地点：科技楼南702

时间：2017年5月7日

1、8：30-10：00：开幕式

主持人：张平文

2、10：30-11：30：学术报告

报告题目：无理数与对称性

报告人：张平文（北京大学数学科学学院）

报告摘要：无理数和对称性都是数学研究的主要对象。本报告将介绍跟无理数相关的拟周期函数、概周期函数、丢番图逼近等概念，跟对称性相关的群论、周期格点、周期函数等概念。准晶是材料中一类特殊的晶体结构，具有旋转对称性，跟无理数本质相关，虽然数学界已有一些研究成果对认识准晶有帮助，但还远远不够，准晶必将引发更多更深刻的数学研究。

3、14：30-15：15：学术报告

报告题目：Mathematics in Data Science

报告人：许跃生（中山大学数学学院）

报告摘要：We shall discuss several mathematical problems crucial in data science. They include representation of data, mathematical models of recovering a fact from raw data, machining learning and solving optimization problems in data analysis.

4、15：15-16：00：学术报告

报告题目：High-Order Accurate Physical- Constraints- Preserving Schemes for Special Relativistic Hydrodynamics

报告人：汤华中(北京大学数学科学学院)

报告摘要：Relativistic hydrodynamics (RHD) plays an essential role in many fields of modern physics, e.g. astrophysics. Relativistic flows appear in numerous astrophysical phenomena from stellar to galactic scales, e.g. active galactic nuclei, super-luminal jets, core collapse super-novae, X-ray binaries, pulsars, coalescing neutron stars and black holes, micro-quasars, and gamma ray bursts, etc. The relativistic description of fluid dynamics should be taken into account if the local velocity of the flow is close to the light speed in vacuum or the local internal energy density is comparable (or larger) than the local rest mass density of the fluid. It should also be used whenever matter is influenced by large gravitational potentials, where the Einstein field theory of gravity has to be considered. The dynamics of the relativistic systems requires solving highly nonlinear equations and the analytic treatment of practical problems is extremely difficult. Hence, studying them numerically is the primary approach.

We develop high-order accurate physical- constraints- preserving finite difference WENO schemes for special relativistic hydrodynamical (RHD) equations, built on the local Lax-Friedrich splitting, the WENO reconstruction, the physical-constraints-preserving flux limiter, and the high order strong stability preserving time discretization. They are formal extensions of the existing positivity-preserving finite difference WENO schemes for the non-relativistic Euler equations. However, developing physical-constraints- preserving methods for the RHD system becomes much more difficult than the non-relativistic case because of the strongly coupling between the RHD equations, no explicit expressions of the conservative vector for the primitive variables and the flux vectors, and one more physical constraint for the fluid velocity in addition to the positivity of the rest-mass density and the pressure. The key is to prove the convexity and other properties of the admissible state set and discover a concave function with respect to the conservative vector replacing the pressure which is an important ingredient to enforce the positivity-preserving property for the non-relativistic case.

Several numerical examples are used to demonstrate accuracy, robustness, and effectiveness of the proposed physical-constraints-preserving schemes in solving relativistic problems with large Lorentz factor.

5、16：15-17：00：学术报告

报告题目：Why spectral methods are preferred in PDE eigenvalue computations in some cases?

报告人：张智民(中国工程物理研究院北京计算科学研究中心)

报告摘要：When approximating PDE eigenvalue problems by numerical methods such as finite difference and finite element, it is common knowledge that only a small portion of numerical eigenvalues are reliable. As a comparison, spectral methods may perform extremely well in some situation, especially for 1-D problems. In addition, we demonstrate that spectral methods can outperform traditional methods in 2-D problems even with singularities.

6、17：00-17：45：学术报告

报告题目：Global Entropy Solutions to Multi-Dimensional Isentropic Gas Dynamics with Spherical Symmetry

报告人：黄飞敏(中国科学院数学与系统科学研究院应用数学研究所)

报告摘要：In this talk,we will present our recent work on the multi-dimensional isentropic gas dynamics system with spherical symmetry.In this case,the system can be reduced to 1-d isentropicgas dynamics with geometric source terms, which have singularity at origin. We prove that if the gas initially move outgoing and the initial values decay to zero with some rates near origin, then there exists a global entropy solution to the 1d system. In particular, the original point is included and the density and velocity tend to zero with some rates near origin.