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NASA NTRS2006

Considerations for Isochronous Data Services over the Proximity-1 Space Link

Future mission concepts for robotic and human explorations will involve a high level of real time control/monitoring operations such as tele-operation for spacecraft rendezvous and surface mobile platforms carrying life-support equipments. The timely dissemination of voice, command, and real-time telemetry for monitoring and coordination purposes is critical for mission success. It is envisioned that future missions will require a network infrastructure capable of supporting isochronous data services. The CCSDS Proximity-1 Space Link Protocol1 could be used to provide isochronous service over the surface-to-Earth relay as well as "beyond-the-horizon" communications between distant Lunar or Mars surface elements. This paper will analyze the latency, jitter, and throughput performance of the Proximity-1 protocol for isochronous applications. In particular we will focus on constrained scenarios where the protocol operates in full-duplex mode, carrying isochronous traffic in one direction and error-controlled traffic in the other direction. We analyze the impact of the strict priority scheme in Proximity-1 on delay jitter and the impact of the isochronous traffic on the efficiency of the reliable data transfer in the other direction, and discuss methods for performance optimization. In general, jitter performance is driving by relative loading of isochronous traffic on the forward link compared to the acknowledgement traffic. Under light loading condition, the upper-bound of the delay jitter is the transmission duration of an acknowledgement frame on the forward link; for higher loading scenarios, the maximum jitter is scaled up by the inverse of the residual bandwidth, i.e., the spare capacity available in the forward link to carry isochronous traffic.

isochronous communications↗

DOE OSTI2023

Complete quantification of parametric uncertainties in ( d , p ) transfer reactions

Deuteron-induced transfer reactions are a popular probe in nuclear structure and nuclear astro physics studies. The interpretation of these transfer measurements relies on reaction theory that takes as input effective interactions between the nucleons and the target nucleus. Previous work quantified the uncertainty associated with the optical potentials between the nucleons and the target. In this study, we extend that work by also including the parameters of the mean field associated with the overlap function of the final bound state, thus obtaining the full parametric uncertainty on transfer observables. We use Bayesian Markov Chain Monte Carlo simulations to obtain parameter posterior distributions. We use elastic-scattering cross sections to constrain the optical potential parameters and use the asymptotic normalization coefficient of the final state to constrain the bound state interaction. We then propagate these posteriors to the transfer angular distributions and obtain confidence intervals for this observable. We study (d,p) reactions on 14 C, 16 O, and 48 Ca at energies in the range $E$ $d$ = 7 - 24 MeV. Our results show a strong reduction in uncertainty by using the asymptotic normalization coefficient as a constraint, particularly for those reactions most sensitive to ambiguities in the mean field. For those reactions, the importance of constraining the bound state interaction is equal to that of constraining the optical potentials. Furthermore, the case of 14 C is an outlier because the cross section is less sensitive to the nuclear interior. When minimal constraints are used on the parameters of the nucleon-target interaction, the 1σ uncertainties on the differential cross sections are large (~ 500-100%). However, if elastic-scattering data and the asymptotic normalization coefficient are used in the analysis, with an error of 10% (5%), this uncertainty reduces to ~ 30% (~ 15%).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1981

Theory and implementation of a fast algorithm linear equalizer

The theory and implementation of a multiplication-free linear mean-square error criterion equalizer for data transmission are considered. For many real-time signal processing situations, a large number of multiplications is objectionable. The linear estimation problem on a binary computer is considered where the estimation parameters are constrained to be powers of two and thus all multiplications are replaced by shifts. The optimal solution is obtained from an integer-programming-like problem except that the allowable discrete points are non-integers. The branch-and-bound algorithm is used to obtain the coefficients of the equalization TDL. Specific experimental performance results are given for an equalizer implemented with a 12 bit A/D device and a 8080 microprocessor.

Yan, T. Y.↗

DOE OSTI2024

Capturing CO 2 in Quadrupolar Binding Pockets: Broadband Microwave Spectroscopy of Pyrimidine-(CO 2 ) n , n = 1,2

