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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Medium controlled aggregative growth as a key step in mesoporous silica nanoparticle formation

Near monodisperse mesoporous silica nanoparticles (MSN) represent a promising and rapidly developing type of mesoporous silica materials; however, the vast data on their synthesis remains unorganized and ill-understood. We systematically studied the formation of MSN under basic and neutral conditions using various temperatures, CTAB concentrations, hydrolyzing agents (triethanolamine, ammonia, phosphate buffers), and media with different colloidal stabilization properties (with ethanol as a cosolvent and monovalent salts). In the typical conditions for the preparation of stable MSN colloids, the particle size was controlled by colloidal stabilization by the medium (solvent type, ionic strength, and surfactant concentration) in agreement with the “aggregative growth” mechanism, rather than by solely the hydrolysis and condensation rates conventionally used for data interpretation in the classical nucleation theory. Medium properties (pH, ion types and concentration, polarity) also defined the efficiency of silica-surfactant cooperative self-assembly, which directly affected the porosity, mesopore size and pore wall thickness. Interestingly, this traditional silica-surfactant route showed a limited effect on the particle size, emphasizing the dominating role of colloidal stabilization in the studied reaction conditions. In situ pH measurements showed that every reaction medium has unique pH evolution profiles depending on the buffer capacity, hydrolysis and condensation rates. Reaction systems that fail to maintain the working pH can lead to non-porous products or undesired particle morphology and size distribution. The established particle formation mechanism allowed us to formulate comprehensive guidelines for preparing relatively concentrated colloids of near monodisperse (PDI 5–15%) mesoporous 30–700 nm silica spheres with variable porosity and mesopore size. Here, these findings will be particularly useful in designing new mesoporous silica-containing materials for biomedical applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Shape Control of Colloidal Semiconductor Nanocrystals through Thermodynamically Driven Aggregative Growth

The optoelectronic properties of colloidal semiconductor nanocrystals (NCs) can be manipulated by changing their geometric shapes. The precise synthetic control over particle morphologies, however, has remained elusive. Conventional growth techniques rely on the kinetic assembly of atomic units, where supersaturation and precipitation processes can lead to a broad distribution of particle shapes. In this paper, we demonstrate that replacing atomic precursors with small-size nanocrystals as building blocks for larger colloids offers an easier, more predictive control over nanoparticle shape evolution. The reported growth strategy is illustrated via shape-selective syntheses of CdSe and CdS NC cubes, spheres, rods, as well as unprecedented “donut” and ring-like structures. Growth of desired particle morphologies was achieved by choosing an appropriate reaction solvent that minimizes the surface free energy through a unique shape formation. This so-called "aggregative growth mechanism" is explained using a thermodynamic model for interacting viscous colloids. We expect that this novel growth strategy will offer a viable platform for shape–selective synthesis of many inorganic colloids, providing pathways to optimizable optoelectronic materials.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Bridging the thermodynamics and kinetics of temperature-induced morphology evolution in polymer/fullerene organic solar cell bulk heterojunction

The performance of organic solar cells (OSC) critically depends on the morphology of the active layer. After deposition, the active layer is in a metastable state and prone to changes that lead to cell degradation. Here, a high efficiency fullerene:polymer blend is used as a model system to follow the temperature-induced morphology evolution through a series of thermal annealing treatments. Electron microscopy analysis of the nano-scale phase evolution during the early stages of thermal annealing revealed that spinodal decomposition, i.e. spontaneous phase separation with no nucleation stage, is possibly responsible for the formation of a fine scale bicontinuous structure. In the later evolution stages, large polycrystalline fullerene aggregates are formed. Optical microscopy and scattering revealed that aggregate-growth follows the Johnson–Mehl–Avrami–Kolmogorov equation indicating a heterogeneous transformation process, i.e., through nucleation and growth. These two mechanisms, spinodal decomposition vs. nucleation and growth, are mutually exclusive and their co-existence is surprising. This unexpected observation is resolved by introducing a metastable monotectic phase diagram and showing that the morphology evolution goes through two distinct and consecutive transformation processes where spinodal decomposition of the amorphous donor:acceptor blend is followed by nucleation and growth of crystalline acceptor aggregates. Lastly, this unified thermodynamic and kinetic mechanism allows us to correlate the morphology evolution with OSC degradation during thermal annealing.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Nucleation, Growth, and Aggregation of Todorokite Nanoparticles from Both Geochemical and Materials Science Perspectives (Final Technical Report)

