Moment Stability Research Articles

Explicit numerical approximations for stochastic differential equations in finite and infinite horizons: truncation methods, convergence in pth moment and stability

Solving stochastic differential equations (SDEs) numerically, explicit Euler-Maruyama (EM) schemes are used most frequently under global Lipschitz conditions for both drift and diffusion coefficients. In contrast, without imposing the global Lipschitz conditions, implicit schemes are often used for SDEs but require additional computational effort; along another line, tamed EM schemes and truncated EM schemes have been developed recently. Taking advantages of being explicit and easily implementable, truncated EM schemes are proposed in this paper. Convergence of the numerical algorithms is studied, and pth moment boundedness is obtained. Furthermore, asymptotic properties of the numerical solutions such as the exponential stability in pth moment and stability in distribution are examined. Several examples are given to illustrate our findings.

Higher order moment stability region for Markov jump systems based on cumulant generating function

This paper is concerned with the solution of higher order moment stability region for Markov jump systems with respect to cases of both known and unknown transition probabilities. By exploring the cumulant generating function, the original stochastic system with Markov jumping modes is transformed to a deterministic system. Then based on the estimation of matrix eigenvalues, the explicit solution for higher order moment stability region is expressed in terms of transition probabilities, operation modes, state transition matrix and its dimension, and the moment order. Several examples are presented to illustrate the effectiveness of the proposed method and its associated algorithm.

Seismic Performance and Lateral Stability of Steel Moment Resisting Building with Vertical Irregular Infill Arrangement

Seismic Performance and Lateral Stability of Steel Moment Resisting Building with Vertical Irregular Infill Arrangement

Stochastic stability of a magnetically affected single-layer graphene sheet resting on a viscoelastic foundation

Abstract In this paper, we analyzed the stochastic stability of a single-layer graphene sheet resting on a viscoelastic foundation and influenced by the in-plane magnetic field. The mechanical model of a graphene sheet is given as an orthotropic and viscoelastic nanoplate while the viscoelastic foundation is of the Kelvin-Voigt type. We assume that the graphene sheet is influenced by the in-plane random forces variable with time and exerted in-plane magnetic field. Based on the Eringen's nonlocal continuum theory and Kirchhoff – Love plate theory, the governing equation of motion is derived by considering the influence of the Lorentz forces obtained from the classical Maxwell relations. In order to investigate the stochastic stability of such system, the maximal and moment Lyapunov exponents are considered by using the perturbation method. The predicted approximated analytical results for the p -th moment Lyapunov exponents are validated by the Monte Carlo method . Moreover, the boundaries of almost-sure and moment stability of the viscoelastic nanoplate are determined as functions of different system parameters. The influences of the nonlocal and magnetic field parameters, stiffness and damping coefficients and spectral density on the moment Lyapunov exponents are investigated through several numerical examples. Presented results reveal that the applied in-plane magnetic field could be successfully used to improve stability performances of nano-electromechanical systems based on graphene sheets.

Complex magnetic order in the kagome ferromagnet Pr3Ru4Al12

In the hexagonal crystal structure of ${\mathrm{Pr}}_{3}{\mathrm{Ru}}_{4}{\mathrm{Al}}_{12}$, the Pr atoms form a distorted kagome lattice, and their magnetic moments, are subject to competing exchange and anisotropy interactions. We performed magnetization, magnetic-susceptibility, specific-heat, electrical-resistivity, and neutron-scattering measurements. ${\mathrm{Pr}}_{3}{\mathrm{Ru}}_{4}{\mathrm{Al}}_{12}$ is a uniaxial ferromagnet with ${T}_{\text{C}}=39$ K that displays a collinear magnetic structure (in the high-temperature range of the magnetically ordered state) for which the only crystallographic position of Pr is split into two sites carrying different magnetic moments. A spin-reorientation phase transition is found at 7 K. Below this temperature, part of the Pr moments rotate towards the basal plane, resulting in a noncollinear magnetic state with a lower magnetic symmetry. We argue that unequal RKKY exchange interactions competing with the crystal electric field lead to a moment instability and qualitatively explain the observed magnetic phases in ${\mathrm{Pr}}_{3}{\mathrm{Ru}}_{4}{\mathrm{Al}}_{12}$.

