Bistable Behavior Research Articles

Effect of imperfections on pseudo-bistability of viscoelastic domes

Snap-through instability of viscoelastic materials is known to generate novel behavior, featured as pseudo-bistability, i.e. the capability of a system in maintaining a deformed configuration for a certain period of time after removal of an external load, followed by snapping back to its initial configuration automatically, due to the combination of time-dependent mechanical property and geometric nonlinearity of the system. This work numerically, experimentally, and analytically examines spherical viscoelastic domes with predesigned geometric imperfections that can control the structural stability and tune the snap time, which is defined as the time that a dome remains almost stationary in the deformed configuration after the release of external forces. The results show that even an imperfection with a small magnitude can play a significant role in pseudo-bistability. An imperfection with a positive amplitude shifts a viscoelastic dome towards bistable behavior, corresponding to a longer snap time, while an imperfection with a negative amplitude shifts the dome towards monostable behavior, resulting in a shorter snap time. This work can open up new opportunities for controlling spatiotemporal behavior of structures for multi-functionalities.

Soft, Bistable Actuators for Reconfigurable 3D Electronics.

Existing strategies for reconfigurable three-dimensional (3D) electronics are greatly constrained by either the complicated driven mechanisms or harsh demands for conductive materials. Developing a simple and robust strategy for 3D electronics reconstruction and function extension remains a challenge. Here, we propose a solvent-driven bistable actuator, which acts as a substrate to reconstruct the combined 3D electronic device. Extraction of silicon oil from a hybrid poly(dimethylsiloxane) (PDMS) circle sheet buckles the dish to a bistable structure. The ultraviolet (UV)/ozone treatment on one surface of the PDMS structure introduces an oxidized layer, yielding a bilayered, solvent-driven bistable smart actuator. The snap-back stimulus to the oxidized layer differs from the snap-through stimulus. Experimental and numerical studies reveal the fundamental regulations for buckling configurations and the bistable behavior of the actuator. The prepared bistable actuator drives the bonded kirigami polyimide (PI) sheets to diverse 3D structures from the original bending configuration, reversibly. A frequency-reconfigurable electrically small monopole antenna is presented as a demonstration, which paves a way for the applications of this actuator in the field of reconfigurable 3D electronics.

Bistability in the synchronization of identical neurons.

We investigate the role of bistability in the synchronization of a network of identical bursting neurons coupled through an generic electrical mean-field scheme. These neurons can exhibit distinct multistable states and, in particular, bistable behavior is observed when their sodium conductance is varied. With this, we consider three different initialization compositions: (i) the whole network is in the same periodic state; (ii) half of the network periodic, half chaotic; (iii) half periodic, and half in a different periodic state. We show that (i) and (ii) reach phase synchronization (PS) for all coupling strengths, while for (iii) small coupling regimes do not induce PS, and instead, there is a coexistence of different frequencies. For stronger coupling, case (iii) synchronizes, but after (i) and (ii). Since PS requires all neurons being in the same state (same frequencies), these different behaviors are governed by transitions between the states. We find that, during these transitions, (ii) and (iii) have transient chimera states and that (iii) has breathing chimeras. By studying the stability of each state, we explain the observed transitions. Therefore, bistability of neurons can play a major role in the synchronization of generic networks, with the simple initialization of the system being capable of drastically changing its asymptotic space.

Nonlinear dynamics of fully developed swirling jets

This paper characterises the steady and time-periodic behaviour of swirling jets using numerical bifurcation analysis. Its objective is to elucidate the dynamics of fully developed, unconfined, laminar swirling jets under variations in the Reynolds number $\textit {Re}$ and swirl ratio $S$ . Within the $(0,0)\leq (\textit {Re},S)\leq (300,3)$ range, the steady, axisymmetric flow exhibits several distinct patterns ranging from a quasi-columnar jet along the central axis at low $S$ to a radial jet attached to the containing wall at high $S$ with various forms of vortex breakdown in between. A cusp bifurcation appears in the steady solution manifold which triggers bistable behaviour due to a competition between inner and outer low pressure regions associated with vortex breakdown and entrainment of the ambient fluid, respectively. Instability of the steady flow is linked to eigenmodes which are singly ( $|m|=1$ ) or doubly ( $|m|=2$ ) azimuthally periodic, although additional instabilities with other azimuthal wavenumbers occur at $(\textit {Re},S)$ -values beyond the leading neutral curves. The various branches of limit cycle solutions stemming from these neutral curves are associated with both super- and sub-critical Hopf bifurcations. The resulting unsteady flow fields exhibit a wide array of rotating, three-dimensional flow structures, and comparisons between the time-averaged and steady flow patterns highlight the role of these unsteady nonlinear interactions on the overall behaviour of swirling jets. Similarities and differences between this laterally unconfined jet and broader classes of swirling flows, including confined swirling jets and unconfined vortex models, are also discussed.