A vast amount of manganese (Mn) nodules exists in ocean sediments, covering about 30% of the ocean floor. Tunneled and layered Mn(IV) oxides, hereafter called TMOs and LMOs, are the primary mineral phases hosting Mn. Owing to their unique structure and properties, these Mn oxides are highly enriched in transition metals, platinum group metals, and rare earth elements, up to several percentages in weight. Thus, many metals are stored in these nodules and the nodules have thus been increasingly considered for their potential as a source of strategic metals for national security applications and the energy industry. The nodules also play an important role in trace metal biogeochemical cycling in the ocean because they control the partition and distribution of trace metals in oceanic sediments. Layered and tunneled structures differ in their mineralogical and chemical properties. For example, TMOs contain fewer metals compared to LMOs in ocean nodules. Therefore, the relative proportion of the two types of minerals in ocean nodules determines the metal sequestration capacities of the nodules, hence the amount of metals stored in the nodules and metal cycling in oceans. The overall objective of this study is to investigate the mechanisms of layered to tunneled structural transform driven by redox reactions. Specifically, we focus on the redox reactions between Mn(IV) and Mn(II) because they often coexist during Mn redox cycling.

58 GEOSCIENCES↗
DOE OSTI2020

Taxon-specific microbial growth and mortality patterns reveal distinct temporal population responses to rewetting in a California grassland soil

Abstract Microbial activity increases after rewetting dry soil, resulting in a pulse of carbon mineralization and nutrient availability. The biogeochemical responses to wet-up are reasonably well understood and known to be microbially mediated. Yet, the population level dynamics, and the resulting changes in microbial community patterns, are not well understood as ecological phenomena. Here, we used sequencing of 16S rRNA genes coupled with heavy water (H218O) DNA quantitative stable isotope probing to estimate population-specific rates of growth and mortality in response to a simulated wet-up event in a California annual grassland soil. Bacterial growth and mortality responded rapidly to wet-up, within 3 h, and continued throughout the 168 h incubation, with patterns of sequential growth observed at the phylum level. Of the 37 phyla detected in the prewet community, growth was found in 18 phyla while mortality was measured in 26 phyla. Rapid growth and mortality rates were measurable within 3 h of wet-up but had contrasting characteristics; growth at 3 h was dominated by select taxa within the Proteobacteria and Firmicutes, whereas mortality was taxonomically widespread. Furthermore, across the community, mortality exhibited density-independence, consistent with the indiscriminate shock resulting from dry-down and wet-up, whereas growth was density-dependent, consistent with control by competition or predation. Total aggregated growth across the community was highly correlated with total soil CO2 production. Together, these results illustrate how previously “invisible” population responses can translate quantitatively to emergent observations of ecosystem-scale biogeochemistry.

58 GEOSCIENCES↗
DOE OSTI2021

Mesoscale-architecture-based crack evolution dictating cycling stability of advanced lithium ion batteries

The cracking phenomenon of Ni-rich NMC (LiNixMnyCo1-x-yO2, x = 0.6) secondary particles is frequently discovered and believed to be one of critical reasons deteriorating the long-term cycling stability of NMC cathode in lithium ion batteries (LIBs). However, the initiation and evolution of those cracks is still controversial due to the limited quantification especially by in situ monitoring, leading to the challenge of identifying an efficient approach to inhibit the formation of the fractures during repeated cycling. Herein, the irreversible, anisotropic cycling lattice and mesoscale expansion/shrinkage of nano-grain during the first cycle, as revealed by in situ X-ray diffraction (XRD) and in situ atomic force microscopy (AFM), have been quantified and confirmed to be the dominant driving forces of microcracks initiation at the grain boundaries. These microcracks preferentially nucleates at the core region with random oriented nano-grains in early stage. The further growth and aggregation of microcracks into macrocrack eventually results in microfracture propagation radially outward to the periphery region with more uniform nano-grain orientation. This mesoscale nano-grain architecture controlled cracking process highlight the importance of predictive synthesis of cathode materials with controllable multiscale crystalline architecture for high-performance LIBs.

