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At least 631 records · Page 35

Thermal Considerations for Reducing the Cooldown and Warmup Duration of the James Webb Space Telescope OTIS Cryo-Vacuum Test

The James Webb Space Telescope (JWST), set to launch in 2018, is NASAs next-generation flagship telescope. The Optical Telescope Element (OTE) and Integrated Science Instrument Module (ISIM) contain all of the optical surfaces and instruments to capture and analyze the telescopes infrared targets. The integrated OTE and ISIM are denoted as OTIS, and will be tested as a single unit in a critical thermal-vacuum test in mid-2017 at NASA Johnson Space Centers Chamber A facility. The payload will be evaluated for workmanship and functionality in a 20K simulated flight environment during this thermal-vacuum test. However, the sheer thermal mass of the OTIS payload as well as the restrictive gradient, rate, and contamination-related constraints placed on test components precludes rapid cooldown or warmup to its steady-state cryo-balance condition. Hardware safety considerations precludes injection of helium gas for free molecular heat transfer. Initial thermal analysis predicted that transient radiative cooldown from ambient temperatures, while meeting all limits and constraints, would take 33.3 days; warmup similarly would take 28.4 days. This paper discusses methods used to reduce transition times from the original predictions through modulation of boundary temperatures and environmental conditions. By optimizing helium shroud transition rates and heater usage, as well as rigorously re-examining previously imposed constraints, savings of up to three days on cooldown and up to a week on warmup can be achieved. The efficiencies gained through these methods allow the JWST thermal test team to create faster cooldown and warmup profiles, thus reducing the overall test duration and cost, while keeping all of the required test operations.

JWST↗

Thermal design verification testing for the ATS-F and -G spacecraft.

There is a wide fluctuation in the internal power dissipation from the components within the earth viewing module (EVM). The electronic component functional reliability required for a two-to-five year mission is the most significant factor for the thermal design criteria. A mathematical thermal model of the EVM and the orbital environment is used to predict the performance of the thermal control system. Comparisons of the results obtained in chamber thermal balance tests with the data computed on the basis of the theoretical model provide the means for validating the thermal design.

Coyle, M.↗

Multibody dynamics: Modeling component flexibility with fixed, free, loaded, constraint, and residual modes

The assumed-modes method in multibody dynamics allows the elastic deformation of each component in the system to be approximated by a sum of products of spatial and temporal functions commonly known as modes and modal coordinates respectively. The choice of component modes used to model articulating and non-articulating flexible multibody systems is examined. Attention is directed toward three classical Component Mode Synthesis (CMS) methods whereby component normal modes are generated by treating the component interface (I/F) as either fixed, free, or loaded with mass and stiffness contributions from the remaining components. The fixed and free I/F normal modes are augmented by static shape functions termed constraint and residual modes respectively. A mode selection procedure is outlined whereby component modes are selected from the Craig-Bampton (fixed I/F plus constraint), MacNeal-Rubin (free I/F plus residual), or Benfield-Hruda (loaded I/F) mode sets in accordance with a modal ordering scheme derived from balance realization theory. The success of the approach is judged by comparing the actuator-to-sensor frequency response of the reduced order system with that of the full order system over the frequency range of interest. A finite element model of the Galileo spacecraft serves as an example in demonstrating the effectiveness of the proposed mode selection method.

Spanos, John T.↗

A critical evaluation of two-equation models for near wall turbulence

A variety of two-equation turbulence models,including several versions of the K-epsilon model as well as the K-omega model, are analyzed critically for near wall turbulent flows from a theoretical and computational standpoint. It is shown that the K-epsilon model has two major problems associated with it: the lack of natural boundary conditions for the dissipation rate and the appearance of higher-order correlations in the balance of terms for the dissipation rate at the wall. In so far as the former problem is concerned, either physically inconsistent boundary conditions have been used or the boundary conditions for the dissipation rate have been tied to higher-order derivatives of the turbulent kinetic energy which leads to numerical stiffness. The K-omega model can alleviate these problems since the asymptotic behavior of omega is known in more detail and since its near wall balance involves only exact viscous terms. However, the modeled form of the omega equation that is used in the literature is incomplete-an exact viscous term is missing which causes the model to behave in an asymptotically inconsistent manner. By including this viscous term and by introducing new wall damping functions with improved asymptotic behavior, a new K-tau model (where tau is identical with 1/omega is turbulent time scale) is developed. It is demonstrated that this new model is computationally robust and yields improved predictions for turbulent boundary layers.

