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At least 145 records · Page 8

Simulation of Avifauna Distributions Using Remote Sensing

Remote sensing has proved a fruitful tool for understanding the distribution and functioning of plant communities at multiple scales and to understand their coupling to bioclimatic and anthropogenic factors. But a similar approach to understanding the distribution and abundance of bird species as well as many other animal organisms is lacking. The increasing need for such understanding is evident with the recent examples of threats to human health via avian vector transmission and the increasing emphasis on global conservation biology. From experimental observations we know that species richness tends to track biological or environmental gradients. In this paper, we explore the fundamental idea that thermal and water-relation environments of birds, as estimated from satellite data and biophysical models, can define the constraints on their Occurrences and richness. We develop individual bird energy budget models and use these models to define the climate space niche of birds. Using satellite data assimilation products to drive our models, we disperse a distribution of virtual or actual bird species across the landscape in accordance to the limits expressed by their climate space niche. Here, we focus on the North American summer breeding season and give two examples to illustrate our approach. The first is a tundra loving bird, e.g. corresponding to the Culidris genus, and a second genus example, Myiurchus, that corresponds to arid or semi-arid regions. We define these birds in terms of their basic physiology and morphological characteristics, construct avian energetic simulations to predict their allowable metabolic ranges and climate space limits.

Smith, James A.↗

Integrating plant physiology into simulation of fire behavior and effects

Summary Wildfires are a global crisis, but current fire models fail to capture vegetation response to changing climate. With drought and elevated temperature increasing the importance of vegetation dynamics to fire behavior, and the advent of next generation models capable of capturing increasingly complex physical processes, we provide a renewed focus on representation of woody vegetation in fire models. Currently, the most advanced representations of fire behavior and biophysical fire effects are found in distinct classes of fine‐scale models and do not capture variation in live fuel (i.e. living plant) properties. We demonstrate that plant water and carbon dynamics, which influence combustion and heat transfer into the plant and often dictate plant survival, provide the mechanistic linkage between fire behavior and effects. Our conceptual framework linking remotely sensed estimates of plant water and carbon to fine‐scale models of fire behavior and effects could be a critical first step toward improving the fidelity of the coarse scale models that are now relied upon for global fire forecasting. This process‐based approach will be essential to capturing the influence of physiological responses to drought and warming on live fuel conditions, strengthening the science needed to guide fire managers in an uncertain future.

54 ENVIRONMENTAL SCIENCES↗

Growth instabilities shape morphology and genetic diversity of microbial colonies

Abstract Cellular populations assume an incredible variety of shapes ranging from circular molds to irregular tumors. While we understand many of the mechanisms responsible for these spatial patterns, little is known about how the shape of a population influences its ecology and evolution. Here, we investigate this relationship in the context of microbial colonies grown on hard agar plates. This a well-studied system that exhibits a transition from smooth circular disks to more irregular and rugged shapes as either the nutrient concentration or cellular motility is decreased. Starting from a mechanistic model of colony growth, we identify two dimensionless quantities that determine how morphology and genetic diversity of the population depend on the model parameters. Our simulations further reveal that population dynamics cannot be accurately described by the commonly-used surface growth models. Instead, one has to explicitly account for the emergent growth instabilities and demographic fluctuations. Overall, our work links together environmental conditions, colony morphology, and evolution. This link is essential for a rational design of concrete, biophysical perturbations to steer evolution in the desired direction.

Golden, Alexander↗

Challenges in simulating economic effects of climate change on global agricultural markets

Abstract Many approaches have been used to investigate climate change impacts on agriculture. However, several caveats remain in this field: (i) analyses focus only on a few major crops, (ii) large differences in yield impacts are observed between projections from site-based crops models and Global Gridded Crop Models (GGCMs), (iii) climate change impacts on livestock are rarely quantified, and (iv) several causal relations among biophysical, environmental, and socioeconomic aspects are usually not taken into account. We investigate how assumptions about these four aspects affect agricultural markets, food supply, consumer well-being, and land use at global level by deploying a large-scale socioeconomic model of the global economy with detailed representation of the agricultural sector. We find global welfare impacts several times larger when climate impacts all crops and all livestock compared to a scenario with impacts limited to major crops. At the regional level, food budget can decrease by 10 to 25% in developing countries, challenging food security. The role of land area expansion as a major source of adaptation is highlighted. Climate impacts on crop yields from site-based process crop models generate more challenging socioeconomic outcomes than those from GGCMs. We conclude that the agricultural research community should expand efforts to estimate climate impacts on many more crops and livestock. Also, careful comparison of the GGCMs and traditional site-based process crop models is needed to understand their major implications for agricultural and food markets.

