Bistable Response Research Articles

Evaluating dynamic models for rigid-foldable origami: unveiling intricate bistable dynamics of stacked-Miura-origami structures as a case study.

Recent advances in origami science and engineering have particularly focused on the challenges of dynamics. While research has primarily focused on statics and kinematics, the need for effective and processable dynamic models has become apparent. This paper evaluates various dynamic modelling techniques for rigid-foldable origami, particularly focusing on their ability to capture nonlinear dynamic behaviours. Two primary methods, the lumped mass-spring-damper approach and the energy-based method, are examined using a bistable stacked Miura-origami (SMO) structure as a case study. Through systematic dynamic experiments, we analyse the effectiveness of these models in predicting bistable dynamic responses, including intra- and interwell oscillations, in different loading conditions. Our findings reveal that the energy-based approach, which considers the structure's inertia and utilizes dynamic experimental data for parameter identification, outperforms other models in terms of validity and accuracy. This model effectively predicts the dynamic response types, the rich and complex nonlinear characteristics and the critical frequency where interwell oscillations occur. Despite its relatively increased complexity in model derivation, it maintains computational efficiency and shows promise for broader applications in origami dynamics. By comparing model predictions with experimental results, this study enhances our understanding of origami dynamics and contributes valuable insights for future research and applications. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Hopping potential wells and gait switching in a fish-like robot with a bistable tail

Fish outperform current underwater robots in speed, agility, and efficiency of locomotion, in part due to their flexible appendages that are capable of rich combinations of modes of motion. In fish-like robots, actuating many different modes of oscillation of tails or fins can become a challenge. This paper presents a highly underactuated (with a single actuator) fish-like robot with a bistable tail that features a double-well elastic potential. Oscillations of such a tail depend on the frequency and amplitude of excitation, and tuning the frequency-amplitude can produce controllable oscillations in different modes leading to different gaits of the robot. This robot design is inspired by recent work on underactuated flexible swimming robots driven by a single rotor. The oscillations of the rotor can propel and steer the robot, but saturation of the rotor makes performing long turns challenging. This paper demonstrates that by adding geometric bistability to the flexible tail, turns can be performed by controllably exciting single-well oscillations in the tail, while exciting double-well oscillations of the tail produces average straight-line motion. The findings of this paper go beyond the application to a narrow class of fish-like robots. More broadly we have demonstrated the use of periodic excitation to produce bistable response that generate different gaits including a steering gait. The mechanics demonstrated here show the feasibility of applications to other mobile soft robots.

Topologically-protected optical bistability based on two-dimensional photonic crystal L6 nanocavity dimer array

We numerically investigate the optical bistability from a two-dimensional photonic crystal L6 nanocavity dimer array structure configured under the Su-Schrieffer-Heeger model. The localized electric field in the topological edge state is highly enhanced, which gives rise to strong nonlinear phenomena such as optical bistability. In comparison, a topologically trivial nanocavity is also designed and its field strength distribution and optical bistable response are also simulated. In order to test the robustness, three types of defects and interferences are introduced in both the topologically non-trivial and trivial cavities. Benefiting from the topological feature, the proposed topological cavity exhibits superior optical bistable performance with low threshold power and high switching contrast compared to that in the trivial cavity. Our work suggests what we believe to be a novel avenue toward the insertion of optical bistable devices with high robustness into future photonic integrated circuits and photonic neural networks.

Piezoelectric energy harvester for wind turbine blades based on bistable response of a composite beam in post-buckling

A bistable piezoelectric energy harvester (PEH) is presented for harvesting power from vibrations occurring at low frequencies, as is the case of wind turbine blades. The axial compressive prestress of a piezoelectric composite beam at post-buckling serves as the bistability source, leading to high mechanical to electric power conversion. An in-house harvesting circuit connected to the piezoelectric terminals is used for demonstration of its harvesting power capabilities. A finite element (FE) model is used to analyze and optimize the coupled nonlinear electromechanical response of the PEH, including structure and circuit. A physical prototype has been manufactured and tested for validation of the electromechanical design and the FE modeling approach. Predictions and measurements indicate an increase of harvested power with applied prestress up to a transition point, where a sudden drop in power occurs. Good comparison between numerical and experimental results verified the modeling approach, whereas deviations related to physical boundary conditions at large compressive forces affected the prediction of the transition point in harvested power. The harvester produced 1.32 mW of electrical power under tonal base excitation of 1 g at 8 Hz. Hence, the nonlinear PEH has demonstrated its capability to harvest energy at frequencies much lower than its first linear modal frequency and could thus serve as a promising solution for powering IoT devices and sensors in large vibrating structures.

