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NASA NTRS2015

Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies

Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L alpha m(sup p) between themean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p approximately equals 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local 'stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 − q with q approximately equaling 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x(sub 1) family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution of galaxies are discussed.

chaos aEuro" galaxies:↗

NASA NTRS2016

Imperfection Insensitivity Analyses of Advanced Composite Tow-Steered Shells

Two advanced composite tow-steered shells, one with tow overlaps and another without overlaps, were previously designed, fabricated and tested in end compression, both without cutouts, and with small and large cutouts. In each case, good agreement was observed between experimental buckling loads and supporting linear bifurcation buckling analyses. However, previous buckling tests and analyses have shown historically poor correlation, perhaps due to the presence of geometric imperfections that serve as failure initiators. For the tow-steered shells, their circumferential variation in axial stiffness may have suppressed this sensitivity to imperfections, leading to the agreement noted between tests and analyses. To investigate this further, a numerical investigation was performed in this study using geometric imperfections measured from both shells. Finite element models of both shells were analyzed first without, and then, with measured imperfections that were then, superposed in different orientations around the shell longitudinal axis. Small variations in both the axial prebuckling stiffness and global buckling load were observed for the range of imperfections studied here, which suggests that the tow steering, and resulting circumferentially varying axial stiffness, may result in the test-analysis correlation observed for these shells.

Wu, K. Chauncey↗

NASA NTRS2016

SUPIN: A Computational Tool for Supersonic Inlet Design

A computational tool named SUPIN is being developed to design and analyze the aerodynamic performance of supersonic inlets. The inlet types available include the axisymmetric pitot, three-dimensional pitot, axisymmetric outward-turning, two-dimensional single-duct, two-dimensional bifurcated-duct, and streamline-traced inlets. The aerodynamic performance is characterized by the flow rates, total pressure recovery, and drag. The inlet flow-field is divided into parts to provide a framework for the geometry and aerodynamic modeling. Each part of the inlet is defined in terms of geometric factors. The low-fidelity aerodynamic analysis and design methods are based on analytic, empirical, and numerical methods which provide for quick design and analysis. SUPIN provides inlet geometry in the form of coordinates, surface angles, and cross-sectional areas. SUPIN can generate inlet surface grids and three-dimensional, structured volume grids for use with higher-fidelity computational fluid dynamics (CFD) analysis. Capabilities highlighted in this paper include the design and analysis of streamline-traced external-compression inlets, modeling of porous bleed, and the design and analysis of mixed-compression inlets. CFD analyses are used to verify the SUPIN results.

computational fluid dynamics↗

NASA NTRS2013

Dynamics of Orbits near 3:1 Resonance in the Earth-Moon System

The Interstellar Boundary Explorer (IBEX) spacecraft is currently in a highly elliptical orbit around Earth with a period near 3:1 resonance with the Moon. Its orbit is oriented so that apogee does not approach the Moon. Simulations show this orbit to be remarkably stable over the next twenty years. This article examines the dynamics of such orbits in the Circular Restricted 3-Body Problem (CR3BP). We look at three types of periodic orbits, each exhibiting a type of symmetry of the CR3BP. For each of the orbit types, we assess the local stability using Floquet analysis. Although not all of the periodic solutions are stable in the mathematical sense, any divergence is so slow as to produce practical stability over several decades. We use Poincare maps with twenty-year propagations to assess the nonlinear stability of the orbits, where the perturbation magnitudes are related to the orbit uncertainty for the IBEX mission. Finally we show that these orbits belong to a family of orbits connected in a bifurcation diagram that exhibits exchange of stability. The analysis of these families of period orbits provides a valuable starting point for a mission orbit trade study.

Dichmann, Donald J.↗

NASA NTRS2016

NASAs VESGEN: Systems Analysis of Vascular Phenotypes from Stress and Other Signaling Pathways Using GeneLab.

