Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Analytical Balance”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6

Improvements in the orbitalwise scaling down of Perdew–Zunger self-interaction correction in many-electron regions

The Perdew-Zunger (PZ) method offers a way to remove the self-interaction (SI) error from density functional approximations on an orbital by orbital basis. The PZ method provides significant improvements for the properties such as barrier heights or dissociation energies but results in over-correcting the properties well described by SI-uncorrected semi-local functional. One cure to rectify the over-correcting tendency is to scale down the magnitude of SI-correction of each orbital in the many electron region. We have implemented the orbitalwise scaled down SI-correction (OSIC) scheme of Vydrov et al. [J. Chem. Phys. 124, 094108 (2006)] using the Fermi-L owdin SI-correction method. After validating the OSIC implementation with previously reported OSICLSDA results, we examine its performance with the most successful non-empirical SCAN meta-GGA functional. Using different forms of scaling factors to identify one-electron regions, we assess the performance of OSIC-SCAN for a wide range of properties: total energies, ionization potentials and electron affinities for atoms, atomization energies, dissociation and reaction energies, and reaction barrier heights of molecules. Our results show that OSIC-SCAN provides superior results than the previously reported OSIC-LSDA, -PBE, and -TPSS results. Furthermore, we propose selective scaling of OSIC (SOSIC) to remove its major shortcoming that destroys the -1/r asymptotic behavior of the potentials. The SOSIC method gives the highest occupied orbital eigenvalues practically identical to those in PZSIC and unlike OSIC provides bound atomic anions even with larger powers of scaling factors. Furthermore, SOSIC compared to PZSIC or OSIC provides more balanced description of total energies and barrier heights.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

High-precision monitoring of outgassing species in model extreme ultraviolet photoresists with a cavity ring-down spectrometer

Background Extreme ultraviolet (EUV) photoresists play a pivotal role in advancing nanopatterning technologies by balancing image quality and sensitivity. The outgassing behavior of photoresist thin films under EUV and deep ultraviolet (DUV) exposure reveals chemical details relevant to their performance. Aim Here, we focus on utilizing an analytical technique not previously used in photolithography, the tabletop cavity ring-down spectrometer, to investigate outgassing dynamics in EUV photoresists, enabling precise chemical identification and deeper insights into resist processing. Approach The spectrometer’s enhanced laser path length (∼ 20 km) and broadband absorption capabilities in the C–H overtone region allow for sensitive and temporally resolved detection of mixtures of outgassed species. Using a model resist comprising a polymer matrix with a photoacid generator and quencher, we analyzed the influence of time delays between exposure and post-exposure bake (PEB) as well as storage under varying environmental conditions. Results Suppression of isobutylene outgassing and thickness loss was observed with extended delays between exposure and PEB, potentially linked to water absorption and acid deactivation. The technique proved highly effective in distinguishing subtle chemical differences between processing stages. Conclusions Delay times and their environmental conditions, particularly humidity, reduce outgassing and thickness loss of photoresists during PEB, suggesting decreased acid-driven deprotection. This can potentially impact sensitivity, defectivity, and roughness of resist patterns, necessitating precise monitoring and control.

Extreme ultraviolet photoresists↗

Web-Based Tools for Data-Informed Remedy Optimization: Software Theory and User Guide

