Bistable States Research Articles

Nonlinear dynamics with Hopf bifurcations by targeted mutation in the system of rock-paper-scissors metaphor

The role of mutation, which is an error process in gene evolution, in systems of cyclically competing species has been studied from various perspectives, and it is regarded as one of the key factors for promoting coexistence of all species. In addition to naturally occurring mutations, many experiments in genetic engineering have involved targeted mutation techniques such as recombination between DNA and somatic cell sequences and have studied genetic modifications through loss or augmentation of cell functions. In this paper, we investigate nonlinear dynamics with targeted mutation in cyclically competing species. In different ways to classic approaches of mutation in cyclic games, we assume that mutation may occur in targeted individuals who have been removed from intraspecific competition. By investigating each scenario depending on the number of objects for targeted mutation analytically and numerically, we found that targeted mutation can lead to persistent coexistence of all species. In addition, under the specific condition of targeted mutation, we found that targeted mutation can lead to emergences of bistable states for species survival. Through the linear stability analysis of rate equations, we found that those phenomena are accompanied by Hopf bifurcation which is supercritical. Our findings may provide more global perspectives on understanding underlying mechanisms to control biodiversity in ecological/biological sciences, and evidences with mathematical foundations to resolve social dilemmas such as a turnover of group members by resigning with intragroup conflicts in social sciences.

Qualitative assessment of the bi-stable states in the wake of a finite-width double backward facing step

The flow past a simplified frigate shape model which is analogous to a finite-width double backward facing step is investigated numerically using well-resolved large eddy simulations at Re≃8×104. The geometric configuration of this model permits the occurrence of bi-stable flow states, with an asymmetrical flow topology being observed in the lateral midplane behind each step. In each flow state, the flow at the top step is anti-symmetrical to that observed on the bottom step, and the two flow states are anti-symmetrical to each other. Furthermore, incorporating a base cavity on the top step leads to the suppression of the asymmetrical flow topology on both the steps. The recirculation bubble formed by the downwash at each step is elongated when the base cavity is used, as compared to that observed in either of the two flow states, resulting in a decrease of the drag coefficient. In each of the two flow states, the unequal strength of the streamwise vortices close to the lateral edges on the top step has been identified as the likely cause of the asymmetrical flow on the bottom step.

The effect of surface roughness on aerodynamic forces and vibrations for a circular cylinder in the critical Reynolds number range

The excitation mechanism of vibrations of circular cylinders in the critical Reynolds number range remains unclear. These vibrations have been observed in wind tunnels many times but rarely in the field. The surface roughness of the cylinder might be a reason for this difference. Aiming to reveal the effect of surface roughness on the aerodynamic forces and vibrations in the critical Reynolds number range, seven circular cylinders with various value of surface roughness were covered with abrasive papers and tested in stationary and elastically mounted wind tunnel tests. The results show that the surface roughness significantly influences the aerodynamic forces in the critical Reynolds number range by reducing the range of transitions on boundary layers. These influences include suppressing the jumps in lift coefficients and other phenomena that relate to a bistable state occurring only for less rough cylinders. Therefore, sufficient surface roughness can mitigate the vibrations in the critical Reynolds number range by suppressing the bistable state in which the vibrations appear.

Facile fabrication of ZnO nanowire memory device based on chemically-treated surface defects

In this study, we demonstrate a transistor-type ZnO nanowire (NW) memory device based on the surface defect states of a rough ZnO NW, which is obtained by introducing facile H2O2 solution treatment. The surface defect states of the ZnO NW are validated by photoluminescence characterisation. A memory device based on the rough ZnO NW exhibits clearly separated bi-stable states (ON and OFF states). A significant current fluctuation does not exist during repetitive endurance cycling test. Stable memory retention characteristics are also achieved at a high temperature of 85 °C and at room temperature. The surface-treated ZnO NW device also exhibits dynamically well-responsive pulse switching under a sequential pulse test configuration, thereby indicating its potential practical memory applications. The simple chemical treatment strategy can be widely used for modulating the surface states of diverse low-dimensional materials.

