Nonlinear Dynamic Range Research Articles

Mode-dependent scaling of nonlinearity and linear dynamic range in a NEMS resonator

Even a relatively weak drive force is enough to push a typical nanomechanical resonator into the nonlinear regime. Consequently, nonlinearities are widespread in nanomechanics and determine the critical characteristics of nanoelectromechanical systems' (NEMSs) resonators. A thorough understanding of the nonlinear dynamics of higher eigenmodes of NEMS resonators would be beneficial for progress, given their use in applications and fundamental studies. Here, we characterize the nonlinearity and the linear dynamic range (LDR) of each eigenmode of two nanomechanical beam resonators with different intrinsic tension values up to eigenmode n = 11. We find that the modal Duffing constant increases as n4, while the critical amplitude for the onset of nonlinearity decreases as 1/n. The LDR, determined from the ratio of the critical amplitude to the thermal noise amplitude, increases weakly with n. Our findings are consistent with our theory treating the beam as a string, with the nonlinearity emerging from stretching at high amplitudes. These scaling laws, observed in experiments and validated theoretically, can be leveraged for pushing the limits of NEMS-based sensing even further.

Parametric magnon transduction to spin qubits.

The integration of heterogeneous modular units for building large-scale quantum networks requires engineering mechanisms that allow suitable transduction of quantum information. Magnon-based transducers are especially attractive due to their wide range of interactions and rich nonlinear dynamics, but most of the work to date has focused on linear magnon transduction in the traditional system composed of yttrium iron garnet and diamond, two materials with difficult integrability into wafer-scale quantum circuits. In this work, we present a different approach by using wafer-compatible materials to engineer a hybrid transducer that exploits magnon nonlinearities in a magnetic microdisc to address quantum spin defects in silicon carbide. The resulting interaction scheme points to the unique transduction behavior that can be obtained when complementing quantum systems with nonlinear magnonics.

Enhancement of the Synaptic Performance of Phosphorus-Enriched, Electric Double-Layer, Thin-Film Transistors

The primary objective of neuromorphic electronic devices is the implementation of neural networks that replicate the memory and learning functions of biological synapses. To exploit the advantages of electrolyte gate synaptic transistors operating like biological synapses, we engineered electric double-layer transistors (EDLTs) using phosphorus-doped silicate glass (PSG). To investigate the effects of phosphorus on the EDL and synaptic behavior, undoped silicate spin-on-glass-based transistors were fabricated as a control group. Initially, we measured the frequency-dependent capacitance and double-sweep transfer curves for the metal-oxide-semiconductor (MOS) capacitors and MOS field-effect transistors. Subsequently, we analyzed the excitatory post-synaptic currents (EPSCs), including pre-synaptic single spikes, double spikes, and frequency variations. The capacitance and hysteresis window characteristics of the PSG for synaptic operations were verified. To assess the specific synaptic operational characteristics of PSG-EDLTs, we examined EPSCs based on the spike number and established synaptic weights in potentiation and depression (P/D) in relation to pre-synaptic variables. Normalizing the P/D results, we extracted the parameter values for the nonlinearity factor, asymmetric ratio, and dynamic range based on the pre-synaptic variables, revealing the trade-off relationships among them. Finally, based on artificial neural network simulations, we verified the high-recognition rate of PSG-EDLTs for handwritten digits. These results suggest that phosphorus-based EDLTs are beneficial for implementing high-performance artificial synaptic hardware.

Nonlinear Dynamic Response of Nanocomposite Microbeams Array for Multiple Mass Sensing.

