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At least 1,261 records · Page 70

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DOE OSTI2015

Nonlinear evolution of the electromagnetic electron-cyclotron instability in bi-Kappa distributed plasma

This paper presents a numerical study of the linear and nonlinear evolution of the electromagnetic electron-cyclotron (EMEC) instability in a bi-Kappa distributed plasma. Distributions with high energy tails described by the Kappa power-laws are often observed in collision-less plasmas (e.g., solar wind and accelerators), where wave-particle interactions control the plasma thermodynamics and keep the particle distributions out of Maxwellian equilibrium. Under certain conditions, the anisotropic bi-Kappa distribution gives rise to plasma instabilities creating low-frequency EMEC waves in the whistler branch. The instability saturates nonlinearly by reducing the temperature anisotropy until marginal stability is reached. Numerical simulations of the Vlasov-Maxwell system of equations show excellent agreement with the growth-rate and real frequency of the unstable modes predicted by linear theory. The wave-amplitude of the EMEC waves at nonlinear saturation is consistent with magnetic trapping of the electrons.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

A Multiplexed Quantitative Analysis of Germline Single Amino Acid Variants by Targeted Proteomics in Nondepleted Human Plasma

Single amino acid variants (SAAVs) in protein sequences are often a direct result of single-nucleotide polymorphisms (SNPs). Certain germline SAAVs have shown biological relevance in different disease conditions but lack precise quantification in circulation, which could hinder functional investigations and progress in biomarker development. Here, we have developed a multiplexed liquid chromatography-selected reaction monitoring (LC-SRM) assay that monitors 5 wild-type and variant peptide pairs (Complement Factor B: CFB-R32Q/R32W, Clusterin: CLU-N317H, Fetuin B: FETUB-K360R, and Kininogen: KNG1-L212P) in nondepleted human plasma. The assay was optimized for imprecision, linearity, stability, and calibration assessments with CVs of under 20%. The wild-type and variant peptide pairs were characterized in a set of healthy individual plasma samples. These target identifications were also validated by SNP genotyping with more than 99% accuracy. For all protein targets, we observed significantly lower concentrations of WT species in the presence variant peptides. In CFB, the concentration of R32Q was significantly lower than its counterpart R32W variant and WT species. Furthermore, our results distinguished phenotypes of homozygosity and heterozygosity of the SAAV presence through direct concentration level characterization. These findings provide some insights into how SAAVs affect quantitative assessments of target peptides. The assay demonstrates a platform for proteogenomic analyses with potential applications in both research and clinical settings.

genetics↗

NASA NTRS1991

Applications of singular value analysis and partial-step algorithm for nonlinear orbit determination

An adaptive method in which cruise and nonlinear orbit determination problems can be solved using a single program is presented. It involves singular value decomposition augmented with an extended partial step algorithm. The extended partial step algorithm constrains the size of the correction to the spacecraft state and other solve-for parameters. The correction is controlled by an a priori covariance and a user-supplied bounds parameter. The extended partial step method is an extension of the update portion of the singular value decomposition algorithm. It thus preserves the numerical stability of the singular value decomposition method, while extending the region over which it converges. In linear cases, this method reduces to the singular value decomposition algorithm with the full rank solution. Two examples are presented to illustrate the method's utility.

Ryne, Mark S.↗

NASA NTRS1986

Nonlinear system controller design based on domain of attaction: An application to CELSS analysis and control

Nonlinear system controller design based on the domain of attraction is presented. This is particularly suited to investigating Closed Ecological Life Support Systems (CELSS) models. In particular, the dynamic consequences of changes in the waste storage capacity and system mass, and how information is used for control in CELSS models are examined. The models' high dimensionality and nonlinear state equations make them difficult to analyze by any other technique. The domain of attraction is the region in initial conditions that tend toward an attractor and it is delineated by randomly selecting initial conditions from the region of state space being investigated. Error analysis is done by repeating the domain simulations with independent samples. A refinement of this region is the domain of performance which is the region of initial conditions meeting a performance criteria. In nonlinear systems, local stability does not insure stability over a larger region. The domain of attraction marks out this stability region; hence, it can be considered a measure of a nonlinear system's ability to recovery from state perturbations. Considering random perturbations, the minimum radius of the domain is a measure of the magnitude of perturbations for which recovery is guaranteed. Design of both linear and nonlinear controllers are shown. Three CELSS models, with 9 to 30 state variable, are presented. Measures of the domain of attraction are used to show the global behavior of these models under a variety of design and controller scenarios.