Vortex formation and evolution for flow over a circular cylinder excited by symmetric synthetic jets

The flow around a circular cylinder is controlled by a pair of synthetic jets symmetrically positioned near the separation points at a Reynolds number of 1200. The flow field in the near wake is measured by a collaboration of the flow visualization and the particle image velocimetry (PIV) techniques. The experiment is conducted under six different momentum coefficients Cμ, ranging from 0.007 to 0.421, while seven excitation frequencies are selected as harmonics of the dominant frequency. Various wake patterns appeared during this study, among which are the 2S asymmetric mode, the 2(P + S) asymmetric mode, the 2P symmetric mode, the 2S symmetric mode and the bistable state where vortices shed with both symmetric and asymmetric modes. The phase averaging method, the proper orthogonal decomposition (POD) based vorticity reconstruction and Fourier analysis are adopted to study the vortex dynamics. Particular attention is given to the vortex-formation mechanism for different modes under Cμ = 0.187, when all of the typical modes emerged. Vortex behaviors under symmetric excitation can be interpreted by looking into the processes of flow separation and vortex shedding. It is shown that synthetic jets can lead to unsteady flow separation and various vortex shedding modes are influenced by the periodic vorticity concertation induced by the synthetic jets.

A Pseudospectral solution of a bistable Fokker–Planck equation that models protein folding

We consider the one-dimensional bistable Fokker–Planck equation proposed by Polotto et al. (2018), with specific drift and diffusion coefficients so as to model protein folding. In this paper, a pseudospectral method is used to solve the Fokker–Planck equation in terms of the eigenvalues (λn) and eigenfunctions (ψn) of the Fokker–Planck operator. Nonclassical polynomials, constructed orthogonal with respect to the equilibrium distribution of the Fokker–Planck equation, are used as basis functions. The eigenvalues determined with the pseudospectral method are compared with the Wentzel–Kramers–Brillouin (WKB) and the SUperSYmmetric (SUSY) Wentzel–Kramers–Brillouin (SWKB) approximations. The eigenvalues calculated differ significantly from those reported by Polotto et al. A detailed study of the role of the lowest non-zero eigenvalue, λ1, to model the rate coefficient for the transition between the bistable states is provided.

Optically Tunable Field Effect Transistors with Conjugated Polymer Entailing Azobenzene Groups in the Side Chains

AbstractSemiconducting conjugated polymers with photoswitching behavior are highly demanded for field‐effect transistors (FETs) with tunable electronic properties. Herein a new design strategy is established for photoresponsive conjugated polymers by incorporating photochromic units (azobenzene) into the flexible side alkyl chains. It is shown that azobenzene groups in the side chains of the DPP (diketopyrrolopyrrole)‐quaterthiophene polymer (PDAZO) can undergo trans/cis photoisomerization in fully reversible and fast manner. Optically tunable FETs with bistable states are successfully fabricated with thin films of PDAZO. The drain‐source currents are reduced by 80.1% after UV light irradiation for ≈28 s, which are easily restored after further visible light irradiation for ≈33 s. Such fast optically tunable FETs are not reported before. Moreover, such current photomodulation can be implemented for multiple light irradiation cycles with good photofatigue resistance. Additionally, thin film charge mobility of PDAZO can be reversibly modulated by alternating UV and visible light irradiations. On the basis of theoretical calculations and GIWAXS data, it is hypothesized that the dipole moment and configuration changes associated with the trans‐/cis‐photoisomerization of azobenzene groups in PDAZO can affect the respective intra‐chain and inter‐chain charge transporting, which is responsible for the optically tunable behavior for FETs with thin films of PDAZO.

The effect of multigame on cooperation in spatial network

In real world, cooperation among unrelated agents remains to represent one open challenge in many disciplines. In some cases, subjects can even change their social dilemmas to ensure their own benefit. Inspired by this fact, here we propose a multigame (composed of prisoner's dilemma game and snowdrift game) and its coevolution mechanism in networked populations: if a player succeeds to study the strategy of its opponent, it also learns the game type of its opponent. Based on numerous computation simulations, it is unveiled that compared with the setup of multigame, coevolution mechanism can effectively resolve the problem of collective cooperation. While for this observation, it is attributed to the fact that vast majority of players changed their games to snowdrift game (i.e. lower social dilemma), where cooperation-defection bistable state guarantees cooperation clusters. We hope our finding can inspire more studies for resolving the social dilemmas.

Dynamics for encircling an exceptional point in a nonlinear non-Hermitian system.

We study the dynamics near an exceptional point in a nonlinear non-Hermitian system consisting of a pair of resonators. One of the resonators has a linear loss, and the other resonator has a saturable gain. We show that the system dynamics exhibit chiral characteristics. And moreover, unique to the nonlinear system, such dynamics allow one to adiabatically switch between bistable states at the same system parameter. Such bistable switching is potentially interesting in optical memory based on coupled laser systems.

