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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

The infinite level normal forms for non-resonant double Hopf singularities

Here, in this paper, we explore hypernormal forms of vector fields that have non-resonant double Hopf singularities with a non-zero radial cubic part. Our primary focus is on investigating the infinite-level normal form classification of this type of singularities. We provide a normal form decomposition in terms of planar-rotating and planar-radial vector fields, which greatly facilitate the pattern recognition and analysis of the corresponding generalized homological maps. Notably, our paper represents the first instance of the normal form classification for general non-resonant double Hopf singularities without structural symmetry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Bounded motion design in the Earth zonal problem using differential algebra based normal form methods

Establishing long-term relative bounded motion between orbits in perturbed dynamics is a key challenge in astrodynamics to enable cluster flight with minimum propellant expenditure. Herein, we present an approach that allows for the design of long-term relative bounded motion considering a zonal gravitational model. Entire sets of orbits are obtained via high-order Taylor expansions of Poincarè return maps about reference fixed points. The high-order normal form algorithm is used to determine a change in expansion variables of the map into normal form space, in which the phase space behavior is circular and can be easily parameterized by action–angle coordinates. The action–angle representation of the normal form coordinates is then used to parameterize the original Poincarè return map and average it over a full phase space revolution by a path integral along the angle parameterization. As a result, the averaged nodal period and drift in the ascending node are obtained, for which the bounded motion conditions are straightforwardly imposed. Sets of highly accurate bounded orbits are obtained, extending over several thousand kilometers, and valid for decades.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Integrability, normal forms, and magnetic axis coordinates

Integrable or near-integrable magnetic fields are prominent in the design of plasma confinement devices. Such a field is characterized by the existence of a singular foliation entirely consisting of invariant submanifolds. A compact regular leaf (a flux surface) of this foliation must be diffeomorphic to the two-torus. In a neighborhood of a flux surface, it is known that the magnetic field admits several exact smooth normal forms in which the field lines are straight. However, these normal forms break down near singular leaves, including elliptic and hyperbolic magnetic axes. In this work, the existence of exact smooth normal forms for integrable magnetic fields near elliptic and hyperbolic magnetic axes is established. In the elliptic case, smooth near-axis Hamada and Boozer coordinates are defined and constructed. Ultimately, these results establish previously conjectured smoothness properties for smooth solutions of the magnetohydrodynamic equilibrium equations. The key arguments are a consequence of a geometric reframing of integrability and magnetic fields: they are presymplectic systems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

A restricted signature normal form for Hermitian matrices, quasi-spectral decompositions, and applications

In recent years, a number of results on the relationships between the inertias of Hermitian matrices and the inertias of their principal submatrices appeared in the literature. We study restricted congruence transformation of Hermitian matrices M which, at the same time, induce a congruence transformation of a given principal submatrix A of M. Such transformations lead to concept of the restricted signature normal form of M. In particular, by means of this normal form, we obtain short proofs of most of the known inertia theorems and also derive some new results of this type. For some applications, a special class of almost unitary restricted congruence transformations turns out to be useful. We show that, with such transformations, M can be reduced to a quasi-diagonal form which, in particular, displays the eigenvalues of A. Finally, applications of this quasi-spectral decomposition to generalize inverses and Hermitian matrix pencils are discussed.

Freund, Roland W.↗
NASA NTRS1990

The simultaneous integration of many trajectories using nilpotent normal forms

Taylor's formula shows how to approximate a certain class of functions by polynomials. The approximations are arbitrarily good in some neighborhood whenever the function is analytic and they are easy to compute. The main goal is to give an efficient algorithm to approximate a neighborhood of the configuration space of a dynamical system by a nilpotent, explicitly integrable dynamical system. The major areas covered include: an approximating map; the generalized Baker-Campbell-Hausdorff formula; the Picard-Taylor method; the main theorem; simultaneous integration of trajectories; and examples.