Speziale, Charles G.↗

Interannual variation of seasonal means and subseasonal variability of cloud streets off the east coast of North America 1984-1987

Convection waves are a strong function of the original forcing by convection in the boundary layer. This convection can take the form of random or 2-D spatial structure. When clouds are formed as a result of 2-D boundary layer forcing, they are called cloud streets. Convective waves may be important in the global momentum balance. Global circulation models presently overestimate wind speeds in the middle and upper troposphere, and do not account for convective waves. If the hypothesis that convective waves significantly contribute to momentum transport in the troposphere is correct, then climatology of cloud streets will help understand convective waves' role in the global momentum balance. If the hypothesis is incorrect, then cloud street climatology is still useful because cloud streets show areas where large amounts of sensible and latent heat are transferred from the ocean to the atmosphere. Interannual variation of seasonal means and subseasonal variability of cloud street occurrence off the east coast of North America is examined and compared. The months of Dec., Jan., and Feb. during 1984-85, 1985-86, and 1986-87 are examined along with each season.

Rademacher, Kurt R.↗

Emissions of biogenic sulfur gases from northern bogs and fens

Sulfur gases are important components of the global cycle of S. They contribute to the acidity of precipitation and they influence global radiation balance and climate. The role of terrestrial sources of biogenic S and their effect on atmospheric chemistry remain as major unanswered questions in our understanding of the natural S cycle. The role of northern wetlands as sources and sinks of gaseous S by measuring rates of S gas exchange as a function of season, hydrologic conditions, and gradients in tropic status was investigated. Experiments were conducted in wetlands in New Hampshire, particularly a poor fen, and in Mire 239, a poor fen at the Experimental Lakes Area (ELA) in Ontario. Emissions were determined using Teflon enclosures, gas cryotrapping methods and gas chromatography (GC) with flame photometric detection. Dynamic (sweep flow) and static enclosures were employed which yielded similar results. Dissolved S gases and methane were determined by gas stripping followed by GC.

Demello, William Zamboni↗

Relative elemental abundance and heating constraints determined for the solar corona from SERTS measurements

Intensities of EUV spectral lines were measured as a function of radius off the solar limb by two flights of Goddard's Solar EUV Rocket Telescope and Spectrograph (SERTS) for three quiet sun regions. The density scale height, line-ratio densities, line-ratio temperatures, and emission measures were determined. The line-ratio temperature determined from the ionization balances of Arnaud and Rothenflug (1985) were more self-consistent than the line-ratio temperatures obtained from the values of Arnaud and Raymond (1992). Limits on the filling factor were determined from the emission measure and the line-ratio densities for all three regions. The relative abundances of silicon, aluminum, and chromium to iron were determined. Results did agree with standard coronal relative elemental abundances for one observation, but did not agree for another. Aluminum was overabundant while silicon was underabundant. Heating was required above 1.15 solar radii for all three regions studied. For two regions, local nonconductive heating is needed for any filling factor, and in all three regions for filling factor of 0.1.

Falconer, David A.↗

Direct numerical simulation of incompressible axisymmetric flows

In the present work, we propose to conduct direct numerical simulations (DNS) of incompressible turbulent axisymmetric jets and wakes. The objectives of the study are to understand the fundamental behavior of axisymmetric jets and wakes, which are perhaps the most technologically relevant free shear flows (e.g. combuster injectors, propulsion jet). Among the data to be generated are various statistical quantities of importance in turbulence modeling, like the mean velocity, turbulent stresses, and all the terms in the Reynolds-stress balance equations. In addition, we will be interested in the evolution of large-scale structures that are common in free shear flow. The axisymmetric jet or wake is also a good problem in which to try the newly developed b-spline numerical method. Using b-splines as interpolating functions in the non-periodic direction offers many advantages. B-splines have local support, which leads to sparse matrices that can be efficiently stored and solved. Also, they offer spectral-like accuracy that are C(exp O-1) continuous, where O is the order of the spline used; this means that derivatives of the velocity such as the vorticity are smoothly and accurately represented. For purposes of validation against existing results, the present code will also be able to simulate internal flows (ones that require a no-slip boundary condition). Implementation of no-slip boundary condition is trivial in the context of the b-splines.

