Near theoretical considerations

The velocity distribution and frictional resistance have been calculated from purely theoretical considerations for the streamline flow of a fluid in a pipe. The boundary layer theory can now be applied in order to calculate, approximately, the conditions when the fluid is turbulent. For this purpose it is assumed that the boundary layer expressions may be applied to flow over a cylindrical surface and that the flow conditions in the region of fully developed flow are the same as those when the boundary layers first join. The thickness of the boundary layer is thus taken to be equal to the radius of the pipe and the velocity at the outer edge of the boundary layer is assumed to be the velocity at the axis. Such assumptions are valid very close to the walls, although significant errors will arise near the centre of the pipe. 

In conclusion of this short account on experiments, which is clearly far from complete, detailed structural data for solutions will be available in the near future. They may serve well to support theoretical calculations of solvation processes and to present challenges for theoretical considerations, which will in any case have to be dynamic ones. Data which may be compared quantitatively with molecular calculations will, however, have to come from gas-phase solvation experiments. There already exists a great variety of according data and their number will certainly increase further. 

The first theoretical considerations concerning n (p) and G (p) of concentrated 3-D emulsions and foams were based on perfectly ordered crystals of droplets [4,5,15-18]. In such models, at a given volume fraction and applied shear strain, all droplets are assumed to be equally compressed, that is, to deform affinely under the applied shear thus all of them should have the same shape. Princen [15,16] initially analyzed an ordered monodisperse 2-D array of deformable cylinders and concluded that G = Qiox(p < (/), and that G jumps to nearly the 2-D Laplace pressure of the cylinders at the approach of ( > = 100%, following a ( — dependence. 

Andersen et al (Ref 6) obtained about the same pressure coefficient of D for NM as Brochet et al. However, theoretical considerations pre diet that this coefficient should decrease at higher ambient pressure. This predicted decrease was not observed. Indeed for NM and a solid aluminized expl, HBX, D increased with ambient pressure in essentially the same manner as it would increase with increasing initial density of the expl due to compression by the ambient pressure. Since the compressibility of liq expls and solid expls at near crystal density is relatively low at moderate ambient pressures, the rather small effect of ambient pressure on D is understandable... 

Lynn (L14), 1960 Theoretical consideration of acceleration of film near inlet slots of various types. Model studies suggested that acceleration should be complete in a very short distance. 

Bejan. A. and Cunnington, G.R., Theoretical Consideration of Transition to Turbulence in Natural Convection Near a Vertical Wall , Int. J. Heat Fluid Flow. Vol. 4. No. 3, pp. 131-139, 1983. 

Analyzing the RS portion of j(F) curves yields a significantly smaller than atheor (204) calculated with s = 4. It has been suggested that a < atheor can be the result of the charge trapped near the contact along linear imperfections [403]. Both, experimental observations and theoretical considerations show that the distribution of imperfections can be linear in crystals [82,404-406], and linear macrotraps formed by an array of dipolar microtraps [371]. Then [403],... 

The concentration of the carriers near the surface is increased by illumination. The steady state concentration increase corresponds to np = (n + An ). Thus the applied light increases the electrode capacities also. This increase is proportional to n/1 + A nj/hj[ for intrinsic samples. For doped Ge it is most pronounced if the minority carriers are enriched in the space charge, in agreement with theoretical considerations. As already shown by Brattain and Garrett (8), illumination increases the dissolution current of Ge. If Ai is the change... 

A full analysis of the rotational structure has not yet been carried out, the resolution being rather too low. The P and R branches appear to be the most prominent feature of the bands and the structure suggests a 77 — W or A — A transition with near case (a) coupling. The former is supported by theoretical considerations which predict a 77 ground state for CIO. ... 

Lutski directed attention to the H bond in simpler molecules by proposing that the influence of ethanol solvent on the UV spectrum of an orthoh.y6.voxy keto- or nitro aromatic provides a criterion for an j n/ramolecular H bond (1287, 1285). Brieglieb and Strohmeier were able to detect the influence of H bonded dimer formation on the spectra of acetic acid vapor at different temperatures (near 2100 A) (279). There have followed many valuable studies directed at the effect of H bonding on the electronic transitions of acids such as phenols, aniline (1483, 1481, 2056), benzoic acid and derivatives (2076, 1998, 671, 190), acetanilides (2075, 2074), HF (1771, 1770), naphthols (1479, 1484), sulfinic acids (521), and amides (1436). The most extensive work, that of Nagakura, Baba, and co-workers, is of particular importance because it led to theoretical consideration of the nature of the H bond (see Section 8.3.2). (See adso 2056,. 1418, 1850.)... 

It is strongly desired that theoretical considerations be used much more in designing electrochemical stereoselective synthesis in the near future. Therefore, in this chapter the theoretical and mechanistic problems of the stereochemistry of electrochemical reactions are discussed, as well as stereoselective synthesis. 

Second, the correlation due to the intermolecular interactions is usually (except for perfect solids or near the critical point) of short range (normally, a few molecular diameters). For the present discussion, diameter could be defined as an average diameter of the species in the system. We do not need any more precise definition of this quantity here. All we need to assume is that the chosen molecular diameter is much smaller than the size of the macroscopic system. Hence, we assume that there exists a correlation distance Rc such that for R> Rc there are no correlations due to intermolecular interactions. The existence of such a correlation distance is supported both by experiments and by theoretical considerations (for more details see Appendix G). 

Owing in part to the relatively recent development of cluster chemistry, there is an almost complete lack of thermodynamic data for cluster compounds. The measurement of appearance potentials of positively charged ions by mass spectrometry has offered a technique for ready measurement of this parameter, but the high values obtained for ionization potentials and heats of formation of ions by this method cast some doubt on its accuracy (358). It would appear that ions are generated in excited states (22). It may be expected that there will be a considerable increase in the thermodynamic investigations of clusters in the near future, so as to provide quantitative data on which to base theoretical considerations. 

If ionizing radiation (X-ray or particle radiation) directly hits a strand of DNA, most probably one of the DNA strands breaks. To obtain a double strand break by the same particle, one would need the second break in the neighborhood of the first one (otherwise repair enzymes would rebuild at least one of the first strands). On the other hand as the experimental number of double strand breaks versus dosage curves show, the linear term is dominant in their mathematical expression.170 This means that the double strand break is caused by a single particle (or by the secondary particles caused by it). On the other hand it is unprobable, from scattering theoretical considerations, that a particle will be scattered inelastically (after a strand break) with a very small space angle (the corresponding cross section is very small) so as to reach the second strand very near to the first one.171... 

---