One fundamental requirement shared by humans with all higher terrestrial life forms, including insect wings, higher land plants and other vertebrates, is a complex, fractally branching vascular system. NASA's VESsel GENeration Analysis (VESGEN) software maps and quantifies vascular trees, networks, and tree-network composites according to weighted physiological rules such as vessel connectivity, tapering and bifurcational branching. According to fluid dynamics, successful vascular transport requires a complex distributed system of highly regulated laminar flow. Microvascular branching rules within vertebrates, dicot leaves and the other organisms therefore display many similarities. One unifying perspective is that vascular patterning offers a useful readout that necessarily integrates complex molecular signaling pathways. VESGEN has elucidated changes in vascular pattern resulting from inflammatory, stress response, developmental and other signaling within numerous tissues and major model organisms studied for Space Biology. For a new VESGEN systems approach, we analyzed differential gene expression in leaves of Arabidopsis thaliana reported by GeneLab (GLDS-7) for spaceflight. Vascular-related changes in leaf gene expression were identified that can potentially be phenocopied by mutants in ground-based experiments. To link transcriptional, protein and other molecular change with phenotype, alterations in the Euclidean and dynamic dimensions (x,y,t) of vascular patterns for Arabidopsis leaves and other model species are being co-localized with signaling patterns of single molecular expression analyzed as information dimensions (i,j,k,...). Previously, Drosophila microarray data returned from space suggested significant changes in genes related to wing venation development that include EGF, Notch, Hedghog, Wingless and Dpp signaling. Phenotypes of increasingly abnormal ectopic wing venation in the (non-spaceflight) Drosophila wing generated by overexpression of a Notch antagonist were analyzed by VESGEN. Other VESGEN research applications include the mouse retina, GI and coronary vessels, avian placental analogs and translational studies in the astronaut retina related to health challenges for long-duration missions.

Venation↗

NASA NTRS2016

Using NASA's GeneLab for VESGEN Systems Analysis of Vascular Phenotypes from Stress and Other Signaling Pathways

One fundamental requirement shared by humans with all higher terrestrial life forms, including other vertebrates, insects, and higher land plants, is a complex, fractally branching vascular system. NASA's VESsel GENeration Analysis (VESGEN) software maps and quantifies vascular trees, networks, and tree-network composites according to weighted physiological rules such as vessel connectivity, tapering and bifurcational branching. According to fluid dynamics, successful vascular transport requires a complex distributed system of highly regulated laminar flow. Microvascular branching rules within vertebrates, dicot leaves and the other organisms therefore display many similarities. A unifying perspective is that vascular patterning offers a useful readout of molecular signaling that necessarily integrates these complex pathways. VESGEN has elucidated changes in vascular pattern resulting from inflammatory, developmental and other signaling within numerous tissues and major model organisms studied for Space Biology. For a new VESGEN systems approach, we analyzed differential gene expression in leaves of Arabidopsis thaliana reported by GeneLab (GLDS-7) for spaceflight. Vascularrelated changes in leaf gene expression were identified that can potentially be phenocopied by mutants in ground-based experiments. To link transcriptional, protein and other molecular change with phenotype, alterations in the spatial and dynamic dimensions of vascular patterns for Arabidopsis leaves and other model species are being co-localized with signaling patterns of single molecular expression analyzed as information dimensions. Previously, Drosophila microarray data returned from space suggested significant changes in genes related to wing venation development that include EGF, Notch, Hedghog, Wingless and Dpp signaling. Phenotypes of increasingly abnormal ectopic wing venation in the (non-spaceflight) Drosophila wing generated by overexpression of a Notch antagonist were analyzed by VESGEN. Other VESGEN research applications include the mouse retina, GI and coronary vessels, avian placental analogs and translational studies in the astronaut retina related to health challenges for long-duration missions.

