M. Najafi

Stabilizability of coupled wave equations in parallel under various boundary conditions

Stability of the wave equations coupled in parallel (suspension system) is investigated for free- and fixed-boundary conditions by energy dissipation boundary controller(s). To this end, the exponential stability criterion and Rouches theorems are used. The former is utilized for uniformly, exponentially decaying systems, and the latter otherwise. The results are characterized by the rate of convergence of the solutions and the system parameters for the stated boundary conditions.

The study of the stabilizability of the coupled wave equations under various end conditions

The stabilizability of coupled wave equations (suspension system) is investigated for free, and energy dissipation boundary conditions. Huang and Rouches theorem is utilized, and the rate of convergence of the solution of such a system for certain boundary conditions is studied. Numerical experiments were carried out to justify the theoretical results.<<ETX>>

Stability treatments of wave system in R n with coupling controllers via energy functional and decomposition methods

In this paper, the stabilizability conditions of a system of wave equations, coupled in parallel with distributed springs and viscous dampers, are investigated via energy perturbation and decomposition methods for different wave propagation speeds.

Energy decay estimates for Euler-Bernoulli beams coupled in parallel

Stability problems associated with a system of Euler-Bernoulli beams coupled in parallel are investigated. The uniform exponential stability and strong stability are established under a damping velocity feedback control as well as a boundary control.<<ETX>>

The boundary stabilization of a linearized self-excited wave equation

We study the linearized self-excited wave equation uu - c2 ▵ u - p(x) u1 = 0, where P(x)  0, and P(x) e L∞ (ohm; ), in a bounded domain Ω ⊂ R n with smooth boundary Γ where boundary damping is present. We observe that the energy is not monotonically non-increasing, owing to negative internal damping P which causes self-excitation. Hence, the system may become unstable. Having considered the partition { Γ +,Γ − } of the boundary f on which u = o on Γ − we find two different bounds for P such that the energy of the system decays exponentially as t tends to infinity (here, we assume ¯Γ + ∩ ¯Γ = φ for n  3)Both bounds depend on Q. Moreover, the second bound depends on the feedback functions Kor more precisely it depends on a positive function k(x)e L∞ (Γ + ) which determines K and L on the partition T+

Exponential stability of wave equations coupled in parallel with viscous damping

In this paper, stabilization of the system of wave equations coupled in parallel with springs and viscous dampers are under investigation due to different boundary conditions and wave propagation speeds. Numerical computations are attempted to confirm the theoretical results.<<ETX>>

The Stabilization of a Linearized Self-Excited Wave Equation by an Energy Absorbing Boundary

We study the linearised self-excited wave equation x<inf>tt</inf> - ¿ x-P(x) x<inf>t</inf>=0, where P(x)¿0, P(x) L^¿(¿), in a bounded domain ¿ ¿ Rⁿ with smooth boundary ¿ where boundary damping is present. Considering the partition {¿<inf>+</inf>, ¿<inf>-</inf>} of the boundary ¿ on which x=0 on ¿, and u<inf>n</inf>+ Ku<inf>t</inf> + Lu= 0, on ¿, we find two different bounds for P such that the energy decays exponentially in the energy space as t tends to infinity (Here we assume ¿<inf>+</inf> ¿ ¿<inf>-</inf> = ¿ for n ≫ 3). Both bounds depend on ¿ (The domain of wave equation in Rⁿ, n ¿ 1). The second bound also depends on the feed-back functions K,L L^¿(¿<inf>+</inf>) or more precisely depends on a positive function k(x) L^¿(¿<inf>+</inf>) which determines K and L on the partition ¿<inf>+</inf>.

Stability analysis and sliding mode control of a single spherical bubble dynamics

The goal of the present paper is to apply control techniques to determine the Blake cavitation threshold for adiabatic bubbles. Considering state space representation of Rayleigh-Plesset (RP) equation, a stability condition is derived to predict the threshold for cavitation which was determined beforehand by mechanical bias. Moreover, sliding mode control has been utilized to regulate the radius of a single spherical bubble to the desired value to prevent collapse occurrence which has a great importance in some industrial applications. Simulation results are presented to show the effectiveness of the proposed method.

Modeling and stability analysis of HIV-1 as a time delay fuzzy T-S system via LMIs

This paper proposes a Time Delay Fuzzy Takagi-Sugeno (T-S) representation of a nonlinear dynamic model ofHIV-1 as well as stability analysis of the model. Asymptotic stability of the resulting T-S fuzzy system with state-delay is investigatedand partially established. The focus is mainly on the delay-dependent stability analysis based on the fuzzy weighting-dependent Lyapunov function method.

Applicability of lattice Boltzmann method in simulation of drops and bubbles formation and transport

Multiphase flows appear in many scientific and engineering applications. On the other hand, there has been a tremendous experimental and numerical investigation trying to understand complex fluid-fluid interfaces better. However, conventional CFD have certain limitations in complicated situations. Fortunately in the past two decades, new approaches, namely SPH and LBM (sometimes called meshless methods) have been developed. Since they are mesoscopic, they have been able to perform much better than conventional CFD. Especially, LBM is becoming more and more popular and has already been divided to many branches.