项目编号：天元前沿论坛QY201804
会议时间：11月2日-4日
会议地点：西北大学太白校区非线性科学研究中心学术报告厅
会议介绍：国家天元数学西北中心天元前沿论坛“医学中的多相流体建模与分析”主要展示与交流近年来国内外多相流体建模与分析中的理论进展及其在医学等相关应用领域取得的科研成果，研讨相关的前沿科研问题；同时为偏微分方程、特别是流体力学理论与应用领域的科研、教学人员提供学术发展动态以及相互交流和学习的平台。
会议日程：
日期 |
主持人 |
时间 |
报告人 |
题目 |
11 月 2 日 |
桂贵龙 教授 （西北大学） |
14:30-14:40 |
开幕式 |
郭真华 教授 （西北大学） |
14:40: -15:20 |
于品 教授 （清华大学） |
从几何的观点看波动方程 |
15:20-16:00 |
何凌冰 教授 （清华大学） |
Global stability of large solutions to Compressible Navier-Stokes equations in the whole space
|
|
16:00-16:20 |
茶 歇 |
桂贵龙 教授 （西北大学） |
16:20-17:00 |
王学成 副教授 （清华大学） |
Global regularity and sharp decay estimates for the 3D Vlasov-Poisson system
|
17:00-17:40 |
杨诗武 助理教授 （北京大学） |
Global solutions for massive Maxwell-Klein-Gordon equations
|
日期 |
主持人 |
时间 |
报告人 |
题目 |
11 月 3 日 |
王俊刚 副教授 （西北工业大学） |
8:30-9:10 |
陈 曦 主治医师 （西京医院） |
超声联合多模式早期评估及预防骨科患者下肢深静脉血栓的价值研究 |
9:10-9:50 |
夏志明 教授 （西北大学） |
Jump information criterion for statistical inference in estimating discontinuous curves |
9:50-10:30 |
张 敏 讲师 （西北大学） |
计算机辅助诊断在医学影像诊断中的几种应用 |
|
10:30-10:50 |
茶 歇 |
夏志明 教授 （西北大学） |
10:50-11:30 |
王俊刚 副教授 （西北工业大学） |
三维空间分数阶方程的有限元方法 |
11:30-12:10 |
侯江勇 讲师 （西北大学） |
Stokes-dual-porosity model and finite element method for coupling dual-porosity flow and free flow |
下 午 |
姚磊 教授 （西北大学） |
14:30-15:10 |
臧爱彬 教授 （宜春学院） |
Some convergent results on incompressible flows in bounded domain |
15:10-15:50 |
赵继红 教授 （宝鸡文理） |
Well-posedness and Gevrey Regularity of the Generalized Keller-Segel System |
|
15:50-16:10 |
茶 歇 |
臧爱彬 教授 （宜春学院） |
16:10-16:50 |
李振邦 博士 （西安工业大学） |
Global well-posedness of the 2-D incompressible Navier-Stokes-Cahn-Hilliard system with a super-linear growth potential |
16:50-17:30 |
刘进静 博士 （西北大学） |
The existence and limit behavior of the shock layer for 1Dstationary compressible non-Newtonian fluid |
报告摘要
从几何的观点看波动方程
于品
（清华大学丘成桐数学科学中心）
yupin@mail.tsinghua.edu.cn
波的传播是自然界中最普通的现象,也是众多经典物理现象中物质演化和能量得以重新分配的基本机制，比如说电磁波、引力波或者可压缩流体中的某些激波。数学上，这些非线性波的传播通常可以用偏微分方程来刻画。这些方程差别很大，对应的物理现象也很不一样。然而，我们将解释它们背后都对应着统一的几何图象并且尝试解释如何用这种几何背景来研究相应的偏微分方程。
Global stability of large solutions to Compressible Navier-Stokes equations in the whole space
何凌冰
(清华大学数学科学系)
lbhe@math.tsinghua.edu.cn
In this talk, we are concerned with the global-in-time strong stability for CNS in the whole space. Assuming that the density is bounded in some Holder space, we first obtain that the solution will converge to its equilibrium with an explicit rate which as the same as that for the heat equation. Based on this new decay estimates, we prove the general global-in-time stability for CNS in the critical spaces. Finally to show that our theory has wide application, we construct some large solution to CNS which is beyond the close-to-equilibrium setting.
Global regularity and sharp decay estimates for the 3D Vlasov-Poisson system
王学成
(清华大学丘成桐数学科学中心)
xuecheng@math.princeton.edu
Based on a Fourier method, we prove small data global regularity for the $3D$ Vlasov-Poisson system for both the relativistic case and the non-relativistic case. Moreover, we obtain sharp decay estimates for the density of particles for both cases.
Global solutions for massive Maxwell-Klein-Gordon equations
杨诗武
(北京大学数学科学学院)
shiwuyang@math.pku.edu.cn
In this talk, I will introduce a new approach to study the asymptotic dynamics for massive Maxwell-Klein-Gordon equations, which is a coupled system of wave equation with massive Klein-Gordon equation. Due to the different decay mechanism of solutions of wave equation and Klein-Gordon equation, the traditional hyperboloid method can only treat compactly supported initial data. Our new approach in particular fits to the exterior region (outside of forward light cone) and can handle the full case. This is jointed work with S. Klainerman and Q. Wang.