Bistable response and quasi-periodicity excitation of the internal dynamics of soliton molecules.

Soliton molecules, a frequently observed phenomenon in most mode-locked lasers, have intriguing characteristics comparable to their matter molecule counterparts. However, there are rare explorations of the deterministic control of the underlying physics within soliton molecules. Here, we demonstrate the bistable response of intramolecular motion to external stimuli and identify a general approach to excite their quasi-periodic oscillations. By introducing frequency-swept gain modulation, the intrinsic resonance frequency of the soliton molecule is observed in the simulation model. Applying stronger modulation, the soliton molecule exhibits divergent response susceptibility to up- and down-sweeping, accompanied by a jump phenomenon. Quasi-periodic intramolecular oscillations appear at the redshifted resonance frequency. Given the leading role of bistability and quasi-periodic dynamics in nonlinear physics, our research provides insights into the complex nonlinear dynamics within dissipative soliton molecules. It may pave the way to related experimental studies on synchronization and chaos at an ultrafast time scale.

Biophysical modeling of the whole-cell dynamics of C. elegans motor and interneurons families.

The nematode Caenorhabditis elegans is a widely used model organism for neuroscience. Although its nervous system has been fully reconstructed, the physiological bases of single-neuron functioning are still poorly explored. Recently, many efforts have been dedicated to measuring signals from C. elegans neurons, revealing a rich repertoire of dynamics, including bistable responses, graded responses, and action potentials. Still, biophysical models able to reproduce such a broad range of electrical responses lack. Realistic electrophysiological descriptions started to be developed only recently, merging gene expression data with electrophysiological recordings, but with a large variety of cells yet to be modeled. In this work, we contribute to filling this gap by providing biophysically accurate models of six classes of C. elegans neurons, the AIY, RIM, and AVA interneurons, and the VA, VB, and VD motor neurons. We test our models by comparing computational and experimental time series and simulate knockout neurons, to identify the biophysical mechanisms at the basis of inter and motor neuron functioning. Our models represent a step forward toward the modeling of C. elegans neuronal networks and virtual experiments on the nematode nervous system.

Global Dynamics and Bifurcations of an Oscillator with Symmetric Irrational Nonlinearities

This study’s objective is an irrationally nonlinear oscillating system, whose bifurcations and consequent multi-stability under the circumstances of single potential well and double potential wells are investigated in detail to further reveal the mechanism of the transition of resonance and its utilization. First, static bifurcations of its nondimensional system are discussed. It is found that variations of two structural parameters can induce different numbers and natures of potential wells. Next, the cases of mono-potential wells and double wells are explored. The forms and stabilities of the resonant responses within each potential well and the inter-well resonant responses are discussed via different theoretical methods. The results show that the natural frequencies and trends of frequency responses in the cases of mono- and double-potential wells are totally different; as a result of the saddle-node bifurcations of resonant solutions, raising the excitation level or frequency can lead to the coexistence of bistable responses within each well and cause an inter-well periodic response. Moreover, in addition to verifying the accuracy of the theoretical prediction, numerical results considering the disturbance of initial conditions are presented to detect complicated dynamical behaviors such as jump between coexisting resonant responses, intra-well period-two responses and chaos. The results herein provide a theoretical foundation for designing and utilizing the multi-stable behaviors of irrationally nonlinear oscillators.

Ultra-Stretchable Kirigami Piezo-Metamaterials for Sensing Coupled Large Deformations.

