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At least 1,639 records · Page 91
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

235-F GoldSim Fate and Transport Model: Uncertainty Quantification

Building 235-F was configured with two missions in mind: Actinide Billet Line (ABL) and the fabrication of Pu-238 oxide for space program applications. ABL produced Np-237 billets for use in SRS reactors, whereas the design process, fabrication, and examination of Pu-238 oxide powder occurred within the following areas, respectively: Plutonium Experimental Facility (PEF), Plutonium Fuel Form (PuFF), and Old Metallography Lab (OML). By 1990 production ceased and by 2006 de-inventory occurred; however, assays have shown significant holdup remains within ABL and PuFF. As a result, 235-F is a Category 2 nuclear facility, with plans to undergo deactivation and decommission (D and D) via In-Situ Disposal (ISD). The purpose of this project is to ensure United States Environmental Protection Agency (USEPA) groundwater radiation maximum contaminant level (MCL) and dosage standards are met during the D and D of 235-F by quantifying uncertainty through probabilistic modeling and evaluation of various ISD alternatives. GoldSim is a dynamic modeling software package with a graphical, object-oriented interface capable of capturing the influence of complex system input variability on probabilistic system outcomes. A GoldSim stochastic fate and transport model for 235-F was developed and matched with a PORFLOW deterministic model to simulate probabilistic release and flow of radionuclides from ABL and PuFF into the vadose zone, the Upper Three Runs (UTR) Aquifer, and UTR Creek. The GoldSim model was used to probabilistically evaluate four ISD scenarios against USEPA groundwater radiation MCLs and dosage standards. The deterministic 235-F GoldSim fate and transport model continues to be refined to match the results of the PORFLOW deterministic model to ensure the model accurately represents radionuclide movement through the groundwater system. The stochastic variables that are utilized within the GoldSim model are founded on the most current data; a conservative perspective is taken where needed. Alignment with the PORFLOW deterministic model, coupled with input stochastic variability, allows the probabilistic 235-F GoldSim model to capture the conservative breadth of possible outcomes for radionuclide fate within this particular system. This ensures that the USEPA MCLs and dosage limits hold even in the worst case scenarios.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

On the characterization of biases arising from methods and approximations used for sensitivity analyses

The preliminary assessment of the performance and safety of advanced reactors, as well as the identification of research and development needs, rely on computer simulations due to the lack of operational experience. Those simulations should be based on verified and validated computational tools, calculation schemes, and nuclear data libraries, and should be accompanied of a proper characterization of the involved uncertainties, providing confidence in the computational-based predictions. Thus, sensitivity and uncertainty studies, together with integral experiments, play an essential role in that process. Sensitivities are then a critical element and guidelines about how to produce accurate enough sensitivities depending on the subsequent analyses to be performed are of interest. The present study addresses the sensitivities biases arising from the use of different nuclear data libraries, computational methods and the assumption of modelling simplifications. Not only sensitivities for multiplication factor but also for safety-relevant reactivity responses have been analyzed. In the study, propagated uncertainties are also included for the considered parameters to illustrate the impact of the sensitivity profiles obtained for each case on the final uncertainty. Then, relevant recommendations are given for sensitivity analyses of highly complex systems. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Deep Learning with Physics Priors as Generalized Regularizers

In various scientific and engineering applications, there is typically an approximate model of the underlying complex system, even though it contains both aleatoric and epistemic uncertainties. In this paper, we present a principled method to incorporate these approximate models as physics priors in modeling, to prevent overfitting and enhancing the generalization capabilities of the trained models. Utilizing the structural risk minimization (SRM) inductive principle pioneered by Vapnik, this approach structures the physics priors into generalized regularizers. The experimental results demonstrate that our method achieves up to two orders of magnitude of improvement in testing accuracy.

