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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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NASA NTRS1972

Canonical fluid thermodynamics

The space-time integral of the thermodynamic pressure plays the role of the thermodynamic potential for compressible, adiabatic flow in the sense that the pressure integral for stable flow is less than for all slightly different flows. This stability criterion can be converted into a variational minimum principle by requiring the molar free-enthalpy and the temperature, which are the arguments of the pressure function, to be generalized velocities, that is, the proper-time derivatives of scalar spare-time functions which are generalized coordinates in the canonical formalism. In a fluid context, proper-time differentiation must be expressed in terms of three independent quantities that specify the fluid velocity. This can be done in several ways, all of which lead to different variants (canonical transformations) of the same constraint-free action integral whose Euler-Lagrange equations are just the well-known equations of motion for adiabatic compressible flow.

Schmid, L. A.↗
NASA NTRS1972

Cable Connected Spinning Spacecraft, 1. the Canonical Equations, 2. Urban Mass Transportation, 3

Work on the dynamics of cable-connected spinning spacecraft was completed by formulating the equations of motion by both the canonical equations and Lagrange's equations and programming them for numerical solution on a digital computer. These energy-based formulations will permit future addition of the effect of cable mass. Comparative runs indicate that the canonical formulation requires less computer time. Available literature on urban mass transportation was surveyed. Areas of the private rapid transit concept of urban transportation are also studied.

Sitchin, A.↗
NASA NTRS1973

An algorithm for calculation of the Jordan canonical form of a matrix

Jordan canonical forms are used extensively in the literature on control systems. However, very few methods are available to compute them numerically. Most numerical methods compute a set of basis vectors in terms of which the given matrix is diagonalized when such a change of basis is possible. Here, a simple and efficient method is suggested for computing the Jordan canonical form and the corresponding transformation matrix. The method is based on the definition of a generalized eigenvector, and a natural extension of Gauss elimination techniques.

Sridhar, B.↗
NASA NTRS1973

Classification of ERTS-1 MSS data by canonical analysis

The objective of canonical analysis is to obtain the maximum separability among a number of catergories. The application of canonical analysis was investigated using the merged MSS ERTS-1 data for one area viewed on two dates. The effect of threshold values on classification regions and confusion regions was investigated.

Lachowski, H. M.↗
NASA NTRS1973

An efficient algorithm for calculation of the Luenberger canonical form.

A new algorithm is presented to obtain the Luenberger canonical form for multivariable systems. A distinct feature of the method is that the canonical form is obtained directly and, if necessary, the similarity transformation can be computed. There is a substantial reduction in the amount of computation compared to Luenberger's method. The reduced computations along with Gaussian techniques lend greater inherent accuracy and the ability to refine the solution with additional computations. An example is presented to illustrate the technique.

Jordan, D.↗
NASA NTRS1974

On the use and computation of the Jordan canonical form in system theory

This paper investigates various aspects of the application of the Jordan canonical form of a matrix in system theory and develops a computational approach to determining the Jordan form for a given matrix. Applications include pole placement, controllability and observability studies, serving as an intermediate step in yielding other canonical forms, and theorem proving. The computational method developed in this paper is both simple and efficient. The method is based on the definition of a generalized eigenvector and a natural extension of Gauss elimination techniques. Examples are included for demonstration purposes.

Sridhar, B.↗
NASA NTRS1986

Canonical solution of the two critical argument problem

The solution by Sessin and Ferraz-Mello (1984) of the Hori auxiliary system for the motion of two planets with periods nearly commensurate in the ratio 2:1 is considerably simplified by the introduction of canonical variables. An analogous canonical transformation simplifies the elliptic restricted problem.

Wisdom, J.↗
NASA NTRS1989

Linear canonical transformations of coherent and squeezed states in the Wigner phase space. II - Quantitative analysis

It is possible to calculate expectation values and transition probabilities from the Wigner phase-space distribution function. Based on the canonical transformation properties of the Wigner function, an algorithm is developed for calculating these quantities in quantum optics for coherent and squeezed states. It is shown that the expectation value of a dynamical variable can be written in terms of its vacuum expectation value of the canonically transformed variable. Parallel-axis theorems are established for the photon number and its variant. It is also shown that the transition probability between two squeezed states can be reduced to that of the transition from one squeezed state to vacuum.

Han, D.↗
NASA NTRS1989

Orthogonal canonical forms for second-order systems

The authors prove that a linear second-order system with arbitrary damping cannot be reduced to Hessenberg-triangular form by means of orthogonal transformations, while this reduction is always possible for the modal damping commonly assumed for models of flexible structures. The type of canonical form obtainable by means of orthogonal transformations acting on a second-order system is heavily dependent on the type of damping considered. If the damping matrix is merely positive semi-definite symmetric, it is generally not possible to obtain a reduction to Hessenberg-triangular form, while this reduction is trivial for zero or Rayleigh damping. If damping is modal, however, as is commonly assumed in structural models, the reduction exists and is nontrivial. Furthermore, reduction to triangular second-order Schur form is always possible for such damping: this canonical form appears likely to have applications to second-order system theory.