OPTICAL BISTABILITY IN A DEGENERATE TWO-LEVEL EIT MEDIUM UNDER THE INFLUENCE OF AN EXTERNAL MAGNETIC FIELD: AN ANALYTICAL APPROACH

We investigate the behavior of optical bistability in a degenerate two-level atomic medium using an external magnetic field to separate the lower level into two distinct levels that both connect to an upper level by the probe and coupling laser fields. Based on analytical solutions, the absorption spectrum and behavior of optical bistability in an electromagnetically induced transparency regime under an external magnetic field are investigated. By controlling the external magnetic field, we find that the appearance and disappearance of the optical bistability can be easily controlled according to the strength of the magnetic field in the transparent window domain. Furthermore, the effects of the intensity of the coupling laser field and the parameters of the system on the behavior of optical bistability are also considered. The proposed model is useful for applications in all-optical switches and magneto-optic storage devices.

Polariton multistability in a nonlinear optomechanical cavity

We theoretically study the polariton multistability in a solid state based optomechanical resonator embedded with a quantum well and a χ (2) second order nonlinear medium. The excitonic transition inside the quantum well is strongly coupled to the optical cavity mode. The polariton formed due to the mixing of cavity photons and exciton states are coupled to the mechanical mode which gives rise to the bistable behavior. A transition from bistability to tristability occurs in the presence of a strong χ (2) nonlinearity. Switching between bistability and tristability can also be controlled using exciton-cavity and optomechanical coupling making the system highly tunable. Tristability appears at low input power making it a suitable candidate for polaritonic devices which requires low input power.

Low threshold optical bistability in graphene/waveguide hybrid structure at terahertz frequencies

Here we propose a planar graphene/dielectric multilayer configuration to realize low threshold optical bistability at terahertz frequencies. This low-threshold optical bistability is achieved by field enhancement owing to the couple of the surface plasmon polaritons and the planar waveguide mode. We discussed the influence of graphene sheets and planar waveguide mode on the hysteretic response of the TM-polarization reflected light. It is found that the switch-up and switch-down threshold electric fields required to observe the optical bistable behavior are affected markedly by the excitation of surface plasmon polaritons or planar waveguide mode. Besides, the switching threshold value can be further reduced by coupling the surface plasmon polaritons and planar waveguide mode, hence providing a way of realizing low threshold and tunable optical bistable devices.

The Static Response of Axisymmetric Conical Shells Exhibiting Bistable Behavior

Abstract Belleville springs are widely used in a variety of mechanical systems. Recent advances in the field of multi-stable structures suggest that these conical axisymmetric washers may be extremely useful as bistable building blocks for multi-stable architected metamaterials. In this paper, we examine the ability of existing analytical models to accurately predict the bistable behavior of Belleville springs, namely, a nonmonotonous force–displacement relation with two branches of positive stiffness separated by a branch of negative stiffness. By comparing with results of finite element (FE) simulations, we find that current analytical models may suffer from significant inaccuracies associated with the assumption of rigid rotation. According to this assumption, adopted by all analytical models of Belleville springs, the cross section of the spring rotates without bending, i.e., maintains zero curvature as the spring deforms. Motivated by this insight, we relax the rigid-rotation assumption and approximate the radial displacement field by a linear relation in terms of the distance from the spring axis. We find, based on extensive finite element simulations, that the functional dependence of the radial displacement on the geometry of the springs is indifferent to the stage of deformation and can be expressed in terms of three geometrical parameters. These findings enable us to derive closed-form expressions that are simple and straightforward to use, yet are significantly more accurate than existing analytical models.

Bivalent chromatin as a therapeutic target in cancer: An in silico predictive approach for combining epigenetic drugs.

