Surface forces at the liquid-solid interface play a fundamental role in a wide range of scientific disciplines including electrochemistry, energy storage, wetting, catalysis, environmental science, biochemistry, biophysics, and physical biology. Dynamic Atomic Force Microscopy (dAFM) is being increasingly used to quantify and map these forces with nanometer resolution. In dynamic AFM surface forces are sensed from the changes they cause in the nonlinear dynamics of the oscillating AFM cantilever. However, the dynamics of the AFM cantilever at liquid-solid interface differs significantly compared to air or vacuum environments due to both the low Q-factor of the cantilever in liquids as well as the unique nature of intermolecular forces at solid-liquid interface. In this article we review the state-of-art of understanding of nonlinear dynamics of AFM microcantilevers in liquid environments and outline the many open areas of research both in mathematical modeling and in experiments that remain to be explored.

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Many applications of microelectromechanical systems utilize mechanical vibratory motion. A number of interesting dynamical effects occur in these minimally damped, precisely manufactured devices. These effects can be caused by the structural mechanics, the actuation mechanism, or both. One such phenomenon, parametric resonance, occurs when displacement-dependent forcing is present in the microsystem. This paper reviews the key dynamic effects, and summarizes some of the development of devices that utilize parametric resonance or parametric amplification. In addition, signal-to-noise issues are discussed with respect to the ultimate sensitivity of mass sensors that use parametric resonance, and strategies for obtaining the highest sensitivity are presented. Here the authors describe parametric resonance phenomenon as a dynamical system, review its experimental observation in microsystems, and conclude by discussing the various applications.

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The experimental linear response spectrum of an auto-resonant intrinsic localized mode (ILM) in a driven 1-D cantilever array is composed of several resonances including a phase mode of the ILM. This autoresonant state is stable in a finite frequency range between the upper and lower bifurcation frequencies. Here we examine the robustness of the lower frequency transition point to an added lattice perturbation. In the unperturbed ILM state an even linear localized mode crosses the phase mode as the transition is approached and bifurcation occurs when the phase mode intersects the highest-frequency odd-symmetry band mode of the lattice. When an impurity mode is introduced into the lattice near the even linear local mode it breaks the local symmetry so that the lower bifurcation frequency of the ILM is now shifted to the point where the even mode and the odd phase mode frequencies coalesce.

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The effects of noise on transient energy localization in a coupled array of nonlinear oscillators are examined. Results obtained through simulations of deterministic systems are compared to those obtained through Euler-Maruyama scheme based simulations of the corresponding stochastic systems. To complement the numerical studies, a Fokker-Planck formalism is also used to analyze the response of the system in the presence of noise. Transient localization phenomena are explored by using time-domain and time-frequency analysis, and the insights gained are discussed. The intent of this study is to further the understanding of related behavior and use it for the benefit of a nonlinear system.

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We reduce the complex mechanics of an Intrinsic Localized Mode (ILM) on an infinite monodirectional nonlinear coupled oscillator array. By using Hamiltonian Mechanics, we derive two systems - a simple case when only the position of the ILM is allowed to vary, and the more complex case where both position and amplitude are allowed to change with time. We arrive at a systems of nonlinear equations of motion. For the position-only system, the dynamics are determined solely by the level sets of the Hamiltonian. The four-variable system has a richer structure. We also analyze the effect of a defect, or an impurity, on the motion of the ILM within our framework.

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This study examined a probe cantilever in an atomic force microscope made to vibrate as a van der Pol-type self-excited oscillator using linear and nonlinear feedback to maintain a sufficiently small amplitude of the probe cantilever. Sample surface shape measurements were conducted based on the method proposed herein. In a liquid environment, changes in the amplitude and the equivalent natural frequency of the probe cantilever depending on the atomic force acting between the sample and the probe were investigated experimentally. Results show that even with the noncontact mode using the proposed method in liquid, observation of the sample surface shape can be performed to nanometer order, which is equivalent to the capabilities of existing techniques.

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The focus of this paper is on the nonlinear dynamics of a resonator model proposed for measurement of electron spin via Magnetic Resonance Force Microscopy. The resonator model augmented by the Bloch equations for the magnetization is analyzed numerically. Orbital instabilities include coexisting solutions and lengthy chaotic transients that occur below a homoclinic jump-to-contact threshold.

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In this paper, we propose an indirect suspension system that is analogous to a nano-suspension system with a cantilever-like atomic force microscope. The proposed system mainly consists of an electromagnet, a permanent magnet and a target. These magnets are arranged perpendicular to each other. In this system, the current flowing in the electromagnet is the only adjustable parameter, and the magnetic field created by the electromagnet hardly affects the target because of the distance between them. Thus suspension of the target is possible by the dynamically controlled permanent magnet. The indirect suspension system is modeled by a magnetic charge model. The validity of the model is confirmed using a simple system where the permanent magnet is suspended by an electromagnet. A proportional-derivative controller is designed for the indirect suspension using the model. The experimental and numerical results confirm that the target is successfully suspended.

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Bidirectional associative memory is a hetero-associative memory which has two layers. It cannot deal with one-to-many associations. Osana et al. proposed a chaotic bidirectional associative memory which can deal with one-to-many association due to the invisible part. Moreover, Yano and Osana proposed a chaotic complex-valued bidirectional associative memory whose all neurons are complex-valued. However, it associates not only training patterns but also patterns referred to as rotated patterns. Thus, the conventional chaotic complex-valued bidirectional associative memory model is insufficient for applications. In this paper, we propose a chaotic complex-valued bidirectional associative memory with a real-valued invisible part. It can prevent the rotated patterns from appearing. Our proposed model almost associates only training patterns and is promising for applications. Moreover, it improves the noise robustness.

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A characteristic sequence pattern of first-order binary sigma-delta (SD) modulated signals was found recently and the pattern detectors are applied to various piecewise linear (PWL) circuits. However, practical analog-to-digital and digital-to-analog converters often employ second and higher-order SD modulations and multi-level oversampled data format. This paper presents sequence features of first-order multi-level and second-order binary SD modulated signals. In addition, the results of investigating the sequence features are applied to PWL-based nonlinear signal processing and signal measurement. The designed signal processing and measurement circuits are lower in hardware complexity than Nyquist-rate long word-length circuits of the same functions.

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