Stability Boundary Research Articles

Leveraging the Interplanetary Superhighway for Propellant–Optimal Orbit Insertion into Saturn–Titan System

This paper presents an innovative approach using Dynamical Systems Theory (DST) for interplanetary orbit insertion into Saturn−Titan three−body orbits. By leveraging DST, this study identifies invariant manifolds guiding a spacecraft into Titan−centered Distant Retrograde Orbits (DROs), strategically selected for their scientific significance. Subsequently, Particle Swarm Optimization (PSO) is employed to fine−tune the insertion parameters, thereby minimizing ΔV. The results demonstrate that the proposed method allows for a reduction in ΔV of over 70% compared to conventional approaches like patched conics−based flybys (2.68 km/s vs. 9.23 km/s), albeit with an extended time of flight, which remains notably faster than weak stability boundary transfers. This paper serves as an interplanetary mission planning methodology to optimize spacecraft trajectories for the exploration of the Saturn−Titan system.

ELM-free H-mode phase and decoupling of peeling-ballooning stability boundary in MAST Upgrade tokamak

Abstract The linear MHD peeling-ballooning stability analysis on the ELM-free phase of MAST Upgrade H-mode plasma is presented. In contrast to other similar discharges, #47018 is found to have significantly higher and wider pedestal during an ELM-free H-mode phase that lasts for approximately 80ms, which is made possible by the reduced core MHD mode activity on q=2 surface. During this period, there is sustained decoupling of peeling and ballooning branches of the stability boundary on J-α space, opening an access channel to the second stability regime with higher peaks in pedestal current density J N,ped and pressure gradient (α). Such decoupling of the stability boundary is not previously observed in MAST Upgrade H-modes, and if such condition can be readily reproduced, it opens a wide range of opportunity for MAST-U to explore low-collisionality peeling-limited pedestal regimes, as well as advanced scenarios such as quiescent H-modes that are relevant to future reactors, such as STEP and ITER.

Light hypernuclei at the boundary of neutron stability

Light hypernuclei at the boundary of neutron stability

Small-Signal Stability Analysis and Voltage Control Parameter Design for DC Microgrids

Small-signal instability issues will occur in the DC microgrid when the high-frequency oscillation peaks of the voltage closed-loop transfer function are not effectively suppressed. To ensure the small-signal stability of DC microgrids, the concept of a small-signal stability domain for voltage control parameters is proposed. Based on the voltage closed-loop transfer function, a small-signal-stability-domain-solving algorithm is proposed. With this stability domain, the impact of voltage-proportional coefficient and voltage-integral coefficient on oscillation frequency (or damping factor) is quantitatively analyzed. In addition, the influence of current control parameters on the small-signal stability boundary is also analyzed. With the introduction of this stability domain, a design method for voltage control parameters has been proposed. The voltage control parameters, which are quantitatively designed by this method, are able to maintain the small-signal stability of the system. Finally, based on the RT-BOX hardware-in-the-loop experimental platform, a switching model for a typical DC microgrid is established. Additionally, the effectiveness of the proposed algorithm and designed control parameters is verified by multiple sets of experimental results.

Effect of droplet charge density on stabilization of oil‐in‐dispersion emulsions co‐stabilized by binary mixed surfactants and nanoparticles

AbstractIonic surfactant and similarly charged nanoparticles can co‐stabilize oil‐in‐dispersion (OID) emulsions at extremely low concentrations (0.001 cmc/0.001 wt%), in which particles do not adsorb at the oil/water interface but distribute in the aqueous phase forming a dispersion. In this paper, the effect of droplet charge density on stabilization of the n‐decane‐in‐water OID emulsion was examined by using a cetyl trimethyl ammonium bromide (CTAB)/C12B (dodecyl dimethyl carboxyl betaine) binary mixture at a low fixed total concentration (0.01 mM) with varying molar fractions of CTAB. A model based on the Derjaguin‐Landau‐Verwey‐Overbeek (DLVO) theory is proposed to calculate interaction energies between droplets and between droplets and particles. It is found that the droplet charge density can be well compensated by particle concentration along the stabilization boundary, and the OID emulsion still follows the DLVO stabilization. Particles tend to surround droplets at large distances but may form a monolayer between approaching droplets at shorter distances, which significantly reduces the van der Waals attraction between droplets. In addition, the induced auxiliary droplet–particle repulsion is proportional to the number of particles per unit area of droplet surfaces, which together with the droplet–droplet repulsion ensures a large total repulsion preventing droplets from flocculation and coalescence. This work explains quantitatively the stabilization of OID emulsions, which have potential applications in emulsion products such as foods, cosmetics, pesticides, and various industrial emulsion systems. Moreover, the development of the OID emulsions represents an important advancement in green chemistry as it substantially reduces the required amounts of emulsifiers and their environmental impact after use.

