Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “stability theory”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory

A mixed shear flexible finite element, with relaxed continuity, is developed for the geometrically linear and nonlinear analysis of layered anisotropic plates. The element formulation is based on a refined higher order theory which satisfies the zero transverse shear stress boundary conditions on the top and bottom faces of the plate and requires no shear correction coefficients. The mixed finite element developed herein consists of eleven degrees of freedom per node which include three displacements, two rotations and six moment resultants. The element is evaluated for its accuracy in the analysis of the stability and vibration of anisotropic rectangular plates with different lamination schemes and boundary conditions. The mixed finite element described here for the higher order theory gives very accurate results for buckling loads and natural frequencies.

Putcha, N. S.↗
DOE OSTI2020

Phonon dispersion throughout the iron spin crossover in ferropericlase

Ferropericlase (Fp), (Mg 1– x Fex)O, is the second most abundant phase in the Earth's lower mantle. At relevant pressure-temperature conditions, iron in Fp undergoes a high spin (HS), $\textit{S}$ = 2, to low spin (LS), $\textit{S}$ = 0, state change. The nature of this phenomenon is quite well understood now, but there are still basic questions regarding the structural stability and the existence of soft phonon modes during this iron state change. General theories exist to explain the volume reduction, the significant thermoelastic anomalies, and the broad nature of this HS-LS crossover. These theories make extensive use of the quasiharmonic approximation. Therefore, dynamical and structural stability is essential to their validity. Here, we investigate the vibrational spectrum of Fp throughout this spin crossover using ab initio density-functional theory $+U_{sc}$ calculations. We address vibrational modes associated with isolated and (second-)nearest-neighbor iron ions undergoing the HS-LS state change. As expected, acoustic modes of this solid solution are resilient, while optical modes are the most affected. In this work, we show that there are no soft phonon modes across this HS-LS crossover, and Fp is dynamically stable at all relevant pressures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Atomic-Level Understanding of Surface Reconstruction Based on Li[Ni x Mn y Co 1–x–y ]O 2 Single-Crystal Studies

The stability of cathode particle surfaces that are directly exposed to the electrolyte is one of the most crucial and determining factors for cathode performance at high operating voltages. Theory has predicted a strong dependence of surface stability on chemical compositions as well as surface facets of layered oxides, yet conflicting results on the correlations exist as most experimental studies focus on cycled secondary particles recovered from composite electrodes. Here, we synthesize well-formed Li[Ni x Mn y Co 1–x–y ]O 2 (NMC) single-crystal samples, carefully define pristine surface properties, and then monitor their evolution with cycling. Atomic-resolution scanning transmission electron microscopy (STEM) imaging and electron energy loss spectroscopy (EELS) analysis show the formation of a surface reconstruction layer (SRL) as well as an extended surface reduction layer on pristine, Li-permeable non-(001) surfaces, even before cycling. We reveal a transition region with chemical gradient, in which the layered structure gradually densifies and eventually transforms into the SRL on the top surface. Contrary to these observations, no SRL is observed on pristine, Li-impermeable (001) surfaces, revealing the facet-dependent nature of surface reconstructions during particle synthesis. Upon electrochemical cycling, significant composition-and facet-dependent SRL growth is observed. The driving force and mechanism for surface reconstruction are further discussed. The present study provides insights into the origin as well as the nature of SRLs, highlighting the significance of surface engineering in cathode material optimization.

25 ENERGY STORAGE↗
NASA NTRS1985

Hopf bifurcation in the presence of symmetry

Group theory is applied to obtain generalized differential equations from the Hopf bifurcation theory on branching to periodic solutions. The conditions under which the symmetry group will admit imaginary eigenvalues are delimited. The action of the symmetry group on the circle group are explored and the Liapunov-Schmidt reduction is used to prove the Hopf theorem in the symmetric case. The emphasis is on simplifying calculations of the stability of bifurcating branches. The resulting general theory is demonstrated in terms of O(2) acting on a plane, O(n) in n-space, and O(3) and an irreducible model for spherical harmonics.

Golubitsky, M.↗
NASA NTRS1992

Improvement in the control aspect of laser frequency stabilization for SUNLITE project

Flight Electronics Division of Langley Research Center is developing a spaceflight experiment called the Stanford University and NASA Laser In-Space Technology (SUNLITE). The objective of the project is to explore the fundamental limits on frequency stability using an FM laser locking technique on a Nd:YAG non-planar ring (free-running linewidth of 5 KHz) oscillator in the vibration free, microgravity environment of space. Compact and automated actively stabilized terahertz laser oscillators will operate in space with an expected linewidth of less than 3 Hz. To implement and verify this experiment, NASA engineers have designed and built a state of the art, space qualified high speed data acquisition system for measuring the linewidth and stability limits of a laser oscillator. In order to achieve greater stability and better performance, an active frequency control scheme requiring the use of a feedback control loop has been applied. In the summer of 1991, the application of control theory in active frequency control as a frequency stabilization technique was investigated. The results and findings were presented in 1992 at the American Control Conference in Chicago, and have been published in Conference Proceedings. The main focus was to seek further improvement in the overall performance of the system by replacing the analogue controller by a digital algorithm.

