario documents how to apply these advances toward new data. This growing iVirus resource should help researchers utilize viromics as yet another tool to elucidate viral roles in nature.

59 BASIC BIOLOGICAL SCIENCES↗

Metamodels for Rapid Analysis of Large Sets of Building Designs for Robotic Constructability: Technology Demonstration Using the NASA 3D Printed Mars Habitat Challenge

Disruptive robotic construction technologies such as additive deposition of cementitious materials like concrete (or "3D concrete printing") require the synchronous operation of multiple pieces of equipment in the production setup. In such an environment, it is crucial to simulate the robotic motions (for toolpath clashes) and the cementitious material behavior (for toolpath failures) to ensure fail-proof constructability of the envisioned building geometry. However, toolpath clash detection requires 4D simulations of the production setup, which are computationally graphics intensive, whereas toolpath failure detection requires actual 3D printing of test parts from the geometry to identify areas prone to failure while 3D printing, which is physically tedious. Both these processes, being computationally and physically intensive, have largely curtailed designers from simulating and exploring large sets of design options with varying geometries and toolpath configurations. To overcome this and allow designers to explore large sets of design possibilities, this paper proposes two novel computational metamodels capable of performing robotic toolpath clash detection and failure detection with significantly reduced times than the earlier approaches. The developed metamodels were used to rapidly simulate large sets of building design options for robotic constructability in the NASA 3D-Printed Mars Habitat Challenge.

clash detection↗

Comment on “Rethinking first-principles electron transport theories with projection operators: The problems caused by partitioning the basis set” [J. Chem. Phys. 139, 114104 (2013)]

In a recent paper Reuter and Harrison [J. Chem. Phys. 139, 114104 (2013)] question the widely used mean-field electron transport theories, which employ nonorthogonal localized basis sets. They claim these can violate an “implicit decoupling assumption,” leading to wrong results for the current, different from what would be obtained by using an orthogonal basis, and dividing surfaces defined in real-space. We argue that this assumption is not required to be fulfilled to get exact results. We show how the current/transmission calculated by the standard Greens function method is independent of whether or not the chosen basis set is nonorthogonal, and that the current for a given basis set is consistent with divisions in real space. The ambiguity known from charge population analysis for nonorthogonal bases does not carry over to calculations of charge flux.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