High-Frequency Stochastic Switching of Graphene Resonators Near Room Temperature.

Stochastic switching between the two bistable states of a strongly driven mechanical resonator enables detection of weak signals based on probability distributions, in a manner that mimics biological systems. However, conventional silicon resonators at the microscale require a large amount of fluctuation power to achieve a switching rate in the order of a few hertz. Here, we employ graphene membrane resonators of atomic thickness to achieve a stochastic switching rate of 4.1 kHz, which is 100 times faster than current state-of-the-art. The (effective) temperature of the fluctuations is approximately 400 K, which is 3000 times lower than the state-of-the-art. This shows that these membranes are potentially useful to transduce weak signals in the audible frequency domain. Furthermore, we perform numerical simulations to understand the transition dynamics of the resonator and use analytical expressions to investigate the relevant scaling parameters that allow high-frequency, low-temperature stochastic switching to be achieved in mechanical resonators.

Voltage Control of a van der Waals Spin-Filter Magnetic Tunnel Junction.

Atomically thin chromium triiodide (CrI3) has recently been identified as a layered antiferromagnetic insulator, in which adjacent ferromagnetic monolayers are antiferromagnetically coupled. This unusual magnetic structure naturally comprises a series of antialigned spin filters, which can be utilized to make spin-filter magnetic tunnel junctions with very large tunneling magnetoresistance (TMR). Here we report voltage control of TMR formed by four-layer CrI3 sandwiched by monolayer graphene contacts in a dual-gated structure. By varying the gate voltages at fixed magnetic field, the device can be switched reversibly between bistable magnetic states with the same net magnetization but drastically different resistance (by a factor of 10 or more). In addition, without switching the state, the TMR can be continuously modulated between 17,000% and 57,000%, due to the combination of spin-dependent tunnel barrier with changing carrier distributions in the graphene contacts. Our work demonstrates new kinds of magnetically moderated transistor action and opens up possibilities for voltage-controlled van der Waals spintronic devices.

Stability analysis of an electrostatically actuated out of plane MEMS structure

In the present research, stability and static analyses of microelectromechanical systems microstructure were investigated by presenting an out-of-plane structure for a lumped mass. The presented model consists of two stationary electrodes in the same plane along with a flexible electrode above and in the middle of the two electrodes. The nonlinear electrostatic force was valuated via numerical methods implemented in COMSOL software where three-dimensional simulations were performed for different gaps. The obtained numerical results were compared to those of previous research works, indicating a good agreement. Continuing with the research, curves of electrostatic and spring forces were demonstrated for different scenarios, with the intersection points (i.e., equilibrium points) further plotted. Also drawn were plots of deflection versus voltage for different cases and phase and time history curves for different values of applied voltage followed by introducing and explaining pull-in and pull-out snap-through voltages in the system for a specific design. It is worth noting that, at voltages between the pull-in and pull-out snap-through voltages, the system was in bi-stable state. Based on the obtained results, it was observed that the gap between the two electrodes and the applied voltage play significant roles in the number and type of the equilibrium points of the system.

Magnetic dynamic properties of defective iron nanorings

Magnetic nanorings can be high-density integrated because their stray field is low in vortex states. In this paper, the magnetic dynamic properties of the defective Fe nanorings are studied. For convenience, we assume the defect to be round in shape, whose coordinate is (0, <i>Y</i>). Based on the Monte Carlo method and fast Fourier transformation micromagnetism method, the magnetic properties of the defective Fe nanorings, such as hysteresis loops, spin configurations, remanence, etc., are studied. The simulation results indicate that the magnetization process of the system can be affected by the sizes and locations of the defects. When the defects are small, the system has a bistable state, which is similar to the system without defects. The transition state of the system increases as the defects are enlarged, and the bistable state will be no longer so visible. The system becomes open when the defects are big enough. Meanwhile, its hysteresis loop presents a rectangular shape which is similar to cluster’s or quantum dot’s. The remanence increases with the radius of defect increasing. These results are in accord with the magnetic properties of asymmetric magnetic nanoring. In order to explain the above results, the spin configurations of the system are shown. The spins of defective nanorings are divided into two parts, i.e., upper half part and lower half part, which are represented as blue and black spins respectively. When the system does not have any defects, the number of blue spins is equal to black spins’. Therefore the remanence is zero when the system is in a vortex state. It is found that the number of blue spins decreases as the radius of defect increases. This situation results in the total magnetic moment increasing, which leads the remanence to increase. However, the relationship between remanence and <i>Y</i> (the distance between center of nanoring and center of defect) is nonlinear. The remanence first increases and then decreases with <i>Y</i> increasing. The simulation results can be explained by changing the spin configuration. By analyzing the spins of the upper and lower part, the magnetic moment of the system is analyzed. It is found that the number of the spins and the local vortexes can affect the remanence significantly. The results show that the magnetic properties of Fe nanorings can be affected by the defect.

