Experimental validation of inviscid linear stability theory applied to an axisymmetric jet

We study the development of perturbations in a submerged air jet with a round cross-section and a long laminar region (five jet diameters) at a Reynolds number of 5400 by both inviscid linear stability theory and experiments. The theoretical analysis shows that there are two modes of growing axisymmetric perturbations, which are generated by three generalized inflection points of the jet's velocity profile. To validate the results of linear stability theory, we conduct experiments with controlled axisymmetric perturbations to the jet. The characteristics of growing waves are obtained by visualization, thermoanemometer measurements and correlation analysis. Experimentally measured wavelengths, growth rates and spatial distributions of velocity fluctuations for both growing modes are in good agreement with theoretical calculations. Therefore, it is demonstrated that small perturbations to the laminar jet closely follow the predictions of inviscid linear stability theory.

Secure Complex Systems: A Dynamic Model in the Synchronization

Chaotic systems are one of the most significant systems of the technological period because their qualities must be updated on a regular basis in order for the speed of security and information transfer to rise, as well as the system’s stability. The purpose of this research is to look at the special features of the nine-dimensional, difficult, and highly nonlinear hyperchaotic model, with a particular focus on synchronization. Furthermore, several criteria for such models have been examined; Hamiltonian, synchronizing, Lyapunov expansions, and stability are some of the terms used. The geometrical requirements, which play an important part in the analysis of dynamic systems, are also included in this research due to their importance. The synchronization and control of complicated networks’ most nonlinear control is important to use and is based on two major techniques. The linearization approach and the Lyapunov stability theory are the foundation for attaining system synchronization in these two ways.

Hegemonic stability in the Indo-Pacific: US-India relations and induced balancing

The United States has improved relations with no other country during the Trump administration as much as it advanced its relationship with India. US-India relations have arguably marked their historical high points since Trump entered office and India seems to be overcoming its suspicion of closer cooperation with the US. Given these developments, this article aims to theorize the relationship through the hegemonic stability theory and explain US strategy toward India. We first demonstrate why India is accepting the hegemonic standing of the US in the Indo-Pacific and then – since balance of power politics are still a staple of policymakers’ approach to stability in the Indo-Pacific – we introduce the notion of induced balancing to show what approach the United States has adopted to empower India to expand its balancing capacity vis-à-vis China. The last section of the article empirically maps the various incentives that Washington offers to New Delhi in order to situate it in the desired position of a proxy China-balancer.

KESTABILAN MODEL PETRI NET DARI SISTEM PEMBAYARAN TAGIHAN LISTRIK PT. PLN (Persero) RAYON AMBON TIMUR

This research develops the previous one of the electricity bill payment system in PT. PLN (Persero) Rayon East Ambon modelled by Petri Net. The previous researcher had built the Petri Net model of this payment system. In this research, we determine whether the system modelled before is stable or not. This stability will be analysed using the Lyapunov stability theory related to the Petri Net. The result shows that the electricity bill payment system modelled by Petri Net before is not stable but can be stabilized. This can be caused there is a transition which is ‘always enable’ in the modelled which is built. This research also performs a stable model of Petri Net that represents the electricity bill payment system with deleting the ‘always enable’ transition

Study of the soil stability theory problems by the simplex method

The questions of linear programming methods application to the main problems of stability theory - problems on slope stability, problems on ultimate pressure of soil on enclosures (case of landslide pressure), and problems on bearing capacity of horizontal base of a die are considered. The problems of stability theory are formulated as linear programming tasks. It is shown that the given systems of equations are linear with respect to the unknowns and may be solved by the Simplex method. The results of soil stability problems calculation by Simplex method are compared with the results of calculations according to the most known classical schemes. It is shown that a great scatter of final results is observed in calculating the stability of slopes by classical methods, and in this case, the results obtained by the Simplex method are the most trustworthy ones. The situation with landslide pressure definition is especially complicated in this sense where classical methods give a scatter of landslide pressure values by several times. It is established that with increasing discretization of the computational domain, the results tend to exact solutions of the limit equilibrium theory, obtained, for example, by the method of characteristics. The latter point is illustrated using the example of the problem of a die pushing into a ground massif with a Hill scheme bulge.

Inherent Stability of Multibody Systems with Variable-Stiffness Springs via Absolute Stability Theory

In this paper, the inherent stability problem for multibody systems with variable-stiffness springs (VSSs) is studied. Since multibody systems with VSSs may consume energy during the variation of stiffness, the inherent stability is not always ensured. The motivation of this paper is to present sufficient conditions that ensure the inherent stability of multibody systems with VSSs. The absolute stability theory is adopted, and N-degree-of-freedom (DOF) systems with VSSs are formulated as a Lur’e form. Furthermore, based on the circle criterion, sufficient conditions for the inherent stability of the systems are obtained. In order to verify these conditions, both frequency-domain and time-domain numerical simulations are conducted for several typical low-DOF systems.

Adaptive Terminal Synergetic Synchronization of Hyperchaotic Systems

This research paper introduces an adaptive terminal synergetic nonlinear control. This control aims at synchronizing two hyperchaotic Zhou systems. Thus, the adaptive terminal synergetic control’s synthesis is applied to synchronize a hyperchaotic i.e., slave system with unknown parameters with another hyperchaotic i.e., master system. Accordingly, simulation results of each system in different initial conditions reveal significant convergence. Moreover, the findings proved stability and robustness of the suggested scheme using Lyapunov stability theory.

A general method for projective-lag synchronization of heterogeneous chaotic maps with different dimensions

Projective-lag synchronization of complex systems has attracted much attention in the past two decades. However, the majority of previous studies concentrated on continuous-time chaotic systems or discrete-time chaotic systems with the same dimensions. In our present study, a general method for projective-lag synchronization of different discrete-time chaotic systems characterized with different dimensions is first demonstrated. On the basis of stability theory of discrete-time dynamical systems and Lyapunov stability theory, general controllers are designed by using the active control method. The method could achieve projective-lag synchronization in both cases: [Formula: see text] and [Formula: see text]. The effectiveness and feasibility of the proposed method is demonstrated by the projective-lag synchronization between two-dimensional Lorenz discrete-time system and three-dimensional Stefanski map, as well as between the three-dimensional generalized Hénon map and the two-dimensional quadratic map, respectively.