A nonlinear MEMS multimass sensor is numerically investigated, designed as a single input-single output (SISO) system consisting of an array of nonlinear microcantilevers clamped to a shuttle mass which, in turn, is constrained by a linear spring and a dashpot. The microcantilevers are made of a nanostructured material, a polymeric hosting matrix reinforced by aligned carbon nanotubes (CNT). The linear as well as the nonlinear detection capabilities of the device are explored by computing the shifts of the frequency response peaks caused by the mass deposition onto one or more microcantilever tips. The frequency response curves of the device are obtained by a pathfollowing algorithm applied to the reduced-order model of the system. The microcantilevers are described by a nonlinear Euler-Bernoulli inextensible beam theory, which is enriched by a meso-scale constitutive law of the nanocomposite. In particular, the microcantilever constitutive law depends on the CNT volume fraction suitably used for each cantilever to tune the frequency bandwidth of the whole device. Through an extensive numerical campaign, the mass sensor sensitivity estimated in the linear and nonlinear dynamic range shows that, for relatively large displacements, the accuracy of the added mass detectability can be improved due to the larger nonlinear frequency shifts at resonance (up to 12%).

Generalized network density matrices for analysis of multiscale functional diversity.

The network density matrix formalism allows for describing the dynamics of information on top of complex structures and it has been successfully used to analyze, e.g., a system's robustness, perturbations, coarse-graining multilayer networks, characterization of emergent network states, and performing multiscale analysis. However, this framework is usually limited to diffusion dynamics on undirected networks. Here, to overcome some limitations, we propose an approach to derive density matrices based on dynamical systems and information theory, which allows for encapsulating a much wider range of linear and nonlinear dynamics and richer classes of structure, such as directed and signed ones. We use our framework to study the response to local stochastic perturbations of synthetic and empirical networks, including neural systems consisting of excitatory and inhibitory links and gene-regulatory interactions. Our findings demonstrate that topological complexity does not necessarily lead to functional diversity, i.e., the complex and heterogeneous response to stimuli or perturbations. Instead, functional diversity is a genuine emergent property which cannot be deduced from the knowledge of topological features such as heterogeneity, modularity, the presence of asymmetries, and dynamical properties of a system.

4-Field spontaneous symmetry breakings in photonic molecules

We present in this work a study of 4-field symmetry breakings in two photonic molecule structures consisting of two identical microresonators with distinct coupling arrangements. Mediated by the Kerr-interaction, the systems also display different 2-field symmetry breakings, periodic switching and chaos. The wide range of nonlinear optical dynamics makes the system ideal for all-optical switching, optical memories, telecommunication systems, polarization controllers and integrated photonic sensors.

Reviving a failed network through microscopic interventions

From mass extinction to cell death, complex networked systems often exhibit abrupt dynamic transitions between desirable and undesirable states. These transitions are often caused by topological perturbations (such as node or link removal, or decreasing link strengths). The problem is that reversing the topological damage, namely, retrieving lost nodes or links or reinforcing weakened interactions, does not guarantee spontaneous recovery to the desired functional state. Indeed, many of the relevant systems exhibit a hysteresis phenomenon, remaining in the dysfunctional state, despite reconstructing their damaged topology. To address this challenge, we develop a two-step recovery scheme: first, topological reconstruction to the point where the system can be revived and then dynamic interventions to reignite the system’s lost functionality. By applying this method to a range of nonlinear network dynamics, we identify the recoverable phase of a complex system, a state in which the system can be reignited by microscopic interventions, for instance, controlling just a single node. Mapping the boundaries of this dynamical phase, we obtain guidelines for our two-step recovery. Perturbations and disturbances can bring complex networks into undesirable states in which global functionality is suppressed. Now, a recovery scheme explains how to revive a damaged network by controlling only a small number of nodes.

