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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 NTRS1980

Energy conservation - A test for scattering approximations

The roles of the extinction theorem and energy conservation in obtaining the scattering and absorption cross sections for several light scattering approximations are explored. It is shown that the Rayleigh, Rayleigh-Gans, anomalous diffraction, geometrical optics, and Shifrin approximations all lead to reasonable values of the cross sections, while the modified Mie approximation does not. Further examination of the modified Mie approximation for the ensembles of nonspherical particles reveals additional problems with that method.

Acquista, C.↗
NASA NTRS1997

Improvements in Block-Krylov Ritz Vectors and the Boundary Flexibility Method of Component Synthesis

A method of dynamic substructuring is presented which utilizes a set of static Ritz vectors as a replacement for normal eigenvectors in component mode synthesis. This set of Ritz vectors is generated in a recurrence relationship, proposed by Wilson, which has the form of a block-Krylov subspace. The initial seed to the recurrence algorithm is based upon the boundary flexibility vectors of the component. Improvements have been made in the formulation of the initial seed to the Krylov sequence, through the use of block-filtering. A method to shift the Krylov sequence to create Ritz vectors that will represent the dynamic behavior of the component at target frequencies, the target frequency being determined by the applied forcing functions, has been developed. A method to terminate the Krylov sequence has also been developed. Various orthonormalization schemes have been developed and evaluated, including the Cholesky/QR method. Several auxiliary theorems and proofs which illustrate issues in component mode synthesis and loss of orthogonality in the Krylov sequence have also been presented. The resulting methodology is applicable to both fixed and free- interface boundary components, and results in a general component model appropriate for any type of dynamic analysis. The accuracy is found to be comparable to that of component synthesis based upon normal modes, using fewer generalized coordinates. In addition, the block-Krylov recurrence algorithm is a series of static solutions and so requires significantly less computation than solving the normal eigenspace problem. The requirement for less vectors to form the component, coupled with the lower computational expense of calculating these Ritz vectors, combine to create a method more efficient than traditional component mode synthesis.

Carney, Kelly Scott↗
NASA NTRS2014

Formal Methods Case Studies for DO-333

RTCA DO-333, Formal Methods Supplement to DO-178C and DO-278A provides guidance for software developers wishing to use formal methods in the certification of airborne systems and air traffic management systems. The supplement identifies the modifications and additions to DO-178C and DO-278A objectives, activities, and software life cycle data that should be addressed when formal methods are used as part of the software development process. This report presents three case studies describing the use of different classes of formal methods to satisfy certification objectives for a common avionics example - a dual-channel Flight Guidance System. The three case studies illustrate the use of theorem proving, model checking, and abstract interpretation. The material presented is not intended to represent a complete certification effort. Rather, the purpose is to illustrate how formal methods can be used in a realistic avionics software development project, with a focus on the evidence produced that could be used to satisfy the verification objectives found in Section 6 of DO-178C.

Cofer, Darren↗
NASA NTRS1981

Sturm-Liouville eigenproblems with an interior pole

The eigenvalues and eigenfunctions of self-adjoint Sturm-Liouville problems with a simple pole on the interior of an interval are investigated. Three general theorems are proved, and it is shown that as n approaches infinity, the eigenfunctions more and more closely resemble those of an ordinary Sturm-Liouville problem. The low-order modes differ significantly from those of a nonsingular eigenproblem in that both eigenvalues and eigenfunctions are complex, and the eigenvalues for all small n may cluster about a common value in contrast to the widely separated eigenvalues of the corresponding nonsingular problem. In addition, the WKB is shown to be accurate for all n, and all eigenvalues of a normal one-dimensional Sturm-Liouville equation with nonperiodic boundary conditions are well separated.

