Stability Arguments Research Articles

On the self-similarity of unbounded viscous Marangoni flows

The Marangoni flow induced by an insoluble surfactant on a fluid–fluid interface is a fundamental problem investigated extensively due to its implications in colloid science, biology, the environment and industrial applications. Here, we study the limit of a deep liquid subphase with negligible inertia (low Reynolds number, $Re\ll {1}$ ), where the two-dimensional problem has been shown to be described by the complex Burgers equation. We analyse the problem through a self-similar formulation, providing further insights into its structure and revealing its universal features. Six different similarity solutions are found. One of the solutions includes surfactant diffusion, whereas the other five, which are identified through a phase-plane formalism, hold only in the limit of negligible diffusion (high surface Péclet number $Pe_s\gg {1}$ ). Surfactant ‘pulses’, with a locally higher concentration that spreads outward, lead to two similarity solutions of the first kind with a similarity exponent $\beta =1/2$ . On the other hand, distributions that are locally depleted and flow inwards lead to similarity of the second kind, with two different exponents that we obtain exactly using stability arguments. We distinguish between ‘dimple’ solutions, where the surfactant has a quadratic minimum and $\beta =2$ , from ‘hole’ solutions, where the concentration profile is flatter than quadratic and $\beta =3/2$ . Each of these two cases exhibits two similarity solutions, one valid prior to a critical time $t_*$ when the derivative of the concentration is singular, and another one valid after $t_*$ . We obtain all six solutions in closed form, and discuss predictions that can be extracted from these results.

Simultaneous compensation of input delay and state/input quantization for linear systems via switched predictor feedback

We develop a switched predictor-feedback law, which achieves global asymptotic stabilization of linear systems with input delay and with the plant and actuator states available only in (almost) quantized form. The control design relies on a quantized version of the nominal predictor-feedback law for linear systems, in which quantized measurements of the plant and actuator states enter the predictor state formula. A switching strategy is constructed to dynamically adjust the tunable parameter of the quantizer (in a piecewise constant manner), in order to initially increase the range and subsequently decrease the error of the quantizers. The key element in the proof of global asymptotic stability in the supremum norm of the actuator state is derivation of solutions’ estimates combining a backstepping transformation with small-gain and input-to-state stability arguments, for addressing the error due to quantization. We extend this result to the input quantization case and illustrate our theory with a numerical example.

Bipartite tracking for Euler–Lagrange systems via prescribed‐time hierarchical control based on the matrix‐weighted signed digraphs

AbstractThe goal of this article is to investigate the bipartite tracking control problem using a prescribed‐time convergence method for Euler–Lagrange systems (ELSs) with external disturbances. Agent interactions are represented by a matrix‐weighted signed directed graph. There are not only cooperative but also adversarial interactions. An essential component of the system, the prescribed‐time hierarchical control (PTHC) algorithm, including a more general time‐varying function, is newly developed to guarantee that all agents converge to the same leader state but with opposite signs within a prescribed time. The salient feature of the introduced method lies in the fact that the convergence time of the control objective can be prespecified by the user. The state transformation, the property of the matrix‐weighted Laplacian, and the generalized Lyapunov stability argument are employed to theoretically validate the proposed algorithms. Finally, the effectiveness of the algorithm is confirmed through the execution of numerical examples.

Does banking consolidation improve bank stability? Evidence from Sub-Saharan Africa

PurposeThis study aims to investigate the influence of banking consolidations on bank stability in Sub-Saharan African (SSA) countries for the period 2003–2019, following a series of bank mergers and acquisitions (M&As) in the region and whether regulation-induced bank M&As affect banking sector stability.Design/methodology/approachThe fixed effect panel regression model is used to understand the influence of regulation-induced and voluntary bank mergers and acquisitions on banking stability in SSA. The study also controlled for bank-specific factors, market concentration and macroeconomic variables that affect banking stability. The study used three measures of bank stability: the Z-score, risk-adjusted return on assets and risk-adjusted bank capital.FindingsThe study results reveal that voluntary bank M&As, market concentration, net interest margin, bank capital, bank deposits and income diversification influence banking sector stability positively. However, the findings show that regulation-induced bank mergers and acquisitions impact banking stability negatively. Where bank M&As were a result of banking regulatory reforms, called regulation-induced mergers and acquisitions (RIM&As), banking stability suffered, but voluntary bank M&As improved banking stability. Again, the study supports the concentration–stability argument rather than the competition–stability hypothesis. Therefore, more concentrated banking markets in SSA countries have more stable banks and fewer risks of system-wide bank failures. Other factors influencing banking stability in SSA are return on equity, bank efficiency (cost-to-income), bank size and deposits-to-assets ratio. However, their relationship is negative with the stability of the banking sector.Practical implicationsThe findings imply that the regulatory authorities should encourage voluntary bank M&As and not regulation-induced bank M&As to improve the stability of the banking systems in SSA.Originality/valueThe study provides new evidence on the effects of regulation-induced bank M&As on the stability of banks.

