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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

Robustness and computational aspects of nonlinear stochastic estimators and regulators

Robustness properties of nonlinear extended Kalman filters with constant gains and modeling errors are presented. Sufficient conditions for the nondivergence of state estimates generated by such nonlinear estimators are given. In addition, the overall robustness and stability properties of closed-loop stochastic regulators, based upon the Linear-Quadratic-Gaussian design methodology using linearized dynamics, are presented; the sufficient conditions for closed-loop stability have 'separation-type' property.

Safonov, M. G.↗
NASA NTRS1975

Stability criteria for two-variable polynomials

Recursive algebraic algorithms are developed for testing various stability properties of two-variable polynomials in a finite number of steps. Stability is tested with respect to either the half-plane or the unit circle applying only two times the equivalent of the Routh or Marden test, regardless of the degree of the polynomial.

Siljak, D. D.↗
NASA NTRS1979

A note on a corrector formula for the numerical solution of ordinary differential equations

A new corrector formula for predictor-corrector methods for numerical solutions of ordinary differential equations is presented. Two considerations for choosing corrector formulas are given: (1) the coefficient in the error term and (2) its stability properties. The graph of the roots of an equation plotted against its stability region, of different values, is presented along with the tables that correspond to various corrector equations, including Hamming's and Milne and Reynolds'.

Chien, Y.-C.↗
NASA NTRS1978

Robustness and computational aspects of nonlinear stochastic estimators and regulators

Robustness properties of nonlinear extended Kalman filters with constant gains and modeling errors are presented. Sufficient conditions for the nondivergence of state estimates generated by such nonlinear estimators are given. In addition, the overall robustness and stability properties of closed-loop stochastic regulators, based upon the linear-quadratic Gaussian design methodology using linearized dynamics, are presented; the sufficient conditions for closed-loop stability have a 'separation-type' property.

Safonov, M. G.↗
NASA NTRS1987

The structure and stability of coronal magnetic fields

The high degree of symmetry often assumed in studies of the structure and stability of coronal magnetic field configurations is restrictive and can yield misleading results. Fully three-dimensional numerical methods for constructing force-free equilibria and for examining their stability properties are developed which make no assumptions about symmetry. A test of the stability analysis has been performed by applying it to the Gold-Hoyle twisted flux tube, which is known to be kink-unstable if the helical field makes more than about one turn between the line-tying end-plates. The preliminary result is that the critical number of turns is about 1.1, in good agreement with the previous best estimate. However, it is found that the growth rate, which has not been discussed previously, is orders of magnitude smaller than expected, even when the flux tube is twisted far beyond the stability limit.

Mcclymont, A. N.↗
DOE OSTI2025

Identification of a window for quiescent H-mode operation in MHD stability diagram of DIII-D plasmas

A window for quiescent H-mode (QH-mode) operation in DIII-D plasmas in the diagram of pedestal magnetohydrodynamic (MHD) stability was identified through linear MHD stability analysis, accounting for the effects of plasma rotation and ion diamagnetic drift. The operation window lies between the stability boundaries of the kink/peeling mode (K/PM) identified with and without the inclusion of plasma rotation effects. In this region, the mode remains unstable unless rotation effects are considered alongside the ion diamagnetic drift, which is consistently included in the analysis. The stabilization of the MHD mode, facilitated by the coupled effects of plasma rotation and ion diamagnetic drift, plays a crucial role in widening the window, enabling the attainment of the QH-mode state. Furthermore, the suppression of edge localized modes (ELM) can be achieved by controlling the pedestal structure to ensure the plasma state remains within the operation window. The location of the operation window in the stability diagram depends on the K/PM stability properties. Therefore, optimizing conditions for QH-mode requires adjustments based on changes in stability characteristics. A pressure pedestal and its associated bootstrap current density near the last closed flux surface are advantageous for situating the plasma state within the window. However, excessive current density can trigger ELMs. This trend was confirmed through comparisons of MHD stability diagrams between QH-mode and ELMy H-mode plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1991

Improved Notch Filter For Synchronous-Response Control

Tracking differential-notch filter (TDNF) developed to retain good synchronous-response performance of notch filter, but with vastly improved stability properties. Measurement error perfectly filtered from feedback signal used to drive compensator. Provides good stability of simple lead/lag compensator combined with good synchronous-response performance gained by addition of notch filter.

