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NASA NTRS2020

Dynamic Stability And Adaptive Control of Networked Evolving Formations with Weak Nonlinearities

The dynamic stability of formation geometry is vital to the design of large scale multiagent systems. In this paper, we probe into the structure of the formation system matrix using the Laplacian of a digraph to develop several fundamental theoretical results on the stability of formation geometry. Our key-results include the integration of the graph Laplacian into linear and weak-nonlinear relative dynamics, the development of several new coordinate transformations that expose the influence of the graph Laplacian matrix on the control laws of the agents, and the use of direct adaptive control as stability restoring devices. We also develop two fundamental results that provide upper bounds for stable formation evolution under nonlinear perturbations of agent dynamics. Finally, we use an illustrative example to demonstrate our theoretical findings.

Gehlot, Vinod P.↗

NASA NTRS1989

Direct simulations of turbulent flow using finite-difference schemes

A high-order accurate finite-difference approach is presented for calculating incompressible turbulent flow. The methods used include a kinetic energy conserving central difference scheme and an upwind difference scheme. The methods are evaluated in test cases for the evolution of small-amplitude disturbances and fully developed turbulent channel flow. It is suggested that the finite-difference approach can be applied to complex geometries more easilty than highly accurate spectral methods. It is concluded that the upwind scheme is a good candidate for direct simulations of turbulent flows over complex geometries.

Rai, Man Mohan↗

NASA NTRS1991

Orbital decay in aspherical galaxies. II - Triaxial systems

A previous analysis of orbital decay of small satellite galaxies into moderately oblate, axisymmetrical cannibal galaxies with Staeckel potentials is generalized here to triaxial systems with arbitary anisotropy and internal streaming. The orbital evolution to be expected in systems with differing degrees of anisotropy or rotation is briefly discussed. The evolution of some representative orbits is presented in detail using the orbit-averaged anisotropic Chandrasekhar drag and the distribution functions for perfect ellipsoids. The validity of orbit averaging is assessed by comparing the results with ensembles of single-particle orbits integrated directly in the same potential and the same drag prescription. An attempt is made to gauge the validity of the Chandrasekhar formula by comparison with restricted N-body solutions. It is found that the orbit-averaged evolution is consistent with such simulations.

Statler, Thomas S.↗

NASA NTRS2011

Black Hole Coalescence: The Gravitational Wave Driven Phase

When two supermassive black holes (SMBHS) approach within 1-10 mpc, gravitational wave (GW) losses begin to dominate the evolution of the binary, pushing the system to merge in a relatively small time. During this final inspiral regime, the system will emit copious energy in GWs, which should be directly detectable by pulsar timing arrays and space-based interferometers. At the same time, any gas or stars in the immediate vicinity of the merging 5MBHs can get heated and produce bright electromagnetic (EM) counterparts to the GW signals. We present here a number of possible mechanisms by which simultaneous EM and GW signals will yield valuable new information about galaxy evolution, accretion disk dynamics, and fundamental physics in the most extreme gravitational fields.

Schnittman, Jeremy D.↗

NASA NTRS2011

The Astrophysics of Merging Black Holes

When two supermassive black holes (SMBHs) approach within 1-10 mpc, gravitational wave (GW) losses begin to dominate the evolution of the binary, pushing the system to merge in a relatively small time. During this final inspiral regime, the system will emit copious energy in GWs, which should be directly detectable by pulsar timing arrays and space-based interferometers. At the same time, any gas or stars in the immediate vicinity of the merging 5MBHs can get heated and produce bright electromagnetic (EM) counterparts to the GW signals. We present here a number of possible mechanisms by which simultaneous EM and GW signals will yield valuable new information about galaxy evolution, accretion disk dynamics, and fundamental physics in the most extreme gravitational fields.

Schnittman, Jeremy D.↗

NASA NTRS2012

Electromagnetic Signatures of SMBH Coalescence

Schnittman, Jeremy↗

NASA NTRS1993

Stochastic damage evolution in textile laminates

A probabilistic model utilizing random material characteristics to predict damage evolution in textile laminates is presented. Model is based on a division of each ply into two sublaminas consisting of cells. The probability of cell failure is calculated using stochastic function theory and maximal strain failure criterion. Three modes of failure, i.e. fiber breakage, matrix failure in transverse direction, as well as matrix or interface shear cracking, are taken into account. Computed failure probabilities are utilized in reducing cell stiffness based on the mesovolume concept. A numerical algorithm is developed predicting the damage evolution and deformation history of textile laminates. Effect of scatter of fiber orientation on cell properties is discussed. Weave influence on damage accumulation is illustrated with the help of an example of a Kevlar/epoxy laminate.

