石墨烯是由一层碳原子通过共价键连接而形成的"膜"。石墨烯碳膜有明显的起伏，这种起伏是石墨烯的内禀性质，它使得石墨烯可以在室温下稳定存在。在一定的条件下石墨烯可以有不同的稳定的起伏状态，比如周期性的涟漪。为了从理论上研究石墨烯的起伏对石墨烯的性质的影响, 本项目计划发展膜的弹性理论，借助非平衡分子动力学模拟和Jarzynski等式，研究石墨烯涟漪的形成能，给出石墨烯涟漪形成能的简洁理论模型。再进一步研究外场如何影响石墨烯的起伏状态。最后本项目还将分析控制石墨烯起伏对实现石墨烯器件功能的意义。

Graphene is a carbon membrane formed by one layer of carbon atoms connected by covalent bonds. Undulations of membrane, which make the graphene stable at room temperature, is an intrinsic property of graphene. In particular, the formation of periodical ripple under certain conditions is one of the most attractive undulation phenomena. To theoretically understand the effect of undulations to the properties of graphene, we will develope the elastic theory of membrane for graphene, obtain the compact model of ripple's formation energy based on the results of non-equilibrium molecular dynamic simulations with the application of Jarzynski equality. We will also study how the external fields influence the undulations of graphene, as well as the physical implications of controllable undulations to the graphene devices.