Bistability region

Fig. 3. Data for sample 2. (a) H-dependence of dV/dl at specified values of I, (b) /-dependence of dV/dl at specified values of H. (c) Magnetization stability diagram extracted from I scans such as shown in (b). Upward (downward) triangles P AP(AP P) switching. A H = —0.5 kOe section shown with dashed fine, (d) MR curves at / = 8 mA, at the specified in-plane angles between H and the nominal easy axis of the nanopillar. AP, P denote the stability region of the respective configurations, P/AP is a bistable region. In (a),(b),(d), thick curves scan from left to right, thin curves scan in opposite direction, curves are offset for clarity.

For a given N-shaped I/ DL curve, there are two parameters that determine the bistable region, Rq and U. In the U/Rq, parameter diagram, this region becomes broader while shifting toward larger values of U for increasing Rq, irrespective of the electrochemical reaction (Fig. 9c). 

Eq. (42) gives rise to a negative feedback loop if the current potential curve is S-shaped, but not for Z-shaped characteristics. Thus, in S-NDR systems DL may stabilize the middle branch of the S, or it may induce oscillations. This is not possible in Z-shaped systems, where an incorporation of DL in the dynamic description only increases the width of the bistable region but never results in qualitatively different behavior. For this reason, DL is not an essential variable in the latter type of systems. Thus, they have to be classified as systems with chemical instabilities only and will not be further treated here. 

The observed shift of the measured bistability region of the Pt/ceria sample compared to the Pt/silica sample can qualitatively be explained by oxygen spillover between ceria and Pt. This can be understood by considering that for Pt/ceria O2 may adsorb on ceria and diffuse to the Pt-ceria boundary and react with CO on the Pt particles, even if the Pt particle is covered by CO. The spillover channel thus extends the gas mixing (/ ) regime, where a high reaction rate can be maintained. The data shown in Fig. 4.33 is particularly... 

Fig. 4.33. Measured CO oxidation rate on EBL-fabricated model catalysts with different support materials and particle sizes (a) The inlet gas mixture represented by the parameter (3 = Pco/ Pco + P02) has been scanned up/down at a constant temperature of 450 K, and the rate of CO2 production has been monitored during the gas scan in j3. This has been made for three different samples (a) 750-nm Pt/Si02 (blue), (b) 750-nm Pt/CeOj, (black), and (c) Pt/CeOj, sample (200mn, red, disintegrated particles). Results both from experiments (filled circles) and simulations solid lines) are shown. The arrows indicate which reaction rate branch that has been observed while scanning up/down in (3. A bistable region (hysteresis) is observed for all samples, (b) The bistability diagrams determined from a series of measurements as those shown in (a) at different temperatures (Pt/Si02, blue and open squares) Pt/CeOj, black hatch marks and crosses and the 200-nm Pt/CeOj, red hatched area and open squares). The observed differences can be traced back to a pronounced O-spillover effect on ceria. Note the logarithmic scale for the /3-value (from [29])...

The appearance of bistability regions in clusters of pp chromophores is a very interesting result. It represents the extreme consequence of cooperativity, and has no counterpart for isolated molecules. Moreover, if we are able to prepare our material in the close proximity of the bistability region, any tiny variation of external conditions can easily switch the material between two phases with macroscopically different properties, a quite appealing phenomenon in view of the possibility to produce molecular-based switches. 

The different regions in Figure 3.7.5 are labeled according to the stable fixed points that exist. The refuge level a is the only stable state for low r, and the outbreak level c is the only stable state for large r. In the bistable region, both stable states exist. 

The experimental observations suggest that for a young forest, typically k >=> 300 and r < (jl so the parameters lie in the bistable region. The budworm population is kept down by the birds, which find it easy to search the small number of branches per acre. However, as the forest grows, 5 increases and therefore the point (k, r) drifts upward in parameter space toward the outbreak region of Figure... 

The consequences of a variation in P on the dynamic behavior of a galvanostatically controlled system are illustrated in Fig. 45. Shown again are transitions in the bistable region for two different values of a. For small o (first row) and small P (left column), the influences of the two coupling... 

The cubic equation (9.66) can have three roots which indicates bistability - two values of I correspond to one pumping intensity (the third root corresponds to an unstable state). The plot of the function I(Ipump) is shown in Fig. 9.8, where one can see the bistability region 0 < ipUmp < 0.15 Ic (with I — c = 1 /1) = 1). 

---