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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Breast dose in mammography is about 30% lower when realistic heterogeneous glandular distributions are considered

Purpose: Current dosimetry methods in mammography assume that the breast is comprised of a homogeneous mixture of glandular and adipose tissues. Three-dimensional (3D) dedicated breast CT (bCT) data sets were used previously to assess the complex anatomical structure within the breast, characterizing the statistical distribution of glandular tissue in the breast. The purpose of this work was to investigate the effect of bCT-derived heterogeneous glandular distributions on dosimetry in mammography. Methods: bCT-derived breast diameters, volumes, and 3D fibroglandular distributions were used to design realistic compressed breast models comprised of heterogeneous distributions of glandular tissue. The bCT-derived glandular distributions were fit to biGaussian functions and used as probability density maps to assign the density distributions within compressed breast models. The MCNPX 2.6.0 Monte Carlo code was used to estimate monoenergetic normalized mean glandular dose “DgN(E)” values in mammography geometry. The DgN(E) values were then weighted by typical mammography x-ray spectra to determine polyenergetic DgN (pDgN) coefficients for heterogeneous (pDgN{sub hetero}) and homogeneous (pDgN{sub homo}) cases. The dependence of estimated pDgN values on phantom size, volumetric glandular fraction (VGF), x-ray technique factors, and location of the heterogeneous glandular distributions was investigated. Results: The pDgN{sub hetero} coefficients were on average 35.3% (SD, 4.1) and 24.2% (SD, 3.0) lower than the pDgN{sub homo} coefficients for the Mo–Mo and W–Rh x-ray spectra, respectively, across all phantom sizes and VGFs when the glandular distributions were centered within the breast phantom in the coronal plane. At constant breast size, increasing VGF from 7.3% to 19.1% lead to a reduction in pDgN{sub hetero} relative to pDgN{sub homo} of 23.6%–27.4% for a W–Rh spectrum. Displacement of the glandular distribution, at a distance equal to 10% of the compressed breast width in the superior and inferior directions, resulted in a 37.3% and a −26.6% change in the pDgN{sub hetero} coefficient, respectively, relative to the centered distribution for the Mo–Mo spectrum. Lateral displacement of the glandular distribution, at a distance equal to 10% of the compressed breast width, resulted in a 1.5% change in the pDgN{sub hetero} coefficient relative to the centered distribution for the W–Rh spectrum. Conclusions: Introducing bCT-derived heterogeneous glandular distributions into mammography phantom design resulted in decreased glandular dose relative to the widely used homogeneous assumption. A homogeneous distribution overestimates the amount of glandular tissue near the entrant surface of the breast, where dose deposition is exponentially higher. While these findings are based on clinically measured distributions of glandular tissue using a large cohort of women, future work is required to improve the classification of glandular distributions based on breast size and overall glandular fraction.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

SU-F-R-13: Decoding 18F-FDG Uptake Heterogeneity for Primary and Lymphoma Tumors by Using Texture Analysis in PET Images

Purpose: To explore 18F-FDG uptake heterogeneity of primary tumor and lymphoma tumor by texture features of PET image and quantify the heterogeneity difference between primary tumor and lymphoma tumor. Methods: 18 patients with primary tumor and lymphoma tumor in lung cancer were enrolled. All patients underwent whole-body 18F-FDG PET/CT scans before treatment. Texture features, based on Gray-level Co-occurrence Matrix, second and high order matrices are extracted from code using MATLAB software to quantify 18F-FDG uptake heterogeneity. The relationships of volume between energy, entropy, correlation, homogeneity and contrast were analyzed. Results: For different cases, tumor heterogeneity was not the same. Texture parameters (contrast, entropy, and correlation) of lymphoma were lower than primary tumor. On the contrast, the texture parameters (energy, homogeneity and inverse different moment) of lymphoma were higher than primary tumor. Significantly, correlations were observed between volume and energy (primary, r=−0.194, p=0.441; lymphoma, r=−0.339, p=0.582), homogeneity (primary, r=−0.146, p=0.382; lymphoma, r=−0.193, p=0.44), inverse difference moment (primary, r=−0.14, p=0.374; lymphoma, r=−0.172, p=0.414) and a positive correlation between volume and entropy (primary, r=0.233, p=0.483; lymphoma, r=0.462, p=0.680), contrast (primary, r=0.159, p=0.399; lymphoma, r=0.341, p=0.584), correlation (primary, r=0.027, p=0.165; lymphoma, r=0.046, p=0.215). For the same patient, energy for primary and lymphoma tumor is equal. The volume of lymphoma is smaller than primary tumor, but the homogeneity were higher than primary tumor. Conclusion: This study showed that there were effective heterogeneity differences between primary and lymphoma tumor by FDG-PET image texture analysis.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