Boyd, J. P.↗
NASA NTRS1993

On the dispersion relations for parametric instabilities of parallel-propagating Alfven waves

We consider the dispersion relation for the parametric instabilities of large-amplitude circularly polarized Alfven waves propagating parallel to the ambient magnetic field. A linear perturbation analysis is employed, and the perturbations are taken to propagate along the ambient field. We present an analysis based on Floquet's theorem. The result is a hierarchy of dispersion relations. However, all the dispersion relations are found to be equivalent to the one obtained via the standard analysis; the differences between them are due only to how ca and k are defined. Thus we conclude that physically there is really only one dispersion relation, namely the 'electrostatic dispersion relation', which is in agreement with earlier works. However, we disagree with Vinas and Goldstein (1991), who obtained additional dispersion relations which they have called the 'electromagnetic dispersion relations'. Their additional dispersion relations are a consequence of first truncating the dispersion relation for obliquely propagating perturbations and then taking the limit of parallel-propagating perturbations.

Yajanti, Venku↗
NASA NTRS2003

New Experiment to Measure the Electron Electric Dipole Moment

An electron can possess an electric dipole moment (edm) only if time reversal symmetry (T) is violated. No edm of any particle has yet been discovered. CP-violation, equivalent to T-violation by the CPT theorem, does occur in Kaon decays and can be accounted for by the standard model. However, this mechanism leads to an electron edm d(sub e) of the order of 10(exp -38) e cm, whereas the current experimental bound on d(sub e) is about 10(exp -27) e cm. However, well-motivated extensions of the standard model such as supersymmetric theories do predict that de could be as large as the current bound. In addition, CP violation in the early universe is required to explain the preponderance of matter over anti-matter, but the exact mechanism of this CP violation is unclear. For these reasons, we are undertaking a new experimental program to determine de to an improved accuracy of 10(exp -29) e cm. Our experiment will use laser-cooled, trapped Cesium atoms to measure the atomic edm d(sub Cs) that occurs if d(sub e) is not zero. In order to do this, we will measure the energy splitting between the atoms spin states in parallel electric and magnetic fields. The signature of an edm would be a linear dependence of the splitting on the electric field E due to the interaction - d(sub Cs) dot E. Our measurement will be much more sensitive than previous measurements because atoms can be stored in the trap for tens of seconds, allowing for much narrower Zeeman resonance linewidths. Also, our method eliminates the most important systematic errors, proportional to atomic velocity, which have limited previous experiments. In this presentation, we will describe the design of our new apparatus, which is presently under construction. An important feature of our experimental apparatus is that magnetic field noise will be suppressed to a very low value of the order of 1 fT/(Hz)1/2. This requires careful attention to the Johnson noise currents in the chamber, which have not been important in previous experiments. In addition we will present estimates of the limits of the various errors that we expect for our experiment.

Kittle, Melanie↗
NASA NTRS1984

Thermal emission of nonspherical particles

The thermal emission of nonspherical particles is studied by applying the fluctuation dissipation theorem to calculate the Stokes' vector source terms in radiative transfer theory. Generally, all the four Stokes' parameters in the source term are nonzero and are proportional to the absorption coefficient in the backward direction. The measurements of active and passive remote sensing are related by showing that within the framework of radiative transfer theory, the emissivity of vertically and horizontally polarized waves can be expressed in terms of the bistatic scattering coefficients in the usual manner. In addition, the emissions of the third and fourth Stokes' parameters are also expressed in terms of bistatic scattering coefficients.

