Moment Stability Research Articles

New shape optimization method for tree structures based on BP neural network

To realize the intelligent optimization for the tree structures supporting freeform surface roof or bearing uneven load, a new shape optimization method based on the back-propagation (BP) neural network is proposed. This method enables the intelligent positioning of hierarchical nodes through a recursive approach from top-down, with the aim of satisfying the zero bending moment and structural stability. Using three-dimensional tree structures as an example, this study provides a detailed description of the implementation method and steps of intelligent shape optimization, along with a comparative analysis with the reverse-hang recursive approach. Results indicate that the proposed approach effectively addresses the challenge of locating load-bearing centers in tree structures with uneven loads or freeform surface roofs. It not only demonstrates universality for tree structures under complex engineering conditions, but also enhances efficiency and intelligence in the structure optimization design.

The ergodicity and uniform large deviations for the 1D stochastic Landau-Lifshitz-Bloch equation

In this article, we consider two aspects asymptotic behaviors for the 1D stochastic Landau-Lifshitz-Bloch equation driven by additive noise including the unique ergodicity and the uniform large deviations. Using a deterministic argument relying on the exponential moment and exponential stability estimates, we first establish the unique ergodicity of invariant measure in H 1. Then, the uniform large deviations is established in C ( [ 0 , T ] ; H 1 ) by the uniform contraction principle.

On [formula omitted]-error moment stability and stabilization for discrete-time semi-Markov jump linear systems

In this paper, we study the σ-error moment stability and stabilization for a class of discrete-time semi-Markov jump linear systems (S-MJLS). It is shown that the existing results on σ-error moment stability for discrete-time S-MJLS can be obtained under weaker conditions, and based on the established stability results, the high-order moment stabilization problem is investigated for the first time.

Asymptotic moment stability of solutions to systems of nonlinear differential Itô equations with aftereffect

Asymptotic moment stability of solutions to systems of nonlinear differential Itô equations with aftereffect

Stability, Uniqueness and Existence of Solutions to McKean–Vlasov Stochastic Differential Equations in Arbitrary Moments

We deduce stability and pathwise uniqueness for a McKean–Vlasov equation with random coefficients and a multidimensional Brownian motion as driver. Our analysis focuses on a non-Lipschitz continuous drift and includes moment estimates for random Itô processes that are of independent interest. For deterministic coefficients, we provide unique strong solutions even if the drift fails to be of affine growth. The theory that we develop rests on Itô’s formula and leads to pth moment and pathwise exponential stability for p≥2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p\\ge 2$$\\end{document} with explicit Lyapunov exponents.

Existence and exponential stability in pth moment of non-autonomous stochastic integro-differential equations

This study is concerned with the existence and exponential stability of solutions of non-autonomous neutral stochastic integro-differential equations with delay; the linear part of this equation is dependent on time and generates a linear evolution system. The obtained results are applied to some neutral stochastic integro-differential equations. These kinds of equations arise in systems related to couple oscillators in a noisy environment or in viscoelastic materials under random or stochastic influences. Finally, we provide an example to illustrate the results.

Approximations in Mean Square Analysis of Stochastically Forced Equilibria for Nonlinear Dynamical Systems

Motivated by important applications to the analysis of complex noise-induced phenomena, we consider a problem of the constructive description of randomly forced equilibria for nonlinear systems with multiplicative noise. Using the apparatus of the first approximation systems, we construct an approximation of mean square deviations that explicitly takes into account the presence of multiplicative noises, depending on the current system state. A spectral criterion of existence and exponential stability of the stationary second moments for the solution of the first approximation system is presented. For mean square deviation, we derive an expansion in powers of the small parameter of noise intensity. Based on this theory, we derive a new, more accurate approximation of mean square deviations in a general nonlinear system with multiplicative noises. This approximation is compared with the widely used approximation based on the stochastic sensitivity technique. The general mathematical results are illustrated with examples of the model of climate dynamics and the van der Pol oscillator with hard excitement.