A survey of CPU-GPU heterogeneous computing techniques

As both CPU and GPU become employed in a wide range of applications, it has been acknowledged that both of these processing units (PUs) have their unique features and strengths and hence, CPU-GPU collaboration is inevitable to achieve high-performance computing. This has motivated significant amount of research on heterogeneous computing techniques, along with the design of CPU-GPU fused chips and petascale heterogeneous supercomputers. In this paper, we survey heterogeneous computing techniques (HCTs) such as workload-partitioning which enable utilizing both CPU and GPU to improve performance and/or energy efficiency. We review heterogeneous computing approaches at runtime, algorithm, programming, compiler and application level. Further, we review both discrete and fused CPU-GPU systems; and discuss benchmark suites designed for evaluating heterogeneous computing systems (HCSs). Furthermore, we believe that this paper will provide insights into working and scope of applications of HCTs to researchers and motivate them to further harness the computational powers of CPUs and GPUs to achieve the goal of exascale performance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Chemical Heterogeneity in PAN/LLZTO Composite Electrolytes by Synchrotron Imaging

Solid polymer/ceramic composite electrolytes are promising for batteries due to their attractive thermal stability and mechanical properties. Chemical heterogeneity in solid composite electrolytes, such as the inhomogeneity in the ceramic phase and salt distribution at the polymer/ceramic interface, is critical to the performance of solid composite electrolytes. However, such heterogeneity has not been well understood yet. In this work, we use Synchrotron-based X-ray fluorescence imaging (XRF) and Transmission X-ray Microscope (TXM) to image nanoscale chemical heterogeneity in polyacrylamide/Li 7+x La 3 Zr 2–x Ta x O 12 (LLZTO) composite electrolytes and investigate the effects of lithium salt, salt concentration, and plasticizer. We find that LLZTO particles show strong inter- and intra-particles chemical heterogeneities, and the off-stoichiometry of Zr in an LLZTO particle is unlikely to be only balanced by Ta substitution. Moreover, statistical analysis suggests that LiI tends to accumulate at the ceramic/polymer interface at a low concentration of 5 wt%, but no such tendency was observed in samples with 10 wt% LiI. However, composite electrolytes with LiTFSI show interfacial accumulation at both 5 wt% and 10 wt%. Furthermore, this report provides insight into element distributions in solid composite electrolytes, and we hope further researches can shed light on the connections between chemical heterogeneity and ionic transport pathway inside.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Unraveling heterogeneous susceptibility and the evolution of breast cancer using a systems biology approach

Background: An essential question in cancer is why individuals with the same disease have different clinical outcomes. Progress toward a more personalized medicine in cancer patients requires taking into account the underlying heterogeneity at different molecular levels. Results: Here, we present a model in which there are complex interactions at different cellular and systemic levels that account for the heterogeneity of susceptibility to and evolution of ERBB2-positive breast cancers. Our model is based on our analyses of a cohort of mice that are characterized by heterogeneous susceptibility to ERBB2-positive breast cancers. Our analysis reveals that there are similarities between ERBB2 tumors in humans and those of backcross mice at clinical, genomic, expression, and signaling levels. We also show that mice that have tumors with intrinsically high levels of active AKT and ERK are more resistant to tumor metastasis. Our findings suggest for the first time that a site-specific phosphorylation at the serine 473 residue of AKT1 modifies the capacity for tumors to disseminate. Finally, we present two predictive models that can explain the heterogeneous behavior of the disease in the mouse population when we consider simultaneously certain genetic markers, liver cell signaling and serum biomarkers that are identified before the onset of the disease. Conclusions: Considering simultaneously tumor pathophenotypes and several molecular levels, we show the heterogeneous behavior of ERBB2-positive breast cancer in terms of disease progression. This and similar studies should help to better understand disease variability in patient populations.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2015

A numerical homogenization method for heterogeneous, anisotropic elastic media based on multiscale theory