Symmetry-breaking bifurcations of pure-quartic solitons in dual-core couplers.

We investigate spontaneous symmetry- and antisymmetry-breaking bifurcations of solitons in a nonlinear dual-core waveguide with the pure-quartic dispersion and Kerr nonlinearity. Symmetric, antisymmetric, and asymmetric pure-quartic solitons (PQSs) are found, and their stability domains are identified. The bifurcations for both the symmetric and antisymmetric PQSs are of the supercritical type (alias phase transitions of the second kind). Direct simulations of the perturbed evolution of PQSs corroborate their stability boundaries predicted by the analysis of small perturbations.

Chatter stability analysis for non-circular high-speed grinding process with dynamic force modelling

To avoid instability and resulting chatter during the non-circular grinding process, it is necessary to elucidate the potential occurrence of periodic chatter behavior when high-speed grinding loses stability and to define the stability boundary of the grinding system. Building upon an analysis of the geometric kinematic characteristics of non-circular profiled components, a dynamic grinding force model for non-circular high-speed grinding was derived by considering both the delay effect and the elastic yielding mechanism between the grinding wheel and workpiece. Then, A multi-factor coupled dynamic model of non-circular grinding was established. By employing a multi-scale approach, bifurcation analysis and classification of the instability process in the grinding system were conducted, using a typical non-circular profiled shaft component, such as a camshaft, for theoretical analysis and experimental validation. The research determined the stability boundary of the high-speed grinding process for non-circular profile components, validated the possibility of the existence of a conditionally stable chatter region in the non-circular high-speed grinding process, and identified differences in grinding chatter characteristics among different segments of the cam profile, with a greater propensity for chatter at the juncture of the cam fall and base circle.

Three-dimensional resonant sloshing in an upright cylindrical container with a ring baffle

The effect of ring baffles on suppressing the three-dimensional (3D) resonant sloshing in an upright cylindrical container is experimentally investigated. The main objectives of this work are to examine the effectiveness of various baffle configurations, to establish the stability boundaries of the stable steady-state waves in the unbaffled and baffled containers, to provide accurate experimental data for the verification of the analytical and numerical models, and to prompt future investigations. For this purpose, hundreds of sloshing experiments are conducted in a cylindrical container with or without a ring baffle. An analytical potential-flow solution and an asymptotic multimodal method are used to elucidate the experimental results. It is found that the vertical location of the ring baffle has small influence on the fundamental natural frequency of the system; however, it has a significant influence on the viscous damping and the damping rate increases gradually with the ascension of the baffle. When the distance between the baffle and the free liquid surface is sufficiently large, the system exhibits three types of resonant wave patterns, namely stable planar, stable swirling, and irregular chaotic. These wave patterns are qualitatively and quantitatively similar to those in the unbaffled container. When the baffle is near the free liquid surface, neither the chaotic waves nor the swirling waves take place, but a new wave pattern with the characteristic of multiple wave crests is observed. Probably, this is the first time that the 3D resonant sloshing in the baffled cylindrical container has been systematically investigated.

Sedimentary Greigite Formation

Revised thermodynamic data for greigite (Fe3S4) indicate that it is a stable sedimentary Fe-S phase. Greigite was previously regarded as metastable. Equilibrium computations using revised data explain apparently contradictory observations regarding greigite occurrences in sediments and sedimentary rocks. Greigite has a large stability area in pe-pH space relative to pyrite. It dominates in low pe regimes especially near the lower water stability boundary, which is consistent with its widespread occurrence in methanic sediments. It also has a small but significant stability zone near the sulfate-sulfide stability boundary. Its significance increases in regimes with relatively high dissolved Fe:S ratios, which explains its occurrence in freshwater sediments and iron-enriched marine sediments. It is also a paleoenvironmental marker for transitional environments, especially between freshwater and marine systems. It is stable relative to pyrrhotite and smythite, although their formation together with greigite in low pe environments may be facilitated by catalytic processes. The greigite-smythite (pyrrhotite)-siderite association is a potential marker for ancient methanogenesis. Greigite is relatively sensitive to oxidation and its long-term geological preservation depends mostly on protection from oxidation by low sediment permeability or enclosure in other minerals or organic remains. Most sedimentary and biological greigite forms via equilibrium reactions involving mackinawite-like precursors, with no direct coupling of greigite with pyrite; these minerals form independently during sedimentary diagenesis. Magnetosomal greigite production by magnetotactic bacteria is a consequence of relative greigite stability, its decoupling from pyrite, and its protection from oxidation by cell membranes.