Planar curved path following controller for a small fixed-wing unmanned aerial vehicle with constrained parameters optimized by nonlinear model predictive control

Path following presents a pivotal challenge within the realm of small fixed-wing unmanned aerial vehicles. Firstly, a Lyapunov-stable path guidance law was formulated to follow specific planar curved paths. To ensure differentiability of the guidance law, a modified, smooth saturation function was derived. Secondly, an analysis was conducted to ascertain the interrelationship between control parameters and input constraints, thereby identifying the relevant parameter domains. Thirdly, the nonlinear model predictive control technique was harnessed to optimize both guidance law parameters, enhancing the unmanned aerial vehicle’s capacity to achieve optimal performance in both straight-line and circular path following, hereafter referred to as PFC_NMPC. By leveraging Lyapunov stability arguments for switched systems, the stability of the corresponding nonlinear switched system was guaranteed. In this study, square and circular paths were generated to assess the path-following control of a simulated fixed-wing unmanned aerial vehicle. The performance of various guidance laws, including those with fixed parameters (PFC), those with parameters tuned using fuzzy logic (PFC_FL), PFC_NMPC, vector field, and pure pursuit with line-of-sight, was compared. Notably, the proposed PFC_NMPC method exhibited the ability to expedite the unmanned aerial vehicle’s convergence to the desired path while maximizing the effective flight path length.

Nonlinear Stability and Asymptotic Behavior of Periodic Wave Trains in Reaction–Diffusion Systems Against Cub\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_{\ extrm{ub}}$$\\end{document}-perturbations

We present a nonlinear stability theory for periodic wave trains in reaction–diffusion systems, which relies on pure L∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^\\infty $$\\end{document}-estimates only. Our analysis shows that localization or periodicity requirements on perturbations, as present in the current literature, can be completely lifted. Inspired by previous works considering localized perturbations, we decompose the semigroup generated by the linearization about the wave train and introduce a spatio-temporal phase modulation to capture the most critical dynamics, which is governed by a viscous Burgers’ equation. We then aim to close a nonlinear stability argument by iterative estimates on the corresponding Duhamel formulation, where, hampered by the lack of localization, we must rely on diffusive smoothing to render decay of the semigroup. However, this decay is not strong enough to control all terms in the Duhamel formulation. We address this difficulty by applying the Cole–Hopf transform to eliminate the critical Burgers’-type nonlinearities. Ultimately, we establish nonlinear stability of diffusively spectrally stable wave trains against Cub\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_{\ extrm{ub}}$$\\end{document}-perturbations. Moreover, we show that the perturbed solution converges to a modulated wave train, whose phase and wavenumber are approximated by solutions to the associated viscous Hamilton–Jacobi and Burgers’ equation, respectively.

A new approach for dynamic output feedback control design of time-delayed nonlinear systems

This paper introduces a full-order dynamic output-feedback (DOF) controller for discrete-time nonlinear systems with time-varying delays represented by Linear Parameter-Varying (LPV) systems. The controller design is carried out by developing delay-dependent Linear Matrix Inequality based conditions using Lyapunov–Krasovskii stability arguments. A notable characteristic of the proposed approach is that the dynamic controller gains are directly obtained, without the need for variable transformations, equality constraints, or iterative algorithms. This feature sets it apart from many existing approaches in the literature and simplifies the design process. Furthermore, the proposed approach guarantees the local asymptotic stability of the origin of the closed-loop system and provides an estimated admissible initial condition region. The correct operation of the system is ensured once the state trajectories initiated within the admissible initial condition region remain enclosed in the validity domain of the LPV model. Numerical examples are provided to illustrate the potential and effectiveness of the proposed conditions.

