应数学系郭玉坤副教授的邀请，东北师范大学数学与统计学院刁怀安副教授将于近日来访我校，并做两场学术讲座，报告内容涉及弹性波反散射、传输特征函数的几何应用等。以下是报告信息，欢迎感兴趣的师生参加。

报告1： Inverse elastic surface scattering with far-field data

时间：2018年11月18日（周日）下午15:00-16:00

地点：格物楼503报告厅

摘要：A rigorous mathematical model and an efficient computational method are proposed to solving the inverse elastic surface scattering problem which arises from the near-field imaging of periodic structures. We demonstrate how an enhanced resolution can be achieved by using more easily measurable far-field data. The surface is assumed to be a small and smooth perturbation of an elastically rigid plane. By placing a rectangular slab of a homogeneous and isotropic elastic medium with larger mass density above the surface, more propagating wave modes can be utilized from the far-field data which contributes to the reconstruction resolution. Requiring only a single illumination, the method begins with the far-to-near (FtN) field data conversion and utilizes the transformed field expansion to derive an analytic solution for the direct problem, which leads to an explicit inversion formula for the inverse problem. Moreover, a nonlinear correction scheme is developed to improve the accuracy of the reconstruction. Results show that the proposed method is capable of stably reconstructing surfaces with resolution controlled by the slab's density.

报告2：On the geometric structures of conductive transmission eigenfunctions and its application

时间：2018年11月20日（周二）上午10:00-11:00

地点：格物楼503报告厅

摘要：This talk is concerned with the intrinsic geometric structures of conductive transmission eigenfunctions. The geometric properties of interior transmission eigenfunctions were first studied in [Blåsten & Liu, JFA, 2017]. It is shown in two scenarios that the interior transmission eigenfunction must be locally vanishing near a corner of the domain with an interior angle less than $\pi$. We significantly extend and generalize those results in several aspects. First, we consider the conductive transmission eigenfunctions which include the interior transmission eigenfunctions as a special case. The geometric structures established for the conductive transmission eigenfunctions in this paper include the results in [Blåsten & Liu, JFA, 2017] as a special case. Second, the vanishing property of the conductive transmission eigenfunctions is established for any corner as long as its interior angle is not $\pi$. That means, as long as the corner singularity is not degenerate, the vanishing property holds. Third, the regularity requirements on the interior transmission eigenfunctions in [Blåsten & Liu, JFA, 2017] are significantly relaxed in the present study for the conductive transmission eigenfunctions. In order to establish the geometric properties for the conductive transmission eigenfunctions, we develop technically new methods and the corresponding analysis is much more complicated than that in [Blåsten & Liu, JFA, 2017]. Finally, as interesting and practical applications of the obtained geometric results, we establish a unique recovery result for the inverse scattering problem by a single far-field measurement in simultaneously determining a polygonal conductive obstacle and its surface conductivity.

报告人简介：刁怀安，博士毕业于香港城市大学数学系，现为东北师范大学数学与统计学院副教授。他的研究方向为数值代数与反散射问题。他已发表SCI论文30余篇；出版专著1部，曾主持国家自然科学基金青年基金项目1项，数学天元基金1项，教育部博士点新教师基金1项；曾赴德国汉堡工业大学，加拿大麦克马斯特大学，美国普渡大学，香港科技大学，香港浸会大学等高校进行交流访问与合作研究。据Web of Science显示他的单篇论文最高被引用51次。