Search NASA⌕ Search

SEARCH · Search NASA

Results for “Analytic linearization”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 415 records · Page 23

Development of lateral-directional departure criteria

Current departure prediction indicators for both open and closed loop flight are developed using the same rigorous analytical approach applied to a linear version of the aircraft model. Emphasis on the assumptions made and terms omitted indicate why the results are somewhat limited. A second approach is presented which is shown to lead to the same results as the first, but is more applicable to the nonlinear problem. Some ideas concerning the application of the linear methods to the nonlinear problem are presented.

Lutze, F. H.↗

Vorticity Transport and Wave Emission in the Protoplanetary Nebula

Higher order numerical algorithms (4th order in time, 3rd order in space) are applied to the Euler/Energy equations and are used to examine vorticity transport and wave motion in a non-self gravitating, initially isentropic Keplerian disk. In this talk we will examine the response of the nebula to an isolated vortex with a circulation about equal to the rotation rate of Jupiter. The vortex is located on the 4 AU circle and the nebula is simulated from 1 to 24 AU. We show that the vortex emits pressure-supported density and Rossby-type wave packets before it decays within a few orbits. The acoustic density waves evolve into weak (non entropy preserving) shock waves that propagate over the entire disk. The Rossby waves remain in the vicinity of the initial vortex disturbance, but are rapidly damped. Temporal frequencies and spatial wavenumbers are derived using the simulation data and compared with analytical dispersion relations from the linearized Euler/Energy equations.

Davis, S. S.↗

Vorticity Transport and Wave Emission In A Protoplanetary Disk

Higher order numerical algorithms (4th order in time, 3rd order in space) are applied to the Euler equations and are used to examine vorticity transport and wave motion in a non-self gravitating, initially isentropic Keplerian disk. In this talk we will examine the response of the disk to an isolated vortex with a circulation about equal to the rotation rate of Jupiter. The vortex is located on the 4 AU circle and the nebula is simulated from 1 to 24 AU. We show that the vortex emits pressure-supported density and Rossby-type wave packets before it decays within a few orbits. The acoustic density waves evolve into weak (non entropy preserving) shock waves that propagate over the entire disk. The Rossby waves remain in the vicinity of the initial vortex disturbance, but are rapidly damped. Temporal frequencies and spatial wavenumbers are derived from the nonlinear simulation data and correlated with analytical dispersion relations from the linearized Euler and energy equations.

Davis, S. S.↗

Experimental Validation of an Integrated Controls-Structures Design Methodology

The first experimental validation of an integrated controls-structures design methodology for a class of large order, flexible space structures is described. Integrated redesign of the controls-structures-interaction evolutionary model, a laboratory testbed at NASA Langley, was described earlier. The redesigned structure was fabricated, assembled in the laboratory, and experimentally tested against the original structure. Experimental results indicate that the structure redesigned using the integrated design methodology requires significantly less average control power than the nominal structure with control-optimized designs, while maintaining the required line-of-sight pointing performance. Thus, the superiority of the integrated design methodology over the conventional design approach is experimentally demonstrated. Furthermore, amenability of the integrated design structure to other control strategies is evaluated, both analytically and experimentally. Using Linear-Quadratic-Guassian optimal dissipative controllers, it is observed that the redesigned structure leads to significantly improved performance with alternate controllers as well.

Maghami, Peiman G.↗

Rapid Acceleration of a Coronal Mass Ejection in the Low Corona and Implications of Propagation

A high-velocity Coronal Mass Ejection (CME) associated with the 2002 April 21 X1.5 flare is studied using a unique set of observations from the Transition Region and Coronal Explorer (TRACE), the Ultraviolet Coronagraph Spectrometer (UVCS), and the Large-Angle Spectrometric Coronagraph (LASCO). The event is first observed as a rapid rise in GOES X-rays, followed by simultaneous conjugate footpoint brightenings connected by an ascending loop or flux-rope feature. While expanding, the appearance of the feature remains remarkably constant as it passes through the TRACE 195 A passband and LASCO fields-of-view, allowing its height-time behavior to be accurately determined. An analytic function, having exponential and linear components, is found to represent the height-time evolution of the CME in the range 1.05-26 R. The CME acceleration rises exponentially to approx. 900 km/sq s within approximately 20-min, peaking at approx.1400 m/sq s when the leading edge is at approx. 1.7 R. The acceleration subsequently falls off as a slowly varying exponential for approx.,90-min. At distances beyond approx. 3.4 R, the height-time profile is approximately linear with a constant velocity of approx. 2400 km/s. These results are briefly discussed in light of recent kinematic models of CMEs.