Бистабильное и многодоменное состояния ферромагнитных микропроводов alpha-Fe/(PrDy)(FeCo)B

Microwire of α-Fe(50 at.%)(PrDy)(FeCo)B(48 at.%) was obtained by extracting a hanging melt drop of (PrDy)(FeCo)B in an electron beam. It was shown that a single microwire with a diameter of 50 μm and a length of 0.8 - 6 mm with an amorphous phase (PrDy)(FeCo)B content of ~ 48% and a polycrystalline α-Fe phase of ~ 52% has a rectangular narrow magnetic hysteresis loop and, accordingly, a bistable state with a switching field of ~ 100 Oe. The shortening of the wire to ~ 0.6 mm leads to a sharp deviation from the squareness of the loop, reducing the slope of the dependence of the magnetization on the field and the coercive force to 20 Oe. In the subsurface layers consisting of the amorphous phase (PrDy)(FeCo)B, oriented areas of reverse magnetization are observed. The role of the magnetic dipole interaction in the formation of a magnetic hysteresis loop of chaotic microwire assemblies of various compositions is discussed.

Sliding Dynamics of a Filippov Forest‐Pest Model with Threshold Policy Control

A novel Filippov forest‐pest system with threshold policy control (TPC) is established while an economic threshold (ET) is used to guide switching. The aim of our work is to address how to reasonably and successfully control pests by means of sliding dynamics for the Filippov system. On the basis of the above considerations, conditions for the existence and stability of equilibria of subsystems are addressed, and the sliding segments and several types of equilibria of the proposed system are defined. These equilibria include the regular/virtual equilibrium, pseudoequilibrium, boundary equilibrium, and tangent point. Further, not only are the relations between nullclines and equilibria of the Filippov system discussed, but the relations between pseudoequilibrium, nullclines, and the sliding segment are discussed. More importantly, four cases of sliding bifurcations of the Filippov system with respect to different types of equilibria of subsystems are investigated, and the corresponding biological implications concerning integrated pest management (IPM) are analyzed. Our results show that the points of intersection between nullclines are equilibria of the system, and the two endpoints of the sliding segment are on the nullclines. It is also verified that the pseudoequilibrium is the point of intersection of the sliding segment and nullclines of the Filippov system, and the pseudoequilibrium exists on the sliding segment. More interestingly, sliding dynamics analysis reveals that the Filippov system has sliding limit cycles, a bistable state and a stable refuge equilibrium point, and the optimal time and strategy for controlling pests are provided.

Atomic-Scale Insight into the Reversibility of Polar Order in Ultrathin Epitaxial Nb:SrTiO <sub>3</sub>/BaTiO <sub>3</sub> Heterostructure and Its Implication to Resistive Switching

Ferroelectric heterostructures with bi-stable state of polarization are appealing for data storage as well as tunable functionalities such as memristor behavior. While an increasing number of experimental and theoretical studies suggest that polarization persists in ultrathin epitaxial heterostructures approaching just a couple of unit cells, the switching of such polar order is much less well understood, and whether polarization can be reversed in ultrathin ferroelectric heterostructures remains to be answered. Here we fabricate high-quality 7-unit cell thick BaTiO3 (BTO) films on Nb-doped single crystalline SrTiO3 (NSTO) substrate, and demonstrate their apparent yet unambiguously false polarization reversal due to charge injection using comprehensive piezoresponse force microscopy (PFM) studies. The presence of weak polar order consistent with linear piezoelectricity is confirmed at the atomic scale by high resolution integrated differential phase contrast (IDPC) of transmission electron microscopy (TEM) as well as macroscopic second harmonic generation (SHG), while the lack of polarization reversal under the voltage applied is supported by density functional theory calculation showing the persistence of dead layer on the surface. Nevertheless, poling-induced electric conduction differing by two orders of magnitude is observed, demonstrating resistive switching in ferroelectric heterostructure in the absence of polarization reversal, even with weak polar order. Our finding has technological implications on emerging memristor applications with potentially more accessible states than bi-stable polarization modulated mechanism, and raises technical challenges to unambiguously demonstrate polarization switching in ultrathin films at their critical size limit.