Zia, Omar↗
NASA NTRS1982

A nonlocal theory of an electrostatic sinusoidal density drift instability

The stability of space plasmas in which the macroscopic variables vary in the direction x perpendicular to the magnetic field is usually studied by means of the local approximation, in which the fluctuating potential is assumed to be independent of x. To remove this approximation, a nonlocal problem is studied in which the background density, and hence the fluctuating potentials, are periodic in x. From the linear Vlasov/Poisson equations, a set of coupled, linear, homogeneous, algebraic equations relating the Fourier amplitudes of the eigensolution is derived. The equations are solved numerically and a hierarchy of exact eigenmodes characterized by different growth rates and spatial structures is found. At points where the density gradient is locally zero, the mode amplitude is generally several orders of magnitude lower than the peak amplitude. The dependence of these solutions on the parameters which define the background density perturbation is studied and a correspondence between these nonlocal results and those obtained with the local approximation is demonstrated.

Thomsen, M. F.↗
NASA NTRS1984

Phase stability of weakly crosslinked interpenerating polymer networks

A phenomenological theory is formulated for chemically quenched binary interpenetrating polymer networks (IPNs), considering both simultaneously crosslinked networks and sequentially crosslinked networks, as well as pseudointerpenetrating networks (where only one component is crosslinked and the other is a linear polymer). The construction of free energy functionals for homogeneous weakly crosslinked IPNs and pseudo-IPNs and their spinodal curves and critical points of unmixing is described. These free energy functionals are augmented with gradient energy terms in order to consider effects due to spatially varying small inhomogeneities in the network chain concentration. The dynamic response and the initial spinodal decomposition of IPNs are discussed.

Binder, K.↗
NASA NTRS1991

Resonant triad in boundary-layer stability. Part 1: Fully nonlinear interaction

A first principles theory is developed to study the nonlinear spatial evolution of a near-resonance triad of instability waves in boundary layer transition. This triad consists of a plane wave at fundamental frequency and a pair of symmetrical, oblique waves at the subharmonic frequency. A low frequency, high Reynolds number asymptotic scaling leads to a distinct critical layer where nonlinearity first becomes important; the development of the triad's waves is determined by the critical layer's nonlinear, viscous dynamics. The resulting theory is fully nonlinear in that all nonlinearly generated oscillatory and nonoscillatory components are accounted for. The presence of the plane wave initially causes exponential of exponential growth of the oblique waves. However, the plane wave continues to follow the linear theory, even when the oblique waves' amplitude attains the same order of magnitude as that of the plane wave. A fully interactive stage then comes into effect when the oblique waves exceed a certain level compared to that of the plane wave. The oblique waves react back on the fundamental, slowing its growth rate. The oblique waves' saturation results from their self-interaction - a mechanism that does not require the presence of the plane wave. The oblique waves' saturation level is independent of their initial level, but decreases as the obliqueness angle increases.

Mankbadi, Reda R.↗
NASA NTRS1989

Ballooning stability of axisymmetric plasmas with sheared equilibrium flows

A WKB theory is formulated for large-n ballooning modes in axisymmetric, toroidal plasmas with sheared equilibrium flows. The validity of the standard ballooning respresentation is severely restricted in the presence of sheared toroidal flow, despite the fact that to leading order in (1/n), where n is the azimuthal number, the eigenmode equation contains only derivatives along a field line. Necessary and sufficient conditions for stability are obtained in a high-beta ordering for rigid toroidal rotation as well as field-aligned flows.

Bhattacharjee, A.↗
DOE OSTI2025

Computational Design of Cost-Effective High-Entropy Thermal/Environmental Barrier Coatings

Developing cost-effective thermal/environmental barrier coatings (TEBC) requires balance among various properties including low thermal conductivity, matching coefficient of thermal expansion (CTE), high thermal stability, high fracture toughness, and high recession resistance while being affordable. Low oxygen diffusivity is desirable as it can slow down oxygen transport to reach the underlying bond coating and hence delay oxidation of the bond coating. This project aims to design low-cost high-performance TEBC based on high entropy rare earth disilicates to protect SiC-based ceramic matrix composites from chemical and thermal attack for better performance of components in the hot section of gas turbine engines. To accelerate the TEBC design, we utilize first-principles density functional theory to predict key properties including phase stability, CTE, lattice thermal conductivity, temperature-dependent elastic constants, and oxygen diffusivity. Alloying elements including Yb, Y, Er, Eu, Gd, Lu, La, and Ce are considered, and modeling prediction are compared with available experimental results.