Liu, Frank↗
DOE OSTI2024

Distributed Multi-GPU Community Detection on Exascale Computing Platforms

Community detection is a fundamental operation in graph mining, and by uncovering hidden structures and patterns within complex systems it helps solve fundamental problems pertaining to social networks, such as information diffusion, epidemics, and recommender systems. Scaling graph algorithms for massive networks becomes challenging on modern distributed-memory multi-GPU (Graphics Processing Unit) systems due to limitations such as irregular memory access patterns, load imbalances, higher communication-computation ratios, and cross-platform support. We present a novel algorithm HiPDPL-GPU (Distributed Parallel Louvain) to address these challenges. We conduct experiments involving different partitioning techniques to achieve an optimized performance of HiPDPL-GPU on the two largest supercomputers: Frontier and Summit. Remarkably, HiPDPL-GPU processes a graph with 4.2 billion edges in less than 3 minutes using 1024 GPUs. Qualitatively, the performance of HiPDPL-GPU is similar or better compared to other state-of-the-art CPU- and GPU-based implementations. While prior GPU implementations have predominantly employed CUDA, our first-of-its-kind implementation for community detection is cross-platform, accommodating both AMD and NVIDIA GPUs.

Sattar, Naw Safrin↗
DOE OSTI2026

Optimizing Heat Recovery with Storage: Control Validation and Sensitivity Analysis of the Time-Independent Energy Recovery Plant Using Modelica

Heat recovery in large building central plants saves energy but traditionally requires simultaneous heating and cooling. The Time-Independent Energy Recovery (TIER) plant shifts this paradigm by integrating thermal energy storage (TES) to enable heat recovery regardless of concurrent demand, offering a highly efficient, space-saving solution to achieve California’s energy goals. However, its integration of heat recovery chillers, cooling-only chillers, cooling towers, and trim air-source heat pumps (ASHPs) creates growing control and sizing complexity. To overcome this, this study employs high-fidelity Modelica dynamic simulation to validate TIER control sequences and optimize equipment sizing. We translated the written Sequences of Operation into executable Control Description Language (CDL) to test logic against sub-hourly loads. This verification workflow successfully identified and resolved critical vulnerabilities, such as thermal storage freezing and equipment short-cycling, in a virtual environment prior to physical deployment. Then, the study analyzes TIER plant performance across three simulated building types in three locations, and a real building load profile, ensuring variety in heating and cooling loads, and simultaneity factors and explores sizing rules for the TES and ASHP capacity. The analysis shows that the TIER plant operates equipment efficiently leading to a plant SCOP of around 7.5 across all scenarios, higher than a traditional ASHP plant, and a viable pathway to de-risk complex system design and control through simulation to identify optimal designs that maximize energy efficiency, minimize operational costs, and ensure robust operation in varied environmental conditions, thereby facilitating the broader adoption of such a solution for large buildings.

Zanetti, Ettore↗
NASA NTRSDate not supplied

Toward an IMU-based Space Suit Motion Capture System

Spacesuits are complex engineering systems that sustain human health and enable performance outside of Earth-like environments. These systems must support human mobility and physical workload demands while minimizing injury risk during extravehicular activity (EVA). Future EVA on the lunar surface during the Artemis program is expected to be more frequent and require higher physical workloads than previous EVAs during the ISS, Shuttle, or Apollo programs. Hence it is important to optimize future as well as current spacesuits to be efficient and comfortable for the success of space and planetary missions. To enable this, an efficient method is needed to test these spacesuits on the ground.When testing spacesuits in ground environments, it is often necessary to understand the kinematics of the suit to validate the design against relevant requirements or characterize the physical workload necessary to operate the suit. This is a challenging task for traditional optical motion capture (OMC) approaches: suit-mounted OMC markers are easily occluded by the subject or environment and may become detached during testing. Controlling lighting and reflectivity of objects in the motion capture volume is also difficult. Fixed-position OMC cameras also constrain testing to a small and contrived laboratory environment, disallowing kinematics capture in field environments.One promising alternative is the use of suit-mounted inertial measurement units (IMUs). These sensors are small, unobtrusive, and portable, but come at the cost of increased sensor noise and complexity of the software and mathematics to analyze the collected data. To this end, engineers at NASA are developing the Augmented Suit Inverse Kinematics (ASIK) system, a complete motion capture methodand inverse kinematics solver which relies solely on a network of wireless IMUs attached to the major kinematic segments of the spacesuit. The ASIK modeling language allows for the simple inclusion of probabilistic priors such as suit size and shape or IMU positions and rotations. Furthermore, to increase accuracy and reduce operational overhead to use this motion capture approach, the developed inverse kinematics solver exploits so-called self-calibratingalgorithmic techniques, which reduce the need for precise alignment of the sensors on the segments or scripted functional calibration procedures. The ASIK system was tested in a 7-subject pilot study. Each subject donned NASA’s new prototype exploration spacesuit in the Active Response Gravity Offload System (ARGOS) facility at the NASA Johnson Space Center. The subjects were outfitted with a set of 14 APDM (Portland, OR, USA) Opal IMUs, 12 of which were used in the ASIK model to estimate lower body and trunk kinematics. The subjects were also outfitted with a set of reflective OMC markers and traditional OMC data was collected and processed. Presented results will include characterization of ASIK-derived suit joint angles accuracy against an optical motion capture datum. Discussion of these results, as well as discussion of system calibration and nuances of mathematical observability, will be included.If successful, IMU-based motion capture will enable testing and validation of spacesuits more frequently, with less overhead, in more extreme environments. Future work will apply these techniques to common spacesuit testing tasks, such as gait, mobility, and balance assessment, physical workload characterization, and ergonomics evaluations.