Intelligent Breathing Soliton Generation in Ultrafast Fiber Lasers

AbstractHarnessing pulse generation from an ultrafast laser is a challenging task as reaching a specific mode‐locked regime generally involves adjusting multiple control parameters, in connection with a wide range of accessible pulse dynamics. Machine‐learning tools have recently shown promising for the design of smart lasers that can tune themselves to desired operating states. Yet, machine‐learning algorithms are mainly designed to target regimes of parameter‐invariant, stationary pulse generation, while the intelligent excitation of evolving pulse patterns in a laser remains largely unexplored. Breathing solitons exhibiting periodic oscillatory behavior, emerging as ubiquitous mode‐locked regime of ultrafast fiber lasers, are attracting considerable interest by virtue of their connection with a range of important nonlinear dynamics, such as exceptional points, and the Fermi‐Pasta‐Ulam paradox. Here, an evolutionary algorithm is implemented for the self‐optimization of the breather regime in a fiber laser mode‐locked through a four‐parameter nonlinear polarization evolution. Depending on the specifications of the merit function used for the optimization procedure, various breathing‐soliton states are obtained, including single breathers with controllable oscillation period and breathing ratio, and breather molecular complexes with a controllable number of elementary constituents. This work opens up a novel avenue for exploration and optimization of complex dynamics in nonlinear systems.

Experimental characteristics and coupled nonlinear forced vibrations of axially travelling hyperelastic beams

Comprehensively investigated in this paper is the coupled nonlinear dynamics of hyperelastic beams. Experimental testing is performed to accurately model the hyperelasticity using different hyperelastic energy density models. Samples were fabricated using 3D printing technique for flexible thermoplastic polyurethane filaments following the ASTM D638 guidance and tested using a tensile testing machine. For a proper hyperelastic energy density model, coupled nonlinear equations of motion are obtained via the von Kármán geometrical nonlinearity and Hamilton’s principle. Free natural vibration response of the gyroscopic system is analysed using a generalised modal decomposition method and the influence of different parameters such as the hyperelastic stiffness term and the axial velocity on the natural frequencies is investigated. Complex mode shapes are obtained and the influence of axial velocity on altering the real and imaginary parts is discussed. Furthermore, a comprehensive analysis on the coupled nonlinear dynamics of the system is presented using a combination of Galerkin’s scheme and a dynamic equilibrium technique. The frequency response to different design parameters such as axial speed, axial tension, harmonic external load, hyperelastic parameters and geometrical imperfection is discussed in detail. It is shown that the system shows a wide range of rich nonlinear dynamics including hardening depending on the characteristics of the system.

An adaptive transmission line cochlear model based front-end for replay attack detection

The cochlea is a remarkable spectrum analyser with desirable properties including sharp frequency tuning and level-dependent compression and the potential advantages of incorporating these characteristics in a speech processing front-end are investigated. This paper develops a framework for an active transmission line cochlear model employing adaptive notch and resonant filters. The proposed model reproduces the observed asymmetric auditory filter shape with a sharp high-frequency roll-off and level-dependent nonlinear dynamic range compression characteristics. Experimental analysis demonstrates that sharp frequency tuning and dynamic range compression of the proposed model lead to an enhanced spectral representation compared with other spectral analysis methods. The proposed model was employed in the front-end of replay spoofing attack detection systems, and experiments on the ASVspoof 2017 version 2.0 and ASVspoof 2019 databases demonstrate that the proposed model outperforms linear and nonlinear level-dependent parallel filter bank auditory models and classical spectro-temporal front-ends. The use of the proposed model leads to relative improvements of 45.6%, 51.9% and 60.8% over the baseline feature CQCCs of ASVspoof version 2.0 and CQCCs and LFCCs of ASVspoof2019 on evaluation datasets, respectively.

A Low-g MEMS Accelerometer with High Sensitivity, Low Nonlinearity and Large Dynamic Range Based on Mode-Localization of 3-DoF Weakly Coupled Resonators.

This paper presents a new design of microelectromechanical systems (MEMS) based low-g accelerometer utilizing mode-localization effect in the three degree-of-freedom (3-DoF) weakly coupled MEMS resonators. Two sets of the 3-DoF mechanically coupled resonators are used on either side of the single proof mass and difference in the amplitude ratio of two resonator sets is considered as an output metric for the input acceleration measurement. The proof mass is electrostatically coupled to the perturbation resonators and for the sensitivity and input dynamic range tuning of MEMS accelerometer, electrostatic electrodes are used with each resonator in two sets of 3-DoF coupled resonators. The MEMS accelerometer is designed considering the foundry process constraints of silicon-on-insulator multi-user MEMS processes (SOIMUMPs). The performance of the MEMS accelerometer is analyzed through finite-element-method (FEM) based simulations. The sensitivity of the MEMS accelerometer in terms of amplitude ratio difference is obtained as 10.61/g for an input acceleration range of ±2 g with thermomechanical noise based resolution of 0.22 and nonlinearity less than 0.5%.