This report documents the development and application of two web-based decision-support tools for pump-and-treat (P&T) groundwater remediation systems: PTOLEMY (Pump-and-Treat Optimized Location Evaluation to Maximize Yields) and OPTIMA (Optimization for Pump-and-Treat Implementation, Management, & Assessment). These tools enhance remedy design and management by leveraging advanced computational methods – specifically deep learning and multi-objective optimization – within a user-friendly platform. By integrating data-driven models with established hydrogeological knowledge, PTOLEMY and OPTIMA enable more efficient evaluation of well placement and operational strategies, helping site managers balance multiple remediation objectives under complex conditions. Both tools are implemented as modules within the SOCRATES (Suite Of Comprehensive Rapid Analysis Tools for Environmental Sites) web platform, which provides data access, visualization, and analytics to support remedy optimization across sites in the U.S. Department of Energy Office of Environmental Management complex. PTOLEMY is a rapid screening module designed to identify promising locations for new extraction wells. It employs a multi-channel three-dimensional convolutional neural network (MC3D-CNN) trained on high-fidelity simulation data to predict the relative performance (in terms of contaminant mass recovery) of potential well sites. Through an interactive web interface, PTOLEMY visualizes the probability of high performance across a site, highlighting areas where an extraction well is likely to yield above-threshold contaminant removal over a multi-year period. PTOLEMY’s map-based displays and exportable results support transparent communication of screening analyses. By focusing attention on the most favorable candidate locations, the tool augments traditional engineering judgment and physics-based modeling, providing a data informed basis for subsequent detailed evaluations. OPTIMA is a multi objective optimization module designed to find wellfield layouts and operating schedules that meet various cleanup goals. It quickly evaluates thousands of candidate setups – combinations of well locations, timing, and rates – and returns a small set of best trade-off options for comparison. At its core, OPTIMA uses a U-Net-based surrogate model – a deep-learning emulator of a groundwater flow and transport simulator – to dramatically accelerate scenario evaluations. Coupling this fast surrogate with the NSGA-II (Non-dominated Sorting Genetic Algorithm II) evolutionary algorithm, OPTIMA explores a wide decision space of well locations and schedules to identify Pareto-optimal solutions that trade off key objectives (e.g., minimizing cleanup time, maximizing contaminant mass removal, and minimizing plume extent). The tool outputs a family of optimal configurations and visualizes their trade-offs (Pareto frontiers of cleanup metrics and maps of optimized well placements). Site managers can use these results to understand the range of viable strategies and to select candidate designs for more detailed verification. OPTIMA is currently under active development and not yet fully released; this guide provides early documentation to support planning and gather user feedback.

54 ENVIRONMENTAL SCIENCES↗

Expanding the Domain of Applicability of Machine Learning Models with Limited Data for Drug Property Prediction

Accurate machine learning models for predicting small molecule interactions with biological targets are essential for therapeutic discovery, biothreat response, and computational drug design, but their performance is often limited for understudied targets with sparse experimental data. To address this challenge, we developed and evaluated methods to improve molecular property prediction under low-data conditions, using the NimA-related kinase (NEK) family as a proof-of-concept. This work focused on two complementary goals within the ATOM Modeling PipeLine (AMPL) and the Generative Molecular Design (GMD) loop: expanding model applicability through transfer learning, representation learning, feature scaling, sampling strategies, and active-learning-inspired compound selection; and enabling efficient virtual screening to prioritize compounds that balance predicted activity, design objectives, and synthetic accessibility.

organic↗

Differential Privacy in Grid Kitchen: Implementation & Software Documentation

Sharing of power grid feeder models faces significant challenges due to the potential risk of exposing sensitive operational information. Traditional anonymization techniques have shown notable limitations in other sensitive domains, as evidenced by documented re-identification attacks that combine supposedly anonymized datasets with auxiliary information, raising concerns that similar vulnerabilities could affect power grid data. Consequently, there is a pressing need for a more rigorous privacy protection strategy that not only delivers formal mathematical guarantees but also preserves the analytical value of the shared models. To address this challenge, we have enhanced the Grid Kitchen framework by implementing differential privacy mechanisms within the distribution model dehydration pipeline. This implementation carefully calibrates and applies noise to sensitive attributes in feeder models according to configurable privacy levels—low, moderate, and high—each offering different balances between data utility and privacy protection. Our approach uses established noise functions (Gaussian for continuous data and Discrete Laplace for integer values) with parameters carefully calibrated so that the impact of individual data points is effectively masked in the final output. The integration leverages our Noise Catalog, which we developed to categorize feeder model properties by component type, data type, and sensitivity. This catalog guides the application of appropriate noise functions and privacy parameters ($\varepsilon$ and $\delta$) to each attribute, ensuring consistent privacy protection across the model while maintaining its structural integrity and analytical usefulness. This implementation also includes evaluation tools that allow model owners to assess the impact of privacy-preserving transformations before sharing data with external parties. This report provides documentation for the differential privacy capabilities added to the Grid Kitchen project. It includes a primer on differential privacy concepts and their importance in modern data sharing, details the architecture of our implementation, explains the privacy modes and parameter configurations, and offers practical guidance on using the code for applying differential privacy to grid feeder models. Through examples and code snippets, we demonstrate the effective application of these privacy-enhancing technologies, enabling utility operators and researchers to confidently share grid data while protecting sensitive information.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Plasma parameters and the reduction potential at a plasma-liquid interface

