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All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Metrics for More than Two Points at Once

The conventional definition of a topological metric over a space specifies properties that must be obeyed by any measure of "how separated" two points in that space are. Here it is shown how to extend that definition, and in particular the triangle inequality, to concern arbitrary numbers of points. Such a measure of how separated the points within a collection are can be bootstrapped, to measure "how separated" from each other are two (or more) collections. The measure presented here also allows fractional membership of an element in a collection. This means it directly concerns measures of "how spread out" a probability distribution over a space is. When such a measure is bootstrapped to compare two collections, it allows us to measure how separated two probability distributions are, or more generally, how separated a distribution of distributions is.

Wolpert, David H.↗
NASA NTRSDate not supplied

Computational Investigation of Oxidative Etch Pitting in FiberForm and Its Impact on Material Properties

Oxidation-driven carbon erosion does not occur uniformly but rather through the development of localized etch pits at active surface sites. These active sites form due to atomic defects on the carbon surface, making them significantly more reactive than the surrounding, non-defective areas. As a result, these sites are the first to react during ablation, leading to their removal. This process creates new defects in neighboring atoms, increasing their reactivity and causing localized carbon removal around these active sites. In this way, the highly reactive defective areas serve as nucleation points for the formation and growth of etch pits, which can have adverse effects on structural integrity of FiberForm. To better understand how these etch pits impact the material properties of carbon fiber microstructures, we have developed a new capability within the direct simulation Monte Carlo (DSMC) framework to capture the etch pit formation process. This capability, integrated into the DSMC code SPARTA (Stochastic Parallel Rarefied-gas Time-accurate Analyzer), models material removal in the presence of active sites, leading to the formation of etch pits. The current work focuses on studying the effects of these etch pits on the material properties of FiberForm, a widely used base material in thermal protection systems (TPS). The microstructure of virgin FiberForm, obtained via X-ray microtomography, is imported into SPARTA to generate the ablated geometries with etch pits. These modified microstructures are then analyzed using the Porous Microstructure Analysis (PuMA) software to compute various material properties, including elasticity, thermal conductivity, and permeability. We investigate the variation of these properties due to the complex surface topology changes caused by etch pit formation. Additionally, we compare the effects of pitting with the conventional model of shrinking fibers, traditionally used to simulate the ablation of carbon structures. Significant differences emerge between the two approaches. Consequently, this physically realistic model of material removal through etch pit formation offers improved accuracy in predicting the degradation of carbon-based TPS during oxidation. It also provides insights into other mechanisms, such as spallation, where chunks of material are removed into the flow due to etch pit growth. Ultimately, this model enhances our understanding of failure modes in these materials during ablation.

PuMA↗
NASA NTRS1997

The Topology of Symmetric Tensor Fields

Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

Levin, Yingmei↗
NASA NTRS1978

Multispectral data acquisition and classification - Statistical models for system design

In this paper we relate the statistical processes that are involved in multispectral data acquisition and classification to a simple radiometric model of the earth surface and atmosphere. If generalized, these formulations could provide an analytical link between the steadily improving models of our environment and the performance characteristics of rapidly advancing device technology. This link is needed to bring system analysis tools to the task of optimizing remote sensing and (real-time) signal processing systems as a function of target and atmospheric properties, remote sensor spectral bands and system topology (e.g., image-plane processing), radiometric sensitivity and calibration accuracy, compensation for imaging conditions (e.g., atmospheric effects), and classification rates and errors.

Huck, F. O.↗
NASA NTRS1999

Phase Diagrams of Electric-Fduced Aggregation in Conducting Colloids

Under the application of a sufficiently strong electric field, a suspension may undergo reversible phase transitions from a homogeneous random arrangement of particles into a variety of ordered aggregation patterns. The surprising fact about electric-field driven phase transitions is that the aggregation patterns, that are observed in very diverse systems of colloids, display a number of common structural features and modes of evolution thereby implying that a universal mechanism may exist to account for these phenomena. It is now generally believed that this mechanism emanates from the presence of the long-range anisotropic interactions between colloidal particles due to their polarization in an applied field. But, in spite of numerous applications of the electric-field-driven phenomena in biotechnology, separation, materials engineering, chemical analysis, etc. our understanding of these phenomena is far from complete. Thus, it is the purpose of the proposed research to develop a theory and then test experimentally, under normal- and low-gravity conditions, the accuracy of the theoretical predictions regarding the effect of the synergism of the interparticle electric and hydrodynamic interactions on the phase diagram of a suspension. The main results from our theoretical studies performed to-date enable one to trace how the variations of the electrical properties of the constituent materials influence the topology of the suspension phase diagram and then, by using an appropriate phase diagram, to evaluate how the electric-field-induced transformations will depend on the frequency and the strength of the applied field.