Gurgel, Angelo C. (ORCID:0000000183319508)↗

Carbon nanotube porin diffusion in mixed composition supported lipid bilayers

Carbon nanotube porins (CNTPs), short pieces of carbon nanotubes capable of self-inserting into a lipid bilayer, represent a simplified model of biological membrane channels. We have used high-speed atomic force microscopy (HS-AFM) and all-atom molecular dynamics (MD) simulations to study the behavior of CNTPs in a mixed lipid membrane consisting of DOPC lipid with a variable percentage of DMPC lipid added to it. HS-AFM data reveal that the CNTPs undergo diffusive motion in the bilayer plane. Motion trajectories extracted from the HS-AFM movies indicate that CNTPs exhibit diffusion coefficient values broadly similar to values reported for membrane proteins in supported lipid bilayers. The data also indicate that increasing the percentage of DMPC leads to a marked slowing of CNTP diffusion. MD simulations reveal a CNTP-lipid assembly that diffuses in the membrane and show trends that are consistent with the experimental observations.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Agroecosystem model simulations reveal spatial variability in relative productivity in biomass sorghum and maize in Iowa, USA

Biomass sorghum (Sorghum bicolor L. Moench) is an annual C 4 grass that has emerged as a candidate bioenergy crop but has not been widely grown in the United States. Corn (Zea mays L.), another annual C 4 grass, has been produced on a large scale in the United States for biofuels. Iowa leads the nation in both corn and ethanol production. The high productivity of corn in Iowa creates the research question: could biomass sorghum be as or more productive than corn in the state in terms of bioenergy? Efforts to use crop models to fill the gaps left by field experimentation on biomass sorghum have also been limited thus far. To address our research question, we collected biophysical data on biomass sorghum grown in Iowa for two growing seasons, used them to develop a biomass sorghum module in an agroecosystem model (Agro-IBIS), and predict the potential performance of biomass sorghum across Iowa compared to maize. Despite dry conditions in 2019 and 2020, average biomass sorghum yields were 17.20 Mg ha –1 . By comparison, average corn aboveground biomass was higher in 2020 (22.02 Mg ha –1 ). Soil cores indicated average belowground biomass of 1.46 Mg ha –1 , with roots concentrated near the surface (73% of biomass above 50 cm in a 1 m core). When biomass sorghum model parameters were calibrated with measured values, model output was in close agreement with measured biomass (slope = 0.932, R 2 = 0.91) and evapotranspiration (slope = 0.757, R 2 = 0.64). Subsequent regional simulations revealed a notable latitudinal gradient in biomass sorghum yield, with a strong linear relationship between yield and seasonal growing degree-days (R 2 = 0.89). When these yields were compared to simulated corn aboveground biomass yields, only 3.4% of the state had biomass sorghum yields that were significantly higher than corn. This number was reduced to 0.3% when comparing the crops in terms of energy ethanol yield. Thus, we conclude biomass sorghum must be improved to be competitive with corn as an annual biofuel crop in Iowa. This study provides a baseline against which to compare advancements in sorghum breeding for biomass and stress tolerance in Iowa.

Agro-IBIS↗

Limits to forests-based mitigation in integrated assessment modelling: global potentials and impacts under constraining factors

