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Liapunov stability theory applied to class of partial differential equations, and generation of contraction groups related to equivalent norms
Since the Voyager encounters in 1979, it has been known that Jupiter's cloud-top zonal winds violate the barotropic stability criterion. A vortex-tube stretching analysis of the Voyager wind data indicates that the more general Charney-Stern stability criterion is also violated. On the other hand, the zonal winds determined by tracking cloud features in Hubble Space Telescope images taken in 1991 precisely match the zonal winds determined by tracking cloud features in Voyager images, and it is hard to understand how a complicated zonal wind profile like Jupiter's could be unstable and yet not change at all in 12 years. In fact, there are at least two unknown ways to violate the Charney-Stern stability criterion and still have a stable flow. The better known of these is called Fjortoft's theorem, or Arnol'd's 1st theorem for the case of large-amplitude perturbations. Although the Fjortoft-Arnol'd theorem has been extended from the quasi-geostrophic equations to the primitive equations, the basic requirement that the potential vorticity be an increasing function of streamfunction is opposite to the case found in Jupiter, where the Voyager data indicate that the potential vorticity is a decreasing function of streamfunction. But this second case is precisely that which is covered by Arnol'd's 2nd stability theorem. In fact, the Voyager data suggest that Jupiter's zonal winds are neutrally stable with respect to Arnol'd's 2nd stability theorem. Here, we analyze the linear stability problem of a one-parameter family of sinusoidal zonal wind profiles that are close to neutral stability with respect to Arnol'd's 2nd stability theorem. We find numerically that the most unstable mode is always stationary, which may help to explain the slowly moving mode 10 waves observed on Jupiter. We find that violation of Arnol'd's 2nd stability theorem is both necessary and sufficient for instability of sinusoidal profiles. However, there appears to be no simple extension of Arnol'd's 2nd stability theorem to the primitive equations. Nevertheless, the primitive growth rates are small, and the primitive system is still governed by the quasi-geostrophic neutral-stability configuration.
Metal halide perovskite solar cell (PSC) technology has an impressive power conversion efficiency (PCE) exceeding 26.1% and demonstrates cost-effective manufacturing. However, the stability of these PSCs poses a significant challenge, hindering their widespread manufacturing and commercialization. To tackle the degradation issue inherent in PSCs, surface passivation techniques, particularly employing a thin layer of two-dimensional (2D) perovskites, create a 2D/3D heterostructure. Beyond this, the exploration of metal halide double perovskites adds a new dimension to the chemical and band gap phase space of materials for optoelectronic applications. In this study, we leverage a wide band gap double perovskite interlayer to enhance the stability of 3D metal halide perovskite. Specifically, the double perovskite nanoparticle Cs 2 AgBiBr 6 , with its substantial band gap of 2.2 eV and exceptional air stability, is utilized. Through optimization, a Cs 2 AgBiBr 6 -treated PSC achieves an open-circuit voltage of 1.12 V and an impressive PCE of 19.52%. Additionally, the Cs 2 AgBiBr 6 passivation layer proves to be effective in bolstering the stability of PSCs. This work demonstrates an additional strategy and design motif to simultaneously increase the PCE of PSCs along with achieving improved stability.
Synopsis Understanding how the structure of biological systems impacts their resilience (broadly defined) is a recurring question across multiple levels of biological organization. In ecology, considerable effort has been devoted to understanding how the structure of interactions between species in ecological networks is linked to different broad resilience outcomes, especially local stability. Still, nearly all of that work has focused on interaction structure in presence-absence terms and has not investigated quantitative structure, i.e., the arrangement of interaction strengths in ecological networks. We investigated how the interplay between binary and quantitative structure impacts stability in mutualistic interaction networks (those in which species interactions are mutually beneficial), using community matrix approaches. We additionally examined the effects of network complexity and within-guild competition for context. In terms of structure, we focused on understanding the stability impacts of nestedness, a structure in which more-specialized species interact with smaller subsets of the same species that more-generalized species interact with. Most mutualistic networks in nature display binary nestedness, which is puzzling because both binary and quantitative nestedness are known to be destabilizing on their own. We found that quantitative network structure has important consequences for local stability. In more-complex networks, binary-nested structures were the most stable configurations, depending on the quantitative structures, but which quantitative structure was stabilizing depended on network complexity and competitive context. As complexity increases and in the absence of within-guild competition, the most stable configurations have a nested binary structure with a complementary (i.e., anti-nested) quantitative structure. In the presence of within-guild competition, however, the most stable networks are those with a nested binary structure and a nested quantitative structure. In other words, the impact of interaction overlap on community persistence is dependent on the competitive context. These results help to explain the prevalence of binary-nested structures in nature and underscore the need for future empirical work on quantitative structure.