Tsang, L.↗
NASA NTRS2001

Crack Turning Mechanics of Composite Wing Skin Panels

The safety of future composite wing skin integral stiffener panels requires a full understanding of failure mechanisms of these damage tolerance critical structures under both in-plane and bending loads. Of primary interest is to derive mathematical models using fracture mechanics in anisotropic cracked plate structures, to assess the crack turning mechanisms, and thereby to enhance the residual strength in the integral stiffener composite structures. The use of fracture mechanics to assess the failure behavior in a cracked structure requires the identification of critical fracture parameters which govern the severity of stress and deformation field ahead of the flaw, and which can be evaluated using information obtained from the flaw tip. In the three-year grant, the crack-tip fields under plane deformation, crack-tip fields for anisotropic plates and anisotropic shells have been obtained. In addition, methods for determining the stress intensity factors, energy release rate, and the T-stresses have been proposed and verified. The research accomplishments can be summarized as follows: (1) Under plane deformation in anisotropic solids, the asymptotic crack-tip fields have been obtained using Stroh formalism; (2) The T-stress and the coefficient of the second term for sigma(sub y), g(sub 32), have been obtained using path-independent integral, the J-integral and Betti's reciprocal theorem together with auxiliary fields; (3) With experimental data performed by NASA, analyses indicated that the mode-I critical stress intensity factor K(sub Q) provides a satisfactory characterization of fracture initiation for a given laminate thickness, provided the failure is fiber-dominated and crack extends in a self-similar manner; (4) The high constraint specimens, especially for CT specimens, due to large T-stress and large magnitude of negative g(sub 32) term may be expected to inhibit the crack extension in the same plane and promote crack turning; (5) Crack turning out of crack plane in generally anisotropic solids under plane deformation has been studied; (6) The role of T-stress and the higher-order term of sigma(sub y) on the crack turning and stability of the kinked crack has been quantified; (7) Asymptotic crack-tip fields including the effect of transverse shear deformation (Reissner plate theory) in an anisotropic plate under bending, twisting moments, and transverse shear loads has been presented; (8) The expression of the path-independent J-integral in terms of the generalized stress and strain has been derived; (9) Asymptotic crack-tip fields including the effect of transverse shear deformation (Reissner shallow shell theory) in a general anisotropic shell has been developed; (10) The Stroh formalism was used to characterize the crack tip fields in shells up to the second term and the energy release rate was expressed in a very compact form.

Yuan, F. G.↗
NASA NTRS2000

An Improved Elastic and Nonelastic Neutron Transport Algorithm for Space Radiation

A neutron transport algorithm including both elastic and nonelastic particle interaction processes for use in space radiation protection for arbitrary shield material is developed. The algorithm is based upon a multiple energy grouping and analysis of the straight-ahead Boltzmann equation by using a mean value theorem for integrals. The algorithm is then coupled to the Langley HZETRN code through a bidirectional neutron evaporation source term. Evaluation of the neutron fluence generated by the solar particle event of February 23, 1956, for an aluminum water shield-target configuration is then compared with MCNPX and LAHET Monte Carlo calculations for the same shield-target configuration. With the Monte Carlo calculation as a benchmark, the algorithm developed in this paper showed a great improvement in results over the unmodified HZETRN solution. In addition, a high-energy bidirectional neutron source based on a formula by Ranft showed even further improvement of the fluence results over previous results near the front of the water target where diffusion out the front surface is important. Effects of improved interaction cross sections are modest compared with the addition of the high-energy bidirectional source terms.

Clowdsley, Martha S.↗
NASA NTRS1975

A Theoretical Investigation of the Input Characteristics of a Rectangular Cavity-Backed Slot Antenna

Equations which represent the magnetic and electric stored energies are derived for an infinite section of rectangular waveguide and a rectangular cavity. These representations which are referred to as being physically observable are obtained by considering the difference in the volume integrals appearing in the complex Poynting theorem. It is shown that the physically observable stored energies are determined by the field components that vanish in a reference plane outside the aperture. These physically observable representations are used to compute the input admittance of a rectangular cavity-backed slot antenna in which a single propagating wave is assumed to exist in the cavity. The slot is excited by a voltage source connected across its center; a sinusoidal distribution is assumed in the slot. Input-admittance calculations are compared with measured data. In addition, input-admittance curves as a function of electrical slot length are presented for several size cavities. For the rectangular cavity backed slot antenna, the quality factor and relative bandwidth were computed independently by using these energy relationships. It is shown that the asymptotic relationship which is usually assumed to exist between the quality bandwidth and the reciprocal of relative bandwidth is equally valid for the rectangular cavity backed slot antenna.

