Related papers: Optimal Control of Sliding Droplets using the Cont…
We consider a system that is exactly controllable. For given initial state, terminal state and objective function, an optimal control is often well-defined. Such an optimal control has the disadvantage that although it works perfectly well…
The moving-contact line between a fluid, liquid and a solid is a ubiquitous phenomenon, and determining the maximum speed at which a liquid can wet/dewet a solid is a practically important problem. Using continuum models, previous studies…
We propose an approach toward understanding the spin glass phase at zero and low temperature by studying the stability of a spin glass ground state against perturbations of a single coupling. After reviewing the concepts of flexibility,…
Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…
The fluid-mechanics community is currently divided in assessing the boundaries of applicability of the macroscopic approach to fluid mechanical problems. Can the dynamics of nano-droplets be described by the same macroscopic equations as…
We study the finite-horizon optimal control problem with quadratic functionals for an established fluid-structure interaction model. The coupled PDE system under investigation comprises a parabolic (the fluid) and a hyperbolic (the solid)…
When a droplet gently lands on an atomically smooth substrate, it will most likely contact the underlying surface in about 0.1 s. However, theoretical estimation from fluid mechanics predicts a contact time of 10 to 100 s. What causes this…
We consider a linear-quadratic pde constrained optimal control problem on an evolving surface with pointwise state constraints. We reformulate the optimization problem on a fixed surface and approximate the reformulated problem by a…
We study the interaction of a liquid drop with an elastic beam in the case where bending effects dominate. We use a variational approach to derive equilibrium equations for the system in the presence of gravity and in the presence or…
The relaxation dynamics of the contact angle between a viscous liquid and a smooth substrate is studied at the nanoscale. Through atomic force microscopy measurements of polystyrene nanostripes we monitor simultaneously the temporal…
Frictional forces are a key ingredient of any physical description of the macroscopic world, as they account for the phenomena causing transformation of mechanical energy into heat. They are ubiquitous in nature, and a wide range of…
We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely-many atoms. In particular, we show that this problem can be converted to…
We consider two minimal models of active fluid droplets that exhibit complex dynamics including steady motion, deformation, rotation and oscillating motion. First we consider a droplet with a concentration of active contractile matter…
The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…
In this paper, we present some properties of time optimal controls for linear ODEs with the ball-type control constraint. More precisely, for an optimal control, we build up an upper bound for the number of its switching points; show that…
The conventional no-slip boundary condition leads to a non-integrable stress singularity at a contact line. This is a main challenge in numerical simulations of two-phase flows with moving contact lines. We derive a two-dimensional…
We present an analysis and numerical study of an optimal control problem for the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs), which is a crucial component in modern technology. They exhibit long range orientational order…
This work is concerned with the time optimal control problem for evolution equations in Hilbert spaces. The attention is focused on the maximum principle for the time optimal controllers having the dimension smaller that of the state…
As opposed to the distributed control of parabolic PDE's, very few contributions currently exist pertaining to the Dirichlet boundary condition control for parabolic PDE's. This motivates our interest in the Dirichlet boundary condition…