We report nonthermal plasmas in contact with liquids have been shown to generate a variety of reactive species capable of initiating reduction–oxidation (redox) reactions at the electrochemically active plasma–liquid interface. In conventional electrochemical cells, selective redox chemistry is achieved by controlling the reduction potential at the solid electrode–electrolyte interface by applying a bias via an external circuit. In the case of plasma–liquid systems, an analogous means of tuning the reduction potential near the interface has not clearly been identified. When treated as a floating surface, the liquid is expected to adopt a net negative charge to balance the flux of hot electrons and relatively cold positive ions. The reduction potential near the plasma–liquid interface is hypothesized to be proportional to the floating potential, which can be approximated using an analytical model provided the plasma parameters are known. Herein, we present a framework for correlating the electron density and electron temperature of a noble gas plasma jet to the reduction potential near the plasma–liquid interface. The plasma parameters were acquired for an argon atmospheric plasma jet in contact with an aqueous solution by means of laser Thomson scattering. The reduction potential was determined using identical reference electrodes to measure the potential difference between the plasma–liquid interface and bulk solution. Interestingly, the measured reduction potentials near the plasma–liquid interface were found to be in good agreement with the model-predicted values determined using the plasma parameters obtained from the Thomson scattering experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Measurement report: Molecular composition, optical properties, and radiative effects of water-soluble organic carbon in snowpack samples from northern Xinjiang, China

Abstract. Water-soluble organic carbon (WSOC) in the cryosphere has an important impact on the biogeochemistry cycling and snow–ice surface energy balance through changes in the surface albedo. This work reports on the chemical characterization of WSOC in 28 representative snowpack samples collected across a regional area of northern Xinjiang, northwestern China. We employed multimodal analytical chemistry techniques to investigate both bulk and molecular-level composition of WSOC and its optical properties, informing the follow-up radiative forcing (RF) modeling estimates. Based on the geographic differences and proximity of emission sources, the snowpack collection sites were grouped as urban/industrial (U), rural/remote (R), and soil-influenced (S) sites, for which average WSOC total mass loadings were measured as 1968 ± 953 ng g−1 (U), 885 ± 328 ng g−1 (R), and 2082 ± 1438 ng g−1 (S), respectively. The S sites showed the higher mass absorption coefficients at 365 nm (MAC365) of 0.94 ± 0.31 m2 g−1 compared to those of U and R sites (0.39 ± 0.11 m2 g−1 and 0.38 ± 0.12 m2 g−1, respectively). Bulk composition of WSOC in the snowpack samples and its basic source apportionment was inferred from the excitation–emission matrices and the parallel factor analysis featuring relative contributions of one protein-like (PRLIS) and two humic-like (HULIS-1 and HULIS-2) components with ratios specific to each of the S, U, and R sites. Additionally, a sample from site 120 showed unique pollutant concentrations and spectroscopic features remarkably different from all other U, R, and S samples. Molecular-level characterization of WSOC using high-resolution mass spectrometry (HRMS) provided further insights into chemical differences among four types of samples (U, R, S, and 120). Specifically, many reduced-sulfur-containing species with high degrees of unsaturation and aromaticity were uniquely identified in U samples, suggesting an anthropogenic source. Aliphatic/protein-like species showed the highest contribution in R samples, indicating their biogenic origin. The WSOC components from S samples showed high oxygenation and saturation levels. A few unique CHON and CHONS compounds with high unsaturation degree and molecular weight were detected in the 120 sample, which might be anthraquinone derivatives from plant debris. Modeling of the WSOC-induced RF values showed warming effects of 0.04 to 0.59 W m−2 among different groups of sites, which contribute up to 16 % of that caused by black carbon (BC), demonstrating the important influences of WSOC on the snow energy budget.