Improved Razumikhin and Krasovskii stability criteria for time-varying stochastic time-delay systems

The problem of pth moment stability for time-varying stochastic time-delay systems with Markovian switching is investigated in this paper. Some novel stability criteria are obtained by applying the generalized Razumikhin and Krasovskii stability approaches. Both pth moment asymptotic stability and (integral) input-to-state stability are considered based on the notion and properties of uniformly stable functions and the improved comparison lemmas. The established results show that time-derivatives of the constructed Razumikhin functions and Krasovskii functionals are allowed to be indefinite, which improve the existing results on this topic. By applying the obtained results for stochastic systems, we also analyze briefly the stability of time-varying deterministic time-delay systems. Finally, examples are provided to illustrate the effectiveness of the proposed results.

Electrically tunable magnetic configuration on vacancy-doped GaSe monolayer

Group-IIIA metal-monochalcogenides with the enticing properties have attracted tremendous attention across various scientific disciplines. With the aim to satisfy the multiple demands of device applications, here we report a design framework on GaSe monolayer in an effort to tune the electronic and magnetic properties through a dual modulation of vacancy doping and electric field. A half-metallicity with a 100% spin polarization is generated in a Ga vacancy doped GaSe monolayer due to the nonbonding 4p electronic orbital of the surrounding Se atoms. The stability of magnetic moment is found to be determined by the direction of applied electric field. A switchable magnetic configuration in Ga vacancy doped GaSe monolayer is achieved under a critical electric field of 0.6 V/Å. Electric field induces redistribution of the electronic states. Finally, charge transfers are found to be responsible for the controllable magnetic structure in this system. The magnetic modulation on GaSe monolayer in this work offers some references for the design and fabrication of tunable two-dimensional spintronic device.

Stability of Switched Systems on Randomly Switching Durations With Random Interaction Matrices

In this paper, we investigate the almost sure stability of switched systems on randomly switching durations simultaneously with randomly switching interaction matrices. We not only allow the interaction matrix on each switching duration to take values randomly from either a countable, an uncountable, or even an unbounded state space, but also allow the corresponding probability density function to be time varying with the switching. We provide an example to show the difference between the almost sure stability and the moment stability. Then, we establish several practical stability criteria for switched systems, which may have linear or nonlinear subsystems. These stability criteria also enable us to find suitable conditions for realizing almost sure synchronization in complex networks, such as small-world networks, with both randomly switching durations and a few switching couplings that take values randomly in either an uncountable or an unbounded state space.

Existence and exponential stability for neutral stochastic fractional differential equations with impulses driven by Poisson jumps

The paper is mainly concerned with a class of neutral stochastic fractional integro-differential equation with Poisson jumps. First, the existence and uniqueness for mild solution of an impulsive stochastic system driven by Poisson jumps is established by using the Banach fixed point theorem and resolvent operator. The exponential stability in the pth moment for mild solution to neutral stochastic fractional integro-differential equations with Poisson jump is obtained by establishing an integral inequality.

Synthesis, characterization, computational studies and biological evaluation of S-benzyl-β-N-[3-(4-hydroxy-3-methoxy-phenylallylidene)]dithiocarbazate

S-Benzyl-β-N-[3-(4-hydroxy-3-methoxy-phenylallylidene)]dithiocarbazate (HL1), Schiff base of S-benzyl dithiocarbazate, was synthesized by 1:1 condensation between S-benzyl dithiocarbazate and 4-hydroxy-3-methoxy cinnamaldehyde. The nitrogen-sulfur Schiff base (HL1) was characterized by Mass, FT-IR, H1-NMR, Raman, and UV-VIS spectroscopic techniques. Theoretical quantum chemical calculations were performed using DFT in combination with B3LYP exchange correlation functional and 6–311++ G (d, p) basis sets level. The calculated values of chemical potential (μ), HOMO-LUMO energy gap, chemical hardness, softness (S), ionization energy (IE), electron affinity (EA), dipole moment (D) and relative stabilization energy of the compound were 0.14881 eV, 0.12542 eV, 0.06271 eV, 3.37299 eV, −0.21152 eV, −0.08610 eV, 4.4090 Debye and −1753.350 eV respectively. Theoretically calculated parameters like H1-NMR, FT-IR, UV-VIS, Raman, electrostatic potential and HOMO-LUMO energy gap are in good agreement with experimental results. Also, in-vitro cytotoxicity studies were done against two habitually infection causing bacteria strains including gram-positive (S. aureus) and gram-negative (E. coli) for antibacterial activity. The results showed appreciable biological activity and the activity increased with increase in dose.

