Totally unstable

From the discussion presented above, it is clear that the stability of the debond process can be evaluated by a single parameter, Zmax, which is the shortest (remaining) bond length needed to maintain the debond process stable, and is a constant for a given composite system. Therefore, three different interface debond processes are identified in the following totally unstable, partially stable and totally stable debond processes. The schematic plots of the applied stress versus displacement curves are illustrated in Fig. 4.25 for these debond processes. 

Fig. 4.25. Schematic presentations of applied stress versus displacement (

Due to its long, thin shape, there is a lack of rigidity, and the flechette turns into a hook on impact with the target. It becomes totally unstable and imparts its full kinetic energy to die target, producing an explosive-type wound... 

In Fig. 3 the binodal curves represent the equilibrium phase boundaries and determine the compositions of the phases in equilibrium at any temperature. The spinodals represent the boundaries between totally unstable (inside the spinodal) and metastable (between the spinodal and binodal) homogeneous phases if created. The curves in Fig. 3 represent the variations in composition of the points in Fig. 4 with temperature. Phases with compositions between the binodal and spinodal are metastable and nucleation is required to initiate phase separation. In contrast, compositions within the spinodal are totally unstable and will inevitably imdergo phase separation if there is sufficient mobility to permit the necessary molecular motions. The mechanisms by which phase separation occurs in those two regions are different and give rise to different morphologies in the phase-separated materials. Thus, the curves define phase behaviour at equilibriiun and also define the limits of operation of mechanisms of phase separation, when appropriate. 

At locations where variable support reactions are not tolerable over the required movement range, constant-effort springs or counterweights ate used. Piping systems supported entirely by constant-effort devices requite precise accuracy to counterbalance the total piping load, otherwise the system may be vertically unstable. 

Thromboxanes. Because of its highly unstable nature, TXA2 (3) eluded total synthesis until 1985. However, following the disclosure in 1975 of its proposed stmcture and pharmacological importance, a great deal of effort was expended to develop syntheses of its stable metaboHte, TXB2 (15). A practical, short synthesis (220) from the 9,15-diacetate of PGF2Q, (89) follows. 

The situation simplifies when V Q) is a parabola, since the mean position of the particle now behaves as a classical coordinate. For the parabolic barrier (1.5) the total system consisting of particle and bath is represented by a multidimensional harmonic potential, and all one should do is diagonalize it. On doing so, one finds a single unstable mode with imaginary frequency iA and a spectrum of normal modes orthogonal to this coordinate. The quantity A is the renormalized parabolic barrier frequency which replaces in a. multidimensional theory. In order to calculate... 

Figure 21-9 is a stability wind rose that indicates Pasquill stability class frequencies for each direction. For this location, the various stabilities seem to be nearly a set proportion of the frequency for that direction the larger the total frequency for that direction, the greater the frequency for each stability. Since the frequencies of A and B stabilities are quite small (0.72% for A and 4.92% for all three unstable classes (A, B, and C) are added together and indicated by the single line. 

In Fig. 9.1, orbitals below the dashed reference line are bonding orbitals when they are filled, the molecule is stabilized. The orbitals that fall on the reference line are nonbonding placing electrons in these orbitals has no effect on the total bonding energy of the molecule. The orbitals above the reference line are antibonding the presence of electrons in these orbitals destabilizes the molecule. The dramatic difference in properties of cyclobutadiene (extremely unstable) and benzene (very stable) is explicable in terms of... 

The predictions of relative stability obtained by the various approaches diverge more widely when nonbenzenoid systems are considered. The simple Hiickel method using total n delocalization energies relative to an isolated double-bond reference energy (a + fi) fails. This approach predicts stabilization of the same order of magnitude for such unstable systems as pentalene and fulvalene as it does for much more stable aromatics. The HMO, RE, and SCF-MO methods, which use polyene reference energies, do much better. All show drastically reduced stabilization for such systems and, in fact, indicate destabilization of systems such as butalene and pentalene (Scheme 9.2). 

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