Tumour cell heterogeneity is a major barrier for efficient design of targeted anti-cancer therapies. A diverse distribution of phenotypically distinct tumour-cell subpopulations prior to drug treatment predisposes to non-uniform responses, leading to the elimination of sensitive cancer cells whilst leaving resistant subpopulations unharmed. Few strategies have been proposed for quantifying the variability associated to individual cancer-cell heterogeneity and minimizing its undesirable impact on clinical outcomes. Here, we report a computational approach that allows the rational design of combinatorial therapies involving epigenetic drugs against chromatin modifiers. We have formulated a stochastic model of a bivalent transcription factor that allows us to characterise three different qualitative behaviours, namely: bistable, high- and low-gene expression. Comparison between analytical results and experimental data determined that the so-called bistable and high-gene expression behaviours can be identified with undifferentiated and differentiated cell types, respectively. Since undifferentiated cells with an aberrant self-renewing potential might exhibit a cancer/metastasis-initiating phenotype, we analysed the efficiency of combining epigenetic drugs against the background of heterogeneity within the bistable sub-ensemble. Whereas single-targeted approaches mostly failed to circumvent the therapeutic problems represented by tumour heterogeneity, combinatorial strategies fared much better. Specifically, the more successful combinations were predicted to involve modulators of the histone H3K4 and H3K27 demethylases KDM5 and KDM6A/UTX. Those strategies involving the H3K4 and H3K27 methyltransferases MLL2 and EZH2, however, were predicted to be less effective. Our theoretical framework provides a coherent basis for the development of an in silico platform capable of identifying the epigenetic drugs combinations best-suited to therapeutically manage non-uniform responses of heterogenous cancer cell populations.

Tunable optical bistability at microwave frequency based on 1D sandwich photonic structure consisting of a nonlinear dielectric slab and two magnetized cold plasma layers

In this paper, tunable optical bistability that denotes the relationship between input intensity and output intensity is numerically investigated in the microwave frequency region based on the one-dimensional (1D) sandwich photonic structure consisting of a Kerr-type nonlinear material slab and two magnetized cold plasma layers. Results show that, in the case of TM-polarized electromagnetic wave, width and switching thresholds of the bistability loops are dependent on the working frequency, initial incidence angle, layer thickness, plasma density, and external magnetic field, which should be judiciously selected to obtain a required bistability behavior. Compared to the case of switch-down threshold, the switch-up threshold in the bistability loop is more sensitive to the changes of parameters. Through this study, the suggested 1D sandwich photonic structure is beneficial to the all-optical signal processing.

Morphological Evolution of Bistable Copper Electrodeposition during Potentiodynamic and Galvanodynamic Measurements on Microelectrodes

Copper electrodeposition from an electrolyte containing a polyether suppressor and chloride exhibits bistable behavior characteristic of s-shaped negative differential (S-NDR) critical systems. The polyether and chloride form a co-adsorbed adlayer on the electrode that inhibits copper electrodeposition by sterically blocking cupric ion from accessing the interface. At sufficiently negative overpotentials, the adlayer is disrupted and copper electrodeposition occurs freely. In cyclic voltammetry (CV) measurements this behavior manifests as large hysteretic windows. The current response is negligible during the forward sweep until potential-dependent breakdown of the suppressor-halide adlayer occurs. The return sweep exhibits elevated current levels until the blocking layer is reformed at potentials 100s of millivolts more positive than the breakdown potential. When operating at a potential within the hysteretic window, and in an electrochemical configuration with sufficient ohmic resistance, copper electrodeposition exhibits bistable, passive – active deposition on the electrode surface. On macroscale planar electrodes this manifests as random Turing patterns whereas on topographically engineered electrodes, common in electronics manufacturing applications, deposition is localized to the most recessed regions of the interface and progresses in a bottom-up manner.The inversion associated with NDR behavior is only apparent in CV measurements after post-experimental correction for the iR-drop in the electrochemical cell. Thus, linear or cyclic galvanodynamic sweeps (GDS) offer an alternative measurement method to capture the overpotential inversion associated with critical systems. Electroanalytical measurements on microelectrodes further offer an avenue for exploring systems without significant iR-drop in solution. In this work, CV and GDS measurements on microdisk electrodes are used to explore the influence of additive (suppressor and chloride) concentration on critical behavior during copper electrodeposition. Further, in-situ optical microscopy during electroanalytical measurements is used to correlate characteristics of global potential/current responses to observations of copper growth dynamics. Continuum simulations capture key characteristics, such as hysteresis and overpotential inversion, of CV and GDS measurements as well as the different deposit growth profiles observed for potentiodynamic versus galvanodynamic operating modes.

The role of tunable nonlinear dark resonances on vacuum Rabi splitting and optical bistability in an atom-cavity system

The phenomenon of “dark resonances” is a well-known concept in quantum optics and laser spectroscopy. As a general rule, interactions involving in such a “dark state” lead to multiple quantum superposition states that interact coherently and are undesirable. In this paper, two types nonlinear interaction in an atomic cavity, namely the nested and cascaded interactions, are theoretically analyzed how the dark resonances form the dark state peak to modulate the vacuum Rabi splitting (VRS) and optical bistability (OB) behavior. In both the zero- and high order modes, there are four VRS peaks generated in the nested interaction and three in the cascade interaction. Dark resonance can modulate not only the peak number of VRS, but also the OB thresholds. It is found that dark state can determine the asymmetric OB distribution of nested type and symmetric OB distribution of cascade type. Besides that, the distinctive OB thresholds in two kinds of interaction also be studied. The observations not only conceptually extend the conventional “dark resonances” phenomenon, but also opens the door for a variety of new applications in tunable all-optical switch and quantum communication.