Gallagher, Peter T.↗

Neutronics and Depletion Methods for Parametric Studies of Fluoride Salt Cooled High Temperature Reactors with Slab Fuel Geometry and Multi-Batch Fuel Management Schemes

The Advanced High Temperature Reactor (AHTR) is a 3400 MWth fluoride salt cooled high temperature reactor (FHR) that uses TRISO particle fuel compacted into slabs rather than spherical fuel pebbles or cylindrical fuel compacts. Simplified methods are required for parametric design studies such that analyzing the entire feasible design space for an AHTR is tractable. These simplifications include fuel homogenization techniques to increase the speed of neutron transport calculations in depletion analysis and equilibrium depletion analysis methods to analyze systems with multi-batch fuel management schemes. This paper presents three elements of significant novelty. First, the reactivity-equivalent physical transformation (RPT) methodology usually applied in systems with coated particle fuel in cylindrical and spherical geometries was extended to slab geometries. Secondly, based on this newly developed RPT method for slab geometries, a methodology that uses Monte Carlo depletion approaches was further developed to search for the maximum discharge burnup in a multi-batch system by iteratively estimating the beginning of equilibrium cycle composition and sampling different discharge burnups. This iterative equilibrium depletion search (IEDS) method fully defines an equilibrium fuel cycle (keff, power, flux and composition evolutions across space and time), but is computationally demanding, although feasible on single-processor workstations. Finally, an analytical method, the non-linear reactivity model, was developed by expanding the linear reactivity model to include an arbitrary number of higher order terms to extrapolate single-batch depletion results to estimate the maximum discharge burnup and BOEC keff in systems with multi-batch fuel management schemes. Results from this method were benchmarked against equilibrium depletion analysis results using the IEDS.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Neutronics and Depletion Methods for Parametric Studies of Fluoride Salt Cooled High Temperature Reactors with Slab Fuel Geometry and Multi-Batch Fuel Management Schemes

The Advanced High-Temperature Reactor (AHTR) is a 3400 MWth fluoride-salt-cooled high-temperature reactor (FHR) that uses TRISO particle fuel compacted into slabs rather than spherical or cylindrical fuel compacts. Simplified methods are required for parametric design studies such that analyzing the entire feasible design space for an AHTR is tractable. These simplifications include fuel homogenization techniques to increase the speed of neutron transport calculations in depletion analysis and equilibrium depletion analysis methods to analyze systems with multi-batch fuel management schemes. This paper presents three elements of significant novelty. First, the Reactivity-Equivalent Physical Transformation (RPT) methodology usually applied in systems with coated-particle fuel in cylindrical and spherical geometries has been extended to slab geometries. Secondly, based on this newly developed RPT method for slab geometries, a methodology that uses Monte Carlo depletion approaches was further developed to search for the maximum discharge burnup in a multi-batch system by iteratively estimating the beginning of equilibrium cycle (BOEC) composition and sampling different discharge burnups. This Iterative Equilibrium Depletion Search (IEDS) method fully defines an equilibrium fuel cycle (keff, power, flux, and composition evolutions) but is computationally demanding, although feasible on single-processor workstations. Finally, an analytical method, the Non-Linear Reactivity Model, was developed by expanding the linear reactivity model to include an arbitrary number of higher order terms so that single-batch depletion results could be extrapolated to estimate the maximum discharge burnup and BOEC keff in systems with multi-batch fuel management schemes. Results from this method were benchmarked against equilibrium depletion analysis results using the IEDS.

fluoride-salt-cooled high-temperature reactor (FHR↗

Hydrodynamic Design Optimization and Wave Tank Testing of a Self-Reacting Two-Body Wave Energy Converter

As worldwide energy consumption continues to increase, so does the demand for renewable energy sources. The total available wave energy resource for the United States alone is 2,640 TWh/yr; nearly two thirds of the 4,000 TWh of electricity used in the United States each year. It is estimated that nearly half of that available energy is recoverable through wave energy conversion techniques. In this thesis, a two-body ‘point absorber’ type wave energy converter with a mechanical power-takeoff is investigated. The two-body wave energy converter extracts energy through the relative motion of a floating buoy and a neutrally buoyant submerged body. Using a linear frequency-domain model, analytical solutions of the optimal power and the corresponding power-takeoff components are derived for the two-body wave energy converter. Using these solutions, a case study is conducted to investigate the influence of the submerged body size on the absorbed power of the device in regular and irregular waves. Here it is found that an optimal mass ratio between the submerged body and floating buoy exists where the device will achieve resonance. Furthermore, a case study to investigate the influence of the submerged body shape on the absorbed power is conducted using a time-domain numerical model. Here it is found that the submerged body should be designed to reduce the effects of drag, but to maintain relatively large hydrodynamic added mass and excitation force. To validate the analytical and numerical models, a 1/30th scale model of a two-body wave energy converter is tested in a wave tank. The results of the wave tank tests show that the two-body wave energy converter can absorb nearly twice the energy of a single-body ‘point absorber’ type wave energy converter.

