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D. Platz, D. Forchheimer, U. Schmid, J. E. Sader, D. Haviland:
"Reconstructing Nonlinear Interactions in Micro- and Nanosystems with the Numerical Kernel Estimate Method";
Talk: ICoNSoM 2019 - International Conference on Nonlinear Solid Mechanics, Rom, I; 06-20-2019 - 06-23-2019; in: "International Conference on Nonlinear Solid Mechanics", (2019), 1.

Nonlinearity plays a prominent role in micro- and nanosystems. On the one hand intrinsic nonlinearities become dominant as miniaturization proceeds. For the development of novel devices such as graphene-based nanoelectromechanical systems, it is thus important to characterize and understand intrinsic nonlinearities. On the other hand, in measurement applications the physical quantity of interest often manifests itself in a nonlinear interaction with a micro- or nanosensor. Often nonlinearity is indirectly characterized by a measurement of oscillatory motion of a micro- and nanosystem. However, it is generally not well understood how information about the nonlinearity can be extracted from the measured data. Here, we present a method for characterizing nonlinearity from measured periodic motion of a micro- and nanosystem. We analyze the motion in the Fourier domain and show that the spectral frequency components can be interpreted as spatially weighted averages of the nonlinearity. The corresponding weighting kernels can often not be determined analytically. We introduce a method, called numerical kernel estimate (NKE), for numerically approximating the weighting kernels which allows for a rigorous analysis of the information content of a measurement. We demonstrate this information analysis by studying the NKE kernels for several multifrequency atomic force microscopy (AFM) imaging modes. Using this analysis we show how in measured data long-range force can be separated from short-range force with unprecedented ease. What is more, we can reconstruct quantitatively the tip-sample interaction from measured AFM data as shown in figure 1. We anticipate that NKE will be beneficial not only in measurement applications such as AFM but also in characterization of intrinsic nonlinearities of micro- and nanosystems and pave the way for a deep understanding of nonlinear micro- and nanosystems.