Simple Stability Analysis Research Articles

Controlling viscous fingering instabilities of complex fluids

Despite their aesthetic elegance, wavy or fingering patterns emerge when a fluid of low viscosity pushes another immiscible fluid of high viscosity in a porous medium, producing an incomplete sweep and hampering several crucial technologies. Some examples include chromatography, printing, coating flows, oil-well cementing, as well as large-scale technologies of groundwater and enhanced oil recovery. Controlling such fingering instabilities is notoriously challenging and unresolved for complex fluids of varying viscosity because the fluids’ mobility contrast is often predetermined and yet the predominant drive in determining a stable, flat or unstable, wavy interface. Here we show, experimentally and theoretically, how to suppress or control the primary viscous fingering patterns of a common type of complex fluids (of shear-thinning with a low yield stress) using a radially tapered cell of linearly varying gap thickness, h(r). Experimentally, we displace a complex viscous (PAA) solution with gas under a constant flow rate (Q), varied between 0.02 and 2 slpm (standard liter per minute), in a radially converging cell with a constant gap-thickness gradient, α=dh/dr<0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha = dh/dr < 0$$\\end{document}. A stable, uniform interface emerges at low Q and in a steeper cell (i.e., greater |α|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\alpha |$$\\end{document}) for the complex fluids, whereas unstable fingering pattern at high Q and smaller |α|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\alpha |$$\\end{document}. Our theoretical predictions with a simplified linear stability analysis show an agreeable stability criterion with experimental data, quantitatively offering strategies to control complex fluid-fluid patterns and displacements in microfluidics and porous media.

Impedance-Based Stability Analysis of Grid-Connected Inverters under the Unbalanced Grid Condition

As a common interface circuit for renewable energy integrated into the power grid, the inverter is prone to work under a three-phase unbalanced weak grid. In this paper, the instability of grid-connected inverters under the unbalanced grid condition is investigated. First, a dual second-order generalized integrator phase-locked loop (DSOGI-PLL)-based inverter under balanced and unbalanced conditions is modeled. A fourth-order impedance model is established to describe its impedance characteristics under the unbalanced grid condition. To analyze this multi-input multi-output system, a simplified stability analysis method based on the generalized Nyquist stability criterion and matrix theory is proposed. Then, the influences of circuit and control parameters on the stability of the grid-connected inverter system under the unbalanced grid condition are investigated. Finally, the accuracy of the derived frequency-coupled impedance model is verified via simulations, and the effectiveness of the proposed simplified stability analysis method on the system stability analysis is verified via both simulations and hardware experiments.

“Adaptive virtual synchronous generator control using optimized bang-bang for Islanded microgrid stability improvement”

In this paper, a virtual synchronous generator (VSG) controller is applied to a hybrid energy storage system (HESS) containing a battery energy storage system and supercapacitor storage system for maintaining the frequency stability of an isolated microgrid. The microgrid contains a photovoltaic generation system and a diesel generator in addition to the HESS and two constant impedance loads that are fed through a medium voltage radial feeding system. The adaptive virtual inertia constant (H) with constant virtual damping coefficient (D) based on ‘ bang-bang’ control for the microgrid’s frequency stability enhancement is investigated and compared with the constant parameter VSG. In addition, the bang-bang control is modified to adapt the D beside the adaptive H, and the system response is investigated and compared with the conventional adaptive H technique. The VSG parameters are evaluated based on two different methods. The first is a computational method based on the simplified small signal stability analysis, while the other is based on an optimization method using two different objective functions and the particle swarm optimization technique. This paper also investigates the superiority of the proposed technique compared to other techniques in enhancing frequency stability, accelerating steady-state frequency restoration, and reducing the energy requirement of the HESS. The required power from the HESS is shared between the two energy storages using the low pass filter technique so as to reduce battery peak current.

