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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.

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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressible solid structures for cases in which at least part of the solid boundary does not contact the incompressible fluid. Selected grid convergence studies demonstrate second-order convergence in volume conservation and in the pointwise discrepancies between corresponding positions of the two interface representations as well as between first and second-order convergence in the structural displacements. The time stepping scheme is also demonstrated to yield second-order convergence. To assess and validate the robustness and accuracy of the new algorithm, comparisons are made with computational and experimental FSI benchmarks. Test cases include both smooth and sharp geometries in various flow conditions. Furthermore, we also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a geometrically realistic, deformable blood clot in an inferior vena cava filter.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Climate Change Risks to Freshwater Subsistence Fisheries in Arctic Alaska: Insights and Uncertainty from Broad Whitefish Coregonus nasus

Arctic freshwater ecosystems and fish populations are largely shaped by seasonal and long-term watershed hydrology. In this paper, we hypothesize how changing air temperature and precipitation will alter freeze and thaw processes, hydrology, and instream habitat to assess potential indirect effects, such as the change to the foraging and behavioral ecology, on Arctic fishes, using Broad Whitefish Coregonus nasus as an indicator species. Climate change is expected to continue to alter hydrologic pathways, flow regimes, and, therefore, habitat suitability, connectivity, and availability for fishes. Warming and lengthening of the growing season will likely increase fish growth rates; however, the exceedance of threshold stream temperatures will likely increase physiological stress and alter life histories. We expect these changes to have mixed effects on Arctic subsistence fishes and fisheries. Management and conservation approaches focused on preserving the processes that create heterogeneity in aquatic habitats, genes, and communities will help maintain the resilience of Broad Whitefish and other important subsistence fisheries. Long-term effects are uncertain, so filling scientific knowledge gaps, such as identifying important habitats or increasing knowledge of abiotic variables in priority watersheds, is key to understanding and potentially mitigating likely impacts to Arctic fishes in a rapidly changing landscape.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Effects of Radiation Reaction Physics on High-Current Power Flow

In this study, we examine the effects of the radiation reaction force on electrons in a radial magnetically insulated transmission line (MITL) near a load with peak currents of 60+ MA. More specifically, we study the differences in electron motion and kinetic energy with or without radiation reaction physics using a novel guiding center drift approach that incorporates E $\times$ B and ∇B drifts. A key finding of this study is that an electron's magnetic moment, which would be conserved when radiation reaction physics is not incorporated, can be significantly reduced in magnetic fields on the order of 10,000's T when radiation reaction is included. The reduction of magnetic moment gives rise to a significant reduction in cycloidal kinetic energy as well as a reduction in the electron's ∇B drift.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

One-loop matching for quark dipole operators in a gradient-flow scheme

The quark chromoelectric dipole (qCEDM) operator is a CP-violating operator describing, at hadronic energies, beyond-the-standard-model contributions to the electric dipole moment of particles with nonzero spin. In this paper we define renormalized dipole operators in a regularization-independent scheme using the gradient flow, and we perform the matching at one loop in perturbation theory to renormalized operators of the same and lower dimension in the more familiar MS scheme. We also determine the matching coefficients for the quark chromo-magnetic dipole operator (qCMDM), which contributes for example to matrix elements relevant to CP-violating and CP-conserving kaon decays. The calculation provides a basis for future lattice QCD computations of hadronic matrix elements of the qCEDM and qCMDM operators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Design complexity and performance analysis in additively manufactured heat exchangers

The main objective of this research is to investigate the tradeoffs between design complexity and thermal performance in additively manufactured metallic heat exchangers. Such heat exchangers have become a favorite topic for investigation in various fields ranging from air conditioning to aircraft gas turbine engines. In particular, high manufacturing cost has emerged as the major drawback in broad applications of manifold-microchannel heat exchanger (MMHXs). The possibility of cost-effective manufacturing has generated wide interest in applying additive manufacturing (AM) for fabricating MMHXs. Furthermore, AM technologies will provide an opportunity for enhanced design and superior heat transfer performance. In this study, innovative MMHXs are designed and fabricated through selective laser melting. An experimental setup was designed to measure pressure drop and heat transfer for the developed MMHXs with a wide range of Reynolds numbers. Furthermore, the coefficient of performance was calculated based on the heat flow rate, air pressure drop, and air flow rate. Measurement results demonstrated that in some scenarios adding more internal features, i.e., increasing design complexity, does not necessarily improve the MMHX performance.