54 ENVIRONMENTAL SCIENCES↗

WaterTAP3 (The Water Technoeconomic Assessment Pipe-Parity Platform)

The Water Technoeconomic Assessment Pipe-Parity Platform (WaterTAP3) was developed under the National Alliance for Water Innovation (NAWI) to facilitate consistent technoeconomic assessments of desalination treatment trains. The WaterTAP3 is an analytically robust modeling tool that can be used to evaluate water technology cost, energy, environmental, and resiliency tradeoffs across different water sources, sectors, and scales. The model simulates steady-state water treatment train performance and costs including flow and constituent mass balance across unit processes, based on source water conditions, configurations of treatment technologies, and system-level techno-economic assumptions. Users can build a new treatment train by connecting any number of unit processes, specific for their context and system, or selecting a train from the treatment train library. The model contains various technical and cost parameter options for a range of treatment processes and a library of influent water quality characteristics for a variety of source waters and case studies. Users can customize water quality parameters to evaluate the technology performance in their context. The model can be set up for different assessment needs including simulation, optimization, and uncertainty and sensitivity analyses. The results from WaterTAP3 can help identify trade-offs among the different system performance metrics, with insight on how particular technologies or systems promote pipe-parity. The flexibility and comprehensive scope of the tool makes it a promising solution to industry-wide water technoeconomic evaluations, leading to more informed water investment decisions and technologies. As a user-friendly, open-source platform, WaterTAP3 can be used by industry, academia, policymakers, planners, and those with or without extensive analytical experience.

Miara, Ariel↗

Water Technoeconomic Assessment Pipe-Parity Platform (WaterTAP3)

The Water Technoeconomic Assessment Pipe-Parity Platform (WaterTAP3) was developed under the National Alliance for Water Innovation (NAWI) to facilitate consistent technoeconomic assessments of desalination treatment trains. The WaterTAP3 is an analytically robust modeling tool that can be used to evaluate water technology cost, energy, environmental, and resiliency tradeoffs across different water sources, sectors, and scales. The model simulates steady-state water treatment train performance and costs including flow and constituent mass balance across unit processes, based on source water conditions, configurations of treatment technologies, and system-level techno-economic assumptions. Users can build a new treatment train by connecting any number of unit processes, specific for their context and system, or selecting a train from the treatment train library. The model contains various technical and cost parameter options for a range of treatment processes and a library of influent water quality characteristics for a variety of source waters and case studies. Users can customize water quality parameters to evaluate the technology performance in their context. The model can be set up for different assessment needs including simulation, optimization, and uncertainty and sensitivity analyses. The results from WaterTAP3 can help identify trade-offs among the different system performance metrics, with insight on how particular technologies or systems promote pipe-parity. The flexibility and comprehensive scope of the tool makes it a promising solution to industry-wide water technoeconomic evaluations, leading to more informed water investment decisions and technologies. As a user-friendly, open-source platform, WaterTAP3 can be used by industry, academia, policymakers, planners, and those with or without extensive analytical experience. A publicly available graphical user interface is currently under development.

Miara, Ariel↗

The effect of saturated thermal conduction on clouds in a hot plasma

We numerically investigate the internal evolution of multiphase clouds, which are at rest with respect to an ambient, highly ionized medium (HIM) representing the hot component of the circumgalactic medium. Time-dependent saturated thermal conduction and its implications like condensation rates and mixing efficiency are assessed in multiphase clouds. Our simulations are carried out by using the adaptive mesh refinement code FLASH. The model clouds are initially in both hydrostatic and thermal equilibrium and are in pressure balance with the HIM. Thus, they have steep gradients in both temperature and density at the interface to HIM leading to non-negligible thermal conduction. Several physical processes are considered numerically or semi-analytically: thermal conduction, radiative cooling and external heating of gas, self-gravity, mass diffusion, and dissociation of molecules and ionization of atoms. It turns out that saturated thermal conduction triggers a continuous condensation irrespective of cloud mass. Dynamical interactions with ambient HIM all relate to the radial density gradient in the clouds: (1) mass flux due to condensation is the higher the more homogeneous the clouds are; (2) mixing of condensed gas with cloud gas is easier in low-mass clouds, because of their shallower radial density gradient; and thus (3) accreted gas is distributed more efficiently. A distinct and sub-structured transition zone forms at the interface between cloud and HIM, which starts at smaller radii and is much narrower as deduced from analytical theory.