Timothy Mcgrath↗
NASA NTRS1990

GRID2D/3D: A computer program for generating grid systems in complex-shaped two- and three-dimensional spatial domains. Part 1: Theory and method

An efficient computer program, called GRID2D/3D was developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2- and 3-D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation in which the distribution of grid points within the spatial domain is controlled by stretching functions. All single grid systems generated by GRID2D/3D can have grid lines that are continuous and differentiable everywhere up to the second-order. Also, grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For continuous composite grid systems, the grid lines are continuous and differentiable everywhere up to the second-order except at interfaces where different single grid systems meet. At interfaces where different single grid systems meet, the grid lines are only differentiable up to the first-order. For 2-D spatial domains, the boundary curves are described by using either cubic or tension spline interpolation. For 3-D spatial domains, the boundary surfaces are described by using either linear Coon's interpolation, bi-hyperbolic spline interpolation, or a new technique referred to as 3-D bi-directional Hermite interpolation. Since grid systems generated by algebraic methods can have grid lines that overlap one another, GRID2D/3D contains a graphics package for evaluating the grid systems generated. With the graphics package, the user can generate grid systems in an interactive manner with the grid generation part of GRID2D/3D. GRID2D/3D is written in FORTRAN 77 and can be run on any IBM PC, XT, or AT compatible computer. In order to use GRID2D/3D on workstations or mainframe computers, some minor modifications must be made in the graphics part of the program; no modifications are needed in the grid generation part of the program. This technical memorandum describes the theory and method used in GRID2D/3D.

Shih, T. I.-P.↗
DOE OSTI2025

Physics and Components syntax to enable a systems-based approach to multiphysics

Simulations in MOOSE have traditionally used kernel and boundary condition classes to describe the equations. Downstream applications leveraged a system called Actions to define a pre-packaged discretization of the equations they solve. Unfortunately, the Action base class was very limited, and most applications implemented the same concepts in their Actions. This led to an increased maintenance burden and a reduction in coupling opportunities, save for the use of MultiApps which renders each input mostly independent. With the introduction of multi-system capabilities in MOOSE, there is growing interest in defining entire simulations of complex multiphysics systems in a single input file. By introducing a new Physics system, with its dedicated syntax and a new base class providing wide-ranging capabilities, we are now able to define multiple equations in a single input file in a compact and user-friendly way. With new interactions between Physics and the Component system, these equations can be defined on each component of a complex system. In this talk, we will present the capabilities of these new systems, their interactions, and how to define complex systems multiphysics simulations with Physics and Components.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1995

An unstructured-grid software system for solving complex aerodynamic problems

A coordinated effort has been underway over the past four years to elevate unstructured-grid methodology to a mature level. The goal of this endeavor is to provide a validated capability to non-expert users for performing rapid aerodynamic analysis and design of complex configurations. The Euler component of the system is well developed, and is impacting a broad spectrum of engineering needs with capabilities such as rapid grid generation and inviscid flow analysis, inverse design, interactive boundary layers, and propulsion effects. Progress is also being made in the more tenuous Navier-Stokes component of the system. A robust grid generator is under development for constructing quality thin-layer tetrahedral grids, along with a companion Navier-Stokes flow solver. This paper presents an overview of this effort, along with a perspective on the present and future status of the methodology.

