Schematic portrait

Figure 4 shows a schematic portrait of the phase space flows (denoted by arrows) in the ( i(p, q),Pi(p, q)) plane and the caricature of the corresponding... 

Figure 4. A schematic portrait of the stable and unstable invariant manifolds and the phase-space flows on (4i(p,q),Pi(p,q)).

The relation between the form of the phase portrait and the effective thermodynamic potential is schematically demonstrated in Figure 14.8. Figure 14.8 (a) shows the phase portrait of a TGS-crystal and the corresponding thermodynamic potential. In the F-a-alanin doped tgs-... 

Our goal now is to visualize the corresponding bifurcation in phase space. In Exercise 8.5.2, you re asked to show (by numerical computation of the phase portrait) that if a is sufficiently small, the stable limit cycle is destroyed in a homoclinic bifurcation (Section 8.4). The following schematic drawings summarize the results you should get. 

Here s the intuitive picture. For r< the phase portrait near C is shown schematically in Figure 9.2.4. 

Fig. 3.2. Phase plane portrait in the absence of product recycling into substrate. The substrate (a) and product (y) nullclines are represented in a situation corresponding to an unstable steady state (ao> To) surrounded by a stable limit cycle (dashed line). The instability domain extends, schematically, from A to B in the region of negative slope on the product nullcline. The arrow across the substrate nullcline indicates the direction of its displacement when the substrate injection rate v increases. When the two nullclines intersect at C, on the left of the instability domain, the steady state is stable but excitable an increase in product is then amplified in a pulsatory manner (dotted line) when the amplitude of the perturbation exceeds a threshold (Goldbeter Moran, 1987).

The main lines of research at ISOLDE are nuclear structure physics, nuclear astrophysics, atomic physics, solid state physics, life sciences and fundamental interactions. A laboratory portrait been published as a special volume of Hyperfine Interactions [35]. In this volume a complete chapter is devoted to Mossbauer Spectroscopy at ISOLDE [36]. A schematic view of the set-up is shown in Fig. 6.22. 

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