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

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Eigenstate Entanglement: Crossover from the Ground State to Volume Laws

For the typical quantum many-body systems that obey the eigenstate thermalization hypothesis (ETH), we argue that the entanglement entropy of (almost) all energy eigenstates is described by a single crossover function. The ETH implies that the crossover functions can be deduced from subsystem entropies of thermal ensembles and have universal properties. These functions capture the full crossover from the ground-state entanglement regime at low energies and small subsystem size (area or log-area law) to the extensive volume-law regime at high energies or large subsystem size. For critical one-dimensional systems, a universal scaling function follows from conformal field theory and can be adapted for nonlinear dispersions. We use it to also deduce the crossover scaling function for Fermi liquids in d > 1 dimensions. Here, the analytical results are complemented by numerics for large noninteracting systems of fermions in d ≤ 3 dimensions and have also been confirmed for bosonic systems and nonintegrable spin chains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Scaling functions for eigenstate entanglement crossovers in harmonic lattices

For quantum matter, eigenstate entanglement entropies obey an area law or log-area law at low energies and small subsystem sizes and cross over to volume laws for high energies and large subsystems. This transition is captured by crossover functions, which assume a universal scaling form in quantum critical regimes. We demonstrate this for the harmonic lattice model, which describes quantized lattice vibrations and is a regularization for free scalar field theories, modeling, e.g., spin-0 bosonic particles. In one dimension, the ground-state entanglement obeys a log-area law. For dimensions d ≥ 2, it displays area laws, even at criticality. The distribution of excited-state entanglement entropies is found to be sharply peaked around subsystem entropies of corresponding thermodynamic ensembles in accordance with the eigenstate thermalization hypothesis. Numerically, we determine crossover scaling functions for the quantum critical regime of the model and do a large-deviation analysis. We show how infrared singularities of the system can be handled and how to access the thermodynamic limit using a perturbative trick for the covariance matrix. Eigenstates for quasi-free bosonic systems are not Gaussian. Here, we resolve this problem by considering appropriate squeezed states instead. For these, entanglement entropies can be evaluated efficiently.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Quantum criticality using a superconducting quantum processor

Quantum criticality emerges from the collective behavior of many interacting quantum particles, often at the transition between different phases of matter. It is one of the cornerstones of condensed matter physics, which we access on noisy intermediate-scale (NISQ) quantum devices by leveraging a dynamically driven phenomenon. Here we probe the critical properties of the one-dimensional quantum Ising model on a programmable superconducting quantum chip via a Kibble-Zurek process, obtain scaling laws, and estimate critical exponents despite inherent sources of errors on the hardware. In addition, we investigate how the improvement of NISQ computers (more qubits, less noise) will consolidate the computation of those universal physical properties. A one-parameter noise model captures the effect of imperfections and reproduces the experimental data. Its systematic study reveals that the noise, analogously to temperature, induces a new length scale in the system. We introduce and successfully verify modified scaling laws, directly accounting for the noise without any prior knowledge. It makes data analyses for extracting physical properties transparent to noise. By understanding how imperfect quantum hardware modifies the genuine properties of quantum states of matter, we enhance the power of NISQ processors considerably for addressing quantum criticality and potentially other phenomena and algorithms.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Collapse of the effective response time near the spin glass transition temperature

Kenning et al. discovered the collapse of the effective response time, 𝑡$^{eff}_{𝐻}$⁡(𝑡 w ;𝑇), independent of aging time, 𝑡 w , as one approached the spin glass transition temperature 𝑇 g from below. Nordblad and Lundgren observed the same effect by reducing the temperature from 𝑇 g ⁡(𝐻). We analyze the behavior of ln⁡ 𝑡$^{eff}_{𝐻}$⁡(𝑡 w ;𝑇) in the temperature range near and below 𝑇 g using a scaling law that takes into account both the magnetic field 𝐻 and the time-dependent spin-glass coherence length 𝜉⁡(𝑡,𝑡 w ;𝑇). As a result, an overdetermined predictive fit to the experimental data accounts for a quasioscillatory structure of ln ⁡𝑡$^{eff}_{𝐻}$⁡ (𝑡 w ;𝑇) as a function of magnetic field 𝐻 2 for reduced temperatures as large as 𝑇/𝑇 g = 0.98.

