Search NASA⌕ Search

SEARCH · Search NASA

Results for “decomposition”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

Massively Parallel Dantzig-Wolfe Decomposition Applied to Traffic Flow Scheduling

Optimal scheduling of air traffic over the entire National Airspace System is a computationally difficult task. To speed computation, Dantzig-Wolfe decomposition is applied to a known linear integer programming approach for assigning delays to flights. The optimization model is proven to have the block-angular structure necessary for Dantzig-Wolfe decomposition. The subproblems for this decomposition are solved in parallel via independent computation threads. Experimental evidence suggests that as the number of subproblems/threads increases (and their respective sizes decrease), the solution quality, convergence, and runtime improve. A demonstration of this is provided by using one flight per subproblem, which is the finest possible decomposition. This results in thousands of subproblems and associated computation threads. This massively parallel approach is compared to one with few threads and to standard (non-decomposed) approaches in terms of solution quality and runtime. Since this method generally provides a non-integral (relaxed) solution to the original optimization problem, two heuristics are developed to generate an integral solution. Dantzig-Wolfe followed by these heuristics can provide a near-optimal (sometimes optimal) solution to the original problem hundreds of times faster than standard (non-decomposed) approaches. In addition, when massive decomposition is employed, the solution is shown to be more likely integral, which obviates the need for an integerization step. These results indicate that nationwide, real-time, high fidelity, optimal traffic flow scheduling is achievable for (at least) 3 hour planning horizons.

Rios, Joseph Lucio↗
DOE OSTI2025

Arctic shrub and Eriophorum leaf and root decomposition, northern Alaska, 2017-2018

This data package contains litter decomposition data collected from 170 plots of rapidly expanding shrub genera (Alnus, Betula, and Salix) and a widespread sedge (Eriophorum vaginatum) along a latitudinal and temperature gradient in northern Alaska. These data were produced from a litter bag experiment that took place from July 2017 to July 2018 and include mass loss and nitrogen loss decomposition metrics for both leaf and root litters. These raw data support a submitted manuscript that examines the variability in decomposition between shrub and graminoid leaf and root litters across a 1-year experiment across the graminoid-dominated Arctic tundra and reveals how deciduous shrub expansion affects litter decomposition in tundra ecosystems. Data are presented by site (n=5) and patch (shrub or sedge plot) in csv files. The site and plot location data and environmental measurement data are provided in Fraterrigo and Chen (2020). Additional methods regarding plot distribution and environmental measurements are in Chen et al. (2020) and Fraterrigo et al. (2024).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Reaction Pathways and Energy Consumption in NH 3 Decomposition for H 2 Production by Low Temperature, Atmospheric Pressure Plasma

Pathways for NH 3 decomposition to N 2 and N 2 H 4 by atmospheric pressure nonthermal plasma are analyzed using a combination of molecular beam mass spectrometry measurements and zero-dimensional kinetic modeling. Experimental measurements show that NH 3 conversion and selectivity towards N 2 formation scale monotonically with the specific energy input into the plasma with ~ 100% selectivity to N 2 formation achieved at specific energy inputs above 0.12 J cm −3 (3.1 eV (molecule NH 3 ) −1 ). The kinetic model recovers these trends, although it underpredicts N 2 selectivity at low specific energy input. These discrepancies can be explained by the underestimation of reaction rate coefficients for reactions that consume N 2 H x species in collisions with H radicals and/or radial nonuniformities in power deposition, gas temperature, and species concentrations that are not represented by the plug flow approximation used in the model. The kinetic model shows that N 2 formation proceeds through N 2 H x decomposition pathways rather than NH x decomposition pathways in low temperature, atmospheric pressure plasma. Higher selectivity toward N 2 production can be achieved by operating at higher NH 3 conversion and with a higher gas temperature. Furthermore, the high energy cost of NH 3 decomposition by atmospheric pressure nonthermal plasma found in this work (25–50 eV (molecule NH 3 converted) −1 ; 17–33 eV (molecule H 2 formed) −1 ) is a result of the energy requirement for electron-impact dissociation of NH 3 and the significant re-formation of NH 3 by three-body recombination reactions between NH 2 and H.