Dzenis, Yuris A.↗

NASA NTRS2019

Differences in the Vertical and Microphysical Evolution of Volcanic and Pyrocumulonimbus Stratospheric Aerosol Plumes as Observed by CALIOP and CATS Satellite Lidar

For some time, volcanic eruptions have been thought to be the only significant direct injectors of aerosols in the stratosphere. However, recent fire seasons have featured fire events resulting in large volcanic-sized pyrocumulonimbus plumes of smoke aerosols reaching many kilometers into the lower stratosphere. To understand and model the effects of these pyrocumulonimbus events on stratospheric composition and climate, a natural analogy lies with better studied volcanic events; however, differences in plume composition may limit this comparison. Using satellite lidar from both CATS and CALIOP, we show that the stratospheric aerosol plumes from the record-setting Pacific Northwest pyrocumulonimbus event of 2017 and the Calbuco volcanic eruption of 2015 evolve differently both vertically and microphysically. Specifically, depolarization ratios indicate that this pyrocumulonimbus event’s aerosol particles became more irregularly shaped over time in contrast to volcanic aerosols which become more spherical over time. Accounting for these changes in aerosol properties may be significant in assessing the effects of pyrocumulonimbus events on the Earth’s radiative balance and aid in refining stratospheric aerosol typing algorithms to differentiate volcanic from pyrocumulonimbus plumes.

Christian, Kenneth↗

NASA NTRS2010

Parameterizing Coefficients of a POD-Based Dynamical System

A method of parameterizing the coefficients of a dynamical system based of a proper orthogonal decomposition (POD) representing the flow dynamics of a viscous fluid has been introduced. (A brief description of POD is presented in the immediately preceding article.) The present parameterization method is intended to enable construction of the dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers. The need for this or a similar method arises as follows: A procedure that includes direct numerical simulation followed by POD, followed by Galerkin projection to a dynamical system has been proven to enable representation of flow dynamics by a low-dimensional model at the Reynolds number of the simulation. However, a more difficult task is to obtain models that are valid over a range of Reynolds numbers. Extrapolation of low-dimensional models by use of straightforward Reynolds-number-based parameter continuation has proven to be inadequate for successful prediction of flows. A key part of the problem of constructing a dynamical system to accurately represent the temporal evolution of the flow dynamics over a range of Reynolds numbers is the problem of understanding and providing for the variation of the coefficients of the dynamical system with the Reynolds number. Prior methods do not enable capture of temporal dynamics over ranges of Reynolds numbers in low-dimensional models, and are not even satisfactory when large numbers of modes are used. The basic idea of the present method is to solve the problem through a suitable parameterization of the coefficients of the dynamical system. The parameterization computations involve utilization of the transfer of kinetic energy between modes as a function of Reynolds number. The thus-parameterized dynamical system accurately predicts the flow dynamics and is applicable to a range of flow problems in the dynamical regime around the Hopf bifurcation. Parameter-continuation software can be used on the parameterized dynamical system to derive a bifurcation diagram that accurately predicts the temporal flow behavior.

Kalb, Virginia L.↗

NASA NTRS2005

Coronal Current Sheet Evolution in the Aftermath of a CME

We report on SOHO-UVCS observations of coronal restructuring following a Coronal Mass Ejection (CME) on November 26, 2002, at the time of a SOHO-Ulysses quadrature campaign. Starting about 3 hours after the CME, which was directed towards Ulysses, UVCS began taking spectra at 1.7 solar radii, covering emission from both cool and hot plasma. Observations continued, with occasional gaps, for more than 2 days. Emission in the 974.8 Angstrom line of [Fe XVIII], indicating temperatures above 6x10(6) K, was observed throughout the campaign in a spatially limited location. Comparison with EIT images shows the [Fe XVIII] emission to overlie a growing post-flare loop system formed in the aftermath of the CME. The emission most likely originates in a current sheet overlying the arcade. Analysis of the [Fe XVIII] emission allows us to infer the evolution of physical parameters in the current sheet over the entire span of our observations: in particular, we give the temperature vs. time in the current sheet and estimate the density. Ulysses was directly above the location of the CME and intercepted the ejecta. High ionization state Fe was detected by SWICS throughout the magnetic cloud associated with the CME, although the rapid temporal variation suggests bursty, rather than smooth, reconnection in the coronal current sheet. Both the remote and in situ observations are compared with predictions of theoretical CME models.

Bemporad, A.↗

NASA NTRS1992

Characteristics of obliquely propagating, nonlinear Alfven waves

Consideration is given to properties of obliquely propagating (with respect to the large-scale magnetic field) nonlinear Alfven and fast magnetosonic waves as described by the derivative nonlinear Schroedinger equation. The focus is on those waves which in the parallel-propagating limit are circularly polarized, exact solutions to the MHD equations. Results are presented of a study of the changes in the structure of these waves as the propagation angle is increased. Attention is also given to the evolution of initial conditions which do not correspond to stationary wave propagations. It is found that, as the propagation angle with respect to the mean field increases, the functional forms of the wave magnetic field components in the two directions orthogonal to the propagation direction become increasingly dissimilar. The angle about the mean field within which stationary waves resemble parallel-propagating, circularly polarized waves becomes smaller as the wavelength increases. If the 'initial condition' wave train is close to parallel-propagating, then there is little subsequent evolution in its form.

