Using higher-order statistics to infer random forces driving a nano sensor

Abstract

Cantilever-based nanosensors are increasingly be- ing used as gas and chemical sensors. We mechanistically model an important source of stochasticity arising in these systems – the random collisions between the sensor and the surrounding molecules. The sensor dynamics is modeled as an underdamped second-order system with molecular collisions occurring at random times, and each strike adding noise to the sensor velocity. The time between two molecular strikes is drawn from an arbitrary distribution. Our analysis of the steady-state variance in the sensor displacement and velocity reveals two insights: firstly, the variance cannot discriminate between frequent low-impact molecular collisions versus rare high-impact collisions. Secondly, the variance only depends on the mean inter-strike time and is completely independent of other properties of the inter-strike time distribution. We next derive higher-order statistical moments (such as kurtosis) of the sensor displacement/velocity and show that these can be harnessed to discriminate between frequency low-impact strikes and rare high-impact strikes. As expected, these moments converge to Gaussian statistics in the limit of frequent molecular strikes. In summary, our work generalizes Brownian noise-driven models and quantifies deviations from Gaussian statistics that arise from mechanistic modeling of physical collisions. Furthermore, higher-order statistics can be exploited to infer random forces impinging on these nanosystems that ultimately determine the sensor signal-to-noise ratio.