Frustrated magnetism↗
NASA NTRS2004

Network Theory: A Primer and Questions for Air Transportation Systems Applications

A new understanding (with potential applications to air transportation systems) has emerged in the past five years in the scientific field of networks. This development emerges in large part because we now have a new laboratory for developing theories about complex networks: The Internet. The premise of this new understanding is that most complex networks of interest, both of nature and of human contrivance, exhibit a fundamentally different behavior than thought for over two hundred years under classical graph theory. Classical theory held that networks exhibited random behavior, characterized by normal, (e.g., Gaussian or Poisson) degree distributions of the connectivity between nodes by links. The new understanding turns this idea on its head: networks of interest exhibit scale-free (or small world) degree distributions of connectivity, characterized by power law distributions. The implications of scale-free behavior for air transportation systems include the potential that some behaviors of complex system architectures might be analyzed through relatively simple approximations of local elements of the system. For air transportation applications, this presentation proposes a framework for constructing topologies (architectures) that represent the relationships between mobility, flight operations, aircraft requirements, and airspace capacity, and the related externalities in airspace procedures and architectures. The proposed architectures or topologies may serve as a framework for posing comparative and combinative analyses of performance, cost, security, environmental, and related metrics.

Holmes, Bruce J.↗
DOE OSTI2020

Interface learning of multiphysics and multiscale systems

Complex natural or engineered systems comprise multiple characteristic scales, multiple spatiotemporal domains, and even multiple physical closure laws. To address such challenges, we introduce an interface learning paradigm and put forth a data-driven closure approach based on memory embedding to provide physically correct boundary conditions at the interface. To enable the interface learning for hyperbolic systems by considering the domain of influence and wave structures into account, we put forth the concept of upwind learning toward a physics-informed domain decomposition. The promise of the proposed approach is shown for a set of canonical illustrative problems. Here, we highlight that high-performance computing environments can benefit from this methodology to reduce communication costs among processing units in emerging machine-learning-ready heterogeneous platforms toward exascale era.

42 ENGINEERING↗
DOE OSTI2021

How AI Predicts the Untrained and Unseen

Focus Area: Model predictability improvements (Primary); Data optimization (secondary); Data complexity insights (secondary). The Scientific Challenge: If we believe that a future under extreme conditions will look very differently from today, we can likely agree that ML/AI models trained on past and present datasets will not be adequate to make reliable predictions into the future. This is true for water cycling, as well as biogeochemistry and other Earth system components and behaviors. Additionally, ML/AI models are inherently non-physical. Despite the flourishing success of ML/AI in many applications, such as computer vision, natural language process, and gaming, even the most sophisticated AI models don’t understand the very basic physical laws. Therefore, a natural question is: Can we trust ML/AI based predictions of Earth system behaviors that are fundamentally driven by physical laws? So, are physics models with meticulous process representation a better choice? Not exactly. Physical models, when firmly rooted in first principles, work great at predicting behaviors of systems with a well-defined set of boundary conditions and variables. However, as a complex system, the number of parameters and the degree of complexity and dynamics in processes, coupling, and scale dependent emergent behaviors make the Earth system behaviors very challenging to predict with physical models composed of deterministic laws. In addition, due to the lack of fundamental understandings, physical models often implement empirical correlations derived from observations with biases from locality of data generation. Because correlation is not necessarily causation or comply with first principles, scaling of model predictions beyond locality is often invalid. Beyond the limitation of models, physics or AI, our knowledge of the Earth system is limited by the lack of observational technologies and resources. Insufficient data density, dimensionality and diversity only offer a sliced (or projected) view of the Earth system, e.g. Plato’s Cave analogy, limiting our capability to better understand and represent fundamental processes in models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Probing critical phenomena in open quantum systems using atom arrays

At continuous phase transitions, quantum many-body systems exhibit complex, emergent behavior. Most notably, at a quantum critical point, correlations decay as a power law, with exponents determined by a set of universal scaling dimensions. Experimentally probing such power law correlations is extremely challenging, owing to the interplay between decoherence, the vanishing energy gap, and boundary effects. In this work, we used a Rydberg quantum simulator to adiabatically prepare critical ground states of both a one-dimensional ring and a two-dimensional square lattice. By accounting for and tuning the openness of our quantum system, which is well-captured by a single phenomenological length scale, we directly observed power law correlations and extracted the corresponding scaling dimensions. Our work complements recent studies of quantum criticality that use the Kibble-Zurek mechanism and digital quantum circuits.