A numerical investigation on Contact Mechanics applications using eight-node hexahedral elements with underintegration techniques

In the present work the performance of finite element formulations with different reduced integration strategies is evaluated for Contact Mechanics applications. One-point quadrature and selective reduced integration are utilized here using hourglass control to suppress volumetric and shear locking for materials with incompressible plastic behavior and bending-dominated problems. A corotational formulation is adopted to deal with physically and geometrically nonlinear analysis and the generalized-α method is employed for time integration in the nonlinear dynamic range. The contact formulation is based on the penalty method, where the classical Coulomb’s law is used considering a convected coordinate system for three-dimensional friction with large deformation and finite sliding. Contact problems involving deformable and rigid bodies, as well as static and dynamic analysis, are investigated and results are analyzed considering the different underintegration formulations proposed here.

The Oxide Film-Coated Surface Acoustic Wave Resonators for the Measurement of Relative Humidity

The surface acoustic wave (SAW) humidity sensor may possess many attractive sensing characteristics such as high sensitivity, high resolution, high stability, frequency output, ease of interfacing, small size, and broad dynamic range. Mostly, the polymer materials are used for the SAW humidity sensor fabrication. But the polymer SAW sensors suffer from broad bandwidth, instability due to ambient temperature, nonlinearity, and small dynamic range. This article presents the fabrication of metal oxide film humidity sensors using SAW resonators of 433.92-MHz frequency. Five different SAW humidity sensors were fabricated by varying the deposited alumina film thickness to measure humidity in the range of 0%–98% relative humidity (RH). The hydrophilic films were formed by dip coating of alumina solution of different molar concentrations. The alumina film is thermally stable and inert. The static and dynamic response characteristics were determined from the shift in resonant peaks at different humidity using an HP 85046A vector network analyzer (VNA). The minimum sensitivity of the least sensitive sensor was found to be 2.51 kHz/%RH. The sensors show linear response ( $R^{2} \ge0.98$ ), high sensitivity (max. ~ 9 kHz/%RH), negligible hysteresis error (≤0.50%), wide dynamic range, and inexpensive fabrication due to the use of commercial resonators. The response parameters of the sensors were compared with the parameters of other oxide SAW sensors reported in the literature. Finally, the linear sensor was interfaced to the electronic and associated signal conditioning circuits to display humidity in %RH.

(Invited) In-Memory Computing with Memristor Circuit Primitives

The dramatic rise of data-intensive workloads has revived special-purpose hardware and architectures for continuing improvements in computational speed and energy efficiency. While traditional CMOS ASICs deliver some performance gains, typically by limiting data movement or implementing “in-memory computation”, such approaches still suffer from low power efficiency. Therefore, new proposals leveraging non-volatile memristive devices for in-memory computation are highly attractive in a variety of application domains. While originally developed for as digital (binary) high density non-volatile memories, memristive devices have demonstrated a wide range of behaviors and properties – such as a wide range of tunable analog resistance and non-linear dynamics – which motivate their use in novel functions and new computational models. Many recent in-memory compute studies have focused on crossbar circuit architectures, demonstrating their application for neural networks, scientific computing and signal processing. However, other circuit primitives – such as content addressable memories (CAMs) and combined systems such as crossbar arrays and non-linear elements– have shown further promise for mapping a diverse range of complimentary computational models such as finite state machines, pattern matching, hashing algorithms and Hopfield networks for tackling optimization problems. In this talk, I will review the different exciting opportunities for in-memory computational primitives levering non-volatile memristive devices and their circuits and architectures for enabling low power, high-throughput computation in a variety of application domains. I will also highlight the different materials and device requirements which steer material stack design and fabrication for these diverse circuits and application domains. Finally, I will show recent lab demonstrations of various applications mapped to these in-memory computational circuit primitives based on memristor devices, and give an outlook on performance.

