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Results for “asymptotic stability”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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67 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Energizing charged particles by an orbit instability in a slowly rotating magnetic field

In this work, the stability of charged particle motion in a uniform magnetic field with an added spatially uniform transverse rotating magnetic field (RMF) is studied analytically. It is found that the stability diagram of a single particle's orbit depends critically on the chosen boundary conditions. We show that for many boundary conditions and wide regions in the parameter space, RMFs oscillating far below the cyclotron frequency can cause linear instabilities in the motion which break μ invariance and energize particles. Such energization may appear at odds with the adiabatic invariance of μ; however, adiabatic invariance is an asymptotic result and does not preclude such heating by magnetic fields oscillating at slow frequencies. This mechanism may contribute to heating in the edge plasma of field-reversed configurations (FRCs) in rotamak-FRC experiments. Furthermore, these RMF-driven instabilities may significantly enhance azimuthal current drive during the formation of FRCs in such devices.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Lyapunov-based nonlinear control of nonautonomous systems with individual input constraints

A control algorithm that can locally stabilize a specific class of multi-input multi-output nonautonomous nonlinear dynamical systems while satisfying individual input constraints is developed. The proposed Lyapunov-based state-feedback control law inherently accounts for the actuator amplitude saturation limits without the need for computationally expensive real-time optimization techniques. In addition to the control law, a formal definition for the local “controllable region” within which the controller can asymptotically drive the system states to the origin and satisfy the input saturation limits is also presented. The nonautonomous nature of the system dynamics implies that the “controllable region” continuously evolves with time. Therefore, a sufficient condition to maintain the system states within the “controllable region” is proposed in this work to make practical implementation feasible. The effectiveness of the controller is tested for a specific control problem arising in tokamaks, which are toroidal devices that use strong magnetic fields to confine a plasma (hot ionized gas). Here, the primary emphasis of tokamak research is to regulate the plasma properties around predetermined values to achieve stable plasma confinement. Nonlinear simulations show that the proposed controller can achieve the desired plasma control objectives in a DIII-D tokamak scenario.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Interface models for three-dimensional Rayleigh–Taylor instability

We derive interface models for three-dimensional Rayleigh–Taylor instability (RTI), making use of a novel asymptotic expansion in the non-locality of the fluid flow. These interface models are derived for the purpose of studying universal features associated with RTI such as the Froude number in single-mode RTI, the predicted quadratic growth of the interface amplitude under multi-mode random perturbations, the optimal (viscous) mixing rates induced by the RTI and the self-similarity of horizontally averaged density profiles and the remarkable stabilization of the mixing layer growth rate which arises for the three-fluid two-interface heavy–light–heavy configuration, in which the addition of a third fluid bulk slows the growth of the mixing layer to a linear rate. Our interface models can capture the formation of small-scale structures induced by severe interface roll-up, reproduce experimental data in a number of different regimes and study the effects of multiple interface interactions even as the interface separation distance becomes exceedingly small. Compared with traditional numerical schemes used to study such phenomena, our models provide a computational speed-up of at least two orders of magnitude.

Mechanics↗
DOE OSTI2022

Droplet formation simulation using mixed finite elements

Droplet formation happens in finite time due to the surface tension force. The linear stability analysis is useful to estimate the size of a droplet but fails to approximate the shape of the droplet. This is due to a highly nonlinear flow description near the point where the first pinch-off happens. A one-dimensional axisymmetric mathematical model was first developed by Eggers and Dupont [“Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] using asymptotic analysis. This asymptotic approach to the Navier–Stokes equations leads to a universal scaling explaining the self-similar nature of the solution. Numerical models for the one-dimensional model were developed using the finite difference [Eggers and Dupont, “Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] and finite element method [Ambravaneswaran et al., “Drop formation from a capillary tube: Comparison of one-dimensional and two-dimensional analyses and occurrence of satellite drops,” Phys. Fluids 14, 2606–2621 (2002)]. The focus of this study is to provide a robust computational model for one-dimensional axisymmetric droplet formation using the Portable, Extensible Toolkit for Scientific Computation. The code is verified using the Method of Manufactured Solutions and validated using previous experimental studies done by Zhang and Basaran [“An experimental study of dynamics of drop formation,” Phys. Fluids 7, 1184–1203 (1995)]. The present model is used for simulating pendant drops of water, glycerol, and paraffin wax, with an aspiration of extending the application to simulate more complex pinch-off phenomena.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

