Meta-stable state

For nuclear y-resonance absorption to occur, the y-radiation must be emitted by source nuclei of the same isotope as those to be explored in the absorber. This is usually a stable isotope. To obtain such nuclei in the desired excited meta-stable state for y-emission in the source, a long-living radioactive parent isotope is used, the decay of which passes through the Mossbauer level. Figure 3.6a shows such a transition cascade for Co, the y-source for Fe spectroscopy. The isotope has a half-life time //2 of 270 days and decays by K-capmre, yielding Fe in the 136 keV excited state ( Co nuclei capmre an electron from the K-shell which reduces the... 

Fig. 7.19. Photodetachment spectrum for IHI the wavelength of the excitation laser is 266 nm. u s denotes the number of quanta in the anti-symmetric stretch mode in the transition region. The widths of the peaks do not represent the true lifetimes of the meta-stable states. Adapted from Neumark (1990)...

Figure 5.6 shows an example of a total interaction energy curve for a thin liquid film stabilized by the presence of ionic surfactant. It can be seen that either the attractive van der Waals forces or the repulsive electric double-layer forces can predominate at different film thicknesses. In the example shown, attractive forces dominate at large film thicknesses. As the thickness decreases the attraction increases but eventually the repulsive forces become significant so that a minimum in the curve may occur, this is called the secondary minimum and may be thought of as a thickness in which a meta-stable state exists, that of the common black film. As the... 

Fig. 9. Top Native PDB structure of the f3 hairpin. The side chains are left out. The 7 backbone hydrogen bonds are indicated by dotted lines, and counted from the tail. Bottom Spatial 3D structures of the several (meta) stable states. The backbone is represented by a ribbon, the hydrophobic core in stick model with dots to indicate the size of the atoms. AU other residues and solvent molecules are left out...

LJ7 as defined here has one stable state (global minimum) Ml and three meta-stable states (local minima) M2, M3, and M4. They are tabulated in Table I. This system has been well studied in the literatme. The present study adds the determination of... 

Fig.2 Stable state Ml (top left) and meta-stable states M2 (top right), M3 (bottom left), and M4 (bottom right).

Multistability Fronts advancing on meta-stable states... 

From a dynamical point of view the systems in this class typically have multiple steady states and then the autocatalytic process is associated to transitions between them. A special case with a single steady state, that also belongs to this class, is the excitable dynamics where apart from the basic state an excited meta-stable state also exists, that is effectively stable for short times. In any case, late time approach to the final state after the autocatalytic dynamics is usually a decay-type process already described in the previous Chapter. The final state in most of the problems considered in this Chapter is typically a trivial spatially uniform steady state. Thus, the main focus in this Chapter will be on the transient temporal dynamics, i.e. to understand and quantify the influence of the fluid transport on the progress of the autocatalytic process. As we will show, the situation is somewhat different in open flow systems where the same type of autocatalytic processes can produce a non-trivial long-time asymptotic state with complex spatial structure. 

There are two solutions for y. The smaller solution corresponds to the stable or meta-stable state in which Z is at a maximum, as shown in Figure 2.5. The dependence of on y can be obtained numerically. 

To obtain the critical value of 4> when the system starts to appear in the meta-stable state, i.e., the minimum value of for the existence of liquid crystal state, let... 

Equation 2.44 is the well-known Flory formula which is widely used in the study of liquid crystalline polymers. It should be pointed out that cj> is only the minimal solution of Equation 2.41 at which the partition function first shows a maximum. At this volume fraction cf>, Zmax is actually less than the Z at the disordered state (y = x). The system is at a meta-stable state only when the volume fraction further increases to a greater value in which the system is indeed at a stable state. 

Figure 8.3 Stabilization graph of a meta-stable state for a van der Waals complex (BaCic and Simons, 1982).

Nonetheless, there are also strong indications that even smooth films do not necessarily represent equilibrium situations as the actual surface topography depends on the thermal treatment the sample has experienced. In fact, the existence of corrugated block copolymer surfaces is difficult to explain based on equilibrium arguments only. As for the case of defect structures, island-hole patterns might reflect meta-stable states which energetically differ only slightly from the ideally smooth surface states. 

FIGURE 8.3 Gibbs energies for (meta)stable states of wetting. 

Direct observation of the molecular reorientation process is not practical, but models have provided much insight. The first attempt was by Aslaksen [94] in 1972. Noting that the crystal field gives a meta.stable state at a 180° rotation of a chain from the ground state orientation, he based his model on 180° rotation of... 

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