Exact route

Despite many attempts made over more than a century, the exact route to turbulence is still far from clear. This prompted Morkovin (1991) to state One hundred eight years after O. Reynolds demonstrated turbulence in a circular pipe, we still do not understand the nature of the irregular fluctuations at the wall nor the formation of larger coherent eddies convected downstream further from the wall. Neither can we describe the mechanisms of the instabilities that lead to the onset of turbulence in any given pipe nor the Reynolds number (between about 2000 and 100 000) at which it will take place. It is sobering to recall that Reynolds demonstrated this peculiar non-larninar behaviour of fluids before other physicists started on the road to relativity theory, quantum theory, nuclear energy, quarks etc . While some additional researches have clarified some key concepts, the situation about flow transition in a pipe remains the same. 

The latter is involved, for example, in the reduction of aromatics to their dihydro derivatives, of quinones to hydroquinones, carbonyls to alcohols. A priori, there are six plausible different possibilities of transferring two electrons and two protons, depending on the exact order of the steps. These six paths involve the articipation of seven different intermediates A , A , AH", AH , AH ", AH2 ,and AH. It is thus seen that the discussion of the possible mechanism(s) may rapidly become an overwhelming task, particularly when more steps are involved, as in the 4e -f- 4H " sequence in Eq. (126). Thus in order to discuss the exact route followed, a convenient representation of the different possible schemes is highly desirable. Such a representation of all possible paths is given by square-schemes diagrams [101], such as that shown in Scheme 8 for the A/AH2 reduction. The horizontal... 

The Fries rearrangement proceeds via ionic intermediates but the exact mechanistic pathway (whether it is inter- or intramolecular) is still under debate. There are many reports in the literature that present evidence to support either of the pathways, but it appears that the exact route depends on the structure of the substrates and the reaction conditions. The scheme depicts the formation of an ortho-acylated phenol from a substituted phenolic ester in the presence of aluminum trihalide catalyst. The photo-Fries rearrangement proceeds via radical intermediates. ... 

The exact route by which the pyrrole metabolites are formed remains to be established. Although N-oxides are also formed from the alkaloids in biological... 

The symbol qp represents the heat accompanying a chemical change carried out at constant pressure in our previous example this would be equivalent to our specifying the exact route of travel between the two cities. The enthalpy of a system H is related to the energy of a system by the expression ... 

The last case of wild smallpox occurred on September 11,1977. One last victim was claimed by the disease in the United Kingdom in September 1978, when Janet Parker, a medical photographer in the University of Birmingham Medical School, contracted the disease and died, and the Professor responsible for the unit killed himself. A research project on smallpox was being conducted in the building at the time, although the exact route by which Ms. Parker became infected has never been fully elucidated. 

For the calculations of the optical properties of polymer films with embedded nanoparticles, two routes can be selected. In the exact route, the extinction cross sections Cact(v) of single particles are calculated. The calculated extinction spectra for single particles—or, better, a summation of various excitation spectra for a particle assembly—can be compared with the experimental spectra of the embedded nanoparticles. In the statistic route, an effective dielectric function e(v) is calculated from the dielectric function of the metal e(T) and of the polymer material po(v) by using a mixing formula, the so-called effective medium theory. The optical extinction spectra calculated from the effective dielectric functions by using the Fresnel formulas can be compared with the experimental spectra. 

Nuclear magnetic resonance (NMR) is a technique of considerable versatility in polymer science. It is used universally as a probe of chemical configurations, it provides information on the dynamics and relaxation times of a polymer system and it offers a route to the determination of orientation parameters, the exact route depending on the particular nuclei employed. In principle quadrupolar, dipolar, shielding tensor and indirect spin coupling interactions can all be employed " however, in practice only the first two have any universal appeal. Dipolar coupling using proton NMR offers the simplest approach in terms of material preparation and will be considered first. 

These virial equations relate cr to the pair (ot higher) intermolecular potential and to the corresponding distribution functions that describe die density and correlation of density in the surface region. The first YBG equation (4.85) relates the density p(z,) to p (ri2, z Z2) and the pair potential, and the integral equation (4.86) relates p (z,) and p (z2) to the direct correlation function c(r,2, Zi, Z2). What we lack, however, is a practicable and exact route to any of these densities or distribution functions from a knowledge of u(r) alone. Further progress requires approximations for p, p or c, as we shaD see in the following chapters. Here we consider only the simplest approximation, namely that p(z) is a constant p on the liquid side of a divi ng surface, and p 0 on other side ... 

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