Loulou, Patrick↗

Frequency-Modulated, Continuous-Wave Laser Ranging Using Photon-Counting Detectors

Optical ranging is a problem of estimating the round-trip flight time of a phase- or amplitude-modulated optical beam that reflects off of a target. Frequency- modulated, continuous-wave (FMCW) ranging systems obtain this estimate by performing an interferometric measurement between a local frequency- modulated laser beam and a delayed copy returning from the target. The range estimate is formed by mixing the target-return field with the local reference field on a beamsplitter and detecting the resultant beat modulation. In conventional FMCW ranging, the source modulation is linear in instantaneous frequency, the reference-arm field has many more photons than the target-return field, and the time-of-flight estimate is generated by balanced difference- detection of the beamsplitter output, followed by a frequency-domain peak search. This work focused on determining the maximum-likelihood (ML) estimation algorithm when continuous-time photoncounting detectors are used. It is founded on a rigorous statistical characterization of the (random) photoelectron emission times as a function of the incident optical field, including the deleterious effects caused by dark current and dead time. These statistics enable derivation of the Cramér-Rao lower bound (CRB) on the accuracy of FMCW ranging, and derivation of the ML estimator, whose performance approaches this bound at high photon flux. The estimation algorithm was developed, and its optimality properties were shown in simulation. Experimental data show that it performs better than the conventional estimation algorithms used. The demonstrated improvement is a factor of 1.414 over frequency-domainbased estimation. If the target interrogating photons and the local reference field photons are costed equally, the optimal allocation of photons between these two arms is to have them equally distributed. This is different than the state of the art, in which the local field is stronger than the target return. The optimal processing of the photocurrent processes at the outputs of the two detectors is to perform log-matched filtering followed by a summation and peak detection. This implies that neither difference detection, nor Fourier-domain peak detection, which are the staples of the state-of-the-art systems, is optimal when a weak local oscillator is employed.

Erkmen, Baris I.↗

Adaptive Augmenting Control Flight Characterization Experiment on an F/A-18

This paper summarizes the Adaptive Augmenting Control (AAC) flight characterization experiments performed using an F/A-18 (TN 853). AAC was designed and developed specifically for launch vehicles, and is currently part of the baseline autopilot design for NASA's Space Launch System (SLS). The scope covered here includes a brief overview of the algorithm (covered in more detail elsewhere), motivation and benefits of flight testing, top-level SLS flight test objectives, applicability of the F/A-18 as a platform for testing a launch vehicle control design, test cases designed to fully vet the AAC algorithm, flight test results, and conclusions regarding the functionality of AAC. The AAC algorithm developed at Marshall Space Flight Center is a forward loop gain multiplicative adaptive algorithm that modifies the total attitude control system gain in response to sensed model errors or undesirable parasitic mode resonances. The AAC algorithm provides the capability to improve or decrease performance by balancing attitude tracking with the mitigation of parasitic dynamics, such as control-structure interaction or servo-actuator limit cycles. In the case of the latter, if unmodeled or mismodeled parasitic dynamics are present that would otherwise result in a closed-loop instability or near instability, the adaptive controller decreases the total loop gain to reduce the interaction between these dynamics and the controller. This is in contrast to traditional adaptive control logic, which focuses on improving performance by increasing gain. The computationally simple AAC attitude control algorithm has stability properties that are reconcilable in the context of classical frequency-domain criteria (i.e., gain and phase margin). The algorithm assumes that the baseline attitude control design is well-tuned for a nominal trajectory and is designed to adapt only when necessary. Furthermore, the adaptation is attracted to the nominal design and adapts only on an as-needed basis (see Figure 1). The MSFC algorithm design was formulated during the Constellation Program and reached a high maturity level during SLS through simulation-based development and internal and external analytical review. The AAC algorithm design has three summary-level objectives: (1) "Do no harm;" return to baseline control design when not needed, (2) Increase performance; respond to error in ability of vehicle to track command, and (3) Regain stability; respond to undesirable control-structure interaction or other parasitic dynamics. AAC has been successfully implemented as part of the Space Launch System baseline design, including extensive testing in high-fidelity 6-DOF simulations the details of which are described in [1]. The Dryden Flight Research Center's F/A-18 Full-Scale Advanced Systems Testbed (FAST) platform is used to conduct an algorithm flight characterization experiment intended to fully vet the aforementioned design objectives. FAST was specifically designed with this type of test program in mind. The onboard flight control system has full-authority experiment control of ten aerodynamic effectors and two throttles. It has production and research sensor inputs and pilot engage/disengage and real-time configuration of up to eight different experiments on a single flight. It has failure detection and automatic reversion to fail-safe mode. The F/A-18 aircraft has an experiment envelope cleared for full-authority control and maneuvering and exhibits characteristics for robust recovery from unusual attitudes and configurations aided by the presence of a qualified test pilot. The F/A-18 aircraft has relatively high mass and inertia with exceptional performance; the F/A-18 also has a large thrust-to-weight ratio, owing to its military heritage. This enables the simulation of a portion of the ascent trajectory with a high degree of dynamic similarity to a launch vehicle, and the research flight control system can simulate unstable longitudinal dynamics. Parasitic dynamics such as slosh and bending modes, as well as atmospheric disturbances, are being produced by the airframe via modification of bending filters and the use of secondary control surfaces, including leading and trailing edge flaps, symmetric ailerons, and symmetric rudders. The platform also has the ability to inject signals in flight to simulate structural mode resonances or other challenging dynamics. This platform also offers more test maneuvers and longer maneuver times than a single rocket or missile test, which provides ample opportunity to fully and repeatedly exercise all aspects of the algorithm. Prior to testing on an F/A-18, AAC was the only component of the SLS autopilot design that had not been flight tested. The testing described in this paper raises the Technology Readiness Level (TRL) early in the SLS Program and is able to demonstrate its capabilities and robustness in a flight environment.