The development of reliable methods for upscaling fine scale models of elastic media has long been an important topic for rock physics and applied seismology. Several effective medium theories have been developed to provide elastic parameters for materials such as finely layered media or randomly oriented or aligned fractures. In such cases, the analytic solutions for upscaled properties can be used for accurate prediction of wave propagation. However, such theories cannot be applied directly to homogenize elastic media with more complex, arbitrary spatial heterogeneity. We therefore propose a numerical homogenization algorithm based on multiscale finite element methods for simulating elastic wave propagation in heterogeneous, anisotropic elastic media. Specifically, our method used multiscale basis functions obtained from a local linear elasticity problem with appropriately defined boundary conditions. Homogenized, effective medium parameters were then computed using these basis functions, and the approach applied a numerical discretization that is similar to the rotated staggered-grid finite difference scheme. Comparisons of the results from our method and from conventional, analytical approaches for finely layered media showed that the homogenization reliably estimated elastic parameters for this simple geometry. Additional tests examined anisotropic models with arbitrary spatial heterogeneity where the average size of the heterogeneities ranged from several centimeters to several meters, and the ratio between the dominant wavelength and the average size of the arbitrary heterogeneities ranged from 10 to 100. Comparisons to finite-difference simulations proved that the numerical homogenization was equally accurate for these complex cases.

58 GEOSCIENCES↗
DOE OSTI2015

A New Equivalence Theory Method for Treating Doubly Heterogeneous Fuel - I. Theory

A new methodology has been developed to treat resonance self-shielding in doubly heterogeneous very high temperature gas-cooled reactor systems in which the fuel compact region of a reactor lattice consists of small fuel grains dispersed in a graphite matrix. This new method first homogenizes the fuel grain and matrix materials using an analytically derived disadvantage factor from a two-region problem with equivalence theory and intermediate resonance method. This disadvantage factor accounts for spatial self-shielding effects inside each grain within the framework of an infinite array of grains. Then the homogenized fuel compact is self-shielded using a Bondarenko method to account for interactions between the fuel compact regions in the fuel lattice. In the final form of the equations for actual implementations, the double-heterogeneity effects are accounted for by simply using a modified definition of a background cross section, which includes geometry parameters and cross sections for both the grain and fuel compact regions. With the new method, the doubly heterogeneous resonance self-shielding effect can be treated easily even with legacy codes programmed only for a singly heterogeneous system by simple modifications in the background cross section for resonance integral interpolations. This paper presents a detailed derivation of the new method and a sensitivity study of double-heterogeneity parameters introduced during the derivation. The implementation of the method and verification results for various test cases are presented in the companion paper.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Single cell heterogeneity in influenza A virus gene expression shapes the innate antiviral response to infection

Viral infection outcomes are governed by the complex and dynamic interplay between the infecting virus population and the host response. It is increasingly clear that both viral and host cell populations are highly heterogeneous, but little is known about how this heterogeneity influences infection dynamics or viral pathogenicity. To dissect the interactions between influenza A virus (IAV) and host cell heterogeneity, we examined the combined host and viral transcriptomes of thousands of individual cells, each infected with a single IAV virion. We observed complex patterns of viral gene expression and the existence of multiple distinct host transcriptional responses to infection at the single cell level. We show that human H1N1 and H3N2 strains differ significantly in patterns of both viral and host anti-viral gene transcriptional heterogeneity at the single cell level. Our analyses also reveal that semi-infectious particles that fail to express the viral NS can play a dominant role in triggering the innate anti-viral response to infection. Altogether, these data reveal how patterns of viral population heterogeneity can serve as a major determinant of antiviral gene activation.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2012

Investigation into the Relationship between Heterogeneity and Heavy-Tailed Solute Transport (Final Report)