Lyapunov stability of suspension bridges in turbulent flow

In the era of sleek, super slender suspension bridges, facing the issue of stability against dynamic wind actions represents an increasingly complex challenge. Despite the significant progress over the last decades, the impact of atmospheric turbulence on bridge stability remains partially not understood, evoking the need for innovative research approaches. This study aims to address a gap in current research by investigating the random flutter stability associated with variations in the angle of attack due to turbulence, which has not formally been addressed yet. The present investigation employs the 2D rational function approximation model to express self-excited forces in a turbulent flow. The application of this type of models to bridge dynamics yields a viscoelastic coupled dynamic system characterized by memory effects and driven by broad-band long-time-scale noise, described here by a linear homogeneous time-variant differential equation, which shows apparent nonlinear features, and which has rarely been matter of research. Utilizing a Monte Carlo methodology, this work innovates in applying the largest Lyapunov exponent (LE) and the moment Lyapunov exponents (MLE) to study bridge random flutter stability. The calculation of LE and MLE under diverse turbulent wind conditions uncovers lower flutter stability than without turbulence effects. In most cases, sample and low-order p-th moment stability thresholds closely align with the bridge dynamic response pattern; therefore, the flutter critical wind speed is unequivocal. However, under certain turbulence scenarios, it is necessary to resort to MLE for a complete description of stability, evoking some additional consideration of which statistical moments should be considered for the engineering assessment of the flutter limit. Finally, this work provides a qualitative insight into the instability mechanisms by approximating the random parametric excitation with a sinusoidal gust and evaluating the time-periodic system stability via Floquet theory.

An extended stochastic car‐following model and its feedback control

Real‐world traffic flow is influenced by various random factors. Gaussian white noise is employed to describe the inherent randomness of traffic flow. A stochastic optimization velocity model is established for dynamic analysis. To enhance the traffic flow stability, the velocity difference of two successive vehicles ahead is considered. The velocity difference feedback control strategy is proposed, utilizing the velocity differences between the vehicle and the two targeted vehicles as control signals. Stability conditions for both the stochastic optimization velocity model and the feedback control model are derived by using the moment stability theory. The study demonstrates that the random factors can destabilize traffic flow, while the proposed feedback control strategy effectively stabilizes traffic flow. Additionally, the influences of random factors on the stability of traffic flow are discussed extensively, aiding in understanding actual traffic congestion mechanisms and offering insights for traffic control strategies.

Higher-order moment stability of large wind turbine blades under stochastic perturbations

Higher-order moment stability of large wind turbine blades under stochastic perturbations

Scalable Analysis of Dipole Moment Fluctuations for Characterizing Intermolecular Interactions and Structural Stability.

Accurately predicting protein-ligand interactions is essential in computational molecular biochemistry and in silico drug development. Monitoring changes in molecular dipole moments through molecular dynamics simulations provides valuable insights into dipole-dipole interactions, which are critical for understanding protein structure stability and predicting protein-ligand binding affinity. In this study, we propose a novel method to monitor changes in the interangle between dipole vectors of residue molecules within proteins and ligand molecules, aiming to evaluate the strength and consistency of interactions within the complex. Additionally, we extend the concept of positional root-mean-square fluctuation (RMSF), commonly used for protein structure stability analysis, to dipole moments, thus defining dipole moment RMSF. This enables us to analyze the stability of dipole moments for each residue within the protein and compare them across residues and between binding and non-binding complexes. Using the CRBP1-retinoic acid complex as our model system, we observed a significant difference in the interangle change of dipole moments for the key residue at the residue-level between the non-binding and binding complexes. Furthermore, we found that the dipole moment RMSF value of the non-binding complex was substantially larger than that of the binding complex, indicating greater dipole moment instability in the non-binding complex. Leveraging the concept of scalability inherent in the calculation of dipole moment vectors, we systematically expanded the residues within the protein's primary secondary structure. Our dipole moment analysis approach can provide valuable predictive insights into complex candidates, especially in situations where experimental comparisons are challenging.

High-order moment interval stability/stabilization and observability of stochastic impulsive T–S fuzzy systems

This article is concerned with the problems of high-order moment interval stability/stabilization and observability of stochastic impulsive T–S fuzzy systems (SITSFSs). Firstly, the definition of high-order moment interval stability is proposed of SITSFSs in this paper. In consideration of the connection between pole placement and performance of systems, sufficient conditions for the distribution of the eigenvalues of systems within a defined interval are provided, serving as the criterion for the interval stability in high-order moment of SITSFSs. Different from the general concept of stability, besides determining the stability in high-order moment of the system, high-order moment interval stability can also describe the dynamic performance in high-order moment of systems. Then, the proposed approach in combination with fuzzy control theory provides a reliable and effective method for designing an interval state feedback controller that can ensure the stability of systems and regulate convergence rate of systems. Furthermore, moment observability of SITSFSs has also been addressed in this article. Finally, the numerical simulation verifies the validity and suitability of the proposed method.