Nonthermal plasma↗
DOE OSTI2025

An isotopic labeling investigation into the influence of the nitro group on LLM-105 thermal decomposition

Here, this work presents the first application of isotopically labeled LLM-105 (2,6-diamino-3,5-dinitropyrazine-1-oxide) to investigate thermal decomposition pathways. Specially synthesized LLM-105 isotopologues were utilized to isolate the influence of labeled 15 NO 2 nitro groups on the formation of lightgas products. Simultaneous differential scanning calorimetry, thermo-gravimetric, and mass spectrometry measurements were employed to track the evolution of product gases, enabling the direct comparison of isotopically shifted species with unlabeled LLM-105. Key findings show that C 2 N 2 production is mainly dependent on nitrogen sources from either the amine groups or the pyrazine ring (i.e., not the nitro groups). The formation of NO, N 2 , and N 2 O all involves the nitro groups to some extent. NO (nitric oxide) was found to be the predominant gas species directly formed from the nitro group of LLM-105. In contrast, mixed nitrogen isotopologues of N 2 and N 2 O (i.e., 14 N 15 N and 15 NNO) formed more readily in comparison to their pure counterparts (i.e., 15 N 2 and 15 N 2 O). This indicates the amine and/or pyrazine groups of LLM-105, in addition to the nitro group, are involved in the decomposition pathways forming N 2 and N 2 O. In addition, our investigation led to the discovery of two previously unreported decomposition products (CHO and HNCO), which were confirmed through hydrogen labelling utilizing deuterium isotopes. These results provide detailed speciation trends of gaseous products during LLM-105 decomposition, offering new insights into reaction pathways. Experimental data reported here will support the development of a detailed chemical kinetics model for LLM-105, essential for the safe handling of high explosives.

Chemistry - Chemical explosives↗
DOE OSTI2025

Effects of co-adsorbed water on different bond cleavages involved in acetic acid decomposition on Pt (111)

Acetic acid decomposition on Pt (111) in the presence of co-adsorbed water is a good model system for oxygenate decomposition on Pt (111) in aqueous phase, with application in hydrogen production and biomass conversion. Here, in this study, we present a density functional theory (DFT) theory calculation of how co-adsorbed water affects different bond cleavages of acetic acid decomposition on Pt (111). The presence of co-adsorbed water generally enhances O$-$H bond cleavage while inhibiting OC$-$O and OC$-$OH bond cleavage. The influence of co-adsorbed water on C$-$H bond cleavage varies the most and depends on the nature of the transition state and how co-adsorbed water stabilizes the initial and final state. Although these trends are useful as general guidance, they are not sufficient to predict the effect on a complex reaction network such as acetic acid decomposition on Pt (111) which has several parallel reaction paths with similar energies. In the absence of co-adsorbed water, the two lowest energy pathways are decarboxylation (DCX) and decarbonylation (DCN) pathways through a common CH 2 COO intermediate, in which the DCX pathway (C$-$H bond cleavage of CH 2 COO) is more favorable than DCN pathway (OC$-$O bond cleavage of CH 2 COO). In the presence of co-adsorbed water, the energy difference between Csingle bondH bond cleavage and OC$-$O bond cleavage of CH 2 COO increases, suggesting an increase in the favorability of acetic acid decarboxylation (formation of carbon dioxide) over acetic acid decarbonylation (formation of carbon monoxide) on Pt (111).

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

Plasmon-Driven Ammonia Decomposition on Pd(111): Hole Transfer’s Role in Changing Rate-Limiting Steps