VanZwieten, Tannen S.↗

Analysis of the surface heat balance over the world ocean

The net surface heat fluxes over the global ocean for all calendar months were evaluated. To obtain a formula in the form Qs = Q2(T*A - Ts), where Qs is the net surface heat flux, Ts is the sea surface temperature, T*A is the apparent atmospheric equilibrium temperature, and Q2 is the proportionality constant. Here T*A and Q2, derived from the original heat flux formulas, are functions of the surface meteorological parameters (e.g., surface wind speed, air temperature, dew point, etc.) and the surface radiation parameters. This formulation of the net surface heat flux together with climatological atmospheric parameters provides a realistic and computationally efficient upper boundary condition for oceanic climate modeling.

Esbenson, S. K.↗

Altering the cellular mechanical force balance results in integrated changes in cell, cytoskeletal and nuclear shape

Studies were carried out with capillary endothelial cells cultured on fibronectin (FN)-coated dishes in order to analyze the mechanism of cell and nuclear shape control by extracellular matrix (ECM). To examine the role of the cytoskeleton in shape determination independent of changes in transmembrane osmotic pressure, membranes of adherent cells were permeabilized with saponin (25 micrograms/ml) using a buffer that maintains the functional integrity of contractile microfilaments. Real-time videomicroscopic studies revealed that addition of 250 microM ATP resulted in time-dependent retraction and rounding of permeabilized cells and nuclei in a manner similar to that observed in intact living cells following detachment using trypsin-EDTA. Computerized image analysis confirmed that permeabilized cells remained essentially rigid in the absence of ATP and that retraction was stimulated in a dose-dependent manner as the concentration of ATP was raised from 10 to 250 microM. Maximal rounding occurred by 30 min with projected cell and nuclear areas being reduced by 69 and 41%, respectively. ATP-induced rounding was also accompanied by a redistribution of microfilaments resulting in formation of a dense net of F-actin surrounding retracted nuclei. Importantly, ATP-stimulated changes in cell, cytoskeletal, and nuclear form were prevented in permeabilized cells using a synthetic myosin peptide (IRICRKG) that has been previously shown to inhibit actomyosin filament sliding in muscle. In contrast, both the rate and extent of cell and nuclear rounding were increased in permeabilized cells exposed to ATP when the soluble FN peptide, GRGDSP, was used to dislodge immobilized FN from cell surface integrin receptors.(ABSTRACT TRUNCATED AT 250 WORDS).