This project combines outcrop-scale heterogeneity characterization, laboratory experiments, and numerical simulations. The study is designed to test whether established dispersion theory accurately predicts the behavior of solute transport through heterogeneous media and to investigate the relationship between heterogeneity and the parameters that populate these models. The dispersion theory tested by this work is based upon the fractional advection-dispersion equation (fADE) model. Unlike most dispersion studies that develop a solute transport model by fitting the solute transport breakthrough curve, this project will explore the nature of the heterogeneous media to better understand the connection between the model parameters and the aquifer heterogeneity. Our work at the Colorado School of Mines was focused on the following questions: 1) What are the effects of multi-scale geologic variability on transport of conservative and reactive solutes? 2) Can those transport effects be accounted for by classical methods, and if not, can the nonlocal fractional-order equations provide better predictions? 3) Can the fractional-order equations be parameterized through a link to some simple observable geologic features? 4) Are the classical equations of transport and reaction sufficient? 5) What is the effect of anomalous transport on chemical reaction in groundwater systems? The work is predicated on the observation that upscaled transport is defined by loss of information, or spatio-temporal averaging. This averaging tends to make the transport laws such as Fick's 2nd-order diffusion equation similar to central limit theory. The fractional-order advection-dispersion equations rely on limit theory for heavy-tailed random motion that has some diverging moments. The equations predict larger tails of a plume in space and/or time than those predicted by the classical 2nd-order advection-dispersion equation. The heavy tails are often seen in plumes at field sites.

58 GEOSCIENCES↗
DOE OSTI2018

The impacts of pore-scale physical and chemical heterogeneities on the transport of radionuclide-carrying colloids

Independent of the methods of nuclear waste disposal, the degradation of packaging materials could lead to mobilization and transport of radionuclides into the geosphere. This process can be significantly accelerated due to the association of radionuclides with the backfill materials or mobile colloids in groundwater. The transport of these colloids is complicated by the inherent coupling of physical and chemical heterogeneities (e.g., pore space geometry, grain size, charge heterogeneity, and surface hydrophobicity) in natural porous media that can exist on the length scale of a few grains. In addition, natural colloids themselves are often heterogeneous in their surface properties (e.g., clay platelets possess opposite charges on the surface and along the rim). Both physical and chemical heterogeneities influence the transport and retention of radionuclides under various groundwater conditions. However, the precise mechanisms how these coupled heterogeneities influence colloidal transport are largely elusive. This knowledge gap is a major source of uncertainty in developing accurate models to represent the transport process and to predict distribution of radionuclides in the geosphere.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Molecular-Level Design of Heterogeneous Chiral Catalysts

A recent major focus of catalyst research has been on improving the selectivity or atom efficiency of catalytic processes. Perhaps the most subtle and difficult form of selectivity to control is enantioselectivity, a catalyst’s ability to preferentially yield one enantiomer of a chiral product. Since two enantiomers are identical in all respects except for their mirror reflection symmetry, both are formed in non-chiral environments at exactly equal rates; only by introducing some type of chiral modification to the system can the rate of formation of one enantiomer be favored over the other. This has been successfully achieved for homogeneous-phase, organometallic catalysts, but the empirical development of heterogeneous-phase analogs has proven elusive. The design of such heterogeneous-phase catalysts would obviate the need for inefficient purification steps to remove the heavy-metal catalysts. The goal of the proposed research by the Chiral Catalysis Group is to understand the interactions of prochiral reactants on chirally modified surfaces that lead to the preferential formation of one enantiomer over the other. There are two general concepts for designing heterogeneous-phase enantioselective catalysts. The first adopts the strategy used in homogeneous phase, by adding a chiral modifier to the surface. This approach, while conceptually simple has challenges associated with modifying an extended surface. The second concept, which is unique to extended surfaces, is the idea of creating surfaces that are themselves naturally chiral. A fundamental understanding of the interactions that control enantioselectivity will enable the Chiral Catalysis Group to develop the concepts necessary to design novel, heterogenous catalytic materials. Enantioselectivity is also central to catalytic processes that underpin the pharmaceutical and agrochemical industries. With funding from the Department of Energy, the Chiral Catalysis Group has played a leading role in developing a fundamental understanding of chiral catalysis and of the adsorbate structures, interactions and kinetic effects that control heterogenous-phase enantioselectivity. The proposed research program is organized conceptually around three types of enantiospecific interactions: interactions with naturally chiral surfaces; those with modified surfaces categorized as chirally templated surfaces; and one-to-one interactions of prochiral molecules with chiral surface modifiers. Our specific goals are to: (1) determine the structures of chiral surfaces, prochiral reactants, chiral products and chiral modifiers; (2) understand the enantiospecific interactions that occur between prochiral reactants and chiral products with chirally modified surfaces; (3) develop methods for detection of enantiospecific surface phenomena; and (4) elucidate enantioselective reaction pathways and the interactions that control them. The range of expertise within the Chiral Catalysis Group includes molecular-scale theory, surface science experiments, state-of-the-art spectroscopic, kinetic and atomic-scale imaging capabilities carried out in vacuum and under more-realistic liquid- and gas-phase environments complemented by catalytic measurements. By fully integrating such a breadth of approaches and extensive expertise, the Chiral Catalysis Group will, for the first time, be able to understand, rationally design and then control active sites for optimal enantioselectivity. In addition to having a significant impact on the field of chiral catalysis, the proposed research program will further our general understanding of the molecular-scale origins of catalytic selectivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