10 SYNTHETIC FUELS↗
DOE OSTI2024

Retrofittable Thermal Switches for Dynamic Building Envelopes Integrated with Thermal Energy Storage: Preprint

Buildings in the United States consume about 40 quadrillion BTU of primary energy annually, which accounts for the nation's 40% of total energy use, 75% of all electricity use, and 35% of the net carbon emissions. Deploying thermal energy storage in the form of phase change material (PCM) in building envelopes is an effective method to reduce space heating/cooling loads, provide load shedding, and shift demand to periods of lower energy cost. However, the full potential of PCM-integrated envelopes can only be realized if the PCM undergoes complete phase change using free ambient heating/cooling, and the stored energy is effectively transferred between the exterior and the interior environments. Conventional thermal insulation (with a fixed thermal resistance) limits PCM utilization, particularly with the increasing emphasis on higher R-value in building envelopes, which negatively affects the energy-saving potential of a PCM-integrated envelope. In contrast, dynamic building envelopes integrated with PCMs provide the option of varying the thermal resistance based on the indoor and outdoor conditions, thereby enhancing utilization of free ambient cooling and heating to charge/discharge the PCM thermal storage, reducing the buildings' heating and cooling load, and shifting the peak energy demand. In this study, we demonstrate innovative retrofittable thermal switches in the form of the insertable plugs inside an insulation to provide variable thermal resistance depending on the operating temperature and direction of temperature gradient, thus allowing preferential directional heat flow. Notably, they are passive in nature, requiring no external power, and work solely based on the ambient temperature.

buildings↗
DOE OSTI2020

Projecting spatiotemporally explicit effects of climate change on stream temperature: A model comparison and implications for coldwater fishes

Conservation planners and resource managers seek information about how the availability and locations of cold-water habitats will change in the future and how these predictions vary among models. In this work, we used a physical process-based model to demonstrate the implications of climate change for streamflow and water temperature in two watersheds with distinctive flow regimes: the Snoqualmie watershed (WA) and Siletz watershed (OR), USA. Our model incorporated a downscaled ensemble of global climate model outputs and was calibrated with in situ and remotely sensed water temperatures. Furthermore, we compared predictions from our processed-based model to those from a publicly available and widely used statistical model. The process-based model projected greater changes in summer maximum water temperatures for the mixed-rain-snow Snoqualmie watershed than for the rain-dominated Siletz watershed as a result of the near-complete loss of winter snowpack and significant reduction in summer flow in the Snoqualmie watershed expected by the 2080s. Both models projected generally similar future spatial patterns of maximum water temperature in the two rivers, with cool reaches distributed farther upstream and fewer in number. However, the process-based model projected higher spatial heterogeneity in water temperature due to our spatially explicit simulation of streamflow and because we calibrated the model with spatially continuous remotely sensed water temperature data. We used stream temperature projections to assess the vulnerability of Pacific salmon and trout to changes in the spatial distribution of cold-water habitats during August by the 2080s. Results suggest that salmonids may have fewer summertime cold-water habitats in both watersheds. Projected stream warming may further limit particular species and life stages, especially in the Snoqualmie watershed. Our comparison of models highlights the importance of considering what might be gained by using a process-based model for evaluating and prioritizing management actions that mitigate climate impacts on cold-water habitats for stream fishes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Fluid dynamic mathematical aspects of supernova remnants

Supernovae—explosions of stars—are a central problem in astrophysics since they contain information on the entire process of stellar evolution and nucleosynthesis. Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities, developing during the supernova blast, lead to intense interfacial RT/RM mixing of the star's materials and couple astrophysical to atomic scales. This work analyzes some fluid dynamic mathematical aspects of the titanic task of supernova's blast. We handle mathematical challenges of RT/RM dynamics in supernova relevant conditions by directly linking the conservation laws governing RT/RM dynamics to symmetry-based momentum model, by exactly deriving the model parameters in the scale-dependent and scale-invariant regimes, and by exploring the special self-similar class for RT/RM interfacial mixing with variable accelerations. Here we reveal that RT/RM dynamics is strongly influenced by deterministic (the initial and the flow) conditions in the scale-dependent linear and nonlinear regimes and in the self-similar mixing regime. The theory outcomes are consistent with the observations of supernova remnants, explain the results of the scaled laboratory experiments in high energy density plasmas, and yield the design of future experiments for the accurate quantification of RT/RM dynamics in supernova relevant conditions. We find that from fluid dynamic mathematical perspectives, supernovae can be regarded as an astrophysical initial value problem. Along with the guidance of what explodes at microscopic scales, supernova remnants encapsulate information on the explosion hydrodynamics and the associated deterministic conditions at macroscopic scales. We urge such effects be considered in interpretations of the observational data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Local analysis of fast magnetic reconnection