The DECam Ecliptic Exploration Project (DEEP). IV. Constraints on the Shape Distribution of Bright Trans-Neptunian Objects

We present the methods and results from the discovery and photometric measurement of 26 bright VR > 24 trans-Neptunian objects (TNOs) during the first year (2019–20) of the DECam Ecliptic Exploration Project (DEEP). The DEEP survey is an observational TNO survey with wide sky coverage, high sensitivity, and a fast photometric cadence. We apply a computer vision technique known as a progressive probabilistic Hough transform to identify linearly moving transient sources within DEEP photometric catalogs. After subsequent visual vetting, we provide a photometric and astrometric catalog of our TNOs. By modeling the partial lightcurve amplitude distribution of the DEEP TNOs using Monte Carlo techniques, we find our data to be most consistent with an average TNO axis ratio b/a < 0.5, implying a population dominated by non-spherical objects. Based on ellipsoidal gravitational stability arguments, we find our data to be consistent with a TNO population containing a high fraction of contact binaries or other extremely non-spherical objects. We also discuss our data as evidence that the expected binarity fraction of TNOs may be size-dependent.

A multiwavelength study of Swift J0503.7-2819: a chimeric magnetic CV

ABSTRACT We present multiwavelength temporal and spectral characteristics of a magnetic cataclysmic variable (MCV) Swift J0503.7-2819, using far ultraviolet and X-ray data from AstroSat, supplemented with optical data from the Southern African Large Telescope and X-ray data from the XMM-Newton and Swift observatories. The X-ray modulations at 4897.6657 s and 3932.0355 s are interpreted as the orbital (PΩ) and spin (Pω) period, respectively, and are consistent with prior reports. With a spin-orbit period ratio of 0.8 and PΩ falling below the period gap (2–3 h) of CVs, Swift J0503.7-2819 would be the newest addition to the growing population of nearly synchronous MCVs, which we call EX Hya-like systems. Hard X-ray luminosity of &amp;lt;2.5 × 1032 erg s−1, as measured with the Swift Burst Alert Telescope, identifies it to be a low-luminosity intermediate polar, similar to other EX Hya-like systems. The phenomenology of the light curves and the spectral characteristics rule out a purely disc-fed/stream-fed model and instead reveal the presence of complex accretion structures around the white dwarf. We propose a ring-like accretion flow, akin to EX Hya, using period ratio, stability arguments, and observational features. An attempt is made to differentiate between the asynchronous polar/nearly synchronous intermediate polar nature of Swift J0503.7-2819. Further, we note that with the advent of sensitive surveys, a growing population of MCVs that exhibit characteristics of both polars and intermediate polars is beginning to be identified, likely forming a genealogical link between the two conventional classes of MCVs.

Quantized-data resource allocation for reinforcement learning cooperative control of networked Euler-Lagrange agents with input saturation

This paper investigates the resource allocation problem of networked Euler-Lagrange agents (NELAs) with quantized-data interactions and input saturation in the framework of reinforcement learning (RL). We propose a hierarchical control strategy that includes a distributed resource allocation estimator (DRAE) and a local RL linear sliding mode controller (RL-LSMC). Specifically, the DRAE based on the gradient descent and state feedback is proposed, which aims to achieve optimal resource allocation by estimated states. The local RL-LSMC is designed through utilizing the feedback of critic neural network and the approximation capacity of actor neural network, which prompts the states of the NELAs to track the optimal estimated states. Several sufficient conditions are established with the help of Lyapunov stability argument. Finally, the effectiveness of the proposed hierarchical control algorithm is verified by the two simulation examples.

Exploring the angular momentum – atomic gas content connection with eagle and IllustrisTNG

ABSTRACT We use the Evolution and Assembly of GaLaxies and their Environments (eagle) and IllustrisTNG (The Next Generation) cosmological simulations to investigate the properties of the baryonic specific angular momentum (j), baryonic mass (M), and atomic gas fraction (fatm) plane for nearby galaxies. We find EAGLE and TNG to be in excellent agreement with each other. These simulations are also consistent with the results obtained with eXtended GALEX Arecibo SDSS Survey (xGASS) for gas fractions greater than 0.01. This implies that the disagreements previously identified between xGASS and predictions from simple analytical disc stability arguments also holds true for eagle and tng. For lower gas fraction (the regime currently unconstrained by observations), both simulations deviate from the plane but still maintain good agreement with each other. Despite the challenges posed by resolution limits at low gas fractions, our findings suggest a potential disconnect between angular momentum and gas fraction in the gas-poor regime, implying that not all gas-poor galaxies have low specific angular momentum.