On a variational formulation of the weakly nonlinear magnetic Rayleigh–Taylor instability

The magnetic-Rayleigh–Taylor (MRT) instability is a ubiquitous phenomenon that occurs in magnetically-driven Z-pinch implosions. It is important to understand this instability since it can decrease the performance of such implosions. In this work, I present a theoretical model for the weakly nonlinear MRT instability. I obtain such a model by asymptotically expanding an action principle, whose Lagrangian leads to the fully nonlinear MRT equations. After introducing a suitable choice of coordinates, I show that the theory can be cast as a Hamiltonian system, whose Hamiltonian is calculated up to the sixth order in a perturbation parameter. The resulting theory captures the harmonic generation of MRT modes. It is shown that the amplitude at which the linear magnetic-Rayleigh–Taylor instability exponential growth saturates depends on the stabilization effect of the magnetic-field tension. Overall, the theory provides an intuitive interpretation of the weakly nonlinear MRT instability and provides a systematic approach for studying this instability in more complex settings.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Suppression of electroconvective and morphological instabilities by an imposed cross flow of the electrolyte

Electroconvective (EC) instability and its influence on surface morphological perturbations (Morph) are important in many applications, including electrodialysis, batteries, and fuel cells. In this work, we study the effects of a two-dimensional channel flow on the EC and Morph instabilities using two approaches. In the bulk analysis, we derive the asymptotic solutions for small and large wave numbers by neglecting the space charge layer and imposing a second kind electroosmosis slip velocity boundary condition on the electroneutral bulk region. In the full analysis, the instability of the entire region of the liquid electrolyte is analyzed using the ultraspherical spectral method. Both studies show that the flow significantly affects the EC instability. The imposed flow distorts the concentration field, causing a sheltering effect which hinders the ion transport from low- to high-concentration regions, and therefore suppresses the EC instability below a certain wave number. In combination with the viscous stabilization of the high wave number modes by the space charge layer, a sufficiently strong imposed flow can fully suppress the EC instability. The increment in the critical voltage for the instability onset is roughly proportional to the square root of the product of imposed velocity and double layer thickness. The imposed flow has a smaller effect on the Morph instability, except that it may remove the morphological modes resulting from the EC instability and thereby change the wave number of the most unstable mode.

42 ENGINEERING↗
DOE OSTI2022

Real-Time Distribution System State Estimation with Asynchronous Measurements

We report state estimation is a fundamental task in power systems. Although distribution systems are increasingly equipped with sensing devices and smart meters, measurements are typically reported at different rates and asynchronously; these aspects pose severe strains on workhorse state estimation algorithms, which are designed to process batches of data collected in a synchronous manner from all the measurement units. In this paper, we develop a novel state estimation algorithm to continuously update the estimate of the state based on measurements received in an asynchronous manner from measurement units. The synthesis of the algorithm hinges on a proximal-point type method, implemented in an online fashion, and capable of processing measurements received sequentially from sensors. A performance analysis is presented by providing bounds on the estimation error in terms of the mean and variance that hold at each iteration and asymptotically. The scheme is also compared with a more traditional Weighted Least Squares estimator that compensates for the lack of measurement data by using, as pseudo measurements, the measurement retrieved during a certain time window. Numerical simulations on the IEEE 37-bus feeder corroborate the analytical findings.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Silver Adsorption on Calcium Niobate(001) Nanosheets: Calorimetric Energies That Explain Sinter-Resistant Support