Khusid, B.↗
NASA NTRS2005

Dual-Band Deramp Radar Design for Ocean Current Measurements

A mission has been proposed to remotely measure ocean surface currents and surface wind velocities. It will provide the highest resolution and repeat time of these measurements to date for ocean current models with scientific and societal applications. A ground-based experimental radar unit is needed for proof of concept. The proposed experiment set up is to mount the radar on an oil rig to imitate satellite data acquisition. This summer, I completed the radar design. The design employs chirp/deramp topology with simultaneous transmit/receive channels. These two properties allow large system bandwidth, extended sample time, close range imaging, and low sampling rate. The radar operates in the Ku and Ka microwave bands, at 13.5 and 35.5 GHz, respectively, with a system bandwidth of 300 MHz. I completed the radar frequency analysis and research on potential components and antenna configurations. Subsequent work is needed to procure components, as well as to build, test, and deploy the radar.

Haynes, Mark S.↗
NASA NTRS2010

The Vector Vortex Coronagraph: Sensitivity to Low-Order Aberrations, Central Obscuration, Chromaticism, and Polarization

The Vector Vortex Coronagraph is a phase-based coronagraph, one of the most efficient in terms of inner working angle, throughput, discovery space, contrast, and simplicity. Using liquid-crystal polymer technology, this new coronagraph has recently been the subject of lab demonstrations in the near-infrared, visible and was also used on sky at the Palomar observatory in the H and K bands (1.65 and 2.2 micrometers, respectively) to image the brown dwarf companion to HR 7672, and the three extasolar planets around HR 8799. However, despite these recent successes, the Vector Vortex Coronagraph is, as are most coronagraphs, sensitive to the central obscuration and secondary support structures, low-order aberrations (tip-tilt, focus, etc), bandwidth (chromaticism), and polarization when image-plane wavefront sensing is performed. Here, we consider in detail these sensitivities as a function of the topological charge of the vortex and design properties inherent to the manufacturing technology, and show that in practice all of them can be mitigated to meet specific needs.

large ground-based telescopes↗
NASA NTRS1997

Structure-Property Relationships of Bismaleimides

The purpose of this research was to control and systematically vary the network topology of bismaleimides through cure temperature and chemistry (addition of various coreactants) and subsequently attempt to determine structure-mechanical property relationships. Characterization of the bismaleimide structures by dielectric, rheological, and thermal analyses, and density measurements was subsequently correlated with mechanical properties such as modulus, yield strength, fracture energy, and stress relaxation. The model material used in this investigation was 4,4'-BismaleiMidodIphenyl methane (BMI). BMI was coreacted with either 4,4'-Methylene Dianiline (MDA), o,o'-diallyl bisphenol A (DABA) from Ciba Geigy, or Diamino Diphenyl Sulfone (DDS). Three cure paths were employed: a low- temperature cure of 140 C where chain extension should predominate, a high-temperature cure of 220 C where both chain extension and crosslinking should occur simultaneously, and a low-temperature (140 C) cure followed immediately by a high-temperature (220 C) cure where the chain extension reaction or amine addition precedes BMI homopolymerization or crosslinking. Samples of cured and postcured PMR-15 were also tested to determine the effects of postcuring on the mechanical properties. The low-temperature cure condition of BMI/MDA exhibited the highest modulus values for a given mole fraction of BMI with the modulus decreasing with decreasing concentration of BMI. The higher elastic modulus is the result of steric hindrance by unreacted BMI molecules in the glassy state. The moduli values for the high- and low/high-temperature cure conditions of BMI/MDA decreased as the amount of diamine increased. All the moduli values mimic the yield strength and density trends. For the high-temperature cure condition, the room- temperature modulus remained constant with decreasing mole fraction of BMT for the BMI/DABA and BMI/DDS systems. Postcuring PMR-15 increases the modulus over that of the cured material even though density values of cured and postcured PMR were essentially the same. Preliminary results of a continuous and intermittent stress relaxation experiment for BMI:MDA in a 2:1 molar ratio indicate that crosslinking is occurring when the sample is in the undeformed state. Computer simulation of properties such as density, glass transition temperature, and modulus for the low- temperature cure conditions of BMI/MDA and BMI/DABA were completed. The computer modeling was used to help further understand and confirm the structure characterization results. The simulations correctly predicted the trends of these properties versus mole fraction BMI and were extended to other BMI/diamine systems.

Tenteris-Noebe, Anita D.↗
NASA NTRS1988

Static and dynamic properties of incommensurate smectic-A(IC) liquid crystals

The elasticity, topological defects, and hydrodynamics of the incommensurate smectic A(IC) phase liquid crystals are studied. The phase is characterized by two colinear mass density waves of incommensurate spatial frequency. The elastic free energy is formulated in terms of a displacement field and a phason field. It is found that the topological defects of the system are dislocations with a nonzero phason field and phason field components. A two-dimensional Burgers lattice for these dislocations is introduced. It is shown that the hydrodynamic modes of the phase include first- and second-sound modes whose direction-dependent velocities are identical to those in ordinary smectics.

