Piecewise integrable neural network: An interpretable chaos identification framework.

Artificial neural networks (ANNs) are an effective data-driven approach to model chaotic dynamics. Although ANNs are universal approximators that easily incorporate mathematical structure, physical information, and constraints, they are scarcely interpretable. Here, we develop a neural network framework in which the chaotic dynamics is reframed into piecewise models. The discontinuous formulation defines switching laws representative of the bifurcations mechanisms, recovering the system of differential equations and its primitive (or integral), which describe the chaotic regime.

Sensitivity of viscoelastic characterization in multi-harmonic atomic force microscopy.

Quantifying the nanomechanical properties of soft-matter using multi-frequency atomic force microscopy (AFM) is crucial for studying the performance of polymers, ultra-thin coatings, and biological systems. Such characterization processes often make use of cantilever's spectral components to discern nanomechanical properties within a multi-parameter optimization problem. This could inadvertently lead to an over-determined parameter estimation with no clear relation between the identified parameters and their influence on the experimental data. In this work, we explore the sensitivity of viscoelastic characterization in polymeric samples to the experimental observables of multi-frequency intermodulation AFM. By performing simulations and experiments we show that surface viscoelasticity has negligible effect on the experimental data and can lead to inconsistent and often non-physical identified parameters. Our analysis reveals that this lack of influence of the surface parameters relates to a vanishing gradient and non-convexity while minimizing the objective function. By removing the surface dependency from the model, we show that the characterization of bulk properties can be achieved with ease and without any ambiguity. Our work sheds light on the sensitivity issues that can be faced when optimizing for a large number of parameters and observables in AFM operation, and calls for the development of new viscoelastic models at the nanoscale and improved computational methodologies for nanoscale mapping of viscoelasticity using AFM.

Quantifying nanoscale forces using machine learning in dynamic atomic force microscopy.

Dynamic atomic force microscopy (AFM) is a key platform that enables topological and nanomechanical characterization of novel materials. This is achieved by linking the nanoscale forces that exist between the AFM tip and the sample to specific mathematical functions through modeling. However, the main challenge in dynamic AFM is to quantify these nanoscale forces without the use of complex models that are routinely used to explain the physics of tip-sample interaction. Here, we make use of machine learning and data science to characterize tip-sample forces purely from experimental data with sub-microsecond resolution. Our machine learning approach is first trained on standard AFM models and then showcased experimentally on a polymer blend of polystyrene (PS) and low density polyethylene (LDPE) sample. Using this algorithm we probe the complex physics of tip-sample contact in polymers, estimate elasticity, and provide insight into energy dissipation during contact. Our study opens a new route in dynamic AFM characterization where machine learning can be combined with experimental methodologies to probe transient processes involved in phase transformation as well as complex chemical and biological phenomena in real-time.

High-Frequency Stochastic Switching of Graphene Resonators Near Room Temperature.

Stochastic switching between the two bistable states of a strongly driven mechanical resonator enables detection of weak signals based on probability distributions, in a manner that mimics biological systems. However, conventional silicon resonators at the microscale require a large amount of fluctuation power to achieve a switching rate in the order of a few hertz. Here, we employ graphene membrane resonators of atomic thickness to achieve a stochastic switching rate of 4.1 kHz, which is 100 times faster than current state-of-the-art. The (effective) temperature of the fluctuations is approximately 400 K, which is 3000 times lower than the state-of-the-art. This shows that these membranes are potentially useful to transduce weak signals in the audible frequency domain. Furthermore, we perform numerical simulations to understand the transition dynamics of the resonator and use analytical expressions to investigate the relevant scaling parameters that allow high-frequency, low-temperature stochastic switching to be achieved in mechanical resonators.

Inkjet-Printed High-Q Nanocrystalline Diamond Resonators.

Diamond is a highly desirable material for state-of-the-art micro-electromechanical (MEMS) devices, radio-frequency filters and mass sensors, due to its extreme properties and robustness. However, the fabrication/integration of diamond structures into Si-based components remain costly and complex. In this work, a lithography-free, low-cost method is introduced to fabricate diamond-based micro-resonators: a modified home/office desktop inkjet printer is used to locally deposit nanodiamond ink as ∅50-60 µm spots, which are grown into ≈1 µm thick nanocrystalline diamond film disks by chemical vapor deposition, and suspended by reactive ion etching. The frequency response of the fabricated structures is analyzed by laser interferometry, showing resonance frequencies in the range of ≈9-30 MHz, with Q-factors exceeding 104 , and (f0 × Q) figure of merit up to ≈2.5 × 1011 Hz in vacuum. Analysis in controlled atmospheres shows a clear dependence of the Q-factors on gas pressure up until 1 atm, with Q ∝ 1/P. When applied as mass sensors, the inkjet-printed diamond resonators yield mass responsivities up to 981 Hz fg-1 after Au deposition, and ultrahigh mass resolution up to 278 ± 48 zg, thus outperforming many similar devices produced by traditional top-down, lithography-based techniques. In summary, this work demonstrates the fabrication of functional high-performance diamond-based micro-sensors by direct inkjet printing.