This work investigates the control and stability of nonlinear mechanics described by a system of variable-order (VO) differential equations. The VO behavior results from damping with order varying continuously on the bounded domain. A model-predictive method is presented for the development of a timevarying nominal control signal generating a desirable nominal state trajectory in the finite tem...

We propose an effect called information constraint which is characterized by the existence of different decay rates signal strengths propagating along opposite directions. It intrinsic property a type open quantum systems, does not rely on boundary conditions. define value $({I}_{C})$ as ratio and derive analytical representation ${I}_{C}$ for general quadratic Lindbladian systems. Based constr...

By comparing the response of flat and bowl-shaped basins to fixed heat fluxes of various magnitudes, it is determined that coastal topography has a considerable damping influence upon internal decadal oscillations of the thermohaline circulation. It is proposed that this is because the adjustment of baroclinic currents to the no-normal-flow boundary condition at weakly stratified coasts is aide...

Abstract. A viscoelastic equation with Balakrishnan-Taylor damping and nonlinear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions on the relaxation function and with certain initial data and by adopting the perturbed energy method, we establish uniform decay rate of the solution energy in terms of the behavior of the relaxation function, which are not n...

identification of damping parameter is usually more complicated and unreliable comparing to mass or stiffness identification in structural dynamics. there are many factors such as intermolecular friction, coulomb friction and viscous damping affecting the damping mechanisms in a structure. therefore it is difficult, and in some cases impossible, to describe the details of damping mechanisms by ...

Based on a distributed parameter model for vibrations, an approximate nite dimensional dynamic compensator is designed to suppress vibrations (multiple modes with a broad band of frequencies) of a circular plate with Kelvin-Voigt damping and clamped boundary conditions. The control is realized via piezoceramic patches bonded to the plate and is calculated from information available from several...

Coulomb collisions at rate ν produce slightly probabilistic rather than fully deterministic charged particle trajectories in weakly collisional plasmas. Their diffusive velocity scattering effects on the response to a wave yield an effective collision rate νeff ν and a narrow dissipative boundary layer for particles with velocities near the wave phase velocity. These dissipative effects produce...

We consider second-order evolution equations in an abstract setting with intermittently delayed/not-delayed damping and give sufficient conditions ensuring asymptotic and exponential stability results. Our abstract framework is then applied to the wave equation, the elasticity system, and the Petrovsky system. For the Petrovsky system with clamped boundary conditions, we further prove an intern...

The inverted pendulum is a canonical problem in both Nonlinear Dynamics and Control Theory. In this article, the phenomenon of dynamic stabilization of the vertically driven inverted pendulum is investigated experimentally and numerically. We resolve the first stabilizing boundary in driving parameter space, as well as investigate the effects of frictional damping on the dynamics of the pendulu...

We address the system of partial differential equations modeling motion of an elastic body inside an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by the damped wave equation with interior damping. The additional boundary stabilization γ, considered in our previous paper, is no longer necessary. We prove the global ex...