This paper investigates the stability and the stability degree of a flexible cracked rotor supported on different kinds of journal bearings. It is found that no matter what kind of bearings is used, the unstable zones caused by rotor crack locate always within the speed ratio (2/N) (1 - Delta K(sub xi)/4) is less than Omega is less than 2/N when gravity parameter W(sub R) is greater than 1.0, and locate always within the speed ratio (2 Omega(sub alpha)/N) (1 - Delta K(sub xi)/4) is less than Omega is less than 2 Omega(sub alpha)/N when W(sub R) is less than 0.1, where Delta K(sub xi) is the crack stiffness ratio, N = 1, 2, 3, 4, 5, ..., and Omega(sub alpha) = ((1 + 2 alpha)/2 alpha)(exp 1/2). When 0.1 is less than W(sub R) is less than 1.0, there is a region where no unstable zones caused by rotor crack exist. Outside the crack ridge zones, the rotor crack has almost no influence on system's stability and stability degree; while within the crack ridge zones, the stability and stability degree depend both on the crack and system's parameters. In some cases, the system may still be stable even when the crack is very large. For small gravity parameter (W(sub R) is less than 0.1), the mass ratio alpha has large influence on the position of unstable region, but its influence on the stability degree is small. The influence of fixed Sommerfeld number S(sub 0) on the crack stability degree is small although S(sub 0) has large influence on the stability degree of uncracked rotor.
Materials and cell components used in CO 2 electrolysis have largely been adapted from technologies initially developed for water electrolysis and fuel cells. However, electrochemical CO 2 reduction introduces distinct material challenges due to the unique chemical environment in this process. Here, in this study, we conducted ex-situ 1000 h stability tests on commonly used anion exchange membranes, exposing them exclusively to electrolytes and organic molecules used or produced during CO 2 electrolysis, at concentrations relevant to and compatible with postseparation processes. Notably, 15% w/w n-propanol and 5 M acetic acid caused complete dissolution or partial disintegration of the membranes unless cross-linking was present and remained stable throughout the test. When the membranes stayed physically intact, most of them exhibited excellent chemical stability in alkaline medium containing alcohols or formic acid, which was confirmed by vibrational spectroscopy and ion exchange capacity measurements. However, exposure to alcohol-and acid-containing solutions led to a substantial increase in swelling and water uptake, with potential implications for mechanical stability, ion/product crossover, and compression management of adjacent components. The potential effects of CO 2 electroreduction products on membrane stability, their subsequent impact on electrolyzer performance, and mitigation strategies are discussed.
Cell-free biocatalysis (CFB) is an efficient and environmentally friendly method to synthesize molecules such as pharmaceuticals, biochemicals, and biofuels through the in vitro use of enzyme cascades. These enzymes often require redox cofactors to drive chemical reactions. Natural redox cofactors (NAD(P)H) are expensive to isolate, motivating synthetic nicotinamide cofactor biomimetics (NCBs) as a cost-effective solution. A select handful of NCBs have been identified as potential NAD(P)H alternatives with comparable or improved redox capabilities, however, they display a tendency to degrade in common buffers. In this study, a library of 132 NCB candidates is systematically generated, over 85% of which have not been characterized in the literature, to expand the diversity of currently explored NCBs. The decomposition mechanism of NCBs in phosphate is evaluated using density functional theory (DFT), revealing protonation at the nicotinamide C5 position as a reporter of cofactor stability. Based on this result, we trained a linear regression model on DFT calculated descriptors to predict NCB stability in phosphate buffer, achieving mean absolute error (MAE) and root mean squared error (RMSE) values within computational accuracy. Analysis of key atomic descriptors and qualitative trends in our dataset informed the design of novel NCB candidates we propose with optimized stability. This work enables researchers to predict the relative stability of NCBs before synthesis, thereby streamlining the process to make CFB more affordable and viable at industry scales.