Babcock, P. S., IV↗

NASA NTRS1990

Numerical prediction of turbulent flame stability in premixed/prevaporized (HSCT) combustors

A numerical analysis of combustion instabilities that induce flashback in a lean, premixed, prevaporized dump combustor is performed. KIVA-II, a finite volume CFD code for the modeling of transient, multidimensional, chemically reactive flows, serves as the principal analytical tool. The experiment of Proctor and T'ien is used as a reference for developing the computational model. An experimentally derived combustion instability mechanism is presented on the basis of the observations of Proctor and T'ien and other investigators of instabilities in low speed (M less than 0.1) dump combustors. The analysis comprises two independent procedures that begin from a calculated stable flame: The first is a linear increase of the equivalence ratio and the second is the linear decrease of the inflow velocity. The objective is to observe changes in the aerothermochemical features of the flow field prior to flashback. It was found that only the linear increase of the equivalence ratio elicits a calculated flashback result. Though this result did not exhibit large scale coherent vortices in the turbulent shear layer coincident with a flame flickering mode as was observed experimentally, there were interesting acoustic effects which were resolved quite well in the calculation. A discussion of the k-e turbulence model used by KIVA-II is prompted by the absence of combustion instabilities in the model as the inflow velocity is linearly decreased. Finally, recommendations are made for further numerical analysis that may improve correlation with experimentally observed combustion instabilities.

Winowich, Nicholas S.↗

DOE OSTI2021

EXPERIMENTAL STUDIES OF NONLINEAR INTEGRABLE OPTICS

State-of-the-art accelerators at energy and intensity frontiers require increasingly bright and powerful particle beams. In conventional linear lattices, intense beams suffer from collective instabilities, resulting in beam losses and maximum beam intensity limits. This thesis presents experimental studies of a novel lattice design concept, the nonlinear integrable optics (NIO), aimed at enhancing beam stability limits with little to no beam dynamics degradation. Single-particle beam dynamics measurements of two NIO devices, the quasi-integrable octupole system and the fully integrable Danilov-Nagaitsev system, were carried out at the purpose-built Integrable Optics Test Accelerator (IOTA) at Fermilab. Their simulation, hardware design, and commissioning process are presented. Extensive model and analysis algorithm development and benchmarking is described. Electron beam data from two scientific runs is analyzed, yielding frequency and phase space dynamics consisten t with m odels. These results demonstrate viability and advantages of the NIO design, providing the groundwork for proton studies in the strong space-charge regime and future integrable accelerators.

Kuklev, Nikita↗

DOE OSTI2024

The AUREX cell: a versatile operando electrochemical cell for studying catalytic materials using X-ray diffraction, total scattering and X-ray absorption spectroscopy under working conditions

Understanding the structure–property relationship in electrocatalysts under working conditions is crucial for the rational design of novel and improved catalytic materials. This paper presents the Aarhus University reactor for electrochemical studies using X-rays (AUREX) operando electrocatalytic flow cell, designed as an easy-to-use versatile setup with a minimal background contribution and a uniform flow field to limit concentration polarization and handle gas formation. The cell has been employed to measure operando total scattering, diffraction and absorption spectroscopy as well as simultaneous combinations thereof on a commercial silver electrocatalyst for proof of concept. This combination of operando techniques allows for monitoring of the short-, medium- and long-range structure under working conditions, including an applied potential, liquid electrolyte and local reaction environment. The structural transformations of the Ag electrocatalyst are monitored with non-negative matrix factorization, linear combination analysis, the Pearson correlation coefficient matrix, and refinements in both real and reciprocal space. Upon application of an oxidative potential in an Ar-saturated aqueous 0.1 M KHCO 3 /K 2 CO 3 electrolyte, the face-centered cubic (f.c.c.) Ag gradually transforms first to a trigonal Ag 2 CO 3 phase, followed by the formation of a monoclinic Ag 2 CO 3 phase. A reducing potential immediately reverts the structure to the Ag (f.c.c.) phase. Following the electrochemical-reaction-induced phase transitions is of fundamental interest and necessary for understanding and improving the stability of electrocatalysts, and the operando cell proves a versatile setup for probing this. In addition, it is demonstrated that, when studying electrochemical reactions, a high energy or short exposure time is needed to circumvent beam-induced effects.

