Search NASA⌕ Search

SEARCH · Search NASA

Results for “CDR”

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 73 records · Page 4

Verification of a New NOAA/NSIDC Passive Microwave Sea-Ice Concentration Climate Record

A new satellite-based passive microwave sea-ice concentration product developed for the National Oceanic and Atmospheric Administration (NOAA)Climate Data Record (CDR) programme is evaluated via comparison with other passive microwave-derived estimates. The new product leverages two well-established concentration algorithms, known as the NASA Team and Bootstrap, both developed at and produced by the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC). The sea ice estimates compare well with similar GSFC products while also fulfilling all NOAA CDR initial operation capability (IOC) requirements, including (1) self describing file format, (2) ISO 19115-2 compliant collection-level metadata,(3) Climate and Forecast (CF) compliant file-level metadata, (4) grid-cell level metadata (data quality fields), (5) fully automated and reproducible processing and (6) open online access to full documentation with version control, including source code and an algorithm theoretical basic document. The primary limitations of the GSFC products are lack of metadata and use of untracked manual corrections to the output fields. Smaller differences occur from minor variations in processing methods by the National Snow and Ice Data Center (for the CDR fields) and NASA (for the GSFC fields). The CDR concentrations do have some differences from the constituent GSFC concentrations, but trends and variability are not substantially different.

Passive Microwave↗

NASA's Space Launch System Transitions From Design To Production

NASA's Space Launch System (SLS) successfully completed its Critical Design Review (CDR) in 2015, a major milestone on the journey to an unprecedented era of exploration for humanity. CDR formally marked the program's transition from design to production phase just four years after the program's inception and the first such milestone for a human launch vehicle in 40 years. While challenges typical of a complex development program lie ahead, CDR evaluators concluded that the design is technically and programmatically sound and ready to press forward to Design Certification Review (DCR) and readiness for launch of Exploration Mission 1 (EM-1) in the 2018 timeframe. SLS is prudently based on existing propulsion systems, infrastructure and knowledge with a clear, evolutionary path as required by mission needs. In its initial configuration, designated Block 1, SLS will a minimum of 70 metric tons (t) (154,324 pounds) of payload to low Earth orbit (LEO). It will evolve to a 130 t (286,601 pound) payload capacity by upgrading its engines, boosters, and upper stage, dramatically increasing the mass and volume of human and robotic exploration while decreasing mission risk, increasing safety, and simplifying ground and mission operations. CDR was the central programmatic accomplishment among many technical accomplishments that will be described in this paper. The government/industry SLS team successfully test-fired a flight-like five-segment solid rocket motor, as well as seven hotfire development tests of the RS-25 core stage engine. The majority of the major test article and flight barrels, rings, and domes for the core stage liquid oxygen, liquid hydrogen, engine section, intertank, and forward skirt were manufactured at NASA's Michoud Assembly Facility in New Orleans, Louisiana. Renovations to the B-2 test stand for stage green run testing were completed at NASA's Stennis Space Center (SSC), near Bay St. Louis, Mississippi. Core stage test stands are reaching completion at NASA's Marshall Space Flight Center in Huntsville, Alabama. The modified Pegasus barge for core stage transportation from manufacturing to testing and launch sites was delivered to SSC. The Interim Cryogenic Propulsion System test article was also completed. This paper will discuss these and other technical and programmatic successes and challenges over the past year and provide a preview of work ahead before the first flight of this new capability.