A number of improvements to the TJ toroidal tearing mode code [Fitzpatrick, Phys. Plasmas 31, 102507 (2024)] are documented. The TJ code is also successfully benchmarked against the STRIDE toroidal tearing mode code [Glasser and Koleman, Phys. Plasmas 25, 082502 (2018)]. Finally, the new capabilities of the TJ code are used to investigate the stability of tearing modes in tokamak plasmas as an ideal stability boundary, associated with either an external-kink or an internal-kink mode, is approached. All elements of the tearing stability matrix are found to tend to infinity as an ideal stability boundary is approached. Furthermore, as the stability boundary is approached, the eigenfunctions of the various tearing modes in the plasma, which are decoupled by sheared plasma rotation, are all found to morph into that of the marginally stable ideal mode. However, the growth-rates and real frequencies of the various “ideal-tearing-modes” are different from one another. Moreover, the growth-rate of the ideal-tearing-mode that reconnects magnetic flux at the rational surface that lies closest to the edge of the plasma is the one that tends to a very large value as the stability boundary is approached. A relatively simple test for ideal stability that is capable of detecting stability boundaries for external-kink and internal-kink modes, even in the presence of a very close-fitting ideal wall, is described and verified.
A method of determining the stability of linear systems with many constant time delays is developed. This technique, an extension of the tau-decomposition method, is used to examine not only the stability but also the relative stability of retarded systems with many delays and a class of neutral equations with one delay. Analytical equations are derived for partitioning the delay space of a retarded system with two time delays. The stability of the system in each of the regions defined by the partitioning curves in the parameter plane is determined using the extended tau-decomposition method. In addition, relative stability boundaries are defined using the extended tau-decompositon method in association with parameter plane techniques. Several applications of the extended tau-decomposition method are presented and compared with stability results obtained from other analyses. In all cases the results obtained using the method outlined herein coincide with and extend those of previous investigations. The extended tau-decomposition method applied to systems with time delays requires less computational effort and yields more complete stability analyses than previous techniques.
This paper presents a small-signal stability analysis of grid-forming (GFM) inverters under current-limiting conditions. It examines how adjustments in virtual impedance angles, implemented through advanced current-limiting and frequency stabilization techniques, influence small-signal stability. This paper studies a GFM inverter control integrating a fictitious power technique stabilizing primary control by adding a virtual power term and a hybrid current limiter integrating virtual impedance in the anti-wind-up feedback with current reference saturation limiting. A small-signal model is developed to assess the impact of virtual impedance angles on GFM inverter dynamics during grid disturbances, such as voltage drops. The findings indicate that although increasing the virtual impedance angle (to make it more inductive) enhances large-signal stability and voltage support during faults, it can induce oscillations and lead to instability if the angle exceeds certain thresholds. Based on the small-signal models, this paper provides design considerations for the current-limiter impedances to ensure reliable GFM inverter behavior under grid disturbances while maintaining small-signal stability.
MATLAB Stability and Control Toolbox (MASCOT) utilizes geometric, aerodynamic, and inertial inputs to calculate air vehicle stability in a variety of critical flight conditions. The code is based on fundamental, non-linear equations of motion and is able to translate results into a qualitative, graphical scale useful to the non-expert. MASCOT was created to provide the conceptual aircraft designer accurate predictions of air vehicle stability and control characteristics. The code takes as input mass property data in the form of an inertia tensor, aerodynamic loading data, and propulsion (i.e. thrust) loading data. Using fundamental nonlinear equations of motion, MASCOT then calculates vehicle trim and static stability data for the desired flight condition(s). Available flight conditions include six horizontal and six landing rotation conditions with varying options for engine out, crosswind, and sideslip, plus three take-off rotation conditions. Results are displayed through a unique graphical interface developed to provide the non-stability and control expert conceptual design engineer a qualitative scale indicating whether the vehicle has acceptable, marginal, or unacceptable static stability characteristics. If desired, the user can also examine the detailed, quantitative results.
Aerogels demonstrate extraordinarily low thermal conductivity and low density, presenting a promising form of lightweight insulation for aerospace applications. The primary challenge is stabilization of the highly porous structure at temperatures to 1200 °C. Upon collapse of the pore structure, the favorable thermal properties and low density are diminished. Yttria-stabilized zirconia (YSZ) aerogels are synthesized to investigate the effect of composition on morphology, phase behavior, and thermal stability (specific surface area, pore size distribution). This work demonstrates the improvement in thermal stability of zirconia aerogels with increased yttria content. To develop insight on the influence of structure on thermal stability, the effects of water content and solids loading are studied and in elucidation of the mechanism by which yttria stabilizes the pore structure. With an improved understanding of aerogel structure and performance, metal oxide aerogels can be developed to withstand the extreme environments of space exploration.