超声联合多模式早期评估及预防骨科患者下肢深静脉血栓的价值研究
陈曦
(西京医院超声科)
chenxi851012@163.com
以往超声扫查下肢深静脉血栓形成早期时通过测量静脉内径及流速来评估静脉张力的变化。然而静脉内径测量易受呼吸、水肿软组织挤压等因素的影响，静脉流速测量受彩色取样框、取样线角度等因素的限制，上述方法对于评估静脉血栓形成早期静脉张力变化的准确度存在误差。利用静脉血管横截面积/周长这一指标评估血管张力变化在下肢深静脉血栓前期的应用中尚属探索阶段，本研究通过测量正常对照组、流速减低组、静脉血栓组3组双侧下肢股总静脉的横截面积值、管径周长值及二者比值，初步探讨静脉血管横截面积/周长比值评估血管张力变化的价值，为临床早期干预提供一定的参考依据。
方法：随机选择2014年6月—2015年4月我院骨科住院患者450例行超声检查。（150例正常患者；150例静脉流速减低者；150例静脉血栓形成者），入选标准：既往无下肢深静脉血管疾病者。男性294例，女性156例。年龄8—67岁；平均（36.8±11.0）岁。
全部患者按照静脉血栓的发展过程分为3组：正常对照组，流速减低组，血栓形成组；入选患者摆外旋外展位，超声检查使用日立公司HITACHI-Hi Vision Preirus超声诊断仪，线阵探头，频率4—12MHz；沿腹股沟区血管走行扫查双侧下肢股总静脉，压力标准：探头压力以股总静脉不发生形变为准，测量流速、横切面测量横截面积值、管径周长值及二者比值，股总静脉于中段测量（大隐静脉汇入处），流速减低标准：平均流速V<15cm/s。
组间定量资料采用单因素方差分析，P<0.05时有统计学差异。
结果：正常对照组：股总静脉横截面积均值：66.13±11.25mm2，管径周长均值：28.84±5.14mm，横截面积/周长比均值：2.65±0.34；流速减低组：股总静脉横截面积均值：94.82±12.57mm2，管径周长均值：32.49±4.73mm，横截面积/周长比均值：3.26±0.27；静脉血栓组：股总静脉横截面积均值：151.63±17.41mm2，管径周长均值：43.62±6.61mm，横截面积/周长比均值：3.94±0.53。
组间比较：股总静脉横截面积均值P（正常对照组与静脉血栓组）<0.05，有统计学差异；余组间P值均>0.05，无明显统计学差异；管径周长均值P（正常对照组与流速减低组）>0.05，无明显统计学差异；余组间P值均<0.05，有明显统计学差异；横截面积/周长比均值各组间P值均<0.05，有明显统计学差异。
随着静脉血栓病情的逐步迁延发展，股总静脉横截面积、管径周长值、二者比值逐步增大，静脉流速逐渐减低，横截面积/周长比值与病情严重程度呈正向发展，A/C比值评估DVT早期静脉张力变化的最佳截点值2.91，此时ROC曲线下面积为0.891，敏感度90.0%，特异性77.6%。
结论：静脉血管横截面积/周长指标测量静脉张力受干扰因素相对较少，将抽象静脉张力改变用具体数值量化表达，评估结果更稳定，为临床早期干预DVT发生提供新的思路方法和参考依据。
Jump information criterion for statistical inference in estimating discontinuous curves
夏志明
（西北大学）
statxzm@nwu.edu.cn
Nonparametric regression analysis when the regression function is discontinuous has broad applications. Existing methods for estimating a discontinuous regression curve usually assume that the number of jumps in the regression curve is known beforehand, which is unrealistic in certain cases. Although there is some existing research on estimation of a discontinuous regression curve when the number of jumps is unknown, this problem is still mostly open because such a research often requires assumptions on other related quantities such as a known minimum jump size. In this paper, we try to solve the problem by proposing a jump information criterion, which consists of a term measuring the fidelity of the estimated regression curve to the observed data and a penalty related to the number of jumps and jump sizes. Then, the number of jumps can be determined by minimizing our criterion.
