Distributed and boundary optimal control of the Allen–Cahn equation with regular potential and dynamic boundary conditions

This paper is concerned with an optimal control problem (P) (both distributed control as well as boundary control) for the nonlinear phase-field (Allen–Cahn) equation, involving a regular potential and dynamic boundary condition. A family of approximate optimal control problems (P^?) is introduced and results for the existence of an optimal control for problems (P) and (P^?) are proven. Furthermore, the convergence result of the optimal solution of problem (P^?) to the optimal solution of problem (P) is proved. Besides the existence of an optimal control in problem (P^?), necessary optimality conditions (Pontryagin's principle) as well as a conceptual gradient-type algorithm to approximate the optimal control, were established in the end.     

Kinetic boundary conditions for vapor–gas binary mixture

Using molecular dynamics simulations, the present study investigated the precise characteristics of the binary mixture of condensable gas (vapor) and non-condensable gas (NC gas) molecules creating kinetic boundary conditions (KBCs) at a gas–liquid interface in equilibrium. We counted the molecules utilizing the improved two-boundary method proposed in previous studies by Kobayashi et al. (Heat Mass Trans 52:1851–1859, 2016. doi: 10.1007/s00231-015-1700-6). In this study, we employed Ar for the vapor molecules, and Ne for the NC gas molecules. The present method allowed us to count easily the evaporating, condensing, degassing, dissolving, and reflecting molecules in order to investigate the detailed motion of the molecules, and also to evaluate the velocity distribution function of the KBCs at the interface. Our results showed that the evaporation and condensation coefficients for vapor and NC gas molecules decrease with the increase in the molar fraction of the NC gas molecules in the liquid. We also found that the KBCs can be specified as a function of the molar fraction and liquid temperature. Furthermore, we discussed the method to construct the KBCs of vapor and NC gas molecules.     

Corner block list representation and its application with boundary constraints

Floorplanning is a critical phase in physical design of VLSI circuits. The stochastic optimization method is widely used to handle this NP-hard problem. The key to the floorplanning algorithm based on stochastic optimization is to encode the floorplan structure properly. In this paper, corner block list (CBL)-a new efficient topological representation for non-slicing floorplan-is proposed with applications to VLSI floorplan. Given a corner block list, it takes only linear time to construct the floorplan. In floorplanning of typical VLSI design, some blocks are required to satisfy some constraints in the final packing. Boundary constraint is one kind of those constraints to pack some blocks along the pre-specified boundaries of the final chip so that the blocks are easier to be connected to certain I/O pads. We implement the boundary constraint algorithm for general floorplan by extending CBL. Our contribution is to find the necessary and sufficient characterization of the blocks along the boundary repre     

Local stabilization of the Burgers–Fisher equation via boundary control

Locally exponential stabilization for the Burgers–Fisher system is addressed by boundary control in this paper. For the nonlinear partial differential equation, a linear boundary feedback control law is applied to control the Burgers–Fisher system. Locally exponential stabilization of the closed loop system is established based on the relationship between operator theories and relations of different norms. Finally, the theory is validated through numerical simulations.     

Bridging digital boundary in healthcare systems — An interoperability enactment perspective

Researches indicated that interoperability promotes the enabling of information transparency and data fluidity for collaborating healthcare system enterprises, but due to issues of data ownership, distributed IT governance and cyber-security, valuable data continue to be isolated by intangible digital boundaries among healthcare institutions. That is, most existing institutional arrangements, organizational structures, and management processes do not support the required level of cross-boundary collaboration, trust, and attention to privacy. As data or information exchange involves an organization change process, it appears vital to enhance the interactions and participation of stakeholders within the healthcare systems. This study argues that an enactment model, which comprises both cognition and action, often leads to stakeholder commitments for facilitating change, is able to address the required level of institutional cross-boundary collaboration in healthcare.     

Galerkin–Legendre spectral method for Neumann boundary value problems in three dimensions

In this paper, we investigate the Legendre spectral methods for problems with the essential imposition of Neumann boundary condition in three dimensions. A double diagonalization process has been employed, instead of the full stiffness matrices encountered in the classical variational formulation of the problem with a weak natural imposition of Neumann boundary condition. For analysing numerical errors, some results on Legendre orthogonal approximation in Jacobi weighted Sobolev space are established. As examples of applications, the spectral schemes are provided for two model problems. The convergences of the proposed schemes are proved, too. Numerical results demonstrate the spectral accuracy in space, and which confirm theoretical analysis well.     

Delay-independent stability of stochastic reaction–diffusion neural networks with Dirichlet boundary conditions

This paper deals with the problem of global stability of stochastic reaction–diffusion recurrent neural networks with continuously distributed delays and Dirichlet boundary conditions. The influence of diffusion, noise and continuously distributed delays upon the stability of the concerned system is discussed. New stability conditions are presented by using of Lyapunov method, inequality techniques and stochastic analysis. Under these sufficient conditions, globally exponential stability in the mean square holds, regardless of system delays. The proposed results extend those in the earlier literature and are easier to verify.     