Reservoir engineering is a powerful technique to autonomously stabilize a quantum state. Traditional schemes involving multi-body states typically function for discrete entangled states. In this work, we enhance the stabilization capability to a continuous manifold of states with programmable stabilized state selection using multiple continuous tuning parameters. We experimentally achieve 84.6% and 82.5% stabilization fidelity for the odd and even-parity Bell states as two special points in the manifold. We also perform fast dissipative switching between these opposite parity states within 1.8 μs and 0.9 μs by sequentially applying different stabilization drives. Our result is a precursor for new reservoir engineering-based error correction schemes.
A method is presented for obtaining the value of the phase stability from time domain frequency stability measurements. Definition of frequency and phase stability are presented. The various types of noise sources in an oscillator and how their location in the oscillator circuitry determines the resultant phase and frequency noise spectrum are described. With this knowledge, the type of noise spectrum from time domain frequency stability measurements is determined. Using certain conversions, the total phase noise spectrum is obtained, which is integrated to obtain the phase stability. Examples of the conversion process are also presented.
A comparison is made between the stability criteria of Hill and that of Laplace to determine the stability of outer planetary orbits encircling binary stars. The restricted, analytically determined results of Hill's method by Szebehely and coworkers and the general, numerically integrated results of Laplace's method by Graziani and Black (1981) are compared for varying values of the mass parameter mu. For mu = 0 to 0.15, the closest orbit (lower limit of radius) an outer planet in a binary system can have and still remain stable is determined by Hill's stability criterion. For mu greater than 0.15, the critical radius is determined by Laplace's stability criterion. It appears that the Graziani-Black stability criterion describes the critical orbit within a few percent for all values of mu.
Part I of this report presents a brief review of methods available to the helicopter designer for obtaining desired stability characteristics by modifications to the airframe design. The discussion is based on modifications made during the establishment of flying-qualities criteria and includes sample results of theoretical studies of additional methods. The conclusion is reached that it is now feasible to utilize combinations of methods whereby stability-parameter values are realized which in turn provide the desired stability characteristics. Part II reviews some of the methods of predicting rotor stability derivatives. The procedures by which these rotor derivatives are employed to estimate helicopter stability characteristics have been summarized.
Maintaining high surface area and porosity at high temperatures is important when considering aerogels for use in thermal management systems. The mesoporous structure of aerogels results in extremely low thermal conductivity, making them lightweight, high performance insulating materials. Maintaining these properties requires innovative routes to suppress sintering and pore collapse as use temperatures rise. The current work aims to improve the pore structure stability of yttria-stabilized zirconia aerogels by the addition of a SiO 2 coating. The functionalization of surface hydroxyl groups by the addition of SiO 2 is hypothesized to mitigate condensation reactions, which are a driving force for shrinkage and pore structure collapse. Zirconia aerogels with 0, 10 and 30 mol% yttria (YO 1.5 ) additions were coated in a tetraethyl orthosilicate (TEOS) solution and exposed to temperatures up to 1200°C. Crystal structure, pore structure, and aerogel morphology were investigated to understand changes in aerogel thermal stability. The SiO 2 coating exhibited a greater influence on pore stability over yttria concentration, with specific surface area of the coated aerogels being twice that of the uncoated aerogels up to 1000°C. However, the presence of the SiO 2 coating promoted rapid sintering and densification at 1200°C, establishing an upper use temperature for SiO 2 and a need to develop other coating chemistries.
Stability of perovskite solar cells (PSCs) under light, heat, humidity and their combinations have been notably improved recently. However, PSCs have poor reverse-bias stability that limits their real-world application. Here we report a systematic study on the degradation mechanisms of p-i-n structure PSCs under reverse bias. The oxidation of iodide by injected holes at the cathode side initialize the reverse-bias-induced degradation, then the generated neutral iodine oxidizes metal electrode such as copper, followed by drift of Cu+ into perovskites and its reduction by injected electrons, resulting in localized metallic filaments and thus device breakdown. A reinforced barrier with combined lithium fluoride, tin oxide and indium tin oxide at the cathode side reduces device dark current and avoids the corrosion of Cu0. It dramatically increases breakdown voltage to above -20 V and improved the T90 lifetime of PSCs to ~1,000 h under -1.6 V. The modified minimodule also maintained over 90% of its initial performance after 720 h of shadow tests.