Non-NASA Center↗

An analysis of scatter decomposition

A formal analysis of a mapping method known as scatter decomposition (SD) is presented. SD divides an irregular domain into many equal-size pieces and distributes them modularly among processors. It is shown that, if a correlation in workload is a convex function of distance, then scattering a more finely decomposed domain yields a lower average processor workload variance; if the workload process is stationary Gaussian and the correlation function decreases linearly in distance to zero and then remains zero, scattering a more finely decomposed domain yields a lower expected maximum processor workload. Finally, 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) SD minimizes the average processor workload variance. The dependence of these results on the assumption of decreasing correlation is illustrated with cases where a coarser granularity actually achieves better load balance.

Nicol, David M.↗

Integration and use of Microgravity Research Facility: Lessons learned by the crystals by vapor transport experiment and Space Experiments Facility programs

The Crystals by Vapor Transport Experiment (CVTE) and Space Experiments Facility (SEF) are materials processing facilities designed and built for use on the Space Shuttle mid deck. The CVTE was built as a commercial facility owned by the Boeing Company. The SEF was built under contract to the UAH Center for Commercial Development of Space (CCDS). Both facilities include up to three furnaces capable of reaching 850 C minimum, stand-alone electronics and software, and independent cooling control. In addition, the CVTE includes a dedicated stowage locker for cameras, a laptop computer, and other ancillary equipment. Both systems are designed to fly in a Middeck Accommodations Rack (MAR), though the SEF is currently being integrated into a Spacehab rack. The CVTE hardware includes two transparent furnaces capable of achieving temperatures in the 850 to 870 C range. The transparent feature allows scientists/astronauts to directly observe and affect crystal growth both on the ground and in space. Cameras mounted to the rack provide photodocumentation of the crystal growth. The basic design of the furnace allows for modification to accommodate techniques other than vapor crystal growth. Early in the CVTE program, the decision was made to assign a principal scientist to develop the experiment plan, affect the hardware/software design, run the ground and flight research effort, and interface with the scientific community. The principal scientist is responsible to the program manager and is a critical member of the engineering development team. As a result of this decision, the hardware/experiment requirements were established in such a way as to balance the engineering and science demands on the equipment. Program schedules for hardware development, experiment definition and material selection, flight operations development and crew training, both ground support and astronauts, were all planned and carried out with the understanding that the success of the program science was as important as the hardware functionality. How the CVTE payload was designed and what it is capable of, the philosophy of including the scientists in design and operations decisions, and the lessons learned during the integration process are descussed.