Almost Sure Stability of Complex-Valued Complex Networks: A Noise-Based Delayed Coupling Under Random Denial-of-Service Attacks.

This article is concerned with stability for stochastic complex-valued delayed complex networks under random denial-of-service (RDoS) attacks. Different from the existing literature on the stability of stochastic complex-valued systems that concentrate on moment stability, we investigate almost sure stability (ASS), where noise plays a stabilizing role. It is noted that, besides the vertex systems influenced by noise, the interactions among vertices are also at the mercy of noise. As a consequence, an innovative noise-based delayed coupling (NDC) in the presence of RDoS attacks is proposed first to accomplish the stability of complex-valued networks, where the RDoS attacks have a certain probability of triumphantly interfering with communications at active intervals of attackers. Namely, RDoS attacks considered are randomly launched at active periods, which is more realistic. In terms of the Lyapunov method and stochastic analysis theory, an almost sure exponential stability (ASES) criterion of the system discussed straightforwardly is developed by constructing a delay-free auxiliary system, while removing the traditional assumption of moment stability. The criterion strongly linked with topological structure, RDoS frequency, attack successful probability, and noise intensity reveals that the higher the noise intensity, the faster the convergence rate is for the stability of the network. In light of the criterion established, we present an algorithm that can be employed to analyze the tolerable attack parameters and the upper bound of the coupling delays, under the prerequisite of guaranteeing the stability of the network. Eventually, the theoretical results are applied to inertial complex-valued neural networks (ICNNs) and an illustrative example is presented to substantiate the efficiency of the theoretical works.

Magnetic properties and microstructure of Ce and Zr synergetic stabilizing Ti-lean SmFe12-based strip-casting flakes

Recently ThMn12-type samarium iron alloys have been promising materials for permanent magnets. Due to the high abundance and low cost, Ce as a possible stabilizer can be introduced into ThMn12-type alloys. The effect of Ce doping on the magnetic moment and phase stability in Ti-lean (Ce,Sm,Zr)(Fe,Co,Ti)12 compounds were predicted by the first-principles calculations. The CexSm0.8-xZr0.2(Fe0.8Co0.2)11.5Ti0.5 (x = 0–0.8) alloys with ThMn12 structure were produced by strip-casting into flakes by a wheel speed of 1.5 m/s and annealed at 1000 °C for 24 h. The Ce0.8Zr0.2(Fe0.8Co0.2)11.5Ti0.5 annealed flake shows a high saturation magnetization value of 13.6 kGs at room temperature. With the increase of Ce substitution in the annealed flakes, the content of α-(Fe,Co,Ti) phase decreases and the saturation magnetization increases. The 1:12 phase and the 1:9 phase have an orientation relationship that can be expressed as [0 0 –1]1:12//[100]1:9 and (020)1:12//(010)1:9. Besides, annealing process promotes the formation of 1:12 phase transformed from 1:9 phase. Coercivity is expected to be improved by obtaining uniform microstructure and suppressing the formation of soft α-(Fe,Co,Ti) phase in the ThMn12-based alloys.

Exponential stability results for second-order impulsive neutral stochastic differential equations

This paper is aimed to discuss the existence and exponential stability of mild solutions for second-order impulsive neutral stochastic differential equations (INSDEs). Firstly, we derive the existence of mild solutions for INSDEs by using the Banach fixed point theorem. Then, the exponential stability in the pth moment of mild solution for the considered INSDEs is proved by means of the generalized impulsive-integral inequality, which can effectively improve some known existing ones. Finally, as an application, an example is given to illustrate the efficiency of the obtained theoretical results.

Moment Lyapunov exponent and stochastic stability of a vibro-impact system driven by non-Gaussian colored noise

Vibro-impact phenomena are prevalent in practical engineering, making research on their stochastic dynamic characteristic of great practical significance. However, the research on stochastic stability and bifurcation of vibro-impact systems is still limited, especially the moment stability. In this paper, based on the pth moment Lyapunov exponent, the stochastic stability of a vibro-impact system driven by non-Gaussian colored noise is investigated. Firstly, the smooth stochastic dynamic system is obtained making use of a non-smooth transformation and the non-Gaussian colored noise is simplified to an Ornstein-Uhlenbeck process by utilizing the path-integral method. Thereafter, through applying the L.Arnold perturbation method, the second-order approximate solution of the pth moment Lyapunov exponent is calculated, which agree well with the simulation results given by the Monte Carlo method. Finally, the effects of the noise parameters, natural frequency, coefficient of restitution, and damping coefficient on the stochastic stability of the vibro-impact are studied. Due to the existence of impact factor, the natural frequency has a direct and significant effect on the stochastic stability of the system.