Johnson, Bruce G.↗
NASA NTRS2001

High Order Difference Method for Low Mach Number Aeroacoustics

A high order finite difference method with improved accuracy and stability properties for computational aeroacoustics (CAA) at low Mach numbers is proposed. The Euler equations are split into a conservative and a symmetric non- conservative portion to allow the derivation of a generalized energy estimate. Since the symmetrization is based on entropy variables, that splitting of the flux derivatives is referred to as entropy splitting. Its discretization by high order central differences was found to need less numerical dissipation than conventional conservative schemes. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the split Euler equations are formulated in perturbation form. The unknowns are the small changes of the conservative variables with respect to their large stagnation values. All nonlinearities and the conservation form of the conservative portion of the split flux derivatives can be retained, while cancellation errors are avoided with its discretization opposed to the conventional conservative form. The finite difference method is third-order accurate at the boundary and the conventional central sixth-order accurate stencil in the interior. The difference operator satisfies the summation by parts property analogous to the integration by parts in the continuous energy estimate. Thus, strict stability of the difference method follows automatically. Spurious high frequency oscillations are suppressed by a characteristic-based filter similar to but without limiter. The time derivative is approximated by a 4-stage low-storage second-order explicit Runge-Kutta method. The method has been applied to simulate vortex sound at low Mach numbers. We consider the Kirchhoff vortex, which is an elliptical patch of constant vorticity rotating with constant angular frequency in irrotational flow. The acoustic pressure generated by the Kirchhoff vortex is governed by the 2D Helmholtz equation, which can be solved analytically using separation of variables.

Mueller, B.↗
NASA NTRS1988

Stability analysis and control of tethered satellites

Issues of stability and stabilization of the Shuttle/Tethered Satellite System (TSS) are considered. The basic, nonlinear equations of motion of the TSS are derived using the system Lagrangian. A tension control strategy in feedback form is introduced to stabilize the TSS during station-keeping. In addition, the stability properties of a constant angle control method for deployment and retrieval are investigated using Liapunov stability theory.

Liaw, D.-C.↗
DOE OSTI2021

Stability Analysis of Parameter Varying Genetic Toggle Switches Using Koopman Operators

The genetic toggle switch is a well known model in synthetic biology that represents the dynamic interactions between two genes that repress each other. The mathematical models for the genetic toggle switch that currently exist have been useful in describing circuit dynamics in rapidly dividing cells, assuming fixed or time-invariant kinetic rates. There is a growing interest in being able to model and extend synthetic biological function for growth conditions such as stationary phase or during nutrient starvation. As cells transition from one growth phase to another, kinetic rates become time-varying parameters. In this paper, we propose a novel class of parameter varying nonlinear models that can be used to describe the dynamics of genetic circuits, including the toggle switch, as they transition from different phases of growth. We show that there exists unique solutions for this class of systems, as well as for a class of systems that incorporates the microbial phenomena of quorum sensing. Further, we show that the domain of these systems, which is the positive orthant, is positively invariant. We also showcase a theoretical control strategy for these systems that would grant asymptotic monostability of a desired fixed point. We then take the general form of these systems and analyze their stability properties through the framework of time-varying Koopman operator theory. A necessary condition for asymptotic stability is also provided as well as a sufficient condition for instability. A Koopman control strategy for the system is also proposed, as well as an analogous discrete time-varying Koopman framework for applications with regularly sampled measurements.

Harrison, Jamiree (ORCID:0000000265351579)↗
NASA NTRS1993

Weakly nonlinear stability of vicsous vortices in three-dimensional boundary layers

Attention is given to the weakly nonlinear stability of essentially viscous vortices in 3D boundary layers. These modes are unstable in the absence of crossflow, but the imposition of small crossflow has a stabilizing effect. Bassom and Hall (1991) demonstrated the existence of neutrally stable vortices for certain crossflow/wave number combinations, and the weakly nonlinear stability properties of these disturbances are described. It is shown that the effect of crossflow is to stabilize the nonlinear modes, and the present calculations allow stable finite-amplitude vortices to be found. Predictions are made concerning the likelihood of observing some of these viscous modes within a practical setting.

Bassom, Andrew P.↗
DOE OSTI2022

Application of Poly(ether sulfone)‐Based Membranes in Clean Energy Technology

Abstract Poly(ether sulfone) (PES) is a kind of polymer materials with excellent electrical insulation and acid/alkali stability. PES can be operated at high temperature continuously for a long time and still maintain excellent property stability in the environments with rapidly changed temperature, namely, great thermostability. Moreover, PES has low molding shrinkage, good dimensional stability and excellent film‐forming characteristics. Compared with inorganic membranes, PES‐based membranes have lower cost, which have received more attention and wide recognition in the field of clean energy technologies in recent years, such as flow batteries, fuel cells, water treatment, and gas separation. Therefore, this review summarizes the research status and prospect of the utilization of PES‐based membranes in clean energy fields, in order to further promote their development and application.