Mechanical metamaterials are known for their prominent mechanical characteristics such as programmable deformation that are due to periodic microstructures. Recent research trends have shifted to utilizing mechanical metamaterials as structural substrates to integrate with functional materials for advanced functionalities beyond mechanical, such as active sensing. This study reports on the ultra-stretchable kirigami piezo-metamaterials (KPM) for sensing coupled large deformations caused by in- and out-of-plane displacements using the lead zirconate titanate (PZT) and barium titanate (BaTiO3 ) composite films. The KPM are fabricated by uniformly compounding and polarizing piezoelectric particles (i.e., PZT and BaTiO3 ) in silicon rubber and structured by cutting the piezoelectric rubbery films into ligaments. Characterizes the electrical properties of the KPM and investigates the bistable mechanical response under the coupled large deformations with the stretching ratio up to 200% strains. Finally, the PZT KPM sensors are integrated into wireless sensing systems for the detection of vehicle tire bulge, and the non-toxic BaTiO3 KPM are applied for human posture monitoring. The reported kirigami piezo-metamaterials open an exciting venue for the control and manipulation of mechanically functional metamaterials for active sensing under complex deformation scenarios in many applications.

Cooperative optical pattern formation in an ultrathin atomic layer

Spontaneous pattern formation from a uniform state is a widely studied nonlinear optical phenomenon that shares similarities with non-equilibrium pattern formation in other scientific domains. Here we show how a single layer of atoms in an array can undergo nonlinear amplification of fluctuations, leading to the formation of intricate optical patterns. The origin of the patterns is intrinsically cooperative, eliminating the necessity of mirrors or cavities, although introduction of a mirror in the vicinity of the atoms significantly modifies the scattering profiles. The emergence of these optical patterns is tied to a bistable collective response, which can be qualitatively described by a long-wavelength approximation, similar to a nonlinear Schrödinger equation of optical Kerr media or ring cavities. These collective excitations have the ability to form singular defects and unveil atomic position fluctuations through wave-like distortions.

Bistable composites with intrinsic pneumatic actuation and non-cylindrical curved shapes

This study presents a novel mechanically-prestressed laminate with non-cylindrical shapes and pneumatic actuation. A third-order analytical model is proposed to determine the laminates’ quasi-static responses to different prestrains with arbitrary θ and pressures. Three laminates are fabricated to validate the model. Model-based sensitivity studies reveal the bistability response to multiple design factors, including the angle of non-orthogonal prestress, prestrains, and pneumatic pressure.

Shape reconfiguring bistable structures using heat activated fibers

Engineering structures have increasingly begun to utilize mechanical instability in areas such as energy absorption, shape reconfiguration, and vibration attenuation. Most multi-stable mechanisms use 1D architectures such as pre-curved beams or inclined trusses to achieve multiple strain energy minima. These structures pose several limitations, (1) they generally require external support for functionality, (2) they often balance the competing demands of large stiffness and large amplitude in shape change, and (3) they are inherently less energetically dense compared to shell-based structures as there is negligible stretching in the material. In this work, we introduce a novel class of 4D printed bistable shell structures that morph from flat surfaces. We investigate both the formation of the structural geometry, and the mechanics of the shells once morphed. Following the precepts of 4D printing, the structural geometry is achieved in two stages. First 3D printing is used to fabricate flat polygon unit cells which are then morphed into symmetrical bistable shells. Utilizing Fused Filament Fabrication, a viscoelastic material is pre-strained as it is deposited on the print bed. By tuning the printing parameters, a predictable 2D to 3D shape morphing is triggered with heat, resulting in a height increase of up to 22.9 times the original size. Some resulting unit cells exhibit an elastic bistable response with a high peak force from a point indentation. Shape morphing and structural bistability is predicted using Finite-Element Analysis with prescribed pre-strain aligned with the fiber extrusion direction. The resulting geometries are analyzed for their mechanical behavior. Buckling simulations show good agreement with experimental results. To demonstrate an energy-dissipating metamaterial, we fabricate a planar meta-surface tiled using triangular unit cells to create an auxetic pattern. This sheet morphs to conform to a doubly curved surface globally, with each unit-cell transforming to a bistable shell locally. With this approach, we create a new generation of 4D printed bistable structures that can be applied to a variety of engineering applications.

Jump and Pull-in Instability of a MEMS Gyroscope Vibrating System.

