Bistable behavior

The results are shown in Figure 2. Spectra are plotted for various values of normalised input intensity yinc = n2 inc which can be considered as the strength of the nonlinearity. A positive nonlinearity, yjnc > 0, that shifts the spectra to the right was used. As expected the nonlinearity (spectral shift) is enhanced with increasing number of the periods. Moreover the structures with 2 and 3 periods exhibit bistable behavior for A, > Aq. In this case bistable switching is controlled by frequency tuning while input intensity is fixed. 

Figure 12. (A) Behavior of a bistable ABC, 2(1)5,2kc system as a function of the incident photon flux /o (AbsJj = 10 and ba/ ca = 300°) (B) Corresponding curve for Abs = 2, illustrating the disappearance of the bistable behavior when AbsJ, is too small.

Dynamic analysis is also a powerful method for the study of complex behavior. The description of an ideal ABC system with the possibility of multiple photostationary states illustrates the dynamic bistable behavior of TPID. 

Fig. 4.35. Particle size-dependent bistability and hysteresis. On model system I (500-nm EBL-fabricated particles), the CO oxidation shows a perfectly stable bistability behavior. On the time scale accessible by the experiment (>10 s), we can arbitrarily switch between the two states by pulsing either pure CO or O2 (a and d). For the model system II (6-nm particles), a very slow transition toward a single global state is observed in the transition region between the CO- and O-rich reaction regimes (b and e). This behavior is assigned to fluctuation-induced transitions, which are accelerated by the presence of defect sites. For the smallest particles of the model system III (1.8 nm), a globally monostable kinetics is rapidly established under all conditions (c and f). For all experiments, the total flux of CO and O2 beams at the sample position was equivalent to a local pressure of 10" Pa. The surface temperature in (a-c) was 400 K and in (d-f) 415 K (from [147])...

Since dp/dz< 0, for repulsive lattices M > 0) the p M slope varies smoothly with M, and hence we observe fairly smooth p(in) curves. For attractive clusters (M < 0) the dp/dM slope can eventually change sign when M Increases in magnitude, going through a divergence at M = —2. This explains the sharp curves calculated for B and C clusters (cf panels (c) and (e) in Fig. 4), and also leads to the interesting prediction of bistable behavior in attractive lattices as it will be discussed in the next Section. 

Hence, and not surprisingly, just as for the one-dimensional system (Eq. 1), Eq. (5) predicts a bistable behavior for a sufficiently large series resistance. 

Figure 5 shows experimental cyclic voltammograms of the reduction of S2OJ at a rotating Ag electrode for three different rotation rates. For high rotation rates, which correspond to a thin diffusion layer and hence to a small value of 5 in Eq. (4b), the system exhibits bistable behavior. The... 

The simplest manifestation of self-organization in a reacting system is the occurrence of bistability, that is, the coexistence of two locally stable homogeneous states. In all electrical models, bistable behavior results from the interaction of an N-shaped stationary polarization curve with a sufficiently large ohmic resistor in the external circuit. These two features also represent the backbone for all more complex forms of self-organization where, owing to exactly these two properties of the system, the double-layer potential takes on the role of the autocatalytic variable. 

Specific examples of such bistable behavior arise in models of combustion. In the simplest case, a two-component system, that includes the distribution of the fuel and of the temperature field, is appropriate. The reaction takes place only when the temperature is above a certain ignition temperature, with a burning rate that is an increasing function of the local temperature following the Arrhenius law (Eq. (3.43)). The burning of fuel is an exothermic reaction that increases the local temperature and results in even higher reaction rates. This leads to the autocatalytic character of the system, while the ignition temperature acts as a threshold, responsible for the bistability. 

Bhalla, U.S. and Iyengar, R. (2001). Robustness of the bistable behavior of a biological signaling feedback loop. Chaos 11, 221-226. 

Such effects can, for example, be observed by applpng the field ion microscope (FIM) to sharp tips exposing different crystal planes. Quite interesting observations in this connection were made with the H2 + O2 reaction on Pt [56]. With an extended Pt(l 0 0) surface under the applied conditions, no kinetic oscillations but only bistable behavior are found. If the same plane is, however, exposed as a small area on a field emitter tip, then under certain conditions oscillatory behavior is observed. This... 

