Tristable States Research Articles

Multistability of a long droplet in a capillary tube under transverse body force

Bistable states for a sufficiently large amount of liquid can appear in an eccentric capillary due to the eccentricity effect under zero gravity (J. Fluid Mech, vol. 863, 2019, pp. 364–385). A transverse body force, which can lead to rich physical phenomena of a droplet, may lead to multistable states (bistability, tristability and the likes) of a sufficiently large amount of liquid in a capillary. We theoretically investigate this situation in a circular or annular capillary tube under a transverse body force. The results show that there can be tristable (bistable) states in an annular (circular) capillary tube: an occluding configuration and two (one) non-occluding configurations. In the annular tube, for one of the non-occluding configurations, the gas–liquid interface in the middle cross-section of the droplet meets both the inner and outer walls of the tube (bridging configuration); for the other non-occluding configuration, the gas–liquid interface in the middle cross-section of the droplet does not meet the inner wall (non-bridging configuration). The multistability is dependent on the Bond number, the contact angle and the cross-sectional shape. The multistability cannot occur for a zero or very large Bond number. A hydrophilic condition (the contact angle smaller than 90°) contributes to the non-occluding non-bridging configuration, while the hydrophobic condition (the contact angle larger than 90°) contributes to the non-occluding bridging configuration (only for the annular capillary). For the annular capillary with a not-so-large contact angle, increasing the inner-to-outer radius ratio can lead to a larger range of Bond numbers, in which the multistability occurs.

Stability of pairwise social dilemma games: Destructive agents, constructive agents, and their joint effects.

Destructive agents, who opt out of the game and indiscriminately harm others, paradoxically foster cooperation, representing an intriguing variant of the voluntary participation strategy. Yet, their impact on cooperation remains inadequately understood, particularly in the context of pairwise social dilemma games and in comparison to their counterparts, constructive agents, who opt out of the game but indiscriminately benefit others. Furthermore, little is known about the combined effects of both agent types on cooperation dynamics. Using replicator dynamics in infinite and well-mixed populations, we find that contrary to their role in facilitating cooperation in multiplayer games, destructive agents fail to encourage cooperation in pairwise social dilemmas. Instead, they replace defection in the prisoners' dilemma and stag-hunt games. Similarly, in the chicken game, they can destabilize or replace the mixed equilibrium of cooperation and defection, undermining cooperation in the harmony (trivial) game. Conversely, constructive agents, when their payoffs exceed their contributions to opponents, can exhibit effects similar to destructive agents. However, if their payoffs are lower, while they destabilize defection in prisoners' dilemma and stag-hunt games, they do not disrupt the cooperation equilibrium in harmony games and have a negligible impact on the coexistence of cooperation in chicken games. The combination of destructive and constructive agents does not facilitate cooperation, but instead generates complex evolutionary dynamics, including bistable, tristable, and quadstable states, with outcomes contingent on their relative payoffs and game types. These results, taken together, enhance our understanding of the impact of the voluntary participation mechanism on cooperation, contributing to a more comprehensive understanding of its influence.

Tristable TaOx-based memristor by controlling oxygen vacancy transportion based on valence transition mechanism

It is always a hot and difficult problem of how to realize multi-bit data storage by preparing multi-resistance memristors by a simple process compatible with standard CMOS processes. In this work, a tristable TaOx-based memristor with tunable oxygen vacancies is fabricated by physical vapor deposition, consisting of a high-resistance state and two low-resistance states. Its set and reset voltages are low −1.1V, −2.1V, and -1V, 3.3V, respectively. The XPS characterization demonstrates the presence of three valence states within the TaOx film. It has been suggested that different barriers lead to different switching voltages during the transition of the trivalent state, resulting in the formation of stable states. Interestingly, when increasing the concentration of oxygen during preparation to decrease the concentration of oxygen vacancies in TaOx film, the volt-ampere properties of memristor change from tristable to bistable, which further proves the above point. This work provides a viable strategy for switching between bistable and tristable states in memristors prepared from transition metal oxides.