A soft gripper of fast speed and low energy consumption

Grasping of complicated objects is an active research area which is developing fast throughout the years. Soft grippers can be an effective solution, since they are capable of holding workpieces of various shapes and interacting with unstructured environments effectively. Soft grippers generally consist of soft, flexible and compliant materials, which are able to conform to the shape of the object so that the gripper will not deform or bruise the soft object. Fast grasping of objects with various sizes and shapes remains a challenging task for soft grippers. In the present article, a soft gripper based on bi-stable dielectric elastomer actuator (DEA) inspired by the insect-catching ability of the Venus flytrap, is designed. This soft gripper can achieve good performances in grasping various objects by a simple actuation system. The gripper can switch from one stable state to another when subject to an impulse voltage of 0.04 s. The time duration for each grasping action is 0.17 s, and no continuous voltage is required for holding the gripped object. Thus, energy consumption can be achieved as low as 0.1386 J per grasping action. The mechanism of achieving bi-stable states is related to the duration of impulse voltage applied and the resonant frequency of the structure. The present study demonstrates that bi-stable dielectric elastomer actuators are capable of achieving fast speed for grasping with very low energy consumption, which is significant in the applications to soft grippers and biomimetic robots.

Bistable switching in electromagnetically induced-transparency-like meta-molecule

We present a bistable electromagnetically induced-transparency-like meta-molecule configuration consisting of a microstrip line side-coupled with an open-ended comb line and a varactor-embedded split ring resonator. We find that such a configuration can generate an extremely high transmission contrast up to 15 dB between two bistable states in its transmission with a low bistability threshold of − 1.7 dBm. We also show that the sample length is shorter than one-twelfth of wavelength in the transmission line. These features may be useful in the applications based on nonlinear devices.

Wide Magnetic Thermal Memory Effect (∼55 K) Above Room Temperature Coupled to a Structure Phase Transition of Lattice Symmetry Reduction in High-Temperature Phase in an S = 1/2 Spin Chain Molecule Crystal.

One-dimensional (1D) S = 1/2 Heisenberg antiferromagnetic (AFM) chain system shows frequently a spin-Peierls-type transition owing to strong spin-lattice coupling. From high-temperature phase (HTP) to low-temperature phase (LTP), the spin chain distortion leads to the reduction in lattice symmetry in LTP, called the symmetry breaking (SB) phase transition. Herein, we report the first example of 1D S = 1/2 AFM molecular crystal, [Et3( n-Pr)N][Ni(dmit)2] (Et3( n-Pr)N+ = triethylpropylammonium, dmit2- = 2-thioxo-1,3-dithiole-4,5-dithiolate), which shows a structural phase transition with lattice symmetry increase in LTP, which is contrary to the SB phase transition. Particularly, the structure phase transition leads to magnetically bistable state with TC↑ ≈ 375 K, TC↓ ≈ 320 K, and surprisingly large thermal hysteresis (∼55 K). Additionally, LTP and HTP coexist in a temperature region near TC but not at TC in this 1D spin system. The large hysteresis is related to the huge deformation of anion stack, which needs high activation energy for the structure transformation and magnetic transition between LTP and HTP. This study would not only provide new insight into the relationship of spin-Peierls-type transition and structure phase transition but also offer a roadmap for searching molecular-scale magnetic bistable materials, which are in huge demand in future electronic, magnetic, and photonic technologies.

Dynamics of the Magnetic Moment of an Anisotropic Nanoparticle and a Plane Lattice in an Alternating Field

Dynamic regimes of the magnetic moment of a nanoparticle with an uniaxial or cubic anisotropy are studied. Regular oscillations with different attractor shapes and periods and regimes of chaotic and quasi-periodical dynamics are revealed. The dynamic bistability states are discovered; the transitions between the oscillation regimes belonging to bistability are obtained by means of the pulsed change in the alternating field amplitude. It has been shown that the 90°-remagnatization of the nanoparticle is caused by the alternating field action. The nanoparticle lattice parameters at which the dipole interaction effect on the oscillation regimes of magnetic momenta can be neglected are revealed.