Jump and pull-in instability are common nonlinear dynamic behaviors leading to the loss of the performance reliability and structural safety of electrostatic micro gyroscopes. To achieve a better understanding of these initial-sensitive phenomena, the dynamics of a micro gyroscope system considering the nonlinearities of the stiffness and electrostatic forces are explored from a global perspective. Static and dynamic analyses of the system are performed to estimate the threshold of the detecting voltage for static pull-in, and dynamic responses are analyzed in the driving and detecting modes for the case of primary resonance and 1:1 internal resonance. The results show that, when the driving voltage frequency is a bit higher than the natural frequency, a high amplitude of the driving AC voltage may induce the coexistence of bistable periodic responses due to saddle-node bifurcation of the periodic solution. Basins of attraction of bistable attractors provide evidence that disturbance of the initial conditions can trigger a jump between bistable attractors. Moreover, the Melnikov method is applied to discuss the condition for pull-in instability, which can be ascribed to heteroclinic bifurcation. The validity of the prediction is verified using the sequences of safe basins and unsafe zones for dynamic pull-in. It follows that pull-in instability can be caused and aggravated by the increase in the amplitude of the driving AC voltage.

Optical bistability and entanglement in two optically coupled cavities under the effect of a nonlinear medium

We theoretically investigate optical bistability and entanglement in a hybrid nonlinear system of two coupled cavities via a single-mode waveguide. The left cavity contains an ensemble of N quantum dots (QDs) and a Kerr medium to enhance the nonlinearity as it causes to observe the bistable behaviour of the system. We study the Kerr medium, QD ensemble, and cavity coupling effect on bistability response shown by mean intracavity photons in the left cavity. In addition, we have shown entanglement between different subsystems and found that entanglement can be generated between the two coupled cavity photons, cavity photons, and QD ensembles. Additionally, we investigate the effect of different parameters on entanglement. Our findings show that Kerr nonlinearity and the hopping parameter between the two cavities can effectively control the optical properties of the proposed hybrid system, which can be used to design efficient optical devices and the entangled optical photons have applications such as quantum information transfer.

Optical bistability and four-wave mixing response of a quantum dot coupled to an optomechanical photonic crystal nanocavity

We theoretically explore the nonlinear optical response including optical bistability and four-wave mixing (FWM) process in a hybrid cavity quantum electrodynamic (C-QED) system. The hybrid C-QED system consists of a quantum dot (QD) which is coherently driven by two-tone laser fields and embedded in an optomechanical photonic crystal (PhC) nanocavity. Our theoretical analysis demonstrates optical bistability, where the steady-state photon number follows a constant rise in the gain of the switch by controlling a strong pump field driving the QD. A strong coupling between quantised fields and matter (e.g. in optical cavities) is a successful approach for conventionally modifying the dressed state and by altering the field parameters, the modulation of QD dressed state is accomplished. In addition, we list the influence of off-resonant detuning, exciton-nanocavity coupling strength and Rabi coupling strength in our proposed system which generates a controllable four-wave mixing (FWM) signal in the output probe field of the system. The intensity of the FWM is significantly changed when strong coupling and high pump power are present simultaneously and results in the formation of an optomechanically induced transparency (OMIT) window and slow light. The investigation of the proposed system have potential application towards on-chip QD-based nanophotonic devices.

First-Order Reversal Curves of Sets of Bistable Magnetostrictive Microwires.

Amorphous microwires have attracted substantial attention in the past decade because of their useful technological applications. Their bistable magnetic response is determined by positive or negative magnetostriction, respectively. First-order reversal curves (FORC) are a powerful tool for analyzing the magnetization reversal processes of many-body ferromagnetic systems that are essential for a deeper understanding of those applications. After theoretical considerations about magnetostatic interactions among microwires, this work introduces a systematic experimental study and analysis of the FORC diagrams for magnetostrictive microwires exhibiting an individually bistable hysteresis loop, from a single microwire to sets of an increasing number of coupled microwires, the latter considered as an intermediate case to the standard many-body problem. We performed the study for sets of quasi-identical and different hysteretic microwires where we obtained the coercivity Hc and interaction Hu fields. In the cases with relevant magnetostatic interactions, FORC analysis supplies deeper information than standard hysteresis loops since the intrinsic fluctuations of the switching field generate a complex response. For sets of microwires with very different coercivity, the coercivity distributions of the individual microwires characterize the FORC diagram.

