Nonlinear coarse-graining of Graphene nanoresonators: realistic boundary conditions and the origin ofnonlinear damping

该项目将为石墨烯纳米谐振器开发一个高效的仿真平台，即由单个分子组成的振荡系统，该系统是一个石墨原子层的横向夹持膜。为此，我们利用Mori-Zwanzig形式将计算代价高昂的原子分子动力学模型简化为具有几个相关自由度的模型，从而可以更有效地计算。在简化模型中，被丢弃的自由度作为振荡的波动和耗散（阻尼）。与之前的项目相比，本项目特别侧重于正确表示非线性和边界条件（夹紧）对作用于相关变量的波动力和耗散力形式的影响的挑战。考虑夹紧条件明确意味着考虑特定的衬底材料（铜，镍，硅等），石墨烯膜附着在哪里。非线性和夹紧条件对于正确预测谐振器的质量因子，即预测显著振动能量损失之前的时间至关重要。质量因子决定了谐振器测量原子质量、位移、频率、检测分子或用于频率滤波的精度。了解耗散的起源及其在原子尺度上的非线性，并将这些知识转化为简化的模型，将为共振特性的有效和直接的原子设计打开大门，例如最小化损耗，或将它们转移到非临界频率。

The project will develop a highly efficient simulation platform for Graphene nanoresonators, i.e., for oscillating systems consisting of a single molecule, which is a laterally clamped membrane of one atomic layer of Graphite. For this purpose we reduce the computationally expensive atomistic Molecular dynamics models by means of the Mori-Zwanzig formalism to models with a few relevant degrees of freedom, which can be computed more efficiently. The discarded degrees of freedom act in the reduced model as fluctuations and dissipation (damping) of the oscillations. In contrast to the previous project, this project focusses especially on the challenge to represent correctly the influence of the nonlinearities and of the boundary conditions (the clamping) on the form of the fluctuating and dissipative forces acting on the relevant variables. Considering the clamping conditions explicitly implies to take the specific substrate material (Copper, Nickel, Silicon, etc.) into account, where the Graphene membrane is attached. The nonlinearities and clamping conditions are essential for the correct prediction of the resonator's quality factor, i.e., the prediction of the time before significant loss of vibrational energy. The quality factor determines the precision of the resonator to measure atomic masses, displacements, frequencies, to detect molecules, or for frequency filtering. Understanding the origins of dissipation and of its nonlinearities on an atomic scale, and the transfer of this knowledge into a reduced model will open the door to an efficient and direct atomistic design of resonance properties, for example to minimise losses, or to shift them into uncritical frequencies.