Bistable Zone Research Articles

How a small noise generates large-amplitude oscillations of volcanic plug and provides high seismicity

A non-linear behavior of dynamic model of the magma-plug system under the action of N-shaped friction force and stochastic disturbances is studied. It is shown that the deterministic dynamics essentially depends on the mutual arrangement of an equilibrium point and the friction force branches. Variations of this arrangement imply bifurcations, birth and disappearance of stable limit cycles, changes of the stability of equilibria, system transformations between mono- and bistable regimes. A slope of the right increasing branch of the friction function is responsible for the formation of such regimes. In a bistable zone, the noise generates transitions between small and large amplitude stochastic oscillations. In a monostable zone with single stable equilibrium, a new dynamic phenomenon of noise-induced generation of large amplitude stochastic oscillations in the plug rate and pressure is revealed. A beat-type dynamics of the plug displacement under the influence of stochastic forcing is studied as well.

Stochastic Phenomena in One-Dimensional Rulkov Model of Neuronal Dynamics

We study the nonlinear Rulkov map-based neuron model forced by random disturbances. For this model, an overview of the variety of stochastic regimes is given. For the parametric analysis of these regimes, the stochastic sensitivity functions technique is used. In a period-doubling zone, we analyze backward stochastic bifurcations modelling changes of modality of noisy neuron spiking. Noise-induced transitions in a zone of bistability are considered. It is shown how such random transitions can generate a new neuronal regime of the stochastic bursting and transfer the system from order to chaos. A transient zone of values of noise intensity corresponding to the onset of noise-induced bursting and chaotization is localized by the stochastic sensitivity functions technique.

Rectangular sharp-crested weir calibration for low head and clinging flow regime

The classical head–discharge relation for rectangular sharp-crested weirs is applicable only to free flow conditions, not valid at low head when flow becomes clinging. Based on experimental data for eight sharp-crested rectangular weirs of different sizes, a new method for calculating discharge at the low head bistable and clinging flow regime was proposed in this study. In the bistable zone, the head–discharge relationship can be covered partly by the classical weir–discharge equations of free flow. The discharge coefficient is quite similar to Rehbock’s equation for free flow with a surface tension term. In the clinging flow regime, the head had to be transformed into an equivalent head obtained by regression. All the regression parameters were about the same for the weirs of different sizes. In the clinging zone, discharge was also directly proportional to weir width, while unit width discharge was directly proportional to the square of head, independent of weir height. The errors of model-predicted discharge were less than 10 % for more than 90 % of the data points. Therefore, the proposed method for discharge of clinging flow is applicable to rectangular sharp-crested weirs at very low head, while the classical formulas often fail under these flow conditions.

Influence of Feedback Level on Laser Polarization in Polarized Optical Feedback

The influence of feedback level (or the amplitude of feedback light) on laser polarization in polarized optical feedback is investigated. A polarizer is placed in the feedback cavity to form the polarized feedback, and an attenuator is placed in the feedback cavity to tune the feedback level. The laser intensity and polarization vary dramatically at different transmissivities of the attenuator. According to the experimental phenomenon, the range of the attenuator transmissivity is divided into three zones: the flipping zone, monostable zone, and bistable zone. In the monostable zone, the laser polarization is always perpendicular to the axis of the polarizer in the feedback cavity. This may provide an effective way to choose or control laser polarization. A theoretical model based on the self-consistency of laser oscillation is presented to analyze the experimental results.

Polarization characteristics of He–Ne laser with different directions of polarized feedback

A polarizer is placed in an external feedback cavity to form polarized optical feedback. The effect of the different directions of polarized optical feedback on laser polarization characteristics (LPCs) is investigated experimentally and theoretically. The angle between the optical axis of the polarizer and the laser polarization is changed from 0° to 90°. It is found that LPCs vary greatly under different directions of polarized optical feedback. The angle range can be divided into five zones (two flipping zones, ⊥-polarization zone, bistable zone, and ∥-polarization zone) according to the different LPCs. When the angle is in the range of the ⊥-polarization zone (∥-polarization zone), the laser outputs ⊥-polarization (∥-polarization). Thus, one can choose either ⊥-polarization or ∥-polarization by properly aligning the axis of the polarizer.

Classical and semiclassical studies of nonlinear nano-optomechanical oscillators

This paper presents a study of the effects of geometrical nonlinearity on the behavior of a Fabry-Perot cavity whose entrance face is a fixed mirror while the rear is a moving mirror behaving as a cantilever nanobeam. The study is done in classical and semiclassical approaches. In the semiclassical approach, the expression of the anharmonic Hamiltonian describing such a system is given. The nonlinearity reduces both the cantilever energy and optical intracavity energy and tends to decouple the optical and mechanical parts of the system. The nonlinear semiclassical approach is shown to be in good agreement with the quantum limit. The optical bistable zones degenerate leading to applications in optical communications and quantum information.