79 ASTRONOMY AND ASTROPHYSICS↗

Hybrid Analytics Solution to Improve Coal Power Plant Operations

This project focused on developing advanced methods for thermal performance monitoring of a coal-fueled power plant. The specific goal was to develop and demonstrate a new thermal performance monitoring approach using a hybrid model that integrates a physics-based heat balance model with a machine learning-based pattern recognition model. The hybrid model enables increased accuracy and scope of the thermal analysis and an improved ability to monitor and detect changes in plant operation. This new approach takes full advantage of the individual model capabilities and creates an important new set of capabilities not previously possible using the two types of models separately. Using the heat balance model, a rich set of derived parameters (virtual sensors) are calculated from the measured plant operating data at each time point. The combined measured and derived data values are used by machine learning algorithms to create pattern recognition models over the range of normal unit operation. To create the monitoring models, historical data from normal operation of the plant is first processed by the heat balance model to compute the derived parameter data. The result is a greatly expanded set of normal operating data that can be used as input to create the pattern recognition model. Once the models are calibrated for normal operation, the hybrid model is suitable for use in continuous online monitoring. During online monitoring, new plant operating data is processed first by the heat balance model and then by the pattern recognition model. Results from the pattern recognition model quantify the deviation of each measured or derived parameter from its expected value in normal operation. The hybrid models can detect abnormal changes in plant operating data with very high accuracy and sensitivity. When abnormal behavior is detected, alerts are generated automatically for evaluation by the plant monitoring staff. The new hybrid solution product was developed and verified in the performance of the project. The hybrid solution was tested first in a simulation environment that mimicked the plant data systems and infrastructure used by U.S. power generating plants and utilities. The hybrid solution was then deployed for real-time, online monitoring of an operating coal-fueled power plant at a field test site. Field testing demonstrated that all hybrid solution development objectives were accomplished. The project work was based on combining the capabilities of two existing software products to create the new hybrid solution product. One of these was the existing MapEx® heat balance product and the other was the existing SureSense® advanced pattern recognition product. Each of these separate products was assessed to be at a Technology Readiness Level (TRL) of 9 at the start of the effort. The hybrid solution product was assessed to be at a TRL of 2 at the start of the project based on early feasibility work by the project team. At completion of the field testing performed in the project, the hybrid solution product was assessed to be at a TRL of 7. The project team expects that the hybrid solution product will be deployed commercially and will achieve a TRL of 9 within one year after completion of the project.

01 COAL, LIGNITE, AND PEAT↗

Natural isotopic compositions of titanium, iron, and nickel observed in commercial fuel pellets – Promising candidate elements for stable isotope tagging

Stable isotope taggants would constitute unique identifiers for nuclear fuel cycle materials, resulting in expedited timelines and high confidence provenance assessments for nuclear forensics investigations. However, reliably identifying and interpreting stable isotope taggants in nuclear materials recovered from outside of regulatory control will largely be predicated on the assumption that the taggant element intrinsic to the untagged nuclear material exhibits natural isotopic ratios. Here, we present high-precision Ti, Fe, and Ni isotope compositions in 13 commercial low-enriched uranium (LEU) fuel pellets to assess the suitability of these transition metals as stable isotope taggants. Our investigations reveal limited isotope variations among the fuel pellets in all three elements, which are consistent with small mass-dependent isotope fractionations, comparable to variations previously reported for natural samples. In practice, isotopically tagged nuclear materials are expected to fall along isotopic mixing lines, since intrinsic background levels of taggant elements dilute the taggant towards natural isotope compositions. Furthermore, the observation that Ti, Fe, and Ni isotope compositions in a suite of LEU fuel pellets are close to or indistinguishable from estimates for the Bulk Silicate Earth demonstrates that a two end-member mixing assumption would be valid for these transition metals, indicating that all three are promising candidate elements for stable isotope tagging. Finally, we present mass balance calculations to quantify isotopic perturbations expected from admixing isotopically anomalous Ti, Fe, and Ni taggants to assess the interplay between elemental and taggant concentrations and find favorable compromises for facilitating successful taggant identification with current analytical methods.