Physical Model Tests of Concrete Buttress Dams with Failure Imposed by Hydrostatic Water Pressure

Although the failure of a concrete dam is a complex and highly dynamic process, the current safety assessments of concrete gravity and buttress dams rely on a simplified 2D stability analysis, which neglects the load redistribution due to 3D monolith interactions and the valley shape. In addition, the estimation of breach parameters in concrete dams is based on assumptions rather than analyses, and better prediction methods are needed. Model tests have been conducted to increase the understanding of the failure behavior of concrete dams. A scale model buttress dam, with a scale of 1:15, consisting of 5 monoliths that were 1.2 m in height and 4 m in width, was constructed and loaded to failure using water pressure. The model dam had detachable abutment supports and shear keys to permit variations in the 3D behavior. The results showed that the shear transfer was large between the monoliths and that the failure of a single dam monolith is unlikely. A greater lateral restraint gives not only a higher failure load but also a better indication of impending failure. These findings suggest that the entire dam, including its boundary conditions, should be considered during a stability assessment. The results also suggest that the common assumption in dam safety codes that a single monolith fails during flooding analysis is not conservative. The dataset obtained provides a foundation for the future development of dam-monitoring alarm limits and for predictive models of dam-breaching processes.

Design and simplified stability analysis of wide-area damping control with variable feedback delay

Poorly damped low-frequency inter-area oscillations are a major concern in large power systems. Wide-area damping controllers which modulate power flow using power electronic systems like HVDC links and FACTS can be used to improve the damping of the critical modes in a targeted manner. These controllers use wide-area measurements, which are communicated from several remote locations. The communication time delay is generally variable in nature, and the data from different locations arrive at the controller with different delays. The overall delay in synthesizing the controller input signal affects the closed-loop damping performance. This paper proposes a delay-handling strategy and derives a discrete-time model which is used to characterize its performance. The relative insensitivity of the mode shape of swing modes to the damping controller is used to facilitate a simplified analysis. A strategy for the adaptation of controller gain when the delays are excessive and persistent is also presented. A case study is presented to illustrate the delay-handling and gain adaptation strategies.

A Simplified Novel Link for A Simplified Stability Analysis of Finite Difference Time Domain Method

Numerical stability and numerical dispersion analyses are critical subjects for Finite Difference Time Domain (FDTD) method. To perform these analyses, first of all, an equivalency of the FDTD numerical dispersion equation for Maxwell’s equations and wave equation is proven in this study. Then, based on those calculations, a simplified version of a novel link is developed. Using this simplified version, a stability criterion and an amplification factor of the FDTD method are more easily extracted. Therefore, the FDTD stability analysis becomes simpler. The theoretical findings are validated by a numerical example of a late time simulation interval in the FDTD method. In particular, the effect of a hard FDTD source and a soft FDTD source on the growth (amplification) factor is also investigated.

Expression Stability Analysis of Candidate References for Normalization of RT-qPCR Data Using RefSeeker R package.

When performing expression analysis either for coding RNA (e.g., mRNA) or non-coding RNA (e.g., miRNA), reverse transcription quantitative real-time polymerase chain reaction (RT-qPCR) is a widely used method. To normalize these data, one or more stable endogenous references must be identified. RefFinder is an online web-based tool using four almost universally used algorithms for assessing candidate endogenous references-delta-Ct, BestKeeper, geNorm, and Normfinder. However, the online interface is presently cumbersome and time consuming. We developed an R package, RefSeeker, which performs easy and straightforward RefFinder analysis by enabling raw data import and calculation of stability from each of the algorithms and provides data output tools to create graphs and tables. This protocol uses RefSeeker R package for fast and simple RefFinder stability analysis. Key features Perform stability analysis using five algorithms: Normfinder, geNorm, delta-Ct, BestKeeper, and RefFinder. Identification of endogenous references for normalization of RT-qPCR data. Create publication-ready graphs and tables output. Step-by-step guide dialog window for novice R users.

A Simple Stability Analysis for a Mathematical Model of Migration Due to Noise and Resources

This research studies a metapopulation model where each patch is considered a form of fragmentation of the environment produced by the spatio-temporal variability of anthropogenic noise. A deterministic mathematical model is proposed that describes two processes of migration between patches. The first process consists of migration due to chronic critical noise produced by an anthropogenic and biological source (self-generated acoustic signals of higher intensity, due to the Lombard effect). The second process consists of migration due to a higher level of stain occupancy. A simple and classical analysis of the local stability of the model is performed. The results indicate that no subpopulation goes extinct; in fact, a necessary condition for long-term stabilization of the size of the subpopulations is that the noise attenuation rate is higher. Moreover, as long as the noise is of low intensity the differences in the carrying capacity of each patch do not produce substantial, long-term differences in the sizes of the subpopulations. However, as the noise intensity increases, the difference in carrying capacities produce noticeable, long-term differences between subpopulation sizes. Finally, the results are corroborated by numerical simulations.

