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For a simple Jeffcott model with deadband, a method is developed to determine stability margins by an analysis of the Discrete Fourier transform of the system response. The viability of this method is demonstrated by means of numerical simulations. The circular behavior of the system response on the stability boundary is also explained.
Zirconia (ZrO2) has great technological importance in structural, electrical, and chemical applications. It is the crucial component for state-of-the art thermal barrier coatings and an enabling component as a solid electrolyte for solid-oxide fuel cell systems. Pure ZrO2 is of limited use for industrial applications because of the phase transformations that occur. Upon the addition of stabilizers, cubic (c-ZrO2) and tetragonal (t-ZrO2) forms can be preserved. It is the stabilized and partially stabilized forms of zirconia that function as thermal barrier coatings, solid electrolytes, and oxygen sensors and that have numerous applications in the electrochemical industry. The cubic form of ZrO2 is typically stabilized through Y2O3 additions. However, Y2O3-stabilized zirconia is susceptible to deformation at high temperatures (greater than 900 C) because of the large number of slip systems and the high oxygen diffusion rates, which result in high creep rates at high temperatures. Successful use of ZrO2 at high temperatures requires that new dopant additives be found that will retain or enhance the desirable properties of cubic ZrO2 and yet produce a material with lower creep rates. At the NASA Glenn Research Center, erbium oxide (Er2O3) was identified as a promising dopant for improving the creep resistance of. ZrO2. The selection of Er2O3 was based on the strong interactions of point defects and dislocations. Single crystals of 5 mol% Er2O3- doped ZrO2 rods (4 mm in diameter) and monofilaments (200 to 300 mm in diameter and 30 cm long) were grown using the laser-heated float zone technique, and their creep behavior was measured as a function of temperature. The addition of 5 mol% Er2O3 to single-crystal ZrO2 improved its creep resistance at high temperatures by 2 to 3 orders of magnitude over state-of-the-art Y2O3-doped crystals. Detailed microstructural characterization of ZrO2-Er2O3 single crystals has identified new mechanisms for improving the creep resistance of this class of materials. Adding Er2O3 to ZrO2 results in microstructure of stable and metastable tetragonal precipitates that with thermal treatment evolve to a tweed structure of nanosize tetragonal lamellae. The superior high-temperature creep resistance of Er2O3-doped ZrO2 is attributed to nanoscale precipitation hardening. Doping with Er2O3 will significantly increase the upper-use temperature limit of ZrO2. Potential applications include using Er2O3-doped ZrO2 as a high-temperature fiber for structural applications and adding Er2O3 to reduce the sintering rates of ZrO2 thermal barrier coatings. This work was conducted at Dpto. de F sica de la Materia Condensada, Universidad de Sevilla, Spain, and at NASA Glenn.
We investigated the dynamical stability of high-multiplicity Kepler and K2 planetary systems. Our numerical simulations find instabilities in ∼20% of the cases on a wide range of timescales (up to 5 × 10{sup 9} orbits) and over an unexpectedly wide range of initial dynamical spacings. To identify the triggers of long-term instability in multiplanet systems, we investigated in detail the five-planet Kepler-102 system. Despite having several near-resonant period ratios, we find that mean-motion resonances are unlikely to directly cause instability for plausible planet masses in this system. Instead, we find strong evidence that slow inward transfer of angular momentum deficit (AMD) via secular chaos excites the eccentricity of the innermost planet, Kepler-102 b, eventually leading to planet–planet collisions in ∼80% of Kepler-102 simulations. Kepler-102 b likely needs a mass ≳0.1 M {sub ⊕}, hence a bulk density exceeding about half Earth’s, in order to avoid dynamical instability. To investigate the role of secular chaos in our wider set of simulations, we characterize each planetary system’s AMD evolution with a “spectral fraction” calculated from the power spectrum of short integrations (∼5 × 10{sup 6} orbits). We find that small spectral fractions (≲0.01) are strongly associated with dynamical stability on long timescales (5 × 10{sup 9} orbits) and that the median time to instability decreases with increasing spectral fraction. Our results support the hypothesis that secular chaos is the driver of instabilities in many nonresonant multiplanet systems and also demonstrate that the spectral analysis method is an efficient numerical tool to diagnose long-term (in)stability of multiplanet systems from short simulations.
A method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one-point quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2 and 1 for the normalized stabilization parameter lead to the 5-point finite difference, 9-point finite difference and fully integrated finite element operators, respectively, for rectangular meshes; numerical experiments reported here show that the three have identical rates of convergence in the L2 norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.