Chemistry↗
DOE OSTI2021

Gyrokinetic and extended-MHD simulations of a flow shear stabilized Z-pinch experiment

Axisymmetric (m = 0) gyrokinetic and extended-MHD simulations of a sheared-flow Z-pinch plasma are performed with the high-order finite volume code COGENT. The present gyrokinetic model solves the long-wavelength limit of the gyrokinetic equation for both ion and electron species coupled to the electrostatic gyro-Poisson equation for the electrostatic potential. The extended-MHD model is electromagnetic and includes the effects of the gyro-viscous pressure tensor, diamagnetic electron and ion heat fluxes, and generalized Ohm's law. Additionally, a prominent feature of this work is that the radial profiles for the plasma density and temperature are taken from the fusion Z-pinch experiment (FuZE), and the magnetic field profile is obtained as a solution of the MHD force balance equation. Such an approach allows to address realistic plasma parameters and provide insights into the current and planned experiments. In particular, it is demonstrated that the radial profiles play an important role in stabilization, as the embedded guiding center (E×B ) drift has a strong radial shear, which can contribute to the Z-pinch stabilization even in the absence of the fluid flow shear. The results of simulations for the FuZE plasma parameters show a decrease in the linear growth rate with an increase in the flow shear; however, full stabilization in the linear regime is not observed even for large (comparable to the Alfvén velocity) radial variations of the axial flow. Nonlinear stability properties of the FuZE plasmas are also studied, and it is found that profile broadening can have a pronounced stabilizing effect in the nonlinear regime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1993

The effect of crossflow on Taylor vortices: A model problem

A number of practically relevant problems involving the impulsive motion or the rapid rotation of bodies immersed in fluid are susceptible to vortex-like instability modes. Depending upon the configuration of any particular problem the stability properties of any high-wavenumber vortices can take on one of two distinct forms. One of these is akin to the structure of Gortler vortices in boundary layer flows while the other is similar to the situation for classical Taylor vortices. Both the Gortler and Taylor problems have been extensively studied when crossflow effects are excluded from the underlying base flows. Recently, studies were made concerning the influence of crossflow on Gortler modes and a linearized stability analysis is used to examine crossflow properties for the Taylor mode. This work allows us to identify the most unstable vortex as the crossflow component increases and it is shown how, like the Gortler case, only a very small crossflow component is required in order to completely stabilize the flow. Our investigation forms the basis for an extension to the nonlinear problem and is of potential applicability to a range of pertinent flows.

Otto, S. R.↗
DOE OSTI2023

Diagonally implicit Runge–Kutta schemes: Discrete energy-balance laws and compactness properties

Abstract We study diagonally implicit Runge–Kutta (DIRK) schemes when applied to abstract evolution problems that fit into the Gelfand-triple framework. We introduce novel stability notions that are well-suited to this setting and provide simple, necessary and sufficient, conditions to verify that a DIRK scheme is stable in our sense and in Bochner-type norms. We use several popular DIRK schemes in order to illustrate cases that satisfy the required structural stability properties and cases that do not. In addition, under some mild structural conditions on the problem we can guarantee compactness of families of discrete solutions with respect to time discretization.

Mathematics↗
NASA NTRS1975

Improving the toughness of refractory compounds

Composition and processing studies were conducted on silicon nitride and silicon carbide materials. Charpy mode impact testing to 2415 F established the effectiveness of higher purity silicon nitride powder sources in reducing the scatter of measurements and in improving short time bend strengths as well as bend stress rupture properties. Stabilized zirconia additions in particular were observed to dramatically enhance low and high temperature bend strengths and stress rupture properties for all grades of silicon nitride powder. Silicon carbide samples showed relatively poor impact resistance, although the maxima in stress rupture behavior was exhibited by this material.

Vasilos, T.↗
NASA NTRS1974

Exponential stability of large-scale discrete systems

The concept of vector Liapunov functions is used to obtain conditions for the exponential stability of large-scale discrete systems which can be decomposed into a number of interconnected subsystems with the same stability property. Both the structurally invariant composite systems and the large-scale systems under structural perturbations are considered. Connective absolute stability of a large-scale system composed of the interconnected Lur'e-type subsystems is defined and resolved in this context, resulting in a computationally and conceptually attractive alternative to a straightforward stability analysis of the system by frequency-domain criteria.

Grujic, L. T.↗