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DOE OSTI2023

Establishing metrics to quantify spatial similarity in spherical and red blood cell distributions

As computational power increases and systems with millions of red blood cells can be simulated, it is important to note that varying spatial distributions of cells may affect simulation outcomes. Since a single simulation may not represent the ensemble behavior, many different configurations may need to be sampled to adequately assess the entire collection of potential cell arrangements. In order to determine both the number of distributions needed and which ones to run, we must first establish methods to identify well-generated, randomly placed cell distributions and to quantify distinct cell configurations. We utilize metrics to assess (1) the presence of any underlying structure to the initial cell distribution and (2) similarity between cell configurations. We propose the use of the radial distribution function to identify long-range structure in a cell configuration and apply it to a randomly distributed and structured set of red blood cells. To quantify spatial similarity between two configurations, we make use of the Jaccard index, and characterize sets of red blood cell and sphere initializations. As an extension to our work submitted to the International Conference on Computational Science, we significantly increase our data set size from 72 to 1048 cells, include a similar set of studies using spheres, compare the effects of varying sphere size, and utilize the Jaccard index distribution to probe sets of extremely similar configurations. Our results show that the radial distribution function can be used as a metric to determine long-range structure in both distributions of spheres and RBCs. We determine that the ideal case of spheres within a cube versus bi-concave shaped cells within a cylinder affects the shape of the Jaccard index distributions, as well as the range of Jaccard values, showing that both the shape of particle and the domain may play a role. Furthermore, we also find that the distribution is able to capture very similar configurations through Jaccard index values greater than 95% when appending several nearly identical configurations into the data set.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions

The statistics of velocity and density fields are crucial for cosmic structure formation and evolution. Here, this paper extends our previous work on the two-point second-order statistics for the velocity field [Phys. Fluids 35, 077105 (2023)] to one-point probability distributions for both density and velocity fields. The scale and redshift variation of density and velocity distributions are studied by a halo-based non-projection approach. First, all particles are divided into halo and out-of-halo particles so that the redshift variation can be studied via generalized kurtosis of distributions for halo and out-of-halo particles, respectively. Second, without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales $r$. We demonstrate that: (i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; (ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade on small scales with a constant rate $\varepsilon_u$; (iii) On small scales, the even order moments of pairwise velocity $\Delta u_L$ follow a two-thirds law $\propto{(-\varepsilon_ur)}^{2/3}$, while the odd order moments follow a linear scaling $\langle(\Delta u_L)^{2n+1}\rangle=(2n+1)\langle(\Delta u_L)^{2n}\rangle\langle\Delta u_L\rangle\propto{r}$; (iv) The scale variation of the velocity distributions was studied for longitudinal velocities $u_L$ or $u_L^{'}$, pairwise velocity (velocity difference) $\Delta u_L$=$u_L^{'}$-$u_L$ and velocity sum $\Sigma u_L$=$u^{'}_L$+$u_L$. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; (v) On small scales, $u_L$ and $\Sigma u_L$ can be modeled by a $X$ distribution to maximize the entropy of the system. The distribution of $\Delta u_L$ can be different; (vi) On large scales, $\Delta u_L$ and $\Sigma u_L$ can be modeled by a logistic or a $X$ distribution, while $u_L$ has a different distribution; (vii) the redshift variation of the velocity distributions follows the evolution of the $X$ distribution involving a shape parameter $\alpha(z)$ decreasing with time.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

The Value of Distributed Wind: A Valuation Framework

While there has been an increase in distributed energy resource (DER) adoption, particularly for solar photovoltaic (PV) DERs, distributed wind deployment is still relatively low. However, distributed wind has significant growth potential for behind-the-meter applications and can provide improved resource diversity and resilience in high-DER grid systems. In order to make optimized decisions about distributed wind deployment, it is important to identify and characterize the value streams of distributed wind in a way that will help policy makers, microgrid developers, utilities, project developers, and others understand the potential value of distributed wind. In our paper, we develop a framework to provide a consistent and comprehensive approach to finding the net benefits of distributed wind to various stakeholders in different scenarios. We do this by considering the main use cases for distributed wind, and then developing a framework which is flexible for these various use cases and the relevant stakeholders while maintaining the same overall structure for analysis. Ongoing work includes applying this framework to valuing two distributed wind power systems, one in a remote village in Alaska and one in a front-of-the-meter deployment in Iowa. Our analysis aims to understand the full value that distributed wind is providing in these systems, including the resilience benefits it is contributing. As a better understanding of distributed wind valuation is gained, it will be easier for stakeholders to make informed decisions in order to have resilient renewable energy systems.