Fast magnetic reconnection is defined by the topology of the magnetic field lines changing on a timescale that is approximately an order of magnitude longer than the topology-conserving ideal-evolution timescale. Fast reconnection is an intrinsic property of Faraday's law when the evolving magnetic field depends non-trivially on all three spatial coordinates and is commonly observed—even when the effects that allow topology breaking are arbitrarily small. The associated current density need only be enhanced by a factor of approximately ten and flows in thin but broad ribbons along the magnetic field. These results follow from the variation in the separation of neighboring pairs of magnetic field lines, which in an ideal evolution typically increases exponentially with time, and the existence of a spatial scale below which magnetic field lines freely change their identities due to non-ideal effects, such as resistivity. Traditional reconnection theory ignores exponentially large variations and relies on the current density reaching a magnitude that is exponentially larger than is actually required. Here, an analysis of the behavior of magnetic field lines in the neighborhood of an arbitrarily chosen line is used to obtain more precise and rigorous results on intrinsic reconnection. The maximum parallel kinetic energy of collisionless charged particles is shown to have an exponential increase in time during a generic magnetic evolution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Improving air leakage prediction of buildings using the fan pressurization method with the Weighted Line of Organic Correlation

In many countries, the fan pressurization method is the most frequently chosen approach for measuring the air leakage of houses. The measurements are usually performed at pressures that far exceed pressures to which buildings are exposed to under normal conditions. A fit of these tests to the power-law formulation allows an extrapolation to data points outside the measured pressure range. With the Ordinary Least Square (OLS) fitting method, the pressure exponent and flow coefficient can be determined. However, the measurement results are highly sensitive to uncertainties induced by external factors like changing wind conditions during the tests, which is neglected by OLS. This may lead to errors in the prediction of flows at lower pressures. The Weighted Line of Organic Correlation (WLOC) is an alternative approach and takes measurement uncertainty into account. In this paper, a statistical analysis of an extensive data set of pressurization measurements has been performed. Both regression techniques have been compared for almost 7500 fan pressurization measurements of six houses in 109 different house leak configurations. The variability in predicting pressure exponent and flow coefficient for both WLOC and OLS regression was analyzed using probability density functions. It was found that the Weighted Line of Organic Correlation significantly decreases the uncertainty in predicting pressure exponent, flow coefficient, and other low-pressure air leakage metrics compared to the Ordinary Least Square fitting. Here, the authors highly recommend the implementation of WLOC in current measurement standards and test equipment.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Comparative genomics reveals electron transfer and syntrophic mechanisms differentiating methanotrophic and methanogenic archaea

The anaerobic oxidation of methane coupled to sulfate reduction is a microbially mediated process requiring a syntrophic partnership between anaerobic methanotrophic (ANME) archaea and sulfate-reducing bacteria (SRB). Based on genome taxonomy, ANME lineages are polyphyletic within the phylum Halobacterota , none of which have been isolated in pure culture. Here, we reconstruct 28 ANME genomes from environmental metagenomes and flow sorted syntrophic consortia. Together with a reanalysis of previously published datasets, these genomes enable a comparative analysis of all marine ANME clades. We review the genomic features that separate ANME from their methanogenic relatives and identify what differentiates ANME clades. Large multiheme cytochromes and bioenergetic complexes predicted to be involved in novel electron bifurcation reactions are well distributed and conserved in the ANME archaea, while significant variations in the anabolic C1 pathways exists between clades. Our analysis raises the possibility that methylotrophic methanogenesis may have evolved from a methanotrophic ancestor.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Improvements to CTF for Modeling of Boiling Water Reactor Geometry and Operating Conditions

This report documents work done to improve CTF modeling of boiling water reactor (BWR) designs during FY 2020. Several improvements were made to the geometry modeling capabilities, including adding support for modeling of inlet flow orifices, axially varying large water rods, channel boxes with large corner round radii, and quarter symmetry models. Work was also done to improve on the numerical stability and run-time performance of CTF in Virtual Environment for Reactor Applications (VERA) for core-scale BWR problems. An outer iteration loop was implemented that ensures mass and energy are conserved before moving on to the next time step in the solution. The ability to use a direct solver for the pressure matrix was also added, which reduces the matrix solution error and improves code stability and run-time performance. Improvements to the pressure balance iteration loop were needed to allow CTF to be used in a coupled VERA solution of a model of Hatch that was developed. Finally, various improvements have led to a 2×reduction in the total VERA walltime for the Hatch model.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Smart Methane Emission Detection System Development (Final Report)