Enhanced sensing of optomechanically induced nonlinearity by linewidth suppression and optical bistability in cavity-waveguide systems.

We study the enhanced sensing of optomechanically induced nonlinearity (OMIN) in a cavity-waveguide coupled system. The Hamiltonian of the system is anti-PT symmetric, with the two involved cavities being dissipatively coupled via the waveguide. The anti-PT symmetry may break down when a weak waveguide-mediated coherent coupling is introduced. However, we find a strong bistable response of the cavity intensity to the OMIN near the cavity resonance, benefiting from linewidth suppression caused by the vacuum induced coherence. The joint effect of optical bistability and the linewidth suppression is inaccessible by the anti-PT symmetric system involving only dissipative coupling. Due to that, the sensitivity measured by an enhancement factor is greatly enhanced by two orders of magnitude compared to that for the anti-PT symmetric model. Moreover, the enhancement factor shows resistance to a reasonably large cavity decay and robustness to fluctuations in the cavity-waveguide detuning. Based on the integrated optomechanical cavity-waveguide systems, the scheme can be used for sensing different physical quantities related to the single-photon coupling strength and has potential applications in high-precision measurements with systems involving Kerr-type nonlinearity.

Unraveling context-specific mechanisms governing calcium-YAP/TAZ distinct relationships through computational modeling.

Yes-associated protein (YAP) and its homolog TAZ are transducers of several biochemical and biomechanical signals, serving to integrate multiplexed inputs from the microenvironment into higher level cellular functions such as proliferation, differentiation, apoptosis, migration, and hemostasis. Emerging evidence suggests that calcium is a key second messenger that closely connects microenvironmental input signals and YAP/TAZ regulation. However, studies that directly modulate Ca2+ have reported contradictory YAP/TAZ responses: In some studies, a reduction in Ca2+ influx increases the activity of YAP/TAZ, while in others an increase in Ca2+ influx activates YAP/TAZ. Importantly, Ca2+ and YAP/TAZ exhibit distinct spatiotemporal dynamics, making it difficult to unravel their connections from a purely experimental approach. In this study, we developed a network model of Ca2+-mediated YAP/TAZ signaling to investigate how temporal dynamics and crosstalk of signaling pathways interacting with calcium can alter YAP/TAZ response. By including six signaling modules (e.g., GPCR, IP3- Ca2+, Kinases, RhoA, F-actin, and Hippo-YAP/TAZ) that interact with calcium, we investigated both transient and steady-state cell response to Angiotensin II, Thapsigargin, and ECM stiffness stimuli. The model predicts a context-dependent relationship between calcium signaling and YAP/TAZ activation primarily mediated by PKC, DAG, CaMKII, and F-actin. Model results illustrate the role of calcium dynamics and CaMKII bistable response in switching the direction of changes in Ca2+-induced YAP/TAZ activity. Frequency-dependent YAP/TAZ response revealed the competition between upstream regulators of LATS1/2, leading to the YAP/TAZ non-monotonic response to periodic GPCR stimulation. We also identified key roles of Ca2+ and CaMKII dynamics in shaping the nonlinear relationship between cell size and YAP/TAZ activity. The model predicts Ca2+-YAP/TAZ distinct relationships in different settings consistent with experiments. The model predictions provide new insights into the underlying mechanisms responsible for the controversial Ca2+-YAP/TAZ relationship observed in experiments.

Mechanisms underlying divergent relationships between Ca2+ and YAP/TAZ signalling.