Frink, Neal T.↗
NASA NTRSDate not supplied

Toward an IMU-Based Space Suit Motion Capture System

Spacesuits are complex engineering systems that sustain human health and enable performance outside Earth-like environments. These systems must support human mobility and physical workload demands while minimizing injury risk during extravehicular activity (EVA). Future EVA operations on the Lunar surface are expected to be more frequent and require higher physical workloads than previously during the ISS, Shuttle, and Apollo programs. To characterize the workloads and ergonomics needs a suit must support, the kinematics of the space suit must be measured during operationally-relevant tasks in ground analog environments. Kinematics capture of the suit is challenging for traditional optical motion capture (OMC) approaches due to marker occlusion, harsh lighting or environmental conditions, and tests with suit surrogates in outdoor field environments. To this end, engineers at NASA are developing the Augmented Suit Inverse Kinematics (ASIK) system, a complete motion capture method and inverse kinematics solver which relies solely on a network of wireless inertial measurement units (IMUs) attached to the major kinematic segments of the spacesuit. The ASIK modeling language allows for the simple inclusion of probabilistic priors such as suit size and shape or IMU poses. The ASIK system was tested in a 7-subject pilot study. Each subject donned NASA’s new prototype exploration spacesuit in the Active Response Gravity Offload System (ARGOS) facility at Johnson Space Center in Houston, TX. The suits were outfitted with 12 IMUs to estimate lower body and trunk kinematics. The suits were also outfitted with a set of reflective OMC markers, and traditional OMC data was collected and processed. Characterization of the ASIK-derived suit joint angles’ accuracy against an optical motion capture datum will be presented. Discussion of these results, as well as discussion of system calibration and nuances of mathematical observability, will be included.

IMU↗
NASA NTRS1995

Mode Transitions in Glass Cockpit Aircraft: Results of a Field Study

One consequence of increased levels of automation in complex control systems is the presence of modes. A mode is a particular configuration of a control system that defines how human command inputs are interpreted. In complex systems, modes also often determine a specific allocation of control authority between the human and automated systems. Even in simple static devices (e.g., electronic watches, word processors), the presence of modes has been found to cause problems in either-the acquisition or production of skilled performance. Many of these problems arise due to the fact that the selection of a mode causes device behavior to be mediated by hidden internal state information. For these simple systems, many of these interaction problems can be solved by the design of appropriate feedback to communicate internal state information to the human operator. In complex dynamic systems, however, the design issues associated with modes seem to trancend the problem of merely communicating internal state information via displayed feedback. In complex supervisory control systems (e.g., aircraft, spacecraft, military command and control), a key function of modes is the selection of a particular configuration of control authority between the human operator and automated control systems. One mode may result in full manual control, another may result in a mix of manual and automatic control, while a third may result in full automatic control over the entire system. The human operator selects an appropriate mode as a function of current goals, operating conditions, and operating procedures. Thus, the operator is put in a position of essentially trying to control two coupled dynamic systems: the target system itself, and also a highly complex suite of automation controlling the target system. From a historical perspective, it should probably not come as a surprise that very little information is available to guide the design of mode-oriented control systems. The topic of function allocation (i.e., the proper division of control authority among human and computer) has a long history in human-machine systems research. Although this research has produced some relevant guidelines, a design approach capable of defining appropriate allocations of control function between the human and automation is not yet available. As a result, the function allocation decision itself has been allocated to the operator, to be performed in real-time, in the operation of mode-oriented control systems. A variety of documented aircraft accidents and incidents suggest that the real-time selection and monitoring of control modes is a weak link in the effective operation of complex supervisory control systems. Research in human-machine systems and human-computer interaction has barely scraped the surface of the problem of understanding how operators manage this task.The purpose of this paper is to present the results of a field study which examined how operators manage mode selection in a complex supervisory control system. Data on mode engagements using the Boeing B757/767 auto-flight system were collected during approach and descent into four major airports in the East Coast of the United States. Protocols documenting mode selection, automatic mode changes, pilot actions, quantitative records of flight-path variables, and verbal reports during and after mode engagements were collected by an observer from the jumpseat. Observations were conducted on two typical trips between three airports. Each trip was be replicated 11 times, which yielded a total of 22 trips and 66 legs on which data were collected. All data collected concerned the same flight numbers, and therefore, the same time of day, same type of aircraft, and identical operational environments (e.g., ATC facilities, weather patterns, traffic flow etc.)