Forests-based measures such as afforestation/reforestation (A/R) and reducing deforestation (RDF) are considered promising options to mitigate climate change, yet their mitigation potentials are limited by economic and biophysical factors that are largely uncertain. The range of mitigation potential estimates from integrated assessment models raises concerns about the capacity of land systems to provide realistic, cost-effective and permanent land-based mitigation. We use the Global Change Analysis Model to quantify the economic mitigation potential of forests-based measures by simulating a climate policy including a tax on greenhouse gas emissions from agriculture, forestry, and other land uses. In addition, we assess how constraining unused arable land (UAL) availability, forestland expansion rates, and global bioenergy demand may influence the forests-based mitigation potential by simulating scenarios with alternative combinations of constraints. Results show that the average forests-based mitigation potential in 2020–2050 increases from 738 MtCO 2 .yr -1 through a forestland increase of 86 Mha in the fully constrained scenario to 1394 MtCO 2 .yr -1 through a forestland increase of 146 Mha when all constraints are relaxed. Regional potentials in terms of A/R and RDF differ strongly between scenarios: unconstrained forest expansion rates mostly increase A/R potentials in northern regions (e.g., +120 MtCO 2 .yr -1 in North America); while unconstrained UAL conversion and low bioenergy demand mostly increase RDF potentials in tropical regions (e.g., +76 and +68 MtCO 2 .yr -1 in Southeast Asia, respectively). This study shows that forests-based mitigation is limited by many factors that constrain the rates of land use change across regions. These factors, often overlooked in modelling exercises, should be carefully addressed for understanding the role of forests in global climate mitigation and defining pledges towards the Paris Agreement.

54 ENVIRONMENTAL SCIENCES↗

Molecular dynamics simulations of the secondary-binding site in disaccharide-modified glycopeptide antibiotics

Oritavancin is a semisynthetic glycopeptide antibiotic used to treat severe infections by multidrug-resistant Gram-positive pathogens. Oritavancin is known to be a thousand times more potent than vancomycin against Gram-positive bacteria due to the additional interactions with bacterial peptidoglycan (PG) facilitated by a secondary-binding site. The presence of this secondary-binding site is evident in desleucyl-oritavancin, an Edman degradation product of oritavancin, still retaining its potency against Gram-positive bacteria, whereas desleucyl-vancomycin is devoid of any antimicrobial activities. Herein, using explicit solvent molecular dynamics (MD) simulations, steered MD simulations, and umbrella sampling, we show evidence of a secondary-binding site mediated by the disaccharide-modified hydrophobic sidechain of oritavancin interactions with the pentaglycyl-bridge segment of the PG. The interactions were characterized through comparison to the interaction of PG with chloroeremomycin, vancomycin, and the desleucyl analogs of the glycopeptides. Our results show that the enhanced binding of oritavancin to PG over the binding of the other complexes studied is due to an increase in the hydrophobic effect, electrostatic and van der Waals interactions, and not the average number of hydrogen bonds. Our ranking of the binding interactions of the biomolecular complexes directly correlates with the order based on their experimental minimum inhibitory concentrations. The results of our simulations provide insight into the modification of glycopeptides to increase their antimicrobial activities or the design of novel antibiotics against pathogenic Gram-positive bacteria.

60 APPLIED LIFE SCIENCES↗

On The Development of Biophysical Models for Space Radiation Risk Assessment

Experimental techniques in molecular biology are being applied to study biological risks from space radiation. The use of molecular assays presents a challenge to biophysical models which in the past have relied on descriptions of energy deposition and phenomenological treatments of repair. We describe a biochemical kinetics model of cell cycle control and DNA damage response proteins in order to model cellular responses to radiation exposures. Using models of cyclin-cdk, pRB, E2F's, p53, and GI inhibitors we show that simulations of cell cycle populations and GI arrest can be described by our biochemical approach. We consider radiation damaged DNA as a substrate for signal transduction processes and consider a dose and dose-rate reduction effectiveness factor (DDREF) for protein expression.

Cucinotta, F. A.↗

Molecular simulations and NMR reveal how lipid fluctuations affect membrane mechanics

Lipid bilayers form the main matrix of functional cell membranes, and their dynamics underlie a host of physical and biological processes. Here we show that elastic membrane properties and collective molecular dynamics (MD) are related by the mean-square amplitudes (order parameters) and relaxation rates (correlation times) of lipid acyl chain motions. We performed all-atom MD simulations of liquid-crystalline bilayers that allow direct comparison with carbon-hydrogen (CH) bond relaxations measured with NMR spectroscopy. Previous computational and theoretical approaches have assumed isotropic relaxation, which yields inaccurate description of lipid chain dynamics and incorrect data interpretation. Instead, the new framework includes a fixed bilayer normal (director axis) and restricted anisotropic motion of the CH bonds in accord with their segmental order parameters, enabling robust validation of lipid force fields. Simulated spectral densities of thermally excited CH bond fluctuations exhibited well-defined spin-lattice (Zeeman) relaxations analogous to those in NMR measurements. Their frequency signature could be fit to a simple power-law function, indicative of nematic-like collective dynamics. Moreover, calculated relaxation rates scaled as the squared order parameters yielding an apparent K C modulus for bilayer bending. Our results show a strong correlation with K C values obtained from solid-state NMR studies of bilayers without and with cholesterol as validated by neutron spin-echo measurements of membrane elasticity. The simulations uncover a critical role of interleaflet coupling in membrane mechanics and thus provide important insights into molecular sites of emerging elastic properties within lipid bilayers.