Pyrimidine has two in-plane CH(δ+)/N̈(δ–)/CH(δ+) binding sites that are complementary to the (δ–/2δ+/δ–) quadrupole moment of CO 2 . For this study, we recorded broadband microwave spectra over the 7.5–17.5 GHz range for pyrimidine-(CO 2 ) n with n = 1 and 2 formed in a supersonic expansion. Based on fits of the rotational transitions, including nuclear hyperfine splitting due to the two 14 N nuclei, we have assigned 313 hyperfine components across 105 rotational transitions for the n = 1 complex and 208 hyperfine components across 105 rotational transitions for the n = 2 complex. The pyrimidine-CO 2 complex is planar, with CO 2 occupying one of the quadrupolar binding sites, forming a structure in which the CO 2 is stabilized in the plane by interactions with the C–H hydrogens adjacent to the nitrogen atom. This structure is closely analogous to that of the pyridine-CO 2 complex studied previously by (Doran, J. L. J. Mol. Struct. 2012, 1019, 191–195). The fit to the n = 2 cluster gives rotational constants consistent with a planar cluster of C 2v symmetry in which the second CO 2 molecule binds in the second quadrupolar binding pocket on the opposite side of the ring. The calculated total binding energy in pyrimidine-CO 2 is –13.7 kJ mol –1 , including corrections for basis set superposition error and zero-point energy, at the CCSD(T)/ 6-311++G(3df,2p) level, while that in pyrimidine-(CO 2 ) 2 is almost exactly double that size, indicating little interaction between the two CO 2 molecules in the two binding sites. The enthalpy, entropy, and free energy of binding are also calculated at 300 K within the harmonic oscillator/rigid-rotor model. This model is shown to lack quantitative accuracy when it is applied to the formation of weakly bound complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1994

Equilibrium fluid interface behavior under low- and zero-gravity conditions

We describe here some of our recent mathematical work, which forms a basis for the Interface Configuration Experiment scheduled for USML-2. The work relates to the design of apparatus that exploits microgravity conditions for accurate determination of contact angle. The underlying motivation for the procedures rests on a discontinuous dependence of the capillary free surface interface S on the contact angle gamma, in a cylindrical capillary tube whose section (base) omega contains a protruding corner with opening angle 2 alpha. Specifically, in a gravity-free environment, omega can be chosen so that, for all sufficiently large fluid volume, the height of S is uniquely determined as a (single-valued) function mu(x,y) entirely covering the base; the height mu is bounded over omega uniformly in gamma throughout the range absolute value of (gamma -(pion/2)) less than or equal to alpha, while for absolute value of (gamma - (pion/2)) greater than alpha fluid will necessarily move to the corner and uncover the base, rising to infinity (or falling to negative infinity) at the vertex, regardless of volume. We mention here only that procedures based on the phenomenon promise excellent accuracy when gamma is close pion/2 but may be subject to experimental error when gamma is close to zero (orpion), as the 'singular' part of the domain over which the fluid accumulates (or disappears) when a critical angle gamma theta is crossed then becomes very small and may be difficult to observe. We ignore the trivial case gamma is equal to pion/2 (planar free surface), to simplify the discussion.

Concus, Paul↗

NASA NTRS1995

The Topographic Torque on a Bounding Surface of a Rotating Gravitating Fluid and the Excitation by Core Motions of Decadal Fluctuations in the Earth's Rotation

General expressions (with potential applications in several areas of geophysical fluid dynamics) are derived for all three components of the contribution made by the geostrophic part of the pressure field associated with flow in a rotating gravitating fluid to the topographic torque exerted by the fluid on a rigid impermeable bounding surface of any shape. When applied to the Earth's liquid metallic core, which is bounded by nearly spherical surfaces and can be divided into two main regions, the "torosphere" and "polosphere," the expressions reduce to formulae given previously by the author, thereby providing further support for his work and that of others on the role of topographic coupling at the core-mantle boundary in the excitation by core motions of Earth rotation fluctuations on decadal time scales. They also show that recent criticisms of that work are vitiated by mathematical and physical errors. Contrary to these criticisms, the author's scheme for exploiting Earth rotation and other geophysical data (either real or simulated in computer models) in quantitative studies of the topography of the core-mantle boundary (CMB) by intercomparing various models of (a) motions in the core based on geomagnetic secular variation data and (b) CMB topography based on seismological and gravity data has a sound theoretical basis. The practical scope of the scheme is of course limited by the accuracy of real data, but this is a matter for investigation, not a priori assessment.