Venation↗

NASA NTRS2016

MMS Observations of Large Guide Field Symmetric Reconnection Between Colliding Reconnection Jets at the Center of a Magnetic Flux Rope at the Magnetopause

We report evidence for reconnection between colliding reconnection jets in a compressed current sheet at the center of a magnetic flux rope at Earth's magnetopause. The reconnection involved nearly symmetric Inflow boundary conditions with a strong guide field of two. The thin (2.5 ion-skin depth (d(sub i) width) current sheet (at approximately 12 d(sub i) downstream of the X line) was well resolved by MMS, which revealed large asymmetries in plasma and field structures in the exhaust. Ion perpendicular heating, electron parallel heating, and density compression occurred on one side of the exhaust, while ion parallel heating and density depression were shifted to the other side. The normal electric field and double out-of-plane (bifurcated) currents spanned almost the entire exhaust. These observations are in good agreement with a kinetic simulation for similar boundary conditions, demonstrating in new detail that the structure of large guide field symmetric reconnection is distinctly different from antiparallel reconnection.

Oieroset, M.↗

NASA NTRS2016

What Would Happen to Superstorm Sandy Under the Influence of a Substantially Warmer Atlantic Ocean?

Based on ensemble numerical simulations, we find that possible responses of Sandy-like superstorms under the influence of a substantially warmer Atlantic Ocean bifurcate into two groups. In the first group, storms are similar to present-day Sandy from genesis to extratropical transition, except they are much stronger, with peak Power Destructive Index (PDI) increased by 50-80%, heavy rain by 30-50%, and maximum storm size (MSS) approximately doubled. In the second group, storms amplify substantially over the interior of the Atlantic warm pool, with peak PDI increased by 100-160%, heavy rain by 70-180%, and MSS more than tripled compared to present-day Superstorm Sandy. These storms when exiting the warm pool, recurve northeastward out to sea, subsequently interact with the developing midlatitude storm by mutual counterclockwise rotation around each other and eventually amplify into a severe Northeastern coastal storm, making landfall over the extreme northeastern regions from Maine to Nova Scotia.

radar reflectivities↗

NASA NTRS2017

Prominence Eruption Initiated by Helical Kink Instability of an Embedded Flux Rope

We study the triggering mechanism of a limb-prominence eruption and the associated coronal mass ejection (CME) near AR 12342 using Solar Dynamics Observatory and Large Angle and Spectrometric Coronagraph/Solar Heliospheric Observatory observations. The prominence is seen with an embedded flux thread (FT) at one end and bifurcates from the middle to a different footpoint location. The morphological evolution of the FT is similar to that of an unstable flux rope (FR), which we regard as a prominence-embedded FR. The FR twist exceeds the critical value. In addition, the morphology of the prominence plasma in 304 Å images marks the helical nature of the magnetic skeleton, with a total of 2.96 turns along arc length. The potential field extrapolation model indicates that the critical height of the background magnetic field gradient falls within the inner corona (105 Mm), which is consistent with the extent of coronal plasma loops. These results suggest that the helical kink instability in the embedded FR caused the slow rise of the prominence to the height of the torus instability domain. Moreover, the differential emission measure analysis unveils heating of the prominence plasma to coronal temperatures during an eruption, suggesting reconnection-related heating underneath the upward rising embedded FR. The prominence starts with a slow rise motion of 10 km s(exp. -1), which is followed by fast and slow acceleration phases that have an average acceleration of 28.9 m s(exp. -2) and 2.4 m s(exp. -2) in C2 and C3 field of view, respectively. As predicted by previous numerical simulations, the observed synchronous kinematic profiles of the CME leading edge and the core support the involved FR instability in the prominence initiation.

Vemareddy, P.↗

NASA NTRS2017

Vascular Patterning Analysis by VESGEN 2D/3D with Bioinformatics: Updates for Rodent Tissues