17 WIND ENERGY↗

NASA NTRS2000

A Tool for Automatic Data Distribution for CFD Applications on Structured Grids

Development of HPF versions of NPB and ARC3D has shown that HPF provides an efficient, concise way to express parallelism and to organize data traffic. The use of HPF, as noted in the papers, requires an intimate knowledge of the applications and a detailed analysis of data affinity, data movement, and data granularity. To simplify and accelerate the task of developing HPF versions of existing CFD applications we have designed and implemented ADAPT (Automatic Data Alignment and Placement Tool). ADAPT analyzes a CFD application working on a single structured grid and generates HPF TEMPLATE, (RE)DISTRIBUTION, ALIGNMENT, and INDEPENDENT directives. The directives can be generated on the nest level, subroutine level, application level, or on the application interface level. ADAPT annotates an existing CFD FORTRAN application, performing computations on single or multiple grids. On each grid the application is considered as a sequence of operators, each applied to a set of variables defined in a particular grid domain. ADAPT automatically detects implicit operators (i.e., having data dependences) and explicit operators (without data dependences). For parallelization of an explicit operator ADAPT creates a template for the operator domain, aligns arrays used in the operator with the template, distributes the template, and declares the loops over the distributed dimensions as INDEPENDENT. For parallelization of an implicit operator, the distribution of the operator's domain should be consistent with the operator's dependences. Any dependence between sections distributed on different processors would preclude parallelization if the compiler does not have an ability to pipeline computations. If a data distribution is "orthogonal" to the dependences of an implicit operator, then the loop which implements the operator can be declared as INDEPENDENT. ADAPT starts with an analysis of array index expressions of the loop nests. For each pair of arrays referenced in an assignment statement, it generates an arc in the alignment graph and annotates it with an affinity relation. The template, alignment, and distribution directives for a particular loop nest are then derived from a transitive closure of the affinity relation. A compromise of data distributions in different nests and subroutines is achieved by merging annotated alignment graphs for adjacent nests/stibroutine calls in the nest/call graph of the application in the process called distribution lifting. ADAPT has been implemented as a C++ program running in conjunction with a parallelization tool called CAPTools. ADAPT uses the parse tree, interprocedural analysis and application database generated by CAPTools. It also uses the Directed Graph class, initially implemented in p2d2 (parallel debugger oi distributed programs), and some other classes supporting symbolic computations. ADAPT uses data distribution techniques described. ADAPT was tested with ARC3D and the FT benchmark and has demonstrated a code performance within a factor of 1.5 of handwritten versions.

Frumkin, Michael↗

NASA NTRS2002

Wave-Particle Interactions Associated with Nongyrotropic Distribution Functions: A Hybrid Simulation Study

Nongyrotropic plasma distribution functions can be formed in regions of space where guiding center motion breaks down as a result of strongly curved and weak ambient magnetic fields. Such are the conditions near the current sheet in the Earth's middle and distant magnetotail, where observations of nongyrotropic ion distributions have been made. Here a systematic parameter study of nongyrotropic proton distributions using electromagnetic hybrid simulations is made. We model the observed nongyrotropic distributions by removing a number of arc length segments from a cold ring distribution and find significant differences with the results of simulations that initially have a gyrotropic ring distribution. Model nongyrotropic distributions with initially small perpendicular thermalization produce growing fluctuations that diffuse the ions into a stable Maxwellian-like distribution within a few proton gyro periods. The growing waves produced by nongyrotropic distributions are similar to the electromagnetic proton cyclotron waves produced by a gyrotropic proton ring distribution in that they propagate parallel to the background magnetic field and occur at frequencies on the order of the proton gyrofrequency, The maximum energy of the fluctuating magnetic field increases as the initial proton distribution is made more nongyrotropic, that is, more highly bunched in perpendicular velocity space. This increase can be as much as twice the energy produced in the gyrotropic case.