Lubensky, T. C.↗
NASA NTRS1990

On the topology of flux transfer events

A topological analysis is made of a simple model magnetic field of a perturbation at the magnetopause that shares magnetic properties with flux transfer events. The aim is to clarify a number of topological aspects that arise in the case of fully three-dimensional magnetic fields. It is shown that a localized perturbation at the magnetopause can in principle open a closed magnetosphere by establishing magnetic connections across the magnetopause by the formation of a ropelike magnetic field structure. For this purpose a global topological model of a closed magnetosphere is considered as the unperturbed state. The topological substructure of the model flux rope is discussed in detail.

Hesse, Michael↗
NASA NTRS1990

Heating of the corona by magnetic singularities

Theoretical models of current-sheet formation and magnetic heating in the solar corona are examined analytically. The role of photospheric connectivity in determining the topology of the coronal magnetic field and its equilibrium properties is explored; nonequilibrium models of current-sheet formation (assuming an initially well connected field) are described; and particular attention is given to models with discontinuous connectivity, where magnetic singularities arise from smooth footpoint motions. It is shown that current sheets arise from connectivities in which the photospheric flux structure is complex, with three or more polarity regions and a magnetic null point within the corona.

Antiochos, Spiro K.↗
NASA NTRS2023

Parameter Dependencies of Early-Stage Tangential Discontinuity-Driven Foreshock Bubbles in Local Hybrid Simulations

Foreshock bubbles (FBs) are significant foreshock transients that can accelerate particles and disturb the magnetosphere-ionosphere system. In the kinetic formation model, foreshock ions interact with the discontinuity by performing partial gyrations to generate currents that change the magnetic field topology around the discontinuity. However, how different foreshock ion properties affect the growth of the field variations is not well understood. Therefore, we use 2-D local hybrid simulations to study the effects of different foreshock ion distributions and properties on the growth of tangential discontinuity (TD)-driven FBs. We discover that for a gyrophase-bunched distribution with an initial phase where the guiding center is on the other side of the TD, the foreshock ions gyrate together across the TD, causing more foreshock ions to cross the TD and leading to a faster expansion of the structure than for a Maxwellian distribution. A ring distribution also yields higher expansion speeds because of the higher projected velocity into the new perpendicular direction. For Maxwellian distributions, there are positive and linear correlations of the FB expansion speeds with the initial foreshock ion densities, thermal speeds, parallel speeds, and sine of the TD magnetic shear angles. These parameter dependencies grow in strength as the structures evolve with time. The foreshock ion distributions and properties that lead to stronger currents produce more significant magnetic field variations and higher expansion speeds. Our study helps quantify the formation and expansion of FBs to forecast their space weather effects and contribution to shock acceleration.

Andrew Vu↗
NASA NTRSDate not supplied

Simulation of Oxidative Etch Pit Formation and Growth on FiberForm

Erosion of carbon surfaces due to oxidation does not occur uniformly but through the formation of localized etch pits because of active surface sites. These active sites are formed due to the presence of atomic defects on the carbon surface and have much higher reactivity compared to average non-defective sites. Thus, these active sites are the first to react during ablation, resulting in their removal. This causes all the neighboring atoms to be defective, and increasing their reactivity, thus leading to localized carbon removal around these “active” sites. In this manner, these highly reactive defects serve as nucleation sites for the formation and growth of etch pits, with detrimental effects on the structural integrity. In order to understand the influence of these etch pits on the material properties of carbon fiber microstructures, we have developed a new capability within direct simulation Monte Carlo (DSMC) to capture the etch pit formation process. This capability is developed within the DSMC code SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer) and can model the material removal in the presence of active sites leading to the formation of etch pits. The focus of the current work will be to study the effect of etch pits on the material properties of FiberForm, the precursor substrate of the PICA Thermal Protection System (TPS) material. The microstructure of virgin FiberForm obtained directly from X-ray microtomography scans is used within SPARTA to obtain the ablated geometries with etch pits. These pitted microstructures are then imported into the Porous Microstructure Analysis (PuMA) software and various material properties such as thermal conductivity, elasticity, and permeability are computed. The variation of these properties because of the complex evolution of the surface topology due to the formation of etch pits is studied and analyzed. Furthermore, the effect of pitting is compared to the case of uniform radial shrinking of fibers, which has been the standard for modelling ablation of carbon structures, and significant differences are observed. Thus, a physically realistic model of material removal through the formation of etch pits will be helpful in predicting the degradation of carbon-based TPS more accurately during oxidation; as well as other mechanisms such as spallation, which involves the removal of chunks of material into the flow due to the growth of etch pits. This will ultimately improve our understanding of the failure modes in these materials due to ablation.