Hide, Raymond↗

DOE OSTI2022

Optimal Experimental Design for Inverse Problems in the Presence of Observation Correlations

Optimal experimental design (OED) is the general formalism of sensor placement and decisions on the data collection strategy for engineered or natural experiments. This problem is prevalent in many critical fields such as battery design, numerical weather prediction, geosciences, environmental and urban studies. State-of-the-art computational methods for experimental design do not accommodate correlation structure in observational errors produced by many expensive-to-operate devices such as X-ray machines, radars, and satellites. Discarding evident data correlations leads to biased results, higher expenses, and waste of valuable resources. We present a general formulation of the OED formalism for model-constrained large-scale Bayesian linear inverse problems, where measurement errors are generally correlated. The proposed approach utilizes the Hadamard product of matrices to formulate the weighted-likelihood, and is valid for both finite as well as infinite-dimensional Bayesian inverse problems. Extensive numerical experiments are carried out for empirical verification of the proposed approach using an advection-diffusion model, where the objective is to optimally place a small set of sensors, under a limited budget, to predict the concentration of a contaminant in a closed and bounded domain.

Correlated observations↗

NASA NTRS1971

A system debugging model.

Consideration of the nature of the 'debugging' process applied to a new complex system during the initial period of its life. During this period failures and errors are corrected as they occur, with resulting improvement in the subsequent performance of the system. One mathematical idealization of this process leads to the assumption that system failure rate is decreasing with time. In practice, the debugging phase is considered completed when the failure rate reaches an equilibrium or constant value. Models are formulated for this phenomenon. Maximum likelihood estimates are obtained for relevant failure rate functions and for the end of the debugging period. A conservative upper confidence bound on the stable failure rate is obtained.

Barlow, R. E.↗

NASA NTRS1982

Attitude and translation control of a low-altitude Gravsat

Dynamic simulation of the Gravsat's attitude and translation control system is used to provide an upper bound for the fuel supply and test the feasibility of the preliminary design. A preliminary design is made for the disturbance compensation system (DISCOS) sensor, the thruster control laws, reaction wheel control laws, and the onboard state estimators. The sensor analysis and noise measurements show no problems in scaling the Triad navigation satellite sensor design up to meet the Gravsat requirements, except for proof mass center-of-mass offset. A promising technique is proposed to measure and eliminate this error. The covariance analysis confirms that a sophisticated post-flight data fit will be necessary to reconstruct a scientifically useful proof mass state. The DISCOS sensor will have to be continuously calibrated from the inflight data to achieve this reconstruction.

Ray, J. C.↗

NASA NTRS2014

Impact of Satellite Viewing-Swath Width on Global and Regional Aerosol Optical Thickness Statistics and Trends

We use the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite aerosol optical thickness (AOT) product to assess the impact of reduced swath width on global and regional AOT statistics and trends. Alongtrack and across-track sampling strategies are employed, in which the full MODIS data set is sub-sampled with various narrow-swath (approximately 400-800 km) and single pixel width (approximately 10 km) configurations. Although view-angle artifacts in the MODIS AOT retrieval confound direct comparisons between averages derived from different sub-samples, careful analysis shows that with many portions of the Earth essentially unobserved, spatial sampling introduces uncertainty in the derived seasonal-regional mean AOT. These AOT spatial sampling artifacts comprise up to 60%of the full-swath AOT value under moderate aerosol loading, and can be as large as 0.1 in some regions under high aerosol loading. Compared to full-swath observations, narrower swath and single pixel width sampling exhibits a reduced ability to detect AOT trends with statistical significance. On the other hand, estimates of the global, annual mean AOT do not vary significantly from the full-swath values as spatial sampling is reduced. Aggregation of the MODIS data at coarse grid scales (10 deg) shows consistency in the aerosol trends across sampling strategies, with increased statistical confidence, but quantitative errors in the derived trends are found even for the full-swath data when compared to high spatial resolution (0.5 deg) aggregations. Using results of a model-derived aerosol reanalysis, we find consistency in our conclusions about a seasonal-regional spatial sampling artifact in AOT Furthermore, the model shows that reduced spatial sampling can amount to uncertainty in computed shortwave top-ofatmosphere aerosol radiative forcing of 2-3 W m(sup−2). These artifacts are lower bounds, as possibly other unconsidered sampling strategies would perform less well. These results suggest that future aerosol satellite missions having significantly less than full-swath viewing are unlikely to sample the true AOT distribution well enough to obtain the statistics needed to reduce uncertainty in aerosol direct forcing of climate.