Convery, P. D.↗

NASA NTRS2006

Implementing Access to Data Distributed on Many Processors

A reference architecture is defined for an object-oriented implementation of domains, arrays, and distributions written in the programming language Chapel. This technology primarily addresses domains that contain arrays that have regular index sets with the low-level implementation details being beyond the scope of this discussion. What is defined is a complete set of object-oriented operators that allows one to perform data distributions for domain arrays involving regular arithmetic index sets. What is unique is that these operators allow for the arbitrary regions of the arrays to be fragmented and distributed across multiple processors with a single point of access giving the programmer the illusion that all the elements are collocated on a single processor. Today's massively parallel High Productivity Computing Systems (HPCS) are characterized by a modular structure, with a large number of processing and memory units connected by a high-speed network. Locality of access as well as load balancing are primary concerns in these systems that are typically used for high-performance scientific computation. Data distributions address these issues by providing a range of methods for spreading large data sets across the components of a system. Over the past two decades, many languages, systems, tools, and libraries have been developed for the support of distributions. Since the performance of data parallel applications is directly influenced by the distribution strategy, users often resort to low-level programming models that allow fine-tuning of the distribution aspects affecting performance, but, at the same time, are tedious and error-prone. This technology presents a reusable design of a data-distribution framework for data parallel high-performance applications. Distributions are a means to express locality in systems composed of large numbers of processor and memory components connected by a network. Since distributions have a great effect on the performance of applications, it is important that the distribution strategy is flexible, so its behavior can change depending on the needs of the application. At the same time, high productivity concerns require that the user be shielded from error-prone, tedious details such as communication and synchronization.

James, Mark↗

NASA NTRS2019

Conceptual Design of a Counter-Rotating Fan System for Distributed Boundary Layer Ingesting Propulsion

The present paper details the design of the counter rotating fans for a Turboelectric Distributed Propulsion (TeDP) system. Sixteen propulsors installed in mail-slot-shape nacelles are embedded on an aerodynamically optimized hybrid wing-body configuration. The hybrid-wing/body (HWB) configuration which was previously designed to satisfy the conditions of trim, longitudinally static stability and specific cargo space is employed as the baseline configuration in pursuing an optimal distributed propulsion system. A set of distributed propulsors is conceptually designed and the collective performance is evaluated against the target thrust mandated by the mission requirements. The concept of the distributed propulsion allows the fan pressure ratio to be around 1.27~1.32 for the target thrust. In addition, further splitting of the fan pressure ratio by using the counter-rotating fans for each slot realizes the target pressure ratio with low tip speed. In the distributed propulsion system, the nature of the flow conditions and/or the thickness of the ingested boundary layer may differ and result in different propulsive reaction of each individual propulsor. The optimization is, thus, approached from both the propulsion system and individual propulsor perspectives. An optimal distribution of the thrust and power output is determined by how the system utilizes each passage's propulsive characteristics and its interaction with the airframe. These system level analysis and optimization are conducted using an actuator disk model to account for the propulsion-airframe integration numerically. With respect to the propulsor level, aerodynamic shape optimizations of the fan blades are performed in a sequential multi-objective optimization process for various design objectives, such as mass flow rate condition, fan pressure ratio, efficiency and the exit flow angle of the fan stage by using a genetic algorithm, NSGA-II. The radial chord distribution, and meanline distribution of the rotors are designed on the circumferentially averaged axi-symmetric inlet profiles and tested on the six inlet profiles from six divided sectors to reckon flow distortion. The performances of the counter rotating fans are, thus, evaluated accordingly for obtaining distortion tolerant fan. The performance of the distributed propulsion system is evaluated by two CFD tools, i.e., a multi-stage turbo-machinery CFD code and one propulsion-airframe integration flow solver coupled with a body-force model. The optimized boundary layer ingestion propulsion system of 16 distributed slots not only reaches the system target thrust, but also delivers a close to 20% fuel saving benefit against its counterpart 12 distributed clean inlet propulsion system.

