Wiggles

Our approach in this chapter is to alternate between experimental results and theoretical models to acquire familiarity with both the phenomena and the theories proposed to explain them. We shall consider a model for viscous flow due to Eyring which is based on the migration of vacancies or holes in the liquid. A theory developed by Debye will give a first view of the molecular weight dependence of viscosity an equation derived by Bueche will extend that view. Finally, a model for the snakelike wiggling of a polymer chain through an array of other molecules, due to deGennes, Doi, and Edwards, will be taken up. 

Remember that the hump which causes the instability with respect to phase separation arises from an unfavorable AH considerations of configurational entropy alone favor mixing. Since AS is multiplied by T in the evaluation of AGj, we anticipate that as the temperature increases, curves like that shown in Fig. 8.2b will gradually smooth out and eventually pass over to the form shown in Fig. 8.2a. The temperature at which the wiggles in the curve finally vanish will be a critical temperature for this particular phase separation. We shall presently turn to the Flory-Huggins theory for some mathematical descriptions of this critical point. The following example reminds us of a similar problem encountered elsewhere in physical chemistry. 

For the phase separation problem, the maximum and minima in Fig. 8.2b and the inflection points between them must also merge into a common point at the critical temperature for the two-phase region. This is the mathematical criterion for the smoothing out of wiggles, as the critical point was described above. 

Looks like an alien, said the bartender who served it, wiggling his fingers like antennae on either side of Iris lanky hair. Are you a fan of Wylie s Mr. Dufresne, mutton-chopped and pony-tailed, was visible in the kitchen at the back, corralled like a quarterback by cooks, directing his food into the dining room. 

Fig. 18-8 Characteristic temperature-depth distributions at an ice divide. For a climatic temperature history as shown in (a) the temperature-depth distribution changes as shown in (b). Following the step increase in surface temperature, the initial steady temperature profile (fi in (b)) is altered by a warming wave (e.g., at time fa) but eventually reaches a new steady profile by time t. (c) Temperature data from Greenland measured by Gary Clow of the US Geological Survey, showing wiggles due to climate variations (Cuffey et ah, 1995).

Skin snips may be useful in the diagnosis of microfilarial infections such as onchocerciasis in which the parasites circulate in the skin and not the blood. A small (2-mm) skin snip is taken with a needle and a knife. The needle point is stuck into the skin, and the skin is raised. With a sharp knife or razor blade, the skin is excised just below the needle. Alternatively, a scleral punch may be used. The skin snip is then placed in a small volume (0.2 ml) of saline in a tube or a microtiter well, teased, and allowed to stand for 30 min or more. The microfilariae migrate from the tissue into the saline, which is then examined microscopically to demonstrate the wiggling microfilariae. 

The case of Oetzi (or the Iceman), the frozen mummy found in 1991 on the Alps on the border between Austria and Italy and now kept at the Archaeological Museum of Bolzano (Italy), is also well known. AMS radiocarbon measurements from the laboratories of Zurich[78] and Oxford[79] on tissue and bone samples from the Iceman dated him to 4550 19 years BP. When calibrated, this radiocarbon age corresponds to three probable calendar time intervals between 3350 BC and 3100 BC. Consistent measurements were obtained by dating some of his equipment and also botanic remains from the discovery site. [80] In this context, it is important to note that dating of Oetzi represents a good example of the relevance of the behaviour of the calibration curve in the final precision of a radiocarbon measurement. Actually, in this case, despite a very high precision of the radiocarbon age ( 19 years), the special trend in the calibration curve around the dated period, i.e. in particular the so-called wiggles, prevents a more exact and unambiguous absolute age determination. 

Figure 7-4 Damping Out the High AV/At Wiggle by Inserting a Small Lossy Ni-Zn Ferrite Bead... 

During the last 15 years intensive studies on the history of the atmospheric 14C/C ratio have been performed on tree-rings [20]. The results can be summarized as follows from 7000 BP (before present) to 2000 BP the average atmospheric 14C/C ratio had decreased by about 10 percent. Superimposed on this general trend are secular variations (Suess-Wiggles) of the order of 1 to 2 percent. In some time intervals a basic period of about 200 years is visible. 

Figure 3. Wiggle curve in A (per mil) vs. dendrodate with the trend in Figure 2...

The heavy line is produced by Fourier analysis of the residuals around the sixth-order logarithmic function. There are about 35 pronounced wiggles in 7,000 years on an average of one every 200 years. Note that some of the wiggles appear to have a greater amplitude than the SpSrer and Maunder minima which occurred between a.d. 1450 and... 

Figure 4. Segment of Fourier analysis wiggle curve (Figure 2) for the last millennium (6).

The values of E(t) so computed are listed in Table 4. The correction for fractionation of carbon dioxide at the sea surface is a serious one. It makes the interpretation of 13C/12C variations in wood difficult and militates against the use of the isotope ratio of carbon as a thermometer. This correction, when applied to variations of carbon-14 in wood, is able to explain the Suess radiocarbon "wiggles" of about 100 years duration each, without the need to invoke changes in the neutron flux from the sun [54]. 

Nitpicking a spectrum. Don t try to interpret every wiggle. There is a lot of information in an IR, but sometimes it is confusing. Think about what it is you re trying to show, then show it. 

One of the further refinements which seems desirable is to modify Eq. (9) so that it has wiggles (damped oscillatory behavior). Wiggles are expected in any realistic MM-level pair potential as a consequence of the molecular structure of the solvent (2,3,10,11,21,22) they would be found even for two hard sphere solute particles in a hard-sphere liquid or for two H2I80 solute molecules in ordinary liquid HpO, and are found in simulation studies of solutions based on BO-level models. In ionic solutions in a polar solvent another source of wiggles, evidenced in Fig. 2, may be associated with an oscillatory nonlocal dielectric function e(r). ( 36) These various studies may be used to guide the introduction of wiggles into Eq. (9) in a realistic way. 

---