Techniques for the numerical simulation of compressible and incompressible viscous flows are described and demonstrated. The focus is on a multidomain spectral method based on the flux-balance domain-interface scheme of Macaraeg and Streett (1986). The fundamental principles of the method are reviewed, and it is shown that the multidomain spectral approach facilitates the treatment of instability and the transition to turbulence. Typical numerical results for the Taylor-Couette problem and for bounded compressible high-speed mixing layers are presented in graphs and briefly characterized.
The boundary layer stability within the high-area-ratio nozzle at NASA Lewis was tested at five chamber pressure conditions. For all nozzle conditions examined, Taylor-Goertler vortices grew more rapidly than Tollmien-Schlichting waves. The experimental heat flux was accurately predicted by a laminar boundary layer computation, thereby confirming the laminar nature of the nozzle boundary layer flow. When the chamber pressure was increased in a series of cases, the transition point occurred farther upstream. The number of vortices contained in the dominant instability increased with chamber pressure.
We report dry reforming of methane (DRM) involves the conversion of carbon dioxide (CO 2 ) and methane (CH 4 ) into syngas (a mixture of hydrogen, H 2 , and carbon monoxide, CO), which can then be used to produce a wide range of products by means of Fischer-Tropsch synthesis. DRM has gained much attention as a means of mitigating damage from anthropogenic greenhouse gas (GHGs) emissions to the environment and instead utilizing these gases as precursors for value-added chemicals or to synthesize sustainable fuels and chemicals. Carbon deposition or coke formation, a primary cause of catalyst deactivation, has proven to be a major challenge in the development of DRM catalysts. The use of nickel- and cobalt-based catalysts has been extensively explored for DRM for their high activity and low cost but suffer from poor stability due to coke formation that has hindered their commercialization. Numerous articles have reviewed the various aspects of catalyst deactivation and strategies for mitigation, but few has focused on the benefit of bimetallic catalysts for mitigating coke formation. Bimetallic catalysts, often improve the catalytic stability over their monometallic counterparts due to synergistic effects resulting from two metal-to-metal interactions. This review will cover DRM literature for various bimetallic catalyst systems, including the effect of supports and promoters, on the mitigation of carbonaceous deactivation
This study is concerned with the computation and linear stability of a class of laminar compressible wake flows. The emphasis is on correct basic flow profiles that satisfy the steady equations of motion, and to this end the unperturbed state is obtained through numerical integration of the compressible boundary-layer equations. The linear stability of the flow is examined via the Rayleigh equation that describes evolution of inviscid disturbances. Analytical results are given for short- and long-wavelength disturbances and some numerical results of the general eigenvalue problem are also reported.
A two-layer configuration of thermohaline convection is studied, with the principal aim of explaining the observed independence of the buoyancy-flux ratio on the stability parameter when the latter is large. Temperature is destabilizing and salinity is stabilizing, so diffusive interfaces separate the convecting layers. The convection is treated in the single-mode approximation, with a prescribed horizontal planform and wavenumber. Surveys of numerical solutions are presented for a selection of Rayleigh numbers R, stability parameters lambda and horizontal wavenumbers. The solutions yield a buoyancy flux ratio chi that is insensitive to lambda, in accord with laboratory experiments. However chi increases with increasing R, in contradiction to laboratory observations.
Fully implicit Runge--Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic preconditioning framework for solving the systems of equations that arise from IRK methods applied to linear numerical PDEs (without algebraic constraints). Additionally, this framework also naturally applies to discontinuous Galerkin discretizations in time. Under quite general assumptions on the spatial discretization that yield stable time integration, the preconditioned operator is proven to have condition number bounded by a small, order-one constant, independent of the spatial mesh and time-step size, and with only weak dependence on number of stages/polynomial order; for example, the preconditioned operator for 10th-order Gauss IRK has condition number less than two, independent of the spatial discretization and time step. The new method can be used with arbitrary existing preconditioners for backward Euler-type time-stepping schemes and is amenable to the use of three-term recursion Krylov methods when the underlying spatial discretization is symmetric. The new method is demonstrated to be effective on various high-order finite-difference and finite element discretizations of linear parabolic and hyperbolic problems, demonstrating fast, scalable solution of up to 10th-order accuracy. The new method consistently outperforms existing block preconditioning approaches, and in several cases, the new method can achieve 4th-order accuracy using Gauss integration with roughly half the number of preconditioner applications and wallclock time as required using standard diagonally IRK methods.