Probability analysis of bistable composite laminates using the subset simulation method

Bistable composite laminates are advanced composite structures which are potential candidates for morphing structure applications. The geometrical dimensions, material properties, ambient temperature and moisture have significant effects on the bistable behaviour, and the effect of uncertain parameters should be quantified. Reliability analysis is well established for the quantitative assessment of the probability of an event due to parameter uncertainty. Thus, subset simulation is applied to the reliability and sensitivity analysis of bistable composite plates with multiple random parameters. The bistability probability is estimated using the principle of minimum energy; the Rayleigh-Ritz method is used to develop the equations of motion and the limit state function. The results indicate that the stacking sequence has a large effect on bistability probability, and cross-ply composite laminates are most likely to be bistable. Moreover, moisture absorption by the laminate can dramatically reduce this probability. The sensitivity reliability analysis demonstrates that for bistable laminates subject to humidity, the coefficient of thermal and moisture expansions have the greatest influence on the bistability probability. However, for bistable laminates without moisture the thickness is the most important factor. The accuracy and efficiency of the subset simulation method is validated by Monte Carlo simulation.

A systematic search for switch-like behavior in type II toxin-antitoxin systems.

Bistable switch-like behavior is a ubiquitous feature of gene regulatory networks with decision-making capabilities. Type II toxin-antitoxin (TA) systems are hypothesized to facilitate a bistable switch in toxin concentration that influences the dormancy transition in persister cells. However, a series of recent retractions has raised fundamental questions concerning the exact mechanism of toxin propagation in persister cells and the relationship between type II TA systems and cellular dormancy. Through a careful modeling search, we identify how sp: bistablilty can emerge in type II TA systems by systematically modifying a basic model for the RelBE system with other common biological mechanisms. Our systematic search uncovers a new combination of mechanisms influencing bistability in type II TA systems and explores how toxin bistability emerges through synergistic interactions between paired type II TA systems. Our analysis also illustrates how Descartes' rule of signs and the resultant can be used as a powerful delineator of bistability in mathematical systems regardless of application.

Irreversible Resistive State Switching in Devices with a Homoleptic Cobalt(II) Complex Active Layer.

Molecules with bi-stable electronic transport behaviour have been in upfront research topics of the molecular semiconductor devices in the past few decades due to the use of such materials in resistive data storage devices. Transition metal complexes (TMC) are expected to be potential candidates in regard to the tunable and manifold redox behaviour expecting multiple bulk transport states. Finding alternate mechanisms in such devices with TMC as the active layer materials would revoke the multifaceted approach to the functional gain. We have succeeded in demonstrating write once-read many (WORM) type of resistive memory device using a homoleptic Cobalt(II) (Co(II)) complex with large on/off current ratio ensuring the easy readout process at lower voltage. The advantage of this device was the turn on voltage was found to be the low (<2.7 V) operational voltage and the success ratio of the devices were more than 83%. The durability of the stored data was found to be more than 35,000 seconds which ensures the stability of the bistable state in the fabricated devices. Such ambient stable, solution processable devices are important for the large-scale printable devices. The manuscript describes the preparation, optical and electrochemical characterisation of the metal complex used along with a detailed mechanistic investigations and electrical characterisation of memory device obtained from a stable cobalt complex.

Fully compliant bistable mechanisms with enhanced pitch stiffness

For compliant bistable mechanisms with planar configurations and exhibiting two in-plane stable states, their flexible beams are supposed to undergo in-plane bending deflections, but the out-of-plane deflections can significantly influence the kinetostatics of the mechanism, resulting in inconsistent bistable behaviors when off-axis or eccentric loads present. In this paper, we propose a novel bistable mechanism utilizing torsion-stiffness enhanced flexible beams to restrain the shuttle from out-of-plane rotation. An analytical kinetostatic model is developed for the proposed bistable mechanism. Five bistable examples are presented to demonstrate the effectiveness of the proposed bistable mechanism in suppressing unwanted motions and the correctness of the proposed kinetostatic model. The results show that the novel bistable designs are much stiffer along the out-of-plane rotation thus are more robust against off-axis or eccentric loading condition, especially when the shuttle is displaced to a position around the second equilibrium stable position (where the flexible beams are in the post-buckling states).