Printable Nonenzymatic Glucose Biosensors Using Carbon Nanotube-PtNP Nanocomposites Modified with AuRu for Improved Selectivity.

Nonenzymatic glucose biosensors have the potential for a more reliable in vivo functionality due to the reduced risk of biorecognition element degradation. However, these novel sensing mechanisms often are nanoparticle-based and have nonlinear responses, which makes it difficult to gauge their potential utility against more conventional enzymatic biosensors. Moreover, these nonenzymatic biosensors often suffer from poor selectivity that needs to be better addressed before being used in vivo. To address these problems, here we present an amperometric nonenzymatic glucose biosensor fabricated using one-step electrodeposition of Au and Ru nanoparticles on the surface of a carbon-nanotube-based platinum-nanoparticle hybrid in conductive polymer. Using benchtop evaluations, we demonstrate that the bimetallic catalyst of Au-Ru nanoparticles can enable the nonenzymatic detection of glucose with a superior performance and stability. Furthermore, our biosensor shows good selectivity against other interferents, with a nonlinear dynamic range of 1-19 mM glucose. The Au-Ru catalyst has a conventional linear range of 1-10 mM, with a sensitivity of 0.2347 nA/(μM mm2) ± 0.0198 (n = 3) and a limit of detection of 0.068 mM (signal-to-noise, S/N = 3). The biosensor also exhibits a good repeatability and stability at 37 °C over a 3 week incubation period. Finally, we use a modified Butler-Volmer nonlinear analytical model to evaluate the impact of geometrical and chemical design parameters on our nonenzymatic biosensor's performance, which may be used to help optimize the performance of this class of biosensors.

A PAPR reduction scheme combining superimposed O-OFDM and [formula omitted]-law mapping for VLC-OFDM systems

Due to the high peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals, the inherent nonlinearity of light emitting diodes (LEDs) is a challenge for optical OFDM (O-OFDM) schemes in visible light communication (VLC) systems. In order to reduce PAPR to mitigate the effects of the nonlinearity of LEDs, and avoid the asymmetric clipping interference in the conventional hybrid O-OFDM schemes, a novel superimposed O-OFDM scheme is proposed in this paper, which reduce the PAPR by combining the μ-law mapping and the superposition modulation. Moreover, at the transmitter, the hybrid O-OFDM components are superimposed in an interference-free way, the receiver does not require the operation of interference cancellation, and the symbols of each branch can be demodulated independently. Simulation results verify that the proposed scheme can significantly reduce the PAPR. At the same time, the comprehensive performance of the proposed scheme outperforms other competing schemes under the constraints of the nonlinearity and limited dynamic range of LEDs.

A 6D interferometric inertial isolation system

We present the conceptual design and noise analysis of a novel inertial-isolation scheme based on six degree-of-freedom (6D) interferometric sensing of a single reference mass. It is capable of reducing inertial motion by more than two orders of magnitude at 100 mHz compared with what is achievable with state-of-the-art seismometers. This will enable substantial improvements in the low-frequency sensitivity of gravitational-wave detectors. The scheme is inherently two-stage, the reference mass is softly suspended within the platform to be isolated, which is itself suspended from the ground. The platform is held constant relative to the reference mass and this closed-loop control effectively transfers the low acceleration-noise of the reference mass to the platform. The loop gain also reduces non-linear couplings and dynamic range requirements in the soft-suspension mechanics and the interferometric sensing.