Boundary-Layer-Ingestion Propulsion↗

DOE OSTI2022

Categorizing distributed wind energy installations in the United States to inform research and stakeholder priorities

Abstract Background Distributed wind energy adoption in the United States can contribute to the diverse portfolio of energy technologies needed to achieve ambitious decarbonization goals. However, with limited deployment to date, the current distributed wind market must be better understood; these efforts will support the range of stakeholders who will drive successful deployment. This article first distinguishes three categories of distributed wind from existing literature: (1) behind the meter, (2) intended for explicit local load, and (3) physically distributed. A novel methodology to classify individual wind installations into each of these categories is then presented and applied to two data sets of wind installations in the United States to categorize and illuminate distinct segments in the distributed wind market. Results Physically distributed installations, constituted by small to moderately sized projects serving local loads on distribution systems solely because of their proximity to them, account for the highest amount of capacity but the lowest number of installations out of the three categories. The inverse is true for behind-the-meter installations, which are used to serve on-site loads. Installations intended for explicit local load, which are interconnected on the utility side of the distribution system and intentionally built to provide energy to loads on the same distribution system, rank in the middle for both installed capacity and number of installations. Conclusions Distributed wind energy deployment in the United States is geographically widespread, but the extent to which a single category is developed in each state varies. Policies, wind resources, and broad energy technology trends contribute to these deployment patterns. By identifying the extent to which each category of installations exists, decision-makers are empowered with data necessary to tailor research and development programs and address stakeholder priorities through policy and other means, ultimately supporting future deployment.

17 WIND ENERGY↗

DOE OSTI2021

Standardizing Performance Metrics for Building-Level Electrical Distribution Systems

Building-level electrical distribution systems comprise a myriad of current-carrying equipment, conversion devices, and protection devices that deliver power from the utility or local distributed energy resources to end-use building loads. Electric power has traditionally been generated, transmitted, and distributed in alternating current (AC). However, the last decade has seen a significant increase in the integration of native direct current (DC) equipment that has elevated the importance of DC distribution systems. Numerous studies have comparatively examined the performance of various electrical distribution systems in buildings but have failed to achieve uniform conclusions, primarily because of a lack of consistent and analogous performance evaluation methods. This paper aims to fill this gap by providing a standard set of metrics and measurement boundaries to consistently evaluate the performance of AC, DC, or hybrid AC/DC electrical distribution systems. The efficacy of the proposed approach is evaluated on a representative medium-sized commercial office building model with AC distribution and an equivalent hybrid AC/DC and DC distribution model, wherein the AC distribution model is concluded to be the most efficient. The simulation results show variation in computed metrics with different selected boundaries that verify the effectiveness of the proposed approach in ensuring consistent computation of the performance of building-level electrical distribution systems. This paper provides an initial set of guidelines for building energy system stakeholders to adopt appropriate solutions, thus leading to more efficient energy systems.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2026

Electric Utility Distribution Costs: Scoping Study on Trends, Drivers, and Possible Response Strategies [Slides]

This scoping study synthesizes information that will help stakeholders understand the scope, scale, and drivers of recent increases in investor-owned utility (IOU) expenditures on local distribution power grids, while providing regulators and other decision-makers with potential strategies to keep electricity bills down. The study includes five distinct components. Drawing first on data from FERC Form 1, it summarizes key trends in past and recent IOU distribution costs. Next, through a review of a sample of distribution-system plans, it characterizes material drivers of planned distribution expenditures. Ultimately, regulators must approve cost recovery for IOU expenditures, including those for the distribution system. The study therefore also: examines trends in utility requests and regulatory approvals related to changes in retail rates and return on equity; identifies areas where utility shareholder and customer incentives may be misaligned; and develops a menu of options that state regulators might consider to optimize distribution system expenditures. Some of the key findings include: - IOU distribution spending at a national level has grown by 6%/yr since 2014 in real dollar terms, 4x faster than in the prior 20 years and consisting mostly of capital (not operating) expenditure. - On a per-kWh basis, increases in IOU distribution costs since 2014 represent over 30% of the overall national-average increase in retail electricity rates. - Regional spending growth has ranged from 2-8%/yr, with larger estimated rate impacts in CAISO, then NYISO & ISO-NE, and then the Southeast, MISO & PJM (see figure). - Some utilities are planning for significantly increased distribution system spending. Planned spending on managing the existing system (asset replacement, safety & reliability, and resilience are all important drivers) exceeds that for capacity expansion. - IOU rate increase requests ($18 billion in 2025) and public utility commission (PUC) approval levels (average of 64% of requested amounts from 2021-2025) have recently hit multi-decadal highs. - PUCs in New England and the Southeast have recently approved a greater fraction of rate requests (>75%, on average) than in ther regions, while PUCs in California and the Southeast have generally authorized higher equity returns than in other regions. - Regulators have many tools to tackle potential misalignments between utility and customer interests and, more specifically, to optimize and reduce distribution costs. Shorter-term options include those related to return on equity, capital structure, depreciation, trackers, construction work in progress, and securitization. Longer-term options include performance-based regulation and a wide variety of planning-related requirements. All options embed important tradeoffs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Preparing Distribution Utilities for the Future - Evolving Customer Consumption in Renewable Rich Grids: A Novel Analytical Framework