25 ENERGY STORAGE↗
DOE OSTI2024

Residential energy demand, emissions, and expenditures at regional and income-decile level for alternative futures

Income and its distribution profile are important determinants of residential energy demand and carry direct implications for human well-being and climate. We explore the sensitivity of residential energy systems to income growth and distribution across shared socioeconomic pathway-representative concentration pathways scenarios using a global, integrated, multisector dynamics model, Global Change Analysis Model, which tracks national/regional household energy services and fuel choice by income decile. Nation/region energy use patterns across deciles tend to converge over time with aggregate income growth, as higher-income consumers approach satiation levels in floorspace and energy services. However, in some regions, existing within-region inequalities in energy consumption persist over time due to slow income growth in lower income groups. Due to continued differences in fuel types, lower income groups will have higher exposure to household air pollution, despite lower contributions to greenhouse gas emissions. We also find that the share of income dedicated to energy is higher for lower deciles, with strong regional differences.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Study of Microphysical Signatures Based on Spectral Polarimetry during the RELAMPAGO Field Experiment in Argentina

Weather radars with dual-polarization capabilities enable the study of various characteristics of hydrometeors, including their size, shape, and orientation. Radar polarimetric measurements, coupled with Doppler information, allow for analysis in the spectral domain. This analysis can be leveraged to reveal valuable insight into the microphysics and kinematics of hydrometeors in precipitation systems. This paper uses spectral polarimetry to investigate precipitation microphysics and kinematics in storm environments observed during the Remote Sensing of Electrification, Lightning, and Mesoscale/Microscale Processes with Adaptive Ground Observations (RELAMPAGO) field experiment in Argentina. This study uses range–height indicator scan measurements from a C-band polarimetric Doppler weather radar deployed during the field campaign. Here, in this work, the impact of storm dynamics on hydrometeors is studied, including the size sorting of hydrometeors due to vertical wind shear. In addition, particle microphysical processes because of aggregation and growth of ice crystals in anvil clouds, as well as graupel formation resulting from the riming of ice crystals and dendrites, are also analyzed here. The presence of different particle size distributions because of the mixing of hydrometeors in a sheared environment and resulting size sorting has been reported using spectral differential reflectivity (sZ dr ) slope. Spectral reflectivity sZ h and sZ dr have also been used to understand the signature of ice crystal aggregation in an anvil cloud. The regions of pristine ice crystals are identified from vertical profiles of spectral polarimetric variables in anvil cloud because of sZ h < 0 dB and sZ dr values around 2 dB. It is also found that the growth process of these ice crystals causes a skewed bimodal sZ h spectrum due to the presence of both pristine ice crystals and dry snow. Next, graupel formation due to riming has been studied, and it is found that the riming process produces sZ h values of about 10 dB and corresponding sZ dr values of 1 dB. This positive sZ dr indicates the presence of needle/columnar secondary ice particles formed by ice multiplication processes in the riming zones. Last, the temporal evolution of a storm is investigated by analyzing changes in hydrometeor types with time and their influence on the spectral polarimetric variables.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Using small angle x-ray scattering to examine the aggregation mechanism in silica nanoparticle-based ambigels for improved optical clarity

Silica-based aerogels are a promising low-cost solution for improving the insulation efficiency of single-pane windows and reducing the energy consumption required for space heating and cooling. Two key material properties required are high porosity and small pore sizes, which lead to low thermal conductivity and high optical transparency, respectively. However, porosity and pore size are generally directly linked, where high porosity materials also have large pore sizes. This is unfavorable as large pores scatter light, resulting in reduced transmittance in the visible regime. In this work, we utilized preformed silica colloids to explore methods for reducing pore size while maintaining high porosity. Further, the use of preformed colloids allows us to isolate the effect of solution conditions on porous gel network formation by eliminating simultaneous nanoparticle growth and aggregation found when using typical sol–gel molecular-based silica precursors. Specifically, we used in situ synchrotron-based small-angle x-ray scattering during gel formation to better understand how pH, concentration, and colloid size affect particle aggregation and pore structure. Ex situ characterization of dried gels demonstrates that peak pore widths can be reduced from 15 to 13 nm, accompanied by a narrowing of the overall pore size distribution, while maintaining porosities of 70%–80%. Optical transparency is found to increase with decreasing pore sizes while low thermal conductivities ranging from 95 +/− 13 mW/m K are maintained. Mechanical performance was found to depend primarily on effective density and did not show a significant dependence on solution conditions. Overall, our results provide insights into methods to preserve high porosity in nanoparticle-based aerogels while improving optical transparency.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