Working with the Department of Energy's National Energy Technology Laboratory, Southwest Research Institute® (SwRI®) developed a system to identify methane leaks reliably, accurately, and autonomously at critical midstream sections of the natural gas distribution network in real-time for the purpose of mitigating methane emissions using Optical Gas Imaging (OGI) cameras. SwRI's Smart Leak Detection – Methane (SLED/M) adds a high degree of automation to the process of methane leak detection to minimize sources of human error, minimize response time to a leak event, and maximize midstream visibility. Furthermore, SwRI has been working towards integrating Quantitative OGI (QOGI) capabilities into this existing technology. By leveraging Deep Learning, SwRI now has the capability to estimate fugitive emission leak rates quickly and reliably, which allows operators to detect emissions, quantify leak rate, prioritize repairs, and validate the repairs in a single instrument. The next generation QOGI technology leverages the same cameras used in Leak Detection and Repair (LDAR) programs, with improvements in safety and speed for traditional quantification-based repairs, ultimately leading to less overhead cost for the operators. The goals for this research were to develop two types of models with the following goals: Run in real-time on the edge (≥ 12 Hz), Classification: Achieve less than 5% false positive detection, Classification: Achieve ≥ 95% methane plume detection rate, Regression: achieve ≤ 10 standard cubic feet per hour (scfh) prediction > 70% of the time. In order to achieve these results, multiple infrared (IR) and other sensors were investigated in tandem with the midwave IR (MWIR) OGI to provide additional information to train the underlying models. Information on atmospheric conditions including humidity, temperature, pressure, and solar radiation was provided by a weather station. Several machine learning and deep learning architectures and methods, including looking at quantized classification networks and regressions networks, were explored. As further data was collected, curated, and labeled, it allowed for more refined regressive networks to be adequately trained, leading to better insight into the true flow rates being observed. An important valuable deliverable of this research effort was the development of an advanced network which underwent multiple iterations capable of giving a continuous output. The current network has a predicted mean average percentage error (MAPE) of 12.3% just outside our target goal of 10.00%, but an accuracy of 97.78% at ±50 scfh, well within the overall goal for the Department of Energy (DOE) program. Upon closer inspection, it was observed that more than 10% of datapoints contributing to the MAPE predictions were the result of low flow rate predictions and are beyond the sensitivity of instrument measurement as a result of normal operational variation and noise.

03 NATURAL GAS↗
DOE OSTI2024

Rooftop Solar in Lawrence, MA: Community Perspectives, Deceptive Practices, and Financing Options

This report was prepared as part of the U.S. Department of Energy's Communities Local Energy Action Program (Communities LEAP) pilot competitive technical assistance for the Lawrence Massachusetts Stakeholder Coalition (LSC) composed of The City of Lawrence, All In Energy, MassDevelopment, Mill City Community Investments, BlocPower and Groundwork Lawrence, and led by Browning the Green Space. The LSC identified rooftop solar photovoltaics as a top priority for this technical assistance opportunity. Lawrence faces high energy burden and electricity prices, thus rooftop solar can be a tool to help lower those costs. However, the coalition received feedback that some solar companies were using deceptive and unfair practices when marketing, selling, or financing solar energy, costing residents more money than utility rates and increasing the energy burden. This project sought to address rooftop solar community priorities through two pathways: 1. facilitating community engagement to understand community perspectives and experiences with rooftop solar development; and 2. conducting a financial cash-flow analysis highlighting the varying fiscal outcomes for rooftop solar adopters based off rooftop solar leasing, ownership, or buying electricity from the utility (National Grid).

14 SOLAR ENERGY↗
DOE OSTI2021

Hydrogen Component Leak Rate Quantification for System Risk and Reliability Assessment through QRA and PHM Frameworks: Preprint