Investigation of swirl premixed dimethyl ether/methane flame stability and combustion characteristics in an industrial gas turbine combustor

In this paper, a new scheme for DME/methane (CH4) blended fuel combustion in an industrial gas turbine is proposed and numerical calculations are conducted to reveal the swirl premixed flame stability and combustion characteristics. The results show that injecting recirculated flue gas into the inlet gas restrains the flashback induced by high DME blending ratios and achieves the fully substitution of CH4 by DME. The DME/CH4 flame stability boundary is strongly correlaterd with the laminar flame speed and the adiabatic flame temperature. Therefore, it is recommended to set up the operating conditions of DME/CH4 industrial gas turbines by maintaining a fixed value of the laminar flame speed or adiabatic flame temperature to guarantee burner safety. Additionally, the combustion characteristics of DME/CH4 flames were evaluated under different operating conditions. The results indicate that the two uniformity factors PF and γT are largely independent of the DME blending ratio. As the equivalence ratio increases, PF shows a slight overall rise but remains below 1 %. NO and CO emissions are both directly proportional to the DME blending ratio and the equivalence ratio. Notably, as the flame transitions from a stable state to combustion-induced vortex breakdown flashback, the growth rates of NO and CO emissions rise sharply. In this case, NO emissions increase by 136 %, while CO emissions rise by 126 %.

Multi-Period Optimal Transmission Switching with Voltage Stability and Security Constraints by the Minimum Number of Actions

Due to the ever-growing load demand and the deregulation of the electricity market, power systems often run near the stability boundaries, which deteriorates system voltage stability and raises voltage issues for the stable operations of power systems. Transmission switching (TS) has been applied to improve economic benefits and security operations for many applications. In this paper, a multi-period voltage stability-constrained problem (MP-VSTS) is established, intending to improve voltage security and the stability of a power system. Considering the online application of transmission switching, the minimum number of switching actions is taken as the objective function of the proposed MP-VSTS problem, which extends the TS application for real industries. The proposed model provides the switching lines for the upcoming period and the state of power systems for several successive periods. To overcome the solving difficulties of the proposed model, a two-stage approach is presented, which balances speed and accuracy. Numerical studies on the IEEE 118- and 662-bus power systems have demonstrated the proposed approach’s performance.

Robust fractional-order load frequency control for hybrid power system concerning high wind penetration

Hybrid power systems concerning wind farms have witnessed significant dynamic characteristic changes due to unpredicted generation output and integration mode conversion between frequency-sensitive wind plants and non-scheduled ones. This work presents a robust fractional-order load frequency control (LFC) method for a multi-area hybrid power system in the presence of wind penetration uncertainties. To characterize the injection effect of wind farms, the power system is described by a model with an uncertain wind penetration factor in a pre-estimated range. Then, an enhancement of Levy’s identification method is developed to convert this model into a fractional-order reduced structure to design the load frequency controller, which is in a form of fractional-order PID with a filter for ease of engineering implementation. The closed-loop stability is analyzed by the stability boundary locus (SBL) method under different wind penetration levels. It is shown that superior frequency response performance and system robustness can be obtained if the controller is designed in terms of the model with the worse-case wind penetration. Illustrative examples including a three-area hybrid power system under a variety of wind penetration variations are given to show the effectiveness of the proposed method.

Geochemical-hydromechanical couplings during water-serpentinized harzburgite interactions at 20°C and 30 bars

Interaction of groundwater with the serpentinized harzburgites of the upper mantle plays an important role in the geologic carbon cycle and serpentinization processes. In this study, an intact serpentinized harzburgite with more than 60% lizardite from the Semail ophiolite in Oman was reacted with water at near neutral pH and low PCO2 to observe its dissolution behavior and reaction path within the CaO-MgO-SiO2-CO2-H2O system at 20 °C and 30 bars. In the experiment, mass (i.e. H2O, ions) transfer is by diffusion and the selected temperature and pressure conditions mimic water-rock interactions at the shallow portions of most ultramafic rock hosted aquifers. Equilibrium activity-activity diagrams and thermodynamic data were used to compare the experimentally determined reaction path with the theoretical stability boundaries for minerals involved to investigate the evolution of bulk chemical composition, mineralogy, and water composition. The experiments demonstrated that (i) the water-rock interactions increased the pH of the aqueous phase from 5.9 to 7.5 over a period of 18 weeks; (ii) the dissolution of lizardite, orthopyroxene (enstatite), and clinopyroxene (diopside and augite) increased the concentration of Mg, Ca, and Si in the aqueous phase; (iii) the dissolution was incongruent with respect to Mg and Si, favoring Si release at pH > 6 due to (a) breaking of more reactive cation‑oxygen bonds that is consistent with the stoichiometry of magnesium for proton exchange reaction which favors a surface that is enriched in Mg at basic conditions, and (b) preferential dissolution of clinopyroxene Mg1.30Ca0.52Fe0.06Si2O6; (iv) the aqueous phase was undersaturated with respect to carbonate (e.g. calcite, magnesite, and hydromagnesite) and hydrous (e.g. lizardite, chrysotile, brucite, and talc) minerals; (v) the bulk chemical composition and mineralogy of the intact serpentinized harzburgite matrix did not change; (vi) the thermodynamic data can successfully predict water-intact serpentinized harzburgite behavior if the water chemical composition can be constrained; and (vii) no detectable macroscopic form of damage (e.g. microcracks forming as a result of differential stress fields due to changes in volume during chemical reaction) was observed.