Grayson, Matthew A.↗
DOE OSTI2024

Extracting Topological Orders of Generalized Pauli Stabilizer Codes in Two Dimensions

In this paper, we introduce an algorithm for extracting topological data from translation invariant generalized Pauli stabilizer codes in two-dimensional systems, focusing on the analysis of anyon excitations and string operators. The algorithm applies to Z d qudits, including instances where d is a nonprime number. This capability allows the identification of topological orders that differ from the Z d toric codes. It extends our understanding beyond the established theorem that Pauli stabilizer codes for Z p qudits (with p being a prime) are equivalent to finite copies of Z p toric codes and trivial stabilizers. The algorithm is designed to determine all anyons and their string operators, enabling the computation of their fusion rules, topological spins, and braiding statistics. The method converts the identification of topological orders into computational tasks, including Gaussian elimination, the Hermite normal form, and the Smith normal form of truncated Laurent polynomials. Furthermore, the algorithm provides a systematic approach for studying quantum error-correcting codes. We apply it to various codes, such as self-dual CSS quantum codes modified from the two-dimensional honeycomb color code and non-CSS quantum codes that contain the double semion topological order or the six-semion topological order. Published by the American Physical Society 2024

Physics↗
NASA NTRS2008

Behavior of Spinning Space Vehicles with Onboard Liquids, 2nd Edition, Technical Report B8030

Although the fundamental principles of spin stabilization are well established, uncertainty regarding the potential for rapid nutation growth caused by onboard liquids is a continuing concern. NASA and other organizations regularly encounter the issue of rapid nutation growth due to energy dissipation by liquids on spinning vehicles. Of concern is the stability of spinning upper stages and of spacecraft that spin for part or all of their missions. Several missions have required last-minute hardware or operational changes to deal with rapid nutation divergences that were identified late in the program. In some instances, major schedule slips were barely averted. In at least two cases, it was determined that a spinning upper stage was not a viable option. Historically, the "slosh" issue has been addressed by each space vehicle project individually, if it has been addressed at all. Due to budgetary and programmatic constraints, individual projects are unable to address the problem globally. Hence, there has been little effort to collect available test and flight data and use that data to make a coherent, unified picture of the "slosh" effect and how to deal with it. To some extent, each project has had to "reinvent the wheel", which can be both costly and risky. This study is a step toward correcting the situation. Specifically, the goal was to identify and collect available flight and test data for spinning vehicles with onboard liquid propellants. A total of 149 flight data points and 1,692 test points were collected as part of this study. This data was analyzed, correlated, and is presented here in a normalized form. In most cases, the normalization involves a dimensionless nutation time constant that can be used to predict performance of other vehicles with the same type of tank. For some configurations, it was also possible to identify conditions that can lead to resonance between nutational motion and liquid modes. Gaps in the knowledge base are identified and approaches to filling those gaps are outlined. The data presented here has two different but related uses. First, it can be applied directly to current and future spacecraft programs. Second, it can provide truth models for testing analytical techniques. Experience has shown that purely analytical models of the liquid "slosh" effect on spinning vehicles are unreliable unless they are validated against flight or test data. To the author's knowledge, this report contains the most extensive and varied data set available. As such, it should be a good resource for anyone seeking to develop and validate improved analytical techniques. All of the original digital data sets have been archived on disk, with copies provided to NASA/KSC. With some restrictions, many of these data sets can be made available to researchers within the United States. Whenever possible, spacecraft are identified by name in this report. However, several organizations provided access to data with the explicit proviso that their programs not be identified and that parameters be presented only in normalized form. These constraints have been respected.

Hubert, Carl↗
NASA NTRS1983

Transformer induced instability of the series resonant converter

It is shown that the common series resonant power converter is subject to a low frequency oscillation that can lead to the loss of cyclic stability. This oscillation is caused by a low frequency resonant circuit formed by the normal L and C components in series with the magnetizing inductance of the output transformer. Three methods for eliminating this oscillation are presented and analyzed. One of these methods requires a change in the circuit topology during the resonance cycle. This requires a new set of steady state equations which are derived and presented in a normalized form. Experimental results are included which demonstrate the nature of the low frequency oscillation before cyclic stability is lost.

