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All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Asymptotic stability properties of linear Volterra integrodifferential equations.

The Liapunov stability properties of solution to a certain system of Volterra integrodifferential equations is studied. Various types of Liapunov stability are defined; the definitions are natural extensions of the corresponding notions for ordinary differential equations. Necessary and sufficient conditions, in general, for uniform stability and uniform asymptotic stability are obtained in the form of a theorem. Connections between the stability of the system studied and the stability properties of a related Volterra integrodifferential equation with infinite memory are examined. Sufficient conditions in order that the trivial solution to the system studied be stable, uniformly stable, asymptotically stable, or uniformly asymptotically stable are derived.

Miller, R. K.↗
NASA NTRS1983

Convergence and stability properties of minimal polynomial and reduced rank extrapolation algorithms

The minimal polynomial and reduced rank extrapolation algorithms are two acceleration of convergence methods for sequences of vectors. In a recent survey these methods were tested and compared with the scalar, vector, topological epsilon algorithms, and were observed to be more efficient than the latter. It was also observed that the two methods have similar convergence properties. The convergence and stability properties of these methods are analyzed and the performance of the acceleration methods when applied to a class of vector sequences that includes those sequences obtained from systems of linear equations by using matrix iterative methods is discussed.

Sidi, A.↗
NASA NTRS1992

Stochastic stability properties of jump linear systems

Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented.

Feng, Xiangbo↗
NASA NTRS1992

Laboratory test methods for combustion stability properties of solid propellants

An overview is presented of experimental methods for determining the combustion-stability properties of solid propellants. The methods are generally based on either the temporal response to an initial disturbance or on external methods for generating the required oscillations. The size distribution of condensed-phase combustion products are characterized by means of the experimental approaches. The 'T-burner' approach is shown to assist in the derivation of pressure-coupled driving contributions and particle damping in solid-propellant rocket motors. Other techniques examined include the rotating-valve apparatus, the impedance tube, the modulated throat-acoustic damping burner, and the magnetic flowmeter. The paper shows that experimental methods do not exist for measuring the interactions between acoustic velocity oscillations and burning propellant.

Strand, L. D.↗
NASA NTRS2010

Stability Properties and Cross Coupling Performance of the Control Allocation Scheme CAPIO

This paper presents a stability analysis and an application of a recently developed Control Allocator for recovery from Pilot Induced Oscillations (CAPIO). When actuators are rate-saturated due to either aggressive pilot commands, high gain ight control systems or some anomaly in the system, the effective delay in the control loop may increase. This effective delay increase manifests itself as a phase shift between the commanded and actual system signals and can instigate Pilot induced Oscillations (PIO). CAPIO reduces the e ective time delay by minimizing the phase shift between the commanded and the actual attitude accelerations. We present a stability analysis of CAPIO for a scalar system. In addition, we present simulation results for aircraft with cross-coupling which demonstrates the potential of CAPIO serving as an effective PIO handler in adverse conditions.

Yildiz, Yildiray↗
NASA NTRS1974

Stability properties of functional difference equations

Hale and Cruz (1970) have defined the concept of a stable difference operator, and have found that this class of operators is sometimes 'super sensitive' to perturbations. In the present paper, a subclass of general functional difference equations is derived which retain their stability under appropriate perturbations. Also, the results of Hale and Cruz are extended to include difference equations on the Banach space of p-th power integrable functions, and essentially bounded functions.

Melvin, W. R.↗
NASA NTRS1980

The stability properties of cylindrical force-free fields - Effect of an external potential field

A large-scale potential field with an embedded smaller-scale force-free structure gradient x B equals alpha B is studied in cylindrical geometry. Cases in which alpha goes continuously from a constant value alpha 0 on the axis to zero at large r are considered. Such a choice of alpha (r) produces fields which are realistic (few field reversals) but not completely stable. The MHD-unstable wavenumber regime is found. Since the considered equilibrium field exhibits a certain amount of magnetic shear, resistive instabilities can arise. The growth rates of the tearing mode in the limited MHD-stable region of k space are calculated, showing time-scales much shorter than the resistive decay time.