The research collaboration between NREL and BYPL focuses on the challenges caused by renewable integration into the power grid at large. Since the challenges and opportunities vary depending on the point of interconnection (distribution or transmission) the research team identified two tracks for research as listed below: 1. Power procurement - This research track focuses on the challenges and opportunities caused by GW scale renewable integration at the transmission level. Specifically, this track focuses on the contribution that utility-scale renewable energy procurement provides to distribution utilities, both from energy and capacity perspectives. In this track of research, utility customers are only considered as traditional (one-directional) consumers of energy. 2. Distributed energy resources - This research track focuses on the challenges and opportunities caused by many small-scale distributed renewable resource integrations at the distribution systems. At the power distribution level, distribution utilities may face not only new solar energy technologies, but also battery energy storage and electric vehicles as well. These three technologies (solar PV, battery energy storage, and electric vehicles) combined, pose unique challenges to distribution utilities. This track focuses on assessing the net-load evolution that distribution utilities observe as these emerging technologies make their way to the grid.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Numerical methods and hypoexponential approximations for gamma distributed delay differential equations

Abstract Gamma distributed delay differential equations (DDEs) arise naturally in many modelling applications. However, appropriate numerical methods for generic gamma distributed DDEs have not previously been implemented. Modellers have therefore resorted to approximating the gamma distribution with an Erlang distribution and using the linear chain technique to derive an equivalent system of ordinary differential equations (ODEs). In this work, we address the lack of appropriate numerical tools for gamma distributed DDEs in two ways. First, we develop a functional continuous Runge–Kutta (FCRK) method to numerically integrate the gamma distributed DDE without resorting to Erlang approximation. We prove the fourth-order convergence of the FCRK method and perform numerical tests to demonstrate the accuracy of the new numerical method. Nevertheless, FCRK methods for infinite delay DDEs are not widely available in existing scientific software packages. As an alternative approach to solving gamma distributed DDEs, we also derive a hypoexponential approximation of the gamma distributed DDE. This hypoexponential approach is a more accurate approximation of the true gamma distributed DDE than the common Erlang approximation but, like the Erlang approximation, can be formulated as a system of ODEs and solved numerically using standard ODE software. Using our FCRK method to provide reference solutions, we show that the common Erlang approximation may produce solutions that are qualitatively different from the underlying gamma distributed DDE. However, the proposed hypoexponential approximations do not have this limitation. Finally, we apply our hypoexponential approximations to perform statistical inference on synthetic epidemiological data to illustrate the utility of the hypoexponential approximation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

An Exact and Near-Exact Distribution Approach to the Behrens–Fisher Problem

The Behrens–Fisher problem occurs when testing the equality of means of two normal distributions without the assumption that the two variances are equal. This paper presents approaches based on the exact and near-exact distributions for the test statistic of the Behrens–Fisher problem, depending on different combinations of even or odd sample sizes. We present the exact distribution when both sample sizes are odd and the near-exact distribution when one or both sample sizes are even. The near-exact distributions are based on a finite mixture of generalized integer gamma (GIG) distributions, used as an approximation to the exact distribution, which consists of an infinite series. The proposed tests, based on the exact and the near-exact distributions, are compared with Welch’s t-test through Monte Carlo simulations, in particular for small and unbalanced sample sizes. The results show that the proposed approaches are competent solutions to the Behrens–Fisher problem, exhibiting precise sizes and better powers than Welch’s approach for those cases. Numerical studies show that the Welch’s t-test tends to be a bit more conservative than the test statistics based on the exact or near-exact distribution, in particular when sample sizes are small and unbalanced, situations in which the proposed exact or near-exact distributions obtain higher powers than Welch’s t-test.