Optimal milling cutter helix selection for period doubling chatter suppression

In high speed milling, interrupted cutting conditions can lead to period doubling chatter vibrations. While many studies have already confirmed that the use of helical tools can effectively shrink or remove these regions of unstable cutting, none of them has provided clear guidance to select the minimum helix that completely cancels the period doubling lobes. This study addresses this gap by introducing a novel analytical formula for a critical tool helix pitch: if the helix pitch is below the critical flip depth of cut of the straight helix cutter multiplied by π, the flip lobes will totally vanish. This rule is not only valuable for chatter-free process planning purposes, but it also establishes exact limit below which the fast and simple zeroth order stability algorithm can provide exact stability boundaries for helical tools. The effectiveness of the formula is numerically corroborated over three different milling scenarios: thin wall milling, slender tool and machine tool structure chatter cases. Finally, the findings are validated through experimental cutting tests.

Design and aerodynamic stability improvement study of a non-axisymmetric stator fan in a distorted insertion plate configuration

The design of anti-distortion fans must ensure the reliable operation and flight safety of propulsion systems under inlet distortion conditions. This research uses an insertion plate to obtain the inlet distortion flow field for a specific type of turbofan engine. Based on the characteristics of distortion effects, a novel strategy is proposed to rapidly implement a non-axisymmetric stator (NAS) quasi-three-dimensional design to create anti-distortion fan designs and improve the performance and stability of the fan in distortion environments. Numerical studies show that under three rotational speed operating conditions, the NAS effectively improves the total pressure ratio and efficiency characteristics of the fan under inlet distortion conditions. Compared to the prototype, the NAS can significantly increase the stability margins by 10.31 %, 8.31 %, and 7.39 % under the three different speed operating conditions, which effectively expands the stability boundaries. The NAS design directly affects the distortion region, effectively improves the incidence angle of stator vanes in the distortion region, suppresses the development and migration of vortices inside the stator passage, and significantly reduces the stator vane diffusion factor. Because it effectively eliminates corner separations and makes the incidence angle distribution of stator vanes relatively circumferentially uniform, the internal flow field of the fan's stator vanes and overall aerodynamic performance of the fan improve. Furthermore, the NAS design can improve the internal flow field downstream of the fan, direct the nonuniform flow field at the inner bypass outlet toward circumferential uniformity, and effectively improve flow field uniformity.

Intelligent frequency control of AC microgrids with communication delay: An online tuning method subject to stabilizing parameters

Smart control techniques have been implemented to address fluctuating power levels within isolated microgrids, mitigating the risk of unstable frequencies and the potential degradation of power supply quality. However, a challenge lies in the fact that employing these computationally complex methods without stability preservation might not suffice to handle the rapid changes of this highly dynamic environment in real-world scenarios over communication delays. This study introduces a flexible real-time approach for the frequency control problem using an artificial neural network (ANN) constrained to stabilized regions. Our solution integrates stabilizing PID controllers, computed through small-signal analysis and tuned via an automated search for optimal ANN weights and reinforcement learning (RL)-based selected constraints. First, we design stabilizing PID controllers by applying the stability boundary locus method and the Mikhailov criterion, specifically addressing communication delays. Next, we refine the controller parameters online through an automated process that identifies optimal coefficient combinations, leveraging a constrained ANN to manage frequency deviations within a restricted parameter range. Our approach is further enhanced by employing the RL technique, which trains the tuning system using an interpolated stability boundary curve to ensure both stability and performance. This one-of-a-kind combination of ANN, RL, and advanced PID tuning methods is a big step forward in how we handle frequency control problems in isolated AC microgrids. The experiments show that our solution outperforms traditional methods due to its reduced parameter search space. In particular, the proposed method reduces transient and steady-state frequency deviations more than semi- and unconstrained methods. The improved metrics and stability analysis show that the method improves system performance and stability under changing conditions.