Chiuderi, C.↗
NASA NTRS1998

The Impact of Deviation from Michaelis-Menten Saturation on Mathematical Model Stability Properties

Based on purely abstract ecological theory, it has been argued that a system composed of two or more consumers competing for the same resource cannot persist. By analysis on a Monod format mathematical model, Hubble and others demonstrated that this assertion is true for all but very special cases of such competing organisms which are determined by an index formed by a grouping of. the parameters which characterize the biological processes of the competing organisms. In the laboratory, using a bioreactor, Hansen and Hubble obtained confirmatory results for several cases of two competing species, and they characterized it as "qualitative confirmation" of the assertion. This result is amazing, since the analysis required the exact equality of the hey index, and it seems certain that no pair of organism species could have exactly equal values. It is quite plausible, however, that pairs of organism species could have approximately equal indices, and the question of how different they could be and still have coexistence of the two (or more) presents itself. In this paper, the pursuit of this question and a compatible resolution is presented.

Blackwell, Charles↗
NASA NTRS2024

Intrastep, Stage-Value Predictors for Diagonally-Implicit Runge-Kutta Methods

To better identify the necessary attributes of good stage-value predictors (SVPs), numerous SVPs are designed for an existing: ESDIRK4(3)7L[2]SA [26] and a new: ESDIRK4(3)8L[2]SA scheme.1 Both are stifflyaccurate, stage-order two, explicit, singly-diagonally implicit Runge–Kutta (ESDIRK) schemes. Tradeoffs are studied in the parameter spaces enforcing the constraints on accuracy, linear stability, nonlinear stability and coefficient size to determine which objectives correlate with effective predictors. The SVPs are tested on three challenging external aerodynamics problems [107 − 108 degrees of freedom (DoFs)], each with a different level of stiffness. The problems include two 3D airfoils simulations and one canonical turbulence simulation. All simulations use the compressible Navier-Stokes equations (CNSE). An entropy stable spectral collocation formulation is used for discretizing the spatial terms in the equations. Simulations are performed at a wide variety of temporal error tolerances. Problems that are sufficiently stiff (e.g., lax temporal error tolerances) benefit from SVPs designed with second-order accuracy and stability properties: A-stability, and L-stability, rather than high accuracy constraints. Simulations with modest stiffness (e.g., strict error tolerances) are better suited for SVPs designed using high accuracy constraints. Designing SVPs with enhanced stability properties is tedious but worthwhile. Simulation times are reduced with optimal SVPs by as much as 100% on some stages, with combined stepwise improvements of between 50 − 100% for both methods. A comparative study is performed with the two aforementioned methods as well as four other ESDIRKs. The newly designed ESDIRK4(3)8L[2]SA with γ ≈ 1/10, proves to be the most efficient of the six tested ESDIRK schemes simulating the CNSE.

Diagonally-Implicit Runge-Kutta↗
NASA NTRS1983

On the interaction of a sound pulse with the shear layer of an axisymmetric jet. II - Heated jets

The fluctuating field of a heated jet excited by a sound pulse is simulated numerically. The fluctuations in both the flow field and the far field are studied. The flow field results depend crucially on the stability properties of the heated jet. The altered stability properties due to the heating cause a reduction in the overall fluctuations and a shift of the instability waves into lower frequencies. These changes cause a similar downward shift in the far field spectrum and a reduction in the total far field noise. The results provide a partial explanation in terms of stability theory of experimentally observed properties of the noise of heated jets.

Bayliss, A.↗
NASA NTRS1985

Long-term stability and properties of zirconia ceramics for heavy duty diesel engine components

Physical, mechanical, and thermal properties of commercially available transformation-toughened zirconia are measured. Behavior is related to the material microstructure and phase assemblage. The stability of the materials is assessed after long-term exposure appropriate for diesel engine application. Properties measured included flexure strength, elastic modulus, fracture toughness, creep, thermal shock, thermal expansion, internal friction, and thermal diffusivity. Stability is assessed by measuring the residual property after 1000 hr/1000C static exposure. Additionally static fatigue and thermal fatigue testing is performed. Both yttria-stabilized and magnesia-stabilized materials are compared and contrasted. The major limitations of these materials are short term loss of properties with increasing temperature as the metastable tetragonal phase becomes more stable. Fine grain yttria-stabilized material (TZP) is higher strength and has a more stable microstructure with respect to overaging phenomena. The long-term limitation of Y-TZP is excessive creep deformation. Magnesia-stabilized PSZ has relatively poor stability at elevated temperature. Overaging, decomposition, and/or destabilization effects are observed. The major limitation of Mg-PSZ is controlling unwanted phase changes at elevated temperature.