Analysis of Dynamic Characteristics of Tristable Exponential Section of Piezoelectric Energy Harvester

Variable-cross-section beams have better mass and strength distribution compared with constant cross-section beams, which can optimize the harvesting power of piezoelectric vibration energy harvesters, which are widely used in self-supplied and low-power electronic devices, providing more convenience and innovation for the development of micromechanical intelligence and portable mobile devices. This paper proposes a piezoelectric energy harvester with a tristable-exponential-decay cross section, which optimizes the strain distribution of the cantilever beam through exponential decay changes to improve the harvesting efficiency of the harvester in low-frequency environments. First, the nonlinear magnetic force is obtained based on the magnetic dipole, and the dynamic model is established by using the Euler–Bernoulli beam theory and Lagrangian equation. The influence of the structural parameters of the harvester on the system dynamics and output characteristics is analyzed in the two dimensions of time and frequency, and the influence of the exponential decay coefficient on the system dynamic response and output power is deeply studied. The research shows that the exponential decay section can reduce the first natural frequency of the cantilever beam; by changing the amplitude, frequency, d and dg of the excitation acceleration, the switching of the monostable, tristable and bistable states of the system can be realized. With a decrease in the exponential decay coefficient, under a low-frequency excitation of 0–7 Hz, the output power of the cantilever beam per unit volume is significantly improved, and under a 4 Hz low-frequency excitation, the acquisition output power per unit volume of the cantilever beam is increased by 7 times, thus realizing low-frequency, high-efficiency energy harvesting.

Depolarization induced III-V triatomic layers with tristable polarization states.

The integration of ferroelectrics that exhibit high dielectric, piezoelectric, and thermal compatibility with the mainstream semiconductor industry will enable novel device types for widespread applications, and yet there are few silicon-compatible ferroelectrics suitable for device downscaling. We demonstrate with first-principles calculations that the enhanced depolarization field at the nanoscale can be utilized to soften unswitchable wurtzite III-V semiconductors, resulting in ultrathin two-dimensional (2D) sheets possessing reversible polarization states. A 2D sheet of AlSb consisting of three atomic planes is identified to host both ferroelectricity and antiferroelectricity, and the tristate switching is accompanied by a metal-semiconductor transition. The thermodynamic stability and potential synthesizability of the triatomic layer are corroborated with phonon spectrum calculations, ab initio molecular dynamics simulations, and variable-composition evolutionary structure search. We propose a 2D AlSb-based homojunction field effect transistor that supports three distinct and nonvolatile resistance states. This new class of III-V semiconductor-derived 2D materials with dual ferroelectricity and antiferroelectricity opens up the opportunity for nonvolatile multibit-based integrated nanoelectronics.

STOCHASTIC STABILITY AND PARAMETRIC CONTROL IN A GENERALIZED AND TRI-STABLE VAN DER POL SYSTEM WITH FRACTIONAL ELEMENT DRIVEN BY MULTIPLICATIVE NOISE

The stochastic transition behavior of tri-stable states in a fractional-order generalized Van der Pol (VDP) system under multiplicative Gaussian white noise (GWN) excitation is investigated. First, according to the minimal mean square error (MMSE) concept, the fractional derivative can be equivalent to a linear combination of damping and restoring forces, and the original system can be simplified into an equivalent integer-order system. Secondly, the stationary Probability Density Function (PDF) of system amplitude is obtained by stochastic averaging, and based on singularity theory, the critical parameters for stochastic [Formula: see text]-bifurcation of the system are found. Finally, the properties of stationary PDF curves of the system amplitude are qualitatively analyzed by choosing the corresponding parameters in each sub-region divided by the transition set curves. The consistency between numerical results obtained by Monte-Carlo simulation and analytical solutions verified the accuracy of the theoretical analysis process and the method used in this paper has a direct guidance in the design of fractional-order controller to adjust the system behavior.

Squeezed-vacuum-induced optical tristability in an atom-cavity system

In this paper we investigate the model of $N$ two-level atoms coupled to a squeezed vacuum inside a coherently driven cavity. By a linear stability analysis in the semiclassical description, we find that the optical tristability emerges in our system owing to the presence of the squeezed vacuum. Moreover, the transition among monostable, bistable, and tristable states can be realized by manipulating the squeezing phase or the squeezing strength of the squeezed vacuum. We also show the signatures of quantum tristability by using the $Q$ function and quantum trajectory methods for the situation of a single atom and low cavity photon number. Our paper offers a way to realize optical tristability in a two-level atomic system.