Bayesian inversion with α-stable priors

We propose using Lévy α-stable distributions to construct priors for Bayesian inverse problems. The construction is based on Markov fields with stable-distributed increments. Special cases include the Cauchy and Gaussian distributions, with stability indices α = 1, and α = 2, respectively. Our target is to show that these priors provide a rich class of priors for modeling rough features. The main technical issue is that the α-stable probability density functions lack closed-form expressions, and this limits their applicability. For practical purposes, we need to approximate probability density functions through numerical integration or series expansions. For Bayesian inversion, the currently available approximation methods are either too time-consuming or do not function within the range of stability and radius arguments. To address the issue, we propose a new hybrid approximation method for symmetric univariate and bivariate α-stable distributions that is both fast to evaluate and accurate enough from a practical viewpoint. In the numerical implementation of α-stable random field priors, we use the constructed approximation method. We show how the constructed priors can be used to solve specific Bayesian inverse problems, such as the deconvolution problem and the inversion of a function governed by an elliptic partial differential equation. We also demonstrate hierarchical α-stable priors in the one-dimensional deconvolution problem. For all numerical examples, we use maximum a posteriori estimation. To that end, we exploit the limited-memory BFGS and its bounded variant for the estimator.

Asymptotic isoperimetry on non collapsed spaces with lower Ricci bounds

This paper studies sharp and rigid isoperimetric comparison theorems and asymptotic isoperimetric properties for small and large volumes on N-dimensional RCD(K,N)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{RCD}(K,N)$$\\end{document} spaces (X,d,HN)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(X,\ extsf {d},\\mathscr {H}^N)$$\\end{document}. Moreover, we obtain almost regularity theorems formulated in terms of the isoperimetric profile and enhanced consequences at the level of several functional inequalities. Most of our statements seem to be new even in the classical setting of smooth, non compact manifolds with lower Ricci curvature bounds. The synthetic theory plays a key role via compactness and stability arguments.

Constraints on Evolutionary Timescales for M Dwarf Planets from Dynamical Stability Arguments

The diversity of dynamical conditions among exoplanets is now well established. Yet, the relevance of orbital dynamical timescales to biological evolutionary timescales is poorly understood. Given that even minor orbital changes may place significant pressure on any organisms living on a planet, dynamical sculpting has important implications for the putative evolution of life. In this manuscript, we employ a Monte Carlo framework to investigate how a range of exoplanetary dynamical sculpting timescales affects timescales for biological evolution. We proceed with minimal assumptions for how dynamical sculpting proceeds and the emergence and persistence of life. We focus our investigation on M dwarf stars, the most common exoplanetary hosts in the Milky Way. We assign dynamical statuses, dependent on stellar age, to a suite of planetary systems, varying the rate of dynamical disruption within limits that are consistent with present-day planet demographics. We then simulate the observed yield of planets according to the completeness of NASA's Kepler and TESS missions, and investigate the properties of these samples. With this simplified approach, we find that systems hosting multiple transiting planets ought to have, on average, shorter dynamically uninterrupted intervals than single-transiting systems. However, depending upon the rate of dynamical sculpting, planets orbiting older stars will exhibit the opposite trend. Even modest constraints on stellar age would help identify older stars for which this holds. The degree of these effects varies, dependent upon both the intrinsic dynamical demographics of exoplanets and whether we consider planets detected by NASA’s Kepler or TESS missions.

Distributed control of time-delay interconnected nonlinear systems

This paper addresses the distributed control of delayed interconnected nonlinear systems with time-varying delays in both the local subsystems’ dynamics and the physical interconnections among the subsystems. The Takagi–Sugeno fuzzy model with nonlinear consequent parts (N-TS), which is capable to provide less complex representations than standard T–S fuzzy models, is considered to efficiently deal with this class of complex systems. Then, based on Lyapunov–Krasovskii stability arguments, a synthesis condition is proposed to design a distributed control law such that the origin of the closed-loop interconnected system is locally asymptotically stable together with a guaranteed set of admissible initial conditions for which the validity of the N-TS fuzzy model is ensured. Moreover, a quasi-convex optimization procedure is formulated to enlarge the set of admissible initial conditions. The effectiveness of the proposed synthesis condition is validated in two numerical examples, including an interconnected power network with seven generators.

Fake supersymmetry with tadpole potentials

We study tadpole potentials of non-supersymmetric strings, resorting to a first-order formalism known in the literature as fake supersymmetry. We present a detailed analysis for vacua with only gravity and the dilaton, displaying the obstructions that forbid the simplest inclusion of form fluxes. Our focus is on codimension-one vacua, for which we propose a definition of energy that might be suitable for stability arguments. Our findings point to the central role of boundary conditions when supersymmetry is absent or broken.