Fang, Fang [Harvard Univ., Cambridge, MA (United S↗
NASA NTRS2004

Renormalization Group Tutorial

Complex physical systems sometimes have statistical behavior characterized by power- law dependence on the parameters of the system and spatial variability with no particular characteristic scale as the parameters approach critical values. The renormalization group (RG) approach was developed in the fields of statistical mechanics and quantum field theory to derive quantitative predictions of such behavior in cases where conventional methods of analysis fail. Techniques based on these ideas have since been extended to treat problems in many different fields, and in particular, the behavior of turbulent fluids. This lecture will describe a relatively simple but nontrivial example of the RG approach applied to the diffusion of photons out of a stellar medium when the photons have wavelengths near that of an emission line of atoms in the medium.

Bell, Thomas L.↗
NASA NTRS1986

COFS 1: Beam dynamics and control technology overview

The Control of Flexible Structures (COFS) 1 Project provides the invaluable opportunity to test, validate, and measure the effectiveness of theories, structural concepts, control systems, and flight certification processes for future missions through a research program focusing on multiple issues in large flexible structures, dynamics, and controls. The COFS 1 Project consists of a series of ground and flight activities building progressively from modeling and dynamic characterization of large space systems to the more complex issues of flexible-body control. The program objectives are to: determine the degree to which theory and ground testing can predict flight performance of next-generation low-frequency structures; evaluate structural fidelity of representative next-generation large deployable precision structure; assess math modeling requirements for large lightweight complex systems on which ground test results are questionable; determine degree to which scale model analysis and tests can be correlated to full-scale performance; evaluate system identification and state estimation algorithms on complex lightweight structures in the space environment; evaluate and verify controls/structures modeling capability; evaluate control laws and control systems; and evaluate damping effects in micro-g environment.

Allen, John L.↗
NASA NTRS2011

Handling Qualities Evaluations of Low Complexity Model Reference Adaptive Controllers for Reduced Pitch and Roll Damping Scenarios

National Aeronautics and Space Administration (NASA) researchers have conducted a series of flight experiments designed to study the effects of varying levels of adaptive controller complexity on the performance and handling qualities of an aircraft under various simulated failure or damage conditions. A baseline, nonlinear dynamic inversion controller was augmented with three variations of a model reference adaptive control design. The simplest design consisted of a single adaptive parameter in each of the pitch and roll axes computed using a basic gradient-based update law. A second design was built upon the first by increasing the complexity of the update law. The third and most complex design added an additional adaptive parameter to each axis. Flight tests were conducted using NASA s Full-scale Advanced Systems Testbed, a highly modified F-18 aircraft that contains a research flight control system capable of housing advanced flight controls experiments. Each controller was evaluated against a suite of simulated failures and damage ranging from destabilization of the pitch and roll axes to significant coupling between the axes. Two pilots evaluated the three adaptive controllers as well as the non-adaptive baseline controller in a variety of dynamic maneuvers and precision flying tasks designed to uncover potential deficiencies in the handling qualities of the aircraft, and adverse interactions between the pilot and the adaptive controllers. The work was completed as part of the Integrated Resilient Aircraft Control Project under NASA s Aviation Safety Program.

Hanson, Curt↗
DOE OSTI2025

Accurate noncovalent interactions in atomistic systems via quantum Drude oscillators

Accurately modeling polarization and van der Waals (vdW) interactions in atomistic systems typically requires high-level quantum-mechanical methods that are computationally expensive, hence limited in applicability. To address this challenge, efficient yet physically grounded models are needed—ones that not only enable accurate predictions but also provide insight into how noncovalent interactions scale in complex molecular and material systems. This review highlights the quantum Drude oscillator (QDO) model, a physically motivated and computationally efficient framework that captures the essential features of electronic response, including polarization and dispersion forces, across a wide range of chemical and material systems. We discuss how the QDO model quantitatively reproduces the polarization response of many-electron atoms and how key components of noncovalent interactions—exchange-repulsion, polarization, and dispersion—emerge naturally in QDO dimers. Furthermore, the model provides predictive scaling laws that elucidate trends in polarizability and dispersion across the periodic table and in molecular assemblies. By uniting interpretability, accuracy, and efficiency, the QDO model offers a versatile approach for modeling noncovalent interactions in systems ranging from isolated molecules to complex condensed phases and nanostructured materials.

