Boundary Control of Coupled Nonlinear Three Dimensional Marine Risers

This paper presents a design of boundary controllers implemented at the top end for global stabilization of a marine riser in a three dimensional space under environmental loadings. Based on the energy approach, nonlinear partial differential equations of motion, including bending-bending and longitudinal-bending couplings for the risers are derived. The couplings cause mutual effects between the three independent directions in the riser＇s motions, and make it difficult to minimize its vibrations. The Lyapunov direct method is employed to design the boundary controller. It is shown that the proposed boundary controllers can effectively reduce the riser＇s vibration. Stability analysis of the closed-loop system is performed using the Lyapunov direct method. Numerical simulations illustrate the results.

THE COUPLING OF BOUNDARY ELEMENT AND FINITE ELEMENT METHODS FOR THE EXTERIOR NONSTATIONARY NAVIER-STOKES EQUATIONS

In this paper, we represent a new numerical method for solving the nonstationary Stokes equations in an unbounded domain. The technique consists in coupling the boundary integral and finite element methods. The variational formulation and well posedness of the coupling method are obtained. The convergence and optimal estimates for the approximation solution are provided.

A DUAL COUPLED METHOD FOR BOUNDARY VALUE PROBLEMS OF PDE WITH COEFFICIENTS OF SMALL PERIOD

In this paper the homogenization method is improved to develop one kind of dual coupled approximate method, which reflects both the macro-scope properties of whole structure and its loadings, and micro-scope configuration properties of composite materials. The boundary value problem of woven membrane is considered, the dual asymptotic expression of the exact solution is given, and its approximation and error estimation are discussed. Finally the numerical example shows the effectiveness of this dual coupled method.

Multidimensional modeling of the stenosed carotid artery: A novel CAD approach accompanied by an extensive lumped model

This study describes a multidimensional 3D/lumped parameter（LP） model which contains appropriate inflow/outflow boundary conditions in order to model the entire human arterial trees. A new extensive LP model of the entire arterial network（48 arteries） was developed including the effect of vessel diameter tapering and the parameterization of resistance, conductor and inductor variables. A computer aided-design（CAD） algorithm was proposed to effciently handle the coupling of two or more 3D models with the LP model, and substantially lessen the coupling processing time. Realistic boundary conditions and Navier-Stokes equations in healthy and stenosed models of carotid artery bifurcation（CAB） were used to investigate the unsteady Newtonian blood flow velocity distribution in the internal carotid artery（ICA）. The present simulation results agree well with previous experimental and numerical studies. The outcomes of a pure LP model and those of the coupled 3D healthy model were found to be nearly the same in both cases. Concerning the various analyzed 3D zones, the stenosis growth in the ICA was not found as a crucial factor in determining the absorbing boundary conditions.This paper demonstrates the advantages of coupling local and systemic models to comprehend physiological diseases of the cardiovascular system.

Exact Boundary Synchronization for a Coupled System of Wave Equations with Neumann Boundary Controls

In this paper, for a coupled system of wave equations with iNeumann boundary controls, the exact boundary synchronization is taken into consideration. Results are then extended to the case of synchronization by groups. Moreover, the determination of the state of synchronization by groups is discussed with details for the synchronization and for the synchronization by 3-groups, respectively.

THE COUPLING METHOD OF FINITE ELEMENTS AND BOUNDARY ELEMENTS FOR RADIATION PROBLEM

The paper presents the variational formulation and well posedness of the coupling method offinite elements and boundary elements for radiation problem. The convergence and optimal errorestimate for the approximate solution and numerical experiment are provided.

A New Method of Solving the Index Problem for Sturm-Liouville Eigenvalues

Based on some recent results for interlacing eigenvalue intervals from 1-parameter families of se- quences of eigenvalue inequalities, a new method is given to solving the index problem for Sturm-Liouville eigenvalues for coupled self-adjoint boundary conditions in the regular case. The key is a new characteristic principle for indices for Sturm-Liouville eigenvalues. The algorithm corresponding on the characteristic princi- ple are discussed, and numerical examples are presented to illustrate the theoretical results and show that the algorithm is valid.

ANALYSIS OF A NUMERICAL METHOD FOR RADIATIVE TRANSFER EQUATION BASED BIOLUMINESCENCE TOMOGRAPHY

In the bioluminescence tomography （BLT） problem, one constructs quantitatively the bioluminescence source distribution inside a small animal from optical signals detected on the animal＇s body surface. The BLT problem is ill-posed and often the Tikhonov regularization is used to obtain stable approximate solutions. In conventional Tikhonov regularization, it is crucial to choose a proper regularization parameter to balance the accuracy and stability of approximate solutions. In this paper, a parameter-dependent coupled complex boundary method （CCBM） based Tikhonov regularization is applied to the BLT problem governed by the radiative transfer equation （RTE）. By properly adjusting the parameter in the Robin boundary condition, we achieve one important property： the regularized solutions are uniformly stable with respect to the regularization parameter so that the regularization parameter can be chosen based solely on the consideration of the solution accuracy. The discrete-ordinate finite-element method is used to compute numerical solutions. Numerical results are provided to illustrate the performance of the proposed method.