King, R. J.↗
NASA NTRS1976

Zonal and tesseral harmonic coefficients for the geopotential function, from zero to 18th order

Zonal and tesseral harmonic coefficients for the geopotential function are usually tabulated in normalized form to provide immediate information as to the relative significance of the coefficients in the gravity model. The normalized form of the geopotential coefficients cannot be used for computational purposes unless the gravity model has been modified to receive them. This modification is usually not done because the absolute or unnormalized form of the coefficients can be obtained from the simple mathematical relationship that relates the two forms. This computation can be quite tedious for hand calculation, especially for the higher order terms, and can be costly in terms of storage and execution time for machine computation. In this report, zonal and tesseral harmonic coefficients for the geopotential function are tabulated in absolute or unnormalized form. The report is designed to be used as a ready reference for both hand and machine calculation to save the user time and effort.

Kirkpatrick, J. C.↗
NASA NTRS1987

The mechanisms of temporal inference

The properties of a temporal language are determined by its constituent elements: the temporal objects which it can represent, the attributes of those objects, the relationships between them, the axioms which define the default relationships, and the rules which define the statements that can be formulated. The methods of inference which can be applied to a temporal language are derived in part from a small number of axioms which define the meaning of equality and order and how those relationships can be propagated. More complex inferences involve detailed analysis of the stated relationships. Perhaps the most challenging area of temporal inference is reasoning over disjunctive temporal constraints. Simple forms of disjunction do not sufficiently increase the expressive power of a language while unrestricted use of disjunction makes the analysis NP-hard. In many cases a set of disjunctive constraints can be converted to disjunctive normal form and familiar methods of inference can be applied to the conjunctive sub-expressions. This process itself is NP-hard but it is made more tractable by careful expansion of a tree-structured search space.

Fox, B. R.↗
NASA NTRS1994

The Teton fault, Wyoming: Topographic signature, neotectonics, and mechanisms of deformation

We integrated geophysical and geological methods to evalute the structural evolution of the active Teton normal fault, Wyoming, and its role in the development of the dramatic topography of Teton Range and Jackson Hole. Comparison of variations in surface offsets with the topographic expression of the Teton range crest and drainage divide, and the overall structure of the range, suggests that the effects ofpostglacial faulting cannot be discriminated from the influence of pre-extensional structures and differential; erosion on the footwall topography. In contrast, the effects of multiple scarp-forming normal faulting earthquakes are expressed by the anomalous drainage pattern and westward tilt of the hanging wall, Jackson Hole, toward the Teton fault. Kinematic boundary element fault models suggest that the westward tilt of the valley floor is the product of 110-125 m of displacement on a 45 deg-75 deg E dipping Teton fault in the past 25,000-75,000 years. Comparisons with historic normal faulting earthquake displacements imply that this range of displacement corresponds to 10-50, M greater than 7 scarp-forming earthquakes. A total throw of 2.5 to 3.5 km across the Teton fault is suggested by inverse ray-tracing and forward gravity models. These models also suggest that Laramide age structures have been offset across the Teton fault and obscure its geophysical signature but also continue to influence the structural and topographic expression of the footwall and hanging wall blocks. Paleomagnetic analyses of the approximately 2.0 Ma Huckelberry Ridge Tuff suggest that the overall westward tilt of the Teton Range is a result ofabout 10 deg of west side down tilt across the Teton fault since tuff emplacement. This suggests that much if not all of the throw across the Teton fault has accumulated in the past 2 m.y. Complex demagnetization and rock magnetic behavior and local emplacement of the Huckleberry Ridge Tuff on preexisting topogrpahy preclude determination of the amount or variations in throw along strike of the Teton fault from the paleomagnetic data.