An Overview of Mesoscale Convective Systems: Global Climatology, Satellite Observations, and Modeling Strategies

Deep convection is responsible for redistributing water as well as energy and providing vital water resources for many regions of the world. Cumulonimbus clouds aggregation into a single storm system develop mesoscale convective systems (MCS). MCSs have precipitation covering a horizontal region on the scale of 100?km or more. After more than the last seven decades, MCS has been gradually received wide attention in the scientific community as an important component of the Earth's hydrologic cycle and energy balance. MCSs differ from ordinary deep convection because of the mesoscale circulations consisting of a layer of air overturning on a scale much larger than those created by individual convective updrafts or downdrafts. Moreover, a key feature that separates MCS from ordinary deep convection is the significant portion of stratiform precipitation that results in the production and detrainment of a large number of ice particles from their organized convective cores and continues the mesoscale ascent that supports ice growth and aggregation as the crystals fall. This significant stratiform precipitation gives rise to top-heavy latent heating profiles that have substantial impacts on the upper-level global circulations, especially for those MCS that have a larger portion of stratiform rainfall. Top-heavy latent heating profiles are more frequent over the ocean than over the land. These unique features of MCS suggest that they are important for the hydrologic cycle, general circulation, and radiative balance of the climate system. In this chapter, we focus on the recent advances in the climatological perspective of MCS as well as the research tools used to better understand MCS after the advent of the satellite era. We will discuss both tropical and midlatitude MCS, the influence of modes of tropical climate variability on MCS, and the new insight from satellite observations on MCS interaction with the land surface.

Chakraborty, Sudip↗
DOE OSTI2024

Heterogeneous Nucleating Agent for High‐Boiling‐Point Nonhalogenated Solvent‐Processed Organic Solar Cells and Modules

Abstract High‐boiling‐point nonhalogenated solvents are superior solvents to produce large‐area organic solar cells (OSCs) in industry because of their wide processing window and low toxicity; while, these solvents with slow evaporation kinetics will lead excessive aggregation of state‐of‐the‐art small molecule acceptors (e.g. L8‐BO), delivering serious efficiency losses. Here, a heterogeneous nucleating agent strategy is developed by grafting oligo (ethylene glycol) side‐chains on L8‐BO (BTO‐BO). The formation energy of the obtained BTO‐BO; while, changing from liquid in a solvent to a crystalline phase, is lower than that of L8‐BO irrespective of the solvent type. When BTO‐BO is added as the third component into the active layer (e.g. PM6:L8‐BO), it easily assembles to form numerous seed crystals, which serve as nucleation sites to trigger heterogeneous nucleation and increase nucleation density of L8‐BO through strong hydrogen bonding interactions even in high‐boiling‐point nonhalogenated solvents. Therefore, it can effectively suppress excessive aggregation during growth, achieving ideal phase‐separation active layer with small domain sizes and high crystallinity. The resultant toluene‐processed OSCs exhibit a record power conversion efficiency (PCE) of 19.42% (certificated 19.12%) with excellent operational stability. The strategy also has superior advantages in large‐scale devices, showing a 15.03‐cm 2 module with a record PCE of 16.35% (certificated 15.97%).