A Need for Better Management of Heterogenous HPC Resources

Achieving computational rates beyond the petascale requires an increasing amount of heterogeneity in our highperformance computing (HPC) hardware. This heterogeneity, in turn, means that a node of an HPC system can no longer be considered a monolithic resource. Rather, a node has many individual components such as processors, cores, SMT threads, accelerators, and tierd memories that must be further allocated and managed by... something. Currently, that something is an ad-hoc mix of arguments and environments when launching jobs. We follow the same process used on prior HPC systems with nodes of uniform components; unfortunately, the shims introduced to provide the additional specification of node-level components are inconsistent and unwieldy. As we shall see, even at our current moderate level of heterogeneity our effective utilization of HPC software is hampered by poor resource management. Future systems will continue to grow in heterogeneity both in number and type of resources. Our current approach to resource management cannot scale. We need a more cohesive approach to managing heterogeneous resources in HPC systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

WRF-Chem model predictions of the regional impacts of N 2 O 5 heterogeneous processes on night-time chemistry over north-western Europe

Chemical modelling studies have been conducted over north-western Europe in summer conditions, showing that night-time dinitrogen pentoxide (N 2 O 5 ) heterogeneous reactive uptake is important regionally in modulating particulate nitrate and has a~modest influence on oxidative chemistry. Results from Weather Research and Forecasting model with Chemistry (WRF-Chem) model simulations, run with a detailed volatile organic compound (VOC) gas-phase chemistry scheme and the Model for Simulating Aerosol Interactions and Chemistry (MOSAIC) sectional aerosol scheme, were compared with a series of airborne gas and particulate measurements made over the UK in July 2010. Modelled mixing ratios of key gas-phase species were reasonably accurate (correlations with measurements of 0.7–0.9 for NO 2 and O 3 ). However modelled loadings of particulate species were less accurate (correlation with measurements for particulate sulfate and ammonium were between 0.0 and 0.6). Sulfate mass loadings were particularly low (modelled means of 0.5–0.7 μg kg −1 air , compared with measurements of 1.0–1.5 μg kg −1 air ). Two flights from the campaign were used as test cases – one with low relative humidity (RH) (60–70%), the other with high RH (80–90%). N 2 O 5 heterogeneous chemistry was found to not be important in the low-RH test case; but in the high-RH test case it had a strong effect and significantly improved the agreement between modelled and measured NO 3 and N 2 O 5 . When the model failed to capture atmospheric RH correctly, the modelled NO 3 and N 2 O 5 mixing ratios for these flights differed significantly from the measurements. This demonstrates that, for regional modelling which involves heterogeneous processes, it is essential to capture the ambient temperature and water vapour profiles. The night-time NO 3 oxidation of VOCs across the whole region was found to be 100–300 times slower than the daytime OH oxidation of these compounds. The difference in contribution was less for alkenes (× 80) and comparable for dimethylsulfide (DMS). However the suppression of NO 3 mixing ratios across the domain by N 2 O 5 heterogeneous chemistry has only a very slight, negative, influence on this oxidative capacity. The influence on regional particulate nitrate mass loadings is stronger. Night-time N 2 O 5 heterogeneous chemistry maintains the production of particulate nitrate within polluted regions: when this process is taken into consideration, the daytime peak (for the 95th percentile) of PM 10 nitrate mass loadings remains around 5.6 μg kg −1 air , but the night-time minimum increases from 3.5 to 4.6 μg kg −1 air . The sustaining of higher particulate mass loadings through the night by this process improves model skill at matching measured aerosol nitrate diurnal cycles and will negatively impact on regional air quality, requiring this process to be included in regional models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Effect of inorganic-to-organic mass ratio on the heterogeneous OH reaction rates of erythritol: implications for atmospheric chemical stability of 2-methyltetrols