Quantifying the Landscape of Decision Making From Spiking Neural Networks.

The decision making function is governed by the complex coupled neural circuit in the brain. The underlying energy landscape provides a global picture for the dynamics of the neural decision making system and has been described extensively in the literature, but often as illustrations. In this work, we explicitly quantified the landscape for perceptual decision making based on biophysically-realistic cortical network with spiking neurons to mimic a two-alternative visual motion discrimination task. Under certain parameter regions, the underlying landscape displays bistable or tristable attractor states, which quantify the transition dynamics between different decision states. We identified two intermediate states: the spontaneous state which increases the plasticity and robustness of changes of minds and the “double-up” state which facilitates the state transitions. The irreversibility of the bistable and tristable switches due to the probabilistic curl flux demonstrates the inherent non-equilibrium characteristics of the neural decision system. The results of global stability of decision-making quantified by barrier height inferred from landscape topography and mean first passage time are in line with experimental observations. These results advance our understanding of the stochastic and dynamical transition mechanism of decision-making function, and the landscape and kinetic path approach can be applied to other cognitive function related problems (such as working memory) in brain networks.

Possible existence of tristable polarization states in LiNbO3 under an open-circuit boundary condition

Hyperferroelectricity is an intriguing phenomenon in that electric polarization persists under the open-circuit boundary condition (OCBC). Using first-principles density functional calculations, we investigate the hyperferroelectric properties of ${\mathrm{LiNbO}}_{3}$, a technologically important ferroelectric solid. We find that (i) the longitudinal-optic ${\mathrm{A}}_{2\mathrm{u}}({\mathrm{LO}}_{1})$ phonon is soft with imaginary frequency $96i\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ when centrosymmetric ${\mathrm{LiNbO}}_{3}$ is under OCBC, and this soft LO phonon is shown to differ drastically from the corresponding transverse-optic ${\mathrm{A}}_{2\mathrm{u}}({\mathrm{TO}}_{1})$ phonon. (ii) The ${\mathrm{A}}_{2\mathrm{u}}({\mathrm{LO}}_{1})$ phonon is able to yield, under OCBC, a free-energy minimum with well depth of $\ensuremath{-}9$ meV at a nonzero polarization of 0.023 C/${\mathrm{m}}^{2}$, thereby capable of producing hyperferroelectricity. (iii) The origin that ${\mathrm{A}}_{2\mathrm{u}}({\mathrm{LO}}_{1})$ is capable of inducing HyFE is determined, and it stems from the extraordinarily small mode effective charge of this soft LO phonon. This finding also provides a key guiding principle for searching and designing new hyperferroelectrics. (iv) Despite that ${\mathrm{A}}_{2\mathrm{u}}({\mathrm{LO}}_{1})$ is able to induce HyFE, we find that the ground state of ${\mathrm{LiNbO}}_{3}$ under OCBC is nevertheless not polar, revealing that the existence of a soft LO phonon does not guarantee HyFE. (v) Interestingly, we further show that ${\mathrm{LiNbO}}_{3}$ under OCBC may exhibit unusual tristable polarization states, with two potential wells of depth $\ensuremath{-}23$ meV and $\ensuremath{-}1.9$ meV, respectively. Besides providing insightful knowledge for understanding HyFE in general, these results reveal that there is rich and interesting hyperferroelectric physics in ${\mathrm{LiNbO}}_{3}$ under OCBC, in particular.

Tristable flow states and reversal of the large-scale circulation in two-dimensional circular convection cells

Abstract

Effective control and switching of optical multistability in a three-level V-type atomic system

We theoretically analyze the behavior of single optical bistability (OB), double OB, and tristability (OT) in a three-level V-type atomic system confined in a unidirectional optical ring cavity. The physics behind the emergence of various bistable and tristable states, and switching from the absorptive to the dispersive characteristics, are explored. The role of probe- and control-field detunings on the input-output characteristics is probed. Further, it is found that the switching between various bistable phenomena is defined by the ratio between the absolute peak values of the parameters describing dispersion and absorption, respectively. This ratio sets a criterion for obtaining absorptive OB, OT, double OB, and dispersive OB. The role of control-field intensity and detuning as well as the cooperation parameter on the input-output characteristics are explored. Finally, a scheme is discussed to control the width of the middle branch of double OB and OT as well as single OB.