Simplified calculation method and stability analysis of top beam cooperative pile–anchor supporting slope structure

Aiming at the problem of insufficient research on the action mechanism and stability calculation method of the top beam in the pile-anchor support structure, firstly the force and deformation model are established based on the elastic fulcrum method and the deformation coordination principle of the pile-anchor structure at the pile top and the anchor end in this paper. Secondly, the calculation model of the support structure under the synergy of the crown and beam and the simplified calculation method of the internal force, displacement and overall stability of the slope are constructed. Finally, combined with an engineering example, a MATLAB program was compiled for calculation, and the pile-anchor structures with crowned beams and without crowned beams were simulated and calculated by the finite element software PLAXIS 3D and Geo Studio. These three aspects are compared and verified. The results show that the internal force, deformation and minimum safety factor calculated by the method in this paper are basically consistent with the numerical simulation calculation results of the top beam condition; the existence of the top beam effectively enhances the bearing capacity of the pile body, and also restricts the displacement of the pile top development; the synergy of the crown and beam makes the safety factor of the slope increase significantly and improves the safety and stability of the slope. The research in this paper can provide a certain reference value for the theoretical calculation and design of the pile-anchor supported slope considering the top beam in engineering practice.

Dimensional Reduction-Based Moment Model for Probabilistic Slope Stability Analysis

Uncertainty is an inevitable factor that influences the function analysis, design, and safe operation in engineering systems. Due to the complexity property and unclear failure mechanism, uncertainty is an intrinsic property of slope engineering. Hence, stability analysis and design cannot meet the demands of slope engineering based on the traditional deterministic method, which cannot deal with uncertainty. In this study, a practical reliability approach was developed to consider the uncertainty factor in slope stability analysis by combining the multiplicative dimensional reduction method (MDRM) and first-order second moment (FOSM). MDRM was used to approximate the complex, nonlinear, high-dimensional, and implicit limit state function. The statistical moment of safety factor was estimated based on the moment method using MDRM. FOSM is adopted to compute the reliability index based on the statistical moment of the safety factor. The proposed method was illustrated and verified by an infinite slope with an analytical solution. The reliability index and failure probability were compared with Monte Carlo simulations (MCS) in various cases. Then, it was applied to a slope based on numerical solutions. The results show that the proposed method is feasible and effective for probabilistic slope stability analysis. The reliability index obtained from the proposed method shows high consensus with the traditional response surface method (RSM). It shows that the proposed method is effective, efficient, and accurate. MDRM provides a practical, simple, and efficient probabilistic slope stability analysis approach.

A Robust Iterative Learning Control Technique to Efficiently Mitigate Disturbances for Three-Phase Standalone Inverters

This article investigates a robust iterative learning control (ILC) technique that effectively rejects the influence of periodic and nonperiodic disturbances for a three-phase constant-voltage constant-frequency standalone voltage source inverter (VSI) with an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> filter under variable initial states. In conventional ILC, the learning dynamics are more complex when the initial iterative state is different at each iteration due to the fixed initial state value. Unlike conventional ILC, the proposed ILC follows a transformed dynamic model for robust learning rule convergence that is less restricted under varying initial states and significantly eliminates the impact of periodic and nonperiodic disturbances. Moreover, a simplified stability analysis is provided, and the conditions required for robust learning rule convergence are discussed. A comparative verification with the results of conventional ILC using a TI TMS320F28335 digital signal processor based prototype standalone VSI proves that the proposed ILC technique offers robust and effective steady-state performance, with benefits such as reduced steady-state errors and low total harmonic distortion under periodic disturbances. Finally, its improved robustness and fast transient-state performance are validated under nonperiodic disturbances due to the existence of tough load conditions, i.e., step-changes of linear, unbalanced, and nonlinear loads with significantly distorted model parameters.

A Floquet theory‐based fast time‐domain stability analysis for N ‐parallel inverters system

Based on Floquet theory, a simple and fast time-domain stability analysis method for an N-parallel inverters system is proposed. Furthermore, a general time-domain model of the N-parallel inverters system in grid-connected mode and in island mode are derived, and the corresponding stability criteria are derived based on the Floquet theory. Subsequently, simulations and experiments of a two-parallel inverters system in island and grid-connected modes are conducted to verify the correctness and effectiveness of the proposed time-domain stability analysis method. To the end, the complexity comparison between the proposed time-domain method and the traditional frequency-domain method is presented to prove the advantages of the proposed method over the tedious manual derivation.