Here, ammonia (NH 3 ) has the potential to be a hydrogen carrier because it can be transported and stored with ease, but only if it also can be decomposed easily when needed. Understanding how to control the frequently rate-limiting N–H bond breaking and N–N bond forming on catalytic surfaces may help design efficient means for NH 3 decomposition. Yuan et al. recently demonstrated photocatalytically selective N–H bond breaking in NH 3 on plasmon-driven aluminum–palladium (Al–Pd) antenna–reactor heterostructures. Using embedded correlated wavefunction (ECW) theory, we predict that the rate-determining step (RDS) for NH 3 decomposition on Pd(111) via thermocatalysis (dissociating the first N–H bond, *NH 3 → *NH 2 + *H, in the ground state, where * means adsorbed) differs from that via photocatalysis (dissociating the second N–H bond, *NH 2 → *NH + *H, in the excited state). This result is consistent with the measured catalytic efficiency and selectivity of NH 3 -deuterium (D 2 ) exchange reactions (an indirect way to measure N–H bond breaking) on Al–Pd heterodimers. We also determine the origin of the observed selectivity of thermocatalysis and photocatalysis on Pd(111) toward doubly deuterated (NHD 2 ) and monodeuterated (NH 2 D) products, respectively, and explore viability of the full NH 3 decomposition path, also via ECW theory. Additionally, we predict that the associative desorption of *N as N 2 from Pd(111) is extremely difficult in thermocatalysis at least at low surface coverages; metal-to-adsorbate hole transfer in photocatalysis stabilizes the transition state for the first N–H bond dissociation, shifting the RDS to the second N–H bond breaking. Furthermore, the redistribution of electrons around *N upon excitation reduces the electron density in the Pd–N bonds, which may lower the barrier for N 2 associative desorption in photocatalysis. Thus, light-induced, plasmon-mediated, excited-state hole transfer may provide an efficient mechanism to accelerate NH 3 decomposition.

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

Tensor decompositions for count data that leverage stochastic and deterministic optimization

There is growing interest to extend low-rank matrix decompositions to multi-way arrays, or tensors. One fundamental low-rank tensor decomposition is the canonical polyadic decomposition (CPD). The challenge of fitting a low-rank, nonnegative CPD model to Poisson-distributed count data is of particular interest. Several popular algorithms use local search methods to approximate the maximum likelihood estimator (MLE) of the Poisson CPD model. Here, this work presents two new algorithms that extend state-of-the-art local methods for Poisson CPD. Hybrid GCP-CPAPR combines Generalized Canonical Decomposition (GCP) with stochastic optimization and CP Alternating Poisson Regression (CPAPR), a deterministic algorithm, to increase the probability of converging to the MLE over either method used alone. Restarted CPAPR with SVDrop uses a heuristic based on the singular values of the CPD model unfoldings to identify convergence toward optimizers that are not the MLE and restarts within the feasible domain of the optimization problem, thus reducing overall computational cost when using a multi-start strategy. We provide empirical evidence that indicates our approaches outperform existing methods with respect to converging to the Poisson CPD MLE.

CPAPR↗
DOE OSTI2026

Decomposition of methane diluted with inert gas in an RF discharge cell

Decomposition of methane using non-thermal plasmas is an attractive route for producing hydrogen-rich gases and valuable carbon nanomaterials. Understanding how plasma discharge modes influence methane decomposition in optimizing plasma-assisted chemical conversion remains unexplored. This study explores the coupling between the discharge structure and product selectivity in RF capacitively coupled discharges operating in methane/inert gas mixtures in the pressure range of 2–3 torr. Under our experimental conditions the discharge exhibits mode transitions from uniform to striated in Ar and Kr and from diffuse to contracted in Ar and Kr with <5% CH 4 . The discharges in He and Ne remained uniform under our operating conditions, and their mixtures with CH 4 remained diffuse. A 0-d model for Ar/CH 4 discharge established a threshold for contraction while also asserting the importance of Ar$^{*}_{\textrm{m}}$ in the dissociation and ionization processes. The highest degree of methane decomposition, >99.7% with the main products of acetylene and graphitized solid carbon was achieved in the contracted discharge mode for both Kr or Ar with ⩽5% CH 4 . We demonstrate that contraction can play a crucial role in the effective decomposition of methane with value-added products and that both the electronic and thermal properties of plasma gas are responsible for this effect.