Heizer, Barbara L.↗

Spectral and Temporal Properties of Galactic Black Hole Systems

Kusunose, Mineshige & Yamada (1996; hereafter KMY) extended the model of Kusunose & Mineshige (1995) to the Galactic black hole candidates by considering nonthermal electron injection with gamma(EQ\0(,\s\up2(less than),\s\do-l(_))) 10. The effects of pair escape and advection on the disk structure and general relativistic effects on the emission spectrum were also examined. They found that the energy spectral index (alpha)(sub x) of the power law X-rays is about-0.8 and-2.0 when 1(sub soft)/1 = 0.2 and 2, respectively, where 1(sub soft)/1 is the ratio of the compactness of the injected soft photons to that of the gravitational energy. The power law index was found to be nearly independent of the mass accretion which is consistent with the observed luminosity independence. The model with small 1(sub soft)/1 (less than 1) shows promise for explaining the low state observed in Galactic black hole candidates. Model fits were provided for GX339-4 and Cyg X- 1 data from COMPTEL and OSSE on the Compton Gamma Ray Observatory. The difference in emission spectra between thermal disks and the model of KMY appears only in the energy range greater than 100 keV. Li, Kusunose and Liang (1996) studied stochastic particle acceleration to produce nonthermal particle distributions which then were used in the model of Kusunose & Mineshige (1995) to model the spectrum above 1 Mev from GBHC's. Under certain conditions, stochastic electron acceleration overcame Coulomb and Compton losses resulting in a suprathermal electron population. Good fits were obtained by COMPTEL and OSSE observations of Cyg X-1 and GRO J0422+23. Kusunose & Mineshige (1996a) examined the role of electron-positron pairs in advection-dominated disks. They found that the results for advection-dominated disks without pairs are not qualitatively changed by including pairs. Summaries of work sponsored by this grant are given in Wheeler, Kim, Moscoso, Kusunose & Mineshige (1996) and Kusunose (1996) Work was also done on developing a model for an e(+-) pair wind from the inner disk region of a black hole. The model consists of three zones: a pair production/annihilation zone at the base of the wind, a pair annihilation zone slightly further out from the disk and a wind zone extending to infinity where no annihilation occurs. The model assumes an input X-ray / gamma-ray power-law spectrum as a function of photon energy and angular distribution. Pairs are created in the pair production/annihilation zone via photon-photon, photonparticle and particle-particle collisions. The bulk velocity of the pairs is obtained from the momentum component perpendicular to the disk taking into account the radiation pressure acceleration of the pairs. Energy balance in the pair production/annihilation zone is calculated by assuming that the momentum component parallel to the disk is thermalized and by taking into account heating/cooling via anisotropic thermal Compton scattering along with the cooling processes of bremsstrahlung and synchrotron radiation. The pair density is also calculated. The outer boundary of the pair production/annihilation zone is where the optical depth for photon-photon pair produciton is unity. Beyond this point only pair annihilation will occur in the pair annihilation zone. When the pair density becomes small, pair annihilation will be negligible and the pairs will flow freely to infinity. In this model we have found that the X-ray power-law spectral index, alpha(sub x) is the primary parameter which determines the density, temperature and velocity of the pair production/annihilation zone (Moscoso, Kusunose & Wheeler 1996).

Wheeler, J. Craig↗

Using Leaf Chlorophyll to Parameterize Light-Use-Efficiency Within a Thermal-Based Carbon, Water and Energy Exchange Model

Chlorophylls absorb photosynthetically active radiation and thus function as vital pigments for photosynthesis, which makes leaf chlorophyll content (C(sub ab) useful for monitoring vegetation productivity and an important indicator of the overall plant physiological condition. This study investigates the utility of integrating remotely sensed estimates of C(sub ab) into a thermal-based Two-Source Energy Balance (TSEB) model that estimates land-surface CO2 and energy fluxes using an analytical, light-use-efficiency (LUE) based model of canopy resistance. The LUE model component computes canopy-scale carbon assimilation and transpiration fluxes and incorporates LUE modifications from a nominal (species-dependent) value (LUE(sub n)) in response to short term variations in environmental conditions, However LUE(sub n) may need adjustment on a daily timescale to accommodate changes in plant phenology, physiological condition and nutrient status. Day to day variations in LUE(sub n) were assessed for a heterogeneous corn crop field in Maryland, U,S.A. through model calibration with eddy covariance CO2 flux tower observations. The optimized daily LUE(sub n) values were then compared to estimates of C(sub ab) integrated from gridded maps of chlorophyll content weighted over the tower flux source area. The time continuous maps of daily C(sub ab) over the study field were generated by focusing in-situ measurements with retrievals generated with an integrated radiative transfer modeling tool (accurate to within +/-10%) using at-sensor radiances in green, red and near-infrared wavelengths acquired with an aircraft imaging system. The resultant daily changes in C(sub ab) within the tower flux source area generally correlated well with corresponding changes in daily calibrated LUE(sub n) derived from the tower flux data, and hourly water, energy and carbon flux estimation accuracies from TSEB were significantly improved when using C(sub ab) for delineating spatio-temporal variations in LUE(sub n). The results demonstrate the synergy between thermal infrared and shortwave reflective wavebands in producing valuable remote sensing data for operational monitoring of carbon and water fluxes.

Houlborg, Rasmus↗

Electrical contacts to ion cleaned n-type gallium arsenide.

The electrical current through silver contacts evaporated onto n-type gallium arsenide is reported as a function of surface treatment. Contacts to untreated gallium arsenide exhibit the expected high resistance. Surface cleaning by argon ion bombardment reduces the resistance by three orders of magnitude. The electrical resistance beyond 850 eV increases rapidly with ion bombardment energy. The resistance minimum at 850 eV is explained semiquantitatively in terms of a balance between cleaning and surface damage.

Walker, G. H.↗

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.↗