Fractally branching vascular systems are a complex physiological requirement shared by humans with all higher terrestrial life forms, including other vertebrates, insects, and higher land plants. Vascular trees, networks, and tree-network composites are therefore mapped and quantified by the VESsel GENeration Analysis (VESGEN) software according to weighted physiological vascular rules that include vessel connectivity, tapering and bifurcational branching. According to fluid dynamics, successful vascular transport depends upon a complex distributed system of highly regulated laminar flow. VESGEN has elucidated changes in vascular patterning resulting from inflammatory, developmental and other signaling pathways within numerous tissues of major model organisms important for Space Biology, especially for rodents. Important early stage regenerative opportunities have been identified by VESGEN vascular analysis for visual impairments in the human retina, and is currently being used for research into astronaut visual and ocular disorders associated with long duration missions. The VESGEN 2D software is a mature, automated, widely published capability for which beta testing and public release by NASA is planned for the upcoming year. Early-stage capabilities for VESGEN 3D analysis are under development for the rodent retina and intestine as prototype tissues. A prototype VESGEN 2D Bioinformatics software capability has also been developed to associate phenotypic changes in molecular expression with vascular structure and function. By new VESGEN bioinformatic innovations, expression patterns of the genetic, transcriptional, protein and other markers for regulatory molecules such as vascular endothelial growth factor (VEGF) and their receptors, often indicators of tissue oxygenation status, are co-localized with alterations in vascular pattern. Biomarkers are therefore mapped and quantified as information dimensions directly correlated with the spatial dimensions of a vascular pattern. Further important technology innovations by NASA include substantial image segmentation advances for more automated binary extraction of the grayscale vascular patterns, together with informative associated image quality assessments. Vascular mapping and quantification capabilities for the rodent retina and intestine are illustrated for VESGEN 2D, along with technology status reports on VESGEN 3D and Bioinformatic capabilities. Research partially supported by Ames Center Innovation Awards.

Parsons-Wingerter, P.↗

NASA NTRS2018

Magnetic Reconnection on Dayside Crustal Magnetic Fields at Mars: MAVEN Observations

The identification of magnetic reconnection on the dayside of Mars has been elusive owing to the lack of comprehensive plasma and field measurements. Here we present direct measurements of dayside in situ reconnection signatures by the comprehensive particles and fields package on board the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft over strong crustal magnetic fields in the southern hemisphere of Mars. During a crossing of a bifurcated current sheet consisting of northward and southward magnetic fields, MAVEN recorded (i) ionospheric photoelectrons trapped on closed magneticfield lines, (ii) Hall magnetic fields and a nonzero normal field with polarity consistent with a crossing northward of the X line, and (iii) northward Alfvenic ion jets. Dayside magnetic reconnection on crustal magnetic fields could control the global configuration and topology of the Martian magnetosphere and alter the ion escape pattern from the dayside ionosphere.

Magnetic↗

NASA NTRSDate not supplied

Application of Flux Conserved Modeling to an Unsteady Combustion Driven Pseudo-Shock

Quasi-steady correlation-based and flux conserved models of the pseudo-shock pressure profile are experimentally assessed in the Air Force Research Lab RC-18 Sub-Scale DirectConnect Isolator Combustion Facility. A bifurcated normal pseudo-shock is established in the 2.67 aspect ratio isolator test section by a downstream cavity-stabilized combustor. The Waltrup-Billig correlation, Smart flux conserved model, and Fiévet data driven flux conserved models are compared against measured pressure profiles. The literature models are found to perform poorly in a high-amplitude forced environment of RC-18, where shock speeds upwards of 20% the isolator Mach number occur. Two modifications to the quasi-steady Fiévet data driven flux conserved model are proposed including incorporating an estimate of pseudo-shock static pressure recovery and exercising the model in a shock stationary reference frame. It is shown that these modifications allow the quasi-steady flux conserved modeling approach to accurately predict pseudo-shock pressure profiles over the discrete phases of high-amplitude forced dynamics.

Shock Train↗

NASA NTRS2018

Numerical Studies of Hall Thruster Acceleration Region Electron Transport

Azimuthal direction 1-D and azimuthal and axial direction 2-D Particle in Cell (PIC) simulations of the Hall thruster acceleration and near-plume regions are presented. The axial extent of the 2-D computational domain is based on the ExB drift parameter, 𝑫𝑬𝒙𝑩, the number of times around the channel an electron ExB drifts before being scattered. With only high energy main beam ions, the simulations produced a broad potential profile in the acceleration region. The addition of a small amount of ionization in the acceleration domain at a rate consistent with Hall thruster parameters causes the potential profile to develop two distinct regions. In the upstream portion of the computational domain, the potential profile is very steep, typical of Hall thruster acceleration regions. In the downstream portion, the potential profile is almost flat, like potentials in Hall thruster near plume regions. This bifurcation happens naturally; there is no other change in code parameters between the two results. Without the addition of a small amount of ionization in the acceleration region, the axial electron transport is very low. With ionization, the calculated ratio of electron current to ion current is the same order of those measured in Hall thrusters. This suggests that in regions with lower energy electrons and ions, plasma waves are effective in allowing crossfield transport, and axial electric fields are small. In the acceleration region, the plasma waves are less effective at scattering the energetic electrons, and high axial electric fields are needed to produce the observed cross-field electron transport.