16 TIDAL AND WAVE POWER↗

Solvent effects in time-dependent self-consistent field methods. II. Variational formulations and analytical gradients

This study describes variational energy expressions and analytical excited state energy gradients for time-dependent self-consistent field methods with polarizable solvent effects. Linear response, vertical excitation, and state-specific solventmodels are examined. Enforcing a variational ground stateenergy expression in the state-specific model is found to reduce it to the vertical excitation model. Variational excited state energy expressions are then provided for the linear response and vertical excitation models and analytical gradients are formulated. Using semiempiricalmodel chemistry, the variational expressions are verified by numerical and analytical differentiation with respect to a static external electric field. Lastly, analytical gradients are further tested by performing microcanonical excited state molecular dynamics with p-nitroaniline.

74 ATOMIC AND MOLECULAR PHYSICS↗

Signal, Noise and Resolution in Linear and Nonlinear Structured-Illumination Microscopy

Structured-illumination microscopy allows widefield fluorescence imaging with resolution beyond the classical diffraction limit. Its linear form extends resolution by a factor of two, and its nonlinear form by an in-principle infinite factor, the effective resolution in practice being determined by noise. In this article, we analyze the noise properties and achievable resolution of the method from a frequency-space perspective. We develop an analytical theory for a general case of linear or nonlinear fluorescent imaging, and verify the analytical calculations with numerical simulation for a special case where nonlinearity is produced by photo-switching of fluorescent labels. We compare the performance of two alternative implementations, using either two-dimensional illumination patterns or sequentially rotated one-dimensional patterns. We show that one-dimensional patterns are advantageous in the linear case, and that in the nonlinear case two-dimensional patterns provide a slight signal-to-noise advantage under idealized conditions, but perform worse than one-dimensional patterns in the presence of non-switchable fluorescent background.

99 GENERAL AND MISCELLANEOUS↗

A Rayleighian approach for modeling kinetics of ionic transport in polymeric media

Here, we report a theoretical approach for analyzing impedance of ionic liquids (ILs) and charged polymers such as polymerized ionic liquids (PolyILs) within linear response. The approach is based on the Rayleigh dissipation function formalism, which provides a computational framework for a systematic study of various factors, including polymer dynamics, in affecting the impedance. We present an analytical expression for the impedance within linear response by constructing a one-dimensional model for ionic transport in ILs/PolyILs. This expression is used to extract mutual diffusion constants, the length scale of mutual diffusion, and thicknesses of a low-dielectric layer on the electrodes from the broadband dielectric spectroscopy (BDS) measurements done for an IL and three PolyILs. Also, static dielectric permittivities of the IL and the PolyILs are determined. The extracted mutual diffusion constants are compared with the self diffusion constants of ions measured using pulse field gradient (PFG) fluorine nuclear magnetic resonance (NMR). For the first time, excellent agreements between the diffusivities extracted from the Electrode Polarization spectra (EPS) of IL/PolyILs and those measured using the PFG-NMR are found, which allows the use of the EPS and the PFG-NMR techniques in a complimentary manner for a general understanding of the ionic transport.

36 MATERIALS SCIENCE↗

Potential linear and angular momentum in the scalar diquark model

We present an analytic two-loop calculation within the scalar diquark model of the potential linear and angular momenta, defined as the difference between the Jaffe-Manohar and Ji notions of linear and angular momenta. As expected by parity and time-reversal symmetries, a direct calculation confirms that the potential transverse momentum coincides with the Jaffe-Manohar (or canonical) definition of average quark transverse momentum, also known as the quark Sivers shift. We examine whether initial/final-state interactions at the origin of the Sivers asymmetry can also generate a potential angular momentum in the scalar diquark model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Opportunities for supersonic performance gains through non-linear aerodynamics

This paper contains a number of examples wherein basic aerodynamic shapes are shown to achieve improved performance when non-linear effects are taken into account. Analytical, numerical, and experimental results have all been used to demonstrate this conclusion. Improvements in both zero lift drag and drag due to lift have been identified. The results show that the exploitation of these non-linear aerodynamic effects may be a key ingredient of future supersonic aircraft.

Mason, W. H.↗

Application of the variational-asymptotical method to composite plates

A method is developed for the 3D analysis of laminated plate deformation which is an extension of a variational-asymptotical method by Atilgan and Hodges (1991). Both methods are based on the treatment of plate deformation by splitting the 3D analysis into linear through-the-thickness analysis and 2D plate analysis. Whereas the first technique tackles transverse shear deformation in the second asymptotical approximation, the present method simplifies its treatment and restricts it to the first approximation. Both analytical techniques are applied to the linear cylindrical bending problem, and the strain and stress distributions are derived and compared with those of the exact solution. The present theory provides more accurate results than those of the classical laminated-plate theory for the transverse displacement of 2-, 3-, and 4-layer cross-ply laminated plates. The method can give reliable estimates of the in-plane strain and displacement distributions.