59 BASIC BIOLOGICAL SCIENCES↗

Magnetic levitation-based Martian and Lunar gravity simulator

Missions to Mars will subject living specimens to a range of low gravity environments. Deleterious biological effects of prolonged exposure to Martian gravity (0.38 g), Lunar gravity (0.17 g), and microgravity are expected, but the mechanisms involved and potential for remedies are unknown. We are proposing the development of a facility that provides a simulated Martian and Lunar gravity environment for experiments on biological systems in a well controlled laboratory setting. The magnetic adjustable gravity simulator will employ intense, inhomogeneous magnetic fields to exert magnetic body forces on a specimen that oppose the body force of gravity. By adjusting the magnetic field, it is possible to continuously adjust the total body force acting on a specimen. The simulator system considered consists of a superconducting solenoid with a room temperature bore sufficiently large to accommodate small whole organisms, cell cultures, and gravity sensitive bio-molecular solutions. It will have good optical access so that the organisms can be viewed in situ. This facility will be valuable for experimental observations and public demonstrations of systems in simulated reduced gravity. c2005 Published by Elsevier Ltd on behalf of COSPAR.

Non-NASA Center↗

Interdisciplinary Workshop on the Impacts of Land Use and Land Management on Earth System Evolution, Biogeochemical Cycles, Extremes, and Inter-Sectoral Dynamics (Final Report)

The Aspen Global Change Institute (AGCI) convened a week-long interdisciplinary science workshop from September 15-20, 2019 entitled, “Impacts of Land Use and Land Management on Earth System Evolution, Biogeochemical Cycles, Extremes, and Inter-Sectoral Dynamics.” The purpose of the workshop was to advance research on the impacts of land use and land management on climate, carbon emissions, and extremes, as well as the impact of land-use change on important societal issues such as food, water, and energy security. The workshop was co-chaired by Kate Calvin (PNNL), George Hurtt (University of Maryland), and Dave Lawrence (National Center for Atmospheric Research). Co-funders of the workshop included NASA, NOAA, and travel support for European colleagues through CRESCENDO. This workshop brought together 31 professionals with expertise across biogeochemistry, climate impacts, mitigation, land use datasets, and societal impacts to coordinate on upcoming research and publications on the role of biogeochemical and biophysical properties of the Earth surface and their implications for climate, as conducted through the Land Use model Intercomparison Project (LUMIP), which is part of Phase 6 of the Coupled Model Intercomparison Project (CMIP6). A primary outcome of the meeting was the definition and planning of a series of LUMIP papers that will rely on the LUMIP and CMIP6 simulations. By the end of the meeting more than twenty papers and paper lead authors had been identified and scoped out. Around ten of these papers were submitted by the December 31, 2019 IPCC deadline.

54 ENVIRONMENTAL SCIENCES↗

Characterization of vegetation by microwave and optical remote sensing

Two series of carefully controlled experiments were conducted. First, plots of important crops (corn, soybeans, and sorghum), prairie grasses (big bluestem, switchgrass, tal fescue, orchardgrass, bromegrass), and forage legumes (alfalfa, red clover, and crown vetch) were manipulated to produce wide ranges of phytomass, leaf area index, and canopy architecture. Second, coniferous forest canopies were simulated using small balsam fir trees grown in large pots of soil and arranged systematically on a large (5 m) platform. Rotating the platform produced many new canopies for frequency and spatial averaging of the backscatter signal. In both series of experiments, backscatter of 5.0 GHz (C-Band) was measured as a function of view angle and polarization. Biophysical measurements included leaf area index, fresh and dry phytomass, water content of canopy elements, canopy height, and soil roughness and moisture content. For a subset of the above plots, additional measurements were acquired to exercise microwave backscatter models. These measurements included size and shape of leaves, stems, and fruit and the probability density function of leaf and stem angles. The relationships of the backscattering coefficients and the biophysical properties of the canopies were evaluated using statistical correlations, analysis of variance, and regression analysis. Results from the corn density and balsam fir experiments are discussed and analyses of data from the other experiments are summarized.