An 8-Bit Ultra-Low-Power, Low-Voltage Current Steering DAC Utilizing a New Segmented Structure

In this paper, an 8-bit ultra-low-power, low-voltage current steering digital-to-analog converter (DAC) is presented. The proposed DAC employs a new segmented structure that results in low integral nonlinearity (INL) and high spurious-free dynamic range (SFDR). Moreover, this DAC utilizes a low-voltage current cell. The low-voltage characteristic of the current cell is achieved by connecting the body of MOSFET switches to their sources. Utilizing a low supply voltage along with a low bias current in the current cells results in about 623.81-[Formula: see text]W power consumption in 140-MS/s sample rate, which is very small compared to previous reports. The post-layout simulation results in 180-nm CMOS technology and [Formula: see text]-V supply voltage with the sample rate of 140[Formula: see text]MS/s show SFDR [Formula: see text] 64.37[Formula: see text]dB in the Nyquist range. The differential nonlinearity (DNL) and INL of the presented DAC are 0.1254 LSB and 0.1491 LSB, respectively.

Historical masonry building aggregates: advanced numerical insight for an effective seismic assessment on two row housing compounds

Historical masonry aggregates represent a large portion of the cultural heritage in Italy and are highly vulnerable to seismic actions, as shown by past seismic events. Typically, they are large and complex structures for which there is a lack of knowledge and information concerning the structural behavior, in particular as far as the response to seismic actions is concerned. This paper investigates the seismic response of two complex historical masonry aggregates located in Sora (Lazio region, Central Italy), through advanced 3D FE numerical simulations. For each aggregate, a detailed 3D FE model is developed and analyzed in the non-linear dynamic range, assuming that masonry behaves as a damaging-plastic material with almost vanishing tensile strength. The seismic performance of the two aggregates is evaluated in terms of damage distribution, energy density dissipated by tensile damage and maximum normalized displacements. The numerical analyses show the high vulnerability of the perimeter walls. In particular, the units at the extremities of the aggregate are subjected to large displacements, being not efficiently braced by the adjacent units and being subjected to the torsional effects induced by the seismic action. The presence of several openings is a fundamental feature that significantly decreases the strength of the perimeter walls, influencing the damage distribution in the aggregate mainly due to out-of-plane actions. The most damaged elements are generally the walls of the tall units without lateral support and the adjacent slabs covering large spans. Numerical results also show that the structural response of a single building unit is affected by the interactions with adjacent structural parts. Moreover, it can be stated that a preliminary structural assessment through kinematic limit analysis on partial failure mechanisms may be reliable only after a proper estimation of the different structural elements playing a role in the horizontal behavior (e.g. interlocking between walls, typology of masonry, distribution of horizontal loads, constraints and dead loads distribution, etc.). The obtained results will be also used in an accompanying paper to benchmark simplified approaches that can be employed by engineers in common design practice to quickly predict the seismic vulnerability of masonry aggregates and define the most suitable strengthening interventions.

Interaction of photons with a coupled atom-cavity system through a bidirectional time-delayed feedback

In this paper, we have developed a method for describing the dynamics of an arbitrary quantum system under a bidirectional time-delayed feedback loop. For this purpose, we have described the evolution in terms of the time propagation of the quantum system of interest without feedback together with several identical systems, which represent the history of the quantum system under study. This technique provides a numerically efficient solution for describing a system's dynamics in the case of significant time delays in which direct investigation of the state of the reservoirs becomes numerically intractable. Using this method, we have studied two scenarios of multiple scatterings of photons incident on a cavity with a two-level atom positioned inside it, coupled to two waveguides that are connected at their ends. In the first scenario, two photons impinge on the cavity through separate waveguides with a delay between them. We have demonstrated that the maximum difference between the two output photon numbers occurs when the delay between the incident photons becomes close to the inverse of their linewidth. In the second scenario, multiple photons impinge on the cavity through the same waveguide and go through multiple interactions. We have shown that, for a fixed atom-cavity coupling rate, the transmission rate enhances as the number of photons increases and have quantified this enhancement. The developed method enables us to study a broad range of nonlinear dynamics in complex quantum networks.