The effect of convective melt motion on the growth of morphological instabilities in crystal growth has been the focus of many studies in the past decade. While most of the efforts have been directed towards investigating the linear stability aspects, relatively little attention has been devoted to experimental and numerical studies. In a pure morphological case, when there is no flow, morphological changes in the solid-liquid interface are governed by heat conduction and solute distribution. Under the influence of a convective motion, both heat and solute are redistributed, thereby affecting the intrinsic morphological phenomenon. The overall effect of the convective motion could be either stabilizing or destabilizing. Recent investigations have predicted stabilization by a flow parallel to the interface. In the case of non-parallel flows, e.g., stagnation point flow, Brattkus and Davis have found a new flow-induced morphological instability that occurs at long wavelengths and also consists of waves propagating against the flow. Other studies have addressed the nonlinear aspects (Konstantinos and Brown, Wollkind and Segel)). In contrast to the earlier studies, our present investigation focuses on the effects of the potential flow fields typically encountered in Hele-Shaw cells. Such a Hele-Shaw cell can simulate a gravity-free environment in the sense that buoyancy-driven convection is largely suppressed, and hence negligible. Our interest lies both in analyzing the linear stability of the solidification process in the presence of potential flow fields, as well as in performing high-accuracy nonlinear simulations. Linear stability analysis can be performed for the flow configuration mentioned above. It is observed that a parallel potential flow is stabilizing and gives rise to waves traveling downstream. We have built a highly accurate numerical scheme which is validated at small amplitudes by comparing with the analytically predicted results for the pure morphological case. We have been able to observe nonlinear effects at larger times. Preliminary results for the case when flow is imposed also provide good validation at small amplitudes.
Nonheme iron oxygenases utilize dioxygen to accomplish challenging chemical oxidations. Additionally, a further understanding of the Fe-O 2 intermediates implicated in these processes is challenged by their highly transient nature. To that end, we have developed a ligand platform featuring phosphinimide donors intended to stabilize oxidized, high-spin iron complexes. O 2 exposure of single crystals of a three-coordinate Fe(II) complex of this framework allowed for in crystallo trapping of a terminally bound Fe-O 2 complex suitable for XRD characterization. Spectroscopic and computational studies of this species support a high-spin Fe(III) center antiferromagnetically coupled to a superoxide ligand, similar to that proposed for numerous nonheme iron oxygenases. In addition to the apparent stability of this synthetic Fe-O 2 complex, its ability to engage in a range of stoichiometric and catalytic oxidation processes demonstrates that this iron-phosphinimide system is primed for development in modeling oxidizing bioinorganic intermediates and green oxidation chemistry.
Analysis and numerical simulation are used to determine the effect that various heating rates have on the linear and nonlinear evolution of a typical plasma within a solar magnetic flux tube subject to the condensational instability. It is found that linear stability depends strongly on the heating rate. The results of numerical simulations of the nonlinear evolution of the condensational instability in a solar magnetic flux tube are presented. Different heating rates lead to quite different nonlinear evolutions, as evidenced by the behavior of the global internal energy.
Most fluid flows are turbulent rather than laminar and the reason for this was studied. One of the earliest explanations was that laminar flow is unstable, and the linear instability theory was first developed to explore this possibility. A series of early papers by Rayleigh produced many notable results concerning the instability of inviscid flows, such as the discovery of inflectional instability. Viscosity was commonly thought to act only to stabilize the flow, and flows with convex velocity profiles appeared to be stable. The investigations that led to a viscous theory of boundary layer instability was reported. The earliest application of linear stability theory to transition prediction calculated the amplitude ratio of the most amplified frequency as a function of Reynolds number for a Blasius boundary layer, and found that this quantity had values between five and nine at the observed Ret. The experiment of Schubauer and Skramstad (1947) completely reversed the prevailing option and fully vindicated the Gottingen proponents of the theory. This experiment demonstrated the existence of instability waves in a boundary layer, their connection with transition, and the quantitative description of their behavior by the theory of Tollmien and Schlichting. It is generally accepted that flow parameters such as pressure gradient, suction and heat transfer qualitatively affect transition in the manner predicted by the linear theory, and in particular that a flow predicted to be stable by the theory should remain laminar. The linear theory, in the form of the e9, or N-factor is today in routine use in engineering studies of laminar flow. The stability theory to boundary layers with pressure gradients and suction was applied. The only large body of numerical results for exact boundary layer solutions before the advent of the computer age by calculating the stability characteristics of the Falkner-Skan family of velocity profiles are given. When the digital computer reached a stage of development which permit the direct solution of the primary differential equations, numerical results were obtained from the linear theory during the next 10 years for many different boundary layer flows: three dimensional boundary layers; free convention boundary layers; compressible boundary layers; boundary layers on compliant walls; a recomputation of Falkner-Skan flows; unsteady boundary layers; and heated wall boundary layers.