Askins, Bruce R.↗

NASA's Space Launch Transitions: From Design to Production

NASA's Space Launch System (SLS) successfully completed its Critical Design Review (CDR) in 2015, a major milestone on the journey to an unprecedented era of exploration for humanity. CDR formally marked the program's transition from design to production phase just four years after the program's inception and the first such milestone for a human launch vehicle in 40 years. While challenges typical of a complex development program lie ahead, CDR evaluators concluded that the design is technically and programmatically sound and ready to press forward to Design Certification Review (DCR) and readiness for launch of Exploration Mission 1 (EM-1) in the 2018 timeframe. SLS is prudently based on existing propulsion systems, infrastructure and knowledge with a clear, evolutionary path as required by mission needs. In its initial configuration, designated Block I, SLS will a minimum of 70 metric tons (t) of payload to low Earth orbit (LEO). It can evolve to a 130 t payload capacity by upgrading its engines, boosters, and upper stage, dramatically increasing the mass and volume of human and robotic exploration while decreasing mission risk, increasing safety, and simplifying ground and mission operations. CDR was the central programmatic accomplishment among many technical accomplishments that will be described in this paper. The government/industry SLS team successfully test fired a flight-like five-segment solid rocket motor, as well as seven hotfire development tests of the RS-25 core stage engine. The majority of the major test article and flight barrels, rings, and domes for the core stage liquid oxygen, liquid hydrogen, engine section, intertank, and forward skirt were manufactured at NASA's Michoud Assembly Facility. Renovations to the B-2 test stand for stage green run testing were completed at NASA Stennis Space Center. Core stage test stands are rising at NASA Marshall Space Flight Center. The modified Pegasus barge for core stage transportation from manufacturing to testing and launch sites was delivered. The Interim Cryogenic Propulsion System test article was also completed. This paper will discuss these and other technical and programmatic successes and challenges over the past year and provide a preview of work ahead before the first flight of this new capability.

Askins, Bruce↗

Efficient Planning of Wind-Optimal Routes in North Atlantic Oceanic Airspace

The North Atlantic oceanic airspace (NAT) is crossed daily by more than a thousand flights, which are greatly affected by strong jet stream air currents. Several studies devoted to generating wind-optimal (WO) aircraft trajectories in the NAT demonstrated great efficiency of such an approach for individual flights. However, because of the large separation norms imposed in the NAT, previously proposed WO trajectories induce a large number of potential conflicts. Much work has been done on strategic conflict detection and resolution (CDR) in the NAT. The work presented here extends previous methods and attempts to take advantage of the NAT traffic structure to simplify the problem and improve the results of CDR. Four approaches are studied in this work: 1) subdividing the existing CDR problem into sub-problems of smaller sizes, which are easier to handle; 2) more efficient data reorganization within the considered time period; 3) problem localization, i.e. concentrating the resolution effort in the most conflicted regions; 4) applying CDR to the pre-tactical decision horizon (a couple of hours in advance). Obtained results show that these methods efficiently resolve potential conflicts at the strategic and pre-tactical levels by keeping the resulting trajectories close to the initial WO ones.

Rodionova, Olga↗

Homogeneity of a Global Multisatellite Soil Moisture Climate Data Record

Climate Data Records (CDR) that blend multiple satellite products are invaluable for climate studies, trend analysis and risk assessments. Knowledge of any inhomogeneities in the CDR is therefore critical for making correct inferences. This work proposes a methodology to identify the spatiotemporal extent of the inhomogeneities in a 36-year, global multisatellite soil moisture CDR as the result of changing observing systems. Inhomogeneities are detected at up to 24 percent of the tested pixels with spatial extent varying with satellite changeover times. Nevertheless, the contiguous periods without inhomogeneities at changeover times are generally longer than 10 years. Although the inhomogeneities have measurable impact on the derived trends, these trends are similar to those observed in ground data and land surface reanalysis, with an average error less than 0.003 cubic meters per cubic meter per year. These results strengthen the basis of using the product for long-term studies and demonstrate the necessity of homogeneity testing of multisatellite CDRs in general.

CDR↗

Energy Emissions Accounting Methods Can Determine Whether Direct Air Capture with Storage Achieves Net Removal

The voluntary carbon market within the United States has expanded rapidly in recent years and enabled private companies and other organizations to provide revenue streams to carbon dioxide removal (CDR) technologies. For a CDR technology to participate in the voluntary carbon market (VCM), the emissions associated with constructing and operating the technology must be less than the CO 2 captured from the atmosphere. Assessing the extent to which this is true for direct air capture with storage (DACS), a relatively energy-intensive CDR technology, strongly depends on the accounting method used to assess the emissions intensity of purchased energy. We simulate the hourly weather-dependent operation of sorbent- and solvent-based DACS in California, Louisiana, Texas, and Wyoming, representing a wide range of local weather and electric and natural gas grid compositions. In all cases, the single most important emissions accounting decision is the method used to estimate the emissions intensity of purchased grid electricity, which varies the calculated net removal by −1049% to +108%. All other factors influencing net removal introduce a variation of at most ±14%. No electricity emissions accounting method is universally conservative across all scenarios, and none is objectively more accurate. High-spatiotemporal-resolution, high-quality, publicly available data sets and models for electricity emissions accounting do not currently exist and are urgently needed to enable standardization of emissions accounting methods to more accurately determine the true emissions impacts of DACS and other energy-intensive facilities.