Intentional forensics↗

The bill alignment test: Identifying trade-offs with residential rate design options

The proliferation of smart meter data allows the application of new analytic methods to inform regulatory deliberations. The bill alignment test (BAT) method, which compares the costs allocated to each residential customer with their electric bill, is introduced to help regulators consider how a proposed rate design balances various regulatory criteria. The BAT requires an explicit statement of preferences by policymakers or stakeholders and choices about allocating residual costs unassociated with customer-level causality. The BAT is applied to more than 35,000 smart-meter customer load profiles to assess the trade-offs associated with proposed rate designs. Here this example demonstrates the impact of residual cost allocation preferences and tariff design choices on proposed tariff evaluation.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Influence of functional groups on low-temperature combustion chemistry of biofuels

Ongoing progress in synthetic biology, metabolic engineering, and catalysis continues to produce a diverse array of advanced biofuels with complex molecular structure and functional groups. In order to integrate biofuels into existing combustion systems, and to optimize the design of next-generation combustion systems, understanding connections between molecular structure and ignition at low-temperature conditions (< 1000 K) remains a priority that is addressed in part using chemical kinetics modeling. The development of predictive models relies on detailed information, derived from experimental and theoretical studies, on molecular structure and chemical reactivity, both of which influence the balance of chain reactions that occur during combustion – propagation, termination, and branching. In broad context, three main categories of reactions affect ignition behavior: (i) initiation reactions that generate a distribution of organic radicals, ; (ii) competing unimolecular decomposition of and bimolecular reaction of with O2; (iii) decomposition mechanisms of peroxy radical adducts (RO), including isomerization via RO ⇌ OOH. Furthermore, all three categories are influenced by functional groups in different ways, which causes a shift in the balance of chain reactions that unfold over complex temperature- and pressure-dependent mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Construction of linearly independent non-orthogonal AGP states

We show how to construct a linearly independent set of antisymmetrized geminal power (AGP) states, which allows us to rewrite our recently introduced geminal replacement models as linear combinations of non-orthogonal AGPs. Furthermore, this greatly simplifies the evaluation of matrix elements and permits us to introduce an AGP-based selective configuration interaction method, which can reach arbitrary excitation levels relative to a reference AGP, balancing accuracy and cost as we see fit.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Carbon optimized production of 3-hydroxypropionic acid in the Agile BioFoundry organism Rhodosporidium toruloides

The modern global economy relies heavily on carbon-based products that are derived from petroleum, which presents sustainability, resource management, and greenhouse gas exacerbated climate change challenges. Due to these challenges, there is the need for a global industrial transition towards green and sustainable production. Microbial production of valuable chemicals from renewable biomass represents one promising route. However, high-volume low-value products such as commodity chemicals are still difficult to make profitable. One fundamental bottleneck is a waste of more than 1/3 of the feedstock carbon as CO 2 in the fermentation process. Here the project focuses on fundamentally reconfiguring the metabolism to reduce CO 2 loss in central metabolic pathways thereby also improving bioproduct yields. Here we present technologies to prevent CO 2 loss and balance reducing equivalents within the cell to enable complete conversion of glucose from renewable feedstocks into bioproducts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling simultaneous particle shrinkage, dissolution and breakage using the modified moving grid technique

Simultaneous shrinkage, dissolution and breakage are important particle size reduction phenomena that characterize processes like the reactive degradation of solid chemicals. The dynamics of the particle size distribution (PSD) for such processes are non-trivial to model due to the number expending processes brought about by the eventual dissolution of particles. To this end, Population Balance Model (PBM) resolved through the sectional techniques is the natural approach. Here, we introduce a modified Moving Grid technique (m-MGT) to accurately resolve the particle size reduction phenomena. Our technique mimics the perpetual particle shrinkage through a continuously left-moving size grid and incorporates a strategic grid removal routine to capture the disappearance of particles. Coupled with the Fixed Pivot (FP) discretization for breakage, our m-MGT not only preserves the moment-related properties, but also benchmarked very well against the analytical number densities and exhibited a minimum of first-order convergence in all assessed case studies.

97 MATHEMATICS AND COMPUTING↗