Metal nanoparticles deposited on oxide supports are essential to many technologies, including catalysts, fuel cells and electronics. Therefore, understanding the chemical bonding strength between metal nanoparticles and oxide surfaces is of great interest. The adsorption energetics, adhesion energy and adsorbate structure of Ag on dehydrated HCa 2 Nb 3 O 10 (001) nanosheets at 300 K have been studied using metal adsorption calorimetry and surface spectroscopies. These dehydrated (“dh”) calcium niobate nanosheets “(dh-HCa 2 Nb 3 O 10 (001))” have stoichiometry Ca 4 Nb 6 O 19 . They impart unusual stability to metal nanoparticles when used as catalyst supports and are easy-to-prepare by Langmuir-Blodgett (LB) techniques, highly ordered, and essentially single-crystal surfaces of mixed oxides with a huge ratio of terrace to edge sites. Below monolayer coverage, Ag grows on dh-HCa 2 Nb 3 O 10 (001) as 2D islands of thickness ~2 layers. The differential heat of Ag adsorption is initially ~303 kJ/mol, increasing slowly to ~338 kJ/mol by 0.8 ML. At higher coverages, Ag atoms mainly add on top of these 2D islands, growing 3D nanoparticles of increasing thickness, as the heat decreases asymptotically towards silver’s heat of sublimation (285 kJ/mol). The adhesion energy of Ag(s) to this Ca niobate surface is estimated to be 4.33 J/m 2 , larger than on any oxide surface previously measured. This explains the sinter resistance reported for metal nanoparticles on this support. Electron transfer from Ag into the calcium niobate is also measured. Furthermore, these results demonstrate an easy way to do singlecrystal-type surface science studies - and especially thermochemical measurements - on the complex surfaces of mixed oxides: using LB-deposited perovskite nanosheets and ultrahigh vacuum annealing in O 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Dynamics of Three-Dimensional Shock-Wave/Boundary-Layer Interactions

Advances in measuring and understanding separated, nominally two-dimensional (2D) shock-wave/turbulent-boundary-layer interactions (STBLI) have triggered recent campaigns focused on three-dimensional (3D) STBLI, which display far greater configuration diversity. Nonetheless, unifying properties emerge for semi-infinite interactions, taking the form of conical asymptotic behavior where shock-generator specifics become insignificant. The contrast between 2D and 3D separation is substantial; the skewed vortical structure of 3D STBLI reflects the essentially 2D influence of the boundary layer on the 3D character of the swept shock. As with 2D STBLI, conical interactions engender prominent spectral content below that of the turbulent boundary layer. However, the uniform separation length scale, which is crucial to normalizing the lowest-frequency dynamics in 2D STBLI, is absent. Comparatively, the spectra of 3D STBLI are more representative of the mid-frequency, convective, shear-layer dynamics in 2D, while phenomena associated with 2D separation-shock breathing are muted. Asymptotic behavior breaks down in many regions important to 3D-STBLI dynamics, occurring in a configuration-dependent manner. Aspects of inceptive regions near shock generators and symmetry planes are reviewed. Focused efforts toward 3D modal and nonmodalanalyses, moving-shock/boundary-layer interactions, fluid/structure interactions, and flow control are suggested as directions for future work.

42 ENGINEERING↗
DOE OSTI2020

Analysis into Asymptotic Convergence to Full Nonlinear Solutions and Exploration of the Implication of Numerical Operator Mutation of Differential Systems

A robust, sufficiently accurate and practical hydrodynamic simulation toolset is required as a key component of the modeling and simulation of air-gap electrostatic discharge events. This work was performed to complement these ongoing efforts. In particular, hydrodynamic simulations must be vetted to ensure they are robust and sufficiently accurate over relevant characteristic scales. Verification models were generated in order to cultivate the technical knowledge and expertise needed to properly create, implement and execute numerical simulations. Furthermore, this effort was utilized extensively to educate students on the mathematical and numerical principles underlying hydrodynamic simulations. This education opportunity, provided in a holistic and rigorous manner, has greatly benefited developing scientists and engineers with the necessary understandings and toolsets required to excel at accomplishing the task at hand, and, more generally, it has enabled them to generate key programmatic deliverables. This report articulates several subtilties; specifically, how perturbations, nonlinear behavior, and dissipative mechanisms influence numerical stability, how to properly structure mathematical and numerical solutions, and how to properly generate error estimation/assignment. A more rigorous discussion of the consequences of such topics can be found in the body of this report in Chapters 2 and 3 with qualitative findings discussed in Chapter 4.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Multicentered black hole saddles for supersymmetric indices