Stability analysis for positive Markov jump systems in [formula omitted]th moment sense: Necessary and sufficient conditions

This paper focuses on the stability analysis and synthesis of positive Markov jump systems (PMJSs) in pth moment sense, including stability, strong stability, observability, and detectability. First, by the ℋ-representation technique, the extended system method is constructed. With the help of the extended system method, stability analysis of PMJSs in pth moment sense are transformed into those of the extended systems. Furthermore, the necessary and sufficient conditions for stability, observability, and detectability in pth moment sense are obtained. Moreover, the definitions of pth moment strong stability (PMSS) and pth moment stability threshold (PMST) are given for the first time, and the sufficient/necessary conditions for these are derived, respectively. In addition, the problems of stabilization and strong stabilization in pth moment sense are considered. Finally, several examples are presented to show the effectiveness of the obtained results.

Emergent Ferromagnetism in CaRuO3/CaMnO3 (111)-Oriented Superlattices.

The boundary between CaRuO3 and CaMnO3 is an ideal test bed for emergent magnetic ground states stabilized through interfacial electron interactions. In this system, nominally antiferromagnetic and paramagnetic materials combine to yield interfacial ferromagnetism in CaMnO3 due to electron leakage across the interface. In this work, we show that the crystal symmetry at the surface is a critical factor determining the nature of the interfacial interactions. Specifically, by growing CaRuO3/CaMnO3 heterostructures along the (111) instead of the (001) crystallographic axis, we achieve a 3-fold enhancement of the magnetization and involve the CaRuO3 layers in the ferromagnetism, which now spans both constituent materials. The stabilization of a net magnetic moment in CaRuO3 through strain effects has been long-sought but never consistently achieved, and our observations demonstrate the importance of interface engineering in the development of new functional heterostructures.

Formula omitted]th moment stability of discrete-time Markov jump systems by extended system method

This paper studies the pth moment stability of discrete-time Markov jump systems by utilizing the extended system method, which is composed of the operator spectrum technique and the ℋ-representation technique. Firstly, some extended systems are constructed by the operator spectrum technique and the ℋ-representation technique to transform the discrete-time Markov jump systems into the extended systems. Furthermore, the relationship in pth moment stability between the extended systems and the stochastic systems is discussed. Next, with the help of the extended systems, the necessary and sufficient conditions for the even-order moment stability, and several sufficient conditions/necessary conditions for the odd-order moment stability are obtained, respectively. Additionally, as applications of the extended system method, observability and detectability in pth moment sense are discussed, and the necessary and sufficient conditions for observability and detectability in even-order moment are obtained, respectively. Finally, several examples are given to illustrate the validity of the results.

Enhancing the energetic and magnetic stability of atomic hydrogen chemisorbed on graphene using (non)compensated B-N pairs.

In this pioneering study for identifying atomic scale magnetic moment, a single hydrogen atom chemisorbed on pristine graphene exhibits distinct spin polarization. Using first-principles calculations and analyses, we demonstrate that the binding between a H adsorbate and a C substrate is substantially enhanced via compensated B-N pairs embedded into graphene. Surprisingly, the interaction can be further enhanced via non-compensated B-N pair doping. Our established prototype of orbital intercoupling between H 1s and hybridized pz of gapped band edges gives an insight into the enhancing mechanism. For compensated B-N doping, the conduction band minimum (CBM) is pushed upward, which induces stronger interaction between the H 1s and hybridized pz orbitals of the CBM. For non-compensated B-N doping, the orbital interaction occurs between H 1s and hybridized pz orbitals of valence band maximum, thus further lowering the resulting bonding energy due to the enlarged gap. This significantly enhanced interaction between H and C atoms agrees well with the results of charge localization at the gapped band edges. More importantly, the corresponding magnetic moments can be well maintained or even enhanced in both doping; here, one more H atom is needed for non-compensated doping, where its electron occupies the empty CBM. Our findings might provide an effective and practical way to enhance the energetic and magnetic stability of atomic scale magnetic moment on graphene and extensively expand the conception of non-compensated doping.