Khabibrakhmanov, Almaz [Univ. of Luxembourg, Luxem↗
DOE OSTI2023

Electron hopping heat transport in molecules

The realization of single-molecule thermal conductance measurements has driven the need for theoretical tools to describe conduction processes that occur over atomistic length scales. In macroscale systems, the principle that is typically used to understand thermal conductivity is Fourier’s law. At molecular length scales, however, deviations from Fourier’s law are common in part because microscale thermal transport properties typically depend on the complex interplay between multiple heat conduction mechanisms. Here, the thermal transport properties that arise from electron transfer across a thermal gradient in a molecular conduction junction are examined theoretically. We illustrate how transport in a model junction is affected by varying the electronic structure and length of the molecular bridge in the junction as well as the strength of the coupling between the bridge and its surrounding environment. Three findings are of note: First, the transport properties can vary significantly depending on the characteristics of the molecular bridge and its environment; second, the system’s thermal conductance commonly deviates from Fourier’s law; and third, in properly engineered systems, the magnitude of electron hopping thermal conductance is similar to what has been measured in single-molecule devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2012

Cosmic Complexity

What explains the extraordinary complexity of the observed universe, on all scales from quarks to the accelerating universe? My favorite explanation (which I certainty did not invent) ls that the fundamental laws of physics produce natural instability, energy flows, and chaos. Some call the result the Life Force, some note that the Earth is a living system itself (Gaia, a "tough bitch" according to Margulis), and some conclude that the observed complexity requires a supernatural explanation (of which we have many). But my dad was a statistician (of dairy cows) and he told me about cells and genes and evolution and chance when I was very small. So a scientist must look for me explanation of how nature's laws and statistics brought us into conscious existence. And how is that seemll"!gly Improbable events are actually happening a!1 the time? Well, the physicists have countless examples of natural instability, in which energy is released to power change from simplicity to complexity. One of the most common to see is that cooling water vapor below the freezing point produces snowflakes, no two alike, and all complex and beautiful. We see it often so we are not amazed. But physlc!sts have observed so many kinds of these changes from one structure to another (we call them phase transitions) that the Nobel Prize in 1992 could be awarded for understanding the mathematics of their common features. Now for a few examples of how the laws of nature produce the instabilities that lead to our own existence. First, the Big Bang (what an insufficient name!) apparently came from an instability, in which the "false vacuum" eventually decayed into the ordinary vacuum we have today, plus the most fundamental particles we know, the quarks and leptons. So the universe as a whole started with an instability. Then, a great expansion and cooling happened, and the loose quarks, finding themselves unstable too, bound themselves together into today's less elementary particles like protons and neutrons, liberating a little energy and creating complexity. Then, the expanding universe cooled some more, and neutrons and protons, no longer kept apart by immense temperatures, found themselves unstable and formed helium nuclei. Then, a little more cooling, and atomic nuclei and electrons were no longer kept apart, and the universe became transparent. Then a little more cooling, and the next instability began: gravitation pulled matter together across cosmic distances to form stars and galaxies. This instability is described as a "negative heat capadty" in which extracting energy from a gravitating system makes it hotter -- clearly the 2nd law of thermodynamics does not apply here! (This is the physicist's part of the answer to e e cummings' question: what is the wonder that's keeping the stars apart?) Then, the next instability is that hydrogen and helium nuclei can fuse together to release energy and make stars burn for billions of years. And then at the end of the fuel source, stars become unstable and explode and liberate the chemical elements back into space. And because of that, on planets like Earth, sustained energy flows support the development of additional instabilities and all kinds of complex patterns. Gravitational instability pulls the densest materials into the core of the Earth, leaving a thin skin of water and air, and makes the interior churn incessantly as heat flows outwards. And the heat from the sun, received mostly near the equator and flowing towards the poles, supports the complex atmospheric and oceanic circulations. And because or that, the physical Earth is full of natural chemical laboratories, concentrating elements here, mixing them there, raising and lowering temperatures, ceaselessly experimenting with uncountable events where new instabilities can arise. At least one of them was the new experiment called life. Now that we know that there are at least as many planets as there are stars, it is hard to imagine that nature's ceasess experimentation would not be able to produce life elsewhere -- but we don't know for sure. And life went on to cause new Instabilities, constantly evolving, with living things in an extraordinary range of environments, changing the global environment, with boom-and-bust cycles. with predators for every kInd of prey, with criminals for every possible crime, with governments to prevent them, and instabilities of the governments themselves. One of the instabilities Is that humans demand new weapons and new products of all sort, leading to serious investments in science and technology. So the natural/human world of competition and combat is structured to lead to advanced weaponry and cell phones. So here we are In 2012, with people writing essays and wondering whether their descendents will be artificial life forms travelling back into space. And, pondering what are the origins of those forces of nature that give rise to everything. Verllnde has argued that gravitation, the one force that has so far resisted our efforts at a Quantum description, is not even a fundamental force, but is itself it a statistical force, like osmosis. What an amazing turn of events! But after all I've just said, I should not be surprised a bit.