Byrd, John O. D.↗
NASA NTRS1978

Size-frequency distributions of primary and secondary lunar impact craters

The graphs of diameter vs frequency plotted in the present study for primary impact craters produced in four time intervals exhibit an appreciable change in form with age. A deficiency of small craters relative to an extrapolation from the large-diameter parts of the curves is greatest and extends to the largest sizes in the oldest population (pre-Nectarian), whose curve approximates a log-normal form. Successively younger populations (Nectarian, Imbrian, Copernican plus Eratosthenian) have successively more small craters relative to larger ones and more nearly log-log distributions. Many of the craters thought to be small old primaries are here identified as secondary craters of basins, on the basis of previously developed criteria.

Wilhelms, D. E.↗
NASA NTRS2003

On the Use of the Log-Normal Particle Size Distribution to Characterize Global Rain

Although most parameterizations of the drop size distributions (DSD) use the gamma function, there are several advantages to the log-normal form, particularly if we want to characterize the large scale space-time variability of the DSD and rain rate. The advantages of the distribution are twofold: the logarithm of any moment can be expressed as a linear combination of the individual parameters of the distribution; the parameters of the distribution are approximately normally distributed. Since all radar and rainfall-related parameters can be written approximately as a moment of the DSD, the first property allows us to express the logarithm of any radar/rainfall variable as a linear combination of the individual DSD parameters. Another consequence is that any power law relationship between rain rate, reflectivity factor, specific attenuation or water content can be expressed in terms of the covariance matrix of the DSD parameters. The joint-normal property of the DSD parameters has applications to the description of the space-time variation of rainfall in the sense that any radar-rainfall quantity can be specified by the covariance matrix associated with the DSD parameters at two arbitrary space-time points. As such, the parameterization provides a means by which we can use the spaceborne radar-derived DSD parameters to specify in part the covariance matrices globally. However, since satellite observations have coarse temporal sampling, the specification of the temporal covariance must be derived from ancillary measurements and models. Work is presently underway to determine whether the use of instantaneous rain rate data from the TRMM Precipitation Radar can provide good estimates of the spatial correlation in rain rate from data collected in 5(sup 0)x 5(sup 0) x 1 month space-time boxes. To characterize the temporal characteristics of the DSD parameters, disdrometer data are being used from the Wallops Flight Facility site where as many as 4 disdrometers have been used to acquire data over a 2 km path. These data should help quantify the temporal form of the covariance matrix at this site.

Meneghini, Robert↗
DOE OSTI2021

Follow the power—pathways to steady-state tokamak reactors

Abstract Diagramming pathways of dimensionless power is a potent method for extrapolating between operating points on present-day tokamaks and future burning plasma devices. The heat transport power, current drive power, H-mode threshold power and other ‘plasma physics’ powers can be expressed in dimensionally correct (or normalized) form as Pa 3/4 , where P is the power and a is the plasma minor radius, with the relative gyroradius ( ρ * ) dependence ranging from gyro-Bohm-like for transport ( P a 3 / 4 ∝ ρ * − 3 / 2 ), Bohm-like for current drive ( P a 3 / 4 ∝ ρ * − 5 / 2 ) and worse than Bohm-like for H-mode threshold ( P a 3 / 4 ∝ ρ * − 3 ). The D–T fusion power cannot be normalized in the same fashion since it is governed by nuclear physics, but at fixed B T it scales like P a 3 / 4 ∝ ρ * − 9 / 2 . Other ‘mixed physics’ powers can be incorporated into the dimensionless power framework by holding B T fixed in the same manner. Diagramming these dimensionless powers vs ρ * shows how the pathway to a steady-state reactor can be optimized relative to various operational boundaries. Using a steady-state hybrid discharge with β N = 3.2 from DIII-D as the starting point, a multi-parameter optimization finds an attractive pathway to steady-state operation on ITER using 76 MW of current drive power (fusion gain of Q fus = 8), along with a pathway to Q fus = 20 in a JET-sized steady-state reactor with B T = 10 T.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