Hodges, Dewey H.↗

The correlation function for density perturbations in an expanding universe. I - Linear theory

The evolution of the two-point correlation function for adiabatic density perturbations in the early universe is studied. Analytical solutions are obtained for the evolution of linearized spherically symmetric adiabatic density perturbations and the two-point correlation function for these perturbations in the radiation-dominated portion of the early universe. The results are then extended to the regime after decoupling. It is found that: (1) adiabatic spherically symmetric perturbations comparable in scale with the maximum Jeans length would survive the radiation-dominated regime; (2) irregular fluctuations are smoothed out up to the scale of the maximum Jeans length in the radiation era, but regular fluctuations might survive on smaller scales; (3) in general, the only surviving structures for irregularly shaped adiabatic density perturbations of arbitrary but finite scale in the radiation regime are the size of or larger than the maximum Jeans length in that regime; (4) infinite plane waves with a wavelength smaller than the maximum Jeans length but larger than the critical dissipative damping scale could survive the radiation regime; and (5) black holes would also survive the radiation regime and might accrete sufficient mass after decoupling to nucleate the formation of galaxies.

Mcclelland, J.↗

Crack Development in Cross-Ply Laminates Under Uniaxial Tension

This study addresses matrix-dominated failures in carbon fiber/polymer matrix composite laminates in a cross-ply lay-up. The events of interest are interlaminar fracture in the form of transverse cracks in the 90' plies and longitudinal splitting in the 0 deg plies and interlaminar fracture in the form of 0/90 delamination. These events were observed using various nondestructive evaluation (NDE) techniques during static tensile tests. Acoustic emission (AE) x radiography, and edge view microscopy were the principal ones utilized in a real-time environment. A comparison of the NDE results with an analytical model based on the classical linear fracture mechanics concept of strain energy release rate as a criterion for crack growth was performed. The virtual crack closure theory was incorporated with a finite element model to generate strain energy release rate curves for the analytical case. Celion carbon fiber/polyimide matrix (G30-500/PMR-15) was the material tested with cross-ply lay-ups of (0(2)/90(6))s and (0(4)/90(4))s. The test specimens contained thermally induced cracks caused by the high-temperature processing. The analytical model was updated to compensate for the initial damage and to study further accumulation by taking into account the crack interactions. By correlating the experimental and analytical data, the critical energy release rates were found for the observable events of interest.

Gyekenyesi, Andrew L.↗

Low-temperature magnetization relaxation in magnetic molecular solids

The low temperature relaxation of the magnetization in molecular magnetic solids such as Fe{sub 8} is studied using Monte Carlo simulations. A set of rate equations is then developed to understand the simulations, and the results are compared. The simulations show that the magnetization of an initially saturated sample deviates as a square-root in time at short times, as observed experimentally, and this law is derived from the rate equations analytically. -- Highlights: •A novel set of non-linear rate equations for the coupled evolution of the magnetization and dipole field distribution. •An analytic derivation of the short-time square root in time behavior of the magnetization relaxation. •Agreement between theory and simulations without further fitting parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

THE POLARIZATION PROPERTIES OF INVERSE COMPTON EMISSION AND IMPLICATIONS FOR BLAZAR OBSERVATIONS WITH THE GEMS X-RAY POLARIMETER

NASA's Small Explorer Mission GEMS (Gravity and Extreme Magnetism SMEX), scheduled for launch in 2014, will have the sensitivity to detect and measure the linear polarization properties of the 0.5 keV and 2-10 keV X-ray emission of a considerable number of galactic and extragalactic sources. The prospect of sensitive X-ray polarimetry justifies a closer look at the polarization properties of the basic emission mechanisms. In this paper, we present analytical and numerical calculations of the linear polarization properties of inverse Compton scattered radiation. We describe a generally applicable formalism that can be used to numerically compute the polarization properties in the Thomson and Klein-Nishina regimes. We use the code to perform for the first time a detailed comparison of numerical results and the earlier analytical results derived by Bonometto et al. for scatterings in the Thomson regime. Furthermore, we use the numerical formalism to scrutinize the polarization properties of synchrotron self-Compton (SSC) emission, and of inverse Compton radiation emitted in the Klein-Nishina regime. We conclude with a discussion of the scientific potential of future GEMS observations of blazars. The GEMS mission will be able to confirm the synchrotron origin of the low-energy emission component from high-frequency-peaked BL Lac objects. Furthermore, the observations have the potential to decide between an SSC and external-Compton origin of the high-energy emission component from flat spectrum radio quasars and low-frequency-peaked BL Lac objects.

79 ASTRONOMY AND ASTROPHYSICS↗