An impact of the equilibrium radial electric field on energy loss processes after pedestal collapse is numerically investigated using the BOUT++ framework. Using linear stability analysis, the resistive ballooning mode is shown to be stabilized by the radial shear of the equilibrium radial electric field. On the other hand, the energy loss level after the pedestal collapse increases if the equilibrium radial electric field is taken into account. The spatio-temporal and phase diagram analyses show that the equilibrium radial electric field partially cancels the fluctuation-driven toroidally axisymmetric radial electric field and weakens the E × B shearing rate after pedestal collapse, weakening the turbulence suppression by vortex shearing. Finally, the equilibrium radial electric field therefore increases turbulence intensity in nonlinear cyclic oscillations among pressure gradient, E × B shearing rate, and turbulence intensity, which gives rise to subsequent bursts of turbulent transport and increases the energy loss level.
Abstract We propose to extend the composite tetrahedral finite element first introduced by Thoutireddy et al. (2002) and recently reformulated by Ostien et al. (2016). We generalize the gradient operator and mass matrix to curved domains through analytical expressions weighted by subtetrahedra Jacobians. Optimal integration weights are constructed to increase the accuracy of Gaussian quadrature. We preserve the variational structure of the formulation through a new five‐field functional with additional, independent fields for the Jacobian and the pressure. This approach not only obviates volumetric locking but also yields symmetry. A deleterious soft mode, common to both the quadratic and composite tetrahedral element with constant pressure formulations is effectively stabilized through a novel convex energy penalty function. Numerous numerical examples spanning a patch test to the impact of a Taylor bar demonstrate the accuracy, robustness, and convergence of the extended composite tetrahedral element for application to structural metals.
We propose an entropy-stable conservative flux form neural network (CFN) to predict the dynamics of unknown governing conservation laws. The design of the network is based on the entropy-stable, second-order, and non-oscillatory Kurganov-Tadmor (KT) scheme. The proposed entropy-stable CFN, hereafter referred to as ESCFN, uses slope limiting as a denoising mechanism, ensuring accurate predictions in both noisy and sparse observation environments, as well as in both smooth and discontinuous regions. Importantly, our method is designed to predict long term dynamics of the unknown conservation law exclusively from a short temporal window of observed data, that is, without oracle knowledge of the PDE or later-time solution profiles. Numerical experiments demonstrate that the ESCFN achieves both stability and conservation while maintaining accuracy over extended time domains, and successfully predicts shock propagation speeds in long-term simulations. Furthermore, it is also robust to both noisy and sparse data environments.
Magnetohydrodynamics (MHD) provides a useful model to describe the crucial plasma macroscopic equilibrium and stability behaviors in toroidal tokamak devices by considering the plasma as a conducting fluid interacting with a surrounding confining electromagnetic field. MHD is the most basic plasma model, incorporating most large-scale phenomena, including plasma equilibrium and all major instabilities. MHD equations are obtained by taking moments of the Boltzmann equations for different plasma species. They provide a set of comprehensive physics constrains to compute and optimize the equilibrium plasma shape and pressure and current profiles that are critical to its stability and performance. In the ideal case, the equations have special properties that lead to efficient numerical calculation schemes, the most important of which is the ideal MHD energy principle for linear stability against small departures from equilibrium. In a tokamak plasma, equilibrium pressure is mostly destabilizing for MHD modes, whereas equilibrium current is also often a major driving force. Plasma resistivity creates new freedom for a MHD instability to grow, but there are also cases where the plasma resistivity plays a stabilizing role. Equilibrium toroidal flow and/or flow shear can affect MHD instabilities. Principal MHD instabilities include the internal kink mode, sawtooth, fishbone, external kink, resistive wall mode, resistive interchange, tearing and neoclassical tearing modes (NTMs), locked modes, toroidal Alfven eigenmodes (TAEs), and edge localized modes (ELMs). Fast-growing MHD instabilities can lead to an abrupt plasma disruption and termination that can potentially damage the device plasma facing components (PFCs) and in-vessel structures. Furthermore, an important MHD application is to develop robust techniques to mitigate and control MHD instabilities.