The device exhibits electrical bistable behavior as shown in Figure 8.20. The voltage to turn the device from the low-to high-conductivity state is 2.6 V. At this critical voltage, the current increases abruptly from 10 to 10 A, and the... 

The added factor 1/(1 + s/X, s) in Equ. 5.88 represents the toxicity of the substrate at higher concentrations. Let us recall that the condition for calculation of the stationary state with nonvanishing biomass concentration is the relation fx(s) = D. This equation has only one solution if fi(s) is a monotonic function. But with characteristics as in Equ. 5.88, there are two solutions. Together with the washout state ( x, s) we have three stationary states. Two of them are stable ( x, and x, s), one of them is unstable ( x, s). Thus, we have a bistable system. The stationary values of the stable and the unstable stationary state are shown as a function of D in Fig. 6.11. Hysteresis may occur in shift experiments. Figure 6.12 shows how the final biomass concentration depends on the initial concentration. Figure 6.13 demonstrates that the phase plane is divided into two attraction domains. Both domains are touched by a separatrix in which the unstable stationary state lies. Note that, after an external disturbance, the system can cross over the separatrix and shift from one steady state to the other. This bistable behavior is a serious problem in, for example, waste treatment It takes place if substrates such as alcohols, phenols, or hydrocarbons occur in such high concentrations that the utilization of these substrates is inhibited. 

Equation 6 which is the general solution to a variety of exitation schemes, can be solved graphically for ( ij (L). This is shown here for two cases. The solutions for a medium exhibiting Sg — transition (Fig. 2) incorporated in a matched ring resonator. The results for a coherent field pumping are depicted in Fig. The results for are used to calculate the output intensity as a function of lin (Fig. 4). The bistable behavior of this system (lower branch due to almost linear absorption and upper branch due to saturated absorption) can be also demonstrated in many other cases. The solutions for reverse saturable absorber - a medium exhibiting Sg — S. Ay T- —Tjj ( -jn on transitions - in the same optical resonator... 

The limitations on multiplexing any rms-responding monostable liquid crystal effect have been mentioned in Section II.A. Active matrix addressing, described in Sectin IV.A, is one way of overcoming these limitations. Another is to consider alternative liquid crystal effects that are bistable, or at least non-rms responding. With such effects, the maximum number of rows that can be multiplexed is usually determined by the ratio of the frame time (the time period during which the whole picture must be refreshed or updated) to the line time (the time required to address one row of pixels). This is quite demanding of the line time a frame time of 40 msec (only 25-Hz frame rate) would require a line time of 40 /xsec for 1000 lines. Bistable behavior is associated with smectic and cholesteric phases, both of which in completely different ways have translational symmetries added to nematiclike orientational order. In this section, the ferroelectric tilted smectic devices are reviewed, while (untilted) smectic A and cholesteric devices are described in Section IV.C. 

The first systematic design of a chemical oscillator had been achieved There remained some ambiguity, however. Since two autocatalytic reactions had been employed, it was not immediately clear which constituted the fundamental autocatalytic reaction and which provided the feedback in the model scheme. Historically, the arsenite-iodate system had been chosen for the former role, since its bistable behavior had been established first. More careful investigation revealed that, in fact, it was the chlorite-iodide reaction that provides the essential dynamical features of this system. The evidence comes in two forms. First, the chlorite-iodide reaction is also bistable in a CSTR (Dateo et al., 1982) and the relaxation to its steady states is more rapid than the relaxation behavior of the arsenite iodate system. According to our theory,... 

A key element of the mechanism in Table 5.3, which accurately describes both the oscillatory and the bistable behavior found in this system, is the protonation-deprotonation equilibrium of sulfite-bisulfite, reactions B7 and B8, which are represented by eq. (5.13) in the general model ... 

Access to the third dimension via aluminosilicate frameworks, which comprise regular structured nanopores, has been suggested. These hollow networks house conducting polymer chains as wires and semiconductor dots to give a zeolite memory, with potentially 10 cross-points as storage elements, due to their bistable behavior, per cubic centimeter photochromic switches have also been incorporated into silica monoliths. 

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