Frank, Sara (ORCID:0000000163218363)↗

DOE OSTI2017

Stability and Control of Burning Tokamak Plasmas with Resistive Walls: Final Technical Report

This project is focused on theoretical and computational development for quantitative prediction of the stability and control of the equilibrium state evolution in toroidal burning plasmas, including its interaction with the surrounding resistive wall. The stability of long pulse burning plasmas is highly sensitive to the physics of resonant layers in the plasma, sources of momentum and flow, kinetic effects of energetic particles, and boundary conditions at the wall, including feedback control and error fields. In ITER in particular, the low toroidal flow equilibrium state, sustained primarily by energetic alpha particles from fusion reactions, will require the consideration of all of these key elements to predict quantitatively the stability and evolution. The principal investigators on this project have performed theoretical and computational analyses, guided by analytic modeling, to address this physics in realistic configurations. The overall goal has been to understand the key physics mechanisms that describe stable toroidal burning plasmas under active feedback control. Several relevant achievements have occurred during this project, leading to publications and invited conference presentations. In theoretical efforts, with the physics of the resonant layers, resistive wall, and toroidal momentum transport included, this study has extended from cylindrical resistive plasma - resistive wall models with feedback control to toroidal geometry with strong shaping to study mode coupling effects on the stability. These results have given insight into combined tearing and resistive wall mode behavior in simulations and experiment, while enabling a rapid exploration of plasma parameter space, to identify possible domains of interest for large plasma codes to investigate in more detail. Resonant field amplification and quasilinear torques in the presence of error fields and velocity shear have also been investigated. Here it was found, surprisingly, that the Maxwell torque on resonant layers in the plasma which exhibit finite real frequencies ωr in their response is significantly different from the conventional results based on tearing layers with pure real growth (or damping) rates. This observation suggests the possibility that the torque on the tearing layers can lock the plasma rotation to this finite phase velocity, which may lead to locking in which velocity shear is maintained. More broadly, the sources of all torques driving flows in magnetic confinement experiments is not fully understood, and this theoretical work may shed light on puzzling experimental results. It was also found that real frequencies occur over a wide range of plasma response regimes, and are indeed the norm and not the exception, often leading to profound effects on the locking torque. Also, the influence of trapped energetic ions orbiting over the resistive plasma mode structure, a critical effect in burning plasmas, was investigated through analytic modeling and analysis of simulations and experiment. This effort has shown that energetic ions can drive the development of disruptive instabilities, but also damp and stabilize the instabilities, depending on the details of the shear in the equilibrium magnetic field. This finding could be critical to maintaining stable operations in burning plasmas. In the most recent work, a series of simulations have been conducted to study the effect of differential flow and energetic ion effects on entry to the onset of a disruptive instability in the most realistic conditions possible, with preexisting nonlinearly saturated benign instabilities. Throughout this work, the linear and quasilinear theory of resonant layers with differential flow between them, their interaction with resistive wall and error fields, and energetic ions effects, have been used to understand realistic simulations of mode onset and the experimental discharges they represent. These studies will continue to answer remaining questions about the relation between theoretical results obtained in this project and observations of the onset and evolution of disruptive instabilities in experiment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Implementing a Laser Stabilization System for Trapping Ca+ Ions: an Internship Reflection