remote sensing↗

NASA NTRS2021

Extending the Licklider Transmission Protocol to Multi-Band Links

Most deep space missions return data to Earth using links operating at a single frequency band. Indeed, their data requirements are low enough that bandwidth regulations do not constrain the system. In contrast, spacecraft such as Kepler or Europa Clipper are transitioning to a new operational paradigm where engineering and science data are transmitted through simultaneous links operating at different frequency bands (henceforth termed multi-band links). This ensures, for instance, that critical data is correctly received using a well characterized X-band link, while science data at a much larger data rate can be returned efficiently (both in terms of bandwidth and energy) through a Ka-band link.Having a spacecraft establish two simultaneous links with a ground station opens a large span of potential improvements for space communications and mission operations. In this paper, we consider the problem of running a Licklider Transmission Protocol (LTP) session over a multi-band link. LTP is an implementation of a selective Automatic Repeat reQuest (ARQ) protocol, i.e. it ensures correct delivery of data over an error prone link with potentially long propagation delays. To maximize its efficiency in deep space environments, LTP operates in deferred-ACK mode and is typically included as one of the core protocols in the Delay Tolerant Networking (DTN) suite.The contributions of this paper are as follows: First, we propose an extension to LTP for multi-band links (denoted MBLTP) and sketch how it can be implemented without modifying the current definition of LTP data units. Next, we develop bounds on the performance of MBLTP when transmitting a single data file over a multi-band link. Three metrics are considered, file expected delivery time, total energy spent and bundle jitter. The results of the analytic model are first benchmarked against simulations to ensure validity, and then compared against the performance of both traditional LTP and Parallel LTP (PLTP).We demonstrate that MBLTP can significantly reduce the latency and jitter with which data products are delivered to destination over a deep space link compared to LTP at moderate energy cost. Similarly, we also demonstrate that MBLTP outperforms PLTP in all considered metrics.

Sanchez Net, Marc↗

DOE OSTI2023

Incremental Interval Assignment by Integer Linear Algebra with Improvements

Interval Assignment (IA) is the problem of selecting the number of mesh edges (intervals) for each curve for conforming quad and hex meshing. The intervals x is fundamentally integer-valued. Many other approaches perform numerical optimization then convert a floating-point solution into an integer solution, which is slow and error prone. We avoid such steps: we start integer, and stay integer. Incremental Interval Assignment (IIA) uses integer linear algebra (Hermite normal form) to find an initial solution to the meshing constraints, satisfying the integer matrix equation Solving for reduced row echelon form provides integer vectors spanning the nullspace of A. Here we add vectors from the nullspace to improve the initial solution, maintaining Ax = b Heuristics find good integer linear combinations of nullspace vectors that provide strict improvement towards variable bounds or goals. IIA always produces an integer solution if one exists. In practice we usually achieve solutions close to the user goals, but there is no guarantee that the solution is optimal, nor even satisfies variable bounds, e.g. has positive intervals. We describe several algorithmic changes since first publication that tend to improve the final solution. The software is freely available.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

An Optimal Power Control Strategy for Grid-Following Inverters in a Synchronous Frame

This work proposes a power control strategy based on the linear quadratic regulator with optimal reference tracking (LQR-ORT) for a three-phase inverter-based generator (IBG) using an LCL filter. The use of an LQR-ORT controller increases robustness margins and reduces the quadratic value of the power error and control inputs during transient response. A model in a synchronous reference frame that integrates power sharing and voltage–current (V–I) dynamics is also proposed. This model allows for analyzing closed-loop eigenvalue location and robustness margins. The proposed controller was compared against a classical droop approach using proportional-resonant controllers for the inner loops. Mathematical analysis and hardware-in-the-loop (HIL) experiments under variations in the LCL filter components demonstrate fulfillment of robustness and performance bounds of the LQR-ORT controller. Experimental results demonstrate accuracy of the proposed model and the effectiveness of the LQR-ORT controller in improving transient response, robustness, and power decoupling.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1993

Discrete ordinates solutions of nongray radiative transfer with diffusely reflecting walls

Nongray gas radiation in a plane parallel slab bounded by gray, diffusely reflecting walls is studied using the discrete ordinates method. The spectral equation of transfer is averaged over a narrow wavenumber interval preserving the spectral correlation effect. The governing equations are derived by considering the history of multiple reflections between two reflecting wails. A closure approximation is applied so that only a finite number of reflections have to be explicitly included. The closure solutions express the physics of the problem to a very high degree and show relatively little error. Numerical solutions are obtained by applying a statistical narrow-band model for gas properties and a discrete ordinates code. The net radiative wail heat fluxes and the radiative source distributions are obtained for different temperature profiles. A zeroth-degree formulation, where no wall reflection is handled explicitly, is sufficient to predict the radiative transfer accurately for most cases considered, when compared with increasingly accurate solutions based on explicitly tracing a larger number of wail reflections without any closure approximation applied.