Effect of Frequency Coupling on Stability Analysis of a Grid-Connected Modular Multilevel Converter System

Due to the internal dynamics of the modular multilevel converter (MMC), the coupling between the positive and negative sequences in impedance, which is defined as frequency coupling, inherently exists in MMC. Ignoring the frequency coupling of the MMC impedance model may lead to inaccurate stability assessment, and thus the multi-input multi-output (MIMO) impedance model has been developed to consider the frequency coupling effect. However, the generalized Nyquist criterion (GNC), which is used for the stability analysis of an MIMO model, is more complicated than the stability analysis method applied on single-input-single-output (SISO) models. Meanwhile, it is not always the case that the SISO model fails in the stability assessment. Therefore, the conditions when the MIMO impedance model needs to be considered in the stability analysis of an MMC system should be analyzed. This paper quantitatively analyzes the effect of frequency coupling on the stability analysis of grid-connected MMC, and clarifies the frequency range and grid conditions that the coupling effect required to be considered in the stability analysis. Based on the quantitative relations between the frequency coupling and the stability analysis of the grid-connected MMC system, a simple and accurate stability analysis method for the grid-connected MMC system is proposed, where the MIMO impedance model is applied when the frequency coupling has a significant effect and the SISO impedance model is used if the frequency coupling is insignificant.

Nonlinear feature in the spatial uniformity of an atmospheric helium dielectric barrier discharge with the inter-dielectric gap width enlarged

Intuitively, when the breakdown voltage is satisfied, enlarging the inter-dielectric gap width (d g) is prone to filamentary dielectric barrier discharges (DBDs) due to the lengthened electron migration path and the intensified electron cascade. In this letter, we report that in specific conditions, a larger d g can also promote a homogeneous DBD. The calculated results from the two-dimensional fluid model of an atmospheric helium DBD reveal that the incomplete dissipation of glows (residual positive column) induced by the enlarged d g poses an eraser-like role, wiping out the surface charges left behind by the former discharge. Thus, the so-called memory effect cannot be well established, and the uniform DBD ensues. An experiment with similar conditions and a simplified linear stability analysis qualitatively validate the calculated results. This work also provides sufficient feasibility of regulating discharge uniformity of DBDs through manipulating the dissipative characteristic, and some methods of tailoring waveform would be useful.

Electrohydrodynamic analysis of bubble burst in large Leidenfrost droplets

A thin vapor gap forms underneath a liquid drop on a sufficiently hot surface, which prevents solid–liquid contact (the Leidenfrost effect). This vapor gap can be partly eliminated by applying an electrical potential difference across the vapor gap to electrostatically suppress the Leidenfrost state. An interesting hydrodynamics-related phenomenon that can occur in Leidenfrost droplets is the formation of a vapor dome and subsequent bubble burst at the center of the droplet. This work reports a comprehensive study of vapor dome formation and bubble burst in large Leidenfrost droplets under the influence of an electric field. First, a detailed numerical model (non-linear thin film lubrication equation) is developed to analyze the evolution of the vapor dome and bubble burst. Second, a simplified stability analysis is conducted to analytically estimate the critical droplet diameter (for bubble burst) under the influence of an electric field. Third, experiments are conducted to measure the critical diameter of Leidenfrost droplets for bubble burst under the influence of electric fields. The results from the numerical modeling and stability analysis show very good agreement with experimental measurements. The critical diameter for bubble burst and the time period between consecutive vapor bursts reduce with the applied electric field. Comparisons are made between the presently studied vapor burst and film boiling; similarity in the underlying hydrodynamic phenomena results in the length and time scales for bubble burst being similar to those encountered in film boiling.

A Turbo Q-Learning (TQL) for Energy Efficiency Optimization in Heterogeneous Networks

In order to maximize energy efficiency in heterogeneous networks (HetNets), a turbo Q-Learning (TQL) combined with multistage decision process and tabular Q-Learning is proposed to optimize the resource configuration. For the large dimensions of action space, the problem of energy efficiency optimization is designed as a multistage decision process in this paper, according to the resource allocation of optimization objectives, the initial problem is divided into several subproblems which are solved by tabular Q-Learning, and the traditional exponential increasing size of action space is decomposed into linear increase. By iterating the solutions of subproblems, the initial problem is solved. The simple stability analysis of the algorithm is given in this paper. As to the large dimension of state space, we use a deep neural network (DNN) to classify states where the optimization policy of novel Q-Learning is set to label samples. Thus far, the dimensions of action and state space have been solved. The simulation results show that our approach is convergent, improves the convergence speed by 60% while maintaining almost the same energy efficiency and having the characteristics of system adjustment.