Daughtry, C. S. T.↗

Retrieving functional pathways of biomolecules from single-particle snapshots

Abstract A primary reason for the intense interest in structural biology is the fact that knowledge of structure can elucidate macromolecular functions in living organisms. Sustained effort has resulted in an impressive arsenal of tools for determining the static structures. But under physiological conditions, macromolecules undergo continuous conformational changes, a subset of which are functionally important. Techniques for capturing the continuous conformational changes underlying function are essential for further progress. Here, we present chemically-detailed conformational movies of biological function, extracted data-analytically from experimental single-particle cryo-electron microscopy (cryo-EM) snapshots of ryanodine receptor type 1 (RyR1), a calcium-activated calcium channel engaged in the binding of ligands. The functional motions differ substantially from those inferred from static structures in the nature of conformationally active structural domains, the sequence and extent of conformational motions, and the way allosteric signals are transduced within and between domains. Our approach highlights the importance of combining experiment, advanced data analysis, and molecular simulations.

59 BASIC BIOLOGICAL SCIENCES↗

Cooperative multivalent receptor binding promotes exposure of the SARS-CoV-2 fusion machinery core

The molecular events that permit the spike glycoprotein of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) to bind and enter cells are important to understand for both fundamental and therapeutic reasons. Spike proteins consist of S1 and S2 domains, which recognize angiotensin-converting enzyme 2 (ACE2) receptors and contain the viral fusion machinery, respectively. Ostensibly, the binding of spike trimers to ACE2 receptors promotes dissociation of the S1 domains and exposure of the fusion machinery, although the molecular details of this process have yet to be observed. We report the development of bottom-up coarse-grained (CG) models consistent with cryo-electron tomography data, and the use of CG molecular dynamics simulations to investigate viral binding and S2 core exposure. We show that spike trimers cooperatively bind to multiple ACE2 dimers at virion-cell interfaces in a manner distinct from binding between soluble proteins, which processively induces S1 dissociation. We also simulate possible variant behavior using perturbed CG models, and find that ACE2-induced S1 dissociation is primarily sensitive to conformational state populations and the extent of S1/S2 cleavage, rather than ACE2 binding affinity. These simulations reveal an important concerted interaction between spike trimers and ACE2 dimers that primes the virus for membrane fusion and entry.

59 BASIC BIOLOGICAL SCIENCES↗

Biophysical model of eelgrass and water quality in Coos Bay, OR shows greater mitigation potential for ocean acidification than hypoxia

Seagrass beds provide important ecosystem services and are valued, in part, for their potential to mediate stressors such as ocean acidification and hypoxia (OAH) for sensitive species. However, the susceptibility of seagrasses to anthropogenic impacts and recent declines motivate the need to better understand the drivers of seagrass and the water quality consequences that occur with variation in seagrass abundance. To meet this need, we leveraged existing monitoring data (water quality and seagrass), hydrodynamic circulation model, and biogeochemical model framework with seagrass submodel, to produce a biophysical model of Coos Bay estuary, Oregon, U.S. The model includes biogeochemical processes involving water quality, plankton, seagrass, and sediment-water interactions. Ecosystem models like this are useful for evaluating complex estuarine systems because they allow us to extend our understanding of system dynamics beyond existing observations and perform experiments to identify the processes driving observed patterns. We used the biophysical model of Coos Bay to evaluate the dynamics of water quality and native eelgrass (Zostera marina) under three eelgrass abundance scenarios (zero eelgrass, current extent, and maximum observed extent) to elucidate the relationship between eelgrass and OAH. Including eelgrass in the Coos Bay model produced results that more closely resembled water quality observations - dissolved oxygen (DO) and pH were more dynamic in simulations with eelgrass, often having both higher highs and lower lows. While there were some areas of the estuary where DO improved with the addition of eelgrass to the model there was overall a small net increase in harmful DO conditions (based on a salmon physiological threshold). In contrast, ocean acidification conditions, pH and calcium carbonate saturation state for aragonite (Ω), were improved (based on oyster requirements) with the addition of eelgrass - although the magnitude of improvement differed seasonally and spatially. Our new model represents a useful tool - one which accounts for and controls the relevant physical and biogeochemical processes - to evaluate conditions that confer resilience or enhance vulnerability to OAH in an important Pacific Northwest coastal estuary and results can inform the OAH-related dynamics occurring in other eastern boundary current estuaries.