Chemistry↗
DOE OSTI2022

Condensation and growth of amorphous aluminosilicate nanoparticles via an aggregation process

The precipitation of zeolite nanoparticles involves the initial formation of metastable precursors, such as amorphous entities, that crystallize through non-classical pathways. Here, using reactive force field-based simulations, we reveal how aluminosilicate oligomers grow concomitantly to the decondensation of silicate entities during the initial step of the reaction. Aluminate clusters first form in the solution, thus violating the Loewenstein rule in the first instant of the reaction, which is then followed by their connection with silicate oligomers at the terminal silanol groups before reorganization to finally diffuse within the silicate oligomers to form stable amorphous aluminosilicate nanoparticles that do obey the Loewenstein rule. Our results clearly indicate that aluminate does not serve as the nucleation center for the growth of aluminosilicates in a nucleation-like process but rather proceeds via an aggregation process. Furthermore, the coexistence of aluminosilicate oligomers and small silicate entities induces a phase separation that promotes the precipitation of zeolites with aging.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Bassanite Grows Along Distinct Coexisting Pathways and Provides a Low Energy Interface for Gypsum Nucleation

Calcium sulfate is a naturally abundant and industrially important mineral; understanding its formation mechanism contributes to reconstructing geochemical record and controlling its scaling in industry. Formation of gypsum is shown to follow a multistage-processes via bassanite, but the evolution of bassanite and the mechanism by which it is replaced by gypsum are poorly understood. Here we outline a three-stage process: (i) growth of bassanite nanoparticles into nanorods or rosettes, (ii) extension of bassanite rosettes by addition of fundamental growth units and aggregation of bassanite nanorods into aggregates, and (iii) heterogeneous nucleation of gypsum on the tips of bassanite rosettes and aggregates. The findings demonstrate that bassanite grows via distinct coexisting pathways and provides a low energy interface for heterogeneous nucleation of gypsum, thus providing proofs that more than one growth pathway can operate simultaneously in a crystallization system and that the precursors in multistage crystallization processes can imprint their pattern of precipitation onto the final phase.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Effect of Charged Block Length Mismatch on Double Diblock Polyelectrolyte Complex Micelle Cores

Polyelectrolyte complex micelles are hydrophilic nanoparticles that self-assemble in aqueous environments due to associative microphase separation between oppositely charged blocky polyelectrolytes. In this work, we employ a suite of physical characterization tools to examine the effect of charged block length mismatch on the equilibrium structure of double diblock polyelectrolyte complex micelles (D-PCMs) by mixing a diverse library of peptide and synthetic charged-neutral block polyelectrolytes with a wide range of charged block lengths (25–200 units) and chemistries. Early work on D-PCMs suggested that this class of micelles can only be formed from blocky polyelectrolytes with identical charged block lengths, a phenomenon referred to as chain length recognition. Here, we use salt annealing to create PCMs at equilibrium, which shows that chain length recognition, a longstanding hurdle to repeatable self-assembly from mismatched polyelectrolytes, can be overcome. Interestingly, D-PCM structure–property relationships display a range of values that vary systematically with the charged block lengths and chemical identity of constituent polyelectrolyte pairings and cannot be described by generalizable scaling laws. We discuss the interdependent growth behavior of the radius, ionic pair aggregation number, and density in the micelle core for three chemically distinct diblock pairings and suggest a potential physical mechanism that leads to this unique behavior. By comparing the results of these D-PCMs to the scaling laws recently developed for single diblock polyelectrolyte complex micelles (S-PCMs: diblock + homopolymer), we observe that D-PCM design schemes reduce the size and aggregation number and restrict their growth to a function of charged block length relative to S-PCMs. Understanding these favorable attributes enables more predictive use of a wider array of charged molecular building blocks to anticipate and control macroscopic properties of micelles spanning countless storage and delivery applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Chemical structure and complex growth modes of magnesium silicate hydrate: Nanoparticle orientation, aggregation, and fusion

The extent of utilization of magnesium silicate hydrate (MSH) in construction is limited partly because of insufficient data ascertaining the kinetics of its precipitation. In this report MSH grown homogeneously or heterogeneously in the range of magnesium to silicon solution molar concentration ratios, [Mg]/[Si] = 0.5-1.5, and temperature = 25-80 °C was analyzed for its chemical structure and morphology. Infrared spectroscopy and geochemical modeling show that increasing the [Mg]/[Si] ratio results in less silicate polymerization in MSH. Atomic force microscopy reveals the presence of nanoparticles that aggregate and fuse to form films. Oriented attachment of nanoparticles and features indicative of enhanced crystallinity were observed at higher temperatures and longer reaction times. These data provide direct evidence for the persistence of hierarchical structures (i.e., nanoparticles forming 3D microparticles and 2D film layers) at the nanoscale to mesoscale. These findings offer insights into the precise chemical synthesis of MSH and its widespread use as a binder for construction purposes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Machine learning-informed and synthetic biology-enabled semi-continuous algal cultivation to unleash renewable fuel productivity