Atmospheric CO2 forces abrupt vegetation shifts locally, but not globally

It is possible that anthropogenic climate change will drive the Earth system into a qualitatively different state. Although different types of uncertainty limit our capacity to assess this risk, Earth system scientists are particularly concerned about tipping elements, large-scale components of the Earth system that can be switched into qualitatively different states by small perturbations. Despite growing evidence that tipping elements exist in the climate system, whether large-scale vegetation systems can tip into alternative states is poorly understood. Here we show that tropical grassland, savanna and forest ecosystems, areas large enough to have powerful impacts on the Earth system, are likely to shift to alternative states. Specifically, we show that increasing atmospheric CO2 concentration will force transitions to vegetation states characterized by higher biomass and/or woody-plant dominance. The timing of these critical transitions varies as a result of between-site variance in the rate of temperature increase, as well as a dependence on stochastic variation in fire severity and rainfall. We further show that the locations of bistable vegetation zones (zones where alternative vegetation states can exist) will shift as climate changes. We conclude that even though large-scale directional regime shifts in terrestrial ecosystems are likely, asynchrony in the timing of these shifts may serve to dampen, but not nullify, the shock that these changes may represent to the Earth system.

Fast and robust magnetic quantum cellular automata interconnect architectures

Magnetic quantum cellular automata (magnetic QCA or MQCA) circuits, although are very promising, have fundamental and practical limitations. The operation frequency and reliability of MQCA circuits are not encouraging due to slow and robustless MQCA interconnect architectures. Three-phase pipelined clocking signals designed for MQCA bistable zone cells are first presented, and then the authors propose using this clocking integrating mixed magnetic anisotropy to eliminate slow and non-sequential switching in the MQCA interconnects. Micromagnetic simulations on a corner are performed to corroborate the proposed method. More results show that an interconnect comprising NiFe nanomagnets requires lower energy overhead and shows higher operation frequency. Furthermore, the authors study the kink energy of different coupling styles and find that frustration of turning antiferromagnetic state fails MQCA global clocking corner architecture. In general, the proposed interconnect scheme requires no additional magnetic helper blocks and promises fast and robust operation, which is promising in building future nanoscale ultra-high reliability information computation circuits and may inspire wide applications of MQCA devices.

Nonlinear dynamics of milling processes

In this article, dynamics and stability of milling operations with cylindrical end mills are investigated. A unified–mechanics–based model, which allows for both regenerative effects and loss–of–contact effects, is presented for study of partial–immersion, high–immersion and slotting operations. Reduced–order models that can be used for certain milling operations such as full–immersion operations and finishing cuts are also presented. On the basis of these models, the loss of stability of periodic motions of the workpiece–tool system is assessed by using Poincare sections and the numerical predictions of stable and unstable motions are found to correlate well with the corresponding experimental observations. Bifurcations experienced by periodic motions of the workpiece–tool system with respect to quasi–static variation of parameters such as axial depth of cut are examined and discussed. For partial–immersion operations, consideration of both time–delay effects and loss–of–contact effects is shown to have a significant influence on the structure of the stability boundaries in the space of spindle speed and axial depth of cut. The sensitivity of system dynamics to multiple–regenerative effects, mode–coupling effects and feed rate is also discussed.

Effects of Complete and Skeleton Photoperiods on the Circadian Rhythm of the Electroretinogram of the Crayfish

Applying complete photoperiods (PPc), with photophases that varied from 4 to 20 h of the 24-h cycle, we studied entrainment of the circadian rhythm of the electroretinogram (ERG) of crayfish by external light signals. All the PPc regimens tested synchronized the rhythm, which adjusted its circadian period to exactly 24 h; the duration of the photophase affected only other circadian parameters, such as the activity level and the ratio of the duration of active to resting phases. Entrainment of the ERG by skeleton photoperiods (PPs) was also studied. All the PPs tested (each PPs corresponded to a specific PPc regimen) also entrained the ERG rhythm. The use of PPs revealed that the bistability zone of the rhythm lay between light-dark (LD) 11:13 and LD 13:11. When the interval of darkness between the periods of illumination during PPs became less than 11 h, the circadian rhythm of the ERG exhibited a “jump” phase in which the maximal activity period jumped to the period of longer darkness; this result implies that the crayfish requires a minimum tolerable night.