The National Renewable Energy Laboratory's (NREL) Hydrogen Safety Research and Development (HSR&D) program in collaboration with the University of Maryland's Systems Risk and Reliability Analysis Laboratory (SyRRA) are working to improve reliability and reduce risk in hydrogen systems. This approach strives to use quantitative data on component leaks and failures, together with Prognosis and Health Management (PHM), and Quantitative Risk Assessment (QRA) to identify at-risk components, reduce component failures and downtime, and predict when components require maintenance. Hydrogen component failures increase facility maintenance cost, facility downtime, and reduce public acceptance of hydrogen technologies, ultimately increasing facility size and cost because of potentially overly conservative requirements. Leaks are a predominant failure mode for hydrogen components. However, uncertainties in the amount of hydrogen emitted from leaking components and the frequency of those failure events limit the understanding of the risks that they present under real-world operational conditions. NREL has deployed a test fixture, the Leak Rate Quantification Apparatus (LRQA), to quantify the mass flow rate of leaking gases from medium and high-pressure components that have failed while in service. Quantitative hydrogen leak rate data from this system could ultimately be used to better inform risk assessment and Regulation Codes and Standards (RCS). Parallel activity explores the use of PHM and QRA techniques to assess and reduce risk, thereby improving safety and reliability of hydrogen systems. The results of QRAs could further provide a systematic and science-based foundation for the design and implementation of RCS, as in the latest versions of the NFPA 2 code for gaseous hydrogen stations. Alternatively, data-driven techniques of PHM could provide new damage diagnosis and health-state prognosis tools. This research will help end users, station owners and operators, and regulatory bodies move towards risk-informed preventative maintenance versus emergency corrective maintenance, reducing cost and improving reliability. Predictive modelling of failures could improve safety and affect RCS requirements such as setback distances at liquid refuelling sites. The combination of leak rate quantification research, PHM, and QRA can lead to better informed models enabling data-based decision to be made for hydrogen system safety improvements.

codes and standards↗
DOE OSTI2024

A Review of Modeling Approaches for Predicting Frost Growth and Defrosting on Tube-Fin Heat Exchangers: Preprint

Frost formation and growth on the evaporator surface is a common process that deteriorates the air-refrigerant heat transfer and restricts airflow. This degrades the performance of the vapor compression system by increasing temperature lift and air-side pressure drop. To accurately predict these effects during coil frosting, as well as the energy use and duration of the defrost process, there is a need to estimate the heat and mass transfer, momentum transport, and solid-liquid and liquid-vapor phase change. Therefore, in the past few decades, continuous effort has been made to model frosting and defrosting processes using approaches ranging from empirical correlations to computational fluid dynamic models. To provide a clearer overview for researchers, engineers, and manufacturers in this field, this paper provides a comprehensive literature review for frosting and defrosting models. The paper begins with theoretical background of frost formation and defrost processes, and then reviews the common modeling approaches in literature and their underlying assumptions when trying to account for various physical phenomenon. Based on the literature review, the most critical modeling effort for frost formation is the determination of frost densification rate and frost growth rate. Various methods to predict these two parameters are reviewed. Empirical correlations commonly used for frost density and thermal conductivity are presented and compared. For the defrost process, various multi-stage models have been proposed with different assumptions. Some assume the presence of air gap between the tube wall and the frost, while others consider the melted frost flow due to gravity. We also review physics-based and empirical approaches to integrate defrost models into heat pump models. We conclude by identifying research gaps and providing recommendations.

defrost↗
DOE OSTI2021

Identifying and tracking bubbles and drops in simulations: A toolbox for obtaining sizes, lineages, and breakup and coalescence statistics

Knowledge of bubble and drop size distributions in two-phase flows is important for characterizing a wide range of phenomena, including combustor ignition, sonar communication, and cloud formation. The physical mechanisms driving the background flow also drive the time evolution of these distributions. Accurate and robust identification and tracking algorithms for the dispersed phase are necessary to reliably measure this evolution and thereby quantify the underlying mechanisms in interface-resolving flow simulations. The identification of individual bubbles and drops traditionally relies on an algorithm used to identify connected regions. This traditional algorithm can be sensitive to the presence of spurious structures. A cost-effective refinement is proposed to maximize volume accuracy while minimizing the identification of spurious bubbles and drops. An accurate identification scheme is crucial for distinguishing bubble and drop pairs with large size ratios. The identified bubbles and drops need to be tracked in time to obtain breakup and coalescence statistics that characterize the evolution of the size distribution, including breakup and coalescence frequencies, and the probability distributions of parent and child bubble and drop sizes. An algorithm based on mass conservation is proposed to construct bubble and drop lineages using simulation snapshots that are not necessarily from consecutive time steps. These lineages are then used to detect breakup and coalescence events, and obtain the desired statistics. Accurate identification of large-size-ratio bubble and drop pairs enables accurate detection of breakup and coalescence events over a large size range. Accurate detection of successive breakup and coalescence events requires that the snapshot interval be an order of magnitude smaller than the characteristic breakup and coalescence times to capture these successive events while minimizing the identification of repeated confounding events. Together, these algorithms serve as a toolbox for detailed analysis of two-phase simulations, and enable insights into the mechanisms behind bubble and drop formation and evolution in flows of practical importance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