RF plasma↗
DOE OSTI2025

Multi-omics of a model bacterial consortium deciphers details of chitin decomposition in soil

Soil microorganisms interact to carry out decomposition of complex organic carbon and nitrogen compounds, such as chitin, but the high diversity and complexity of the soil microbiome and habitat have posed a challenge to elucidating such interactions. Here, we sought to address this challenge by analysis of a model soil consortium (MSC-2) consisting of eight soil bacterial species. Our aim was to elucidate the specific roles of the member species during chitin metabolism. Samples were collected from MSC-2 incubated in chitin-enriched soil over 3 months. Multi-omics was used to understand how the community composition, transcripts, proteins, and chitin decomposition shifted over time. The data clearly and consistently revealed a temporal shift during chitin decomposition with defined contributions by individual species. A Streptomyces genus member (sp001905665) was a key player in early steps of chitin decomposition, with other MSC-2 members being central in carrying out later steps. These results illustrate how multi-omics applied to a defined consortium untangles the interactions between soil microorganisms.

chitin↗
NASA NTRS2014

Distributed Prognostics based on Structural Model Decomposition

Within systems health management, prognostics focuses on predicting the remaining useful life of a system. In the model-based prognostics paradigm, physics-based models are constructed that describe the operation of a system and how it fails. Such approaches consist of an estimation phase, in which the health state of the system is first identified, and a prediction phase, in which the health state is projected forward in time to determine the end of life. Centralized solutions to these problems are often computationally expensive, do not scale well as the size of the system grows, and introduce a single point of failure. In this paper, we propose a novel distributed model-based prognostics scheme that formally describes how to decompose both the estimation and prediction problems into independent local subproblems whose solutions may be easily composed into a global solution. The decomposition of the prognostics problem is achieved through structural decomposition of the underlying models. The decomposition algorithm creates from the global system model a set of local submodels suitable for prognostics. Independent local estimation and prediction problems are formed based on these local submodels, resulting in a scalable distributed prognostics approach that allows the local subproblems to be solved in parallel, thus offering increases in computational efficiency. Using a centrifugal pump as a case study, we perform a number of simulation-based experiments to demonstrate the distributed approach, compare the performance with a centralized approach, and establish its scalability. Index Terms-model-based prognostics, distributed prognostics, structural model decomposition ABBREVIATIONS

centrifugal pump↗
NASA NTRSDate not supplied

Dynamic Mode Decomposition of Unsteady Pressure-Sensitive Paint Measurements for the NASA Unitary Plan Wind Tunnel Tests

This paper describes the Dynamic Mode Decomposition (DMD) of the pressures on the scale model of the Space Launch System (SLS) Block 1 cargo vehicle with the Unsteady Pressure-Sensitive Paint (uPSP) measurements, which were collected in the Ascent Transient Aerodynamics Tests with the Unitary Plan Wind Tunnel 11-by-11-foot Transonic Wind Tunnel in September 2019 at NASA Ames Research Center. The work described in this paper is a part of NASA’s development of a new state-of-the-art uPSP capability in production wind tunnels. The conventional DMD algorithm is based on the Singular Value Decomposition (SVD) of the data matrix. For the matrix of the uPSP measurements of the SLS ATAT, the number of rows is equal to the number of nodes in the grid of the scale model, and the number of columns is equal to the number of frames in the videos taken with 4 Phantom high-speed cameras. In this paper, it is verified that, for the time series with zero mean value, the DMD is equivalent to the decomposition with the Discrete Fourier Transform (DFT). Considering the uPSP is mainly used in the assessment of the unsteady, aerodynamic phenomena, the DMD of the uPSP measurements can be implemented in two steps: (1) subtract the mean value from the uPSP measurement on each of the grid nodes; (2) apply the Fast Fourier Transform (FFT) on the resulting zero-mean time series. The DMD of the uPSP measurements with FFT has two advantages: (1) the computational complexity of FFT is O(N*logN), where N is the length of the time series; (2) compared to the SVD-based DMD algorithm, the DMD with FFT can be easily implemented in parallel processing. A sample matrix of uPSP measurements, at the size of 341 grid nodes and 128 frames, is generated. Figures 1 and 2 show the eigenvalues and the ratios of the eigenvectors, respectively, of the sample matrix, without and with the mean value removed on each of the grid nodes, computed with the SVD-based DMD and the FFT. The figures demonstrate the equivalence of the SVD-based DMD and the decomposition with DFT/FFT for the time series with zero mean value. The results of DMD of the uPSP measurements of the SLS ATAT in September 2019 are presented in the paper. The DMD modes at different frequencies are shown, the aerodynamic phenomena (e.g. shockwave and vortex shedding) are demonstrated and the correlation of the DMD modes with the test configuration parameter (e.g., the Mach Number) is discussed. Figure 3 shows a software tool to visualize the DMD modes. The code to implement the algorithm described in this paper was written in C, with libraries of FFTW for FFT and MPI/OpenMP for parallel processing, and executed on the NASA Pleiades supercomputer. Funding for this research was provided by the NASA Aerosciences Evaluation and Test Capabilities Project.