Mass Loss from Rotating Hot-stars: Inhibition of Wind Compressed Disks by Nonradial Line-forces

We review the dynamics of radiatively driven mass loss from rapidly rotating hot-stars. We first summarize the angular momentum conservation process that leads to formation of a Wind Compressed Disk(WCD) when material from a rapidly rotating star is driven gradually outward in the radial direction. We next describe how stellar oblateness and asymmetries in the Sobolev line-resonance generally leads to nonradialcomponents of the driving force is a line-driven wind, including an azimuthal spin-down force acting against the sense of the wind rotation, and a latitudinal force away from the equator. We summarize results from radiation-hydrodynamical simulations showing that these nonradial forces can lead to an effective suppressionof the equatorward flow needed to form a WCD, as well as a modest (∼ 25%) spin-downof the wind rotation. Furthermore, contrary to previous expectations that the wind mass flux should be enhanced by the reduced effective gravity near the equator, we show here that gravity darkening effects can actually lead to a reducedmass loss, and thus lower density, in the wind from the equatorial region. Finally, we examine the equatorial bistability model, and show that a sufficiently strong jump in wind driving parameters can, in principle, overcome the effect of reduced radiative driving flux, thus still allowing moderate enhancements in density in an equatorial, bistability zone wind.

Bistability in a surface-reaction model.

A kinetic surface-reaction model, based upon the reaction of carbon monoxide and oxygen on a catalyst surface, is presented. The equations governing the reaction are obtained. A bistability zone is found: One is a reactive stable state producing carbon dioxide, and in the other the catalyst is poisoned. The relation between this reactive stable state and kinetic parameters of the reaction is studied.

Bistabilities and annihilation phenomena in electrophysiological cardiac models.

We have investigated the oscillatory behavior of cardiac cellular elements simulated by two electrophysiological models: the van Capelle and Durrer (VCD) model and the sinoatrial node cell model of Yanagihara, Noma, and Irisawa (YNI). The VCD model behavior was examined systematically by using continuation-bifurcation analysis. Bifurcation diagrams were constructed as a function of Qit1, an intrinsic parameter of the model, which sets both maximum diastolic potential and depolarization threshold of the cell. The existence of stable high amplitude oscillations was evidenced between two Hopf bifurcation points (HB). Near each HB, a zone of bistability was detected. Close to the HB that corresponded to high values of Qit1, a high amplitude periodic stable state coexisted with a stable steady state. Close to the other HB, in a narrow range of lower Qit1 values, a relatively high amplitude periodic stable state coexisted with a low amplitude periodic stable state. There was no stable steady state in the latter bistability zone. Through the use of phase-plane representations and the determination of separatrices between the different attractor basins, we could deduce the conditions of timing, polarity, and strength needed for a pulse perturbation to send the system from one state to another and vice versa. The YNI model was analyzed by numerical simulation, and the oscillatory behavior of the sinoatrial node cell was explored while applying a depolarizing bias current of various strengths. Results were similar to those obtained from the VCD model in that there were two bistability regions for two different ranges of applied bias current. Depending on current intensity, annihilation of pacemaker activity could be achieved in both zones. However, the coexistence of two oscillatory stable states was never observed in the YNI model. From the behavioral similarities of these different models, we can conclude that bistabilities and annihilation phenomena can be found in transitional zones between quiescence and rhythmic activity.

Amplitude and phase fluctuations in a noisy cavity

For absorptive optical bistability in a Fabry-Perot cavity it is shown that fluctuations in the bifurcation parameter dominate fluctuations in the input field amplitude. A step is also taken towards removing the phase-locking approximation and shows that the latter is quite good when the input field phase fluctuations are small and its amplitude is not in the bistable transition zone.

?Skeleton? photoperiods and the control of diapause and development in the flesh-fly,Sarcophaga argyrostoma

1. Larvae of the flesh-flySarcophaga argyrostoma were exposed to ‘skeleton’ photoperiods consisting of two unequal pulses of light (asymmetrical skeletons) or two equal pulses of light (symmetrical skeletons) per 24 h period. Asymmetrical skeletons (‘night interruption experiments’) revealed two apparently light-sensitive phases within the night, the second, occurring about 9 h after ‘dusk’ in all regimes, being thought to correspond to the photoinducible phase (Φi) of the photoperiodic oscillator (Fig. 1). 2. Symmetrical skeletons consisting of two 1 h pulses of light closely simulated the diapause-promoting effects of complete photoperiods of the same duration up to about 10 h. Skeletons longer than 16 h were again diapause-promoting in contrast to the diapause-averting (long day) effects of corresponding complete photoperiods. The incidence of diapause was reduced in the ambiguous symmetrical skeletons close to 12 h (in the ‘Bistability Zone’) (Fig. 3). 3. The ambiguity of symmetrical skeletons in the ‘Bistability Zone’ was eliminated by transferring cultures from continuous light (LL) into regimes consisting of two 1 h pulses placed 11 h apart. When the shorter interval (11 h) was ‘seen’ first after theLL-DD transition, long-day effects (low incidence of diapause) were observed; when the longer interval (15 h) was ‘seen’ first short-day effects (high diapause) were observed (Fg. 5). These results are consistent with the hypothesis that the photoperiodic oscillator is damped out by light periods of more than 12 h and resumes its motion on transfer to darkness.