Ortega, Alejandro Lopez↗

NASA NTRSDate not supplied

Nonlinear Buckling Analysis of Tow-Steered Composite Cylinders with Cutouts

The buckling and postbuckling behavior of two composite tow-steered shells with cutouts of different sizes is assessed using nonlinear finite element (FE) analysis and compared to experimental measurements. The cylindrical shells are manufactured using an automated fiber placement system, where the shells’ fiber orientation angles vary continuously around the shell circumference from ±10 degrees on the crown and keel to ±45 degrees on the sides. One shell features thickness variations due to tow overlaps that result from application of all 24 tows during each pass of the fiber placement system. The second shell uses the system’s tow drop/add capability to achieve a more uniform wall thickness without overlaps. Unreinforced cutouts of two different sizes—the first smaller cutout representing a passenger door on a commercial aircraft and the second larger cutout a cargo door—were machined into each of the two cylinders resulting in a total of four test cases. These cylinders were tested in axial compression and buckled elastically in previous work and are now analyzed using nonlinear FE models to compare bifurcation buckling loads as well as the load-displacement response in the prebuckling and postbuckling regimes. For all four shells analyzed, the prebuckling stiffness, buckling load, and deformation mode sequence throughout the loading-unloading cycle is accurately reproduced by the models. In particular, the shells first buckle locally around the cutouts in a stable (super-critical) manner with only a slight decrease in axial stiffness, which occurs due to the favorable load redistribution facilitated by tow steering. The shells then buckle globally in an unstable (sub-critical) manner with diamond-shaped buckles forming to the left and right of the cutouts. The buckling load of all shells with cutouts is at least 82% of the buckling load of the pristine shells without cutouts. Overall, the ability to sustain local buckling phenomena, and the relatively small reductions in global buckling load compared to pristine shells without cutouts, demonstrates the great potential of using tow steering to mitigate the adverse effects of cutouts in axially-compressed shell structures.

composites↗

NASA NTRSDate not supplied

Nonlinear Buckling Analysis of Tow-Steered Composite Cylinders with Cutouts

The buckling and postbuckling behavior of two composite tow-steered shells with cutouts of different sizes is assessed using nonlinear finite element (FE) analysis and compared to experimental measurements. The cylindrical shells are manufactured using an automated fiber placement system, where the shells’ fiber orientation angles vary continuously around the shell circumference from 10 degrees on the crown and keel to 45 degrees on the sides. One shell features thickness variations due to tow overlaps that result from application of all 24 tows during each pass of the fiber placement system. The second shell uses the system’s tow drop/add capability to achieve a more uniform wall thickness without overlaps. Unreinforced cutouts of two different sizes—the first smaller cutout representing a passenger door on a commercial aircraft and the second larger cutout a cargo door—were machined into each of the two cylinders resulting in a total of four test cases. These cylinders were tested in axial compression and buckled elastically in previous work and are now analyzed using nonlinear FE models to compare bifurcation buckling loads as well as the load-displacement response in the prebuckling and postbuckling regimes. For all four shells analyzed, the prebuckling stiffness, buckling load, and deformation mode sequence throughout the loading-unloading cycle is accurately reproduced by the models. In particular, the shells first buckle locally around the cutouts in a stable (super-critical) manner with only a slight decrease in axial stiffness, which occurs due to the favorable load redistribution facilitated by tow steering. The shells then buckle globally in an unstable (sub-critical) manner with diamond-shaped buckles forming to the left and right of the cutouts. The buckling load of all shells with cutouts is at least 82% of the buckling load of the pristine shells without cutouts. Overall, the ability to sustain local buckling phenomena, and the relatively small reductions in global buckling load compared to pristine shells without cutouts, demonstrates the great potential of using tow steering to mitigate the adverse effects of cutouts in axially-compressed shell structures.

