A Nonlinear Reduced-Order Model of the Corpus Callosum Under Planar Coronal Excitation.

Traumatic brain injury (TBI) is often associated with microstructural tissue damage in the brain, which results from its complex biomechanical behavior. Recent studies have shown that the deep white matter (WM) region of the human brain is susceptible to being damaged due to strain localization in that region. Motivated by these studies, in this paper, we propose a geometrically nonlinear dynamical reduced order model (ROM) to model and study the dynamics of the deep WM region of the human brain under coronal excitation. In this model, the brain hemispheres were modeled as lumped masses connected via viscoelastic links, resembling the geometry of the corpus callosum (CC). Employing system identification techniques, we determined the unknown parameters of the ROM, and ensured the accuracy of the ROM by comparing its response against the response of an advanced finite element (FE) model. Next, utilizing modal analysis techniques, we determined the energy distribution among the governing modes of vibration of the ROM and concluded that the demonstrated nonlinear behavior of the FE model might be predominantly due to the special geometry of the brain deep WM region. Furthermore, we observed that, for sufficiently high input energies, high frequency harmonics at approximately 45 Hz, were generated in the response of the CC, which, in turn, are associated with high-frequency oscillations of the CC. Such harmonics might potentially lead to strain localization in the CC. This work is a step toward understanding the brain dynamics during traumatic injury.

Realization by impedance discontinuity of a unidirectional wave in a duct with harmonically perturbed uniform mean flow.

This paper presents a study of intentionally induced acoustic mode complexity in rigid-walled ducts of separable geometry and with uniform mean flow. An intermediately located perforated plate conceptualized as an impedance discontinuity is employed to maximize the acoustic mode complexity, in turn producing a unidirectional traveling wave from the source to the impedance discontinuity. The impedance of the perforated plate for realization of a unidirectional traveling wave is derived analytically and is found to be a function of the modal wavenumbers, the Mach number of the mean flow, the position of the perforated plate, and the termination impedance. The conditions derived analytically are verified computationally by finite element analysis. A measure of acoustic mode complexity is defined and also evaluated from the finite element analysis. It is found that the realization of a unidirectional traveling wave is robust at low Mach number mean flows, except at the occurrence of resonances. The method presented in this work provides a strategy to control the transmission of acoustic energy in rigid-walled ducts of separable geometry in the presence of uniform mean flow.

Ultimate Decoupling between Surface Topography and Material Functionality in Atomic Force Microscopy Using an Inner-Paddled Cantilever.

Atomic force microscopy (AFM) has been widely utilized to gain insight into various material and structural functionalities on the nanometer scale, leading to numerous discoveries and technologies. Despite the phenomenal success in applying AFM to the simultaneous characterization of topological and functional properties of materials, it has continuously suffered from the crosstalk between the observables, causing undesirable artifacts and complicated interpretations. Here, we introduce a two-field AFM probe, namely an inner-paddled cantilever integrating two discrete pathways such that they respond independently to the variations in surface topography and material functionality. Hence, the proposed design allows reliable and potentially quantitative determination of functional properties. In this paper, the efficacy of the proposed design has been demonstrated via piezoresponse force microscopy of periodically poled lithium niobate and collagen, although it can also be applied to other AFM methods such as AFM-based infrared spectroscopy and electrochemical strain microscopy.

Inducing a nonreflective airborne discontinuity in a circular duct by using a nonresonant side branch to create mode complexity.

A nonreflective airborne discontinuity is created in a one-dimensional rigid-walled duct when the mode complexity introduced by a nonresonant side branch reaches a maximum, so that a sound wave can be spatially separated into physical regions of traveling and standing waves. The nonresonance of the side branch is demonstrated, the mode complexity is quantified, and a computational method to optimize side-branch parameters to maximize mode complexity in the duct in the presence of three-dimensional effects is presented. The optimal side-branch parameters that maximize the mode complexity and thus minimize reflection are found using finite element analysis and a derivative-free optimization routine. Sensitivity of mode complexity near the optimum with respect to side-branch parameters is then examined. The results show reflection from the impedance discontinuity in the duct can be reduced nearly to zero, providing a practical means of achieving a nonreflective discontinuity for a plane wave propagating in a duct of finite length.

Utilizing intentional internal resonance to achieve multi-harmonic atomic force microscopy.

During dynamic atomic force microscopy (AFM), the deflection of a scanning cantilever generates multiple frequency terms due to the nonlinear nature of AFM tip-sample interactions. Even though each frequency term is reasonably expected to encode information about the sample, only the fundamental frequency term is typically decoded to provide topographic mapping of the measured surface. One of main reasons for discarding higher harmonic signals is their low signal-to-noise ratio. Here, we introduce a new design concept for multi-harmonic AFM, exploiting intentional nonlinear internal resonance for the enhancement of higher harmonics. The nonlinear internal resonance, triggered by the non-smooth tip-sample dynamic interactions, results in nonlinear energy transfers from the directly excited fundamental bending mode to the higher-frequency mode and, hence, enhancement of the higher harmonic of the measured response. It is verified through detailed theoretical and experimental study that this AFM design can robustly incorporate the required internal resonance and enable high-frequency AFM measurements. Measurements on an inhomogeneous polymer specimen demonstrate the efficacy of the proposed design, namely that the higher harmonic of the measured response is capable of enhanced simultaneous topography imaging and compositional mapping, exhibiting less crosstalk with an abrupt height change.