Moment stability analysis of linear stochastic human controller model in visuomotor tracking task

We investigate the stability limits of linear stochastic human controller model. In our previous study, we had proposed a model by which the probability distributions of human visuomotor tracking data can be accurately reproduced. In this study, we conduct a stochastic analysis on our model by deriving a system of moment differential equations with respect to random state variables of this model. We evaluate the stability limits of our model by detecting zero-eigenvalue conditions of the Jacobian matrix of the moment differential equations. The resulting stability limits make it possible to characterize the human parameter values that were experimentally identified from the human participants in our previous study; this shows that during the visuomotor tracking experiments, the human participants generated huge fluctuations far from the stability limits while applying almost neutrally stable proportional gain.

Almost sure exponential stability sensitive to small time delay of stochastic neutral functional differential equations

In this work, we establish a theory about the almost sure pathwise exponential stability property for a class of stochastic neutral functional differential equations by developing a semigroup scheme for the drift part of the systems under consideration and dealing with their pathwise stability through a perturbation approach, rather than through that one to get their moment stability first. As an illustration, we can show that some stochastic systems have their almost sure exponential stability not sensitive to small delays.

Voltage Control of Perpendicular Magnetic Anisotropy in Multiferroic (Co/Pt)3/PbMg1/3Nb2/3O3−PbTiO3 Heterostructures

Voltage control of perpendicular magnetic anisotropy (PMA) is a promising approach for high-density, lightweight, energy-efficient information storage. Electric-field regulation of PMA in conventional multiferroic laminates is difficult, though, since the voltage-induced magnetic anisotropy is relatively small. This study combines ferromagnetic resonance and the magneto-optical Kerr effect for significant electric-field manipulation of PMA in multiferroic multilayers containing cobalt. Along the way, the authors also gain interesting insight about the instability of Co orbital moments near a critical transition.

Delay-Based Maximum Power-Weight Scheduling With Heavy-Tailed Traffic

Heavy-tailed (HT) traffic (e.g., the Internet and multimedia traffic) fundamentally challenges the validity of classic scheduling algorithms, designed under conventional light-tailed (LT) assumptions. To address such a challenge, this paper investigates the impact of HT traffic on delay-based maximum weight scheduling (DMWS) algorithms, which have been proven to be throughput-optimal with enhanced delay performance under the LT traffic assumption. First, it is proven that the DMWS policy is not throughput-optimal anymore in the presence of hybrid LT and HT traffic by inducing unbounded queuing delay for LT traffic. Then, to solve the unbounded delay problem, a delay-based maximum power-weight scheduling (DMPWS) policy is proposed that makes scheduling decisions based on queuing delay raised to a certain power. It is shown by the fluid model analysis that DMPWS is throughput-optimal with respect to moment stability by admitting the largest set of traffic rates supportable by the network, while guaranteeing bounded queuing delay for LT traffic. Moreover, a variant of the DMPWS algorithm, namely the IU-DMPWS policy, is proposed, which operates with infrequent queue state updates. It is also shown that compared with DMPWS, the IU-DMPWS policy preserves the throughput optimality with much less signaling overhead, thus expediting its practical implementation.

The pth moment exponential stability of uncertain differential equation

Uncertain variable and uncertain process are often employed to describe uncertainty phenomena. Uncertain variable is a measurable function from an uncertainty space to the real number set and uncertain process is essentially a sequence of uncertain variables indexed by time. Uncertain differential equation is a type of differential equation involving uncertain processes. Stability of an uncertain differential equation plays a very important role in differential equation which means insensitivity of the state of a system to small changes in the initial state. In this paper, we focus on pth moment exponential stability of uncertain differential equation which is regarded as an extension of pth moment stability and exponential stability. Some stability theorems are given for uncertain differential equation, in which a sufficient and necessary condition for a linear uncertain differential equation being pth moment exponentially stable is provided.