Abstract Algal biofuel is regarded as one of the ultimate solutions for renewable energy, but its commercialization is hindered by growth limitations caused by mutual shading and high harvest costs. We overcome these challenges by advancing machine learning to inform the design of a semi-continuous algal cultivation (SAC) to sustain optimal cell growth and minimize mutual shading. An aggregation-based sedimentation (ABS) strategy is then designed to achieve low-cost biomass harvesting and economical SAC. The ABS is achieved by engineering a fast-growing strain, Synechococcus elongatus UTEX 2973, to produce limonene, which increases cyanobacterial cell surface hydrophobicity and enables efficient cell aggregation and sedimentation. SAC unleashes cyanobacterial growth potential with 0.1 g/L/hour biomass productivity and 0.2 mg/L/hour limonene productivity over a sustained period in photobioreactors. Scaling-up the SAC with an outdoor pond system achieves a biomass yield of 43.3 g/m 2 /day, bringing the minimum biomass selling price down to approximately $281 per ton.

09 BIOMASS FUELS↗
DOE OSTI2021

Polarimetric Signatures in Landfalling Tropical Cyclones

Polarimetric radar observations from the NEXRAD WSR-88D operational radar network in the contiguous United States, routinely available since 2013, are used to reveal three prominent microphysical signatures in landfalling tropical cyclones: 1) hydrometeor size sorting within the eyewall convection, 2) vertical displacement of the melting layer within the inner core, and 3) dendritic growth layers within stratiform regions of the inner core. Size sorting signatures within eyewall convection are observed with greater frequency and prominence in more intense hurricanes, and are observed predominantly within the deep-layer environmental wind shear vector-relative quadrants that harbor the greatest frequency of deep convection (i.e., downshear and left-of-shear). Melting-layer displacements are shown that exceed 1 km in altitude compared to melting-layer altitudes in outer rainbands and are complemented by analyses of archived dropsonde data. Dendritic growth and attendant snow aggregation signatures in the inner core are found to occur more often when echo-top altitudes are low (≤10 km MSL), nearer the -15°C isotherm commonly associated with dendritic growth. These signatures, uniquely observed by polarimetric radar, provide greater insight into the physical structure and thermodynamic characteristics of tropical cyclones, which are important for improving rainfall estimation and the representation of tropical cyclones in numerical models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Aggregation of Leslie matrix models with application to ten diverse animal species

Some grouping is necessary when constructing a Leslie matrix model because it involves discretizing a continuous process of births and deaths. Here, the level of grouping is determined by the number of age classes and frequency of sampling. It is largely unknown what is lost or gained by using fewer age classes, and I address this question using aggregation theory. I derive an aggregator for a Leslie matrix model using weighted least squares, determine what properties an aggregated matrix inherits from the original matrix, evaluate aggregation error, and measure the influence of aggregation on asymptotic and transient behaviors. To gauge transient dynamics, I employ reactivity of the standardized Leslie matrix. I apply the aggregator to 10 Leslie models developed for animal populations drawn from a diverse set of species. Several properties are inherited by the aggregated matrix: (a) it is a Leslie matrix; (b) it is irreducible whenever the original matrix is irreducible; (c) it is primitive whenever the original matrix is primitive; and (d) its stable population growth rate and stable age distribution are consistent with those of the original matrix if the least squares weights are equal to the original stable age distribution. In the application, depending on the population modeled, when the least squares weights do not follow the stable age distribution, the stable population growth rate of the aggregated matrix may or may not be approximately consistent with that of the original matrix. Transient behavior is lost with high aggregation.

54 ENVIRONMENTAL SCIENCES↗