Degani, Asaf↗
NASA NTRS1990

GRID2D/3D: A computer program for generating grid systems in complex-shaped two- and three-dimensional spatial domains. Part 2: User's manual and program listing

An efficient computer program, called GRID2D/3D, was developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2- and 3-D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation in which the distribution of grid points within the spatial domain is controlled by stretching functions. All single grid systems generated by GRID2D/3D can have grid lines that are continuous and differentiable everywhere up to the second-order. Also, grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For continuous composite grid systems, the grid lines are continuous and differentiable everywhere up to the second-order except at interfaces where different single grid systems meet. At interfaces where different single grid systems meet, the grid lines are only differentiable up to the first-order. For 2-D spatial domains, the boundary curves are described by using either cubic or tension spline interpolation. For 3-D spatial domains, the boundary surfaces are described by using either linear Coon's interpolation, bi-hyperbolic spline interpolation, or a new technique referred to as 3-D bi-directional Hermite interpolation. Since grid systems generated by algebraic methods can have grid lines that overlap one another, GRID2D/3D contains a graphics package for evaluating the grid systems generated. With the graphics package, the user can generate grid systems in an interactive manner with the grid generation part of GRID2D/3D. GRID2D/3D is written in FORTRAN 77 and can be run on any IBM PC, XT, or AT compatible computer. In order to use GRID2D/3D on workstations or mainframe computers, some minor modifications must be made in the graphics part of the program; no modifications are needed in the grid generation part of the program. The theory and method used in GRID2D/3D is described.

Bailey, R. T.↗
DOE OSTI2023

Bi-fidelity modeling of uncertain and partially unknown systems using DeepONets

Recent advances in modeling large-scale, complex physical systems have shifted research focuses towards data-driven techniques. However, generating datasets by simulating complex systems can require significant computational resources. Similarly, acquiring experimental datasets can prove difficult. For these systems, often computationally inexpensive, but in general inaccurate models, known as the low-fidelity models, are available. Here in this paper, we propose a bi-fidelity modeling approach for complex physical systems, where we model the discrepancy between the true system's response and a low-fidelity response in the presence of a small training dataset from the true system's response using a deep operator network, a neural network architecture suitable for approximating nonlinear operators. We apply the approach to systems that have parametric uncertainty and are partially unknown. Three numerical examples are used to show the efficacy of the proposed approach to model uncertain and partially unknown physical systems.