At Lawrence Livermore National Laboratory, I contributed to a project developing 3D printed micro ion traps for quantum computing. I designed, implemented, and assessed a laser stabilization system that locked lasers to the frequencies required for calibrating our High Finesse WS8-10 wavelength meter and for laser cooling and trapping of Ca+ ions. I also programmed a Python interface for hardware communication, data collection, and statistical analysis. Additionally, I optimized and aligned laser beam paths, and I implemented a closed digital feedback loop using Proportional, Integral, and Derivative (PID) control parameters. I analyzed both the long-term and short-term behavior of our locked lasers and adjusted PID parameters to enhance performance. Furthermore, I used COMSOL to simulate the capacitance of a linear Paul trap design and predict our trap’s performance. The procedures I developed for the interface, analysis, and simulations will continue to support the ion trapping experiment after my appointment. I strengthened my skills in data analysis, Python coding, and optical alignment for laser systems. My confidence as a researcher grew, particularly in communicating my research. This experience taught me the importance of careful planning and consideration in research and solidified my desire to continue exploring novel quantum technology as an undergraduate

42 ENGINEERING↗

NASA NTRS1991

Linear and nonlinear dynamic analysis by boundary element method

An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons with available analytical and numerical results, the stability and high accuracy of these dynamic analysis techniques are established.

Ahmad, Shahid↗

NASA NTRS1989

Flexible aircraft dynamic modeling for dynamic analysis and control synthesis

The linearization and simplification of a nonlinear, literal model for flexible aircraft is highlighted. Areas of model fidelity that are critical if the model is to be used for control system synthesis are developed and several simplification techniques that can deliver the necessary model fidelity are discussed. These techniques include both numerical and analytical approaches. An analytical approach, based on first-order sensitivity theory is shown to lead not only to excellent numerical results, but also to closed-form analytical expressions for key system dynamic properties such as the pole/zero factors of the vehicle transfer-function matrix. The analytical results are expressed in terms of vehicle mass properties, vibrational characteristics, and rigid-body and aeroelastic stability derivatives, thus leading to the underlying causes for critical dynamic characteristics.

Schmidt, David K.↗

NASA NTRS1989

An Entropy-Based Approach to Nonlinear Stability

Many numerical methods used in computational fluid dynamics (CFD) incorporate an artificial dissipation term to suppress spurious oscillations and control nonlinear instabilities. The same effect can be accomplished by using upwind techniques, sometimes augmented with limiters to form Total Variation Diminishing (TVD) schemes. An analysis based on numerical satisfaction of the second law of thermodynamics allows many such methods to be compared and improved upon. A nonlinear stability proof is given for discrete scalar equations arising from a conservation law. Solutions to such equations are bounded in the L sub 2 norm if the second law of thermodynamics is satisfied in a global sense over a periodic domain. It is conjectured that an analogous statement is true for discrete equations arising from systems of conservation laws. Analysis and numerical experiments suggest that a more restrictive condition, a positive entropy production rate in each cell, is sufficient to exclude unphysical phenomena such as oscillations and expansion shocks. Construction of schemes which satisfy this condition is demonstrated for linear and nonlinear wave equations and for the one-dimensional Euler equations.

Merriam, Marshal L.↗

DOE OSTI2018

Prediction of Stable and Active (Oxy-Hydro) Oxide Nanoislands on Noble-Metal Supports for Electrochemical Oxygen Reduction Reaction

Developing cost-effective oxygen electrocatalysts with high activity and stability is key to their commercialization. However, economical earth-abundant catalysts based on first-row transition-metal oxides suffer from low electrochemical stability, which is difficult to improve without compromising their activity. In this paper, using density functional theory calculations, we demonstrate that noble-metal supports lead to bifunctional enhancement of both the stability and the oxygen reduction reaction (ORR) activity of metal (oxy-hydro) oxide nanoislands. We observe a significant stabilization of supported nanoislands beyond the intrinsic stability limits of bulk phases, which originates from a favorable lattice mismatch and reductive charge transfer from oxophilic supports. Additionally, we discover that interfacial active sites (located between the nanoisland and the support) reinforce the binding strength of reaction intermediates, hence boosting ORR activity. Considering that both stability and activity lead to discovery of CoOOH|Pt, NiOOH|Ag, and FeO 2 |Ag as viable systems for alkaline ORR, we then use a multivariant linear regression method to identify elementary descriptors for efficient screening of promising cost-effective nanoisland|support catalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1984