Hong, Serim↗

NASA NTRS1986

Field size distributions for selected agricultural crops in the United States and Canada

Digitized agricultural field boundary taken in the United States and Canada during the LACIE and AgRISTARS programs, in 1977 through 1980, were used to construct histograms showing the distributions of field area, width, and length for crops for which there were data for 700 or more fields per state. The observed distributions of area and width for fields of 10 crops grown in 13 states of the United States and Canada were compared with best-fit inverse Gaussian distributions and with log-normal distributions. For 28 distributions of area and 16 distributions of width there was found to be a probability of greater than .01 of their being inverse Gaussian. There were 10 distributions of area for which there was probability of greater than .005 of their being log-normal. Distributions of area and width stratified by state and crop type appear to be unique. The inverse Gaussian, which represents a wide range of statistical distributions from skewed to almost symmetrical, can provide a useful model for distributions of field area.

Ferguson, M. C.↗

NASA NTRS1994

Distributions of the interplanetary magnetic field revisited

The adequacy of the power spectrum to characterize the variations of a parameter depends on whether or not the parameter has a Gaussian distribution. We here perform very simple tests of Gaussianity on the distribution. We here perform very simple tests of Gaussianity on the distributions of the magnitudes of the interplanetary magnetic field, and on the distributions of the components; that is, we find the first four cumulants of the distributions (mean, variance, skewness, and kurtosis) and their solar cycle variations. We find, consistent with other recent analyses, that the traditional distributions of the 1-hour averaged magnitude are not distributed normally or lognomally as has often been assumed and the 1-hour averaged z component is found to have a nonzero kurtosis. Thus the power spectrum is insufficient to completely characterize these variations and polyspectra are needed. We have isolated variations in the 1/f frequency region of the spectrum and show that the distributions of the magnitudes have nonzero skewness and kurtosis, the magnitudes are not distributed lognormally, and the distributions of the components have nonzero kurtosis. Thus higher-order spectra are again needed for a full characterization.

Feynman, Joan↗

NASA NTRS2001

Considerations and Architectures for Inter-Satellite Communications in Distributed Spacecraft Systems

This paper will identify the important characteristics and requirements necessary for inter-satellite communications in distributed spacecraft systems and present analysis results focusing on architectural and protocol comparisons. Emerging spacecraft systems plan to deploy multiple satellites in various "distributed" configurations ranging from close proximity formation flying to widely separated constellations. Distributed spacecraft configurations provide advantages for science exploration and operations since many activities useful for missions may be better served by distributing them between spacecraft. For example, many scientific observations can be enhanced through spatially separated platforms, such as for deep space interferometry. operating multiple distributed spacecraft as a mission requires coordination that may be best provided through inter-satellite communications. For example, several future distributed spacecraft systems envision autonomous operations requiring relative navigational calculations and coordinated attitude and position corrections. To conduct these operations, data must be exchanged between spacecraft. Direct cross-links between satellites provides an efficient and practical method for transferring data and commands. Unlike existing "bent-pipe" relay networks supporting space missions, no standard or widely-used method exists for cross-link communications. Consequently, to support these future missions, the characteristics necessary for inter-satellite communications need to be examined. At first glance, all of the missions look extremely different. Some missions call for tens to hundreds of nano-satellites in constant communications in close proximity to each other. Other missions call for a handful of satellites communicating very slowly over thousands to hundreds of thousands of kilometers. The paper will first classify distributed spacecraft missions to help guide the evaluation and definition of cross-link architectures and approaches. Based on this general classification, the paper will examine general physical layer parameters, such as frequency bands and data rates, necessary to support the missions. The paper will also identify classes of communication architectures that may be employed, ranging from fully distributed to centralized topologies. Numerous factors, such as number of spacecraft, must be evaluated when attempting to pick a communications architecture. Also important is the stability of the formation from a communications standpoint. For example, do all of the spacecraft require equal bandwidth and are spacecraft allowed to enter and leave a formation? The type of science mission being attempted may also heavily influence the communications architecture. In addition, the paper will assess various parameters and characteristics typically associated with the data link layer. The paper will analyze the performance of various multiple access techniques given the operational scenario, requirements, and communication topologies envisioned for missions. This assessment will also include a survey of existing standards and their applicability for distributed spacecraft systems. An important consideration includes the interoperability of the lower layers (physical and data link) examined in this paper with the higher layer protocols(network) envisioned for future space internetworking. Finally, the paper will define a suggested path, including preliminary recommendations, for defining and developing a standard for intersatellite communications based on the classes of distributed spacecraft missions and analysis results.

