1,872 research outputs found
Interior feedback stabilization of wave equations with dynamic boundary delay
In this paper we consider an interior stabilization problem for the wave
equation with dynamic boundary delay.We prove some stability results under the
choice of damping operator. The proof of the main result is based on a
frequency domain method and combines a contradiction argument with the
multiplier technique to carry out a special analysis for the resolvent
Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions
In this paper we consider a multi-dimensional wave equation with dynamic
boundary conditions, related to the Kelvin-Voigt damping. Global existence and
asymptotic stability of solutions starting in a stable set are proved. Blow up
for solutions of the problem with linear dynamic boundary conditions with
initial data in the unstable set is also obtained
Boundary Stabilization of Torsional Vibrations of a Solar Panel
In this paper, we study a boundary stabilization of the torsional vibrations of a solar panel. The panel is held by a rigid hub at one end and is totally free at the other. The dynamics of the overall system leads to hybrid system of equations. It is set to a certain initial vibrations with a control torque as a stabilizer at the hub end only. Taking a non-linear damping as boundary stabilizer, a uniform exponential energy decay rate is obtained directly. Thus an explicit form of uniform stabilization of the system is achieved by means of the exponential energy decay estimate
Uniform Stabilization of n-Dimensional Vibrating Equation Modeling ‘Standard Linear Model’ of Viscoelasticity
In this paper, we deal with the elastic vibrations of flexible structures modeled by the ‘standard linear model’ of viscoelasticity in n-dimensional space. We study the uniform exponential stabilization of such kind of vibrations after incorporating separately very small amount of passive viscous damping and internal material damping of Kelvin-Viogt type in the model. Explicit forms of exponential energy decay rates are obtained by a direct method, for the solution of such boundary value problems without having to introduce any boundary feedback
Effects of viscoelasticity on droplet dynamics and break-up in microfluidic T-Junctions: a lattice Boltzmann study
The effects of viscoelasticity on the dynamics and break-up of fluid threads
in microfluidic T-junctions are investigated using numerical simulations of
dilute polymer solutions at changing the Capillary number (\mbox {Ca}), i.e.
at changing the balance between the viscous forces and the surface tension at
the interface, up to \mbox{Ca} \approx 3 \times 10^{-2}. A Navier-Stokes (NS)
description of the solvent based on the lattice Boltzmann models (LBM) is here
coupled to constitutive equations for finite extensible non-linear elastic
dumbbells with the closure proposed by Peterlin (FENE-P model). We present the
results of three-dimensional simulations in a range of \mbox{Ca} which is
broad enough to characterize all the three characteristic mechanisms of breakup
in the confined T-junction, i.e. , and regimes. The various model parameters of the FENE-P constitutive
equations, including the polymer relaxation time and the finite
extensibility parameter , are changed to provide quantitative details on
how the dynamics and break-up properties are affected by viscoelasticity. We
will analyze cases with (DV), where
viscoelastic properties are confined in the dispersed (d) phase, as well as
cases with (MV), where viscoelastic properties
are confined in the continuous (c) phase. Moderate flow-rate ratios of the two phases are considered in the present study. Overall, we
find that the effects are more pronounced in the case with MV, as the flow
driving the break-up process upstream of the emerging thread can be sensibly
perturbed by the polymer stresses.Comment: 16 pages, 14 figures; This Work applies the Numerical Methodology
described in arXiv:1406.2686 to the Problem of Droplet Generation in
Microfluidic T-Junctions. arXiv admin note: substantial text overlap with
arXiv:1508.0055
Simulating structured fluids with tensorial viscoelasticity
We consider an immersed elastic body that is actively driven through a
structured fluid by a motor or an external force. The behavior of such a system
generally cannot be solved analytically, necessitating the use of numerical
methods. However, current numerical methods omit important details of the
microscopic structure and dynamics of the fluid, which can modulate the
magnitudes and directions of viscoelastic restoring forces. To address this
issue, we develop a simulation platform for modeling viscoelastic media with
tensorial elasticity. We build on the lattice Boltzmann algorithm and
incorporate viscoelastic forces, elastic immersed objects, a microscopic
orientation field, and coupling between viscoelasticity and the orientation
field. We demonstrate our method by characterizing how the viscoelastic
restoring force on a driven immersed object depends on various key parameters
as well as the tensorial character of the elastic response. We find that the
restoring force depends non-monotonically on the rate of diffusion of the
stress and the size of the object. We further show how the restoring force
depends on the relative orientation of the microscopic structure and the
pulling direction. These results imply that accounting for previously neglected
physical features, such as stress diffusion and the microscopic orientation
field, can improve the realism of viscoelastic simulations. We discuss possible
applications and extensions to the method.Comment: 17 pages, 11 figure
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