Cockrell, C. R.↗
NASA NTRS2007

Symmetry, Statistics and Structure in MHD Turbulence

Here, we examine homogeneous MHD turbulence in terms of truncated Fourier series. The ideal MHD equations and the associated statistical theory of absolute equilibrium ensembles are symmetric under P, C and T. However, the presence of invariant helicities, which are pseudoscalars under P and C, dynamically breaks this symmetry. This occurs because the surface of constant energy in phase space has disjoint parts, called components: while ensemble averages are taken over all components, a dynamical phase trajectory is confined to only one component. As the Birkhoff-Khinchin theorem tells us, ideal MHD turbulence is thus non-ergodic. This non-ergodicity manifests itself in low-wave number Fourier modes that have large mean values (while absolute ensemble theory predicts mean values of zero). Therefore, we have coherent structure in ideal MHD turbulence. The level of non-ergodicity and amount of energy contained in the associated coherent structure depends on the values of the helicities, as well as on the presence, or not, of a mean magnetic field and/or overall rotation. In addition to the well known cross and magnetic helicities, we also present a new invariant, which we call the parallel helicity, since it occurs when mean field and rotation axis are aligned. The question of applicability of these results to real (i.e., dissipative) MHD turbulence is also examined. Several long-time numerical simulations on a 64(exp 3) grid are given as examples. It is seen that coherent structure begins to form before decay dominates over nonlinearity. The connection of these results with inverse spectral cascades, selective decay, and magnetic dynamos is also discussed.

Shebalin, John V.↗
NASA NTRS2002

Self-Consistent Magnetosphere-Ionosphere Coupling and Associated Plasma Energization Processes

Magnetosphere-Ionosphere (MI) coupling and associated with this process electron and ion energization processes have interested scientists for decades and, in spite of experimental and theoretical research efforts, are still ones of the least well known dynamic processes in space plasma physics. The reason for this is that the numerous physical processes associated with MI coupling occur over multiple spatial lengths and temporal scales. One typical example of MI coupling is large scale ring current (RC) electrodynamic coupling that includes calculation of the magnetospheric electric field that is consistent with the ring current (RC) distribution. A general scheme for numerical simulation of such large-scale magnetosphere-ionosphere coupling processes has been presented earlier in many works. The mathematical formulation of these models are based on "modified frozen-in flux theorem" for an ensemble of adiabatically drifting particles in the magnetosphere. By tracking the flow of particles through the inner magnetosphere, the bounce-averaged phase space density of the hot ions and electrons can be reconstructed and the magnetospheric electric field can be calculated such that it is consistent with the particle distribution in the magnetosphere. The new a self-consistent ring current model has been developed that couples electron and ion magnetospheric dynamics with calculation of electric field. Two new features were taken into account in addition to the RC ions, we solve an electron kinetic equation in our model, self-consistently including these results in the solution. Second, using different analytical relationships, we calculate the height integrated ionospheric conductances as the function of precipitated high energy magnetospheric electrons and ions as produced by our model. This results in fundamental changes to the electric potential pattern in the inner magnetosphere, with a smaller Alfven boundary than previous potential formulations would predict but one consistent with recent satellite observations. This leads to deeper penetration of the plasma sheet ions and electrons into the inner magnetosphere and more effective ring current ions and electron energization.