FVCOM-ICM↗

Design of synthetic collagens that assemble into supramolecular banded fibers as a functional biomaterial testbed

Collagens are the most abundant proteins of the extracellular matrix, and the hierarchical folding and supramolecular assembly of collagens into banded fibers is essential for mediating cell-matrix interactions and tissue mechanics. Collagen extracted from animal tissues is a valuable commodity, but suffers from safety and purity issues, limiting its biomaterials applications. Synthetic collagen biomaterials could address these issues, but their construction requires molecular-level control of folding and supramolecular assembly into ordered banded fibers, comparable to those of natural collagens. Here, we show an innovative class of banded fiber-forming synthetic collagens that recapitulate the morphology and some biological properties of natural collagens. The synthetic collagens comprise a functional-driver module that is flanked by adhesive modules that effectively promote their supramolecular assembly. Multiscale simulations support a plausible molecular-level mechanism of supramolecular assembly, allowing precise design of banded fiber morphology. We also experimentally demonstrate that synthetic fibers stimulate osteoblast differentiation at levels comparable to natural collagen. This work thus deepens understanding of collagen biology and disease by providing a ready source of safe, functional biomaterials that bridge the current gap between the simplicity of peptide biophysical models and the complexity of in vivo animal systems.

Jinyuan Hu↗

Remote sensing of earth terrain

In remote sensing, the encountered geophysical media such as agricultural canopy, forest, snow, or ice are inhomogeneous and contain scatters in a random manner. Furthermore, weather conditions such as fog, mist, or snow cover can intervene the electromagnetic observation of the remotely sensed media. In the modelling of such media accounting for the weather effects, a multi-layer random medium model has been developed. The scattering effects of the random media are described by three-dimensional correlation functions with variances and correlation lengths corresponding to the fluctuation strengths and the physical geometry of the inhomogeneities, respectively. With proper consideration of the dyadic Green's function and its singularities, the strong fluctuation theory is used to calculate the effective permittivities which account for the modification of the wave speed and attenuation in the presence of the scatters. The distorted Born approximation is then applied to obtain the correlations of the scattered fields. From the correlation of the scattered field, calculated is the complete set of scattering coefficients for polarimetric radar observation or brightness temperature in passive radiometer applications. In the remote sensing of terrestrial ecosystems, the development of microwave remote sensing technology and the potential of SAR to measure vegetation structure and biomass have increased effort to conduct experimental and theoretical researches on the interactions between microwave and vegetation canopies. The overall objective is to develop inversion algorithms to retrieve biophysical parameters from radar data. In this perspective, theoretical models and experimental data are methodically interconnected in the following manner: Due to the complexity of the interactions involved, all theoretical models have limited domains of validity; the proposed solution is to use theoretical models, which is validated by experiments, to establish the region in which the radar response is most sensitive to the parameters of interest; theoretically simulated data will be used to generate simple invertible models over the region. For applications to the remote sensing of sea ice, the developed theoretical models need to be tested with experimental measurements. With measured ground truth such as ice thickness, temperature, salinity, and structure, input parameters to the theoretical models can be obtained to calculate the polarimetric scattering coefficients for radars or brightness temperature for radiometers and then compare theoretical results with experimental data. Validated models will play an important role in the interpretation and classification of ice in monitoring global ice cover from space borne remote sensors in the future. We present an inversion algorithm based on a recently developed inversion method referred to as the Renormalized Source-Type Integral Equation approach. The objective of this method is to overcome some of the limitations and difficulties of the iterative Born technique. It recasts the inversion, which is nonlinear in nature, in terms of the solution of a set of linear equations; however, the final inversion equation is still nonlinear. The derived inversion equation is an exact equation which sums up the iterative Neuman (or Born) series in a closed form and, thus, is a valid representation even in the case when the Born series diverges; hence, the name Renormalized Source-Type Integral Equation Approach.

Yueh, Herng-Aung↗