54 ENVIRONMENTAL SCIENCES↗

Metrics for quantifying the efficiency of atmospheric CO 2 reduction by marine carbon dioxide removal (mCDR)

Abstract Marine carbon dioxide removal (mCDR) is gaining interest as a tool to meet global climate goals. Because the response of the ocean–atmosphere system to mCDR takes years to centuries, modeling is required to assess the impact of mCDR on atmospheric CO 2 reduction. Here, we use a coupled ocean–atmosphere model to quantify the atmospheric CO 2 reduction in response to a CDR perturbation. We define two metrics to characterize the atmospheric CO 2 response to both instantaneous ocean alkalinity enhancement (OAE) and direct air capture (DAC): the cumulative additionality ( α ) measures the reduction in atmospheric CO 2 relative to the magnitude of the CDR perturbation, while the relative efficiency ( ϵ ) quantifies the cumulative additionality of mCDR relative to that of DAC. For DAC, α is 100% immediately following CDR deployment, but declines to roughly 50% by 100 years post-deployment as the ocean degasses CO 2 in response to the removal of carbon from the atmosphere. For instantaneous OAE, α is zero initially and reaches a maximum of 40%–90% several years to decades later, depending on regional CO 2 equilibration rates and ocean circulation processes. The global mean ϵ approaches 100% after 40 years, showing that instantaneous OAE is nearly as effective as DAC after several decades. However, there are significant geographic variations, with ϵ approaching 100% most rapidly in the low latitudes while ϵ stays well under 100% for decades to centuries near deep and intermediate water formation sites. These metrics provide a quantitative framework for evaluating sequestration timescales and carbon market valuation that can be applied to any mCDR strategy.

Yamamoto, Kana (ORCID:0009000731519234)↗

Baseline [ 18 F]GTP1 tau PET imaging is associated with subsequent cognitive decline in Alzheimer’s disease

Background: The role and implementation of tau PET imaging for predicting subsequent cognitive decline in Alzheimer’s disease (AD) remains uncertain. This study was designed to evaluate the relationship between baseline [ 18 F]GTP1 tau PET and subsequent longitudinal change across multiple cognitive measures over 18 months. Methods: Our analyses incorporated data from 67 participants, including cognitively normal controls (n = 10) and β-amyloid (Aβ)-positive individuals ([ 18 F] florbetapir Aβ PET) with prodromal (n = 26), mild (n = 16), or moderate (n = 15) AD. Baseline measurements included cortical volume (MRI), tau burden ([ 18 F]GTP1 tau PET), and cognitive assessments [Mini-Mental State Examination (MMSE), Clinical Dementia Rating (CDR), 13-item version of the Alzheimer’s Disease Assessment Scale-Cognitive Subscale (ADAS-Cog13), and Repeatable Battery for the Assessment of Neuropsychological Status (RBANS)]. Cognitive assessments were repeated at 6-month intervals over an 18-month period. Associations between baseline [ 18 F]GTP1 tau PET indices and longitudinal cognitive performance were assessed via univariate (Spearman correlations) and multivariate (linear mixed effects models) approaches. The utility of potential prognostic tau PET cut points was assessed with ROC curves. Results: Univariate analyses indicated that greater baseline [ 18 F]GTP1 tau PET signal was associated with faster rates of subsequent decline on the MMSE, CDR, and ADAS-Cog13 across regions of interest (ROIs). In multivariate analyses adjusted for baseline age, cognitive performance, cortical volume, and Aβ PET SUVR, the prognostic performance of [ 18 F]GTP1 SUVR was most robust in the whole cortical gray ROI. When AD participants were dichotomized into low versus high tau subgroups based on baseline [ 18 F]GTP1 PET standardized uptake value ratios (SUVR) in the temporal (cutoff = 1.325) or whole cortical gray (cutoff = 1.245) ROIs, high tau subgroups demonstrated significantly more decline on the MMSE, CDR, and ADAS-Cog13. Conclusions: Our results suggest that [ 18 F]GTP1 tau PET represents a prognostic biomarker in AD and are consistent with data from other tau PET tracers. Tau PET imaging may have utility for identifying AD patients at risk for more rapid cognitive decline and for stratification and/or enrichment of participant selection in AD clinical trials.