Optimal boundary control of coupled parabolic PDE–ODE systems using infinite-dimensional representation

The optimal boundary control problem is studied for coupled parabolic PDE–ODE systems. The linear quadratic method is used and exploits an infinite-dimensional state-space representation of the coupled PDE–ODE system. Linearization of the nonlinear system is established around a steady-state profile. Using appropriate state transformations, the linearized system has been formulated as a well-posed infinite-dimensional system with bounded input and output operators. It has been shown that the resulting system is a Riesz spectral system. The linear quadratic control problem has been solved using the corresponding Riccati equation and the solution of the corresponding eigenvalue problem. The results were applied to the case study of a catalytic cracking reactor with catalyst deactivation. Numerical simulations are performed to illustrate the performance of the proposed controller.     

Digital at the edge – antecedents and performance effects of boundary resource deployment

With business ecosystems digitalizing by the force of digital innovation, the deployment of boundary resources (such as application programming interfaces: APIs) becomes a strategic option across contexts. We distinguish between boundary resources that provide access openness and those that provide resource openness, and theorize the antecedents and consequences of their deployment. Employing panel data regressions to a longitudinal cross-industry dataset, we find that the digital knowledge base of the focal firm and the existence of potential digital complementors drive boundary resource deployment. Such deployment benefits firm performance depending on the firm’s market power. From our empirical analysis, we reveal a differentiated perspective on the quality of the confined openness provided by boundary resources as well as the embeddedness of their deployment in the rationales and motivations of the associated actors in digital business ecosystems. We complement the existent theoretical framework on boundary resources and provide valuable insights to managers reflecting about deploying boundary resources in a beneficial way.     

A lattice Boltzmann based implicit immersed boundary method for fluid–structure interaction

The immersed boundary method is a practical and effective method for fluid–structure interaction problems. It has been applied to a variety of problems. Most of the time-stepping schemes used in the method are explicit, which suffer a drawback in terms of stability and restriction on the time step. We propose a lattice Boltzmann based implicit immersed boundary method where the immersed boundary force is computed at the unknown configuration of the structure at each time step. The fully nonlinear algebraic system resulting from discretizations is solved by an Inexact Newton–Krylov method in a Jacobian-free manner. The test problem of a flexible filament in a flowing viscous fluid is considered. Numerical results show that the proposed implicit immersed boundary method is much more stable with larger time steps and significantly outperforms the explicit version in terms of computational cost.     

A Newton method for Bernoulli’s free boundary problem in three dimensions

Summary The present paper is dedicated to the numerical solution of Bernoulli’s free boundary problem in three dimensions. We reformulate the given free boundary problem as a shape optimization problem and compute the shape gradient and Hessian of the given shape functional. To approximate the shape problem we apply a Ritz–Galerkin discretization. The necessary optimality condition is resolved by Newton’s method. All information of the state equation, required for the optimization algorithm, are derived by boundary integral equations which we solve numerically by a fast wavelet Galerkin scheme. Numerical results confirm that the proposed Newton method yields an efficient algorithm to treat the considered class of problems.      

On boundary feedback stabilization of Timoshenko beam with rotor inertia at the tip

The feedback stabilization problem of a nonuniform Timoshenko beam system with rotor inertia at the tip of the beam is studied. First, as a special kind of linear boundary force feedback and moment control is applied to the beam‘ s tip, the strict mathematical treatment, a suitable state Hilbert space is chosen, and the well-poseness of the corresponding closed loop system is proved by using the semigroup theory of bounded linear operators. Then the energy corresponding to the closed loop system is shown to be exponentially stable. Finally, in the special case of umform beam, some sufficient and necessary conditions for the corresponding closed loop system to be asymptotically stable are derived.     

Adomian decomposition method with Green’s function for sixth-order boundary value problems

In this paper, the Adomian decomposition method with Green’s function is applied to solve linear and nonlinear sixth-order boundary value problems. The numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the decomposition method is of high accuracy, more convenient and efficient for solving high-order boundary value problems.     

Feedback stabilisation of an Euler–Bernoulli beam with the boundary time-delay disturbance

In this paper, we consider the feedback stabilisation of an Euler–Bernoulli beam with the boundary time-delay disturbance. Due to unknown time-delay coefficient, the system might be exponentially increasing at the lack of control. We design the feedback control law based on Lyapunov function method. Different from usual use of Lyapunov function method, our approach is to combine the construction of Lyapunov functionals with the controller design, which will guarantee the system energy function decays exponentially. In this procedure, we deduce the inequality equations satisfied by the system parameters. We prove the well-posedness of the corresponding closed-loop system by using semigroup theory and the inequality equations are solvable. Moreover, the exponential decay rate of the system is estimated. In addition, some numerical simulations are also presented to support the obtained results.     

Stabilization of the Euler–Bernoulli equation via boundary connection with heat equation

In this paper, we are concerned with the stabilization of a coupled system of Euler–Bernoulli beam or plate with heat equation, where the heat equation (or vice versa the beam equation) is considered as the controller of the whole system. The dissipative damping is produced in the heat equation via the boundary connections only. The one-dimensional problem is thoroughly studied by Riesz basis approach: The closed-loop system is showed to be a Riesz spectral system and the spectrum-determined growth condition holds. As the consequences, the boundary connections with dissipation only in heat equation can stabilize exponentially the whole system, and the solution of the system has the Gevrey regularity. The exponential stability is proved for a two dimensional system with additional dissipation in the boundary of the plate part. The study gives rise to a different design in control of distributed parameter systems through weak connections with subsystems where the controls are imposed.