LANDSAT instruments characterization

Work performed for the LANDSAT instrument characterization task in the areas of absolute radiometry, coherent noise analysis, and between-date smoothing is reported. Absolute radiometric calibration for LANDSAT-5 TM under ambient conditions was performed. The TM Radiometric Algorithms and Performance Program (TRAPP) was modified to create optional midscan data files and to match the TM Image Processing System (TIPS) algorithm for pulse determination. Several data reduction programs were developed, including a linear regression and its plotted result. A fast Fourier transformation study was conducted on the resequenced TM data. Subscenes of homogeneous water within scenes over Pensacola, Florida were used for testing the FFT on the resequenced data. Finally, a gain and pulse height stability study of LANDSAT 5 TM spectral bands was performed.

Lee, Y.↗

NASA NTRS1990

Collisionless tearing instability in magnetotail plasmas

The problem of the linear stability of collisionless tearing modes in the earth's magnetotail is revisited. It is found that the collisionless tearing mode is linearly unstable with wavelengths of the order of 10 R(E). It is shown that an important feature neglected in earlier theories is a nonzero equilibrium B(y)-field. The physics of the instability is elucidated in the context of a simple slab model and a sheared parabolic model which is representative of the magnetotail in which all three components of the magnetic field are nonzero. The dispersion equation for the instability is obtained by a boundary-layer analysis. The implications of the theory for recent observations on current disruption and diversion during substorms is discussed.

Wang, Xiaogang↗

NASA NTRS2020

Verification of Anisotropic Mesh Adaptation for Turbulent Simulations over ONERA M6 Wing

Unstructured anisotropic mesh adaptation is known to be an efficient way to control discretization errors in Computational Fluid Dynamics (CFD) simulations. Method verification is required to provide the confidence for routine use in production analysis. The current work aims at verification of anisotropic mesh adaptation for RANS simulations over the ONERA M6 wing. The present verification study is performed using four different flow solvers, three different implementations of the metric field, and three mesh mechanics packages. Two of the flow solvers use stabilized finite-element discretizations (FUN3D-SFE and GGNS), one uses finite-volume discretization (FUN3D-FV), and the last one uses mixed finite-volume and finite element discretizations (Wolf). The mesh adaptation is based on an error estimator that aims to control the quadratic error term in the linear interpolation of Mach number. Two sets of adaptations were performed; the first one controls the interpolation error in L2 norm and the second one controls the interpolation error in L4 norm. Convergence studies were performed on the forces and the pitching moment using all four solvers, and the results are compared with previously verified convergence studies on fixed (nonadapted) meshes. Both forces and pitching moment on adapted meshes are found to be converging to the fine mesh values faster than those on fixed meshes. In addition to forces and moments, convergence of surface pressure and skin friction coefficients at various measurement locations on the wing are also presented. Adapted-mesh surface pressure distributions agree with the fine fixed mesh pressure distributions. Adapted-mesh skin friction distributions contain high frequency noise with mean values approaching the fixed mesh pressure skin friction distributions.

