Surrogate-based modeling and dimension reduction techniques for multi-scale mechanics problems

Successful modeling and/or design of engineering systems often requires one to address the impact of multiple "design variables" on the prescribed outcome.There are often multiple,competing objectives based on which we assess the outcome of optimization.Since accurate,high fidelity models are typically time consuming and computationally expensive,comprehensive evaluations can be conducted only if an efficient framework is available.Furthermore,informed decisions of the model/hardware’s overall performance rely on an adequate understanding of the global,not local,sensitivity of the individual design variables on the objectives.The surrogate-based approach,which involves approximating the objectives as continuous functions of design variables from limited data,offers a rational framework to reduce the number of important input variables,i.e.,the dimension of a design or modeling space.In this paper,we review the fundamental issues that arise in surrogate-based analysis and optimization,highlighting concepts,methods,techniques,as well as modeling implications for mechanics problems.To aid the discussions of the issues involved,we summarize recent efforts in investigating cryogenic cavitating flows,active flow control based on dielectric barrier discharge concepts,and lithium(Li)-ion batteries.It is also stressed that many multi-scale mechanics problems can naturally benefit from the surrogate approach for "scale bridging."     

周期性点阵桁架材料力学性能分析的一种新的多尺度计算方法

论文提出一种周期性点阵桁架材料力学性能分析的新的多尺度方法.方法的主要思想是通过数值构造能反映周期性桁架材料单胞内部非均质性的多尺度基函数,从而在大尺度上求得单胞的等效刚度阵,大大减小了模型计算量.通过引入基函数的耦合附加项,以考虑多维矢量场问题不同方向问的耦合作用.数值研究表明,采用线性边界条件构造基函数有时会产生较...     

Networks Emerging from the Competition of Pullulation and Decrepitude

In real-world network evolution, the aging effect is universal. We propose a microscopic model for aging networks,which suggests that the activity of a vertex is the result of the competition of two factors: pullulatlon and decrepitude. By incorporating the pullulation factor into previous models of aging networks, both the global and individual aging effect curves in our model are single peaked, which agrees with the empirical data well. This model can generate networks with scale-free degree distribution, large clustering coefficient and small average distance when the decrepitude intensity is small and the network size not very large. The results of our model show that pullulation may be one of the most important factors affecting the structure and function of aging networks and should not be neglected at all.     

近场光学显微镜观察到纳米尺度的折射率变化

日本京都大学研究人员用近场光学显微镜(ＮＳＯＭ)在透明的聚合物膜上制作了纳米尺度的折射率图样 ,而薄膜的透明度及表面形态均未受到严重影响 .实验中用的是 3μｍ厚的聚合物薄膜 ,它是用自转镀层法在甲苯溶液中把在聚合物 (异丁烯酸甲脂ｍｅｔｈｙｌｍｅｔｈａｃｒｙｌａｔｅ)中掺杂的 3 苯基 2 ,5 诺卜拿丁 2羧酸 (3 ｐｈｅｎｙｌ 2 ,5 ｎｏｒｂｏｒｎａｄｉｅｎｅ 2 ｃａｒｂｏｘｙｌｉｃａｃｉｄ)镀到盖板玻璃片上而成的 .折射率图样是用照明模式ＮＳＯＭ设备制作的 ,该设备具有一个剪切力尖端取样距离调节功能 ,以及一个锥形探…     

在离散多尺度分析框架下的数据分解和回复的数值特征(英)

本文在离散多尺度分析框架了讨论了关于给定数据的分解和回复过程的数值特征．它给出了数据分解和回复算法的一般设计原则，它能有效地解释在正交小波基和双正交小波基下的数据分解回复过程．据此设计原则，文中还给出了一种新的数据分解回复方法，它可以在线性分层基背景下得到解释．     

小周期型复合材料稳态热传导问题的一种双尺度渐近展开收敛性分析

给出一类具有某种对称性小周期复合材料稳态热传导问题解的渐近表示方法.区别于传统多尺度计算方法,将计算过程中需要求解的关于单胞Q的H_per¹(Q)周期边值问题改为齐次边值问题,这样数值方法求解时协调元空间容易构造;另一方面传统的多尺度渐近解不满足原始问题的边界条件,新构造的渐近形式不仅满足原始问题的物理边界条件,同时保持一定的收敛阶,更能被工程上所接受.     

DFP变尺度法与FR共轭梯度法的二次等价性

研究了求解无约束极值问题的DFP变尺度法和FR共轭梯度法的关系问题.证明了在应用于求解二次函数的极值问题时,若将初始尺度矩阵取为单位矩阵,二者实际上是等价的,即两种方法求出的极小化点列是相同的.     

Y. Meyer小波的一般形式

首先我们证明了，如果尺度函数有紧支集，来自多尺度分析的小波函数的支集形式，然后我们证明了Y．Meyer小波的尺度函的一般形式。最后给出了它的另外两种形式和对应的Y．Meyer小波。     

Weibull分布尺度参数的收缩估计

讨论了Ｗｅｉｂｕｌｌ分面尺度参数的收缩估计。在两种不同的参数先验信息场合，给出了不同的收缩估计。对以检验统计量函数形式给出的收缩系数进行了讨论，并用Ｍｉｏｎｔｅ－Ｃａｒｌｏ模拟方法研究了收缩估计的相对效。     

现代物理信息

 1.电子与μ子统用性的确证.新的分支比测量得到R_?=Γ（Π→ev+Π→evγ）/Γ（π→μv+Π→μvγ）=（1.2265±0.0034±0.0044）×10^-4.结果与标准模型一致.并在0.2％的精度内确证e-μ统用性的假设是成立的,（D.I.Britton et al.,No.20）2.低温下光子质量的上限.基于安培定律的零检验,给出了一个确定低温下光子质量m_r的新方法.测量的结果是,在1.24K时,m_r≤（8.4±0.8）×10^-46g.