Experimental study into the effects of pitch and coning angles on the flight performance of the natural samara.

Using their light wing and through the use of a leading-edge vortex (LEV), autorotating samaras can generate high lift while descending at extremely low speeds. But the flight performance of the samara, with respect to the wide design envelope, is still not well understood. Therefore, this paper aims to experimentally assess how the flight performance of three natural samara wings varies with differing wind speeds and flight conditions. The tests were conducted within a vertical wind tunnel and a novel rig was devised to effectively measure the vertical thrust and rotational rate of the autorotating samara at near frictionless conditions. Furthermore, a bespoke hub was implemented to control the coning and pitch angles of the samara wing. The tests generated a novel and comprehensive set of experimental data of autorotating samaras with changing wind speed, coning and pitch angles. The results also revealed that coning angles between 5 and 15 degrees can increase the vertical thrust produced by the samara by up to a maximum of . Additionally, it was found that samaras operate at extremely low pitch angles between -0.7 and -2.6 degrees to maximise their thrust, even though the conditions are close to the autorotational stability boundary.

Nonlinear stability analysis of thermal convection in a fluid layer with slip flow and general temperature boundary condition

The current article presents a comprehensive analysis of the influence of inconstant viscosity into thermal convection, incorporating the influence of generalized velocity (slip boundary condition) and temperature boundary conditions (physically represent imperfectly conducting boundary) within a fluid layer. Slip boundary conditions are often considered more practical than no-slip conditions (Neto et al. (2003)). Therefore, in the present work, slip boundary condition is used to discuss the effect of temperature and pressure dependent viscosity. Both linear and nonlinear stability analyses are explored, revealing a noteworthy finding: the precise alignment of the nonlinear stability boundary with the linear instability threshold. Additionally, the exchange of stability is illustrated, indicating that convection exclusively manifests in a stationary mode. The findings are derived across a spectrum of boundary scenarios, ranging from free-free to rigid-free, and rigid-rigid boundaries, encompassing both isothermal and adiabatic conditions. Notably, the slip length parameter exhibits a destabilizing effect, while convection is observed to occur more swiftly under adiabatic boundary conditions compared to isothermal conditions. The Chebyshev pseudo-spectral technique is applied to solve the eigenvalue problems obtained from linear and nonlinear stability analysis.

Bifurcation boundaries analysis of the thin-walled internal resonance energy harvester

The dynamic instability of the thin-walled 1: 2 internal resonant piezoelectric vibration energy harvester is investigated. Previously work (Nie et al., 2019) derived the nonlinear electromechanical-coupled governing equations and validated them experimentally. The modulation equations are performed by the method of multiple scales. The system stability is obtained from the eigenvalues of the Jacobi matrix. Then, three types of bifurcation boundaries of the system are determined analytically and simulated numerically via Routh–Hurwitz criterion. Results show that internal resonance complicates the dynamic properties of the bifurcation region. For a large external excitation, new saddle node bifurcation regions appear in the stability diagram. Moreover, the new saddle node and Hopf bifurcation regions may intertwine. Furthermore, as the acceleration excitation increases, the system can be observed to transition to stable–unstable–stable states. The system’s high and low branch responses are fed back by the system’s large and small initial conditions. The system’s periodic and quasi-periodic motions are characterized by time response, FFT, phase trajectory, and Poincaré map. The study of the stability boundary of the piezoelectric energy harvester contributes to the harvesting of energy from ambient vibrations over a broader frequency range.

Exact discrete-time stability analysis of multi-DOF haptic rendering: Impact of multi-rate, time-delay, and mechanical parameters

Previous studies on the stability analysis of haptic devices have predominantly focused on single-DOF devices, thereby limiting attention to multi-DOF devices, particularly those employing multi-rate sampling schemes. In this paper, we introduce a formulation for the coupled dynamics between the haptic device and the virtual environment for a multi-DOF haptic device controlled using a dual-rate sampling scheme. Subsequently, we analyze its stability through the application of a dynamic decoupling strategy within an exact discrete-time state-space framework while the device is engaged in rendering a virtual wall along one of its operational space coordinates. Furthermore, we explore how the combined influence of the dual-rate sampling approach, time delay, and the mechanical design affects the stability boundaries of the multi-DOF haptic device at a fixed workspace location as well as within the entire usable workspace. Additionally, we utilize a model-order reduction (MOR) framework to simplify the determination of the device’s stability limits, irrespective of the specific combinations of time delay and sampling rates employed.