Khazanov, G. V.↗
NASA NTRSDate not supplied

Towards Formalization of Advanced Linear Algebra with Applications to Dynamical Systems using PVS

Linear Algebra is essential for numerous aerospace problems of interest. Formal reasoning about hybrid systems that contain variables modeled by differential equations rely on concepts from Linear Algebra such as eigenvalues, matrix decompositions, and matrix valued functions. For example, the long-term dynamics of a system of differential equations depend on the stability/instability of its equilibrium points, which often reduces to an eigenvalue problem. This talk will embark on a quest to formalize theorems and results about eigenvalues and eigenvectors using PVS. We shall start our journey with 2 x 2 complex matrices, where we will apply our PVS code to a simple example of a dynamical system. Since it can be difficult or impossible to give simple expressions of eigenvalues for larger matrices (i.e. 5 x 5 or higher), we then move towards specifying the power method for verified computation of eigenvalue approximations in PVS. This effort requires development of multivariate complex arithmetic. At the end of the day, having such additions to the PVS NASA libraries will help move towards the use of formal methods to verify concepts of control theory and system level verification.

Linear Algebra↗
NASA NTRS1985

Geocoronal structure - The effects of solar radiation pressure and the plasmasphere interaction

The theory of planetary exospheres is extended to incorporate solar radiation pressure in a rigorous manner, and an evaporative geocoronal prototype (classical, motionless exobase) is constructed using Liouville's theorem. Model calculations for density and kinetic temperature at points along the earth-sun axis (solar and antisolar directions) reveal an extensive satellite component, comprising approximately 2/3 of the total hydrogen density near 10 earth radii, and a temperature profile suggestive of an isotropic quasi-Maxwellian velocity distribution for the bound component. A geotail is also evident as an enhancement of the density at local midnight compared to local noon that increases outward (from approximately 25 percent at 10 earth radii to over 60 percent at 20 earth radii). Additional mechanisms acting upon the geocorona alter the basic evaporative case in notable ways. Solar ionization has been included in a simple fashion; the effect is to partially deplete the density without otherwise altering the structure. Interaction with a simple plasmasphere via the Boltzmann equation results in 'heating' the geocorona and enhancing the escape flux at the expense of the density of the bound component, an effect not appreciated in earlier studies; the geotail survives this interaction.

Bishop, J.↗
NASA NTRS1992

Conservative-variable average states for equilibrium gas multi-dimensional fluxes

Modern split component evaluations of the flux vector Jacobians are thoroughly analyzed for equilibrium-gas average-state determinations. It is shown that all such derivations satisfy a fundamental eigenvalue consistency theorem. A conservative-variable average state is then developed for arbitrary equilibrium-gas equations of state and curvilinear-coordinate fluxes. Original expressions for eigenvalues, sound speed, Mach number, and eigenvectors are then determined for a general average Jacobian, and it is shown that the average eigenvalues, Mach number, and eigenvectors may not coincide with their classical pointwise counterparts. A general equilibrium-gas equation of state is then discussed for conservative-variable computational fluid dynamics (CFD) Euler formulations. The associated derivations lead to unique compatibility relations that constrain the pressure Jacobian derivatives. Thereafter, alternative forms for the pressure variation and average sound speed are developed in terms of two average pressure Jacobian derivatives. Significantly, no additional degree of freedom exists in the determination of these two average partial derivatives of pressure. Therefore, they are simultaneously computed exactly without any auxiliary relation, hence without any geometric solution projection or arbitrary scale factors. Several alternative formulations are then compared and key differences highlighted with emphasis on the determination of the pressure variation and average sound speed. The relevant underlying assumptions are identified, including some subtle approximations that are inherently employed in published average-state procedures. Finally, a representative test case is discussed for which an intrinsically exact average state is determined. This exact state is then compared with the predictions of recent methods, and their inherent approximations are appropriately quantified.