Complex nonlinear dynamics in the limit of weak coupling of a system of microcantilevers connected by a geometrically nonlinear tunable nanomembrane.

Intentional utilization of geometric nonlinearity in micro/nanomechanical resonators provides a breakthrough to overcome the narrow bandwidth limitation of linear dynamic systems. In past works, implementation of intentional geometric nonlinearity to an otherwise linear nano/micromechanical resonator has been successfully achieved by local modification of the system through nonlinear attachments of nanoscale size, such as nanotubes and nanowires. However, the conventional fabrication method involving manual integration of nanoscale components produced a low yield rate in these systems. In the present work, we employed a transfer-printing assembly technique to reliably integrate a silicon nanomembrane as a nonlinear coupling component onto a linear dynamic system with two discrete microcantilevers. The dynamics of the developed system was modeled analytically and investigated experimentally as the coupling strength was finely tuned via FIB post-processing. The transition from the linear to the nonlinear dynamic regime with gradual change in the coupling strength was experimentally studied. In addition, we observed for the weakly coupled system that oscillation was asynchronous in the vicinity of the resonance, thus exhibiting a nonlinear complex mode. We conjectured that the emergence of this nonlinear complex mode could be attributed to the nonlinear damping arising from the attached nanomembrane.

Improved atomic force microscope infrared spectroscopy for rapid nanometer-scale chemical identification.

Atomic force microscope infrared spectroscopy (AFM-IR) can perform IR spectroscopic chemical identification with sub-100 nm spatial resolution, but is relatively slow due to its low signal-to-noise ratio (SNR). In AFM-IR, tunable IR laser light is incident upon a sample, which results in a rise in temperature and thermomechanical expansion of the sample. An AFM tip in contact with the sample senses this nanometer-scale photothermal expansion. The tip motion induces cantilever vibrations, which are measured either in terms of the peak-to-peak amplitude of time-domain data or the integrated magnitude of frequency-domain data. Using a continuous Morlet wavelet transform to the cantilever dynamic response, we show that the cantilever dynamics during AFM-IR vary as a function of both time and frequency. Based on the observed cantilever response, we tailor a time-frequency-domain filter to identify the region of highest vibrational energy. This approach can increase the SNR of the AFM cantilever signal, such that the throughput is increased 32-fold compared to state-of-the art procedures. We further demonstrate significant increases in AFM-IR imaging speed and chemical identification of nanometer-scale domains in polymer films.

Modeling and measurement of geometrically nonlinear damping in a microcantilever-nanotube system.

Nonlinear mechanical systems promise broadband resonance and instantaneous hysteretic switching that can be used for high sensitivity sensing. However, to introduce nonlinear resonances in widely used microcantilever systems, such as AFM probes, requires driving the cantilever to an amplitude that is too large for any practical applications. We introduce a novel design for a microcantilever with a strong nonlinearity at small cantilever oscillation amplitude arising from the geometrical integration of a single BN nanotube. The dynamics of the system was modeled theoretically and confirmed experimentally. The system, besides providing a practical design of a nonlinear microcantilever-based probe, demonstrates also an effective method of studying the nonlinear damping properties of the attached nanotube. Beyond the typical linear mechanical damping, the nonlinear damping contribution from the attached nanotube was found to be essential for understanding the dynamical behavior of the designed system. Experimental results obtained through laser microvibrometry validated the developed model incorporating the nonlinear damping contribution.

Atomic force microscope infrared spectroscopy on 15 nm scale polymer nanostructures.

We measure the infrared spectra of polyethylene nanostructures of height 15 nm using atomic force microscope infrared spectroscopy (AFM-IR), which is about an order of magnitude improvement over state of the art. In AFM-IR, infrared light incident upon a sample induces photothermal expansion, which is measured by an AFM tip. The thermomechanical response of the sample-tip-cantilever system results in cantilever vibrations that vary in time and frequency. A time-frequency domain analysis of the cantilever vibration signal reveals how sample thermomechanical response and cantilever dynamics affect the AFM-IR signal. By appropriately filtering the cantilever vibration signal in both the time domain and the frequency domain, it is possible to measure infrared absorption spectra on polyethylene nanostructures as small as 15 nm.

Tunable, broadband nonlinear nanomechanical resonator.

A nanomechanical resonator incorporating intrinsically geometric nonlinearity and operated in a highly nonlinear regime is modeled and developed. The nanoresonator is capable of extreme broadband resonance, with tunable resonance bandwidth up to many times its natural frequency. Its resonance bandwidth and drop frequency (the upper jump-down frequency) are found to be very sensitive to added mass and energy dissipation due to damping. We demonstrate a prototype nonlinear mechanical nanoresonator integrating a doubly clamped carbon nanotube and show its broadband resonance over tens of MHz (over 3 times its natural resonance frequency) and its sensitivity to femtogram added mass at room temperature.