Menart, J. A.↗

NASA NTRS1993

On the dynamics of approximating schemes for dissipative nonlinear equations

Since one can rarely write down the analytical solutions to nonlinear dissipative partial differential equations (PDE's), it is important to understand whether, and in what sense, the behavior of approximating schemes to these equations reflects the true dynamics of the original equations. Further, because standard error estimates between approximations of the true solutions coming from spectral methods - finite difference or finite element schemes, for example - and the exact solutions grow exponentially in time, this analysis provides little value in understanding the infinite time behavior of a given approximating scheme. The notion of the global attractor has been useful in quantifying the infinite time behavior of dissipative PDEs, such as the Navier-Stokes equations. Loosely speaking, the global attractor is all that remains of a sufficiently large bounded set in phase space mapped infinitely forward in time under the evolution of the PDE. Though the attractor has been shown to have some nice properties - it is compact, connected, and finite dimensional, for example - it is in general quite complicated. Nevertheless, the global attractor gives a way to understand how the infinite time behavior of approximating schemes such as the ones coming from a finite difference, finite element, or spectral method relates to that of the original PDE. Indeed, one can often show that such approximations also have a global attractor. We therefore only need to understand how the structure of the attractor for the PDE behaves under approximation. This is by no means a trivial task. Several interesting results have been obtained in this direction. However, we will not go into the details. We mention here that approximations generally lose information about the system no matter how accurate they are. There are examples that show certain parts of the attractor may be lost by arbitrary small perturbations of the original equations.

Jones, Donald A.↗

NASA NTRS2002

On the Numerical Convergence to Steady State of Hypersonic Flows Over Bodies with Concavities

Two recent numerical studies of hypersonic flows over bodies with concavities revealed problems with convergence to a steady state with an oft-used application of local-time-stepping. Both simulated flows showed a time-like, periodic shedding of vortices in a subsonic domain bounded by supersonic external flow although the simulations, using local-time-stepping, were not time accurate. Simple modifications to the numerical algorithm were implemented to enable implicit, first-order accurate in time simulations. Subsequent time-accurate simulations of the two test problems converged to a steady state. The baseline algorithm and modifications for temporal accuracy are described. The requirement for sub-iterations to achieve convergence is demonstrated. Failure to achieve convergence without time accuracy is conjectured to arise from temporal errors being continuously refocused into a subsonic domain.

Gnoffo, Peter A.↗

DOE OSTI2021

Bounds on the Rate-Dependent Plastic Flow of Tantalum up to 75 GPa

In this study we report on the continued development of thermodynamics-based analysis of shock waves propagation with the objective of extracting information related to materials strength at high strain rates and pressures. Building on previous results reported for peak stresses of 10 GPa and 25 GPa, we present a series of three-step gas-gun shock experiments designed to explore the pressure and strain rate dependence of plastic flow in polycrystalline tantalum. These experiments at nominal peak stresses of 50 GPa and 75 GPa show the irreversible deformation before pullback to be almost entirely confined to the shock loading, with negligible plastic relaxation on the post-shock plateau. We also add a reverse-ballistics shot at 25 GPa, which was designed to reveal the pullback response with negligible interference from free-surface effects. General thermodynamic considerations allow us to place bounds on the plastic behavior even for parts of the curve that change far too rapidly for the velocimetric time resolution of (conservatively) ~ 5 ns. To analyze the data, we found it necessary to substantially improve the interpolation/extrapolation scheme in order to improve its robustness, flexibility and range of applicability. We describe the new scheme based on splines, as well as an extension of free-surface corrections to the post-shock rarefaction waves. Reanalysis with the new scheme produces results essentially within the error bars previously reported, showing that the known systematic errors associated with free-surface effects are relatively inconsequential for determining thermodynamic paths.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Variational approach to relative entropies with an application to QFT

Abstract We define a new divergence of von Neumann algebras using a variational expression similar in nature to Kosaki’s formula for Umegaki’s relative entropy. Our divergence satisfies several of the usual desirable properties, upper bounds the sandwiched Renyi entropy and reduces to the fidelity in a limit. As an illustration, we use the formula in quantum field theory to compute our divergence between the vacuum in a bipartite system and an “orbifolded”—in the sense of a conditional expectation—system in terms of the Jones index. We take the opportunity to point out an entropic certainty relation associated with an inclusion of von Neumann factors related to the relative entropy. This certainty relation has an equivalent formulation in terms of error correcting codes.

Hollands, Stefan↗