Regions recalling

We recall from our earlier discussion of chaos in one-dimensional continuous systems (see section 4.1) that period-doubling is not the only mechanism by which chaos can be generated. Another frequently occurring route to chaos is intermittency. But while intermittency in low dimensional dynamical systems appears to be constrained to purely temporal behavior [pomeau80], CMLs exhibit a spatio-temporal intermittency in which laminar eddies are intermixed with turbulent regions in a complex pattern in space-time. 

You will recall (page 139) that an orbital occupied by an electron in an atom can be represented physically by showing the region of space in which there is a 90% probability of finding the electron. Orbitals are commonly designated by citing the corresponding sublevels. Thus we refer to Is, 2s, 2p, 3s, 3p, 3d,... orbitals. 

It will be recalled that one of the key operations in the synthesis of IJK ring system 86 is the intramolecular conjugate addition reaction (see 90—>89, Scheme 17b) to form ring J. In the context of compound 90, the electrophilic a,/ -unsaturated ester moiety and the potentially nucleophilic tertiary hydroxyl group reside in proximal regions of space, a circumstance that would seem to favor the desired cyclization evept (see Scheme 19). Indeed, exposure of a solution of 90 in THFto sodium hydride (1 equiv.) for one hour at 25 °C results in the formation of compound 89 in 92% yield. In... 

Recall that red regions indicate negative potential (an accumulation of electrons) and blue regions indicate positive potential (a deficiency of electrons). 

When two or more waves pass through the same region of space, the phenomenon of interference is observed as an increase or a decrease in the total amplitude of the wave (recall Fig. 1.20). Constructive interference, an increase in the total amplitude of the wave, occurs when the peaks of one wave coincide with the peaks of another wave. If the waves are electromagnetic radiation, the increased amplitude corresponds to an increased intensity of the radiation. Destructive interference, a decrease in the total amplitude of the waves, occurs when the peaks of one wave coincide with the troughs of the other wave it results in a reduction in intensity. 

Recall from Chapter 8 that the term regiochemistry refers to where the reaction takes place. In other words, in what region of the molecule is the reaction taking place When H and X are eliminated (where X is some leaving group), it is sometimes possible for more than one alkene to form. Consider the following example, in which two possible alkenes can be formed ... 

Electrons with the same / value but different values of JItt/ do not screen one another effectively. For example, when electrons occupy different p orbitals, the amount of mutual screening is slight. This is because screening is effective only when much of the electron density of one orbital lies between the nucleus and the electron density of another. Recall from Chapter 7 (Figure ) that the p orbitals are perpendicular to one another, with high electron densities in different regions of space. The electron density of the 2 p orbital does not lie between the 2 Py... 

Beyond the buffer region, when nearly all of the acetic acid has been consumed, the pH increases sharply with each added drop of hydroxide solution. The titration curve passes through an almost vertical region before leveling off again. Recall from Chapter 4 that the stoichiometric point of an acid titration (also called the equivalence point) is the point at which the number of moles of added base is exactly equal to the number of moles of acid present in the original solution. At the stoichiometric point of a weak acid titration, the conjugate base is a major species in solution, but the weak acid is not. 

The volume fraction dependence of /cq/(4>) is plotted in Fig. 21b and shows that it increases strongly with 4>- Recall that this rate coefficient is independent of 4> if simple binary collision dynamics is assumed to govern the boundary layer region. The observed increase arises from the obstacle distribution in the vicinity of the catalytic sphere surface. When obstacles are present, a reactive... 

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