The 2-methyltetrols have been widely chosen as chemical tracers for isoprene-derived secondary organic aerosols. While they are often assumed to be relatively unreactive, a laboratory study reported that pure erythritol particles (an analog of 2-methyltetrols) can be heterogeneously oxidized by gas-phase OH radicals at a significant rate. This might question the efficacy of these compounds as tracers in aerosol source-apportionment studies. Additional uncertainty could arise as organic compounds and inorganic salts often coexist in atmospheric particles. To gain more insights into the chemical stability of 2-methyltetrols in atmospheric particles, this study investigates the heterogeneous OH oxidation of pure erythritol particles and particles containing erythritol and ammonium sulfate (AS) at different dry inorganic-to-organic mass ratios (IOR) in an aerosol flow tube reactor at a high relative humidity of 85 %. The same reaction products are formed upon heterogenous OH oxidation of erythritol and erythritol–AS particles, suggesting that the reaction pathways are not strongly affected by the presence and amount of AS. On the other hand, the effective OH uptake coefficient, $γ_{eff}$, is found to decrease by about a factor of ~20 from 0.45±0.025 to 0.02±0.001 when the relative abundance of AS increases and the IOR increases from 0.0 to 5.0. One likely explanation is the presence of dissolved ions slows down the reaction rates by decreasing the surface concentration of erythritol and reducing the frequency of collision between erythritol and gas-phase OH radicals at the particle surface. Hence, the heterogeneous OH reactivity of erythritol and likely 2-methyltetrols in atmospheric particles would be slower than previously thought when the salts are present. Given 2-methyltetrols often coexist with a significant amount of AS in many environments, where ambient IOR can vary from ~1.89 to ~250, our kinetic data would suggest that 2-methyltetrols in atmospheric particles are likely chemically stable against heterogeneous OH oxidation under humid conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Scaling impacts on environmental controls and spatial heterogeneity of soil organic carbon stocks

The spatial heterogeneity of land surfaces affects energy, moisture, and greenhouse gas exchanges with the atmosphere. However, representing the heterogeneity of terrestrial hydrological and biogeochemical processes in Earth system models (ESMs) remains a critical scientific challenge. We report the impact of spatial scaling on environmental controls, spatial structure, and statistical properties of soil organic carbon (SOC) stocks across the US state of Alaska. We used soil profile observations and environmental factors such as topography, climate, land cover types, and surficial geology to predict the SOC stocks at a 50 m spatial scale. These spatially heterogeneous estimates provide a data set with reasonable fidelity to the observations at a sufficiently high resolution to examine the environmental controls on the spatial structure of SOC stocks. We upscaled both the predicted SOC stocks and environmental variables from finer to coarser spatial scales ( s = 100, 200, and 500 m and 1, 2, 5, and 10 km) and generated various statistical properties of SOC stock estimates. We found different environmental factors to be statistically significant predictors at different spatial scales. Only elevation, temperature, potential evapotranspiration, and scrub land cover types were significant predictors at all scales. The strengths of control (the median value of geographically weighted regression coefficients) of these four environmental variables on SOC stocks decreased with increasing scale and were accurately represented using mathematical functions ( R 2 = 0.83–0.97). The spatial structure of SOC stocks across Alaska changed with spatial scale. Although the variance (sill) and unstructured variability (nugget) of the calculated variograms of SOC stocks decreased exponentially with scale, the correlation length (range) remained relatively constant across scale. The variance of predicted SOC stocks decreased with spatial scale over the range of 50 m to ~ 500 m, and remained constant beyond this scale. The fitted exponential function accounted for 98 % of variability in the variance of SOC stocks. We found moderately accurate linear relationships between mean and higher-order moments of predicted SOC stocks ( R 2 ∼ 0.55–0.63). Current ESMs operate at coarse spatial scales (50–100 km), and are therefore unable to represent environmental controllers and spatial heterogeneity of high-latitude SOC stocks consistent with observations. We conclude that improved understanding of the scaling behavior of environmental controls and statistical properties of SOC stocks could improve ESM land model benchmarking and perhaps allow representation of spatial heterogeneity of biogeochemistry at scales finer than those currently resolved by ESMs.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Scaling impacts on environmental controls and spatial heterogeneity of soil organic carbon stocks