Yes-associated protein (YAP) and its homologue TAZ are transducers of several biochemical and biomechanical signals, integrating multiplexed inputs from the microenvironment into higher level cellular functions such as proliferation, differentiation and migration. Emerging evidence suggests that Ca2+ is a key second messenger that connects microenvironmental input signals and YAP/TAZ regulation. However, studies that directly modulate Ca2+ have reported contradictory YAP/TAZ responses: in some studies, a reduction in Ca2+ influx increases the activity of YAP/TAZ, while in others, an increase in Ca2+ influx activates YAP/TAZ. Importantly, Ca2+ and YAP/TAZ exhibit distinct spatiotemporal dynamics, making it difficult to unravel their connections from a purely experimental approach. In this study, we developed a network model of Ca2+ -mediated YAP/TAZ signalling to investigate how temporal dynamics and crosstalk of signalling pathways interacting with Ca2+ can alter the YAP/TAZ response, as observed in experiments. By including six signalling modules (e.g. GPCR, IP3-Ca2+ , kinases, RhoA, F-actin and Hippo-YAP/TAZ) that interact with Ca2+ , we investigated both transient and steady-state cell response to angiotensin II and thapsigargin stimuli. The model predicts that stimuli, Ca2+ transients and frequency-dependent relationships between Ca2+ and YAP/TAZ are primarily mediated by cPKC, DAG, CaMKII and F-actin. Simulation results illustrate the role of Ca2+ dynamics and CaMKII bistable response in switching the direction of changes in Ca2+ -induced YAP/TAZ activity. A frequency-dependent YAP/TAZ response revealed the competition between upstream regulators of LATS1/2, leading to the YAP/TAZ non-monotonic response to periodic GPCR stimulation. This study provides new insights into underlying mechanisms responsible for the controversial Ca2+ -YAP/TAZ relationship observed in experiments. KEY POINTS: YAP/TAZ integrates biochemical and biomechanical inputs to regulate cellular functions, and Ca2+ acts as a key second messenger linking cellular inputs to YAP/TAZ. Studies have reported contradictory Ca2+ -YAP/TAZ relationships for different cell types and stimuli. A network model of Ca2+ -mediated YAP/TAZ signalling was developed to investigate the underlying mechanisms of divergent Ca2+ -YAP/TAZ relationships. The model predicts context-dependent Ca2+ transient, CaMKII bistable response and frequency-dependent activation of LATS1/2 upstream regulators as mechanisms governing the Ca2+ -YAP/TAZ relationship. This study provides new insights into the underlying mechanisms of the controversial Ca2+ -YAP/TAZ relationship to better understand the dynamics of cellular functions controlled by YAP/TAZ activity.

Optimization with photonic wave-based annealers.

Many NP-hard combinatorial optimization (CO) problems can be cast as a quadratic unconstrained binary optimization model, which maps naturally to an Ising model. The final spin configuration in the Ising model can adiabatically arrive at a solution to a Hamiltonian, given a known set of interactions between spins. We enhance two photonic Ising machines (PIMs) and compare their performance against classical (Gurobi) and quantum (D-Wave) solvers. The temporal multiplexed coherent Ising machine (TMCIM) uses the bistable response of an electro-optic modulator to mimic the spin up and down states. We compare TMCIM performance on Max-cut problems. A spatial photonic Ising machine (SPIM) convolves the wavefront of a coherent laser beam with the pixel distribution of a spatial light modulator to adiabatically achieve a minimum energy configuration, and solve a number partitioning problem (NPP). Our computational results on Max-cut indicate that classical solvers are still a better choice, while our NPP results show that SPIM is better as the problem size increases. In both cases, connectivity in Ising hardware is crucial for performance. Our results also highlight the importance of better understanding which CO problems are most likely to benefit from which type of PIM. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.

Bistable insulin response: The win-win solution for glycemic control.

To satisfy both the safety and rapidity of glycemic control, muscles' insulin response must be bistable, as theoretically predicted. Here, we test the bistability hypothesis by combining cellular experiments (to measure the threshold values invitro) with mathematical modeling (to test the relevance of bistability invivo). We examine bistability in C2C12 myotubes by both single-cell analysis (Fӧrster resonance energy transfer) and cultured cells analysis (immunoblot). These technologies demonstrate bistable insulin response, with typical switch-on and switch-off thresholds of approximately 300 and 100 pM, respectively. Our mathematical model demonstrates the indispensability of bistability in interpreting experimental data, reveals fine details of plasma glucose-insulin dynamics, and explains unclear phenomena. These results suggest that the body's ability to simultaneously avoid both hypoglycemia and hyperglycemia is mediated by bistability. The switch-on threshold is a promising biomarker for metabolic complications due to its deep quantitative connection with body composition, which is easy to measure.