ON DECOMPOSITION METHOD FOR ACOUSTIC WAVE SCATTERING BY MULTIPLE OBSTACLES

Consider acoustic wave scattering by multiple obstacles with different sound properties on the boundary, which can be modeled by a mixed boundary value problem for the Helmholtz equation in frequency domain. Compared with the standard scattering problem for one obstacle, the difficulty of such a new problem is the interaction of scattered wave by different obstacles. A decomposition method for solving this multiple scattering problem is developed. Using the boundary integral equation method, we decompose the total scattered field into a sum of contributions by separated obstacles. Each contribution corresponds to scattering problem of single obstacle. However, all the single scattering problems are coupled via the boundary conditions, representing the physical interaction of scattered wave by different obstacles. We prove the feasibility of such a decomposition. To compute these contributions efficiently, an iteration algorithm of Jacobi type is proposed, decoupling the interaction of scattered wave from the numerical points of view. Under the well-separation assumptions on multiple obstacles, we prove the convergence of iteration sequence generated by the Jacobi algorithm, and give the error estimate between exact scattered wave and the iteration solution in terms of the obstacle size and the minimal distance of multiple obstacles. Such a quantitative description reveals the essences of wave scattering by multiple obstacles. Numerical examples showing the accuracy and convergence of our method are presented.

On a Hybrid Approach for Recovering Multiple Obstacles

In this paper,a hybrid approach which combines linear sampling method and the Bayesian method is proposed to simultaneously reconstruct multiple obsta-cles.The number of obstacles and the approximate geometric information arefirst qualitatively obtained by the linear sampling method.Based on the reconstructions of the linear sampling method,the Bayesian method is employed to obtain more refined details of the obstacles.The well-posedness of the posterior distribution is proved by using the Hellinger metric.The Markov Chain Monte Carlo algorithm is proposed to explore the posterior density with the initial guesses provided by the linear sampling method.Numerical experiments are provided to testify the effectiveness and efficiency of the proposed method.

Advanced delivery strategies facilitating oral absorption of heparins

Heparins show great anticoagulant effect with few side effects,and are administered by subcutaneous or intravenous route in clinics.To improve patient compliance,oral administration is an alternative route.Nonetheless,oral administration of heparins still faces enormous challenges due to the multiple obstacles.This review briefly analyzes a series of barriers ranging from poorly physicochemical properties of heparins,to harsh biological barriers including gastrointestinal degradation and pre-systemic metabolism.Moreover,several approaches have been developed to overcome these obstacles,such as improving stability of heparins in the gastrointestinal tract,enhancing the intestinal epithelia permeability and facilitating lymphatic delivery of heparins.Overall,this review aims to provide insights concerning advanced delivery strategies facilitating oral absorption of heparins.