60 APPLIED LIFE SCIENCES↗

Coupling Circularity With Carbon Negativity in Food and Agriculture Systems

Achieving a circular economy is critical for a sustainable future, particularly in sectors that currently produce resource-intensive products in a linear fashion, such as food and agriculture. At the same time, technologies that remove atmospheric CO 2 , often referred to as carbon dioxide removal (CDR) or carbon negativity, must be developed and deployed rapidly if we are to avoid the worst effects of climate change. Circularity and CDR are often assessed and discussed independently, even though they are highly intertwined. Innovations to food and agriculture systems are essential to achieving a circular economy and enabling rapid deployment of CDR technologies. We explore critical areas of technology that must undergo rapid innovation (upstream and downstream) to food processing and consumption, namely precision and regenerative agriculture and biorefining, respectively. If implemented at scale, these two areas of technology have the potential to couple circularity with carbon negativity in food production systems.

Biorefining↗

A Novel Framework to Evaluate the Costs and Potential of Bioenergy in Decarbonization of the U.S. Economy

The long-term strategy of the United States targets reaching economy-wide net-zero emissions by 2050 and a carbon-neutral electricity grid by 2035 (U.S. Department of State and U.S. Executive Office of the President, 2021). Meeting these targets would require considerable changes to the energy system. Some key characteristics of illustrative net-zero energy systems include increased penetration of renewable energy and carbon sources, use of CO2 capture and storage (CCS) in hard-to-abate sectors, and a greater role for energy carriers such as electricity and hydrogen (Davis et al, 2018). Another common feature of such energy systems is the need for carbon dioxide removal (CDR) approaches (Horowitz et al, 2022). Across all these characteristics of net-zero energy systems, bioenergy and biomass feedstock is anticipated to play an important role. Biomass feedstock serves as a renewable carbon source. This can enable conversion of such feedstock into fuels and energy carriers for hard-to-abate sectors such as aviation. Indeed, the U.S. Government has a target to meet all jet fuel demand by 2050 from sustainable aviation fuel (SAF), where biofuel pathways are likely to have an important role (EERE, 2020). Bioenergy is also highly versatile with the possibility to convert feedstock into electricity, hydrogen, liquid fuels, heat or high-value products, based on biomass type, demand and technology availability (Clarke et al, 2022). Combination of bioenergy with CCS can also nominally deliver CDR (Fuhrman et al, 2023). As such, the share of bioenergy is expected to grow by at least five time across scenarios studied for the long-term strategy of the U.S. between 2020 and 2050 (Horowitz et al, 2022). Notwithstanding the role of bioenergy in the energy systems, its deployment, costs and scalability are influenced by a number of factors. Some of these factors pertain to policy interventions such as imposition of a binding decarbonization target either at an economy-wide level or the sectoral level. Resource availability and type of biomass feedstock also varies considerably across regions. From a technological perspective, the readiness of bioenergy conversion pathways is subject to high variability. This influences the costs of deployment. Moreover, the sourcing of feedstock, grid carbon intensity, and co-product handling approaches all affect the life cycle efficacy of bioenergy. The latter, in turn, is particularly important in determining the extent to which bioenergy with CCS or BECCS can effectively deliver CDR (Fajardy and Mac Dowell, 2017).

air emission↗

Mission Analysis for Marine Renewable Energy to Provide Power for Marine Carbon Dioxide Removal

The mission of this project was to provide a preliminary feasibility assessment of powering different marine carbon dioxide removal (mCDR), marine carbon capture, and marine carbon sequestration strategies with marine energy. In this report, carbon capture refers to methods that can separate or capture carbon dioxide (CO 2 ) from the air or ocean; carbon sequestration refers to methods that store CO 2 obtained by capture methods out of the atmosphere for long periods of time; and carbon dioxide removal (CDR) refers to methods that do both. The project found that mCDR powered by marine energy and offshore wind energy available in the United States could meet global CDR scales needed by 2040 and 2050 to limit warming to 1.5 degrees C by 2100. Note that this preliminary estimate assumes that it is possible to harvest all the marine and offshore wind resources available in the United States with existing technology options, and it does not account for the power needed for monitoring these methods, as these power needs are not yet well defined and require further research. Additionally, these CDR scales will still require emissions reductions.

