The Algorithm for Langevin Equation and Phonon Transport in Low Dimensional Systems

本文第一章介绍了用双色根树图数值求解随机微分方程的方法，并将该方法应用到Langevin方程的情形下，提出了精度为o(7，4.5)的Langevin方程数值算法，从而提高了数值积分求解Langevin方程的精度。为了验证我们这套算法的可行性和普适性，我们给出了四个实例。第一、二个例子使用我们的算法计算了双势阱中的能量驰豫和倾斜Smoluchowski-Feynman棘轮中的粒子流和外力的关系，第三、四个例子我们数值积分了含时Langevin方程和多Langevin方程。我们将我们的算法与Euler算法、Heun算法分别进行了比较，发现在保证计算精度的前提下，这两套算法的最大积分步幅分别为0.0...Chapter 1 of this thesis introduces the numerical algorithm for stochastic differential equation by Bicolour Rooted Tree method, and then applies this method to Langevin equation. We propose an algorithm for Langevin equation and improve the accuracy to order o(7,4.5). To demonstrate the validity and universality of our algorithm, we give four examples. In the first and second examples, we c...学位：理学硕士院系专业：物理与机电工程学院物理学系_理论物理学号：1982007115232

表面电性可控磁珠微流控芯片在DNA提取中的应用

制备了表面电性可控的氨基化SiO2@Fe3O4磁性复合微球,采用激光刻蚀和热压键合的方法制作了聚甲基丙烯酸甲酯（PMMA）材质的DNA固相萃取芯片,将磁珠灌注于芯片通道中,借助永磁铁固定并控制磁珠,将磁珠芯片应用于人类全血中的基因组DNA提取,优化了提取实验条件,并对提取产物进行凝胶电泳和PCR分析。实验结果表明,磁珠微流控芯片成功地从全血中提取出纯度较高的基因组DNA,提取效率约35%,提取液的凝胶电泳条带与商品化试剂盒提取的基因组DNA一致,提取液可用于进一步的PCR反应。国家星火计划项目(No.2015GA721002);;黄土与第四纪地质国家重点实验室开放基金(No.SKLLQG1607);;福建省中青年教师科技计划项目(No.JAT170817)资助~

Phonon Spectrum of Graphene

石墨烯的成功制备是纳米材料研究的重大进展。人们发现其具有很高的热导率,从而为解决计算机芯片散热问题提供了一条可能的方案。文章主要应用动力学矩阵的方法,计算了TErSOff势下石墨烯的声子谱,并探讨了该势在研究石墨烯热学性质方面的合理性。通过与实验数据的比较,我们发现,使用TErSOff势得到的声子谱在高对称点处的能量误差最大可以达到70%。因此,TErSOff势不适合于对石墨烯的热学性质进行定量的研究。Discovery of graphene is a breakthrough in the field of nanomaterials.People find that the thermal conductivity of graphene is extremely high so that it provides a possible way to solve the heat sink of computer chip.In this paper,we use the dynamic matrix method to calculate the phonon spectrum of Tersoff potential of graphene and discuss the feasibility of Tersoff potential in the aspect of studying the thermal properties of graphene.By means of comparing our phonon spectrum with experiments,we find that the maximum energy error of our spectrum at the points of high symmetry is 70%.Therefore,Tersoff potential is not a good choice in studying the thermal properties of graphene quantitatively