Pressure-Sensitive Paint↗
DOE OSTI2025

Water‐mediated Decomposition Pathways of ε‐Hexanitrohexaazaisowurtzitane

The dominant initial decomposition mechanism of 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (HNIW) is understood from the literature to be the N─NO 2 bond scission unimolecular mechanism. Here we have found a water-mediated HONO release initial decomposition mechanism energetically competitive with the N─NO 2 bond scission mechanism modeled using ab initio nudged elastic band simulations. The activation energy of the water-mediated HONO mechanism was calculated to be 138.9 kJ/mol with the Perdew, Burke, and Ernzerhof (PBE) functional (177.8 with PBE0), while the double NO 2 release mechanism is 171.9 kJ/mol (203.3 with PBE0). Branching secondary, tertiary, and quaternary decomposition steps were also discovered including oxidation of HONO or H 2 O causing ring-opening that leads to C─N bond breaking and N 2 O or NO release. The reaction rate of HONO oxidation is much faster than HONO release, making the HONO concentration low. The Helmholtz free energy barrier of the double NO 2 release mechanism is lower than the water-mediated HONO release above 438 K (165°C) due to the vibrational contribution to the free energy. This helps explain why the literature reports more NO 2 release at higher temperatures. The present study reveals a physical mechanism for how water can catalyze the decomposition of HNIW at low enough temperatures, and reveals secondary, tertiary, and quaternary reaction mechanisms leading to NO x release. In conclusion, as water is realistically always present, the reported barriers are important for building kinetic models needed to ensure the safety and reliability of HNIW.

Steele, Brad A. [Lawrence Livermore National Labor↗
DOE OSTI2024

Simulated nitrogen deposition and precipitation events alter microbial carbon cycling during early stages of litter decomposition

Plant litter decomposition is a major nutrient input to terrestrial ecosystems that is primarily driven by microorganisms. Litter quality is considered a key drive of decomposition; however, human-induced global disturbance like nitrogen deposition and increasing extreme precipitation events will shift nutrient availability during litter decomposition. Little is known about how shifting nutrient availability will impact dissolved organic matter concentrations and microbially driven carbon cycling that are critical to soil organic matter formation. This study investigated the effect of simulated nitrogen deposition and repeated precipitation events on microbially driven carbon flow during short-term litter decomposition using a ‘common garden’ experiment with microcosms containing sand and blue grama grass litter inoculated with different microbial communities. Overall, nitrogen deposition decoupled respiration and dissolved organic carbon (DOC) by increasing respiration and not affecting DOC concentrations. Moreover, nitrogen deposition had no effect on microbial carbon use efficiency (CUE). Repeated simulated precipitation events significantly increased DOC concentrations, decreased microbial CUE, increased the microbial metabolic quotient (qCO2), and altered microbial composition and diversity. These findings highlight the complex interactions and responses of surface litter decomposers to shifting nutrient availability and contradicts previous findings that nitrogen deposition will increase soil carbon sequestration from a larger supply of DOC and reduced respiration.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

SymProp: Scaling Sparse Symmetric Tucker Decomposition via Symmetry Propagation

Sparse symmetric tensors are an important class of tensors, and their decompositions serve as powerful tools for revealing low-rank structures. This paper introduces SymProp, a novel approach for scaling sparse symmetric Tucker decomposition by propagating symmetry through intermediate computations. SymProp optimizes two key computational kernels: Sparse Symmetric Tensor Times Same Matrix chain (S3 TTMc) for Higher-Order Orthogonal Iteration (HOOI) and Sparse Symmetric Tensor Times Same Matrix chain Times Core (S3 TTMcTC) for Higher-Order QR Iteration (HOQRI). Our method employs a metaprogramming-based index iteration approach to efficiently handle the upper triangular parts of intermediate dense symmetric tensors. SymProp achieves up to 50.9× speedup over SPLATT and up to 360.8× over Compressed Sparse Symmetric (CSS) format on the S3 TTMc operation. Moreover, our S3 TTMc and S3 TTMcTC implementations support tensor orders four levels higher than state-of-the-art methods. Our HOQRI demonstrates superior scalability and up to a 33.6× speedup over optimized HOOI. By enabling more scalable Tucker decompositions for higher orders, decomposition ranks, and dimension sizes, SymProp opens new possibilities for analyzing complex hypergraph structures in fields such as network science, data mining, and machine learning.