Weak fault detection in rotating machineries by using vibrational resonance and coupled varying-stable nonlinear systems

In the era of Industry 4.0, weak faults on a critical component must be detected timely to ensure the reliability of a critical machine. However, in general, a weak fault signal cannot be easily detected due to the presence of strong background noise and weak fault characteristics. Thus, in this work, we investigate a new weak fault detection method based on the vibrational resonance (VR) and coupled varying-stable nonlinear systems. In contrast to most existing noise cancellation fault detection methods, the proposed method can be regarded as a noise utilization method. Furthermore, in contrast to the stochastic resonance (SR) technique, which is a noise utilization fault detection method, the proposed method is easily controllable and exhibits a better performance. Moreover, resonance can be easily and adaptively achieved, and the varying-stable systems can be controlled to exhibit monostable, bistable or tristable states, by tuning the system parameters. In this paper, the nonlinear systems are coupled; therefore, the nonlinear systems are dependent on each other, and the interactions among them are extensively considered. The proposed method is validated by considering an implanted gear fault on a planetary gearbox and several naturally developed bearing faults on a fixed axis gearbox. The mechanism of noise utilization is illustrated, and different nonlinear systems with different configurations are considered. The corresponding results are compared to validate the effectiveness and advantages of the proposed method.

Nonvolatile WORM and rewritable multifunctional resistive switching memory devices from poly(4-vinyl phenol) and 2-amino-5-methyl-1,3,4-thiadiazole composite

A multifunctional resistive switching memory devices with the typical sandwich structure of Al/Poly(4-vinylphenol) (PVP)+2-Amino-5-methyl-1,3,4-thiadiazole/Al is fabricated. Al as the bottom and top electrodes is easy to realize by simple thermal evaporation process, and a PVP and 2-Amino-5-methyl-1,3,4-thiadiazole composite film as the active layer is prepared by sol-gel method and spin coating process. The as-fabricated resistive switching memory device shows write-once-read-many (WORM) and rewritable multifunctional memory behaviors, for the rewritable and WORM memory modes, the ON/OFF ratio is 104 and 80, respectively. The as-fabricated device shows tristable conductivity states which equivalent to “0”, “1” and “2”, and these three conductance states are steady under the constant voltage retention test, as well as during the endurance test, indicating advantageous features of stable operation and dependable endurance. It is noteworthy that the simple preparation process is expected to promisingly hold the post of industrialization low-cost preparation in future electronic devices for ternary data storage utilities.

Complex Dynamics in a Unified SIR and HIV Disease Model: A Bifurcation Theory Approach

This paper is concerned with complex dynamical behaviors of a simple unified SIR and HIV disease model with a convex incidence and four real parameters. Due to the complex nature of the disease dynamics, our goal is to explore bifurcations including multistable states, limit cycles, and homoclinic loops in the whole parameter space. The first contribution is the proof of the existence of multiple limit cycles giving rise from Hopf bifurcation, which further induces bistable or tristable states because of the coexistence of stable equilibria and periodic motion. Next, we propose that the existence of Bogdanov–Takens (BT) bifurcation yields the bifurcation of homoclinic loops, which provides a new mechanism for generating disease recurrence, for example, the relapse–remission, viral blip cycles in HIV infection. Last, we present a novel method for the derivation of the normal forms of codimension two and three BT bifurcations. The method is based on the simplest normal form theory from Yu’s previous works.