Williams, Trevor↗
NASA NTRS1992

Temperature fluctuations in the canonical ensemble

We report the first quantitative measurements of spontaneous temperature fluctuations in a physical system well modeled by a canonical ensemble. Using superconducting magnetometers and a carefully controlled thermal environment, we have measured the noise spectra of paramagnetic salt thermometers that were coupled to thermal reservoirs at 2 K. The noise spectra were found to be in very good agreement with the predictions of the fluctuation-dissipation theorem. Our observations are at variance with some interpretations of fluctuations in the canonical ensemble.

Chui, T. C. P.↗
NASA NTRS2001

A New Ensemble Canonical Correlation Prediction Scheme for Seasonal Precipitation

Department of Mathematical Sciences, University of Alberta, Edmonton, Canada This paper describes the fundamental theory of the ensemble canonical correlation (ECC) algorithm for the seasonal climate forecasting. The algorithm is a statistical regression sch eme based on maximal correlation between the predictor and predictand. The prediction error is estimated by a spectral method using the basis of empirical orthogonal functions. The ECC algorithm treats the predictors and predictands as continuous fields and is an improvement from the traditional canonical correlation prediction. The improvements include the use of area-factor, estimation of prediction error, and the optimal ensemble of multiple forecasts. The ECC is applied to the seasonal forecasting over various parts of the world. The example presented here is for the North America precipitation. The predictor is the sea surface temperature (SST) from different ocean basins. The Climate Prediction Center's reconstructed SST (1951-1999) is used as the predictor's historical data. The optimally interpolated global monthly precipitation is used as the predictand?s historical data. Our forecast experiments show that the ECC algorithm renders very high skill and the optimal ensemble is very important to the high value.

Kim, Kyu-Myong↗
NASA NTRS2001

Ensemble Canonical Correlation Prediction of Seasonal Precipitation Over the United States: Raising the Bar for Dynamical Model Forecasts

This paper presents preliminary results of an ensemble canonical correlation (ECC) prediction scheme developed at the Climate and Radiation Branch, NASA/Goddard Space Flight Center for determining the potential predictability of regional precipitation, and for climate downscaling studies. The scheme is tested on seasonal hindcasts of anomalous precipitation over the continental United States using global sea surface temperature (SST) for 1951-2000. To maximize the forecast skill derived from SST, the world ocean is divided into non-overlapping sectors. The canonical SST modes for each sector are used as the predictor for the ensemble hindcasts. Results show that the ECC yields a substantial (10-25%) increase in prediction skills for all the regions of the US in every season compared to traditional CCA prediction schemes. For the boreal winter, the tropical Pacific contributes the largest potential predictability to precipitation in the southwestern and southeastern regions, while the North Pacific and the North Atlantic are responsible to the enhanced forecast skills in the Pacific Northwest, the northern Great Plains and Ohio Valley. Most importantly, the ECC increases skill for summertime precipitation prediction and substantially reduces the spring predictability barrier over all the regions of the US continent. Besides SST, the ECC is designed with the flexibility to include any number of predictor fields, such as soil moisture, snow cover and additional local observations. The enhanced ECC forecast skill provides a new benchmark for evaluating dynamical model forecasts.

Lau, William K. M.↗
NASA NTRS2005

Evidence for a Canonical GRB Afterglow Light Curve in the Swift/XRT Data

We present new observations of the early X-ray afterglows of the first 27 gamma-ray bursts (GRBs) detected with the Swift X-ray Telescope (XRT). The early X-ray afterglows show a canonical behavior, where the light curve broadly consists of three distinct power law segments. These power law segments are separated by two corresponding break times. On top of this canonical behavior of the early X-ray light curve, many events have superimposed X-ray flares, which are most likely caused by internal shocks due to long lasting sporadx activity of the central engine, up to several hours after the GRB. We find that the initial steep decay is consistent with it being the tail of the prompt emission: from photons that are radiated at large angles relative to our line of sight. The first break in the light curve takes place when the forward shock emission becomes dominant, with the intermediate shallow flux decay likely caused by the continuous energy injection into the external shock. When this energy injection stops, a second break is then observed in the light curve. This energy injection increases the energy of the afterglow shock by at least a factor of f greater than or approx. equal to 4, and augments the already severe requirements for the efficiency of the prompt gamma-ray emission.

Nousek, J. A.↗