Spangler, Steven R.↗

NASA NTRS1991

Language evolution and human-computer interaction

Many of the issues that confront designers of interactive computer systems also appear in natural language evolution. Natural languages and human-computer interfaces share as their primary mission the support of extended 'dialogues' between responsive entities. Because in each case one participant is a human being, some of the pressures operating on natural languages, causing them to evolve in order to better support such dialogue, also operate on human-computer 'languages' or interfaces. This does not necessarily push interfaces in the direction of natural language - since one entity in this dialogue is not a human, this is not to be expected. Nonetheless, by discerning where the pressures that guide natural language evolution also appear in human-computer interaction, we can contribute to the design of computer systems and obtain a new perspective on natural languages.

Grudin, Jonathan↗

NASA NTRS1992

Relative timing of substorm features in MHD simulations

An investigation of the temporal sequence of substorm phenomena based on three dimensional MHD (magnetohydrodynamic) simulations of magnetic reconnection and plasmoid formation is presented. The investigation utilizes a spatially localized resistivity model which leads to a significantly faster evolution than found in previous investigations. The analysis of the results concentrates on substorm features that have received considerable attention in the past. The formation of magnetic neutral lines, the occurrence of fast flows directed both earthward and tailward, and the magnetic field changes leading to the formation of the substorm current wedge, and to the depolarization of the magnetic field earthward of the reconnection region and its dependence on the spatial distribution of resistivity, are discussed. These phenomena are seen as an integral part of the nonlinear evolution of the three dimensional tearing instability.

Hesse, Michael↗

NASA NTRS1975

Current and future opportunities in aeronautical engineering

Current demand for aeronautical engineers is approximately balanced with supply, with some shortfall in certain specialties. In the near term (5 years), demand will exceed supply of new graduates. A number of factors have brought on the state of imbalance: (1) the cyclic nature of the demand of our defense requirements; (2) drastic changes in DOD aircraft procurement; (3) the emergence of the space age; (4) evolution of social attitudes toward technology with resultant decline in enrollments; and (5) the universities themselves through their influences in the direction of careers selected by engineers. These factors have been counteracted somewhat by increased DOD emphasis on aircraft development programs but more importantly by the favorable growth in civil aircraft requirements.

Brizendine, J. C.↗

NASA NTRS1984

Nonlinear evolution of the resistive tearing mode

The nonlinear behavior of the tearing instability is investigated with the aid of numerical solutions of the resistive incompressible magnetohydrodynamic equations. This study is directed toward solar applications, such as flares. Simulations were carried out for values of the Lundquist number S from 100 to 1,000,000 and wavelength parameter alpha from 0.042 to 0.5. The influence of linear conditions, such as the constancy of psi, on nonlinear growth characteristics is investigated. For high S and low alpha, secondary-flow vortices, opposite in direction to the linear vortices, were found to generate a new magnetic island centered at the initial X point. The nonlinear spatial distributions of the physical variables differ greatly from the linear behavior, and growth slows considerably once nonlinear effects become important.

Steinolfson, R. S.↗

NASA NTRS1984

Evidence for an infrared disk in the core of the extraordinary planetary nebula Abell 30

High spatial resolution infrared maps of the core of the evolved planetary nebula Abell 30, which has been shown to be composed of heavily processed material, are presented. These maps reveal an elongated, disklike structure that is not evident on optical pictures. Multicolor photometry at several positions in this disk shows that this emission is due to dust, some of which is near the evaporation temperature of graphite. Lyman-alpha trapping is shown to be inadequate as a heating source for these grains, but direct absorption of stellar photons is sufficient. In view of the unusual chemical composition, A30 represents a late stage in the evolution of a planetary nebula progenitor. The observed infrared structure may provide clues to the ejection mechanism at this stage of development.

Lester, D. F.↗

NASA NTRS1988

Phenomenological modeling of hardening and thermal recovery in metals

Modeling of hardening and thermal recovery in metals is considered within the context of unified elastic-viscoplastic theories. Specifically, the choices of internal variables and hardening measures, and the resulting hardening response obtained by incorporating saturation-type evolution equations into two general forms of the flow law are examined. Based on the analytical considerations, a procedure for delineating directional and isotropic hardening from uniaxial hardening data has been developed for the Bodner-Partom model and applied to a nickel-base superalloy, B1900 + Hf. Predictions based on the directional hardening properties deduced from the monotonic loading data are shown to be in good agreement with results of cyclic tests.

Chan, K. S.↗

NASA NTRS1987

A full simulation of a vortex ring

A three-dimensional spectral method is developed for the solution to the incompressible Navier-Stokes equations in an unbounded domain. The spectral method relies on divergence-free basis functions as proposed by Leonard (1981). The basis functions are formed using vector spherical harmonics and Jacobi polynomials together with a mapping in the radial direction. An axisymmetric code was written and is verified using an exact solution of the Stokes equations. Preliminary results for the evolution of a vortex ring according to the Navier-Stokes equations are presented.

Stanaway, S. K.↗