Upcoming Talks

        Title: Babuska Problem in Composite Materials and Some Applications

        Time: 14:00-15:00. Friday, October 22, 2021.

        Location: 雁栖湖应用数学研究院1110，线上：Zoom Meeting ID: 361 038 6975, Passcode: BIMSA

        Speaker: 李海刚 （北京师范大学）

        Abstract:  In high-contrast fiber-reinforced composite materials, the stress concentration between two adjacent inclusions is a common phenomenon, which always causes damage initiation. For the original problem proposed by Ivo Babuska concerning the system of linear elasticity, we develop an iteration technique with respect to the energy integral to overcome the difficulty from the lack of maximal principle in PDE theory and obtain the blow-up asymptotic expressions of the gradients of solutions to the Lame system with partially infinite coefficients in the narrow region between inclusions when they are close to touch. Our results hold for convex inclusions with arbitrary shape and in all dimensions. As an application, we recently proved an extended Flaherty-Keller formula on the effective elastic property of a periodic composite with densely packed fibers, which is related to the “Vigdergauz microstructure” in the shape optimizition of fibers. On the other hand, we recently applied our results to deal with the resonant behavior between two close-to-touching convex acoustic subwavelength resonators.

        About the speaker: 李海刚，北京师范大学教授、博士生导师，主要从事材料科学中的偏微分方程理论研究。在复合材料中的Babuska问题及其相关领域做出一系列深刻原创成果，在Adv. Math.、ARMA、JMPA、JFA等杂志发表论文30余篇。2016年获得教育部霍英东青年教师基金，2018年获得教育部自然科学二等奖，2020年入选教育部长江学者奖励计划青年学者。

        Title:Global solutions of 2D isentropic compressible Navier-Stokes equations with one slow variable

        Time: 14:00-15:00. Friday, October 29, 2021.

        Location: 雁栖湖应用数学研究院1110，线上：Zoom Meeting ID: 361 038 6975, Passcode: BIMSA

        Speaker: 吕勇 （南京大学）

        Abstract: We prove the global existence of solutions to the two-dimensional isentropic compressible Navier-Stokes equations with smooth initial data which is slowly varying in one direction and with initial density being away from vacuum. In particular, we present examples of initial data which generate unique global smooth solutions to  2D compressible Navier-Stokes equations with constant viscosity and with initial data which are neither small perturbation of constant state nor of small energy. This talk is based on a joint paper with P. Zhang (AMSS)

        Title: TBA

        Time: 15:00-16:00. Friday, November 12, 2021.

        Location: 雁栖湖应用数学研究院1110，线上：Zoom Meeting ID: 361 038 6975, Passcode: BIMSA

        Speaker: Florian Feppon （ETH Zürich）

        Abstract: TBA

        Title: TBA

        Time: 14:00-15:00. Friday, November 19, 2021.

        Location: 雁栖湖应用数学研究院1110，线上：Zoom Meeting ID: 361 038 6975, Passcode: BIMSA

        Speaker: 张镭 （上海交通大学）

        Abstract: TBA

        Title: TBA

        Time: 15:00-16:00. Friday, November 19, 2021.

        Location: 雁栖湖应用数学研究院1110，线上：Zoom Meeting ID: 361 038 6975, Passcode: BIMSA

        Speaker: 耿俊 （兰州大学）

        Abstract: TBA

        Title: A Semilinear Interface Problem Arising from Population Genetics

        Time: 14:00-15:00. Friday, November 26, 2021.

        Location: 雁栖湖应用数学研究院1110，线上：Zoom Meeting ID: 361 038 6975, Passcode: BIMSA

        Speaker: 苏琳琳 （南方科技大学）

        Abstract: We study a semilinear parabolic problem that models the evolution of gene frequencies under the joint action of migration and selection with a geographical barrier. The barrier locates at an embedded interface and is of Kedem-Katchalsky type. Our main goal is to investigate the effects of the barrier on the global dynamics and on the existence, stability, and profile of spatially nonconstant equilibria. 

        Title: 多组分渗流数值模拟开源软件开发

        Time: 15:00-16:00. Friday, November 26, 2021.

        Location: 雁栖湖应用数学研究院1110，线上：Zoom Meeting ID: 361 038 6975, Passcode: BIMSA

        Speaker: 张晨松（中科院数学与系统科学研究院）

        Abstract: 由于油气资源的成分复杂，油藏工程师在描述原油的性质时，需要使用不同的数学模型。除了常用的黑油模型之外，还有多种组分模型，如常平衡系数K模型、EOS状态方程组分模型等。一些复杂的驱油技术常基于组分模型的框架来进行数值模拟，例如聚合物驱油剂、表面活化剂驱油剂、碱驱油剂、微生物驱油剂、低盐度水驱等。一些在多孔介质中的流体运动，如二氧化碳的埋藏、地下水污染的处理、地热资源的开采等，也可使用组分模型来模拟。这些重要的应用使得组分模型逐渐成为油藏数值模拟的一个重要研究方向，但组分模型求解变量多、方程复杂，计算工作量也更大。我们基于一个通用组分模型框架，面向并行计算机体系结构，来构建快速求解方法及其开源软件平台。我们将讨论多组分渗流力学的工业应用、物理背景、数学模型、离散方法、快速求解、并行计算及其软件开发。

        About the speaker: 张晨松，2002年获南京大学计算数学硕士学位，2007年获得美国马里兰大学应用数学博士学位，此后在宾州州立大学数学系从事博士后研究工作，于2011年进入中国科学院数学与系统科学研究院计算数学所，任副研究员。主要研究兴趣：自适应有限元方法、多层迭代法及其在流固耦合、油藏模拟等问题中的应用。2012年在第二十一届国际区域分解法会议（法国）做大会特邀报告，2013年在第16届全国流体力学数值方法会议做大会特邀报告。曾在Numer Math、SINUM、SIAM MMS、M3AS、JCP、Handbook of Numerical Analysis等国际一流期刊发表了多篇学术论文。

        Past Talks

        Title (题目): Homogenization of elliptic systems with multiscales

        Speaker: 钮维生 (安徽大学)

        Abstract (摘要): We review some quantitative results in the homogenization of second-order elliptic systems with periodic coefficientsthat oscillate on multiple separated scales. The results include convergence rates and some uniform regularity estimates we obtained recently.

        Meeting time (时间): 14:00-15:00, October 15, 2021.
Location (地点): 雁栖湖应用数学研究院1110
Online (线上): Zoom Meeting ID: 361 038 6975, Passcode: BIMSA