The spatial heterogeneity of land surfaces affects energy, moisture, and greenhouse gas exchanges with the atmosphere. However, representing heterogeneity of terrestrial hydrological and biogeochemical processes in earth system models (ESMs) remains a critical scientific challenge. We report the impact of spatial scaling on environmental controls, spatial structure, and statistical properties of soil organic carbon (SOC) stocks across the US state of Alaska. We used soil profile observations and environmental factors such as topography, climate, land cover types, and surficial geology to predict the SOC stocks at a 50 m spatial scale. These spatially heterogeneous estimates provide a dataset with reasonable fidelity to the observations at a sufficiently high resolution to examine the environmental controls on the spatial structure of SOC stocks. We upscaled both the predicted SOC stocks and environmental variables from finer to coarser spatial scales ( s = 100, 200, 500 m, 1, 2, 5, 10 km) and generated various statistical properties of SOC stock estimates. We found different environmental factors to be statistically significant predictors at different spatial scales. Only elevation, temperature, potential evapotranspiration, and scrub land cover types were significant predictors at all scales. The strengths of control (the median value of geographically weighted regression coefficients) of these four environmental variables on SOC stocks decreased with increasing scale and were accurately represented using mathematical functions ( R 2 = 0.83–0.97). The spatial structure of SOC stocks across Alaska changed with spatial scale. Although the variance (sill) and unstructured variability (nugget) of the calculated variograms of SOC stocks decreased exponentially with scale, the correlation length (range) remained relatively constant across scale. The variance of predicted SOC stocks decreased with spatial scale over the range of 50 to ~ 500 m, and remained constant beyond this scale. The fitted exponential function accounted for 98% of variability in the variance of SOC stocks. We found moderately-accurate linear relationships between mean and higher-order moments of predicted SOC stocks ( R 2 ~ 0.55–0.63). Current ESMs operate at coarse spatial scales (50–100 km), and are therefore unable to represent environmental controllers and spatial heterogeneity of high-latitude SOC stocks consistent with observations. We conclude that improved understanding of the scaling behavior of environmental controls and statistical properties of SOC stocks can improve ESM land model benchmarking and perhaps allow representation of spatial heterogeneity of biogeochemistry at scales finer than those currently resolved by ESMs.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1988

Heterogeneous physicochemistry of the winter polar stratosphere

Present chemical theories of the Antarctic ozone hole assume that heterogeneous reactions involving polar stratospheric clouds (PSCs) are the precursor of springtime ozone depletions. However, none of the theories quantify the rates of proposed heterogeneous processed, and none utilize the extensive data base on PSC's. Thus, all of the theories must be considered incomplete until the heterogeneous mechanisms are properly defined. A unified treatment developed of the cloud related processes, both physical and chemical, and the importance of these processes using observation data is calibrated. The rates are compared competitive heterogeneous processes to place reasonable limits on critical mechanisms such as the denitrification and dechlorination of the polar winter stratosphere. Among the subjects addressed here are the physical/chemical properties of PSC's including their relevant microphysical, optical and compositional characteristics, mass transfer rates of gaseous constituents to cloud particles, adsorption, accommodation and sticking coefficients on cloud particles, time constants for condensation, absorption and other microphysical processes, effects of solubility and vapor pressure on cloud composition, the statistics of cloud processing of chemically active condensible species, rate limiting steps in heterogeneous chemical reactions, and the nonlinear dependence of ozone loss on physical and chemical parameters.

Turco, R. P.↗
NASA NTRS1992

The effect of material heterogeneity in curved composite beams for use in aircraft structures

A design tool is presented for predicting the effect of material heterogeneity on the performance of curved composite beams for use in aircraft fuselage structures. Material heterogeneity can be induced during processes such as sheet forming and stretch forming of thermoplastic composites. This heterogeneity can be introduced in the form of fiber realignment and spreading during the manufacturing process causing a gradient in material properties in both the radial and tangential directions. The analysis procedure uses a separate two-dimensional elasticity solution for the stresses in the flanges and web sections of the beam. The separate solutions are coupled by requiring the forces and displacements match at the section boundaries. Analysis is performed for curved beams loaded in pure bending and uniform pressure. The beams can be of any general cross-section such as a hat, T-, I-, or J-beam. Preliminary results show that geometry of the beam dictates the effect of heterogeneity on performance. Heterogeneity plays a much larger role in beams with a small average radius to depth ratio, R/t, where R is the average radius of the beam and t is the difference between the inside and outside radius. Results of the analysis are in the form of stresses and displacements, and they are compared to both mechanics of materials and numerical solutions obtained using finite element analysis.

Otoole, Brendan J.↗