Iannelli, G. S.↗
NASA NTRS2005

Bayesian Retrieval of Complete Posterior PDFs of Oceanic Rain Rate From Microwave Observations

This paper presents a new Bayesian algorithm for retrieving surface rain rate from Tropical Rainfall Measurements Mission (TRMM) Microwave Imager (TMI) over the ocean, along with validations against estimates from the TRMM Precipitation Radar (PR). The Bayesian approach offers a rigorous basis for optimally combining multichannel observations with prior knowledge. While other rain rate algorithms have been published that are based at least partly on Bayesian reasoning, this is believed to be the first self-contained algorithm that fully exploits Bayes Theorem to yield not just a single rain rate, but rather a continuous posterior probability distribution of rain rate. To advance our understanding of theoretical benefits of the Bayesian approach, we have conducted sensitivity analyses based on two synthetic datasets for which the true conditional and prior distribution are known. Results demonstrate that even when the prior and conditional likelihoods are specified perfectly, biased retrievals may occur at high rain rates. This bias is not the result of a defect of the Bayesian formalism but rather represents the expected outcome when the physical constraint imposed by the radiometric observations is weak, due to saturation effects. It is also suggested that the choice of the estimators and the prior information are both crucial to the retrieval. In addition, the performance of our Bayesian algorithm is found to be comparable to that of other benchmark algorithms in real-world applications, while having the additional advantage of providing a complete continuous posterior probability distribution of surface rain rate.

Chiu, J. Christine↗
NASA NTRS2000

An Improved Neutron Transport Algorithm for Space Radiation

A low-energy neutron transport algorithm for use in space radiation protection is developed. The algorithm is based upon a multigroup analysis of the straight-ahead Boltzmann equation by using a mean value theorem for integrals. This analysis is accomplished by solving a realistic but simplified neutron transport test problem. The test problem is analyzed by using numerical and analytical procedures to obtain an accurate solution within specified error bounds. Results from the test problem are then used for determining mean values associated with rescattering terms that are associated with a multigroup solution of the straight-ahead Boltzmann equation. The algorithm is then coupled to the Langley HZETRN code through the evaporation source term. Evaluation of the neutron fluence generated by the solar particle event of February 23, 1956, for a water and an aluminum-water shield-target configuration is then compared with LAHET and MCNPX Monte Carlo code calculations for the same shield-target configuration. The algorithm developed showed a great improvement in results over the unmodified HZETRN solution. In addition, a two-directional solution of the evaporation source showed even further improvement of the fluence near the front of the water target where diffusion from the front surface is important.

Heinbockel, John H.↗
NASA NTRS1995

Dissipative rendering and neural network control system design

Model-based control system designs are limited by the accuracy of the models of the plant, plant uncertainty, and exogenous signals. Although better models can be obtained with system identification, the models and control designs still have limitations. One approach to reduce the dependency on particular models is to design a set of compensators that will guarantee robust stability to a set of plants. Optimization over the compensator parameters can then be used to get the desired performance. Conservativeness of this approach can be reduced by integrating fundamental properties of the plant models. This is the approach of dissipative control design. Dissipative control designs are based on several variations of the Passivity Theorem, which have been proven for nonlinear/linear and continuous-time/discrete-time systems. These theorems depend not on a specific model of a plant, but on its general dissipative properties. Dissipative control design has found wide applicability in flexible space structures and robotic systems that can be configured to be dissipative. Currently, there is ongoing research to improve the performance of dissipative control designs. For aircraft systems that are not dissipative active control may be used to make them dissipative and then a dissipative control design technique can be used. It is also possible that rendering a system dissipative and dissipative control design may be combined into one step. Furthermore, the transformation of a non-dissipative system to dissipative can be done robustly. One sequential design procedure for finite dimensional linear time-invariant systems has been developed. For nonlinear plants that cannot be controlled adequately with a single linear controller, model-based techniques have additional problems. Nonlinear system identification is still a research topic. Lacking analytical models for model-based design, artificial neural network algorithms have recently received considerable attention. Using their universal approximation property, neural networks have been introduced into nonlinear control designs in several ways. Unfortunately, little work has appeared that analyzes neural network control systems and establishes margins for stability and performance. One approach for this analysis is to set up neural network control systems in the framework presented above. For example, one neural network could be used to render a system to be dissipative, a second strictly dissipative neural network controller could be used to guarantee robust stability.

Gonzalez, Oscar R.↗