Strategic Narratives in International Tax Policy Making: BEPS Action 1 and the Stability Argument

Drawing on narrative analysis developed by communications scholars, and applied by scholars of economics and international law and in policy analysis, this article studies action 1 of the Organisation for Economic Co-operation and Development's (OECD's) base erosion and profit shifting (BEPS) project as a policy narrative. The authors outline the role of narrative in international tax policy making and evaluate the probability and the argumentative and material coherence of the OECD's story about the need to ensure the stability of the international tax framework and system. Focusing on the narrative strategy adopted by the OECD to promote its pillar one proposal, the authors assess the likely persuasiveness of the OECD's stability argument—in particular, how it may have influenced the response to the proposal by the members of the Inclusive Framework on BEPS. The authors conclude that the OECD's concern about potentially destabilizing effects of digital services taxes and similar taxes on the international income tax system propagates a global fiscal illusion, and may not sustain long-term support for pillar one by many members of the Inclusive Framework.

Cooperative Fault-Estimation-Based Event-Triggered Fault-Tolerant Voltage Restoration in Islanded AC Microgrids

In this paper, the problem of secondary voltage restoration in an islanded microgrid (MG) is considered, in which the actuator of the distributed generators (DGs) may coexist with partial loss of effectiveness (PLOE) fault and bias fault. For each DG, an adaptive event-triggered fault-tolerant (ETFT) control protocol is designed to compensate for the effects of actuator faults in the DGs, thereby restoring the voltage to the reference value. The dependent event triggering mechanism saves the processor&#x2019;s computational resources. A desirable feature of the protocol proposed in this paper is that the control protocol relies only on relative information between neighboring DG&#x2019;s, independent of global information about the network graph, fault boundaries, and network scale. It means that the protocol is implemented in a fully distributed framework. The protocol fully applies to the common ETFT consensus control problem of linear multiagent systems (MASs) with actuator faults. Furthermore, comprehensive theoretical arguments for consensus stability and analysis of Zeno behavior ensure the approach&#x2019;s feasibility. The simulation results verify the effectiveness of the algorithm. <i>Note to Practitioners</i>&#x2014;This paper aims to propose a fully ETFT control protocol for secondary voltage restoration of an islanded MG. The control protocol consists of a linear term and a nonlinear time that compensates for the multiplicative and additive fault of the actuator. Moreover, DGs&#x2019; communication structure and global fault boundaries may be unknown in practice. Hence, adaptive coupling gains that depend only on the sampled relative information of DGs are introduced to estimate the controller gain, thus avoiding global information. A feasible strategy is provided for industrial applications.

High-sensitivity Observations of the H2O Megamasers of NGC 1068: Precise Astrometry and Detailed Kinematics

We present High Sensitivity Array observations of the H2O megamasers of NGC 1068. We obtain absolute astrometry with 0.3 mas precision that confirms the association of the disk masers with the nuclear radio continuum source S1. The new observations reveal two new blueshifted groups of disk masers. We also detect the 22 GHz continuum on short interferometric baselines. The position–velocity diagram of the disk masers shows a curve consistent with a nonaxisymmetric distribution of maser spots. This curve is probably the result of spiral arms with a constant pitch angle ∼5°. The disk kinematics are consistent with Keplerian rotation and low turbulent speeds. The inferred central mass is 17 × 106 M ☉. On the basis of disk stability arguments, the mass of the molecular disk is ≈110 × 103 M ☉. The disk masers further resolve into filamentary structures suggesting an ordered magnetic field threading the maser disk. The magnetic field strengths must be ≳2 mG to withstand turbulent motions in the partially ionized molecular gas. We note apparent asymmetries in the molecular disk that might be explained by anisotropic heating by a misaligned inner accretion disk. The new observations also detect the fainter jet masers north of the disk masers. The distribution and kinematics of the jet masers are consistent with an expanding ring of molecular gas.

On the non-linear stability of the Cosmological region of the Schwarzschild-de Sitter spacetime

The non-linear stability of the sub-extremal Schwarzschild-de Sitter spacetime in the stationary region near the conformal boundary is analysed using a technique based on the extended conformal Einstein field equations and a conformal Gaussian gauge. This strategy relies on the observation that the Cosmological stationary region of this exact solution can be covered by a non-intersecting congruence of conformal geodesics. Thus, the future domain of dependence of suitable spacelike hypersurfaces in the Cosmological region of the spacetime can be expressed in terms of a conformal Gaussian gauge. A perturbative argument then allows to prove existence and stability results close to the conformal boundary and away from the asymptotic points where the Cosmological horizon intersects the conformal boundary. In particular, we show that small enough perturbations of initial data for the sub-extremal Schwarzschild-de Sitter spacetime give rise to a solution to the Einstein field equations which is regular at the conformal boundary. The analysis in this article can be regarded as a first step towards a stability argument for perturbation data on the Cosmological horizons.