Modeling of mesenchymal hybrid epithelial state and phenotypic transitions in EMT and MET processes of cancer cells

Based on the transcriptional regulatory mechanisms between microRNA-200 and transcription factor ZEB in an individual cancer cell, a minimal dynamic model is proposed to study the epithelial-mesenchymal transition (EMT) and mesenchymal-epithelial transition (MET) processes of cancer cells. It is shown that each cancer cell can exit in any of three phenotypic states: the epithelial (E) state, the mesenchymal (M) state, and the epithelial/mesenchymal (E/M) hybrid state, and the state of cancer cell can interconvert between different states. The phase diagram shows that there are monostable, bistable, and tristable phenotypic states regions in a parameters plane. It is found that different pathway in the phase diagram can correspond to the EMT or the MET process of cancer cells, and there are two possible EMT processes. It is important that the experimental phenomenon of E/M hybrid state appearing in the EMT process but rather in the MET process can be understood through different pathways in the phase diagram. Our numerical simulations show that the effects of noise are opposite to these of time delay on the expression of transcription factor ZEB, and there is competition between noise and time delay in phenotypic transitions process of cancer cells.

Phenomenological theory in dielectric tunable materials with the tristable states

ABSTRACTBoth ferroelectrics near the critical endpoint and antiferroelectrics are konwn to take the tristable states under the electric field as a common character, showing the double hysteresis loop. This common character may become a guiding principle for searching high-tunability materials. We theoretically investigated the dielectric tunabilities in ferroelectrics and antiferroelectrics on the basis of the phenomenological theory under the assumption of the homogeneous system. It was confirmed that the large tunability is realized with no field hysteresis just above the critical temperature in ferroelectrics, while in antiferroelectric materials, it may be obtained in a limited temperature range in the antiferroelectric state.

Improving energy harvesting in a tri-stable piezomagnetoelastic beam with two attractive external magnets subjected to random excitation

A novel tri-stable energy harvester (TEH) is developed to improve the efficiency of harvesting vibration energy. The corresponding dynamical model was established, and its motion equations were derived. The potential energy shows that the TEH owns shallower and wider potential wells than bi-stable energy harvester (BEH). The bifurcation diagrams of stable equilibrium positions show that the TEH can experience mono-stable, bi-stable, and tri-stable states by altering the separation and gap distances. The simulations were carried out. Validate experiments were performed for several random excitation levels. The results verify that the TEH can realize interwell oscillation easier and generate a dense of high output voltages. So the presented TEH is a promising alternative for improving the energy harvesting performance.

The angular dependence of the exchange bias under the planar domain wall model

Based on the principle of minimal energy, the angular dependence of exchange bias (ADEB) under planar domain wall model has been investigated in detail. Three different types of the initial states, monostable, bistable and tristable states, will be formed in exchange-biased systems by adjusting the relative strength of the uniaxial anisotropy, unidirectional anisotropy and the planar domain wall energy. These initial states determine the ADEB directly. The jump phenomena were still existent in the ADEB. Additionally, it can be found that the magnetization reversal mode is sensitive to the orientation of the magnetic field. Two distinct modes of the magnetization rotation, half-plane rotation and whole-plane rotation, can be observed when the applied field points along different orientations. These modes of the magnetization rotation can be identified by different features of the transverse hysteresis loops. Our investigations about the ADEB and the magnetization reversal modes are helpful to interpret the magnetic behaviors of some exchange-biased systems, which can be described by planar domain wall model.

Tristability of an orthotropic doubly curved shell

In this work, the structural response of a doubly curved orthotropic shell is tailored to achieve tristable geometries. This is done by varying both material properties and the Gaussian curvature of the surface profile. Tristability is predicted analytically, verified with finite element analysis and, for the first time, demonstrated experimentally. Predicted geometries of the tristable states are shown to compare well with experiment.

Biphotonic effect-induced phase transition in dye-doped cholesteric liquid crystals and their applications

This work studies the biphotonic effect in samples that are cholesteric liquid crystals (CLCs) doped with azo-C5. The experimental results show that the photo-isomerization of azo-C5 not only changes the clearing point of the sample, but also shifts the reflection band that is associated with the planar texture. Additionally, azo dye-doped CLCs (DDCLCs) have bi-stable or tri-stable states, as determined by the ambient temperature. Photo-switching between these bi-stable/tri-stable states is systematically studied. The result indicates that photo-addressing one of these states (planar, focal conic, and isotropic states) using a low- or high-intensity Ar + laser beam is feasible. The results thus obtained are used to fabricate a photo-rewritable DDCLC display.