The supersymmetric index in string theory can sometimes have a discontinuous integer-valued jump at co-dimension one surfaces in moduli space called walls of marginal stability. When the index counts black hole microstates, crossing such walls of marginal stability amounts to the appearance or disappearance of a large number of such states. While wall-crossing has been understood in string theory and through the disappearance of extremal Lorentzian supergravity solutions as the moduli are varied, there has been no understanding about how the discontinuous changes in the index occur at the level of the gravitational path integral. In this paper, we find the finite-temperature saddles in $4d$ flatspace supergravity in which fermionic fields are periodic when going around the thermal circle that correspond to the multi-center black hole contributions to the index. By analyzing these saddles, we can explain how wall-crossing occurs: as the scalar moduli in supergravity are varied at the asymptotic boundary, for a given split of the charges, the saddle point equations can no longer be solved and, consequently, the corresponding multi-center saddle no longer contributes to the index. While the values of the scalars and the jump in the index when a wall is crossed all agree with the prediction from previously found Lorentzian supergravity solutions, the saddles in the index exhibit a much richer moduli space, which we analyze in detail.

FOS: Physical sciences↗
DOE OSTI2023

New linear stability parameter to describe low-β electromagnetic microinstabilities driven by passing electrons in axisymmetric toroidal geometry

In magnetic confinement fusion devices, the ratio of the plasma pressure to the magnetic field energy, β, can become sufficiently large that electromagnetic microinstabilities become unstable, driving turbulence that distorts or reconnects the equilibrium magnetic field. In this paper, a theory is proposed for electromagnetic, electron-driven linear instabilities that have current layers localised to mode-rational surfaces and binormal wavelengths comparable to the ion gyroradius. The model retains axisymmetric toroidal geometry with arbitrary shaping, and consists of orbit-averaged equations for the mode-rational surface layer, with a ballooning space kinetic matching condition for passing electrons. The matching condition connects the current layer to the large scale electromagnetic fluctuations, and is derived in the limit that β is comparable to the square root of the electron-to-ion-mass ratio. Electromagnetic fluctuations only enter through the matching condition, allowing for the identification of an effective β that includes the effects of equilibrium flux surface shaping. The scaling predictions made by the asymptotic theory are tested with comparisons to results from linear simulations of micro-tearing and electrostatic microinstabilities in MAST discharge #6252, showing excellent agreement. In particular, it is demonstrated that the effective β can explain the dependence of the local micro-tearing mode (MTM) growth rate on the ballooning parameter θ 0 – possibly providing a route to optimise local flux surfaces for reduced MTM-driven transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Linear stability analysis of two fluid columns of different densities and viscosities in a gravity field

The linear stability of a vertical interface separating two miscible fluid columns of different densities and viscosities under the influence of gravity is investigated. This flow possesses a time-dependent reference state (each column accelerates at different rates owing to their different densities) and the interface thickness grows as the square root of time (by diffusion). Numerical integration of the linear initial-value problem is carried out and discussed in detail as a function of vertical and spanwise wavenumbers and the flow parameters. Adjoint-based optimization is performed in order to determine initial conditions that lead to maximum growth of disturbances in finite time. Results indicate that the rate of growth of the perturbation energy at small wavenumbers (less affected by viscosity initially) is dominated by two-dimensional modes (no spanwise variation). Substantial transient growth is observed at higher wave modes initially, followed by asymptotic decay of the perturbations at large time. Sensitivity of perturbation growth with respect to initial time, density and viscosity ratios is investigated. This work is complementary to previous inviscid analysis of this configuration, which showed that the interface was unconditionally unstable at all wave modes, even in the presence of surface tension, and that instability grew as the exponential of time squared.

Mechanics↗