16 TIDAL AND WAVE POWER↗

Voucher Opportunity 5-15: Independent Assessment of Monitoring, Reporting, and Verification (MRV) Technologies and Practices for Enhanced Rock Weathering (CRADA 718) Abstract

Development of robust, transparent, and precise monitoring, reporting, and verification (MRV) technologies and practices is critical for carbon dioxide removal (CDR) project developers to comply with regulatory and permitting requirements, voluntary carbon market (VCM) protocols, and to ensure safety while reducing environmental impacts. Enhanced rock weathering (ERW)-based CDR technologies focus on removing atmospheric carbon through conversion into thermodynamically stable solid or aqueous carbonate forms for permanent storage (i.e., mineralization). This highly durable form of CDR enhances naturally occurring silicate rock weathering cycles by optimizing application of finely-ground silicate rock particles (i.e., from basalt) on terrestrial agricultural lands to accelerate natural silicate rock weathering and mineralization. Enhanced rock weathering may also provide improved crop yields and enhance soil health. A critical aspect for commercialization of these technologies is the development of MRV to quantify the net removal and durable storage of atmospheric CO 2 . For ERW systems, it is essential to accurately characterize the mineral feedstock selected for application to establish the baseline geochemical composition, mineral dissolution rates, and carbon removal potential of the feedstocks to estimate overall net removal. Given the difficulty with conducting MRV for ERW in diverse soil/environment types, over large application areas, and due to complex chemical reaction networks, this project will accelerate understanding towards consensus on best practices for MRV. The overall objectives of the proposed voucher project are to: 1) Characterize and analyze feedstock(s) intended for ERW field application by Lithos Carbon (“Voucher Recipient”/ “CRADA Participant”) to determine overall mineralization potential; 2) Facilitate knowledge transfer and documentation of experimental protocols, instrumentation, and other relevant best practices; and 3) Support the Voucher Recipient’s broader technology commercialization and ERW Research Facility development plans. This work will align with the Voucher Recipient’s MRV plans for field sites and build upon complementary efforts conducted by PNNL on mineralization MRV.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Evidence for carbon dioxide removal via enhanced rock weathering with steel slag, though not basalt, in a midwestern U.S. field trial

Enhanced weathering is an emergent pathway for permanent atmospheric carbon dioxide removal (CDR). However, despite a dramatic increase in academic and commercial research, there remain relatively few published examples of field evidence demonstrating the effectiveness of enhanced weathering. Here, we present results from a three-year field trial that evaluated steel slag and crushed basalt applied as amendments in a conventional agricultural system in the Midwestern United States. Steel slag applied to initially acidic soil increased porewater pH and alkalinity and increased soil pH and Ca-saturation. Together, changes in porewater chemistry and soil properties provide strong evidence for steel slag weathering and CDR. However, steel slag applied to soils with a neutral initial pH did not generate significant changes in soil or porewater chemistry. In addition, coarse-grained crushed basalt did not generate significant change in any of the soils. Strong acid effects were apparent in all 3 years of monitoring soil porewater chemistry. Overall, our results demonstrate clear evidence of CDR from applying steel slag amendments to acidic cropland soils while also highlighting the difficulty of greenhouse gas reduction accounting from enhanced weathering and the variable outcomes that can occur depending on feedstock and soil type.

Geosciences↗

Methods for Measuring Carbon Dioxide Uptake and Permanence: Review and Implications for Macroalgae Aquaculture

Carbon dioxide removal (CDR) is gaining recognition as a necessary action in addition to emissions reduction to prevent some of the worst effects of climate change. Macroalgae aquaculture has been identified as a potential CDR strategy and significant research investments have been made in this area. This article reviews current methods for monitoring carbon to assess the potential for application in the context of macroalgae aquaculture as a CDR strategy. In total, 382 papers were included in the review and categorized by carbon uptake methods, carbon permanence methods, and comprehensive frameworks for assessing carbon capture. While methods for measuring carbon uptake are well established, methods to assess the permanence of carbon in the natural life cycle of macroalgae and in products following harvest are lacking. To achieve the full benefit of macroalgae cultivation as a climate solution, monitoring, reporting, and verification standards and improved methods for assessing carbon uptake and permanence need to be developed.