Edwards, Bernard↗

NASA NTRS2003

Statistical Distribution of Inflation on Lava Flows: Analysis of Flow Surfaces on Earth and Mars

The surface morphology of a lava flow results from processes that take place during the emplacement of the flow. Certain types of features, such as tumuli, lava rises and lava rise pits, are indicators of flow inflation or endogenous growth of a lava flow. Tumuli in particular have been identified as possible indicators of tube location, indicating that their distribution on the surface of a lava flow is a junction of the internal pathways of lava present during flow emplacement. However, the distribution of tumuli on lava flows has not been examined in a statistically thorough manner. In order to more rigorously examine the distribution of tumuli on a lava flow, we examined a discrete flow lobe with numerous lava rises and tumuli on the 1969 - 1974 Mauna Ulu flow at Kilauea, Hawaii. The lobe is located in the distal portion of the flow below Holei Pali, which is characterized by hummocky pahoehoe flows emplaced from tubes. We chose this flow due to its discrete nature allowing complete mapping of surface morphologies, well-defined boundaries, well-constrained emplacement parameters, and known flow thicknesses. In addition, tube locations for this Mauna Ulu flow were mapped by Holcomb (1976) during flow emplacement. We also examine the distribution of tumuli on the distal portion of the hummocky Thrainsskjoldur flow field provided by Rossi and Gudmundsson (1996). Analysis of the Mauna Ulu and Thrainsskjoldur flow lobes and the availability of high-resolution MOC images motivated us to look for possible tumuli-dominated flow lobes on the surface of Mars. We identified a MOC image of a lava flow south of Elysium Mons with features morphologically similar to tumuli. The flow is characterized by raised elliptical to circular mounds, some with axial cracks, that are similar in size to the tumuli measured on Earth. One potential avenue of determining whether they are tumuli is to look at the spatial distribution to see if any patterns similar to those of tumuli-dominated terrestrial flows can be identified. Since tumuli form by the injection of lava beneath a crust, the distribution of tumuli on a flow should represent the distribution of thermally preferred pathways beneath the surface of the crust. That distribution of thermally preferred pathways may be a function of the evolution of a basaltic lava flow. As a longer-lived flow evolves, initially broad thermally preferred pathways would evolve to narrower, more well-defined tube-like pathways. The final flow morphology clearly preserves the growth of the flow over time, with inflation features indicating pathways that were not necessarily contemporaneously active. Here, we test using statistical analysis whether this final flow morphology produces distinct distributions that can be used to readily determine the distribution of thermally preferred pathways beneath the surface of the crust.

Glazel, L. S.↗

NASA NTRS2007

Managing Uncertainty Due to a Fundamental Error Source Arising from Scatterer Distribution Complexity in Radar Remote Sensing of Precipitation

The assumption that cloud and rain drops are spatially distributed according to a Poisson distribution within a scattering volume probed by a radar being used to estimate precipitation has represented bedrock theory in establishing 'rules of the game' for pulse averaging--the process needed to beat down noise to an acceptable level in the measurement of radar reflectivity factor. Based on relatively recent observations of 'realistic' spatial distributions of hydrometeor scatterers in a cloudy atmosphere motivates a renewed examination of the consequences of using a too simplified assumption underlying volume scattering--particularly in regards to the standard pulse averaging rule. Our investigation addresses two extremes, simple to complex, insofar as allowed for complexities in an underlying scatterer distribution. It is demonstrated that as the spatial distribution ranges from Poisson (a narrow distribution) to multi-fractal (much broader distribution), uncertainty in a measurement increases if the rule for pulse averaging goes unchanged from its Poisson distribution reference county. [A bounded cascade is used for the multi-fractal distribution, a regularly observed distribution vis-a-vis cloud liquid water content.] The resultant measurement uncertainty leads to a fundamental source of error in the estimation of rain rate from radar measurements, one that has been disregarded since the early 1950s when radar sets first began to be used for rainfall measuring. It is shown how this source of error can be 'managed'--under the assumption that number of data analysis experiments would be carried out, experiments involving pulse-by-pulse measurements obtained from a radar set modified to output individual pulses of reflectivity factor. For practical applications, a new parameter called normalized k-sample intensity invariance is developed to enable defining the required pulse average count according to a preferred degree of uncertainty.

Smith, Eric A.↗