中國(guó)科學(xué)院數(shù)學(xué)與系統(tǒng)科學(xué)研究院明平兵教授作了題為在多尺度建模中的的關(guān)鍵問(wèn)題和固體中的方法的講座，明平兵教授主要的研究方向是固體的數(shù)學(xué)理論及計(jì)算，多尺度模型及模擬，下面是在職研究生講座的主要內(nèi)容：

　　多尺度建模與仿真已經(jīng)近二十年一直很受歡迎，在許多領(lǐng)域。我會(huì)在多尺度建模和仿真討論幾個(gè)關(guān)鍵問(wèn)題，特別是結(jié)晶固體�？挛� - Born準(zhǔn)則和準(zhǔn)連續(xù)體方法作為展示柜。前者是原子論模型和結(jié)晶固體的連續(xù)力學(xué)模型之間的橋，而后者則是用于模擬的彈性變形的結(jié)晶固體的最流行的多尺度方法中。在一方面，我們將討論柯西 - Born準(zhǔn)則的有效性和準(zhǔn)連續(xù)體方法在經(jīng)典的數(shù)值分析框架的準(zhǔn)確性。在另一方面，我們也將討論經(jīng)典的數(shù)值分析框架的限制，當(dāng)應(yīng)用到多尺度建模。

　　明平兵教授的主要成果有：對(duì)Cauchy-Born該準(zhǔn)則作了較為徹底的研究，該準(zhǔn)則是連接固體物理和固體力學(xué)的橋梁。建立了一些成熟的多尺度方法的數(shù)學(xué)理論，如提出了擬連續(xù)體方法的收斂性框架并對(duì)一維問(wèn)題作了徹底的分析;對(duì)橢圓及拋物均勻化問(wèn)題的異質(zhì)多尺度方法做了完整系統(tǒng)的分析。利用第一原理計(jì)算方法預(yù)測(cè)了石墨烯的理想強(qiáng)度，先于實(shí)驗(yàn)并與實(shí)驗(yàn)結(jié)果非常吻合，從而證實(shí)了石墨烯是目前人類(lèi)已知的最為牢固的材料。

　　原文：Multiscale modeling and simulation have been quite popular in many fileds for almost two decades. I will discuss several critical issues in multiscale modeling and simulation, in particluar for crystalline solids. Cauchy-Born rule and quasicontinuum method are used as showcases. The former is the bridge between the atomistic model and the continuum mechanics model of crystalline solids, while the latter is among the most popular multiscale method for modeling the elastically deformation of the crystalline solids. On the one hand, we shall discuss the validity of Cauchy-Born rule and the accuracy of quasicontinuum method in the framework of the classical numerical analysis. On the other hand, we shall also discuss the limitation of the classical numerical analysis framework when applied to multiscale modeling.