Li, Zecheng [North Carolina State University]↗
DOE OSTI2026

Data from "What regulates decomposition in agroecosystems? Insights from reading the tea leaves"

Litter decomposition is a critical Earth process, recycling nutrients and setting a portion of plant tissue on a path toward soil organic matter. Despite this importance, we still lack a good understanding of local factors that regulate decomposition, especially in agroecosystems where management plays an outsized role. To help understand these factors, 1308 tea bags containing green and rooibos tea leaves were buried in 109 plots being exposed to a variety of management practices. This dataset contains the decomposition measurements (mass) of those tea bags that were collected 6 times during the 2018 growing season at 9 long-term experimental farms in Iowa, USA. Additionally, the dataset contains a variety of soil and crop measurements to support the understanding of the soils and the decomposition measurements. Files are presented in .csv format.

Agricultural land management↗
NASA NTRS1972

Microscopic observations of X-ray and gamma-ray induced decomposition of ammonium perchlorate crystals

The X-ray and gamma-ray induced decomposition of ammonium perchlorate was studied by optical, transmission, and scanning electron microscopy. This material is a commonly used oxidizer in solid propellents which could be employed in deep-space probes, and where they will be subjected to a variety of radiations for as long as ten years. In some respects the radiation-induced damage closely resembles the effects produced by thermal decomposition, but in other respects the results differ markedly. Similar radiation and thermal effects include the following: (1) irregular or ill-defined circular etch pits are formed in both cases; (2) approximately the same size pits are produced; (3) the pit density is similar; (4) the c face is considerably more reactive than the m face; and (5) most importantly, many of the etch pits are aligned in crystallographic directions which are the same for thermal or radiolytic decomposition. Thus, dislocations play an important role in the radiolytic decomposition process.

Herley, P. J.↗
NASA NTRS1980

The thermal decomposition of 1,3,5-trinitrohexahydro-1,3,5-triazine (RDX) and RDXd6 at high temperatures

The ballistics behavior of nitramine propellants containing RDX in an inert binder was examined. It is shown that at 2000 to 5000 psi, depending on the particle size, a slope break or discontinuity in the log burning rate versus log pressure curve occurs. It is shown that at higher pressures the nitramine decomposition proceeds predominately by C-N bond rupture and gives CH2 and N20. At still higher pressures (after the slope break) the decomposition proceeds by N-N rupture. The decomposition of RDX was investigated from 170 to 800 C at atmospheric pressure. The major decomposition products were CH2, CO, CO2, N20, N2, and H20. The ratio of the products varied with the pyrolysis rate and temperature.

Miller, P. J.↗
NASA NTRS1990

An analysis of scatter decomposition

A formal analysis of a powerful mapping technique known as scatter decomposition is presented. Scatter decomposition divides an irregular computational domain into a large number of equal sized pieces, and distributes them modularly among processors. A probabilistic model of workload in one dimension is used to formally explain why, and when scatter decomposition works. The first result is that if correlation in workload is a convex function of distance, then scattering a more finely decomposed domain yields a lower average processor workload variance. The second result shows that if the workload process is stationary Gaussian and the correlation function decreases linearly in distance until becoming zero and then remains zero, scattering a more finely decomposed domain yields a lower expected maximum processor workload. Finally it is shown that if the correlation function decreases linearly across the entire domain, then among all mappings that assign an equal number of domain pieces to each processor, scatter decomposition minimizes the average processor workload variance. The dependence of these results on the assumption of decreasing correlation is illustrated with situations where a coarser granularity actually achieves better load balance.

Nicol, David M.↗