Aravind Balan↗

NASA NTRS1986

Dynamic posture analysis of Spacelab-1 crew members

Dynamic posture testing was conducted on the science crew of the Spacelab-1 mission on a single axis linear motion platform. Tests took place in pre- and post-flight sessions lasting approximately 20 min each. The pre-flight tests were widely spaced over the several months prior to the mission while the post-flight tests were conducted over the first, second, fourth, and sixth days after landing. Two of the crew members were also tested on the day of landing. Consistent with previous postural testing conducted on flight crews, these crew members were able to complete simple postural tasks to an acceptable level even in the first few hours after landing. Our tests were designed to induce dynamic postural responses using a variety of stimuli and from these responses, evaluate subtle changes in the postural control system which had occurred over the duration of the flight. Periodic sampling post-flight allowed us to observe the time course of readaptation to terrestrial life. Our observations of hip and shoulder position, when subjected to careful analysis, indicated modification of the postural response from pre- to post-flight and that demonstrable adjustments in the dynamic control of their postural systems were taking place in the first few days after flight. For transient stimuli where the platform on which they were asked to stand quickly moved a few centimeters fore or aft then stopped, ballistic or open loop 'programs' would closely characterize the response. During these responses the desired target position was not always achieved and of equal importance not always properly corrected some 15 seconds after the platform ceased to move. The persistent observation was that the subjects had a much stronger dependence on visual stabilization post-flight than pre-flight. This was best illustrated by a slow or only partial recovery to an upward posture after a transient base-of-support movement with eyes open. Postural responses to persistent wideband pseudorandom base-of-support translation were modeled as time invarient linear systems arrived at by Kalman adaptive filter techniques. Derived model parameters such as damping factor and fundamental frequency of the closed loop system showed significant modification between pre- and post-flight. This phenomenon is best characterized by movement of the poles toward increasing stability. While pre-flight data tended to show shoulders and hips moving in phase with each other, post-flight data showed a more disjoint behavior.(ABSTRACT TRUNCATED AT 400 WORDS).

Non-NASA Center↗

NASA NTRS1994

Inner loop flight control for the High-Speed Civil Transport

High-speed aerospace vehicles which employ high strength, light weight, yet deformable materials may exhibit significant interaction between the rigid-body and vibrational dynamics. Preliminary High-Speed Civil Transport (HSCT) configurations are a prime example. Traditionally, separate control systems have been used to augment the rigid-body and vibrational dynamics. In the HSCT arena, the highly coupled motions may not allow this design freedom. The research activity addresses two specific issues associated with the design and development of an integrated flight control system (FCS) for HSCT configurations, which are discussed next. The HSCT is expected to have a short period instability at subsonic speeds. Flight vehicles with this characteristic (i.e., F-16, F-22, X-29, Space Shuttle) are stabilized with what is called a superaugmented pitch rate loop. One concern is 'Will this stability augmentation logic work for a HSCT?' Studies show that an idealized pitch rate design would be acceptable, but is not realistic. Investigations using a contaminated pitch rate design reveal serious hurdles to overcome in the FCS design. Mounting location for the pitch rate sensor is critical. Results indicate a forward location leads to destabilizing pick-up of aeroelastic modes, while aft locations lead to undesirable coupling of the dominate pitch mode with the first aeroelastic mode. Intermediate locations for the sensor may not be acceptable. The source of the problem is the presence of low frequency aeroelastic modes in HSCT configurations, which are not present in vehicles currently using the superaugmented logic. To say the least, a conventional superaugmented pitch rate loop strategy may have undesirable characteristics. An unconventional strategy, which attempts to eliminate the above deficiencies by blending several pitch rate signals, indicates an improvement in the FCS architecture feasibility, but is still lacking in some respects. The HSCT configuration does not have aerodynamic surfaces in the vicinity of the nose (i.e., no canard or vane). A second concern is 'Can the fuselage bending/torsion aeroelastic modes be effectively augmented without sufficient control input near the vehicle nose?' The superaugmented FCS results above may be suggesting the necessity of a secondary feedback loop to achieve an acceptable integrated FCS. Preliminary analysis of HSCT aeroelastic mode shapes indicate the use of existing wing leading edge devices as a second control input may be lacking in control authority for the rigid-body attitude and aeroelastic modes. An effort is underway to incorporate generic wing leading edge devices and canards into a generic HSCT model for the purpose of assessing additional control authority and it's use in candidate FCS designs. A generic HSCT mathematical model was necessary for the studies above. A HSCT category model is available in NASA-CR-172201. This model describes the linear, longitudinal dynamics about the following flight condition: ascent, W = 730,000 lbs, h = 6,500 ft, M = 0.6. The model incorporates the full rigid-body variable set, as well as eighteen aeroelastic modes. Elevator deflection serves as the control input. Modifications to the model include the incorporation of relaxed static stability (i.e., static margin from -7.3% to +10%) and additional control inputs.

Newman, Brett A.↗