On pth moment stabilization of hybrid systems by discrete-time feedback control

ABSTRACTSince Mao initiated the study of stabilization of continuous-time hybrid stochastic differential equations (SDEs) by feedback controls based on discrete-time state observations in 2013, many authors have further studied and developed it. However, so far no work on the pth moment stabilization has been reported. This paper is to investigate how to stabilize a given unstable hybrid SDE by feedback controls based on discrete-time state observations, in the sense of H∞, asymptotic and exponential stability in pth moment for all p > 1. The main techniques used are constructions of the Lyapunov functionals and generalizations of inequalities.

Helical turbulence with small-scale energy and helicity sources and external intermediate scale noises as the origin of large scale generation

Interactions violating the symmetry of positive and negative total helicity components are considered. In the ideal case where one of the components is zero, the system have two sign-definite integrals of motion, which lead to an inverse energy cascade, as occurs in two-dimensional turbulence. The generation of large-scale modes is considered in the quasi-normal approximation and is manifested as the instability of second moments, a mechanism of which was discussed at the end of previous century. A crucial point in this mechanism is the presence of mean turbulence with large-scale helical disturbances and small-scale sources of energy and helicity. In the case of both helicity components being nonzero, the possibility of the large-scale generation is studied by applying numerical experiments with a shell model and by analyzing special cases of interactions between different shells of the model. In all the approaches used, it is shown that an inverse energy flux (from small to large scales) can exist at a certain level of external helical noises in large-scale modes, which depends on the degree of “mixing” oppositely signed helicity components.

Stability analysis of impulsive stochastic Cohen–Grossberg neural networks driven by G-Brownian motion

ABSTRACTThis paper is devoted to study the stability of a class of impulsive stochastic Cohen–Grossberg neural networks driven by G-Brownian motion. By means of G-Lyapunov function, Borel–Cantelli lemma and inequality technique, a series of sufficient conditions on pth moment stability and quasi-sure stability with respect to a general decay function are established. A concrete example is given to illustrate the obtained results.

Evolution of the Spin Magnetic Moments and Atomic Valence of Vanadium in VCux+, VAgx+, and VAux+ Clusters (x = 3-14).

The atomic structures, bonding characteristics, spin magnetic moments, and stability of VCux+, VAgx+, and VAux+ (x = 3-14) clusters were examined using density functional theory. Our studies indicate that the effective valence of vanadium is size-dependent and that at small sizes some of the valence electrons of vanadium are localized on vanadium, while at larger sizes the 3d orbitals of the vanadium participate in metallic bonding eventually quenching the spin magnetic moment. The electronic stability of the clusters may be understood through a split-shell model that partitions the valence electrons in either a delocalized shell or localized on the vanadium atom. A molecular orbital analysis reveals that in planar clusters the delocalization of the 3d orbital of vanadium is enhanced when surrounded by gold due to enhanced 6s-5d hybridization. Once the clusters become three-dimensional, this hybridization is reduced, and copper most readily delocalizes the vanadium's valence electrons. By understanding these unique features, greater insight is offered into the role of a host material's electronic structure in determining the bonding characteristics and stability of localized spin magnetic moments in quantum confined systems.

Refined nonlinear finite element modelling towards ultimate bending moment calculation for concrete composite beams under negative moment

In this study, a refined nonlinear finite-element (FE) model of steel-concrete composite beam (SCCB) capable of accommodating various effects such as the initial geometric imperfection, residual stress, interface slip, geometric nonlinearity, and material nonlinearity is developed to study the distortional instability of SCCBs under negative bending moment. The accuracy of the model is validated by publicly available results previously observed by experiments. On the basis of the refined nonlinear FE model, the ultimate bending moment of 54 groups of SCCBs with varying cross-section parameters is calculated. Also, the effects of the force ratio of the SCCB, width–thickness ratio of the compression flange, shear connection degree, and height–thickness ratio of the web on the ultimate bending moment stability coefficient of SCCB in negative bending moment area are investigated in detail. Results show that the effect of the degree of shear connection on the stability coefficient of the SCCB is insignificant, while the stability coefficient decreases with the increase of the remaining parameters, among which the effect of the height–thickness ratio of the web is proven to be the most significant. Finally, considering various effects aforementioned properly, practical formulas are proposed to compute slenderness ratio and ultimate bending moment stability coefficient of SCCB in a concise form, which are shown to be consistent with the FE modelling and experimental results, and thus are suitable for engineering design.