Buckling↗

NASA NTRS2022

Nonlinear Evolution of Instabilities in a Laminar Separation Bubble at a Hypersonic Mach Number

The development of both convective stationary perturbation as well as global instabilities in the vicinity of a laminar separation bubble above an axisymmetric compression corner in a hypersonic flow is investigated using numerical simulations. The flow configuration of primary interest corresponds to the cone-cylinder-flare model used in experimental measurements in the Boeing/AFOSR Mach-6 Quiet Tunnel at Purdue University. For a flare angle of 10 degrees and a unit Reynolds number of 11.5 x 10 6 m -1 , their surface flow visualizations identified the presence of streamwise elongated thermal streaks near the reattachment position and the dominant azimuthal spacing between the streaks was determined to be approximately 10 degrees (i.e., an azimuthal mode number of 36). Previous linear stability analyses predicted that the amplification characteristics of small amplitude, unsteady, convective instabilities within this flow were consistent with the surface pressure fluctuations measured in the experiment. However, their accompanying analysis of global instabilities had found the separation bubble to be weakly unstable at the 10 degrees flare angle, with the most unstable global mode corresponding to a stationary disturbance with an azimuthal wavenumber of m ≈ 5, which was well below the measured wavenumber of m = 36. Besides confirming the presence of the global instability at these flow conditions, the present numerical simulations quantify the details of the stationary equilibrium state associated with the supercritical bifurcation resulting from the nonlinear saturation of the unstable global mode. Although velocity perturbations associated with the saturated global mode are dominated by the fundamental spanwise wavelength associated with the linear global instability, the surface heat flux downstream of reattachment is dominated by m = 36 in agreement with experimental measurements. However, the shorter wavelength peak ( m = 36) in the azimuthal spectrum is not manifested as streaks with an azimuthal spacing of 10 degrees. An additional simulation of the combined evolution of both unsteady convective and global instabilities indicates that the nonlinear interactions between a broadband spectrum of oblique Mack’s first mode instabilities generate stationary vortex modes with a higher dominant wavenumber ( m = 60) as that observed in the experiments. Additional analyses are performed to predict the global mode behavior at other flare angles and how it differs from the convective centrifugal instability due to concave streamline curvature over the compression corner.

Hypersonic flow↗

NASA NTRS2022

Nonlinear Evolution of Instability in a Laminar Separation Bubble at Hypersonic Mach Number

High speed flow↗

NASA NTRS2021

Lower-Hybrid Drift Waves and Their Interaction With Plasmas in A 3D Symmetric Reconnection Simulation With Zero Guide Field

We investigate lower-hybrid drift waves (LHDW) in symmetric magnetic reconnection with zero guide field using three-dimensional particle-in-cell simulations. The long-wavelength mode with develops in the bifurcated electron current layer around the X-line within the width of the electron meandering motion from the mid-plane, where is the ion (electron) gyroradius. The short-wavelength mode with develops in the separatrix region downstream of the electron outflow jet, producing electron vortices in the background flow frame. Electrons follow the E × B drift with corrections from the diamagnetic drift and are heated inside the vortices with diverging electric fields. In the vortices, ions have comparable E × B and inertia drifts, which together mostly cancel the diamagnetic drift. Toward the center of diverging field vortices, ions are decelerated, leading to a decrease in the perpendicular temperature, while the loss of low-energy ions results in an increase in the parallel temperature. Parallel electric fields exist as a combination of the LHDW wave field projected to the magnetic field direction and the penetration of whistler waves that are mainly outside of the LHDW layer. The magnetic flux tube is twisted in the vortices. The twist may potentially lead to slippage reconnection, as indicated by the non-uniform parallel potential variation across field lines, while the periodic variations of the twisting directions are a limiting factor.

Shan Wang↗