coefficient of thermal expansion↗
NASA NTRS1991

Dynamics of helicopters with dissimilar blades

The dynamics of helicopters with dissimilar rotor blades is investigated for hingeless rotors in hover. An elastic blade model with finite element formulation is used. Hub motions are included by modeling the fuselage as a rigid body with pitch and roll degrees of freedom. The aeromechanical stability solution is solved in the fixed frame via Floquet theory. A parametric study of the effects of dissimilarity among blades' structural stiffness, mass, and damping on aeromechanical stability is presented. It is found that a slight reduction in the lag stiffness of one blade stabilizes the regressing lag mode instability.

Wang, James M.↗
DOE OSTI2022

High critical field superconductivity at ambient pressure in MoB 2 stabilized in the P6/mmm structure via Nb substitution

Recently it was discovered that, under elevated pressures, MoB 2 exhibits superconductivity at a critical temperature T c as high as 32 K. The superconductivity appears to develop following a pressure-induced structural transition from the ambient pressure $\text{R}\bar{3}$⁢m structure to an MgB 2 -like P6/mmm structure. This suggests that remarkably high T c values among diborides are not restricted to MgB 2 as previously appeared to be the case, and that similarly high T c values may occur in other diborides if they can be coerced into the MgB 2 structure. In this paper, we show that density functional theory calculations indicate that phonon free energy stabilizes the P6/mmm structure over the $\text{R}\bar{3}$⁢m at high temperatures across the Nb 1–x ⁢Mo x B 2 series. X-ray diffraction confirms that the synthesized Nb-substituted MoB 2 adopts the MgB 2 crystal structure. Finally, high magnetic field electrical resistivity measurements and specific heat measurements demonstrate that Nb x ⁢Mo 1–x⁢ B 2 exhibits superconductivity with T c as high as 8 K and critical fields approaching 6 T.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1985

Subtle alternating electrocardiographic morphology as an indicator of decreased cardiac electrical stability

Observations from finite-element computer models, together with analytic developments based on percolation theory have suggested that subtle fluctuations of ECG morphology might serve as an indicator diminished cardiac electrical stability. With fixed-rate atrial pacing in canines, we have previously observed a pattern of alternation in T wave energy which correlated with cardiac electrical stability. We report here on a series of 20 canine experiments in which cardiac electrical stability (measured via Ventricular Fibrillation Threshold determination) was compared to a non-degenerate, multidimensional measurement of the degree of alternating activity present in the ECG complex morphology. The decrease in cardiac electrical stability brought on by both coronary artery occlusion and systemic hypothermia was consistently accompanied by subtle alternation in ECG morphology, with the absolute degree of alternating activity being significantly (negatively) correlated with cardiac electrical stability.

Ventricular Fibrillation↗
DOE OSTI2021

On the Stochastic Stability of Deep Markov Models

Deep Markov models (DMM) are generative models which are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we present a novel stability analysis method and provide sufficient conditions of DMM's stochastic stability. The proposed stability analysis is based on the contraction of probabilistic maps modeled by deep neural networks. We make connections between the spectral properties of neural network's weights and different types of used activation function on the stability and overall dynamic behavior of DMMs with Gaussian distributions. Based on the theory, we propose a few practical methods for designing constrained DMMs with guaranteed stability. We empirically substantiate our theoretical results via intuitive numerical experiments using the proposed stability constraints.

Drgona, Jan↗
DOE OSTI2020

Heterotic instantons for monad and extension bundles

We consider non-perturbative superpotentials from world-sheet instantons wrapped on holomorphic genus zero curves in heterotic string theory. These superpotential contributions feature prominently in moduli stabilization and large field axion inflation, which makes their presence or absence, as well as their functional dependence on moduli, an important issue. We develop geometric methods to compute the instanton superpotentials for heterotic string theory with monad and extension bundles. Using our methods, we find a variety of examples with a non-vanishing superpotential. In view of standard vanishing theorems, we speculate that these results are likely to be attributed to the non-compactness of the instanton moduli space. We test this proposal, for the case of monad bundles, by considering gauged linear sigma models where compactness of the instanton moduli space can be explicitly checked. In all such cases, we find that the geometric results are consistent with the vanishing theorems. Surprisingly, linearly dependent Pfaffians even arise for cases with a non-compact instanton moduli space. This suggests some gauged linear sigma models with a non-compact instanton moduli space may still have a vanishing instanton superpotential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