The evolution of communication mechanisms in self-organised ecological aggregations: Impact on pattern formation

Collective behaviours in animal communities are the result of inter-individual communication. However, communication signals are not fixed; they evolve to ensure more effective interactions between the emitter and receiver of these signals. In this study, we use a mathematical approach and investigate the effect of changes in communication signals (at both receiver and emitter levels) on the aggregation patterns displayed by these animal communities. We use simple linear stability analysis to study the impact that the loss/gain in signals strength has on the formation of stationary and moving animal aggregations. We then use numerical simulations to study the impact of these signal strengths on the long-term persistence of some stationary and moving aggregations. We show that a reduction in the strength of such communication signals can stop the movement of some aggregations. Moreover, for very weak signals, one can obtain a variety of standing wave patterns characterised by left-moving and right-moving waves of individuals passing through each other, with or without some individuals joining the opposite-moving group.

Suction as an untapped natural soil reinforcement to reduce embodied carbon in geotechnical structures: the case study of flood embankments in Hamburg area

The commitment to cut CO2 emissions is now becoming a matter of legal obligations in several countries worldwide and the construction industry, one of the main sectors contributing to carbon emissions, is required to develop new approaches for carbon-efficient design. A study was undertaken to examine whether the inclusion of negative pore-water pressures (or ‘suction’) in the design of a flood embankment could reduce the embodied carbon associate with the construction of a new embankment or the retrofitting of an existing one. The case considered here are the embankments of the tidal Elbe area in Germany that require to be raised because of the new projection of extreme river levels due to climate change. Simple uncoupled water flow and stability analyses were considered to examine the performance of given embankment geometry. The purpose of the study is to examine whether incorporating suction into the design could allow for steeper landside slopes of the flood embankment. This would allow raising the embankment by saving considerable material and, hence, reducing the embodied carbon. At the same time, this would reduce the footprint of the raised embankment, which is a design requirement when flood embankments are embedded in the built environment as it happens in Hamburg.

New Perspectives on Stability Analysis of Three-Phase Grid-Connected Inverter Considering System Couplings

This paper considers the three-phase grid-connected inverter (GCI) as a MIMO system, and presents some new perspectives on the stability of GCI. It is found that with traditional Nyquist criterion (NC)-based method which ignores the off-diagonal components of impedance or admittance matrix, the stability results of impedance and admittance models are different. To make up this disadvantage, a simple stability analysis method based on system feedback ratio matrix (SFRM) is proposed. Instead of ignoring the couplings of impedance or admittance, the SFRM in the proposed method can be equivalent to diagonal matrix by adding a perturbation matrix into the system model, so identical results of stability analysis under impedance and admittance models are attained. Furthermore, to ensure the correctness of stability result, the boundary conditions of the proposed method are also provided. Theoretical analysis, simulation and experimental results show that compared with the state of art methods, the proposed SFRM-based method is of low computational complexity and high accuracy, and is more suitable for engineering application.

Nonlinear stability analysis of rotationally-restrained imperfect doubly-curved composite shallow shells

The semi-analytical solution for nonlinear stability analysis of imperfect doubly-curved laminated composite shallow shells with rotationally-restrained edges and under in-plane loading is presented. The nonlinear governing equations are established using the Galerkin method, and the arc-length and quadratic control method is implemented to capture the snapping phenomenon of the doubly-curved composite shells. The nonlinear load-displacement relationships of four special curvature radii of doubly-curved shell structures are obtained, and they are compared and validated with the numerical finite element solutions. A parametric study is conducted to evaluate the effects of the initial imperfection, edge rotationally-restrained spring stiffness, various load parameters, and curvature radius on the nonlinear stability behavior of doubly-curved shells. Finally, the computational efficiency and capability of the semi-analytical solution are demonstrated in comparison with the finite element analysis. The present semi-analytical solution can be effectively and efficiently used in simplified nonlinear stability analysis of complex doubly-curved composite shallow shells with periodic and restrained boundary conditions.