DSMC↗
NASA NTRSDate not supplied

Simulation of Oxidative Etch Pit Formation and Growth on FiberForm

Erosion of carbon surfaces due to oxidation does not occur uniformly but through the formation of localized etch pits because of active surface sites. These active sites are formed due to the presence of atomic defects on the carbon surface and have much higher reactivity compared to average non-defective sites. Thus, these active sites are the first to react during ablation, resulting in their removal. This causes all the neighboring atoms to be defective, and increasing their reactivity, thus leading to localized carbon removal around these “active” sites. In this manner, these highly reactive defects serve as nucleation sites for the formation and growth of etch pits, with detrimental effects on the structural integrity. In order to understand the influence of these etch pits on the material properties of carbon fiber microstructures, we have developed a new capability within direct simulation Monte Carlo (DSMC) to capture the etch pit formation process. This capability is developed within the DSMC code SPARTA (Stochastic PArallel Rarefied-gas Time-accurate Analyzer) and can model the material removal in the presence of active sites leading to the formation of etch pits. The focus of the current work will be to study the effect of etch pits on the material properties of FiberForm, the precursor substrate of the PICA Thermal Protection System (TPS) material. The microstructure of virgin FiberForm obtained directly from X-ray microtomography scans is used within SPARTA to obtain the ablated geometries with etch pits. These pitted microstructures are then imported into the Porous Microstructure Analysis (PuMA) software and various material properties such as thermal conductivity, elasticity, and permeability are computed. The variation of these properties because of the complex evolution of the surface topology due to the formation of etch pits is studied and analyzed. Furthermore, the effect of pitting is compared to the case of uniform radial shrinking of fibers, which has been the standard for modelling ablation of carbon structures, and significant differences are observed. Thus, a physically realistic model of material removal through the formation of etch pits will be helpful in predicting the degradation of carbon-based TPS more accurately during oxidation; as well as other mechanisms such as spallation, which involves the removal of chunks of material into the flow due to the growth of etch pits. This will ultimately improve our understanding of the failure modes in these materials due to ablation.

DSMC↗
NASA NTRS1977

A new optimum topology switching dc-to-dc converter

A novel switching dc-to-dc converter is presented, which has the same general conversion property (increase or decrease of the input dc voltage) as does the conventional buck-boost converter, and which offers through its new optimum topology higher efficiency, lower output voltage ripple, reduced EMI, smaller size and weight, and excellent dynamic response. One of its most significant advantages is that both input and output current are not pulsating but are continuous (essentially dc with small superimposed switching current ripple), thus resulting in a close approximation to the ideal physically nonrealizable dc-to-dc transformer. The converter retains the simplest possible structure with the minimum number of components which, when interconnected in its optimum topology, yield the maximum performance.

Cuk, S.↗
NASA NTRS1993

A two-dimensional MHD global coronal model - Steady-state streamers

We describe a two-dimensional time-dependent, numerical, magnetohydrodynamic model for the determination of the physical properties of coronal streamers from the top of the transition zone (solar radius = 1) to 15 solar radii. Four examples are given: for dipole, quadrupole, and hexapole initial field topologies. The computed parameters are density, temperature, velocity, and magnetic field. In addition to the properties of the solutions, their accuracy is discussed. We use the model as the basis for a general discussion of the way boundary conditions are specified in this and similar simulations.

Wang, A.-H.↗
NASA NTRS1971

Semilinear (topological) spaces and applications

Semivector spaces are defined and some of their algebraic aspects are developed including some structure theory. These spaces are then topologized to obtain semilinear topological spaces for which a hierarchy of local convexity axioms is identified. A number of fixed point and minmax theorems for spaces with various local convexity properties are established. The spaces of concern arise naturally as various hyperspaces of linear and semilinear (topological) spaces. It is indicated briefly how all this can be applied in socio-economic analysis and optimization.

Prakash, P.↗
NASA NTRS1976

A general unified approach to modelling switching-converter power stages

A method for modeling switching-converter power stages is developed, whose starting point is the unified state-space representation of the switched networks and whose end result is either a complete state-space description or its equivalent small-signal low-frequency linear circuit model. A new canonical circuit model is proposed, whose fixed topology contains all the essential input-output and control properties of any dc-to-dc switching converter, regardless of its detailed configuration, and by which different converters can be characterized in the form of a table conveniently stored in a computer data bank to provide a useful tool for computer aided design and optimization. The new canonical circuit model predicts that, in general, switching action introduces both zeros and poles into the duty ratio to output transfer function in addition to those from the effective filter network.

Middlebrook, R. D.↗