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

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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.