59 BASIC BIOLOGICAL SCIENCES↗

Biological Parts for Plant Biodesign to Enhance Land-Based Carbon Dioxide Removal

A grand challenge facing society is climate change caused mainly by rising CO 2 concentration in Earth’s atmosphere. Terrestrial plants are linchpins in global carbon cycling, with a unique capability of capturing CO 2 via photosynthesis and translocating captured carbon to stems, roots, and soils for long-term storage. However, many researchers postulate that existing land plants cannot meet the ambitious requirement for CO 2 removal to mitigate climate change in the future due to low photosynthetic efficiency, limited carbon allocation for long-term storage, and low suitability for the bioeconomy. To address these limitations, there is an urgent need for genetic improvement of existing plants or construction of novel plant systems through biosystems design (or biodesign). Here, we summarize validated biological parts (e.g., protein-encoding genes and noncoding RNAs) for biological engineering of carbon dioxide removal (CDR) traits in terrestrial plants to accelerate land-based decarbonization in bioenergy plantations and agricultural settings and promote a vibrant bioeconomy. Specifically, we first summarize the framework of plant-based CDR (e.g., CO 2 capture, translocation, storage, and conversion to value-added products). Then, we highlight some representative biological parts, with experimental evidence, in this framework. Finally, we discuss challenges and strategies for the identification and curation of biological parts for CDR engineering in plants.

59 BASIC BIOLOGICAL SCIENCES↗

Convection in the vertical midplane of a horizontal cylinder Comparison of two-dimensional approximations with three-dimensional results

Experimental results and numerical data on the flow characteristics of core-driven and boundary-layer-driven regimes (CDRs) and (BLDRs) are compared to two-dimensional solutions for heated convective flow in the vertical midplane of a horizontal cylinder. The data were obtained from laser Doppler velocimetry (LDA) measurements and from three-dimensional numerical solutions. It is shown that the approximate solutions gave the correct Rayleigh-number-dependences and distributions for the velocities in the CDR and BLDR regimes. However, the transition between the CDR and the BLDR, as well as the magnitude of the distribution of velocity components, were found to be dependent on the type of two-dimensional approximation selected. In the case of CDR, core velocities were overestimated by as much as 30 percent by the two-dimensional approximations; and in the case of BLDR, the core velocities were overestimated by 40-50 percent as compared to the measured velocities. A schematic illustration of the flow patterns in the cylinder is provided.

Bontoux, P.↗

Manufacturing and NDE of Large Composite Structures for Space Transportation at MSFC

This paper presents the Marshall Space Flight Center's (MSFC's) vision to manufacture, increase safety and reduce the cost of launch vehicles. Nondestructive evaluations of large composite structures are tested for space transportation at MSFC. The topics include: 1) 6 1/2 Generations of Airplanes in a Century; 2) Shuttle Safety Upgrades; 3) Generations of Reusable Launch Vehicles; 4) RLV Technology Demonstration Path; 5) Second Generation; 6) Key NASA Requirements; 7) X-33 Elements; 8) Future-X Pathfinder Projects and Experiments; 9) Focus Area Technical Goals; 10) X-34 Expanded View; 11) X-38 Spacecraft with De-Orbit Propulsion Stage (DPS); 12) Deorbit Module (DM) Critical Design Review (CDR) Design; 13) Forward Structural Adapter (FSA) CDR Design; 14) X-38 DPS CDR Design; 15) RLV Focused Propulsion Technologies; and 16) Challenges in Technology. This paper is presented in viewgraph form.

McGill, Preston↗

Mapping Closure Approximation to Conditional Dissipation Rate for Turbulent Scalar Mixing

A novel mapping closure approximation (MCA) technique is developed to construct a model for the conditional dissipation rate (CDR) of a scalar in homogeneous turbulence. It is shown that the CDR model from amplitude mapping closure is incorrect in asymptotic behavior for unsymmetric binary mixing. The correct asymptotic behavior can be described by the CDR model formulated by the MCA technique. The MCA approach is outlined for constructing successive approximation to probability density function (PDF) and conditional moment.

He, Gouwei↗