Larsen, D. C.↗
NASA NTRS2020

Structural evolution, electrochemical kinetic properties, and stability of A-site doped perovskite Sr(1-x)Yb(x)CoO(3-δ)

Mixed ionic and electronic conducting (MIEC) perovskite SrCoO(3-δ) is a widely studied (electro)catalyst for the oxygen reduction reaction (ORR) and possesses different crystal structures at different temperatures. These temperature dependent phase transitions significantly impact the ordering of oxygen vacancies and electrochemical kinetic properties as well as the reliability of the related devices. Some of the crystal structures formed, e.g. hexagonal phases, turn out to be almost impermeable to oxygen gas. Therefore, it is important to stabilize the crystal structure of SrCoO(3-δ) that favors the ORR over a wide temperature range. Herein, the partial substitution of the A-site Sr with Yb is systematically studied, including synthesis, characterization and analysis of structural evolution, electrochemical kinetic properties, thermal stability, and stability in a CO2-containing atmosphere. The results indicate that Sr(0.90)Yb(0.10)CoO(3-δ) is able to stabilize the tetragonal crystal structure with less ordered oxygen vacancies, leading to polarization resistances of 0.051, 0.115 and 0.272 U sq.cm at 750, 700 and 650 °C, respectively, on symmetrical cells. Sr(0.90)Yb(0.10)CoO(3-δ) demonstrates a very stable surface oxygen vacancy distribution and electronic structure near oxygen vacancies but dissociation of adsorbed oxygen molecules into atomic oxygen is affected by surface Sr segregation, and polarization resistance degradation is mainly induced by surface Sr segregation. Furthermore, Sr(0.90)Yb(0.10)CoO(3-δ) exhibits excellent thermal stability as well as excellent recovery stability and improved polarization performance after a few pure air/CO2-containing air treatment cycles at 700 °C. However, a hysteresis behavior of polarization performance is observed at 650 °C during gas cycling treatment, which may cause long-term degradation of the Sr(0.90)Yb(0.10)CoO(3-δ) electrode. The different polarization behaviors during gas cycling treatment are induced by different sensitivities of the formed surface strontium carbonate and chemisorbed surface oxo-carbonaceous species to different operating temperatures.

electrochemical kinetic↗
NASA NTRS2001

Polymer/Silicate Nanocomposites Developed for Improved Thermal Stability and Barrier Properties

The nanoscale reinforcement of polymers is becoming an attractive means of improving the properties and stability of polymers. Polymer-silicate nanocomposites are a relatively new class of materials with phase dimensions typically on the order of a few nanometers. Because of their nanometer-size features, nanocomposites possess unique properties typically not shared by more conventional composites. Polymer-layered silicate nanocomposites can attain a certain degree of stiffness, strength, and barrier properties with far less ceramic content than comparable glass- or mineral-reinforced polymers. Reinforcement of existing and new polyimides by this method offers an opportunity to greatly improve existing polymer properties without altering current synthetic or processing procedures.

Campbell, Sandi G.↗
NASA NTRS1973

Decomposition-aggregation stability analysis

This report presents the development and description of the decomposition aggregation approach to stability investigations of high dimension mathematical models of dynamic systems. The high dimension vector differential equation describing a large dynamic system is decomposed into a number of lower dimension vector differential equations which represent interconnected subsystems. Then a method is described by which the stability properties of each subsystem are aggregated into a single vector Liapunov function, representing the aggregate system model, consisting of subsystem Liapunov functions as components. A linear vector differential inequality is then formed in terms of the vector Liapunov function. The matrix of the model, which reflects the stability properties of the subsystems and the nature of their interconnections, is analyzed to conclude over-all system stability characteristics. The technique is applied in detail to investigate the stability characteristics of a dynamic model of a hypothetical spinning Skylab.

Siljak, D. D.↗