Mather, John C.↗
NASA NTRS1989

Integrated control-system design via generalized LQG (GLQG) theory

Thirty years of control systems research has produced an enormous body of theoretical results in feedback synthesis. Yet such results see relatively little practical application, and there remains an unsettling gap between classical single-loop techniques (Nyquist, Bode, root locus, pole placement) and modern multivariable approaches (LQG and H infinity theory). Large scale, complex systems, such as high performance aircraft and flexible space structures, now demand efficient, reliable design of multivariable feedback controllers which optimally tradeoff performance against modeling accuracy, bandwidth, sensor noise, actuator power, and control law complexity. A methodology is described which encompasses numerous practical design constraints within a single unified formulation. The approach, which is based upon coupled systems or modified Riccati and Lyapunov equations, encompasses time-domain linear-quadratic-Gaussian theory and frequency-domain H theory, as well as classical objectives such as gain and phase margin via the Nyquist circle criterion. In addition, this approach encompasses the optimal projection approach to reduced-order controller design. The current status of the overall theory will be reviewed including both continuous-time and discrete-time (sampled-data) formulations.

Bernstein, Dennis S.↗
NASA NTRS1995

Fractal mechanisms and heart rate dynamics. Long-range correlations and their breakdown with disease

Under healthy conditions, the normal cardiac (sinus) interbeat interval fluctuates in a complex manner. Quantitative analysis using techniques adapted from statistical physics reveals the presence of long-range power-law correlations extending over thousands of heartbeats. This scale-invariant (fractal) behavior suggests that the regulatory system generating these fluctuations is operating far from equilibrium. In contrast, it is found that for subjects at high risk of sudden death (e.g., congestive heart failure patients), these long-range correlations break down. Application of fractal scaling analysis and related techniques provides new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as motivating development of novel physiologic models of systems that appear to be heterodynamic rather than homeostatic.

NASA Discipline Cardiopulmonary↗
NASA NTRS1986

Piloted simulation study of the effects of an automated trim system on flight characteristics of a light twin-engine airplane with one engine inoperative

A simulation study was conducted to investigate the piloting problems associated with failure of an engine on a generic light twin-engine airplane. A primary piloting problem for a light twin-engine airplane after an engine failure is maintaining precise control of the airplane in the presence of large steady control forces. To address this problem, a simulated automatic trim system which drives the trim tabs as an open-loop function of propeller slipstream measurements was developed. The simulated automatic trim system was found to greatly increase the controllability in asymmetric powered flight without having to resort to complex control laws or an irreversible control system. However, the trim-tab control rates needed to produce the dramatic increase in controllability may require special design consideration for automatic trim system failures. Limited measurements obtained in full-scale flight tests confirmed the fundamental validity of the proposed control law.

Stewart, E. C.↗
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↗