MATHEMATICS AND COMPUTING↗
NASA NTRS2013

Dynamics and Control of a Disordered System in Space

In this paper, we present some ideas regarding the modeling, dynamics and control aspects of granular spacecraft. Granular spacecraft are complex multibody systems composed of a spatially disordered distribution of a large number of elements, for instance a cloud of N grains in orbit, with N greater than 10(exp 3). These grains can be large (Cubesat-size) or small (mm-size), and can be active, i.e., a fully equipped vehicle capable sensing their own position and attitude, and enabled with propulsion means, or entirely passive. The ultimate objective would be to study the behavior of the single grains and of large ensembles of grains in orbit and to identify ways to guide and control the shape of a cloud composed of these grains so that it can perform a useful function in space, for instance, as an element of an optical imaging system for astrophysical applications. This concept, in which the aperture does not need to be continuous and monolithic, would increase the aperture size several times compared to large NASA observatories such as ATLAST, allowing for a true Terrestrial Planet Imager that would be able to resolve exo-planet details and do meaningful spectroscopy on distant world. In the paper, we address the modeling and autonomous operation of a distributed assembly (the cloud) of large numbers of highly miniaturized space-borne elements (the grains). A multi-scale, multi-physics model is proposed of the dynamics of the cloud in orbit, as well as a control law for cloud shape maintenance, and preliminary simulation studies yield an estimate of the computational effort, indicating a scale factor of approximately N(exp 1.4) as a function of the number of grains. A granular spacecraft can be defined as a collection of a large number of space-borne elements (in the 1000s) designed and controlled such that a desirable collective behavior emerges, either from the interactions among neighboring grains, and/or between the grains and the environment. In this paper, each grain is considered to be a highly miniaturized spacecraft which has limited size and mass, hence it has limited actuation, limited propulsive capability, limited power, limited sensing, limited communication, limited computational resources, limited range of motion, limited lifetime, and may be expendable. The modeling and dynamics of clouds of vehicles is more challenging than with conventional vehicles because we are faced with a probabilistic vehicle composed of a large number of physically disconnected vehicles. First, different scales of motion occur simultaneously in a cloud: translations and rotations of the cloud as a whole (macro-dynamics), relative rotation and translation of one cloud member with respect to another (meso-dynamics), and individual cloud member dynamics (micro-dynamics). Second, the control design needs to be tolerant of the system complexity, of the system architecture (centralized vs. decentralized large scale system control) as well as robust to un-modeled dynamics and noise sources. Figure 1, top left, shows the kinematic parameters of a 1000 element cloud in orbit. The motion of the system is described with respect to a local vertical-local horizontal (LV-LH) orbiting reference frame (x,y,z)=F(sub ORF) of origin O(sub ORF) which rotates with mean motion omega and orbital semi-major axis R(sub 0). The orbital geometry at the initial time is defined in terms of its six orbital elements, and the orbital dynamics equation for point O(sub ORF) is propagated forward in time under the influence of the gravitational field of the primary and other external perturbations, described below. The origin of this frame coincides with the initial position of the center of mass of the system, and the coordinate axes are z along the local vertical, x toward the flight direction, and y in the orbit normal direction. The assumptions we used to model the dynamics are as follows: 1) The inertial frame is fixed at Earth's center. 2) The orbiting Frame ORF follows Keplerian orbit. 3) the cloud system dynamics is referred to ORF. 4) the attitude of each grain uses the principal body frame as body fixed frame. 5) the atmosphere is assumed to be rigidly rotating with the Earth. Regarding the grains forming the cloud: 1) each grain is modeled as a rigid body; 2) a simple attitude estimator provides attitude estimates, 3) a simple guidance logic commands the position and attitude of each grain, 4) a simple local feedback controller based on PD control of local states is used to stabilize the attitude of the vehicle. Regarding the cloud: 1) the cloud as a whole is modeled as an equivalent rigid body in orbit, and 2) an associated graph establishes agent connectivity and enables coupling between modes of motion at the micro and macro scales; 3) a simple guidance and estimation logic is modeled to estimate and command the attitude of this equivalent rigid body; 4) a cloud shape maintenance controller is based on the dynamics of a stable virtual truss in the orbiting frame. Regarding the environmental perturbations acting on the cloud: 1) a non-spherical gravity field including JO (Earth's spherical field) zonal component, J2 (Earth's oblateness) and J3 zonal components is implemented; 2) atmospheric drag is modeled with an exponential model; 3) solar pressure is modeled assuming the Sun is inertially fixed; and 4) the Earth's magnetic field is model using an equivalent dipole model. The equations of motion are written in a referential system with respect to the origin of the orbiting frame and the state is propagated forward in time using an incremental predictor-corrector scheme. A representative cloud with varying number of grains is simulated to identify the limitations in computation time as the number of grains grows. We derive a control law to track a desired surface in the ORF (equivalently to maintain a reference cloud shape) by defining an error from a desired surface shape, and designing a control law that is exponentially stable and reduces the tracking error to zero. Figure 1 (top right) shows a comparison of various requirements for simulation of single spacecraft vs. granular spacecraft, indicating the high degree of complexity that needs to be taken into consideration. The ORF components of control force required by one of the grains is, for this particular case, in the micro-Newton range. However, no attempt has been made yet to reconfigure (or re-orient) the cloud configuration internally, for which forces in the milli-Newton level are expected, depending on the time required to do the reconfiguration. Figure 1, bottom, shows the computation time as a function of the number of grains, indicating an order N(exp 1.43) scaling on a 8 Gb, 1067 MHz RAM MacOSX computer with a 3.06 GHz Intel Core 2 Duo processor. With this metric, the same simulation for a system of N=1000 grains would take 5.4 hours, and 146 hours (i.e., 6 days) for a system with N=10,000 grains. Therefore, efficient ways to simulate this complex system, where not only the time scales of natural system dynamics, but also the sampling times of the Guidance, Navigation, and Control are included, remain to be explored. Additional details on the cloud modeling, dynamics, and control will be described in the paper.

simulation↗