Kerr-Like Nonlinearities in an Optomechanical System with an Asymmetric Anharmonic Mechanical Resonator

In the framework of the nonsecular perturbation theory based on the Bogoliubov averaging method, an optomechanical system with an asymmetric anharmonic mechanical resonator is studied. The cross-Kerr interaction and the Kerr-like self-interaction of photons and vibration quanta arise in the Hamiltonian. These interactions are induced by both cubic and quartic nonlinearities of oscillations of the mechanical resonator and the cavity-resonator interaction that is linear in mechanical displacements. We demonstrate a bistable behavior of the number of vibration quanta and find that this behavior is controlled by the cross-Kerr interaction. It is shown that, without driving and dissipation, the constructed superposition Yurke-Stoler-like states of the cavity (or the mechanical resonator) disentangle at certain times the entangled modes of the system. The obtained results offer new possibilities for control of optomechanical systems with asymmetric mechanical oscillations.

Understanding noise-controlled 2D bistable switch by approximating 1D potential

The potential landscape is an effective tool for describing the nonequilibrium behaviour of multistable system in the phase space. We estimate the 1D potential of a 2D bistable genetic switch model, which is used to understand the noise-controlled bistable switching behaviours. In the additive noise-induced switching, the distinct difference in residential time attributes to the different potential heights of the two states, and lower potential heights allow more frequently switching between two states. Furthermore, the unsymmetric multiplicative noises could change the residential time significantly through modulating the potential height of the state, where the modulated potential height could be obtained through implementing small noise approximation on the noises. The study confirms that the 1D potential of 2D bistable system could be used to understand noise-induced switching.

Experimental and Numerical Analysis of Gas Premix Turbulent Flames Stabilized in a Swirl Burner With Central Bluff Body

Abstract Lean premixed gas turbulent flames stabilized in the flow generated by an industrial swirl burner with a central bluff body are experimentally found to behave bistable. This bistable behavior, which can be triggered via a small change in some of the controlling parameters, for example, the bulk equivalence ratio, consists in a rather sudden transition of the flame from completely lifted to well attached to the bluff body. This has impact on combustion dynamics, emissions, and pressure losses. While several experimental investigations exist on this topic, numerical analysis is limited. This work is therefore also of numerical nature, with a twofold scope: (a) simulation and validation with experiments of the bistable flame behavior via computational fluid dynamics (CFD) in the form of large eddy simulation (LES) and (b) analysis of CFD results to shed light on the flame stabilization properties. LES results, in case of the lifted flame, show that the vortex core is sharply precessing at a given frequency. Phase averaging these results at the frequency of precession clearly indicates a counterintuitive and unexpected presence of reverse flow going all the way through the flame apex and the bluff body tip. The counterintuitive presence of a lifted flame is explained here in terms of the phase averaged data, which show that the flame apex is not placed at the center of the spinning reverse flow region. It is instead slightly shifted radially outward where the axial velocity recovers to low positive values of the order of the turbulent burning rate. A simple one-dimensional flame stabilization model is applied to explain this peculiar flame behavior. This model provides first an estimation of the flame radius of curvature in terms of axial velocity and turbulence quantities. This radius is therefore used to determine the total flux of reactants into the flame, given by an axial convection and radial diffusion contributions. Subsequently, the possibility of the flame positioned at the center of the vortex is excluded based on the balance between this flux and the turbulent burning rate. A clear explanation of the mechanism leading to the sudden flame jump has instead not been identified and only some hypotheses are provided.

Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements

In Veliz-Cuba and Stigler 2011, Boolean models were proposed for the lac operon in Escherichia coli capable of reproducing the operon being OFF, ON and bistable for three (low, medium and high) and two (low and high) parameters, representing the concentration ranges of lactose and glucose, respectively. Of these 6 possible combinations of parameters, 5 produce results that match with the biological experiments of Ozbudak et al., 2004. In the remaining one, the models predict the operon being OFF while biological experiments show a bistable behavior. In this paper, we first explore the robustness of two such models in the sense of how much its attractors change against any deterministic update schedule. We prove mathematically that, in cases where there is no bistability, all the dynamics in both models lack limit cycles while, when bistability appears, one model presents 30% of its dynamics with limit cycles while the other only 23%. Secondly, we propose two alternative improvements consisting of biologically supported modifications; one in which both models match with Ozbudak et al., 2004 in all 6 combinations of parameters and, the other one, where we increase the number of parameters to 9, matching in all these cases with the biological experiments of Ozbudak et al., 2004.