计算机辅助诊断在医学影像诊断中的几种应用
张敏
(西北大学)
dr.zhangmin@xjtu.edu.cn
随着计算机技术的快速发展，计算机辅助诊断（computer-aided diagnosis, CAD）在医学上，特别是在医学影像诊断方面，应用日益广泛，逐渐成为医学诊断学中的研究热点之一。CAD技术可以自动提取图像特征并应用机器学习算法进行病变检出和诊断，目前已广泛应用于多种疾病的多模态影像图像的分析，从而提高医学影像检查的价值，近年来，CAD技术在牙周疾病以及眼底视网膜疾病的自动诊断和治疗中的应用，逐步受到关注，研究表明，CAD技术能够有效地应用于齿周病及视网膜病变中的分割、检测以及自动诊断，对于提高诊断准确率、减少漏诊能够起到积极的作用。
三维空间分数阶方程的有限元方法
王俊刚
(西北工业大学)
wangjungang@nwpu.edu.cn
随着对复杂系统研究和探索的深入, 人们发现复杂系统中的时间记忆效应, 动力学的幂律关系, 空间长程相关性等性质都会导出分数阶微分方程。所以分数阶微分方程的理论和算法越来越受到国内外学者的关注。 经过学者们的不断研究, 目前已经发展了很多求解分数阶微分方程的数值方法, 主要有有限差分法, 有限元法, 谱方法等。在整数阶微分方程的数值求解中, 有限元方法由于其适用复杂区域的特点而被广泛应用于工程实践。 然而, 由于分数阶算子的非局部性, 给有限元求解分数阶问题带来了困难。目前该方面的研究主要局限于一维, 二维区域, 并且以结构化网格为主。本文中我们主要讨论三维区域上空间分数阶微分方程的有限元方法。在算法方面, 我们主要讨论有限元刚度矩阵的组装, 因为有限元求解分数阶问题的主要困难在于分数阶刚度矩阵的组装。分数阶刚度矩阵的组装涉及分数阶积分路径搜索, 我们采用了称为ray-simplex intersection 的算法来提高搜索效率。另外, 我们也讨论了一些针对 MATLAB 实现有限元方法的优化技巧。 最后, 我们应用有限元方法分别求解了三维常/变系数稳态扩散方程和瞬态扩散方程, 数值结果很好的显示了我们算法的收敛性。
Stokes-dual-porosity model and finite element method for coupling dual-porosity flow and free flow
侯江勇
（西北大学）
jiangyonghou@nwu.edu.cn
We propose and numerically solve a new model considering confined flow in dual-porosity media coupled with free flow in embedded macro-fractures and conduits. Such situation arises, for example, for fluid flows in hydraulic fractured tight/shale oil/gas reservoirs. The flow in dual-porosity media, which consists of both matrix and micro-fractures, is described by a dual-porosity model. And the flow in the macro-fractures and conduits is governed by the Stokes equation. Then the two models are coupled through four physically valid interface conditions on the interface between dual-porosity media and macro-fractures/conduits, which play a key role in a physically faithful simulation with high accuracy. All the four interface conditions are constructed based on fundamental properties of the traditional dual-porosity model and the well-known Stokes-Darcy model. The weak formulation is derived for the proposed model and the well-posedness of the model is analyzed. A finite element semi-discretization in space is presented based on the weak formulation and four different schemes are then utilized for the full discretization. Some numerical experiments are presented to validate the proposed model and demonstrate the features of both the model and numerical method, such as the optimal convergence rate of the numerical solution, the detail flow characteristics around macro-fractures and conduits, and the applicability to the real world problems.
Some convergent results on incompressible flows in bounded domain
臧爱彬
(宜春学院)
abzang@jxycu.edu.cn
In this talk, I will present convergent results for Navier-Stokes equations to Euler equations as vanishing viscosity, and Euler- alpha equations converges to Euler equations as alpha goes to zero, respectively.
Well-posedness and Gevrey Regularity of the Generalized Keller-Segel System
赵继红
（宝鸡文理学院&西北农林科技大学）
jihzhao@163.com
In this talk, we are mainly concerned about the well-posedness and Gevrey regularity of the generalized Keller-Segel system with the cell diffusion being ruled by fractional diffusion:
Global well-posedness of the 2-D incompressible Navier-Stokes-Cahn-Hilliard system with a super-linear growth potential
李振邦
（西安工业大学&西北大学）
lizbmath@nwu.edu.cn
This work would focus on the subject of the 2-D incompressible Navier-Stokes-Cahn-Hilliard (NS-CH) system with a super-linear growth potential. Due to lack of the maximum principle for the convective Cahn-Hilliard equation (as a fourth-order parabolic equation), we use basic energy estimates and sobolev embedding to get the norm \|u\|_{L^\infty}. Based on these, we prove the global well-posedness of the 2-D NS-CH equations with bounded domains by using energy estimates and the Logarithmic Sobolev inequality.
The existence and limit behavior of the shock layer for 1D
stationary compressible non-Newtonian fluid
刘进静
(西北大学)
ljj124121@126.com
In this paper, we first define the shock layer to a class of stationary compressible non-Newtonian fluids in one dimension. Then the existence and uniqueness of the shock layer are established. In addition, the limit behavior of the shock layer are analyzed. It is shown that, as the viscosity coefficient and the heat conductivity coefficient vanish, the shock layer to the non-Newtonian fluids tends to a shock wave of the corresponding Euler equations. It is also shown that, as the viscosity coefficient tends to zero,the shock layer goes to a non-viscous shock layer to the non-Newtonian fluids, while as heat-conductivity coefficient tends to zero, the shock layer converges to a thermally non-conducting shock layer to the non-Newtonian fluids.
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